Datasets:
AI4M
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3.34M
function qr=v_rotqc2qr(qc) %V_ROTQC2QR converts a matrix of complex quaternion row vectors into real form % % Inputs: % % QC(2m,...) array of complex-valued quaternions % % Outputs: % % QR(4m,...) array of real-valued quaternions % % The complex-valued quaternion [r+j*b a+j*c] becomes [r a b c] % % Copyright (C) Mike Brookes 2000-2018 % Version: $Id: v_rotqc2qr.m 10865 2018-09-21 17:22:45Z dmb $ % % VOICEBOX is a MATLAB toolbox for speech processing. % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This program is free software; you can redistribute it and/or modify % it under the terms of the GNU General Public License as published by % the Free Software Foundation; either version 2 of the License, or % (at your option) any later version. % % This program is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License for more details. % % You can obtain a copy of the GNU General Public License from % http://www.gnu.org/copyleft/gpl.html or by writing to % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% persistent a b if isempty(a) a=[1 3 2 4]; end s=size(qc); s(1)=2*s(1); % each complex number needs two reals qr=reshape([real(qc(:).'); imag(qc(:).')],4,[]); qr=reshape(qr(a,:),s); if ~nargout qr=qr(1:4); % just select the first one v_rotqr2ro(qr(:)); % plot a rotated cube end
If $f(x) = o(g(x))$, then $|f(x)|^p = o(|g(x)|^p)$ for any $p > 0$.
Formal statement is: lemma analytic_on_UN: "f analytic_on (\<Union>i\<in>I. S i) \<longleftrightarrow> (\<forall>i\<in>I. f analytic_on (S i))" Informal statement is: A function is analytic on the union of a collection of sets if and only if it is analytic on each set in the collection.
(* Copyright (C) 2017 M.A.L. Marques 2019 Susi Lehtola This Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0. If a copy of the MPL was not distributed with this file, You can obtain one at http://mozilla.org/MPL/2.0/. *) (* type: gga_exc *) (* prefix: gga_x_am05_params *params; assert(p->params != NULL); params = (gga_x_am05_params * )(p->params); *) am05_d := 28.23705740248932030511071641312341561894: (* POW(CBRT(4/3) * 2*M_PI/3, 4) *) am05_csi := s -> (3/2 * LambertW(s^(3/2) / (2*sqrt(6))))^(2/3): am05_fb := s -> Pi/3 * s/(am05_csi(s) * (am05_d + am05_csi(s)^2)^(1/4)): am05_flaa := s -> (1 + params_a_c*s^2)/(1 + params_a_c*s^2/am05_fb(s)): am05_XX := s -> 1 - params_a_alpha*s^2/(1 + params_a_alpha*s^2): am05_f := x -> am05_XX(X2S*x) + (1 - am05_XX(X2S*x))*am05_flaa(X2S*x): f := (rs, zeta, xt, xs0, xs1) -> gga_exchange(am05_f, rs, zeta, xs0, xs1):
section \<open>Operation Identification Phase\<close> theory Sepref_Id_Op imports Main Automatic_Refinement.Refine_Lib Automatic_Refinement.Autoref_Tagging Refine_Imperative_HOL.Named_Theorems_Rev begin text \<open> The operation identification phase is adapted from the Autoref tool. The basic idea is to have a type system, which works on so called interface types (also called conceptual types). Each conceptual type denotes an abstract data type, e.g., set, map, priority queue. Each abstract operation, which must be a constant applied to its arguments, is assigned a conceptual type. Additionally, there is a set of {\emph pattern rewrite rules}, which are applied to subterms before type inference takes place, and which may be backtracked over. This way, encodings of abstract operations in Isabelle/HOL, like @{term [source] "\<lambda>_. None"} for the empty map, or @{term [source] "fun_upd m k (Some v)"} for map update, can be rewritten to abstract operations, and get properly typed. \<close> subsection "Proper Protection of Term" text \<open> The following constants are meant to encode abstraction and application as proper HOL-constants, and thus avoid strange effects with HOL's higher-order unification heuristics and automatic beta and eta-contraction. The first step of operation identification is to protect the term by replacing all function applications and abstractions be the constants defined below. \<close> definition [simp]: "PROTECT2 x (y::prop) \<equiv> x" consts DUMMY :: "prop" abbreviation PROTECT2_syn ("'(#_#')") where "PROTECT2_syn t \<equiv> PROTECT2 t DUMMY" abbreviation (input)ABS2 :: "('a\<Rightarrow>'b)\<Rightarrow>'a\<Rightarrow>'b" (binder "\<lambda>\<^sub>2" 10) where "ABS2 f \<equiv> (\<lambda>x. PROTECT2 (f x) DUMMY)" lemma beta: "(\<lambda>\<^sub>2x. f x)$x \<equiv> f x" by simp text \<open> Another version of @{const "APP"}. Treated like @{const APP} by our tool. Required to avoid infinite pattern rewriting in some cases, e.g., map-lookup. \<close> definition APP' (infixl "$''" 900) where [simp, autoref_tag_defs]: "f$'a \<equiv> f a" text \<open> Sometimes, whole terms should be protected from being processed by our tool. For example, our tool should not look into numerals. For this reason, the \<open>PR_CONST\<close> tag indicates terms that our tool shall handle as atomic constants, an never look into them. The special form \<open>UNPROTECT\<close> can be used inside pattern rewrite rules. It has the effect to revert the protection from its argument, and then wrap it into a \<open>PR_CONST\<close>. \<close> definition [simp, autoref_tag_defs]: "PR_CONST x \<equiv> x" \<comment> \<open>Tag to protect constant\<close> definition [simp, autoref_tag_defs]: "UNPROTECT x \<equiv> x" \<comment> \<open>Gets converted to @{term PR_CONST}, after unprotecting its content\<close> subsection \<open>Operation Identification\<close> text \<open> Indicator predicate for conceptual typing of a constant \<close> definition intf_type :: "'a \<Rightarrow> 'b itself \<Rightarrow> bool" (infix "::\<^sub>i" 10) where [simp]: "c::\<^sub>iI \<equiv> True" lemma itypeI: "c::\<^sub>iI" by simp lemma itypeI': "intf_type c TYPE('T)" by (rule itypeI) lemma itype_self: "(c::'a) ::\<^sub>i TYPE('a)" by simp definition CTYPE_ANNOT :: "'b \<Rightarrow> 'a itself \<Rightarrow> 'b" (infix ":::\<^sub>i" 10) where [simp]: "c:::\<^sub>iI \<equiv> c" text \<open> Wrapper predicate for an conceptual type inference \<close> definition ID :: "'a \<Rightarrow> 'a \<Rightarrow> 'c itself \<Rightarrow> bool" where [simp]: "ID t t' T \<equiv> t=t'" subsubsection \<open>Conceptual Typing Rules\<close> lemma ID_unfold_vars: "ID x y T \<Longrightarrow> x\<equiv>y" by simp lemma ID_PR_CONST_trigger: "ID (PR_CONST x) y T \<Longrightarrow> ID (PR_CONST x) y T" . lemma pat_rule: "\<lbrakk> p\<equiv>p'; ID p' t' T \<rbrakk> \<Longrightarrow> ID p t' T" by simp lemma app_rule: "\<lbrakk> ID f f' TYPE('a\<Rightarrow>'b); ID x x' TYPE('a)\<rbrakk> \<Longrightarrow> ID (f$x) (f'$x') TYPE('b)" by simp lemma app'_rule: "\<lbrakk> ID f f' TYPE('a\<Rightarrow>'b); ID x x' TYPE('a)\<rbrakk> \<Longrightarrow> ID (f$'x) (f'$x') TYPE('b)" by simp lemma abs_rule: "\<lbrakk> \<And>x x'. ID x x' TYPE('a) \<Longrightarrow> ID (t x) (t' x x') TYPE('b) \<rbrakk> \<Longrightarrow> ID (\<lambda>\<^sub>2x. t x) (\<lambda>\<^sub>2x'. t' x' x') TYPE('a\<Rightarrow>'b)" by simp lemma id_rule: "c::\<^sub>iI \<Longrightarrow> ID c c I" by simp lemma annot_rule: "ID t t' I \<Longrightarrow> ID (t:::\<^sub>iI) t' I" by simp lemma fallback_rule: "ID (c::'a) c TYPE('c)" by simp lemma unprotect_rl1: "ID (PR_CONST x) t T \<Longrightarrow> ID (UNPROTECT x) t T" by simp subsection \<open> ML-Level code \<close> ML \<open> infix 0 THEN_ELSE_COMB' signature ID_OP_TACTICAL = sig val SOLVE_FWD: tactic' -> tactic' val DF_SOLVE_FWD: bool -> tactic' -> tactic' end structure Id_Op_Tactical :ID_OP_TACTICAL = struct fun SOLVE_FWD tac i st = SOLVED' ( tac THEN_ALL_NEW_FWD (SOLVE_FWD tac)) i st (* Search for solution with DFS-strategy. If dbg-flag is given, return sequence of stuck states if no solution is found. *) fun DF_SOLVE_FWD dbg tac = let val stuck_list_ref = Unsynchronized.ref [] fun stuck_tac _ st = if dbg then ( stuck_list_ref := st :: !stuck_list_ref; Seq.empty ) else Seq.empty fun rec_tac i st = ( (tac THEN_ALL_NEW_FWD (SOLVED' rec_tac)) ORELSE' stuck_tac ) i st fun fail_tac _ _ = if dbg then Seq.of_list (rev (!stuck_list_ref)) else Seq.empty in rec_tac ORELSE' fail_tac end end \<close> named_theorems_rev id_rules "Operation identification rules" named_theorems_rev pat_rules "Operation pattern rules" named_theorems_rev def_pat_rules "Definite operation pattern rules (not backtracked over)" ML \<open> structure Id_Op = struct fun id_a_conv cnv ct = case Thm.term_of ct of @{mpat "ID _ _ _"} => Conv.fun_conv (Conv.fun_conv (Conv.arg_conv cnv)) ct | _ => raise CTERM("id_a_conv",[ct]) fun protect env (@{mpat "?t:::\<^sub>i?I"}) = let val t = protect env t in @{mk_term env: "?t:::\<^sub>i?I"} end | protect _ (t as @{mpat "PR_CONST _"}) = t | protect env (t1$t2) = let val t1 = protect env t1 val t2 = protect env t2 in @{mk_term env: "?t1.0 $ ?t2.0"} end | protect env (Abs (x,T,t)) = let val t = protect (T::env) t in @{mk_term env: "\<lambda>v_x::?'v_T. PROTECT2 ?t DUMMY"} end | protect _ t = t fun protect_conv ctxt = Refine_Util.f_tac_conv ctxt (protect []) (simp_tac (put_simpset HOL_basic_ss ctxt addsimps @{thms PROTECT2_def APP_def}) 1) fun unprotect_conv ctxt = Simplifier.rewrite (put_simpset HOL_basic_ss ctxt addsimps @{thms PROTECT2_def APP_def}) fun do_unprotect_tac ctxt = resolve_tac ctxt @{thms unprotect_rl1} THEN' CONVERSION (Refine_Util.HOL_concl_conv (fn ctxt => id_a_conv (unprotect_conv ctxt)) ctxt) val cfg_id_debug = Attrib.setup_config_bool @{binding id_debug} (K false) val cfg_id_trace_fallback = Attrib.setup_config_bool @{binding id_trace_fallback} (K false) fun dest_id_rl thm = case Thm.concl_of thm of @{mpat (typs) "Trueprop (?c::\<^sub>iTYPE(?'v_T))"} => (c,T) | _ => raise THM("dest_id_rl",~1,[thm]) val add_id_rule = snd oo Thm.proof_attributes [Named_Theorems_Rev.add @{named_theorems_rev id_rules}] datatype id_tac_mode = Init | Step | Normal | Solve fun id_tac ss ctxt = let open Id_Op_Tactical val certT = Thm.ctyp_of ctxt val cert = Thm.cterm_of ctxt val thy = Proof_Context.theory_of ctxt val id_rules = Named_Theorems_Rev.get ctxt @{named_theorems_rev id_rules} val pat_rules = Named_Theorems_Rev.get ctxt @{named_theorems_rev pat_rules} val def_pat_rules = Named_Theorems_Rev.get ctxt @{named_theorems_rev def_pat_rules} val rl_net = Tactic.build_net ( (pat_rules |> map (fn thm => thm RS @{thm pat_rule})) @ @{thms annot_rule app_rule app'_rule abs_rule} @ (id_rules |> map (fn thm => thm RS @{thm id_rule})) ) val def_rl_net = Tactic.build_net ( (def_pat_rules |> map (fn thm => thm RS @{thm pat_rule})) ) val id_pr_const_rename_tac = resolve_tac ctxt @{thms ID_PR_CONST_trigger} THEN' Subgoal.FOCUS (fn { context=ctxt, prems, ... } => let fun is_ID @{mpat "Trueprop (ID _ _ _)"} = true | is_ID _ = false val prems = filter (Thm.prop_of #> is_ID) prems val eqs = map (fn thm => thm RS @{thm ID_unfold_vars}) prems val conv = Conv.rewrs_conv eqs val conv = fn ctxt => (Conv.top_sweep_conv (K conv) ctxt) val conv = fn ctxt => Conv.fun2_conv (Conv.arg_conv (conv ctxt)) val conv = Refine_Util.HOL_concl_conv conv ctxt in CONVERSION conv 1 end ) ctxt THEN' resolve_tac ctxt @{thms id_rule} THEN' resolve_tac ctxt id_rules val ityping = id_rules |> map dest_id_rl |> filter (is_Const o #1) |> map (apfst (#1 o dest_Const)) |> Symtab.make_list val has_type = Symtab.defined ityping fun mk_fallback name cT = case try (Sign.the_const_constraint thy) name of SOME T => try (Thm.instantiate' [SOME (certT cT), SOME (certT T)] [SOME (cert (Const (name,cT)))]) @{thm fallback_rule} | NONE => NONE fun trace_fallback thm = Config.get ctxt cfg_id_trace_fallback andalso let open Pretty val p = block [str "ID_OP: Applying fallback rule: ", Thm.pretty_thm ctxt thm] in string_of p |> tracing; false end val fallback_tac = CONVERSION Thm.eta_conversion THEN' IF_EXGOAL (fn i => fn st => case Logic.concl_of_goal (Thm.prop_of st) i of @{mpat "Trueprop (ID (mpaq_STRUCT (mpaq_Const ?name ?cT)) _ _)"} => ( if not (has_type name) then case mk_fallback name cT of SOME thm => (trace_fallback thm; resolve_tac ctxt [thm] i st) | NONE => Seq.empty else Seq.empty ) | _ => Seq.empty) val init_tac = CONVERSION ( Refine_Util.HOL_concl_conv (fn ctxt => (id_a_conv (protect_conv ctxt))) ctxt ) val step_tac = (FIRST' [ assume_tac ctxt, eresolve_tac ctxt @{thms id_rule}, resolve_from_net_tac ctxt def_rl_net, resolve_from_net_tac ctxt rl_net, id_pr_const_rename_tac, do_unprotect_tac ctxt, fallback_tac]) val solve_tac = DF_SOLVE_FWD (Config.get ctxt cfg_id_debug) step_tac in case ss of Init => init_tac | Step => step_tac | Normal => init_tac THEN' solve_tac | Solve => solve_tac end end \<close> subsection \<open>Default Setup\<close> subsubsection \<open>Numerals\<close> lemma pat_numeral[def_pat_rules]: "numeral$x \<equiv> UNPROTECT (numeral$x)" by simp lemma id_nat_const[id_rules]: "(PR_CONST (a::nat)) ::\<^sub>i TYPE(nat)" by simp lemma id_int_const[id_rules]: "(PR_CONST (a::int)) ::\<^sub>i TYPE(int)" by simp (*subsection \<open>Example\<close> schematic_lemma "ID (\<lambda>a b. (b(1::int\<mapsto>2::nat) |`(-{3})) a, Map.empty, \<lambda>a. case a of None \<Rightarrow> Some a | Some _ \<Rightarrow> None) (?c) (?T::?'d itself)" (*"TERM (?c,?T)"*) using [[id_debug]] apply (tactic {* Id_Op.id_tac Id_Op.Normal @{context} 1 *}) done *) end
(* Title: HOL/Auth/n_g2kAbsAfter_lemma_on_inv__5.thy Author: Yongjian Li and Kaiqiang Duan, State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences Copyright 2016 State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences *) header{*The n_g2kAbsAfter Protocol Case Study*} theory n_g2kAbsAfter_lemma_on_inv__5 imports n_g2kAbsAfter_base begin section{*All lemmas on causal relation between inv__5 and some rule r*} lemma n_n_Store_i1Vsinv__5: assumes a1: "(\<exists> d. d\<le>N\<and>r=n_n_Store_i1 d)" and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain d where a1:"d\<le>N\<and>r=n_n_Store_i1 d" apply fastforce done have "?P3 s" apply (cut_tac a1 a2 , simp, rule_tac x="(neg (andForm (neg (eqn (IVar (Field (Ident ''ACache_1'') ''State'')) (Const I))) (eqn (IVar (Field (Ident ''Cache_1'') ''State'')) (Const E))))" in exI, auto) done then show "invHoldForRule s f r (invariants N)" by auto qed lemma n_n_AStore_i1Vsinv__5: assumes a1: "(\<exists> d. d\<le>N\<and>r=n_n_AStore_i1 d)" and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain d where a1:"d\<le>N\<and>r=n_n_AStore_i1 d" apply fastforce done have "?P1 s" proof(cut_tac a1 a2 , auto) qed then show "invHoldForRule s f r (invariants N)" by auto qed lemma n_n_ASendInvAck_i1Vsinv__5: assumes a1: "(r=n_n_ASendInvAck_i1 )" and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - have "?P1 s" proof(cut_tac a1 a2 , auto) qed then show "invHoldForRule s f r (invariants N)" by auto qed lemma n_n_ARecvGntS_i1Vsinv__5: assumes a1: "(r=n_n_ARecvGntS_i1 )" and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - have "?P3 s" apply (cut_tac a1 a2 , simp, rule_tac x="(neg (andForm (neg (eqn (IVar (Field (Ident ''AChan2_1'') ''Data'')) (IVar (Ident ''AuxData'')))) (eqn (IVar (Field (Ident ''AChan2_1'') ''Cmd'')) (Const GntS))))" in exI, auto) done then show "invHoldForRule s f r (invariants N)" by auto qed lemma n_n_ARecvGntE_i1Vsinv__5: assumes a1: "(r=n_n_ARecvGntE_i1 )" and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - have "?P3 s" apply (cut_tac a1 a2 , simp, rule_tac x="(neg (andForm (neg (eqn (IVar (Field (Ident ''AChan2_1'') ''Data'')) (IVar (Ident ''AuxData'')))) (eqn (IVar (Field (Ident ''AChan2_1'') ''Cmd'')) (Const GntE))))" in exI, auto) done then show "invHoldForRule s f r (invariants N)" by auto qed lemma n_n_RecvReq_i1Vsinv__5: assumes a1: "r=n_n_RecvReq_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_SendInvS_i1Vsinv__5: assumes a1: "r=n_n_SendInvS_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_SendReqEI_i1Vsinv__5: assumes a1: "r=n_n_SendReqEI_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_ASendReqEI_i1Vsinv__5: assumes a1: "r=n_n_ASendReqEI_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_ASendReqIS_j1Vsinv__5: assumes a1: "r=n_n_ASendReqIS_j1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_SendGntE_i1Vsinv__5: assumes a1: "r=n_n_SendGntE_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_ASendReqES_i1Vsinv__5: assumes a1: "r=n_n_ASendReqES_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_ASendGntS_i1Vsinv__5: assumes a1: "r=n_n_ASendGntS_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_ASendInvE_i1Vsinv__5: assumes a1: "r=n_n_ASendInvE_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_SendGntS_i1Vsinv__5: assumes a1: "r=n_n_SendGntS_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_ASendInvS_i1Vsinv__5: assumes a1: "r=n_n_ASendInvS_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_SendReqES_i1Vsinv__5: assumes a1: "r=n_n_SendReqES_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_SendInvE_i1Vsinv__5: assumes a1: "r=n_n_SendInvE_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_ASendReqSE_j1Vsinv__5: assumes a1: "r=n_n_ASendReqSE_j1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_RecvGntS_i1Vsinv__5: assumes a1: "r=n_n_RecvGntS_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_SendReqEE_i1Vsinv__5: assumes a1: "r=n_n_SendReqEE_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_RecvInvAck_i1Vsinv__5: assumes a1: "r=n_n_RecvInvAck_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_RecvGntE_i1Vsinv__5: assumes a1: "r=n_n_RecvGntE_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_ARecvReq_i1Vsinv__5: assumes a1: "r=n_n_ARecvReq_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_SendReqS_j1Vsinv__5: assumes a1: "r=n_n_SendReqS_j1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_ARecvInvAck_i1Vsinv__5: assumes a1: "r=n_n_ARecvInvAck_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_SendInvAck_i1Vsinv__5: assumes a1: "r=n_n_SendInvAck_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_n_ASendGntE_i1Vsinv__5: assumes a1: "r=n_n_ASendGntE_i1 " and a2: "(f=inv__5 )" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done end
+incdir+${UEX}/impl/sv/svsrc ${UEX}/impl/sv/svsrc/uex_pkg.sv
################################################################### # ELECTRONICS.PY # # A library of functions, constants and more that are related # to Power-Electronics and converters in Electrical Engineering. # # April 10th, 2019 # # Written by Joe Stanley # # Special Thanks To: # Dr. Brian Johnson - Faculty University of Idaho # # Included Functions: # - VSC DC Bus Voltage Calculator: vscdcbus # - PLL-VSC Gains Calculator: vscgains #################################################################### # Import the Necessary Library import numpy as np # Define function to find VDC setpoint def vscdcbus(VLL,Zs,P,Q=0,mmax=0.8,debug=False): """ VSCDCBUS Function: Purpose: -------- The purpose of this function is to calculate the required DC-bus voltage for a Voltage-Sourced- Converter (VSC) given the desired P/Q parameters and the known source impedance (Vs) of the VSC. Required Arguments: ------------------- VLL: Line-to-Line voltage on the line-side of the source impedance. Zs: The source impedance of the VSC P: The desired real-power output Optional Arguments: Q: The desired reactive-power output, default=0 mmax: The maximum of the m value for the converter default=0.8 debug: Control value to enable printing stages of the calculation, default=False Return: ------- VDC: The DC bus voltage. """ # Determine the Load Current Iload = np.conj((P+1j*Q) / (VLL*np.sqrt(3))) # Evaluate the Terminal Voltage Vtln = abs(VLL/np.sqrt(3) + Iload*Zs) # Find the Peak Terminal Voltage Vtpk = np.sqrt(2)*Vtln # Calculate the VDC value VDC = 2*Vtpk / mmax if debug: print("Iload", Iload) print("Vtln", Vtln) print("Vtpk", Vtpk) print("VDC", VDC) return(VDC) # Define kp/ki/w0L calculating function def vscgains(Rs,Ls,tau=0.005,f=60): """ VSCGAINS Function: Purpose: -------- This function is designed to calculate the kp, ki, and omega-not-L values for a Phase-Lock-Loop based VSC. Required Arguments: ------------------- Rs: The equiv-resistance (in ohms) of the VSC Ls: The equiv-inductance (in Henrys) of the VSC Optional Arguments: ------------------- tau: The desired time-constant, default=0.005 f: The system frequency (in Hz), default=60 Returns: -------- kp: The Kp-Gain Value ki: The Ki-Gain Value w0L: The omega-not-L gain value """ # Calculate kp kp = Ls / tau # Calculate ki ki = kp*Rs/Ls # Calculate w0L w0L = 2*np.pi*f*Ls return(kp,ki,w0L)
#pragma once #include <gsl/span> #include "simple_math.h" constexpr auto VECTOR_SIZE = sizeof(float) * 4; class CBufferBase; struct CBufferAlign { size_t size; explicit CBufferAlign(size_t size_ = VECTOR_SIZE) : size(size_) {} }; __forceinline CBufferAlign cbuff_align(size_t size = VECTOR_SIZE) { return CBufferAlign(size); } class ICBuffer { public: virtual ~ICBuffer() = default; virtual void write(CBufferBase& cbuf) const = 0; size_t cbuffer_size() const; template <typename T> static size_t cbuffer_size() { T t; return t.cbuffer_size(); } }; class CBufferBase { protected: size_t offset_ = 0; size_t alignment_ = 0; public: virtual ~CBufferBase() = default; bool align(size_t size = VECTOR_SIZE); void add(size_t size); void reset(); size_t offset() const { return offset_; } size_t alignment() const { return alignment_; } template <typename T> CBufferBase& operator<<(const T& data) = delete; template <typename T> CBufferBase& operator<<(const gsl::span<T>& data) = delete; template <typename T> CBufferBase& operator<<(const gsl::span<const T>& data) = delete; CBufferBase& operator<<(const CBufferAlign& align_of); template <typename T, size_t size> __forceinline CBufferBase& operator<<(const std::array<T, size>& array) { return *this << gsl::span<const T>(array); } template <typename T, size_t size> __forceinline CBufferBase& operator<<(const T(&array)[size]) { return *this << gsl::span<const T>(array); } template <typename T> __forceinline CBufferBase& operator<<(const dirty_t<T>& value) { return *this << value.data(); } virtual void write(const void* data, size_t size) { align(size); add(size); } }; template <> CBufferBase& CBufferBase::operator<<(const int32_t& data); template <> CBufferBase& CBufferBase::operator<<(const uint32_t& data); template <> CBufferBase& CBufferBase::operator<<(const float& data); template <> CBufferBase& CBufferBase::operator<<(const DirectX::SimpleMath::Matrix& data); template <> CBufferBase& CBufferBase::operator<<(const DirectX::SimpleMath::Vector2& data); template <> CBufferBase& CBufferBase::operator<<(const DirectX::SimpleMath::Vector3& data); template <> CBufferBase& CBufferBase::operator<<(const DirectX::SimpleMath::Vector4& data); template <> CBufferBase& CBufferBase::operator<<(const gsl::span<float>& data); template <> CBufferBase& CBufferBase::operator<<(const gsl::span<const float>& data); template <> __forceinline CBufferBase& CBufferBase::operator<<(const DWORD& data) { return *this << static_cast<uint32_t>(data); } template <> __forceinline CBufferBase& CBufferBase::operator<<(const bool& data) { return *this << (data ? 1 : 0); } class CBufferWriter : public CBufferBase { uint8_t* ptr = nullptr; public: CBufferWriter(uint8_t* ptr_); private: void write(const void* data, size_t size) override; };
# Homework 5 ## Due Date: Tuesday, October 3rd at 11:59 PM # Problem 1 We discussed documentation and testing in lecture and also briefly touched on code coverage. You must write tests for your code for your final project (and in life). There is a nice way to automate the testing process called continuous integration (CI). This problem will walk you through the basics of CI and show you how to get up and running with some CI software. ### Continuous Integration The idea behind continuous integration is to automate away the testing of your code. We will be using it for our projects. The basic workflow goes something like this: 1. You work on your part of the code in your own branch or fork 2. On every commit you make and push to GitHub, your code is automatically tested on a fresh machine on Travis CI. This ensures that there are no specific dependencies on the structure of your machine that your code needs to run and also ensures that your changes are sane 3. Now you submit a pull request to `master` in the main repo (the one you're hoping to contribute to). The repo manager creates a branch off `master`. 4. This branch is also set to run tests on Travis. If all tests pass, then the pull request is accepted and your code becomes part of master. We use GitHub to integrate our roots library with Travis CI and Coveralls. Note that this is not the only workflow people use. Google git..github..workflow and feel free to choose another one for your group. ### Part 1: Create a repo Create a public GitHub repo called `cs207test` and clone it to your local machine. **Note:** No need to do this in Jupyter. ### Part 2: Create a roots library Use the example from lecture 7 to create a file called `roots.py`, which contains the `quad_roots` and `linear_roots` functions (along with their documentation). Also create a file called `test_roots.py`, which contains the tests from lecture. All of these files should be in your newly created `cs207test` repo. **Don't push yet!!!** ```python %%file cs207test/roots.py def linear_roots(a=1.0, b=0.0): """Returns the roots of a linear equation: ax+ b = 0. INPUTS ======= a: float, optional, default value is 1 Coefficient of linear term b: float, optional, default value is 0 Coefficient of constant term RETURNS ======== roots: 1-tuple of real floats Has the form (root) unless a = 0 in which case a ValueError exception is raised EXAMPLES ========= >>> linear_roots(1.0, 2.0) -2.0 """ if a == 0: raise ValueError("The linear coefficient is zero. This is not a linear equation.") else: return ((-b / a)) def quad_roots(a=1.0, b=2.0, c=0.0): """Returns the roots of a quadratic equation: ax^2 + bx + c = 0. INPUTS ======= a: float, optional, default value is 1 Coefficient of quadratic term b: float, optional, default value is 2 Coefficient of linear term c: float, optional, default value is 0 Constant term RETURNS ======== roots: 2-tuple of complex floats Has the form (root1, root2) unless a = 0 in which case a ValueError exception is raised EXAMPLES ========= >>> quad_roots(1.0, 1.0, -12.0) ((3+0j), (-4+0j)) """ import cmath # Can return complex numbers from square roots if a == 0: raise ValueError("The quadratic coefficient is zero. This is not a quadratic equation.") else: sqrtdisc = cmath.sqrt(b * b - 4.0 * a * c) r1 = -b + sqrtdisc r2 = -b - sqrtdisc return (r1 / 2.0 / a, r2 / 2.0 / a) ``` ```python %%file cs207test/test_roots.py import roots def test_quadroots_result(): assert roots.quad_roots(1.0, 1.0, -12.0) == ((3+0j), (-4+0j)) def test_quadroots_types(): try: roots.quad_roots("", "green", "hi") except TypeError as err: assert(type(err) == TypeError) def test_quadroots_zerocoeff(): try: roots.quad_roots(a=0.0) except ValueError as err: assert(type(err) == ValueError) def test_linearoots_result(): assert roots.linear_roots(2.0, -3.0) == 1.5 def test_linearroots_types(): try: roots.linear_roots("ocean", 6.0) except TypeError as err: assert(type(err) == TypeError) def test_linearroots_zerocoeff(): try: roots.linear_roots(a=0.0) except ValueError as err: assert(type(err) == ValueError) ``` ### Part 3: Create an account on Travis CI and Start Building #### Part A: Create an account on Travis CI and set your `cs207test` repo up for continuous integration once this repo can be seen on Travis. #### Part B: Create an instruction to Travis to make sure that 1. python is installed 2. its python 3.5 3. pytest is installed The file should be called `.travis.yml` and should have the contents: ```yml language: python python: - "3.5" before_install: - pip install pytest pytest-cov script: - pytest ``` You should also create a configuration file called `setup.cfg`: ```cfg [tool:pytest] addopts = --doctest-modules --cov-report term-missing --cov roots ``` #### Part C: Push the new changes to your `cs207test` repo. At this point you should be able to see your build on Travis and if and how your tests pass. ```python %%file cs207test/.travis.yml language: python python: - "3.5" before_install: - pip install pytest pytest-cov script: - pytest ``` ```python %%file cs207test/setup.cfg [tool:pytest] addopts = --doctest-modules --cov-report term-missing --cov roots ``` ### Part 4: Coveralls Integration In class, we also discussed code coverage. Just like Travis CI runs tests automatically for you, Coveralls automatically checks your code coverage. One minor drawback of Coveralls is that it can only work with public GitHub accounts. However, this isn't too big of a problem since your projects will be public. #### Part A: Create an account on [`Coveralls`](https://coveralls.zendesk.com/hc/en-us), connect your GitHub, and turn Coveralls integration on. #### Part B: Update your the `.travis.yml` file as follows: ```yml language: python python: - "3.5" before_install: - pip install pytest pytest-cov - pip install coveralls script: - py.test after_success: - coveralls ``` Be sure to push the latest changes to your new repo. ```python %%file cs207test/.travis.yml language: python python: - "3.5" before_install: - pip install pytest pytest-cov - pip install coveralls script: - py.test after_success: - coveralls ``` ### Part 5: Update README.md in repo You can have your GitHub repo reflect the build status on Travis CI and the code coverage status from Coveralls. To do this, you should modify the `README.md` file in your repo to include some badges. Put the following at the top of your `README.md` file: ``` [](https://travis-ci.org/dsondak/cs207testing.svg?branch=master) [](https://coveralls.io/github/dsondak/cs207testing?branch=master) ``` Of course, you need to make sure that the links are to your repo and not mine. You can find embed code on the Coveralls and Travis CI sites. ```python ``` --- # Problem 2 Write a Python module for reaction rate coefficients. Your module should include functions for constant reaction rate coefficients, Arrhenius reaction rate coefficients, and modified Arrhenius reaction rate coefficients. Here are their mathematical forms: \begin{align} &k_{\textrm{const}} = k \tag{constant} \\ &k_{\textrm{arr}} = A \exp\left(-\frac{E}{RT}\right) \tag{Arrhenius} \\ &k_{\textrm{mod arr}} = A T^{b} \exp\left(-\frac{E}{RT}\right) \tag{Modified Arrhenius} \end{align} Test your functions with the following paramters: $A = 10^7$, $b=0.5$, $E=10^3$. Use $T=10^2$. A few additional comments / suggestions: * The Arrhenius prefactor $A$ is strictly positive * The modified Arrhenius parameter $b$ must be real * $R = 8.314$ is the ideal gas constant. It should never be changed (except to convert units) * The temperature $T$ must be positive (assuming a Kelvin scale) * You may assume that units are consistent * Document each function! * You might want to check for overflows and underflows **Recall:** A Python module is a `.py` file which is not part of the main execution script. The module contains several functions which may be related to each other (like in this problem). Your module will be importable via the execution script. For example, suppose you have called your module `reaction_coeffs.py` and your execution script `kinetics.py`. Inside of `kinetics.py` you will write something like: ```python import reaction_coeffs # Some code to do some things # : # : # : # Time to use a reaction rate coefficient: reaction_coeffs.const() # Need appropriate arguments, etc # Continue on... # : # : # : ``` Be sure to include your module in the same directory as your execution script. ```python ``` ```python %%file reaction_coeffs.py def const(k=1.0): """Returns the constant coefficient k. INPUTS ======= a: float, optional, default value is 1.0 Constant reaction coefficient RETURNS ======== Constant k unless k is not an int or float in which case a TypeError exception is raised EXAMPLES ========= >>> const(1.0) 1.0 """ if type(k) != int and type(k) != float: raise TypeError("Input needs to be a number!") else: return k def arr(A=10^7,T=10^2,E=10^3,R=8.314): """Returns the constant coefficient k. INPUTS ======= A: float, optional, default value is 10^7 Arhenieus constant, needs to be positive T: float, optional, default value is 10^2 temperature, must be positive R: float, fixed value 8.314, should not change RETURNS ======== Constant k unless any of A,T, and E are not numbers in which case a TypeError exception is raised EXAMPLES ========= >>> arr(10^7,10^2,10^2) 11.526748719357375 """ if A < 0: raise ValueError("The Arrhenius constant must be strictly positive") elif T < 0: raise ValueError("Temperature must be positive") elif R != 8.314: raise ValueError("Unless in a stargate, the universal gas constant is 8.314") elif type(A) != int and type(A) != float: raise TypeError("parameters need to be either type int or type float") elif type(T) !=int and type(T) != int: raise TypeError("parameters need to be either type int or type float") elif type(E) != int and type(E) != float: raise TypeError("parameters need to be either type int or type float") else: import numpy as np k=(A)*np.exp(-E/(R*T)) return k def mod_arr(A=10^7,b=0.5,T=10^2,E=10^3,R=8.314): """Returns the constant coefficient k. INPUTS ======= A: float, optional, default value is 10^7 Arhenieus constant, needs to be positive T: float, optional, default value is 10^2 temperature, must be positive R: float, fixed value 8.314, should not change b: float, optional, default value is 0.5, must be a real number RETURNS ======== Constant k unless any of A,T,b and E are not numbers in which case a TypeError exception is raised EXAMPLES ========= >>> mod_arr() 32.116059468138779 """ if A < 0: raise ValueError("The Arrhenius constant must be strictly positive") elif T < 0: raise ValueError("Temperature must be positive") elif isinstance(b,complex): raise ValueError("b must be a real number") elif R != 8.314: raise ValueError("Unless in a stargate, the universal gas constant is 8.314") elif type(A) != int and type(A) != float: raise TypeError("parameters need to be either type int or type float") elif type(T) !=int and type(T) != int: raise TypeError("parameters need to be either type int or type float") elif type(E) != int and type(E) != float: raise TypeError("parameters need to be either type int or type float") else: import numpy as np k=(A)*(T**b)*np.exp(-E/(R*T)) return k ``` Overwriting reaction_coeffs.py ```python import reaction_coeffs print(reaction_coeffs.const()) print(reaction_coeffs.arr()) print(reaction_coeffs.mod_arr()) ``` 1.0 11.3547417175 32.1160594681 ```python !pytest ``` ============================= test session starts ============================== platform darwin -- Python 3.6.1, pytest-3.0.7, py-1.4.33, pluggy-0.4.0 rootdir: /Users/filipmichalsky/cs207_filip_michalsky/homeworks/HW5, inifile: collected 13 items   test_multi_progress_r.py .. test_multi_reaction_r.py ... test_single_progress_r.py .. cs207test/test_roots.py ...... ========================== 13 passed in 0.24 seconds =========================== --- # Problem 3 Write a function that returns the **progress rate** for a reaction of the following form: \begin{align} \nu_{A} A + \nu_{B} B \longrightarrow \nu_{C} C. \end{align} Order your concentration vector so that \begin{align} \mathbf{x} = \begin{bmatrix} \left[A\right] \\ \left[B\right] \\ \left[C\right] \end{bmatrix} \end{align} Test your function with \begin{align} \nu_{i} = \begin{bmatrix} 2.0 \\ 1.0 \\ 0.0 \end{bmatrix} \qquad \mathbf{x} = \begin{bmatrix} 1.0 \\ 2.0 \\ 3.0 \end{bmatrix} \qquad k = 10. \end{align} You must document your function and write some tests in addition to the one suggested. You choose the additional tests, but you must have at least one doctest in addition to a suite of unit tests. ```python import numpy as np ``` ```python %%file single_progress_r.py def progress_rate(v_i,x,k): """Returns the progress rate of a reaction INPUTS ======= v_i: vector of stochiometric coefficients x: vector of concentrations (first dimension needs to match v_i),second dimension is 1 k: float, fixed value 8.314, should not change RETURNS ======== Progress rate of the reaction k*[A]^v_i[a]*[B]*v_i[b]*[C]^v_i[c] unless first dimension of x does not match first dimension of v_i in which case a ValueError exception is raised EXAMPLES ========= >>> import numpy as np >>> progress_rate(np.array([2,1,0]),np.array([1,2,3]),10) 20 """ #v_i=np.array([2,1,0]) #x=np.array([1,2,3]) #k=10 import numpy as np #check that the first dimension matches if x.shape[0] != v_i.shape[0]: raise ValueError("First dimension of x and v_i need to match") else: product_X_to_vi=1 #loop through the rows to multiply each x by its stochiometric coeffs for i,j in zip(v_i,x): product_X_to_vi=product_X_to_vi*(j**i) progress_rate=k*product_X_to_vi return progress_rate if __name__ == "__main__": import doctest doctest.testmod() ``` Overwriting single_progress_r.py ```python import single_progress_r import numpy as np single_progress_r.progress_rate(np.array([2,1,0]),np.array([1,2,3]),10) ``` 20 ```python import single_progress_r import numpy as np single_progress_r.progress_rate(np.array([2,1]),np.array([[2,1],[2,1],[2,1]]),10) ``` ```python %%file test_single_progress_r.py import single_progress_r import numpy as np #!pytest --doctest-modules def test_progress_rate_result(): assert single_progress_r.progress_rate(np.array([2,1,0]),np.array([1,2,3]),10) == 20 def test_progress_rate_shapes(): try: single_progress_r.progress_rate(np.array([2,1]),np.array([[2,1],[2,1],[2,1]]),10) except ValueError as err: assert(type(err) == ValueError) #def test_arr_result(): # assert reaction_coeffs.arr(A=10^7,E=10^3,T=10^2) == XX ``` Overwriting test_single_progress_r.py ```bash %%bash python -m pytest -v test_single_progress_r.py ``` ============================= test session starts ============================== platform darwin -- Python 3.6.1, pytest-3.0.7, py-1.4.33, pluggy-0.4.0 -- /Users/filipmichalsky/anaconda/bin/python cachedir: .cache rootdir: /Users/filipmichalsky/cs207_filip_michalsky/homeworks/HW5, inifile: collecting ... collected 2 items test_single_progress_r.py::test_progress_rate_result PASSED test_single_progress_r.py::test_progress_rate_shapes PASSED =========================== 2 passed in 0.19 seconds =========================== ```bash %%bash python multi_progress_r.py -v #doctest of created file ``` Trying: import numpy as np Expecting nothing ok Trying: progress_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,0.0],[0.0,1.0],[2.0,1.0]]),np.array([1.0,2.0,1.0]),10)[0] Expecting: 40.0 ok Trying: progress_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,0.0],[0.0,1.0],[2.0,1.0]]),np.array([1.0,2.0,1.0]),10)[1] Expecting: 10.0 ok 1 items had no tests: __main__ 1 items passed all tests: 3 tests in __main__.progress_rate_multi 3 tests in 2 items. 3 passed and 0 failed. Test passed. --- # Problem 4 Write a function that returns the **progress rate** for a system of reactions of the following form: \begin{align} \nu_{11}^{\prime} A + \nu_{21}^{\prime} B \longrightarrow \nu_{31}^{\prime\prime} C \\ \nu_{12}^{\prime} A + \nu_{32}^{\prime} C \longrightarrow \nu_{22}^{\prime\prime} B + \nu_{32}^{\prime\prime} C \end{align} Note that $\nu_{ij}^{\prime}$ represents the stoichiometric coefficient of reactant $i$ in reaction $j$ and $\nu_{ij}^{\prime\prime}$ represents the stoichiometric coefficient of product $i$ in reaction $j$. Therefore, in this convention, I have ordered my vector of concentrations as \begin{align} \mathbf{x} = \begin{bmatrix} \left[A\right] \\ \left[B\right] \\ \left[C\right] \end{bmatrix}. \end{align} Test your function with \begin{align} \nu_{ij}^{\prime} = \begin{bmatrix} 1.0 & 2.0 \\ 2.0 & 0.0 \\ 0.0 & 2.0 \end{bmatrix} \qquad \nu_{ij}^{\prime\prime} = \begin{bmatrix} 0.0 & 0.0 \\ 0.0 & 1.0 \\ 2.0 & 1.0 \end{bmatrix} \qquad \mathbf{x} = \begin{bmatrix} 1.0 \\ 2.0 \\ 1.0 \end{bmatrix} \qquad k = 10. \end{align} You must document your function and write some tests in addition to the one suggested. You choose the additional tests, but you must have at least one doctest in addition to a suite of unit tests. Please note I have already generalized the progress rate formula, I only need to subtract now the v_ij product from v_ij reactants to get the correct v_ij's ```python %%file multi_progress_r.py import numpy as np def progress_rate_multi(v_ij_reac,v_ij_proc,x,k): """Returns the progress rate of a set of reactions INPUTS ======= v_ij_reac: vector of stochiometric coefficients of reactants v_ij_proc: vector of stochiometric coefficients of products x: vector of concentrations (first dimension needs to match v_i),second dimension is 1 k: float RETURNS ======== Progress rates of the reactions (a string based on number of reactions) according to the formula k*[A]^v_i[a]*[B]*v_i[b]*[C]^v_i[c] unless v_ij = v_ij_proc-v_ij_reac has the first dimension not matching the first dimension of x which returns a ValueError unless shape of v_ij_proc does not match the shape of x, which will return ValueError as well EXAMPLES ========= >>> import numpy as np >>> progress_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,0.0],[0.0,1.0],[2.0,1.0]]),np.array([1.0,2.0,1.0]),10)[0] 40.0 >>> progress_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,0.0],[0.0,1.0],[2.0,1.0]]),np.array([1.0,2.0,1.0]),10)[1] 10.0 """ import numpy as np #calculate the effective stochiometric coefficients on the reactants side #check length of product coeffs and reac coeffs is the same if v_ij_proc.shape != v_ij_reac.shape: raise ValueError("Dimensions of stochiometric coeffs need to match") #check that the first dimension matches elif x.shape[0] != v_ij_proc.shape[0]: raise ValueError("First dimension of x and v_i need to match") else: v_ij = v_ij_reac product_X_to_vij = 1 #loop through the rows to multiply each x by its stochiometric coeffs for i,j in zip(v_ij,x): #print("i,j") #print(i,j) #print("j**i") #print(j**i) product_X_to_vij=product_X_to_vij*(j**i) #print("product") #print(product_X_to_vij) progress_rate_multi=k*product_X_to_vij return progress_rate_multi if __name__ == "__main__": import doctest doctest.testmod() ``` Overwriting multi_progress_r.py ```python import multi_progress_r multi_progress_r.progress_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,0.0],[0.0,1.0],[2.0,1.0]]),np.array([1.0,2.0,1.0]),10) ``` array([ 40., 10.]) ```python a=np.array([0.25,2.0]) b=np.array([1.,1.]) a*b ``` array([ 0.25, 2. ]) ```python import multi_progress_r v_ij_reac = np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]) v_ij_proc = np.array([[0.0,0.0],[0.0,1.0],[2.0,1.0]]) x = np.array([1.0,2.0,1.0]) k = 10 assert multi_progress_r.progress_rate_multi(v_ij_reac , v_ij_proc, x , k )[0] == 40 assert multi_progress_r.progress_rate_multi(v_ij_reac , v_ij_proc, x , k )[1] == 10 ``` ```python ``` ```python #sample fail of the function based on wrong input import multi_progress_r multi_progress_r.progress_rate_multi(np.array([2,1,1]),np.array([2,1]),np.array([[2,1],[2,1],[2,1]]),10) ``` ```python %%file test_multi_progress_r.py import multi_progress_r import numpy as np import doctest doctest.testmod(verbose=True) def progress_rate_result(): #test the result og the function v_ij_reac = np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]) v_ij_proc = np.array([[0.0,0.0],[0.0,1.0],[2.0,1.0]]) x = np.array([1.0,2.0,1.0]) k = 10 assert multi_progress_r.progress_rate_multi(v_ij_reac , v_ij_proc, x , k )[0] == 40.0 assert progress_rate_multi(v_ij_reac , v_ij_proc, x , k )[1] == 10.0 def test_progress_rate_shapes_with_x(): #test whether shape of coeffs v_i matches shape of concentrations x try: multi_progress_r.progress_rate_multi(np.array([2,1]),np.array([2,1]),np.array([[2,1],[2,1],[2,1]]),10) except ValueError as err: assert(type(err) == ValueError) def test_progress_rate_shapes_coeffs(): #test whether the shape of v_ij's matches try: multi_progress_r.progress_rate_multi(np.array([2,1,1]),np.array([2,1]),np.array([[2,1],[2,1],[2,1]]),10) except ValueError as err: assert(type(err) == ValueError) ``` Overwriting test_multi_progress_r.py ```bash %%bash python multi_progress_r.py -v ``` Trying: import numpy as np Expecting nothing ok Trying: progress_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,0.0],[0.0,1.0],[2.0,1.0]]),np.array([1.0,2.0,1.0]),10)[0] Expecting: 40.0 ok Trying: progress_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,0.0],[0.0,1.0],[2.0,1.0]]),np.array([1.0,2.0,1.0]),10)[1] Expecting: 10.0 ok 1 items had no tests: __main__ 1 items passed all tests: 3 tests in __main__.progress_rate_multi 3 tests in 2 items. 3 passed and 0 failed. Test passed. ```python !pytest ``` ============================= test session starts ============================== platform darwin -- Python 3.6.1, pytest-3.0.7, py-1.4.33, pluggy-0.4.0 rootdir: /Users/filipmichalsky/cs207_filip_michalsky/homeworks/HW5, inifile: collected 13 items   test_multi_progress_r.py .. test_multi_reaction_r.py ... test_single_progress_r.py .. cs207test/test_roots.py ...... ========================== 13 passed in 0.23 seconds =========================== --- # Problem 5 Write a function that returns the **reaction rate** of a system of irreversible reactions of the form: \begin{align} \nu_{11}^{\prime} A + \nu_{21}^{\prime} B &\longrightarrow \nu_{31}^{\prime\prime} C \\ \nu_{32}^{\prime} C &\longrightarrow \nu_{12}^{\prime\prime} A + \nu_{22}^{\prime\prime} B \end{align} Once again $\nu_{ij}^{\prime}$ represents the stoichiometric coefficient of reactant $i$ in reaction $j$ and $\nu_{ij}^{\prime\prime}$ represents the stoichiometric coefficient of product $i$ in reaction $j$. In this convention, I have ordered my vector of concentrations as \begin{align} \mathbf{x} = \begin{bmatrix} \left[A\right] \\ \left[B\right] \\ \left[C\right] \end{bmatrix} \end{align} Test your function with \begin{align} \nu_{ij}^{\prime} = \begin{bmatrix} 1.0 & 0.0 \\ 2.0 & 0.0 \\ 0.0 & 2.0 \end{bmatrix} \qquad \nu_{ij}^{\prime\prime} = \begin{bmatrix} 0.0 & 1.0 \\ 0.0 & 2.0 \\ 1.0 & 0.0 \end{bmatrix} \qquad \mathbf{x} = \begin{bmatrix} 1.0 \\ 2.0 \\ 1.0 \end{bmatrix} \qquad k = 10. \end{align} You must document your function and write some tests in addition to the one suggested. You choose the additional tests, but you must have at least one doctest in addition to a suite of unit tests. ```python #%%file multi_reaction_r.py import numpy as np def reaction_rate_multi(v_ij_reac,v_ij_proc,x,k): """Returns the rection rate for a set of species INPUTS ======= v_ij_reac: vector of stochiometric coefficients of reactants v_ij_proc: vector of stochiometric coefficients of products x: vector of concentrations (first dimension needs to match v_i),second dimension is 1 k: float RETURNS ======== Reaction rates of the species (a string based on number of species) according to the formula k*[A]^v_i[a]*[B]*v_i[b]*[C]^v_i[c] for progress rate and dXi/dt = sum(v_ij_proc-v_ij_reac)*progress rate unless v_ij = v_ij_proc-v_ij_reac has the first dimension not matching the first dimension of x which returns a ValueError unless shape of v_ij_proc does not match the shape of x, which will return ValueError as well EXAMPLES ========= >>> import numpy as np >>> reaction_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,1.0],[0.0,2.0],[1.0,0.0]]),np.array([1.0,2.0,1.0]),10)[0][0] -50.0 >>> reaction_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,1.0],[0.0,2.0],[1.0,0.0]]),np.array([1.0,2.0,1.0]),10)[1][0] -60.0 >>> reaction_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,1.0],[0.0,2.0],[1.0,0.0]]),np.array([1.0,2.0,1.0]),10)[2][0] 20.0 """ import numpy as np #calculate the effective stochiometric coefficients on the reactants side #check length of product coeffs and reac coeffs is the same if v_ij_proc.shape != v_ij_reac.shape: raise ValueError("Dimensions of stochiometric coeffs need to match") #check that the first dimension matches elif x.shape[0] != v_ij_proc.shape[0]: raise ValueError("First dimension of x and v_i need to match") else: v_ij = v_ij_reac product_X_to_vij = 1 #loop through the rows to multiply each x by its stochiometric coeffs for i,j in zip(v_ij,x): product_X_to_vij=product_X_to_vij*(j**i) product_X_to_vij=product_X_to_vij.reshape(len(product_X_to_vij),1) progress_rate_multi=k*product_X_to_vij reaction_rates=np.dot((v_ij_proc-v_ij_reac),progress_rate_multi) return reaction_rates if __name__ == "__main__": import doctest doctest.testmod() ``` ```python k=np.array([[10],[10],[10]]) w_ij=np.array([[1],[2],[3]]) print(k.shape,w_ij.shape) ``` (3, 1) (3, 1) ```python #from multi_reaction_r import reaction_rate_multi import multi_reaction_r multi_reaction_r.reaction_rate_multi(np.array([[1.0,0.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,1.0],[0.0,2.0],[1.0,0.0]]),np.array([1.0,2.0,1.0]),np.array([[10],[10]])) ``` array([[-30.], [-60.], [ 20.]]) ```bash %%bash python multi_reaction_r.py -v ``` Trying: import numpy as np Expecting nothing ok Trying: reaction_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,1.0],[0.0,2.0],[1.0,0.0]]),np.array([1.0,2.0,1.0]),10)[0][0] Expecting: -50.0 ok Trying: reaction_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,1.0],[0.0,2.0],[1.0,0.0]]),np.array([1.0,2.0,1.0]),10)[1][0] Expecting: -60.0 ok Trying: reaction_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,1.0],[0.0,2.0],[1.0,0.0]]),np.array([1.0,2.0,1.0]),10)[2][0] Expecting: 20.0 ok 1 items had no tests: __main__ 1 items passed all tests: 4 tests in __main__.reaction_rate_multi 4 tests in 2 items. 4 passed and 0 failed. Test passed. ```python %%file test_multi_reaction_r.py import multi_reaction_r as mr import numpy as np #import doctest #doctest.testmod(verbose=True) def test_reaction_rate_result(): #test the result og the function v_ij_reac = np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]) v_ij_proc = np.array([[0.0,1.0],[0.0,2.0],[1.0,0.0]]) x = np.array([1.0,2.0,1.0]) k = 10 assert mr.reaction_rate_multi(v_ij_reac , v_ij_proc, x , k )[0][0] == -50.0 assert mr.reaction_rate_multi(v_ij_reac , v_ij_proc, x , k )[1][0] == -60.0 assert mr.reaction_rate_multi(v_ij_reac , v_ij_proc, x , k )[2][0] == 20.0 def test_progress_rate_shapes_with_x(): #test whether shape of coeffs v_i matches shape of concentrations x try: mr.reaction_rate_multi(np.array([2,1]),np.array([2,1]),np.array([[2,1],[2,1],[2,1]]),10) except ValueError as err: assert(type(err) == ValueError) def test_progress_rate_shapes_coeffs(): #test whether the shape of v_ij's matches try: mr.reaction_rate_multi(np.array([2,1,1]),np.array([2,1]),np.array([[2,1],[2,1],[2,1]]),10) except ValueError as err: assert(type(err) == ValueError) ``` Overwriting test_multi_reaction_r.py ```bash %%bash python -m pytest -v test_multi_reaction_r.py ``` ============================= test session starts ============================== platform darwin -- Python 3.6.1, pytest-3.0.7, py-1.4.33, pluggy-0.4.0 -- /Users/filipmichalsky/anaconda/bin/python cachedir: .cache rootdir: /Users/filipmichalsky/cs207_filip_michalsky/homeworks/HW5, inifile: collecting ... collected 3 items test_multi_reaction_r.py::test_reaction_rate_result PASSED test_multi_reaction_r.py::test_progress_rate_shapes_with_x PASSED test_multi_reaction_r.py::test_progress_rate_shapes_coeffs PASSED =========================== 3 passed in 0.22 seconds =========================== --- # Problem 6 Put parts 3, 4, and 5 in a module called `chemkin`. Next, pretend you're a client who needs to compute the reaction rates at three different temperatures ($T = \left\{750, 1500, 2500\right\}$) of the following system of irreversible reactions: \begin{align} 2H_{2} + O_{2} \longrightarrow 2OH + H_{2} \\ OH + HO_{2} \longrightarrow H_{2}O + O_{2} \\ H_{2}O + O_{2} \longrightarrow HO_{2} + OH \end{align} The client also happens to know that reaction 1 is a modified Arrhenius reaction with $A_{1} = 10^{8}$, $b_{1} = 0.5$, $E_{1} = 5\times 10^{4}$, reaction 2 has a constant reaction rate parameter $k = 10^{4}$, and reaction 3 is an Arrhenius reaction with $A_{3} = 10^{7}$ and $E_{3} = 10^{4}$. You should write a script that imports your `chemkin` module and returns the reaction rates of the species at each temperature of interest given the following species concentrations: \begin{align} \mathbf{x} = \begin{bmatrix} H_{2} \\ O_{2} \\ OH \\ HO_{2} \\ H_{2}O \end{bmatrix} = \begin{bmatrix} 2.0 \\ 1.0 \\ 0.5 \\ 1.0 \\ 1.0 \end{bmatrix} \end{align} You may assume that these are elementary reactions. ```python %%file chemkin1.py import numpy as np def const(k=1.0): """Returns the constant coefficient k. INPUTS ======= a: float, optional, default value is 1.0 Constant reaction coefficient RETURNS ======== Constant k unless k is not an int or float in which case a TypeError exception is raised EXAMPLES ========= >>> const(1.0) 1.0 """ if type(k) != int and type(k) != float: raise TypeError("Input needs to be a number!") else: return k def arr(A=10^7,T=10^2,E=10^3,R=8.314): """Returns the constant coefficient k. INPUTS ======= A: float, optional, default value is 10^7 Arhenieus constant, needs to be positive T: float, optional, default value is 10^2 temperature, must be positive R: float, fixed value 8.314, should not change RETURNS ======== Constant k unless any of A,T, and E are not numbers in which case a TypeError exception is raised EXAMPLES ========= >>> arr(10^7,10^2,10^2) 11.526748719357375 """ if A < 0: raise ValueError("The Arrhenius constant must be strictly positive") elif T < 0: raise ValueError("Temperature must be positive") elif R != 8.314: raise ValueError("Unless in a stargate, the universal gas constant is 8.314") elif type(A) != int and type(A) != float: raise TypeError("parameters need to be either type int or type float") elif type(T) !=int and type(T) != int: raise TypeError("parameters need to be either type int or type float") elif type(E) != int and type(E) != float: raise TypeError("parameters need to be either type int or type float") else: import numpy as np k=(A)*np.exp(-E/(R*T)) return k def mod_arr(A=10^7,b=0.5,T=10^2,E=10^3,R=8.314): """Returns the constant coefficient k. INPUTS ======= A: float, optional, default value is 10^7 Arhenieus constant, needs to be positive T: float, optional, default value is 10^2 temperature, must be positive R: float, fixed value 8.314, should not change b: float, optional, default value is 0.5, must be a real number RETURNS ======== Constant k unless any of A,T,b and E are not numbers in which case a TypeError exception is raised EXAMPLES ========= >>> mod_arr() 32.116059468138779 """ if A < 0: raise ValueError("The Arrhenius constant must be strictly positive") elif T < 0: raise ValueError("Temperature must be positive") elif isinstance(b,complex): raise ValueError("b must be a real number") elif R != 8.314: raise ValueError("Unless in a stargate, the universal gas constant is 8.314") elif type(A) != int and type(A) != float: raise TypeError("parameters need to be either type int or type float") elif type(T) !=int and type(T) != int: raise TypeError("parameters need to be either type int or type float") elif type(E) != int and type(E) != float: raise TypeError("parameters need to be either type int or type float") else: import numpy as np k=(A)*(T**b)*np.exp(-E/(R*T)) return k def reaction_rate_multi(v_ij_reac,v_ij_proc,x,k): """Returns the rection rate for a set of species INPUTS ======= v_ij_reac: vector of stochiometric coefficients of reactants v_ij_proc: vector of stochiometric coefficients of products x: vector of concentrations (first dimension needs to match v_i),second dimension is 1 k: float RETURNS ======== Reaction rates of the species (a string based on number of species) according to the formula k*[A]^v_i[a]*[B]*v_i[b]*[C]^v_i[c] for progress rate and dXi/dt = sum(v_ij_proc-v_ij_reac)*progress rate unless v_ij = v_ij_proc-v_ij_reac has the first dimension not matching the first dimension of x which returns a ValueError unless shape of v_ij_proc does not match the shape of x, which will return ValueError as well EXAMPLES ========= >>> import numpy as np >>> reaction_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,1.0],[0.0,2.0],[1.0,0.0]]),np.array([1.0,2.0,1.0]),10)[0][0] -50.0 >>> reaction_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,1.0],[0.0,2.0],[1.0,0.0]]),np.array([1.0,2.0,1.0]),10)[1][0] -60.0 >>> reaction_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,1.0],[0.0,2.0],[1.0,0.0]]),np.array([1.0,2.0,1.0]),10)[2][0] 20.0 """ import numpy as np #calculate the effective stochiometric coefficients on the reactants side #check length of product coeffs and reac coeffs is the same if v_ij_proc.shape != v_ij_reac.shape: raise ValueError("Dimensions of stochiometric coeffs need to match") #check that the first dimension matches elif x.shape[0] != v_ij_proc.shape[0]: raise ValueError("First dimension of x and v_i need to match") else: v_ij = v_ij_reac product_X_to_vij = 1 #loop through the rows to multiply each x by its stochiometric coeffs for i,j in zip(v_ij,x): product_X_to_vij=product_X_to_vij*(j**i) product_X_to_vij=product_X_to_vij.reshape(len(product_X_to_vij),1) progress_rate_multi=k*product_X_to_vij reaction_rates=np.dot((v_ij_proc-v_ij_reac),progress_rate_multi) return reaction_rates if __name__ == "__main__": import doctest doctest.testmod() ``` Overwriting chemkin1.py ```bash %%bash python chemkin1.py -v ``` Trying: arr(10^7,10^2,10^2) Expecting: 11.526748719357375 ok Trying: const(1.0) Expecting: 1.0 ok Trying: mod_arr() Expecting: 32.116059468138779 ok Trying: import numpy as np Expecting nothing ok Trying: reaction_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,1.0],[0.0,2.0],[1.0,0.0]]),np.array([1.0,2.0,1.0]),10)[0][0] Expecting: -50.0 ok Trying: reaction_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,1.0],[0.0,2.0],[1.0,0.0]]),np.array([1.0,2.0,1.0]),10)[1][0] Expecting: -60.0 ok Trying: reaction_rate_multi(np.array([[1.0,2.0],[2.0,0.0],[0.0,2.0]]),np.array([[0.0,1.0],[0.0,2.0],[1.0,0.0]]),np.array([1.0,2.0,1.0]),10)[2][0] Expecting: 20.0 ok 1 items had no tests: __main__ 4 items passed all tests: 1 tests in __main__.arr 1 tests in __main__.const 1 tests in __main__.mod_arr 4 tests in __main__.reaction_rate_multi 7 tests in 5 items. 7 passed and 0 failed. Test passed. ```python import chemkin1 import numpy as np vij_reac = np.array([[2.0,0.0,0.0],[1.0,0.0,1.0],[0.0,1.0,0.0],[0.0,1.0,0.0],[0.0,0.0,1.0]]) vij_proc = np.array([[1.0,0.0,0.0],[0.0,1.0,0.0],[2.0,0.0,1.0],[0.0,0.0,1.0],[0.0,1.0,0.0]]) x = np.array([2.0,1.0,0.5,1.0,1.0]) species = np.array([['H2'],['O2'],['OH'],['OH2'],['H20']]) reaction_rate =[] T = [750,1500,2500] for temp in T: k1= chemkin1.mod_arr(A=10**7,b=0.5,T=temp,E=(5*(10**4)),R=8.314) k2= chemkin1.const(10**4) k3= chemkin1.arr(A=10**8,T=temp,E=5*(10**4),R=8.314) k=np.array([[k1],[k2],[k3]]) this_reaction_rate = chemkin1.reaction_rate_multi(vij_reac,vij_proc,x,k) reaction_rate.append(this_reaction_rate) print("Temperature ",temp) print("Reaction rates of species") for i,j in zip(species,this_reaction_rate): print(i[0],': ',j[0]) ``` Temperature 750 Reaction rates of species H2 : -360707.78728 O2 : -388635.752574 OH : 749343.539854 OH2 : 27927.9652935 H20 : -27927.9652935 Temperature 1500 Reaction rates of species H2 : -28111762.0765 O2 : -29921368.5157 OH : 58033130.5922 OH2 : 1809606.43925 H20 : -1809606.43925 Temperature 2500 Reaction rates of species H2 : -180426142.596 O2 : -189442449.726 OH : 369868592.322 OH2 : 9016307.12982 H20 : -9016307.12982 --- # Problem 7 Get together with your project team, form a GitHub organization (with a descriptive team name), and give the teaching staff access. You can have has many repositories as you like within your organization. However, we will grade the repository called **`cs207-FinalProject`**. Within the `cs207-FinalProject` repo, you must set up Travis CI and Coveralls. Make sure your `README.md` file includes badges indicating how many tests are passing and the coverage of your code.
! ! CalculiX - A 3-dimensional finite element program ! Copyright (C) 1998-2018 Guido Dhondt ! ! This program is free software; you can redistribute it and/or ! modify it under the terms of the GNU General Public License as ! published by the Free Software Foundation(version 2); ! ! ! This program is distributed in the hope that it will be useful, ! but WITHOUT ANY WARRANTY; without even the implied warranty of ! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ! GNU General Public License for more details. ! ! You should have received a copy of the GNU General Public License ! along with this program; if not, write to the Free Software ! Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. ! ! ! Subroutine x_interpolate.f ! ! Triangulates the face and interpolates xstate variables according to ! the plane equations of these planes ! ! by: Jaro Hokkanen ! ! subroutine interpolateinface(kk,xstate,xstateini,numpts,nstate_, & mi,islavsurf,pslavsurf, & ne0,islavsurfold,pslavsurfold) ! implicit none ! integer numpts,i_int,n_int,i,j,k,kk,l,ll,nn, & koncont(3,2*numpts+1),itri,kflag,neigh(1),kneigh, & imastop(3,2*numpts+1),indexcj,nopespringj,list(numpts), & igauss,mi(*),nstate_,itriangle(100),itriold, & ifaceq(8,6),ip(numpts),ne0,itrinew,ntriangle, & ifacet(6,4),ifacew1(4,5),ifacew2(8,5),n,islavsurf(2,*), & ibin(numpts),ivert1,ntriangle_,nterms,m,islavsurfold(2,*), & nx(2*numpts+1),ny(2*numpts+1),isol,id ! real*8 xstate(nstate_,mi(1),*),p(3),pslavsurfold(3,*), & xstateini(nstate_,mi(1),*),coi(2,numpts+3),pneigh(3,3), & cg(2,2*numpts+1),xdist,pslavsurf(3,*),xil,etl,ratio(3), & z(9,3),x(2*numpts+1),xo(2*numpts+1), & y(2*numpts+1),yo(2*numpts+1),straight(9,2*numpts+1),dist ! ! nodes per face for hex elements ! data ifaceq /4,3,2,1,11,10,9,12, & 5,6,7,8,13,14,15,16, & 1,2,6,5,9,18,13,17, & 2,3,7,6,10,19,14,18, & 3,4,8,7,11,20,15,19, & 4,1,5,8,12,17,16,20/ ! ! nodes per face for tet elements ! data ifacet /1,3,2,7,6,5, & 1,2,4,5,9,8, & 2,3,4,6,10,9, & 1,4,3,8,10,7/ ! ! nodes per face for linear wedge elements ! data ifacew1 /1,3,2,0, & 4,5,6,0, & 1,2,5,4, & 2,3,6,5, & 3,1,4,6/ ! ! nodes per face for quadratic wedge elements ! data ifacew2 /1,3,2,9,8,7,0,0, & 4,5,6,10,11,12,0,0, & 1,2,5,4,7,14,10,13, & 2,3,6,5,8,15,11,14, & 3,1,4,6,9,13,12,15/ ! kneigh=1 ! do i=1,numpts list(i)=i enddo ! ! Loop over the old integration points within the face ! ll=0 do l=islavsurfold(2,kk)+1,islavsurfold(2,kk+1) ll=ll+1 coi(1,ll)=pslavsurfold(1,l) coi(2,ll)=pslavsurfold(2,l) ip(ll)=ne0+l enddo ! ! Calling deltri for triangulation ! kflag=2 ! call deltri(numpts,numpts,coi(1,1:numpts+3),coi(2,1:numpts+3), & list,ibin,koncont,imastop,n) ! ! Arranging imastop field corresponding to "imastop" ! nn=0 do i=1,n ivert1=imastop(1,i) imastop(1,i)=imastop(2,i) imastop(2,i)=imastop(3,i) imastop(3,i)=ivert1 enddo ! ! determining the center of gravity and the bounding planes ! of the triangles ! call updatecont2d(koncont,n,coi,cg,straight) ! ! sorting the centers of gravity ! do l=1,n xo(l)=cg(1,l) x(l)=xo(l) nx(l)=l yo(l)=cg(2,l) y(l)=yo(l) ny(l)=l enddo kflag=2 call dsort(x,nx,n,kflag) call dsort(y,ny,n,kflag) ! ! Loop over the new integration points ! do igauss=islavsurf(2,kk)+1,islavsurf(2,kk+1) xdist=9.d0 ! ! coordinates of the new integration point ! p(1)=pslavsurf(1,igauss) p(2)=pslavsurf(2,igauss) ! ! closest triangle center of gravity ! call near2d(xo,yo,x,y,nx,ny,p(1),p(2), & n,neigh,kneigh) ! isol=0 ! itriold=0 itri=neigh(1) ntriangle=0 ntriangle_=100 ! loop1: do do l=1,3 ll=3*l-2 dist=straight(ll,itri)*p(1)+ & straight(ll+1,itri)*p(2)+ & straight(ll+2,itri) ! if(dist.gt.0.d0) then itrinew=imastop(l,itri) if(itrinew.eq.0) then c write(*,*) '**border reached' exit loop1 elseif(itrinew.eq.itriold) then c write(*,*) '**solution in between triangles' isol=itri exit loop1 else call nident(itriangle,itrinew,ntriangle,id) if(id.gt.0) then if(itriangle(id).eq.itrinew) then c write(*,*) '**circular path;no solution' exit loop1 endif endif ntriangle=ntriangle+1 if(ntriangle.gt.ntriangle_) then c write(*,*) '**too many iterations' exit loop1 endif do k=ntriangle,id+2,-1 itriangle(k)=itriangle(k-1) enddo itriangle(id+1)=itrinew itriold=itri itri=itrinew cycle loop1 endif elseif(l.eq.3) then c write(*,*) '**regular solution' isol=itri exit loop1 endif enddo enddo loop1 ! if(isol.eq.0) then ! ! mapping the new integration point onto the nearest ! triangle ! do k=1,3 do m=1,2 pneigh(m,k)=coi(m,koncont(k,itri)) enddo pneigh(3,k)=0.d0 enddo p(3)=0.d0 nterms=3 ! call attach_2d(pneigh,p,nterms,ratio,dist,xil,etl) ! do m=1,2 p(m)=0.d0 do k=1,3 p(m)=p(m)+ratio(k)*pneigh(m,k) enddo enddo endif ! ! Assigning xstate values from the vertices of the triangle ! to the field z (integration point values from xstateini) ! do k=1,3 do i=1,9 z(i,k)=xstateini(i,1,ip(koncont(k,itri))) enddo enddo ! ! Calling plane_eq to interpolate values using plane equation ! do i=1,9 call plane_eq( & coi(1,koncont(1,itri)),coi(2,koncont(1,itri)),z(i,1), & coi(1,koncont(2,itri)),coi(2,koncont(2,itri)),z(i,2), & coi(1,koncont(3,itri)),coi(2,koncont(3,itri)),z(i,3), & p(1),p(2),xstate(i,1,ne0+igauss)) enddo ! enddo ! return end
Require Import Crypto.Specific.Framework.RawCurveParameters. Require Import Crypto.Util.LetIn. (*** Modulus : 2^383 - 421 Base: 32 ***) Definition curve : CurveParameters := {| sz := 12%nat; base := 32; bitwidth := 32; s := 2^383; c := [(1, 421)]; carry_chains := None; a24 := None; coef_div_modulus := None; goldilocks := None; karatsuba := None; montgomery := true; freeze := Some false; ladderstep := false; mul_code := None; square_code := None; upper_bound_of_exponent_loose := None; upper_bound_of_exponent_tight := None; allowable_bit_widths := None; freeze_extra_allowable_bit_widths := None; modinv_fuel := None |}. Ltac extra_prove_mul_eq _ := idtac. Ltac extra_prove_square_eq _ := idtac.
module Main import Oyster.Core %default total {- EBNF grammar: expr ::= term ( + expr | - expr | epsilon ) term ::= factor ( * expr | / expr | epsilon ) factor ::= ( expr ) | integer integer ::= ... -2 | -1 | 0 | 1 | 2 | ... -} mutual partial expr : Parser Int expr = do t <- term do symbol "+" e <- expr pure (t + e) <|> do symbol "-" e <- expr pure (t - e) <|> pure t partial term : Parser Int term = do f <- factor do symbol "*" t <- term pure (f * t) <|> do symbol "/" t <- term pure (f `div` t) <|> pure f partial factor : Parser Int factor = do symbol "(" e <- expr symbol ")" pure e <|> integer eval : String -> Maybe Int eval inp = case parse expr inp of [(n, "")] => Just n _ => Nothing main : IO () main = do expr <- getLine pure ()
= = = Loan in = = =
module Numeral.Natural.Oper.FlooredDivision where import Lvl open import Data open import Data.Boolean.Stmt open import Logic.Propositional.Theorems open import Numeral.Natural open import Numeral.Natural.Oper.Comparisons open import Numeral.Natural.Oper.Comparisons.Proofs open import Numeral.Natural.Relation.Order open import Relator.Equals infixl 10100 _⌊/⌋_ -- Inductive definition of an algorithm for division. -- `[ d , b ] a' div b'` should be interpreted as following: -- `d` is the result of the algorithm that is being incremented as it runs. -- `b` is the predecessor of the original denominator. This is constant throughout the whole process. -- `a'` is the numerator. This is decremented as it runs. -- `b'` is the predecessor of the temporary denominator. This is decremented as it runs. -- By decrementing both `a'` and `b'`, and incrementing `d` when 'b`' reaches 0, it counts how many times `b` "fits into" `a`. -- Note: See Numeral.Natural.Oper.Modulo for a similiar algorithm used to determine the modulo. [_,_]_div_ : ℕ → ℕ → ℕ → ℕ → ℕ [ d , _ ] 𝟎 div _ = d [ d , b ] 𝐒(a') div 𝟎 = [ 𝐒(d) , b ] a' div b [ d , b ] 𝐒(a') div 𝐒(b') = [ d , b ] a' div b' {-# BUILTIN NATDIVSUCAUX [_,_]_div_ #-} -- Floored division operation. _⌊/⌋_ : ℕ → (m : ℕ) → .⦃ _ : IsTrue(positive?(m)) ⦄ → ℕ a ⌊/⌋ 𝐒(m) = [ 𝟎 , m ] a div m _⌊/⌋₀_ : ℕ → ℕ → ℕ _ ⌊/⌋₀ 𝟎 = 𝟎 a ⌊/⌋₀ 𝐒(m) = a ⌊/⌋ 𝐒(m) {-# INLINE _⌊/⌋₀_ #-}
module Decidable.Finite.Fin import Data.Nat import Data.Nat.Order import Data.Fin import Decidable.Decidable.Extra import Data.Fin.Extra ||| Given a decidable predicate on Fin n, ||| it's decidable whether any number in Fin n satisfies it. public export finiteDecEx : {n : Nat} -> {0 p : Fin n -> Type} -> (pdec : (k : Fin n) -> Dec (p k)) -> Dec (k ** p k) finiteDecEx {n = Z} pdec = No (absurd . fst) finiteDecEx {n = S n} pdec = case pdec FZ of Yes pz => Yes (FZ ** pz) No npz => case finiteDecEx {n = n} (\ k => pdec (FS k)) of Yes (k ** pk) => Yes (FS k ** pk) No npk => No $ \case (FZ ** pz) => absurd (npz pz) (FS k ** pk) => absurd (npk (k ** pk)) ||| Given a decidable predicate on Fin n, ||| it's decidable whether all numbers in Fin n satisfy it. public export finiteDecAll : {n : Nat} -> {0 p : Fin n -> Type} -> (pdec : (k : Fin n) -> Dec (p k)) -> Dec ((k : Fin n) -> p k) finiteDecAll pdec = notExistsNotForall pdec $ finiteDecEx (\ x => negateDec (pdec x))
[STATEMENT] lemma lesub_step_typeD: "A {\<sqsubseteq>\<^bsub>r\<^esub>} B \<Longrightarrow> (x,y) \<in> A \<Longrightarrow> \<exists>y'. (x, y') \<in> B \<and> y \<sqsubseteq>\<^sub>r y'" [PROOF STATE] proof (prove) goal (1 subgoal): 1. \<lbrakk>A {\<sqsubseteq>\<^bsub>r\<^esub>} B; (x, y) \<in> A\<rbrakk> \<Longrightarrow> \<exists>y'. (x, y') \<in> B \<and> y \<sqsubseteq>\<^bsub>r\<^esub> y' [PROOF STEP] (*<*) [PROOF STATE] proof (prove) goal (1 subgoal): 1. \<lbrakk>A {\<sqsubseteq>\<^bsub>r\<^esub>} B; (x, y) \<in> A\<rbrakk> \<Longrightarrow> \<exists>y'. (x, y') \<in> B \<and> y \<sqsubseteq>\<^bsub>r\<^esub> y' [PROOF STEP] by (unfold lesubstep_type_def) blast
```python %matplotlib inline %config InlineBackend.figure_format = 'svg' import scqubits as qubit import numpy as np ``` # Defining circuit topology ```python flux_qubit = qubit.Circuit() flux_qubit.add_element(qubit.Capacitance('Cg1'), ['g1', '1']) flux_qubit.add_element(qubit.Capacitance('Cg2'), ['g2', '2']) flux_qubit.add_element(qubit.Capacitance('CJ1'), ['GND', '1']) flux_qubit.add_element(qubit.Capacitance('CJ2'), ['GND', '2']) flux_qubit.add_element(qubit.Capacitance('CJ3'), ['1', '3']) flux_qubit.add_element(qubit.JosephsonJunction('J1'), ['GND', '1']) flux_qubit.add_element(qubit.JosephsonJunction('J2'), ['GND', '2']) flux_qubit.add_element(qubit.JosephsonJunction('J3'), ['1', '3']) ``` # Parametrizing Hamiltonian ```python ϕ1 = qubit.Variable('ϕ_1') ϕ2 = qubit.Variable('ϕ_2') f = qubit.Variable('f') g1 = qubit.Variable('g_1') g2 = qubit.Variable('g_2') flux_qubit.add_variable(ϕ1) flux_qubit.add_variable(ϕ2) flux_qubit.add_variable(f) flux_qubit.add_variable(g1) flux_qubit.add_variable(g2) ``` # Mapping nodal phases to variables ```python flux_qubit.map_nodes_linear(['GND', '1', '2', '3', 'g1', 'g2'], ['ϕ_1', 'ϕ_2', 'f', 'g_1', 'g_2'], np.asarray([[0, 0, 0, 0, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 1, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]])) ``` # Separating variables into external controls and degrees of freedom ```python ϕ1.create_grid(21, 1) # 21 charge states, 2pi wavefunction periodicity ϕ2.create_grid(21, 1) # 21 charge states, 2pi wavefunction periodicity f.set_parameter(0.4*2*np.pi, 0) # external flux: 0.4 quantum, external voltage: 0 g1.set_parameter(0, 0) # external flux: 0 quanta, external voltage: 0 g2.set_parameter(0, 0) # external flux: 0 quanta, external voltage: 0 ``` # Printing symbolic Hamiltonian (using sympy) This part is a bit ugly, but in principle we could improve it so it uses better notation ```python import sympy C_g1, C_g2, C_J1, C_J2, C_J3, E_J1, E_J2, E_J3 = \ sympy.symbols('C_g1, C_g2, C_J1, C_J2, C_J3, E_J1, E_J2, E_J3') flux_qubit.find_element('Cg1').set_capacitance(C_g1) flux_qubit.find_element('Cg2').set_capacitance(C_g2) flux_qubit.find_element('CJ1').set_capacitance(C_J1) flux_qubit.find_element('CJ2').set_capacitance(C_J2) flux_qubit.find_element('CJ3').set_capacitance(C_J3) flux_qubit.find_element('J1').set_critical_current(E_J1) flux_qubit.find_element('J2').set_critical_current(E_J2) flux_qubit.find_element('J3').set_critical_current(E_J3) ``` ## capacitance matrix in terms of the nodal parameterization ```python flux_qubit.capacitance_matrix(symbolic=True) ``` $\displaystyle \left[\begin{matrix}C_{J1} + C_{J2} & 0.0 & - C_{J1} & 0.0 & - C_{J2} & 0.0\\0.0 & C_{g1} & - C_{g1} & 0.0 & 0.0 & 0.0\\- C_{J1} & - C_{g1} & C_{J1} + C_{J3} + C_{g1} & 0.0 & 0.0 & - C_{J3}\\0.0 & 0.0 & 0.0 & C_{g2} & - C_{g2} & 0.0\\- C_{J2} & 0.0 & 0.0 & - C_{g2} & C_{J2} + C_{g2} & 0.0\\0.0 & 0.0 & - C_{J3} & 0.0 & 0.0 & C_{J3}\end{matrix}\right]$ ## Legendre transform of the capacitance matrix (inverse wrt to degrees of freedom) ```python flux_qubit.capacitance_matrix_legendre_transform(symbolic=True) ``` $\displaystyle \left[\begin{matrix}\frac{C_{J2} + C_{J3} + C_{g2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & \frac{C_{J3}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & \frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - \frac{C_{J3} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & \frac{C_{g1} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & \frac{C_{J3} C_{g2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\\\frac{C_{J3}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & \frac{C_{J1} + C_{J3} + C_{g1}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & - \frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \frac{C_{J3} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & \frac{C_{J3} C_{g1}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & \frac{C_{g2} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\\\frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - \frac{C_{J3} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & - \frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \frac{C_{J3} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & C_{J3} \left(- \frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \frac{C_{J3} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right) - C_{J3} \left(\frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - \frac{C_{J3} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right) & - C_{g1} \left(- \frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \frac{C_{J3} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right) & - C_{g2} \left(\frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - \frac{C_{J3} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right)\\\frac{C_{g1} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & \frac{C_{J3} C_{g1}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & \frac{C_{J3}^{2} C_{g1}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - \frac{C_{J3} C_{g1} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & \frac{C_{g1}^{2} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & \frac{C_{J3} C_{g1} C_{g2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\\\frac{C_{J3} C_{g2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & \frac{C_{g2} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & - \frac{C_{J3}^{2} C_{g2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \frac{C_{J3} C_{g2} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & \frac{C_{J3} C_{g1} C_{g2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} & \frac{C_{g2}^{2} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\end{matrix}\right]$ ## Symbolic lagrangian ```python sympy.nsimplify(flux_qubit.symbolic_lagrangian()) ``` $\displaystyle - E_{J1} \left(1 - \cos{\left(ϕ_{1} \right)}\right) - E_{J2} \left(1 - \cos{\left(ϕ_{2} \right)}\right) - E_{J3} \left(1 - \cos{\left(f + ϕ_{1} - ϕ_{2} \right)}\right) + \partial_tg_1 \left(\frac{C_{g1} \partial_tg_1}{2} - \frac{C_{g1} \partial_tϕ_1}{2}\right) + \partial_tg_2 \left(\frac{C_{g2} \partial_tg_2}{2} - \frac{C_{g2} \partial_tϕ_2}{2}\right) + \partial_tϕ_1 \left(- C_{J3} \left(- \frac{\partial_tf}{2} + \frac{\partial_tϕ_2}{2}\right) - \frac{C_{g1} \partial_tg_1}{2} + \frac{\partial_tϕ_1 \left(C_{J1} + C_{J3} + C_{g1}\right)}{2}\right) + \partial_tϕ_2 \left(- \frac{C_{g2} \partial_tg_2}{2} + \frac{\partial_tϕ_2 \left(C_{J2} + C_{g2}\right)}{2}\right) + \left(- \partial_tf + \partial_tϕ_2\right) \left(- \frac{C_{J3} \partial_tϕ_1}{2} + C_{J3} \left(- \frac{\partial_tf}{2} + \frac{\partial_tϕ_2}{2}\right)\right)$ ## Symbolic hamiltonian ```python sympy.nsimplify(flux_qubit.symbolic_hamiltonian()) ``` $\displaystyle E_{J1} \left(1 - \cos{\left(ϕ_{1} \right)}\right) + E_{J2} \left(1 - \cos{\left(ϕ_{2} \right)}\right) + E_{J3} \left(1 - \cos{\left(f + ϕ_{1} - ϕ_{2} \right)}\right) + \frac{\partial_tf \left(\partial_tf \left(C_{J3} \left(- \frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \frac{C_{J3} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right) - C_{J3} \left(\frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - \frac{C_{J3} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right)\right) + \partial_tg_1 \left(\frac{C_{J3}^{2} C_{g1}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - \frac{C_{J3} C_{g1} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right) + \partial_tg_2 \left(- \frac{C_{J3}^{2} C_{g2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \frac{C_{J3} C_{g2} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right) - i \partial_{ϕ_1} \left(\frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - \frac{C_{J3} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right) - i \partial_{ϕ_2} \left(- \frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \frac{C_{J3} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right)\right)}{2} + \frac{\partial_tg_1 \left(\frac{C_{J3} C_{g1} C_{g2} \partial_tg_2}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - \frac{i C_{J3} C_{g1} \partial_{ϕ_2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \frac{C_{g1}^{2} \partial_tg_1 \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - C_{g1} \partial_tf \left(- \frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \frac{C_{J3} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right) - \frac{i C_{g1} \partial_{ϕ_1} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right)}{2} + \frac{\partial_tg_2 \left(\frac{C_{J3} C_{g1} C_{g2} \partial_tg_1}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - \frac{i C_{J3} C_{g2} \partial_{ϕ_1}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \frac{C_{g2}^{2} \partial_tg_2 \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - C_{g2} \partial_tf \left(\frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - \frac{C_{J3} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right) - \frac{i C_{g2} \partial_{ϕ_2} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right)}{2} - \frac{i \partial_{ϕ_1} \left(\frac{C_{J3} C_{g2} \partial_tg_2}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - \frac{i C_{J3} \partial_{ϕ_2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \frac{C_{g1} \partial_tg_1 \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \partial_tf \left(\frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - \frac{C_{J3} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right) - \frac{i \partial_{ϕ_1} \left(C_{J2} + C_{J3} + C_{g2}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right)}{2} - \frac{i \partial_{ϕ_2} \left(\frac{C_{J3} C_{g1} \partial_tg_1}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} - \frac{i C_{J3} \partial_{ϕ_1}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \frac{C_{g2} \partial_tg_2 \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \partial_tf \left(- \frac{C_{J3}^{2}}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)} + \frac{C_{J3} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right) - \frac{i \partial_{ϕ_2} \left(C_{J1} + C_{J3} + C_{g1}\right)}{- C_{J3}^{2} + \left(C_{J1} + C_{J3} + C_{g1}\right) \left(C_{J2} + C_{J3} + C_{g2}\right)}\right)}{2}$ # Replacing symbolic circuit parameters with some numbers ```python RATIO = 60.0 ALPHA = 0.8 flux_qubit.find_element('J1').set_critical_current(1.0) flux_qubit.find_element('J2').set_critical_current(1.0) flux_qubit.find_element('J3').set_critical_current(1.0*ALPHA) flux_qubit.find_element('CJ1').set_capacitance(1/(8*1.0/RATIO)) flux_qubit.find_element('CJ2').set_capacitance(1/(8*1.0/RATIO)) flux_qubit.find_element('CJ3').set_capacitance(1/(8*1.0/RATIO/ALPHA)) flux_qubit.find_element('Cg1').set_capacitance(1/(8*50.0/RATIO)) flux_qubit.find_element('Cg2').set_capacitance(1/(8*50.0/RATIO)) ``` # Eigenvalues and eigensystem using scqubit tools ```python flux_qubit.plot_potential() ``` (<Figure size 750x750 with 2 Axes>, <matplotlib.axes._subplots.AxesSubplot at 0x23542ad3490>) ```python vals, vecs= flux_qubit.eigensys() ``` ```python vals #vecs_phase = np.conj(unitary).T@vecs vals - vals[0] ``` array([0. , 0.26299666, 0.29339598, 0.50146767, 0.55310417, 0.57154646]) # Eigenvalues using circuit tools ```python flux_qubit.calculate_potentials() vals, vecs = flux_qubit.diagonalize_phase(num_states=6) ``` ```python np.real(vals-vals[0]) ``` array([0. , 0.26299666, 0.29339598, 0.50146767, 0.55310417, 0.57154646]) ```python import matplotlib.pyplot as plt vecs = np.reshape(vecs, (21,21,6)) plt.pcolormesh(ϕ1.get_phase_grid(), ϕ2.get_phase_grid(), np.abs(vecs[:,:,0])**2) plt.colorbar() np.sum(np.abs(vecs[:,:,0])**2) ``` 1.0000000000000113 ```python ```
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abstract type JSONLD <: DataRepo end include("JSONLD_Web.jl") include("JSONLD_DOI.jl") data_fullname(::JSONLD, mainpage) = mainpage["name"] website(::JSONLD, mainpage_url, mainpage) = mainpage_url description(repo::JSONLD, mainpage) = filter_html(getfirst(mainpage, "description")) function author(repo::JSONLD, mainpage) inner(authors::Vector) = map(inner, authors) inner(::Missing) = missing inner(author::Dict) = getfirst(author, "name") authors = getfirst(mainpage, "author", "creator") |> inner if !(authors isa AbstractVector) # then there was just one return [authors] end authors end function published_date(repo::JSONLD, mainpage) rawdate = getfirst(mainpage, "datePublished", "dateCreated", "dateModified") # Dates can be like '2007' or '2016-12-20'. Need to account for all. try return Dates.format(Dates.DateTime(rawdate), "U d, yyyy") catch err if err isa MethodError || err isa ArgumentError # `MethodError` occurs if `rawdate==missing` # `ArgumentError` can occur if it is a weirdly formatted string # Either way, it is probably alright return rawdate else rethrow() end end end function license(::JSONLD, mainpage) license = getfirst(mainpage, "license") if license isa Dict license = getfirst(license, "url", "text") end filter_html(license) end function get_urls(repo::JSONLD, page) lift(getfirst(page, "distribution")) do url_list urls = collect(skipmissing(getfirst.(url_list, "contentUrl"))) end end
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl -/ import order.hom.basic import algebra.order.sub.defs import algebra.order.monoid.cancel.defs /-! # Ordered groups > THIS FILE IS SYNCHRONIZED WITH MATHLIB4. > Any changes to this file require a corresponding PR to mathlib4. This file develops the basics of ordered groups. ## Implementation details Unfortunately, the number of `'` appended to lemmas in this file may differ between the multiplicative and the additive version of a lemma. The reason is that we did not want to change existing names in the library. -/ set_option old_structure_cmd true open function universe u variable {α : Type u} /-- An ordered additive commutative group is an additive commutative group with a partial order in which addition is strictly monotone. -/ @[protect_proj, ancestor add_comm_group partial_order] class ordered_add_comm_group (α : Type u) extends add_comm_group α, partial_order α := (add_le_add_left : ∀ a b : α, a ≤ b → ∀ c : α, c + a ≤ c + b) /-- An ordered commutative group is an commutative group with a partial order in which multiplication is strictly monotone. -/ @[protect_proj, ancestor comm_group partial_order] class ordered_comm_group (α : Type u) extends comm_group α, partial_order α := (mul_le_mul_left : ∀ a b : α, a ≤ b → ∀ c : α, c * a ≤ c * b) attribute [to_additive] ordered_comm_group @[to_additive] instance ordered_comm_group.to_covariant_class_left_le (α : Type u) [ordered_comm_group α] : covariant_class α α (*) (≤) := { elim := λ a b c bc, ordered_comm_group.mul_le_mul_left b c bc a } @[priority 100, to_additive] -- See note [lower instance priority] instance ordered_comm_group.to_ordered_cancel_comm_monoid [ordered_comm_group α] : ordered_cancel_comm_monoid α := { le_of_mul_le_mul_left := λ a b c, le_of_mul_le_mul_left', ..‹ordered_comm_group α› } example (α : Type u) [ordered_add_comm_group α] : covariant_class α α (swap (+)) (<) := add_right_cancel_semigroup.covariant_swap_add_lt_of_covariant_swap_add_le α /-- A choice-free shortcut instance. -/ @[to_additive "A choice-free shortcut instance."] instance ordered_comm_group.to_contravariant_class_left_le (α : Type u) [ordered_comm_group α] : contravariant_class α α (*) (≤) := { elim := λ a b c bc, by simpa using mul_le_mul_left' bc a⁻¹, } /-- A choice-free shortcut instance. -/ @[to_additive "A choice-free shortcut instance."] instance ordered_comm_group.to_contravariant_class_right_le (α : Type u) [ordered_comm_group α] : contravariant_class α α (swap (*)) (≤) := { elim := λ a b c bc, by simpa using mul_le_mul_right' bc a⁻¹, } section group variables [group α] section typeclasses_left_le variables [has_le α] [covariant_class α α (*) (≤)] {a b c d : α} /-- Uses `left` co(ntra)variant. -/ @[simp, to_additive left.neg_nonpos_iff "Uses `left` co(ntra)variant."] lemma left.inv_le_one_iff : a⁻¹ ≤ 1 ↔ 1 ≤ a := by { rw [← mul_le_mul_iff_left a], simp } /-- Uses `left` co(ntra)variant. -/ @[simp, to_additive left.nonneg_neg_iff "Uses `left` co(ntra)variant."] lemma left.one_le_inv_iff : 1 ≤ a⁻¹ ↔ a ≤ 1 := by { rw [← mul_le_mul_iff_left a], simp } @[simp, to_additive] lemma le_inv_mul_iff_mul_le : b ≤ a⁻¹ * c ↔ a * b ≤ c := by { rw ← mul_le_mul_iff_left a, simp } @[simp, to_additive] lemma inv_mul_le_iff_le_mul : b⁻¹ * a ≤ c ↔ a ≤ b * c := by rw [← mul_le_mul_iff_left b, mul_inv_cancel_left] @[to_additive neg_le_iff_add_nonneg'] lemma inv_le_iff_one_le_mul' : a⁻¹ ≤ b ↔ 1 ≤ a * b := (mul_le_mul_iff_left a).symm.trans $ by rw mul_inv_self @[to_additive] lemma le_inv_iff_mul_le_one_left : a ≤ b⁻¹ ↔ b * a ≤ 1 := (mul_le_mul_iff_left b).symm.trans $ by rw mul_inv_self @[to_additive] lemma le_inv_mul_iff_le : 1 ≤ b⁻¹ * a ↔ b ≤ a := by rw [← mul_le_mul_iff_left b, mul_one, mul_inv_cancel_left] @[to_additive] lemma inv_mul_le_one_iff : a⁻¹ * b ≤ 1 ↔ b ≤ a := trans (inv_mul_le_iff_le_mul) $ by rw mul_one end typeclasses_left_le section typeclasses_left_lt variables [has_lt α] [covariant_class α α (*) (<)] {a b c : α} /-- Uses `left` co(ntra)variant. -/ @[simp, to_additive left.neg_pos_iff "Uses `left` co(ntra)variant."] lemma left.one_lt_inv_iff : 1 < a⁻¹ ↔ a < 1 := by rw [← mul_lt_mul_iff_left a, mul_inv_self, mul_one] /-- Uses `left` co(ntra)variant. -/ @[simp, to_additive left.neg_neg_iff "Uses `left` co(ntra)variant."] lemma left.inv_lt_one_iff : a⁻¹ < 1 ↔ 1 < a := by rw [← mul_lt_mul_iff_left a, mul_inv_self, mul_one] @[simp, to_additive] lemma lt_inv_mul_iff_mul_lt : b < a⁻¹ * c ↔ a * b < c := by { rw [← mul_lt_mul_iff_left a], simp } @[simp, to_additive] lemma inv_mul_lt_iff_lt_mul : b⁻¹ * a < c ↔ a < b * c := by rw [← mul_lt_mul_iff_left b, mul_inv_cancel_left] @[to_additive] lemma inv_lt_iff_one_lt_mul' : a⁻¹ < b ↔ 1 < a * b := (mul_lt_mul_iff_left a).symm.trans $ by rw mul_inv_self @[to_additive] lemma lt_inv_iff_mul_lt_one' : a < b⁻¹ ↔ b * a < 1 := (mul_lt_mul_iff_left b).symm.trans $ by rw mul_inv_self @[to_additive] lemma lt_inv_mul_iff_lt : 1 < b⁻¹ * a ↔ b < a := by rw [← mul_lt_mul_iff_left b, mul_one, mul_inv_cancel_left] @[to_additive] lemma inv_mul_lt_one_iff : a⁻¹ * b < 1 ↔ b < a := trans (inv_mul_lt_iff_lt_mul) $ by rw mul_one end typeclasses_left_lt section typeclasses_right_le variables [has_le α] [covariant_class α α (swap (*)) (≤)] {a b c : α} /-- Uses `right` co(ntra)variant. -/ @[simp, to_additive right.neg_nonpos_iff "Uses `right` co(ntra)variant."] lemma right.inv_le_one_iff : a⁻¹ ≤ 1 ↔ 1 ≤ a := by { rw [← mul_le_mul_iff_right a], simp } /-- Uses `right` co(ntra)variant. -/ @[simp, to_additive right.nonneg_neg_iff "Uses `right` co(ntra)variant."] lemma right.one_le_inv_iff : 1 ≤ a⁻¹ ↔ a ≤ 1 := by { rw [← mul_le_mul_iff_right a], simp } @[to_additive neg_le_iff_add_nonneg] lemma inv_le_iff_one_le_mul : a⁻¹ ≤ b ↔ 1 ≤ b * a := (mul_le_mul_iff_right a).symm.trans $ by rw inv_mul_self @[to_additive] lemma le_inv_iff_mul_le_one_right : a ≤ b⁻¹ ↔ a * b ≤ 1 := (mul_le_mul_iff_right b).symm.trans $ by rw inv_mul_self @[simp, to_additive] lemma mul_inv_le_iff_le_mul : a * b⁻¹ ≤ c ↔ a ≤ c * b := (mul_le_mul_iff_right b).symm.trans $ by rw inv_mul_cancel_right @[simp, to_additive] lemma le_mul_inv_iff_mul_le : c ≤ a * b⁻¹ ↔ c * b ≤ a := (mul_le_mul_iff_right b).symm.trans $ by rw inv_mul_cancel_right @[simp, to_additive] lemma mul_inv_le_one_iff_le : a * b⁻¹ ≤ 1 ↔ a ≤ b := mul_inv_le_iff_le_mul.trans $ by rw one_mul @[to_additive] lemma le_mul_inv_iff_le : 1 ≤ a * b⁻¹ ↔ b ≤ a := by rw [← mul_le_mul_iff_right b, one_mul, inv_mul_cancel_right] @[to_additive] lemma mul_inv_le_one_iff : b * a⁻¹ ≤ 1 ↔ b ≤ a := trans (mul_inv_le_iff_le_mul) $ by rw one_mul end typeclasses_right_le section typeclasses_right_lt variables [has_lt α] [covariant_class α α (swap (*)) (<)] {a b c : α} /-- Uses `right` co(ntra)variant. -/ @[simp, to_additive right.neg_neg_iff "Uses `right` co(ntra)variant."] lemma right.inv_lt_one_iff : a⁻¹ < 1 ↔ 1 < a := by rw [← mul_lt_mul_iff_right a, inv_mul_self, one_mul] /-- Uses `right` co(ntra)variant. -/ @[simp, to_additive right.neg_pos_iff "Uses `right` co(ntra)variant."] lemma right.one_lt_inv_iff : 1 < a⁻¹ ↔ a < 1 := by rw [← mul_lt_mul_iff_right a, inv_mul_self, one_mul] @[to_additive] lemma inv_lt_iff_one_lt_mul : a⁻¹ < b ↔ 1 < b * a := (mul_lt_mul_iff_right a).symm.trans $ by rw inv_mul_self @[to_additive] lemma lt_inv_iff_mul_lt_one : a < b⁻¹ ↔ a * b < 1 := (mul_lt_mul_iff_right b).symm.trans $ by rw inv_mul_self @[simp, to_additive] lemma mul_inv_lt_iff_lt_mul : a * b⁻¹ < c ↔ a < c * b := by rw [← mul_lt_mul_iff_right b, inv_mul_cancel_right] @[simp, to_additive] lemma lt_mul_inv_iff_mul_lt : c < a * b⁻¹ ↔ c * b < a := (mul_lt_mul_iff_right b).symm.trans $ by rw inv_mul_cancel_right @[simp, to_additive] lemma inv_mul_lt_one_iff_lt : a * b⁻¹ < 1 ↔ a < b := by rw [← mul_lt_mul_iff_right b, inv_mul_cancel_right, one_mul] @[to_additive] lemma lt_mul_inv_iff_lt : 1 < a * b⁻¹ ↔ b < a := by rw [← mul_lt_mul_iff_right b, one_mul, inv_mul_cancel_right] @[to_additive] lemma mul_inv_lt_one_iff : b * a⁻¹ < 1 ↔ b < a := trans (mul_inv_lt_iff_lt_mul) $ by rw one_mul end typeclasses_right_lt section typeclasses_left_right_le variables [has_le α] [covariant_class α α (*) (≤)] [covariant_class α α (swap (*)) (≤)] {a b c d : α} @[simp, to_additive] lemma inv_le_inv_iff : a⁻¹ ≤ b⁻¹ ↔ b ≤ a := by { rw [← mul_le_mul_iff_left a, ← mul_le_mul_iff_right b], simp } alias neg_le_neg_iff ↔ le_of_neg_le_neg _ @[to_additive] lemma mul_inv_le_inv_mul_iff : a * b⁻¹ ≤ d⁻¹ * c ↔ d * a ≤ c * b := by rw [← mul_le_mul_iff_left d, ← mul_le_mul_iff_right b, mul_inv_cancel_left, mul_assoc, inv_mul_cancel_right] @[simp, to_additive] lemma div_le_self_iff (a : α) {b : α} : a / b ≤ a ↔ 1 ≤ b := by simp [div_eq_mul_inv] @[simp, to_additive] lemma le_div_self_iff (a : α) {b : α} : a ≤ a / b ↔ b ≤ 1 := by simp [div_eq_mul_inv] alias sub_le_self_iff ↔ _ sub_le_self end typeclasses_left_right_le section typeclasses_left_right_lt variables [has_lt α] [covariant_class α α (*) (<)] [covariant_class α α (swap (*)) (<)] {a b c d : α} @[simp, to_additive] lemma inv_lt_inv_iff : a⁻¹ < b⁻¹ ↔ b < a := by { rw [← mul_lt_mul_iff_left a, ← mul_lt_mul_iff_right b], simp } @[to_additive neg_lt] lemma inv_lt' : a⁻¹ < b ↔ b⁻¹ < a := by rw [← inv_lt_inv_iff, inv_inv] @[to_additive lt_neg] lemma lt_inv' : a < b⁻¹ ↔ b < a⁻¹ := by rw [← inv_lt_inv_iff, inv_inv] alias lt_inv' ↔ lt_inv_of_lt_inv _ attribute [to_additive] lt_inv_of_lt_inv alias inv_lt' ↔ inv_lt_of_inv_lt' _ attribute [to_additive neg_lt_of_neg_lt] inv_lt_of_inv_lt' @[to_additive] lemma mul_inv_lt_inv_mul_iff : a * b⁻¹ < d⁻¹ * c ↔ d * a < c * b := by rw [← mul_lt_mul_iff_left d, ← mul_lt_mul_iff_right b, mul_inv_cancel_left, mul_assoc, inv_mul_cancel_right] @[simp, to_additive] lemma div_lt_self_iff (a : α) {b : α} : a / b < a ↔ 1 < b := by simp [div_eq_mul_inv] alias sub_lt_self_iff ↔ _ sub_lt_self end typeclasses_left_right_lt section pre_order variable [preorder α] section left_le variables [covariant_class α α (*) (≤)] {a : α} @[to_additive] lemma left.inv_le_self (h : 1 ≤ a) : a⁻¹ ≤ a := le_trans (left.inv_le_one_iff.mpr h) h alias left.neg_le_self ← neg_le_self @[to_additive] lemma left.self_le_inv (h : a ≤ 1) : a ≤ a⁻¹ := le_trans h (left.one_le_inv_iff.mpr h) end left_le section left_lt variables [covariant_class α α (*) (<)] {a : α} @[to_additive] lemma left.inv_lt_self (h : 1 < a) : a⁻¹ < a := (left.inv_lt_one_iff.mpr h).trans h alias left.neg_lt_self ← neg_lt_self @[to_additive] lemma left.self_lt_inv (h : a < 1) : a < a⁻¹ := lt_trans h (left.one_lt_inv_iff.mpr h) end left_lt section right_le variables [covariant_class α α (swap (*)) (≤)] {a : α} @[to_additive] lemma right.inv_le_self (h : 1 ≤ a) : a⁻¹ ≤ a := le_trans (right.inv_le_one_iff.mpr h) h @[to_additive] lemma right.self_le_inv (h : a ≤ 1) : a ≤ a⁻¹ := le_trans h (right.one_le_inv_iff.mpr h) end right_le section right_lt variables [covariant_class α α (swap (*)) (<)] {a : α} @[to_additive] lemma right.inv_lt_self (h : 1 < a) : a⁻¹ < a := (right.inv_lt_one_iff.mpr h).trans h @[to_additive] lemma right.self_lt_inv (h : a < 1) : a < a⁻¹ := lt_trans h (right.one_lt_inv_iff.mpr h) end right_lt end pre_order end group section comm_group variables [comm_group α] section has_le variables [has_le α] [covariant_class α α (*) (≤)] {a b c d : α} @[to_additive] lemma inv_mul_le_iff_le_mul' : c⁻¹ * a ≤ b ↔ a ≤ b * c := by rw [inv_mul_le_iff_le_mul, mul_comm] @[simp, to_additive] lemma mul_inv_le_iff_le_mul' : a * b⁻¹ ≤ c ↔ a ≤ b * c := by rw [← inv_mul_le_iff_le_mul, mul_comm] @[to_additive add_neg_le_add_neg_iff] lemma mul_inv_le_mul_inv_iff' : a * b⁻¹ ≤ c * d⁻¹ ↔ a * d ≤ c * b := by rw [mul_comm c, mul_inv_le_inv_mul_iff, mul_comm] end has_le section has_lt variables [has_lt α] [covariant_class α α (*) (<)] {a b c d : α} @[to_additive] lemma inv_mul_lt_iff_lt_mul' : c⁻¹ * a < b ↔ a < b * c := by rw [inv_mul_lt_iff_lt_mul, mul_comm] @[simp, to_additive] lemma mul_inv_lt_iff_le_mul' : a * b⁻¹ < c ↔ a < b * c := by rw [← inv_mul_lt_iff_lt_mul, mul_comm] @[to_additive add_neg_lt_add_neg_iff] lemma mul_inv_lt_mul_inv_iff' : a * b⁻¹ < c * d⁻¹ ↔ a * d < c * b := by rw [mul_comm c, mul_inv_lt_inv_mul_iff, mul_comm] end has_lt end comm_group alias left.inv_le_one_iff ↔ one_le_of_inv_le_one _ attribute [to_additive] one_le_of_inv_le_one alias left.one_le_inv_iff ↔ le_one_of_one_le_inv _ attribute [to_additive nonpos_of_neg_nonneg] le_one_of_one_le_inv alias inv_lt_inv_iff ↔ lt_of_inv_lt_inv _ attribute [to_additive] lt_of_inv_lt_inv alias left.inv_lt_one_iff ↔ one_lt_of_inv_lt_one _ attribute [to_additive] one_lt_of_inv_lt_one alias left.inv_lt_one_iff ← inv_lt_one_iff_one_lt attribute [to_additive] inv_lt_one_iff_one_lt alias left.inv_lt_one_iff ← inv_lt_one' attribute [to_additive neg_lt_zero] inv_lt_one' alias left.one_lt_inv_iff ↔ inv_of_one_lt_inv _ attribute [to_additive neg_of_neg_pos] inv_of_one_lt_inv alias left.one_lt_inv_iff ↔ _ one_lt_inv_of_inv attribute [to_additive neg_pos_of_neg] one_lt_inv_of_inv alias le_inv_mul_iff_mul_le ↔ mul_le_of_le_inv_mul _ attribute [to_additive] mul_le_of_le_inv_mul alias le_inv_mul_iff_mul_le ↔ _ le_inv_mul_of_mul_le attribute [to_additive] le_inv_mul_of_mul_le alias inv_mul_le_iff_le_mul ↔ _ inv_mul_le_of_le_mul attribute [to_additive] inv_mul_le_iff_le_mul alias lt_inv_mul_iff_mul_lt ↔ mul_lt_of_lt_inv_mul _ attribute [to_additive] mul_lt_of_lt_inv_mul alias lt_inv_mul_iff_mul_lt ↔ _ lt_inv_mul_of_mul_lt attribute [to_additive] lt_inv_mul_of_mul_lt alias inv_mul_lt_iff_lt_mul ↔ lt_mul_of_inv_mul_lt inv_mul_lt_of_lt_mul attribute [to_additive] lt_mul_of_inv_mul_lt attribute [to_additive] inv_mul_lt_of_lt_mul alias lt_mul_of_inv_mul_lt ← lt_mul_of_inv_mul_lt_left attribute [to_additive] lt_mul_of_inv_mul_lt_left alias left.inv_le_one_iff ← inv_le_one' attribute [to_additive neg_nonpos] inv_le_one' alias left.one_le_inv_iff ← one_le_inv' attribute [to_additive neg_nonneg] one_le_inv' alias left.one_lt_inv_iff ← one_lt_inv' attribute [to_additive neg_pos] one_lt_inv' alias mul_lt_mul_left' ← ordered_comm_group.mul_lt_mul_left' attribute [to_additive ordered_add_comm_group.add_lt_add_left] ordered_comm_group.mul_lt_mul_left' alias le_of_mul_le_mul_left' ← ordered_comm_group.le_of_mul_le_mul_left attribute [to_additive ordered_add_comm_group.le_of_add_le_add_left] ordered_comm_group.le_of_mul_le_mul_left alias lt_of_mul_lt_mul_left' ← ordered_comm_group.lt_of_mul_lt_mul_left attribute [to_additive ordered_add_comm_group.lt_of_add_lt_add_left] ordered_comm_group.lt_of_mul_lt_mul_left /- Most of the lemmas that are primed in this section appear in ordered_field. -/ /- I (DT) did not try to minimise the assumptions. -/ section group variables [group α] [has_le α] section right variables [covariant_class α α (swap (*)) (≤)] {a b c d : α} @[simp, to_additive] lemma div_le_div_iff_right (c : α) : a / c ≤ b / c ↔ a ≤ b := by simpa only [div_eq_mul_inv] using mul_le_mul_iff_right _ @[to_additive sub_le_sub_right] lemma div_le_div_right' (h : a ≤ b) (c : α) : a / c ≤ b / c := (div_le_div_iff_right c).2 h @[simp, to_additive sub_nonneg] lemma one_le_div' : 1 ≤ a / b ↔ b ≤ a := by rw [← mul_le_mul_iff_right b, one_mul, div_eq_mul_inv, inv_mul_cancel_right] alias sub_nonneg ↔ le_of_sub_nonneg sub_nonneg_of_le @[simp, to_additive sub_nonpos] lemma div_le_one' : a / b ≤ 1 ↔ a ≤ b := by rw [← mul_le_mul_iff_right b, one_mul, div_eq_mul_inv, inv_mul_cancel_right] alias sub_nonpos ↔ le_of_sub_nonpos sub_nonpos_of_le @[to_additive] lemma le_div_iff_mul_le : a ≤ c / b ↔ a * b ≤ c := by rw [← mul_le_mul_iff_right b, div_eq_mul_inv, inv_mul_cancel_right] alias le_sub_iff_add_le ↔ add_le_of_le_sub_right le_sub_right_of_add_le @[to_additive] lemma div_le_iff_le_mul : a / c ≤ b ↔ a ≤ b * c := by rw [← mul_le_mul_iff_right c, div_eq_mul_inv, inv_mul_cancel_right] -- TODO: Should we get rid of `sub_le_iff_le_add` in favor of -- (a renamed version of) `tsub_le_iff_right`? @[priority 100] -- see Note [lower instance priority] instance add_group.to_has_ordered_sub {α : Type*} [add_group α] [has_le α] [covariant_class α α (swap (+)) (≤)] : has_ordered_sub α := ⟨λ a b c, sub_le_iff_le_add⟩ end right section left variables [covariant_class α α (*) (≤)] variables [covariant_class α α (swap (*)) (≤)] {a b c : α} @[simp, to_additive] lemma div_le_div_iff_left (a : α) : a / b ≤ a / c ↔ c ≤ b := by rw [div_eq_mul_inv, div_eq_mul_inv, ← mul_le_mul_iff_left a⁻¹, inv_mul_cancel_left, inv_mul_cancel_left, inv_le_inv_iff] @[to_additive sub_le_sub_left] lemma div_le_div_left' (h : a ≤ b) (c : α) : c / b ≤ c / a := (div_le_div_iff_left c).2 h end left end group section comm_group variables [comm_group α] section has_le variables [has_le α] [covariant_class α α (*) (≤)] {a b c d : α} @[to_additive sub_le_sub_iff] lemma div_le_div_iff' : a / b ≤ c / d ↔ a * d ≤ c * b := by simpa only [div_eq_mul_inv] using mul_inv_le_mul_inv_iff' @[to_additive] lemma le_div_iff_mul_le' : b ≤ c / a ↔ a * b ≤ c := by rw [le_div_iff_mul_le, mul_comm] alias le_sub_iff_add_le' ↔ add_le_of_le_sub_left le_sub_left_of_add_le @[to_additive] lemma div_le_iff_le_mul' : a / b ≤ c ↔ a ≤ b * c := by rw [div_le_iff_le_mul, mul_comm] alias sub_le_iff_le_add' ↔ le_add_of_sub_left_le sub_left_le_of_le_add @[simp, to_additive] lemma inv_le_div_iff_le_mul : b⁻¹ ≤ a / c ↔ c ≤ a * b := le_div_iff_mul_le.trans inv_mul_le_iff_le_mul' @[to_additive] lemma inv_le_div_iff_le_mul' : a⁻¹ ≤ b / c ↔ c ≤ a * b := by rw [inv_le_div_iff_le_mul, mul_comm] @[to_additive] lemma div_le_comm : a / b ≤ c ↔ a / c ≤ b := div_le_iff_le_mul'.trans div_le_iff_le_mul.symm @[to_additive] lemma le_div_comm : a ≤ b / c ↔ c ≤ b / a := le_div_iff_mul_le'.trans le_div_iff_mul_le.symm end has_le section preorder variables [preorder α] [covariant_class α α (*) (≤)] {a b c d : α} @[to_additive sub_le_sub] lemma div_le_div'' (hab : a ≤ b) (hcd : c ≤ d) : a / d ≤ b / c := begin rw [div_eq_mul_inv, div_eq_mul_inv, mul_comm b, mul_inv_le_inv_mul_iff, mul_comm], exact mul_le_mul' hab hcd end end preorder end comm_group /- Most of the lemmas that are primed in this section appear in ordered_field. -/ /- I (DT) did not try to minimise the assumptions. -/ section group variables [group α] [has_lt α] section right variables [covariant_class α α (swap (*)) (<)] {a b c d : α} @[simp, to_additive] lemma div_lt_div_iff_right (c : α) : a / c < b / c ↔ a < b := by simpa only [div_eq_mul_inv] using mul_lt_mul_iff_right _ @[to_additive sub_lt_sub_right] lemma div_lt_div_right' (h : a < b) (c : α) : a / c < b / c := (div_lt_div_iff_right c).2 h @[simp, to_additive sub_pos] lemma one_lt_div' : 1 < a / b ↔ b < a := by rw [← mul_lt_mul_iff_right b, one_mul, div_eq_mul_inv, inv_mul_cancel_right] alias sub_pos ↔ lt_of_sub_pos sub_pos_of_lt @[simp, to_additive sub_neg] lemma div_lt_one' : a / b < 1 ↔ a < b := by rw [← mul_lt_mul_iff_right b, one_mul, div_eq_mul_inv, inv_mul_cancel_right] alias sub_neg ↔ lt_of_sub_neg sub_neg_of_lt alias sub_neg ← sub_lt_zero @[to_additive] lemma lt_div_iff_mul_lt : a < c / b ↔ a * b < c := by rw [← mul_lt_mul_iff_right b, div_eq_mul_inv, inv_mul_cancel_right] alias lt_sub_iff_add_lt ↔ add_lt_of_lt_sub_right lt_sub_right_of_add_lt @[to_additive] lemma div_lt_iff_lt_mul : a / c < b ↔ a < b * c := by rw [← mul_lt_mul_iff_right c, div_eq_mul_inv, inv_mul_cancel_right] alias sub_lt_iff_lt_add ↔ lt_add_of_sub_right_lt sub_right_lt_of_lt_add end right section left variables [covariant_class α α (*) (<)] [covariant_class α α (swap (*)) (<)] {a b c : α} @[simp, to_additive] lemma div_lt_div_iff_left (a : α) : a / b < a / c ↔ c < b := by rw [div_eq_mul_inv, div_eq_mul_inv, ← mul_lt_mul_iff_left a⁻¹, inv_mul_cancel_left, inv_mul_cancel_left, inv_lt_inv_iff] @[simp, to_additive] lemma inv_lt_div_iff_lt_mul : a⁻¹ < b / c ↔ c < a * b := by rw [div_eq_mul_inv, lt_mul_inv_iff_mul_lt, inv_mul_lt_iff_lt_mul] @[to_additive sub_lt_sub_left] lemma div_lt_div_left' (h : a < b) (c : α) : c / b < c / a := (div_lt_div_iff_left c).2 h end left end group section comm_group variables [comm_group α] section has_lt variables [has_lt α] [covariant_class α α (*) (<)] {a b c d : α} @[to_additive sub_lt_sub_iff] lemma div_lt_div_iff' : a / b < c / d ↔ a * d < c * b := by simpa only [div_eq_mul_inv] using mul_inv_lt_mul_inv_iff' @[to_additive] lemma lt_div_iff_mul_lt' : b < c / a ↔ a * b < c := by rw [lt_div_iff_mul_lt, mul_comm] alias lt_sub_iff_add_lt' ↔ add_lt_of_lt_sub_left lt_sub_left_of_add_lt @[to_additive] lemma div_lt_iff_lt_mul' : a / b < c ↔ a < b * c := by rw [div_lt_iff_lt_mul, mul_comm] alias sub_lt_iff_lt_add' ↔ lt_add_of_sub_left_lt sub_left_lt_of_lt_add @[to_additive] lemma inv_lt_div_iff_lt_mul' : b⁻¹ < a / c ↔ c < a * b := lt_div_iff_mul_lt.trans inv_mul_lt_iff_lt_mul' @[to_additive] lemma div_lt_comm : a / b < c ↔ a / c < b := div_lt_iff_lt_mul'.trans div_lt_iff_lt_mul.symm @[to_additive] lemma lt_div_comm : a < b / c ↔ c < b / a := lt_div_iff_mul_lt'.trans lt_div_iff_mul_lt.symm end has_lt section preorder variables [preorder α] [covariant_class α α (*) (<)] {a b c d : α} @[to_additive sub_lt_sub] lemma div_lt_div'' (hab : a < b) (hcd : c < d) : a / d < b / c := begin rw [div_eq_mul_inv, div_eq_mul_inv, mul_comm b, mul_inv_lt_inv_mul_iff, mul_comm], exact mul_lt_mul_of_lt_of_lt hab hcd end end preorder end comm_group section linear_order variables [group α] [linear_order α] @[simp, to_additive cmp_sub_zero] lemma cmp_div_one' [covariant_class α α (swap (*)) (≤)] (a b : α) : cmp (a / b) 1 = cmp a b := by rw [← cmp_mul_right' _ _ b, one_mul, div_mul_cancel'] variables [covariant_class α α (*) (≤)] section variable_names variables {a b c : α} @[to_additive] lemma le_of_forall_one_lt_lt_mul (h : ∀ ε : α, 1 < ε → a < b * ε) : a ≤ b := le_of_not_lt (λ h₁, lt_irrefl a (by simpa using (h _ (lt_inv_mul_iff_lt.mpr h₁)))) @[to_additive] lemma le_iff_forall_one_lt_lt_mul : a ≤ b ↔ ∀ ε, 1 < ε → a < b * ε := ⟨λ h ε, lt_mul_of_le_of_one_lt h, le_of_forall_one_lt_lt_mul⟩ /- I (DT) introduced this lemma to prove (the additive version `sub_le_sub_flip` of) `div_le_div_flip` below. Now I wonder what is the point of either of these lemmas... -/ @[to_additive] lemma div_le_inv_mul_iff [covariant_class α α (swap (*)) (≤)] : a / b ≤ a⁻¹ * b ↔ a ≤ b := begin rw [div_eq_mul_inv, mul_inv_le_inv_mul_iff], exact ⟨λ h, not_lt.mp (λ k, not_lt.mpr h (mul_lt_mul_of_lt_of_lt k k)), λ h, mul_le_mul' h h⟩, end /- What is the point of this lemma? See comment about `div_le_inv_mul_iff` above. -/ @[simp, to_additive] lemma div_le_div_flip {α : Type*} [comm_group α] [linear_order α] [covariant_class α α (*) (≤)] {a b : α}: a / b ≤ b / a ↔ a ≤ b := begin rw [div_eq_mul_inv b, mul_comm], exact div_le_inv_mul_iff, end end variable_names end linear_order /-! ### Linearly ordered commutative groups -/ /-- A linearly ordered additive commutative group is an additive commutative group with a linear order in which addition is monotone. -/ @[protect_proj, ancestor ordered_add_comm_group linear_order] class linear_ordered_add_comm_group (α : Type u) extends ordered_add_comm_group α, linear_order α /-- A linearly ordered commutative monoid with an additively absorbing `⊤` element. Instances should include number systems with an infinite element adjoined.` -/ @[protect_proj, ancestor linear_ordered_add_comm_monoid_with_top sub_neg_monoid nontrivial] class linear_ordered_add_comm_group_with_top (α : Type*) extends linear_ordered_add_comm_monoid_with_top α, sub_neg_monoid α, nontrivial α := (neg_top : - (⊤ : α) = ⊤) (add_neg_cancel : ∀ a:α, a ≠ ⊤ → a + (- a) = 0) /-- A linearly ordered commutative group is a commutative group with a linear order in which multiplication is monotone. -/ @[protect_proj, ancestor ordered_comm_group linear_order, to_additive] class linear_ordered_comm_group (α : Type u) extends ordered_comm_group α, linear_order α section linear_ordered_comm_group variables [linear_ordered_comm_group α] {a b c : α} @[to_additive linear_ordered_add_comm_group.add_lt_add_left] lemma linear_ordered_comm_group.mul_lt_mul_left' (a b : α) (h : a < b) (c : α) : c * a < c * b := mul_lt_mul_left' h c @[to_additive eq_zero_of_neg_eq] lemma eq_one_of_inv_eq' (h : a⁻¹ = a) : a = 1 := match lt_trichotomy a 1 with | or.inl h₁ := have 1 < a, from h ▸ one_lt_inv_of_inv h₁, absurd h₁ this.asymm | or.inr (or.inl h₁) := h₁ | or.inr (or.inr h₁) := have a < 1, from h ▸ inv_lt_one'.mpr h₁, absurd h₁ this.asymm end @[to_additive exists_zero_lt] lemma exists_one_lt' [nontrivial α] : ∃ (a:α), 1 < a := begin obtain ⟨y, hy⟩ := decidable.exists_ne (1 : α), cases hy.lt_or_lt, { exact ⟨y⁻¹, one_lt_inv'.mpr h⟩ }, { exact ⟨y, h⟩ } end @[priority 100, to_additive] -- see Note [lower instance priority] instance linear_ordered_comm_group.to_no_max_order [nontrivial α] : no_max_order α := ⟨ begin obtain ⟨y, hy⟩ : ∃ (a:α), 1 < a := exists_one_lt', exact λ a, ⟨a * y, lt_mul_of_one_lt_right' a hy⟩ end ⟩ @[priority 100, to_additive] -- see Note [lower instance priority] instance linear_ordered_comm_group.to_no_min_order [nontrivial α] : no_min_order α := ⟨ begin obtain ⟨y, hy⟩ : ∃ (a:α), 1 < a := exists_one_lt', exact λ a, ⟨a / y, (div_lt_self_iff a).mpr hy⟩ end ⟩ @[priority 100, to_additive] -- See note [lower instance priority] instance linear_ordered_comm_group.to_linear_ordered_cancel_comm_monoid : linear_ordered_cancel_comm_monoid α := { ..‹linear_ordered_comm_group α›, ..ordered_comm_group.to_ordered_cancel_comm_monoid } end linear_ordered_comm_group namespace add_comm_group /-- A collection of elements in an `add_comm_group` designated as "non-negative". This is useful for constructing an `ordered_add_commm_group` by choosing a positive cone in an exisiting `add_comm_group`. -/ @[nolint has_nonempty_instance] structure positive_cone (α : Type*) [add_comm_group α] := (nonneg : α → Prop) (pos : α → Prop := λ a, nonneg a ∧ ¬ nonneg (-a)) (pos_iff : ∀ a, pos a ↔ nonneg a ∧ ¬ nonneg (-a) . order_laws_tac) (zero_nonneg : nonneg 0) (add_nonneg : ∀ {a b}, nonneg a → nonneg b → nonneg (a + b)) (nonneg_antisymm : ∀ {a}, nonneg a → nonneg (-a) → a = 0) /-- A positive cone in an `add_comm_group` induces a linear order if for every `a`, either `a` or `-a` is non-negative. -/ @[nolint has_nonempty_instance] structure total_positive_cone (α : Type*) [add_comm_group α] extends positive_cone α := (nonneg_decidable : decidable_pred nonneg) (nonneg_total : ∀ a : α, nonneg a ∨ nonneg (-a)) /-- Forget that a `total_positive_cone` is total. -/ add_decl_doc total_positive_cone.to_positive_cone end add_comm_group namespace ordered_add_comm_group open add_comm_group /-- Construct an `ordered_add_comm_group` by designating a positive cone in an existing `add_comm_group`. -/ def mk_of_positive_cone {α : Type*} [add_comm_group α] (C : positive_cone α) : ordered_add_comm_group α := { le := λ a b, C.nonneg (b - a), lt := λ a b, C.pos (b - a), lt_iff_le_not_le := λ a b, by simp; rw [C.pos_iff]; simp, le_refl := λ a, by simp [C.zero_nonneg], le_trans := λ a b c nab nbc, by simp [-sub_eq_add_neg]; rw ← sub_add_sub_cancel; exact C.add_nonneg nbc nab, le_antisymm := λ a b nab nba, eq_of_sub_eq_zero $ C.nonneg_antisymm nba (by rw neg_sub; exact nab), add_le_add_left := λ a b nab c, by simpa [(≤), preorder.le] using nab, ..‹add_comm_group α› } end ordered_add_comm_group namespace linear_ordered_add_comm_group open add_comm_group /-- Construct a `linear_ordered_add_comm_group` by designating a positive cone in an existing `add_comm_group` such that for every `a`, either `a` or `-a` is non-negative. -/ def mk_of_positive_cone {α : Type*} [add_comm_group α] (C : total_positive_cone α) : linear_ordered_add_comm_group α := { le_total := λ a b, by { convert C.nonneg_total (b - a), change C.nonneg _ = _, congr, simp, }, decidable_le := λ a b, C.nonneg_decidable _, ..ordered_add_comm_group.mk_of_positive_cone C.to_positive_cone } end linear_ordered_add_comm_group section norm_num_lemmas /- The following lemmas are stated so that the `norm_num` tactic can use them with the expected signatures. -/ variables [ordered_comm_group α] {a b : α} @[to_additive neg_le_neg] lemma inv_le_inv' : a ≤ b → b⁻¹ ≤ a⁻¹ := inv_le_inv_iff.mpr @[to_additive neg_lt_neg] lemma inv_lt_inv' : a < b → b⁻¹ < a⁻¹ := inv_lt_inv_iff.mpr /- The additive version is also a `linarith` lemma. -/ @[to_additive] theorem inv_lt_one_of_one_lt : 1 < a → a⁻¹ < 1 := inv_lt_one_iff_one_lt.mpr /- The additive version is also a `linarith` lemma. -/ @[to_additive] lemma inv_le_one_of_one_le : 1 ≤ a → a⁻¹ ≤ 1 := inv_le_one'.mpr @[to_additive neg_nonneg_of_nonpos] lemma one_le_inv_of_le_one : a ≤ 1 → 1 ≤ a⁻¹ := one_le_inv'.mpr end norm_num_lemmas section variables {β : Type*} [group α] [preorder α] [covariant_class α α (*) (≤)] [covariant_class α α (swap (*)) (≤)] [preorder β] {f : β → α} {s : set β} @[to_additive] lemma monotone.inv (hf : monotone f) : antitone (λ x, (f x)⁻¹) := λ x y hxy, inv_le_inv_iff.2 (hf hxy) @[to_additive] lemma antitone.inv (hf : antitone f) : monotone (λ x, (f x)⁻¹) := λ x y hxy, inv_le_inv_iff.2 (hf hxy) @[to_additive] lemma monotone_on.inv (hf : monotone_on f s) : antitone_on (λ x, (f x)⁻¹) s := λ x hx y hy hxy, inv_le_inv_iff.2 (hf hx hy hxy) @[to_additive] lemma antitone_on.inv (hf : antitone_on f s) : monotone_on (λ x, (f x)⁻¹) s := λ x hx y hy hxy, inv_le_inv_iff.2 (hf hx hy hxy) end section variables {β : Type*} [group α] [preorder α] [covariant_class α α (*) (<)] [covariant_class α α (swap (*)) (<)] [preorder β] {f : β → α} {s : set β} @[to_additive] lemma strict_mono.inv (hf : strict_mono f) : strict_anti (λ x, (f x)⁻¹) := λ x y hxy, inv_lt_inv_iff.2 (hf hxy) @[to_additive] lemma strict_anti.inv (hf : strict_anti f) : strict_mono (λ x, (f x)⁻¹) := λ x y hxy, inv_lt_inv_iff.2 (hf hxy) @[to_additive] lemma strict_mono_on.inv (hf : strict_mono_on f s) : strict_anti_on (λ x, (f x)⁻¹) s := λ x hx y hy hxy, inv_lt_inv_iff.2 (hf hx hy hxy) @[to_additive] lemma strict_anti_on.inv (hf : strict_anti_on f s) : strict_mono_on (λ x, (f x)⁻¹) s := λ x hx y hy hxy, inv_lt_inv_iff.2 (hf hx hy hxy) end
% This is a test file to cofirm if Conceal features are enabled and work well. % This file does not aim at checking TeX-compilability. % <DO NOT TRY TO COMPILE THIS FILE!> % Edited by N-yam-my, Dec 7 2021. \documentclass{standalone} \begin{document} % Symbols \[ \alpha, \Omega, \nabla, \emptyset, \Re, \Rightarrow, \to, \mapsto, \P, \S, \aleph, \amalg, \angle, \approx, \cup, \bigcup, \circ, \odot, \bigsqcup, \bot, \bullet, \cdots, \exists, \mp, \parallel, \because, \geq, \hslash, \nparallel, \Uppsi \] % Big Operators \[ \int, \iint, \iiint, \oint, \sum, \prod, \] % Mathfonts \[ \mathbb{1}, \mathbb{a}, \mathbb{Z}, \mathrm{A}, \mathrm{z}, \bm{A}, \bm{z}, \mathscr{A}, \mathfrak{S}, \] % Text \textbf{Bold}, \textit{Italic}, \underline{Underline}, \begin{itemize} \item \end{itemize} ``abcDEF.'' %% if let g:vimtex_syntax_conceal = {'sections':1} \section{Section} \subsection{Subsection} \end{document}
# Musterlösung zu Übungsblatt 1 * [Aufgabe 1](#Aufgabe-1) * [Aufgabe 2](#Aufgabe-2) * [Aufgabe 3](#Aufgabe-3) ```python %matplotlib inline import numpy as np import matplotlib.pyplot as plt import scipy.stats plt.style.use('ggplot') ``` --- ## Aufgabe 1 Gegeben sei eine parametrische Funktion $y = f(x)$, $y = 1 + a_1x + a_2x^2$ mit Parametern $a_1 = 2.0 ± 0.2$, $a_2 = 1.0 ± 0.1$ und Korrelationskoeffizient $ρ = −0.8$. --- ```python a1, a1_err = 2.0, 0.2 a2, a2_err = 1.0, 0.1 rho = -0.8 ``` --- ### 1.1 Geben Sie die Kovarianzmatrix von $a_1$ und $a_2$ an. --- Die Kovarianzmatrix von $a_1$ und $a_2$ lässt sich wie folgt berechnen: $$\mathrm{Cov}(a) = \pmatrix{\sigma^2_{a_1} & \rho\sigma_{a_1}\sigma_{a_2} \\ \rho\sigma_{a_1}\sigma_{a_2} & \sigma^2_{a_2}}$$ ```python c12 = rho * a1_err * a2_err covariance = np.matrix([[a1_err ** 2, c12], [c12, a2_err ** 2]]) covariance ``` matrix([[ 0.04 , -0.016], [-0.016, 0.01 ]]) --- ### 1.2 Bestimmen Sie analytisch die Unsicherheit von $y$ als Funktion von $x$: --- Dazu bestimmen wir zunaechst die Ableitungen von $y$ nach $a_1$ und $a_2$ $$\frac{\partial{}y}{\partial{}a_1} = x \,,\quad \frac{\partial{}y}{\partial{}a_2} = x^2 \,.$$ Daraus können wir die Kovarianz von $y$ nach $$\sigma^2_y = \mathrm{Cov}(y) = \sum_{ij}\frac{\partial{}y}{\partial{}a_i}\frac{\partial{}y}{\partial{}a_j}\mathrm{Cov}(a)_{ij}$$ bestimmen. Einsetzen der eingangs bestimmten Ableitungen liefert $$\sigma^2_y = c_{11}x^2 + 2c_{12}x^3 + c_{22}x^4$$ wobei die $c_{ij}$ die Einträge von $\mathrm{Cov}(a)$ sind. Der Ausdruck lässt sich weiter vereinfachen zu $$\sigma^2_y = x^2\left(\sigma^2_{a_1} + \sigma^2_{a_2}x^2 + 2\rho\sigma_{a_1}\sigma_{a_2}x\right) \,.$$ Daraus ergibt sich für die Unsicherheit $$ \sigma_y = \lvert{}x\rvert\sqrt{\sigma^2_{a_1} + \sigma^2_{a_2}x^2 + 2\rho\sigma_{a_1}\sigma_{a_2}x} \,.$$ --- #### 1.2.1 unter Vernachlässigung der Korrelation --- (also für $\rho = 0$) vereinfacht sich der obige Ausdruck zu $$\sigma_y = \lvert{}x\rvert\sqrt{\sigma^2_{a_1} + \sigma^2_{a_2}x^2} \,.$$ Mit den eingangs berechneten Werten aus `covariance` ergibt sich also $$\sigma_y = \lvert{}x\rvert\sqrt{0.04 + 0.01x^2} = 0.2\lvert{}x\rvert{}\sqrt{1 + 0.25x^2} \,.$$ ```python def err_ana_wo(x): return 0.2 * np.abs(x) * np.sqrt(1 + 0.25 * x ** 2) xs = np.linspace(-10, 10, 10000) ys = 1 + a1 * xs + a2 * xs ** 2 errs = err_ana_wo(xs) plt.plot(xs, ys) plt.fill_between(xs, ys - errs, ys + errs, alpha=0.5) plt.show() ``` --- #### 1.2.2 mit Berücksichtigung der Korrelation --- $$\sigma_y = \lvert{}x\rvert\sqrt{0.04 + 0.01x^2 - 0.016x} = 0.2\lvert{}x\rvert\sqrt{1 + 0.25x^2 - 0.4x} \,.$$ ```python def err_ana(x): return 0.2 * np.abs(x) * np.sqrt(1 + 0.25 * x ** 2 - 0.4 * x) errs = err_ana(xs) plt.plot(xs, ys) plt.fill_between(xs, ys - errs, ys + errs, alpha=0.5) plt.show() ``` --- ### 1.3 Bestimmen Sie per Monte Carlo die Unsicherheit von $y$ als Funktion von $x$: #### 1.3.1 Generieren Sie Wertepaare $(a_1, a_2)$ gemäß ihrer Kovarianzmatrix und visualisieren Sie diese, z.B. mit einem Scatter-Plot. _Hinweis_: Wenn $x_1$ und $x_2$ zwei gaussverteilte Zufallszahlen mit Mittelwert null und Varianz eins sind, erhält man ein Paar korrelierter gaussverteilter Zufallszahlen $(y_1, y_2)$ mit Mittelwert null und Varianz eins durch $(y_1 = x_1; y_2 = x_1ρ + x_2\sqrt{1 − \rho^2})$. --- ```python x1s, x2s = np.random.normal(size=(2, 10000)) plt.hist2d(x1s, x2s, bins=40) plt.title('2-dim Normalverteilung') plt.xlabel('$x_1$') plt.ylabel('$x_2$') plt.show() y1s = x1s y2s = x1s * rho + x2s * np.sqrt(1 - rho ** 2) plt.hist2d(y1s, y2s, bins=40) plt.title('2-dim Normalverteilung mit Korrelation') plt.xlabel('$y_1$') plt.ylabel('$y_2$') plt.show() a1s = a1 + y1s * a1_err a2s = a2 + y2s * a2_err plt.hist2d(a1s, a2s, bins=40) plt.title('Verteilung der $a_1$ und $a_2$') plt.xlabel('$a_1$') plt.ylabel('$a_2$') plt.show() ``` --- #### 1.3.2 Bestimmen Sie die Verteilung von $y$ für $x = \{−1, 0, +1\}$ und vergleichen Sie Mittelwert und Varianz (Standardabweichung) mit den Resultaten der analytischen Rechnung. --- ```python def y(x, a1, a2): return 1 + a1 * x + a2 * x ** 2 def var_analytical(x): xx = x ** 2 return 0.04 * xx * (1 + 0.25 * xx - 0.16 * x) for x in (-1, 0, 1): ys = y(x, a1s, a2s) mean = np.mean(ys) var = np.var(ys) print('〈y({})〉= {:.3f}'.format(x, mean)) print(' σ² = {:.3f}'.format(var)) print(' analytical = {:.3f}'.format(var_analytical(x))) plt.hist(ys, bins=100) plt.xlabel('y({})'.format(x)) plt.ylabel('Absolute Häufigkeit') plt.show() ``` Der Fall $x = 0$ ist hier besonders. Da alle Koeffizienten vor Potenzen von $x$ stehen, ergibt sich für den Fall immer $y=0$ unabhängig von den $a_i$. Wir können also keine Aussage über die Varianz treffen. --- ## Aufgabe 2 Betrachten Sie folgende Reparametrisierung von $y = f(x)$: $$y = 1 + \frac{x(1+x)}{b_1} + \frac{x(1-x)}{b_2}$$ ### 2.1 Bestimmen Sie analytisch die transformierten Parameter $b_1$ und $b_2$ und deren Kovarianzmatrix --- Wir lösen die Reparametrisierung nach Koeffizienten von Potenzen von $x$ auf. Dabei können wir den Term $1$ vernachlässigen, weil er in beiden Definitionen gleichermaßen auftritt. \begin{align} a_1 x + a_2 x^2 &= \frac{x(1 + x)}{b_1} + \frac{x(1 - x)}{b_2} \\ &= \frac{x}{b_1} + \frac{x^2}{b_1} + \frac{x}{b_2} - \frac{x^2}{b_2} \\ &= x\left(\frac{1}{b_1} + \frac{1}{b_2}\right) + x^2\left(\frac{1}{b_1} - \frac{1}{b_2}\right) \end{align} Damit ist $$a_1 = \left(\frac{1}{b_1} + \frac{1}{b_2}\right) \quad\text{und}\quad a_2 = \left(\frac{1}{b_1} - \frac{1}{b_2}\right)$$ also $$b_1 = \frac{2}{a_1 + a_2} \quad\text{und}\quad b_2 = \frac{2}{a_1 - a_2} \,.$$ Für die Jacobimatrix der Transformation ergibt sich \begin{equation} M = \pmatrix{ \frac{-2}{(a_1 + a_2)^2} & \frac{-2}{(a_1 + a_2)^2} \\ \frac{-2}{(a_1 - a_2)^2} & \frac{+2}{(a_1 - a_2)^2} } \quad\text{wobei}\quad m_{ij} = \frac{\partial b_i}{\partial a_j} \end{equation} \begin{equation} M^T = \pmatrix{ \frac{-2}{(a_1 + a_2)^2} & \frac{-2}{(a_1 - a_2)^2} \\ \frac{-2}{(a_1 + a_2)^2} & \frac{+2}{(a_1 - a_2)^2} } \end{equation} Die transformierte Kovarianzmatrix ist dann $\mathrm{Cov}(b) = M\mathrm{Cov}(a)M^T$. ```python b1 = 2 / (a1 + a2) b2 = 2 / (a1 - a2) denom1 = (a1 + a2) ** 2 denom2 = (a1 - a2) ** 2 M = np.matrix([[-2 / denom1, -2 / denom1], [-2 / denom2, 2 / denom2]]) cov_b = M * covariance * M.T cov_b ``` matrix([[ 0.00088889, 0.01333333], [ 0.01333333, 0.328 ]]) --- ### 2.2 Bestimmen Sie die Kovarianzmatrix der transformierten Parameter per Monte Carlo --- ```python b1s = 2 / (a1s + a2s) b2s = 2 / (a1s - a2s) print('b1 = {}'.format(np.mean(b1s))) print('var = {}'.format(np.var(b1s))) print('b2 = {}'.format(np.mean(b2s))) print('var = {}'.format(np.var(b2s))) plt.hist(b1s, bins=100) plt.show() plt.hist(b2s, bins=100) plt.show() ``` Dabei tritt das Problem auf, dass für einige Kombinationen von Werten für $a_1$ und $a_2$ der Nenner sehr nah an `0` kommt. Dadurch ergeben sich sehr große (unrealistische) Werte für $b_2$. Wir können dem entgegenwirken, indem wir einen Bereich festlegen in dem wir die Werte für $b_2$ erwarten. ```python cut = np.logical_and(b2s < 5, b2s > 0) b1s_ = b1s[cut] b2s_ = b2s[cut] print('b2 gefiltert = {}'.format(np.mean(b2s_))) print('var = {}'.format(np.var(b2s_))) plt.hist(b1s_, bins=100) plt.show() plt.hist2d(b1s_, b2s_, bins=100) plt.show() ``` Wenn wir uns das Leben etwas erleichtern wollen, koennen wir auch einfach die Funktion `cov` aus Numpy verwenden, die uns fuer zwei Arrays direkt die Kovarianzmatrix ausrechnet ```python ncov_b = np.cov(b1s_, b2s_) ncov_b ``` array([[ 0.0008353 , 0.01402655], [ 0.01402655, 0.45535159]]) --- ### 2.3 Bestimmen Sie analytisch die Unsicherheit von $y$ als Funktion von $x$: #### 2.3.1 unter Verwendung der analytisch bestimmten Kovarianzmatrix von $(b_1, b_2)$ --- Zunächst berechnen wir die partiellen Ableitungen von $y$ nach den Koeffizienten $b_1$ und $b_2$. \begin{equation} \frac{\partial y}{\partial b_1} = \frac{-x(1+x)}{b_1^2} \quad\text{und}{\quad} \frac{\partial y}{\partial b_2} = \frac{-x(1-x)}{b_2^2} \end{equation} Damit ergibt sich für die Varianz \begin{align} \sigma_y^2 &= \sum_{ij}\frac{\partial y}{\partial b_i}\frac{\partial y}{\partial b_j}\mathrm{Cov}(b)_{ij} \\ &= \frac{x^2(1+x)^2}{b_1^4}\sigma_{b_1}^2 + 2\frac{x^2 - x^3}{b_1^2b_2^2}\rho\sigma_{b_1}\sigma_{b_2} + \frac{x^2(1-x)^2}{b_2^4}\sigma_{b_2}^2 \\ &= x^2\left[(\alpha+\beta)x^2 + (2\alpha - 2\beta - \gamma)x + (\alpha + \beta + \gamma)\right] \\ &= x^2\left(c_2x^2 + c_1x + c_0\right) \end{align} mit den Koeffizienten \begin{equation} \alpha = \frac{\sigma_{b_1}^2}{b_1^4} \quad,\quad \beta = \frac{\sigma_{b_2}^2}{b_2^4} \quad\text{und}\quad \gamma = \frac{\rho\sigma_{b_1}\sigma_{b_2}}{b_1^2b_2^2} \,. \end{equation} In Zahlen ausgedrückt sind die Koeffizienten ```python s2_b1 = cov_b[0, 0] s2_b2 = cov_b[1, 1] rho12 = cov_b[0, 1] alpha = s2_b1 / b1 ** 4 beta = s2_b2 / b2 ** 4 gamma = rho12 / b1 ** 2 / b2 ** 2 c2 = alpha + beta c1 = 2 * c2 - gamma c0 = c2 + gamma c2, c1, c0 ``` (0.025000000000000005, 0.04250000000000001, 0.032500000000000008) Es ist also \begin{equation} \sigma_y^2 = x^2\left(0.025x^2 + 0.0425x + 0.0325\right) \end{equation} und damit \begin{equation} \sigma_y = \lvert{}x\rvert\sqrt{0.025x^2 + 0.0425x + 0.0325} \end{equation} ```python def err_ana(x): return np.abs(x) * np.sqrt(c2 * x ** 2 + c1 * x + c0) xs = np.linspace(-10, 10, 10000) ys = 1 + xs * (xs + 1) / b1 + xs * (xs - 1) / b2 errs = err_ana(xs) plt.plot(xs, ys) plt.fill_between(xs, ys - errs, ys + errs, alpha=0.5) plt.show() ``` --- #### 2.3.2 unter Verwendung der numerisch bestimmten Kovarianzmatrix von $(b_1, b_2)$ --- Die gleiche Rechnung mit den per Monte Carlo bestimmten Werten ```python s2_b1 = ncov_b[0, 0] s2_b2 = ncov_b[1, 1] rho12 = ncov_b[0, 1] alpha = s2_b1 / b1 ** 4 beta = s2_b2 / b2 ** 4 gamma = rho12 / b1 ** 2 / b2 ** 2 c2n = alpha + beta c1n = 2 * c2 - gamma c0n = c2 + gamma c2n, c1n, c0n ``` (0.032688177932642684, 0.042110063518531804, 0.032889936481468214) liefert also ein etwas überschätzte Ungenauigkeit von \begin{equation} \sigma_y = \lvert{}x\rvert\sqrt{0.0320x^2 + 0.0563x + 0.0398} \end{equation} ```python def err_num(x): return np.abs(x) * np.sqrt(c2n * x ** 2 + c1n * x + c0n) errs = err_num(xs) plt.plot(xs, ys) plt.fill_between(xs, ys - errs, ys + errs, alpha=0.5) plt.show() ``` --- ## Aufgabe 3 Lösen Sie die obigen Teilaufgaben für $y = f(x)$ mit $$y = \ln\left(1 + a_1x + a_2x^2\right) \quad \text{bzw.} \quad y = \ln\left(1 + \frac{x(1+x)}{b_1} + \frac{x(x-1)}{b_2}\right)$$ Im folgenden nennen wir das neue $y$ der Einfachheit halber $z$. \begin{equation} z = \ln(1 + a_1x + a_2x^2) = \ln(y) \end{equation} Für die Unsicherheit von $z$ ergibt sich \begin{align} \sigma_z &= \sqrt{\left(\frac{\partial z}{\partial y}\right)^2\sigma_y^2} \\ &= \sqrt{\left(\frac{1}{y}\right)^2\sigma_y^2} \\ &= \left\lvert\frac{\sigma_y}{y}\right\rvert \\ &= \frac{0.2\lvert x\rvert\sqrt{1 + 0.25x^2 - 0.4x}}{\lvert 1 + a_1 x + a_2 x^2 \rvert} \,. \end{align} Völlig analog ist die Rechnung für die Reparametrisierung. Hier ergibt sich \begin{align} \sigma_z &= \left\lvert\frac{\sigma_y}{y}\right\rvert \\ &= \frac{\lvert{}x\rvert\sqrt{0.025x^2 + 0.0425x + 0.0325}}{\left\lvert 1 + \frac{x(1+x)}{b_1} + \frac{x(x-1)}{b_2}\right\rvert} \,. \end{align} ```python def err1(x): return 0.2 * np.abs(x) * np.sqrt(1 + 0.25 * x ** 2 - 0.4 * x) / np.abs(1) def err2(x): return np.abs(x) * np.sqrt(c2 * x ** 2 + c1 * x + c0) / np.abs(1 + xs * (xs + 1) / b1 + xs * (xs - 1) / b2) xs = np.linspace(-10, 10, 10000) ys1 = 1 + a1 * xs + a2 * xs ** 2 ys2 = np.log(1 + xs * (xs + 1) / b1 + xs * (xs - 1) / b2) errs1 = err1(xs) errs2 = err2(xs) plt.plot(xs, ys1) plt.fill_between(xs, ys1 - errs1, ys1 + errs1, alpha=0.5) plt.show() plt.plot(xs, ys2) plt.fill_between(xs, ys2 - errs2, ys2 + errs2, alpha=0.5) plt.show() ```
function [c]=findcntr(H) % % [Center]=findcntr(Handle) % Returns the geometric center of Handle % % This can be used as the ORIGIN input in ROTATE to rotate % an object about its geometric center. % % See also ROTATE, TRNSLATE, SCALHAND % % Richard G. Cobb 3/96 % c=[0 0 0]; tmp=(max(get(H,'Xdata'))+min(get(H,'Xdata')))/2; if tmp ~= [] c(1)=tmp; else set(H,'Xdata',zeros(size(get(H,'Ydata')))) end tmp=(max(get(H,'Ydata'))+min(get(H,'Ydata')))/2; if tmp ~= [] c(2)=tmp; else set(H,'Ydata',zeros(size(get(H,'Xdata')))) end tmp=(max(get(H,'Zdata'))+min(get(H,'Zdata')))/2; if tmp ~= [] c(3)=tmp; else set(H,'Zdata',zeros(size(get(H,'Ydata')))) end %eof
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import number_theory.class_number.admissible_card_pow_degree import number_theory.class_number.finite import number_theory.function_field /-! # Class numbers of function fields This file defines the class number of a function field as the (finite) cardinality of the class group of its ring of integers. It also proves some elementary results on the class number. ## Main definitions - `function_field.class_number`: the class number of a function field is the (finite) cardinality of the class group of its ring of integers -/ namespace function_field open_locale polynomial variables (Fq F : Type) [field Fq] [fintype Fq] [field F] variables [algebra Fq[X] F] [algebra (ratfunc Fq) F] variables [is_scalar_tower Fq[X] (ratfunc Fq) F] variables [function_field Fq F] [is_separable (ratfunc Fq) F] open_locale classical namespace ring_of_integers open function_field noncomputable instance : fintype (class_group (ring_of_integers Fq F) F) := class_group.fintype_of_admissible_of_finite (ratfunc Fq) F (polynomial.card_pow_degree_is_admissible : absolute_value.is_admissible (polynomial.card_pow_degree : absolute_value Fq[X] ℤ)) end ring_of_integers /-- The class number in a function field is the (finite) cardinality of the class group. -/ noncomputable def class_number : ℕ := fintype.card (class_group (ring_of_integers Fq F) F) /-- The class number of a function field is `1` iff the ring of integers is a PID. -/ theorem class_number_eq_one_iff : class_number Fq F = 1 ↔ is_principal_ideal_ring (ring_of_integers Fq F) := card_class_group_eq_one_iff end function_field
# Let E be the surjection operad, as explained by Berger and Fresse # following McClure. We represent a basis element of E(A) by # expressions S(...), where the arguments are elements of A, # each element appears at least once, and no two adjacent elements # are the same. `is_element/surjections` := (A::set) -> proc(x) global reason; local i,y,z; if x = 0 then return true; fi; if type(x,`+`) then return `and`(op(map(`is_element/surjections`(A),[op(x)]))); fi; if type(x,`*`) then y,z := selectremove(type,[op(x)],integer); return (nops(z) = 1 and `is_element/surjections`(A)(z[1])); fi; if not type(x,specfunc(S)) then return false; fi; if {op(x)} <> A then return false; fi; for i from 1 to nops(x) - 1 do if x[i] = x[i+1] then return false; fi; od; return true; end: `is_equal/surjections` := (A::set) -> (x0,x1) -> evalb(expand(x0 - x1) = 0); `is_equal_unsigned/surjections` := (A::set) -> (x0,x1) -> evalb(modp(expand(x0 - x1),2) = 0); `random_basis_element/surjections` := (A) -> proc(m_) local n,m,i,x,ok; n := nops(A); if n = 0 then return FAIL; fi; if n = 1 then if nargs = 0 or m_ = 1 then return S(op(A)); else return FAIL; fi; fi; if nargs > 0 then m := m_; else m := rand(0..5)(); end: ok := false; while not(ok) do x := [op(A),seq(random_element_of(A),i=1..m)]; x := combinat[randperm](x); ok := true; for i from 1 to n + m - 1 do if x[i] = x[i+1] then ok := false; break; fi; od; od; x := S(op(x)); return x; end: `random_element/surjections` := (A) -> proc(coeff_range_,num_terms_) local coeff_range,num_terms; coeff_range := -3..3; num_terms := 5; if nargs > 0 then coeff_range := args[1]; fi; if nargs > 1 then num_terms := args[2]; fi; add(rand(coeff_range)() * `random_basis_element/surjections`(A)(),i=1..num_terms); end: # Let u be a basis element of E(A), of length n say. A gap means # a pair (i,i+1) with 1 <= i < i+1 <= n. The gap is bound if # u[i] = u[j] for some j > i. Here we represent a bound gap # (i,i+1) by its initial index i. The following function # returns the ordered list of bound gaps. `bound_gaps/surjections` := (A) -> proc(u) local G,N,M,a; G := NULL; N := [seq(i,i=1..nops(u))]; for a in A do M := select(i -> op(i,u) = a,N); G := G,op(1..-2,M); od: G := sort([G]); return(G); end: # Auxiliary function feeding into `diff/surjections` `diff0/surjections` := (A::set) -> proc(x) local i,j,m,y,z,s,ss,t,l,r; i := [op(x)]; m := nops(i); y := 0; s := 1; ss := table(); for j from 1 to m do l := [op(1..j-1,i)]; r := [op(j+1..m,i)]; if member(i[j],r) then t := s; ss[i[j]] := t; s := -s; elif member(i[j],l) then t := -ss[i[j]]; ss[i[j]] := t; else t := 0; fi; if 1 < j and j < m and op(j-1,i) = op(j + 1,i) then t := 0; fi; y := y + t * S(op(1..j-1,i),op(j+1..m,i)); od: end: # Differential on the surjection chain complex `diff/surjections` := (A::set) -> apply_linear(`diff0/surjections`(A)); # Auxilary function feeding into `deg/surjections` `deg0/surjections` := (A) -> (u) -> nops(u) - nops(A); # Degree function for the surjection chain complex. `deg/surjections` := (A) -> apply_deg(`deg0/surjections`(A)); `reflect/surjections` := (A) -> proc(u) local c,v; if type(u,`+`) then return map(`reflect/surjections`(A),u); fi; c,v := op(coeff_split(u)); if not(type(v,specfunc(S))) then return FAIL; fi; return (-1)^(nops(v) - nops(A)) * u; end: # This is the circle product for the operad structure. # It is assumed that B is a subset of A and u is in E(A/B) and v is in E(B), # where A/B is implemented as A \ B u {B}. `o0/surjections` := (A,B) -> proc(u,v) local AB,nu,nv,Nu,Nv,M,l,m,JJ,w,J,k,p,i,j,s; AB := A minus B union {B}; nu := nops(u); nv := nops(v); Nu := [seq(i,i=1..nu)]; Nv := [seq(i,i=1..nv)]; M := select(i -> op(i,u) = B,Nu); m := nops(M); JJ := combinat[choose]([seq(i,i=2..nv+m-1)],m-1); JJ := map(J -> [1,seq(J[i]-i,i=1..m-1),nv],JJ); w := 0; for J in JJ do k := NULL; l := NULL; p := 1; for i from 1 to nu do if op(i,u) = B then k := k,seq(op(j,v),j=J[p]..J[p+1]); l := l,seq([i,j],j=J[p]..J[p+1]); p := p+1; else k := k,op(i,u); l := l,[i,0]; fi; od; l := [l]; s := NULL; for i in `bound_gaps/surjections`(AB)(u) do j := nops(l); while j > 1 and l[j][1] <> i do j := j - 1; od; s := s,j; od; for i in `bound_gaps/surjections`(B)(v) do j := nops(l); while j > 1 and l[j][2] <> i do j := j - 1; od; s := s,j; od; w := w + sgn([s]) * S(k); od: return w; end: `o/surjections` := (A,B) -> apply_bilinear(`o0/surjections`(A,B)); `gamma0/surjections` := (A::set,B::set) -> (p) -> proc(y,x) local F,J,I0,J0,b,L,m,n,S0,s; F := fibres(A,B)(p); J := [seq(i,i=0..nops(y)-1)]; I0 := table(): J0 := table(): for b in B do I0[b] := [seq(i,i=0..nops(x[b])-1)]; J0[b] := select(j -> op(j+1,y) = b,J); od: L := [[]]; for b in B do m := nops(J0[b]) - 1; n := nops(I0[b]) - 1; S0 := map(`to_grid_path/shuffles`(m,n),`list_elements/shuffles`(m,n)); S0 := map(s -> [seq(s[i],i=0..n+m)],S0); S0 := map(s -> map(ji -> [J0[b][ji[1]+1],ji[2]],s),S0); L := [seq(seq([op(l),op(s)],s in S0),l in L)]; od: L := map(sort,L); L := map(l -> S(op(map(ji -> op(ji[2]+1,x[op(ji[1]+1,y)]),l))),L); return `+`(op(L)); end: `gamma/surjections` := eval(extend_gamma_linear(`gamma0/surjections`)): # We now have various functions related to an interesting filtration # of the surjections operad. `flip_count/surjections` := (A::set) -> proc(u,s_) local r,m,a,b,c,u0,i; if nargs > 1 then r := `rank_table/ord`(A)(s_); else r := NULL; fi; m := table(): for a in A do for b in A do m[a,b] := 0; u0 := select(p -> p = a or p = b,[op(u)]); for i from 1 to nops(u0) - 1 do if u0[i+1] <> u0[i] then m[a,b] := m[a,b] + 1; fi; od; if m[a,b] > 0 and r <> NULL then c := `if`(r[a] < r[b],a,b); if u0[-1] = c then m[a,b] := m[a,b] + 1; fi; fi; od; od; return eval(m); end: `flip_count_matrix/surjections` := (A::set) -> proc(u,s_) local m; m := `flip_count/surjections`(A)(args); return Matrix([seq([seq(m[a,b],b in A)],a in A)]); end: `max_flip_count/surjections` := (A::set) -> proc(u) local m,mm,a,b; m := `flip_count/surjections`(A)(u); mm := 0; for a in A do for b in A do mm := max(mm,m[a,b]); od; od; return mm; end: `is_cell_member/surjections` := (A::set) -> (ms) -> proc(u) local m0,m1,s,r,i,j,a,b,c,u0,k,l,y,z; if x = 0 then return true; fi; if type(x,`+`) then return `and`(seq(`is_cell_member/surjections`(A)(ms)(y),y in x)); fi; if type(x,`*`) then y,z := selectremove(type,[op(x)],integer); if nops(z) = 1 then return `is_cell_member/surjections`(A)(ms)(z[1]); else return false; fi; fi; m0,s := op(ms); m1 := `flip_count/surjections`(A)(u,s); for a in A do for b in A do if m1[a,b] > m0[a,b] then return false; fi; od; od; return true; end: `filtration0/surjections` := (A::set) -> proc(u) local m,m_max,s,rr,k,i,r0,r1,a,b; if type(u,integer) then return 0; fi; return 1 + `max_flip_count/surjections`(A)(u); end: `filtration/surjections` := (A::set) -> apply_max_deg(`filtration0/surjections`(A)); `rho0/barratt_eccles/surjections` := (A::set) -> proc(x) local rr,d,R,r,y,z,z0,ok,i,m; rr := nops(A); d := nops(x) - 1; R := combinat[choose]([seq(i,i=1..d+rr-1)],d); R := map(r -> [0,op(r),d+rr],R); R := map(r -> [seq(r[i+1]-r[i],i=1..d+1)],R); y := 0; for r in R do z := NULL; z0 := NULL; ok := true; for i from 1 to d+1 do m := select(j -> not(member(j,[z0])),op(i,x)); if nops(m) >= r[i] and ([z] = [] or [z][-1] <> m[1]) then z := z,op(1..r[i],m); z0 := z0,op(1..r[i]-1,m); else ok := false; break; fi; od; if ok then y := y + S(z); fi; od; return y; end: `rho/barratt_eccles/surjections` := (A::set) -> apply_linear(`rho0/barratt_eccles/surjections`(A)); # We now define a map from the surjections operad to the # Barratt-Eccles operad. This is not an operad morphism, # but it is a section of the map in the opposite direction. `sigma0/surjections/barratt_eccles` := (A::set) -> proc(x) local i,j,k,l,r,t,p,m,d,w,ww; i := [op(x)]; m := nops(i); d := m - nops(A); ww := NULL; for k from 0 to d do w := NULL; p := 0; for j from 1 to m do l := [op(1..j-1,i)]; r := [op(j+1..m,i)]; if member(i[j],r) then t := false; p := p + 1; else t := true; fi; if not(member(i[j],[w])) then if t or (p > k) then w := w,i[j]; fi; fi; od: w := [w]; ww := ww,w; od; return T(ww); end: `sigma/surjections/barratt_eccles` := (A::set) -> apply_linear(`sigma0/surjections/barratt_eccles`(A)); # The cut operation construction gives a morphism from the surjection # operad to the Eilenberg-Zilber operad. Unfortunately the EZ operad # cannot be represented properly in our framework because each set # EZ(A) is an infinite product over the natural numbers. To deal with # this we insert natural number indices in various places. `cut_operation0/surjections` := (n::nonnegint) -> (A::set) -> proc(x) local A0,m,d,N,J,p,q,r,j,c,t,a,is_degen; A0 := sort([op(A)]); m := nops(A); d := nops(x) - m; N := [seq(i,i=0..n)]; J := [[0]]; for p from 1 to m + d - 1 do J := [seq(seq([op(j),q],q=j[-1]..n),j in J)]; od: J := map(j -> [op(j),n],J); c := 0; for j in J do t := table(): for a in A0 do t[a] := []: od: for p from 1 to m+d do a := op(p,x); t[a] := [op(t[a]),seq(r,r=j[p]..j[p+1])]; od: is_degen := false; for a in A0 do if nops(t[a]) > nops({op(t[a])}) then is_degen := true; break; fi; od: if not(is_degen) then c := c + `detranspose/eilenberg_zilber`(A)(t); fi; od: return c; end: `cut_operation1/surjections` := (n::nonnegint) -> (A::set) -> proc(x) add(`cut_operation0/surjections`(k)(A)(x),k=0..n); end: `cut_operation/surjections` := (n::nonnegint) -> (A::set) -> apply_linear(`cut_operation1/surjections`(n)(A)); `multiplicity_table/surjections` := (A::set) -> proc(x) local t,a; t := table(): for a in A do t[a] := 0; od: for a in [op(x)] do t[a] := t[a] + 1; od: return eval(t); end: `max_multiplicity/surjections` := (A::set) -> proc(x) local t,m,a; t := `multiplicity_table/surjections`(A)(x); m := 0; for a in A do m := max(m,t[a]); od; return m; end: `is_biased/surjections` := (A::set) -> proc(x,a0_) local a,a0,t; a0 := NULL; if nargs > 1 then a0 := a0_; fi; t := `multiplicity_table/surjections`(A)(x); for a in A do if t[a] > 1 then if a0 = NULL then a0 := a; else if a0 <> a then return false; fi; fi; fi; od: return true; end: `is_strongly_biased/surjections` := (A::set) -> proc(x,a0_) local a,a0,t; a0 := NULL; if nargs > 1 then a0 := a0_; fi; t := `multiplicity_table/surjections`(A)(x); for a in A do if t[a] > 1 then if a0 = NULL then a0 := a; else if a0 <> a then return false; fi; fi; fi; od: if a0 = NULL or t[a0] <= 1 then return false; fi; return true; end:
/* ** Task-related edge density, main algorithm ** ** Ref: Lohmann et al (2016) PLoS One, 11(6):e0158185 ** ** G.Lohmann, MPI-KYB, Jan 2015 */ #include <stdio.h> #include <stdlib.h> #include <math.h> #include <string.h> #include <gsl/gsl_matrix.h> #include <gsl/gsl_vector.h> #include <gsl/gsl_errno.h> #include <gsl/gsl_cblas.h> #include <gsl/gsl_statistics.h> #include <gsl/gsl_rng.h> #include <gsl/gsl_randist.h> #include <gsl/gsl_math.h> #include <gsl/gsl_permutation.h> #include <gsl/gsl_histogram.h> #include <gsl/gsl_sort_float.h> #include "viaio/Vlib.h" #include "viaio/VImage.h" #include "viaio/mu.h" #include "viaio/option.h" #ifdef _OPENMP #include <omp.h> #endif /*_OPENMP*/ #define SQR(x) ((x) * (x)) #define ABS(x) ((x) > 0 ? (x) : -(x)) extern VImage *VImagePointer(VAttrList list,int *nt); extern void VReadImagePointer(VAttrList list,VImage *src); extern VImage VoxelMap(VImage mask,size_t *nvoxels); extern void VDataMatrix(VImage *src,int first,int len,VImage map,gsl_matrix_float *X); extern void VCheckMatrix(gsl_matrix_float *X); extern long VMaskCoverage(VAttrList list,VImage mask); extern float ZMatrix(gsl_histogram *histogram,gsl_matrix_float *SNR1,gsl_matrix_float *SNR2,int n1,int n2, VImage roi,VImage map,VImage,int,float elength,float quantile,int,int); extern void GetSNR(gsl_matrix_float **X1,gsl_matrix_float **X2,int *,int n,gsl_matrix_float *SNR,int); extern void GetMedian(gsl_matrix_float **X1,gsl_matrix_float **X2,int *,int n,gsl_matrix_float *SNR,int); extern void VPrintHistogram(gsl_histogram *histogram,int numperm,VString filename); extern void HistoUpdate(float *A,size_t nvox,gsl_histogram *hist); extern size_t EdgeDensity(float *C,int *I,int *J,size_t nedges, gsl_histogram *histogram,gsl_matrix_float *SNR1,gsl_matrix_float *SNR2,int n1,int n2, VImage roi,VImage map,VImage,int,float,float,int,int,int,float,int); extern size_t EstimateEdges(float *E,int *I,int *J,size_t fulldim, gsl_histogram *TedHist,gsl_matrix_float *SNR1,gsl_matrix_float *SNR2,int n1,int n2, VImage roi,VImage map,VImage mapimage,int adjdef,float elength,float zthreshold,float,int); /* generate permutation table */ int genperm(gsl_rng *rx,int *table,int n,int numperm) { int s=0; int ks = 0; int kc=3; if (numperm < 10) { if (n%2==0) kc = n/2; else kc = n/2-1; } int iter=0; while ((ks < kc || ks > n-kc)) { if (iter > 100) VError(" not possible to generate random permutations, perhaps not enough input data ?"); ks=0; for (s=0; s<n; s++) { table[s] = 0; if (gsl_ran_bernoulli (rx,(double)0.5) == 1) { table[s] = 1; ks++; } } iter++; } return ks; } void VReleaseStorage(VAttrList list) { VImage src; VAttrListPosn posn; for(VFirstAttr(list, & posn); VAttrExists(& posn); VNextAttr(& posn)) { if(VGetAttrRepn(& posn) != VImageRepn) continue; VGetAttrValue(& posn, NULL, VImageRepn, & src); VDestroyImage(src); src = NULL; } } /* Check mask coverage */ VAttrList VCheckMaskCoverage(VStringConst *in_filenames,size_t n,VImage mask) { size_t i; VAttrList list=NULL; VAttrList geolist = NULL; FILE *fp=NULL; for (i=0; i<n; i++) { fp = VOpenInputFile (in_filenames[i], TRUE); list = VReadFile (fp, NULL); if (! list) VError("Error reading image"); fclose(fp); /* read geometry info, if unknown */ if (geolist == NULL) geolist = VGetGeoInfo(list); long count = VMaskCoverage(list,mask); if (count > 100) fprintf(stderr," incomplete mask_coverage %s: %ld\n",in_filenames[i],count); VReleaseStorage(list); list = NULL; } return geolist; } gsl_matrix_float **VReadImageData(VStringConst *in_filenames,VImage *src,VImage map,size_t n,size_t nvox,size_t first,size_t len) { size_t i; VAttrList list=NULL; FILE *fp=NULL; /* allocate data struct */ gsl_matrix_float **X = VCalloc(n,sizeof(gsl_matrix_float)); for (i=0; i<n; i++) { X[i] = gsl_matrix_float_calloc(nvox,len); if (!X[i]) VError(" err allocating data matrix"); } /* read data */ for (i=0; i<n; i++) { fp = VOpenInputFile (in_filenames[i], TRUE); list = VReadFile (fp, NULL); if (! list) VError("Error reading image"); fclose(fp); VReadImagePointer(list,src); VDataMatrix(src,(int)first,(int)len,map,X[i]); VCheckMatrix(X[i]); VReleaseStorage(list); list = NULL; } return X; } VDictEntry ADJDict[] = { { "6", 0 }, { "18", 1 }, { "26", 2 }, { NULL } }; VDictEntry TypeDict[] = { { "SNR", 0 }, { "median", 1 }, { NULL } }; VDictEntry MetricDict[] = { { "pearson", 0 }, { "spearman", 1 }, { NULL } }; int main (int argc,char *argv[]) { static VArgVector in_files1; static VArgVector in_files2; static VString out_filename = ""; static VString mask_filename = ""; static VString roi_filename = ""; static VString hist_filename= ""; static VShort first = 0; static VShort len = 0; static VLong seed = 99402622; static VFloat qthreshold = 0.99; static VFloat elength = 5; static VFloat noise_cutoff = 0.01; static VShort adjdef = 2; static VShort numperm = 0; static VShort type = 0; static VShort metric = 0; static VShort nproc = 10; static VShort step = 2; static VOptionDescRec options[] = { {"in1", VStringRepn, 0, & in_files1, VRequiredOpt, NULL,"Input files 1" }, {"in2", VStringRepn, 0, & in_files2, VRequiredOpt, NULL,"Input files 2" }, {"out", VStringRepn, 1, & out_filename, VOptionalOpt, NULL,"Output file" }, {"mask", VStringRepn, 1, & mask_filename, VRequiredOpt, NULL,"Mask file" }, {"roi", VStringRepn, 1, & roi_filename, VOptionalOpt, NULL,"ROI file" }, {"histogram",VStringRepn,1,(VPointer) &hist_filename,VRequiredOpt,NULL,"Output histogram filename"}, {"permutations",VShortRepn,1,(VPointer) &numperm,VOptionalOpt,NULL,"Number of permutations"}, {"qthreshold",VFloatRepn,1,(VPointer) &qthreshold,VOptionalOpt,NULL,"Initial quantile threshold"}, {"adj",VShortRepn,1,(VPointer) &adjdef,VOptionalOpt,ADJDict,"Definition of adjacency"}, {"seed",VLongRepn,1,(VPointer) &seed,VOptionalOpt,NULL,"Seed for random number generator"}, {"first",VShortRepn,1,(VPointer) &first,VOptionalOpt,NULL,"First timepoint to use within trial"}, {"len",VShortRepn,1,(VPointer) &len,VOptionalOpt,NULL,"Number of timepoints to use, '0' to use all"}, {"type",VShortRepn,1,(VPointer) &type,VOptionalOpt,TypeDict,"Type of trial average"}, {"metric",VShortRepn,1,(VPointer) &metric,VOptionalOpt,MetricDict,"Correlation metric"}, {"edgelength",VFloatRepn,1,(VPointer) &elength,VOptionalOpt,NULL,"Minimal edge length in voxels"}, {"j",VShortRepn,1,(VPointer) &nproc,VOptionalOpt,NULL,"Number of processors to use, '0' to use all"}, /* {"noisecutoff",VFloatRepn,1,(VPointer) &noise_cutoff,VOptionalOpt,NULL,"estimate of noisy edges"}, */ /* {"step",VShortRepn,1,(VPointer) &step,VOptionalOpt,NULL,"first iteration ZMatrix step size"} */ }; FILE *fp=NULL; VAttrList list=NULL,list1=NULL,geolist=NULL; VAttrListPosn posn; VImage mask=NULL; size_t nvox=0,i=0; /* parse command line */ if (! VParseCommand (VNumber (options), options, & argc, argv)) { VReportUsage (argv[0], VNumber (options), options, NULL); exit (EXIT_FAILURE); } if (argc > 1) { VReportBadArgs (argc, argv); exit (EXIT_FAILURE); } /* whether to produce output file, or only compute histogram */ VBoolean histonly = FALSE; if (strlen(out_filename) < 2) histonly = TRUE; /* omp-stuff */ #ifdef _OPENMP int num_procs=omp_get_num_procs(); int jprocs = num_procs; if (nproc > 0 && nproc < num_procs) jprocs = nproc; fprintf(stderr," using %d cores of %d\n",(int)jprocs,(int)num_procs); omp_set_num_threads(jprocs); #endif /* _OPENMP */ /* input filenames */ size_t n1 = (size_t)in_files1.number; size_t n2 = (size_t)in_files2.number; if (n1 != n2) VError(" n1 != n2, %d %d",n1,n2); VStringConst *in_filenames1 = (VStringConst *) VCalloc(n1,sizeof(VStringConst)); for (i=0; i<n1; i++) { in_filenames1[i] = ((VStringConst *) in_files1.vector)[i]; } VStringConst *in_filenames2 = (VStringConst *) VCalloc(n2,sizeof(VStringConst)); for (i=0; i<n2; i++) { in_filenames2[i] = ((VStringConst *) in_files2.vector)[i]; } /* read mask */ fp = VOpenInputFile (mask_filename, TRUE); list1 = VReadFile (fp, NULL); if (! list1) VError("Error reading mask file"); fclose(fp); for (VFirstAttr (list1, & posn); VAttrExists (& posn); VNextAttr (& posn)) { if (VGetAttrRepn (& posn) != VImageRepn) continue; VGetAttrValue (& posn, NULL,VImageRepn, & mask); if (VPixelRepn(mask) == VFloatRepn || VPixelRepn(mask) == VDoubleRepn) { mask = NULL; continue; } } if (mask == NULL) VError(" no mask found"); int nslices = VImageNBands(mask); int nrows = VImageNRows(mask); int ncols = VImageNColumns(mask); /* read ROI */ VAttrList list2 = NULL; VImage roi = NULL; if (strlen(roi_filename) > 1) { fp = VOpenInputFile (roi_filename, TRUE); list2 = VReadFile (fp, NULL); if (! list2) VError("Error reading roi file"); fclose(fp); for (VFirstAttr (list2, & posn); VAttrExists (& posn); VNextAttr (& posn)) { if (VGetAttrRepn (& posn) != VImageRepn) continue; VGetAttrValue (& posn, NULL,VImageRepn, & roi); if (VPixelRepn(roi) == VFloatRepn || VPixelRepn(roi) == VDoubleRepn) { roi = NULL; continue; } } if (roi == NULL) VError(" no roi found"); } /* Check mask coverage */ VAttrList geo=NULL; geo = VCheckMaskCoverage(in_filenames1,n1,mask); geo = VCheckMaskCoverage(in_filenames2,n2,mask); if (geolist == NULL) geolist = geo; /* voxel map */ VImage map = VoxelMap(mask,&nvox); /* get image dimensions */ fp = VOpenInputFile (in_filenames1[0], TRUE); list = VReadFile (fp, NULL); if (! list) VError("Error reading image"); fclose(fp); int nt=0; VImage *src = VImagePointer(list,&nt); if (first >= nt || first < 0) VError(" illegal value, first= %d, nt= %d",first,nt); if (len <= 0) len = nt-first; if (first + len >= nt) len = nt-first; if (len < 2) VError(" len= %d",len); fprintf(stderr," image: %d x %d x %d, nt: %d, nvox: %ld\n",(int)nslices,(int)nrows,(int)ncols,nt,nvox); /* read image data */ gsl_matrix_float **X1 = VReadImageData(in_filenames1,src,map,n1,nvox,first,len); gsl_matrix_float **X2 = VReadImageData(in_filenames2,src,map,n2,nvox,first,len); /* voxel addresses */ VImage mapimage = VCreateImage(nslices,nrows,ncols,VIntegerRepn); VFillImage(mapimage,VAllBands,(VInteger)(-1)); for (i=0; i<nvox; i++) { int b = VPixel(map,0,0,i,VShort); int r = VPixel(map,0,1,i,VShort); int c = VPixel(map,0,2,i,VShort); VPixel(mapimage,b,r,c,VInteger) = (VInteger)i; } /* tmp storage for SNR time courses */ int dim=0; if (type < 3) dim = len; else if (type == 3) dim = len*n1; else VError(" illegal type %d",type); gsl_matrix_float *SNR1 = gsl_matrix_float_calloc(nvox,dim); gsl_matrix_float *SNR2 = gsl_matrix_float_calloc(nvox,dim); /* ini zhist */ size_t hbins = 10000; double hmin = 0.0,hmax = 1.001; gsl_histogram *TedHist = gsl_histogram_alloc (hbins); gsl_histogram_set_ranges_uniform (TedHist,hmin,hmax); gsl_histogram_reset(TedHist); /* fuer z-threshold */ size_t nbins = 25000; hmin = -1.001,hmax = 1.001; gsl_histogram *ZvalHist = gsl_histogram_alloc (nbins); gsl_histogram_set_ranges_uniform (ZvalHist,hmin,hmax); gsl_histogram_reset(ZvalHist); /* ini random */ size_t n = n1; gsl_rng_env_setup(); const gsl_rng_type *T = gsl_rng_default; gsl_rng *rx = gsl_rng_alloc(T); gsl_rng_set(rx,(unsigned long int)seed); int *table = (int *) VCalloc(n,sizeof(int)); for (i=0; i<n; i++) table[i] = 0; /* allocate output structure */ size_t nedges=0; size_t fulldim = (nvox*(nvox+1)/2); double qx = 1.0-qthreshold; qx += 0.001; size_t nedges_estimated = (size_t) (qx*(double)fulldim); /* ini matrices */ float *E=NULL; /* matrix of edge densities */ int *I=NULL; /* row indices in matrix E */ int *J=NULL; /* col indices in matrix E */ if (histonly == FALSE && noise_cutoff < 0.00001) { E = VCalloc(nedges_estimated,sizeof(float)); /* matrix of edge densities */ I = VCalloc(nedges_estimated,sizeof(int)); /* row indices in matrix E */ J = VCalloc(nedges_estimated,sizeof(int)); /* col indices in matrix E */ } /* main loop */ size_t s; int ks=0,nperm=0; int startperm=0; if (numperm > 0) startperm = 1; for (nperm = startperm; nperm <= numperm; nperm++) { fprintf(stderr,"\n perm %3d: ",nperm); if (nperm > 0) { ks = genperm(rx,table,n,(int)numperm); } for (s=0; s<n; s++) { fprintf(stderr,"%d",table[s]); } fprintf(stderr," %3d\n",ks); /* get SNR data */ if (type == 0) { GetSNR(X1,X2,table,n,SNR1,metric); GetSNR(X2,X1,table,n,SNR2,metric); } if (type == 1) { GetMedian(X1,X2,table,n,SNR1,metric); GetMedian(X2,X1,table,n,SNR2,metric); } /* corr matrices */ float zthr = ZMatrix(ZvalHist,SNR1,SNR2,n1,n2,roi,map,mapimage,(int)adjdef, (float)elength,(float)qthreshold,(int)step,(int)metric); /* estimate number of truly needed edges, estimate noise */ if (noise_cutoff > 0.0 && nperm == numperm && histonly == FALSE) { size_t old_estimate = nedges_estimated; nedges_estimated = EstimateEdges(E,I,J,old_estimate,TedHist,SNR1,SNR2,n1,n2,roi,map,mapimage, (int)adjdef,elength,zthr,noise_cutoff,(int)metric); E = VCalloc(nedges_estimated,sizeof(float)); /* matrix of edge densities */ I = VCalloc(nedges_estimated,sizeof(int)); /* row indices in matrix E */ J = VCalloc(nedges_estimated,sizeof(int)); /* col indices in matrix E */ } /* edge densities */ fprintf(stderr," Computing edge densities...\n"); nedges = EdgeDensity(E,I,J,nedges_estimated,TedHist,SNR1,SNR2,n1,n2,roi,map,mapimage,(int)adjdef, elength,zthr,nperm,numperm,(int)1,noise_cutoff,(int)metric); } /* free storage */ for (i=0; i<n; i++) { gsl_matrix_float_free(X1[i]); gsl_matrix_float_free(X2[i]); } gsl_matrix_float_free(SNR1); gsl_matrix_float_free(SNR2); VFree(table); /* print histogram */ VPrintHistogram(TedHist,(int)numperm,hist_filename); if (histonly == TRUE) { fprintf (stderr," %s: done.\n", argv[0]); exit(0); } /* write edge density matrix in triplet sparse format */ size_t edim = nedges*3; float filesize1 = (float)(edim*sizeof(float))/(1000.0*1000.0); float filesize2 = (float)(edim*sizeof(float))/(1000.0*1000.0*1000.0); fprintf(stderr," nedges= %ld, filesize= %.3f MByte (%.3f GByte)\n",nedges,filesize1,filesize2); /* output */ VAttrList elist = VCreateAttrList(); VAttrList ilist = VCreateAttrList(); VAttrList jlist = VCreateAttrList(); VBundle edgedens = VCreateBundle ("data",elist,nedges*sizeof(float),(VPointer)E); VBundle rowindex = VCreateBundle ("data",ilist,nedges*sizeof(int),(VPointer)I); VBundle colindex = VCreateBundle ("data",jlist,nedges*sizeof(int),(VPointer)J); VAttrList out_list = VCreateAttrList(); VSetGeoInfo(geolist,out_list); VAppendAttr(out_list,"EdgeDensity",NULL,VBundleRepn,(VBundle)edgedens); VAppendAttr(out_list,"RowIndex",NULL,VBundleRepn,(VBundle)rowindex); VAppendAttr(out_list,"ColIndex",NULL,VBundleRepn,(VBundle)colindex); VAppendAttr(out_list,"nedges",NULL,VLongRepn,(VLong)nedges); VAppendAttr(out_list,"map",NULL,VImageRepn,map); VAppendAttr(out_list,"qthreshold",NULL,VFloatRepn,(VFloat)qthreshold); FILE *fp_out = VOpenOutputFile (out_filename, TRUE); if (! VWriteFile (fp_out, out_list)) exit (1); fclose(fp_out); fprintf (stderr," %s: done.\n\n", argv[0]); exit(0); }
module lambda.hw7 where open import Data.Product open import Relation.Nullary open import Relation.Nullary.Negation open import Relation.Binary.PropositionalEquality hiding (subst) open import Data.Nat open import Data.Fin hiding (lift) open import lambda.untyped open import lambda.vec open import lambda.system-f renaming (⊢_∶_ to ⊢F_∶_; type to typeF) hiding (subst; ↑; lift; subst₁) open import lambda.system-d renaming (⊢_∶_ to ⊢D_∶_; type to typeD; _⊢_∶_ to _⊢D_∶_; context to contextD) -- Peio BORTHELLE -- Homework 7 -- Maybe it's a bit unusual to present things like this, we didn't do any Agda -- but it would really have been more hassle formalizing the homework in Coq. -- So here it is, there are some utilities in the other files and also some -- bonus simply-typed lambda calculus. It was a bit more fun for me than to -- write again some long derivation tree with no guarantee at all that there -- isn't a stupid mistake kicking in. I tried to get the notations close to -- what we had in the lesson, hope this doesn't look too alien. -- Utilities A B C : typeD A = base 0 B = base 1 C = base 1 V₀ : ∀ {n} → typeF (suc n) V₀ = var zero V₁ : ∀ {n} → typeF (suc (suc n)) V₁ = var (suc zero) module Q₁ where -- Source terms t₁ t₂ t₃ t₄ : term 0 t₁ = lam (app (var zero) (var zero)) t₂ = app t₁ (lam (var zero)) t₃ = app t₁ t₁ t₄ = lam (lam (app (var (suc zero)) (app (var zero) (var (suc zero))))) -- a) system F F₁ F₂ F₄ : typeF 0 F₁ = (∀' V₀ ⇒ V₀) ⇒ (∀' V₀ ⇒ V₀) F₂ = ∀' V₀ ⇒ V₀ F₄ = ∀' ∀' (V₀ ⇒ V₁) ⇒ ((V₀ ⇒ V₁) ⇒ V₀) ⇒ V₁ F₁-p : ⊢F t₁ ∶ F₁ F₁-p = lam (∀' V₀ ⇒ V₀) (app (sub (∀' V₀ ⇒ V₀) ax) ax) F₂-p : ⊢F t₂ ∶ F₂ F₂-p = app (lam (∀' V₀ ⇒ V₀) (app (sub (∀' V₀ ⇒ V₀) ax) ax)) (gen (lam V₀ ax)) -- t₃ is not normalizing: it has a non-trivial beta-reduction to itself. -- Because system F is strongly normalizing this prooves that it has no valid -- typing judgment. t₃-no-norm : t₃ β* t₃ t₃-no-norm = β-beta ← ε F₄-p : ⊢F t₄ ∶ F₄ F₄-p = gen (gen (lam (V₀ ⇒ V₁) (lam ((V₀ ⇒ V₁) ⇒ V₀) (app ax (app ax ax))))) -- b) system D σ₁ σ₂ σ₄ : typeD σ₁ = (A ∧ A ⇒ B) ⇒ B σ₂ = A ⇒ A σ₄ = (A ⇒ B) ⇒ ((A ⇒ B) ⇒ A) ⇒ B σ₁-p : ⊢D t₁ ∶ σ₁ σ₁-p = lam (app (∧ᵉʳ ax) (∧ᵉˡ ax)) σ₂-p : ⊢D t₂ ∶ σ₂ σ₂-p = app (lam (app (∧ᵉʳ ax) (∧ᵉˡ ax))) (∧ⁱ (lam ax) (lam ax)) -- Same as system F for t₃ because of the strongly normalizing property. σ₄-p : ⊢D t₄ ∶ σ₄ σ₄-p = lam (lam (app ax (app ax ax))) module Q₂ where -- σ₁ σ₂ σ₃ σ₄ : typeD σ₁ = ((A ∧ B) ⇒ C) ⇒ A ⇒ B ⇒ C σ₂ = (A ⇒ B ⇒ C) ⇒ (A ∧ B) ⇒ C σ₃ = (C ⇒ A ∧ C ⇒ B) ⇒ C ⇒ (A ∧ B) σ₄ = C ⇒ (A ∧ B) ⇒ (C ⇒ A ∧ C ⇒ B) σ₁-p : ∀ {t} → ¬ ⊢D t ∶ σ₁ σ₁-p p = {!!} σ₂-p : ⊢D lam (lam (app (app (var (suc zero)) (var zero)) (var zero))) ∶ σ₂ σ₂-p = lam (lam (app (app ax (∧ᵉˡ ax)) (∧ᵉʳ ax))) σ₃-p : ⊢D lam (lam (app (var (suc zero)) (var zero))) ∶ σ₃ σ₃-p = lam (lam (∧ⁱ (app (∧ᵉˡ ax) ax) (app (∧ᵉʳ ax) ax))) σ₄-p : ⊢D lam (lam (lam (var (suc zero)))) ∶ σ₄ σ₄-p = lam (lam (∧ⁱ (lam (∧ᵉˡ ax)) (lam (∧ᵉʳ ax)))) module Q₃ where -- I got stuck on applying the substitution lemma on function type that are -- not lambda abstractions but ∧ eliminations. I don't manage to get from -- a proof of that type to a proof with the argument type on the top of the -- context. Maybe the substitution lemma is not well choosen. subj-red : ∀ {n T} → {x y : term n} → {Γ : contextD n} → Γ ⊢D x ∶ T → x →β y → Γ ⊢D y ∶ T subj-red ax () subj-red (∧ⁱ x₁ x₂) p = ∧ⁱ (subj-red x₁ p) (subj-red x₂ p) subj-red (∧ᵉˡ x) p = ∧ᵉˡ (subj-red x p) subj-red (∧ᵉʳ x) p = ∧ᵉʳ (subj-red x p) subj-red (app (lam x) y) β-beta = subst-p x (λ { zero → y; (suc i) → ax }) subj-red (app (∧ᵉˡ x) y) β-beta = {! !} subj-red (app (∧ᵉʳ x) y) β-beta = {! !} subj-red (app x y) (β-app₁ p) = app (subj-red x p) y subj-red (app x y) (β-app₂ p) = app x (subj-red y p) subj-red (lam x) (β-lam p) = lam (subj-red x p) module Q₄ where -- The BNF grammar i use is: -- -- <NF> ::= "λ" <VAR> "." <NF> | <NE> -- <NE> ::= <NE> <NF> | <VAR> -- -- I implemented this grammar as a judgment on untyped lambda terms -- with the datatypes `lambda.untyped.norm` and `lambda.untyped.neut`. -- Proof that NF and NE don't allow further derivation -- This proof as well as the reciprocical were quite mechanized but still -- a bit cumbersome. nf-last : ∀ {n} → {x : term n} → norm x → ¬ ∃[ y ] (x →β y) ne-last : ∀ {n} → {x : term n} → neut x → ¬ ∃[ y ] (x →β y) nf-last (lam x) (lam y , β-lam p) = nf-last x (y , p) nf-last (gnd x) (lam y , p) = ne-last x (lam y , p) nf-last (gnd x) (var i , p) = ne-last x (var i , p) nf-last (gnd x) (app a b , p) = ne-last x (app a b , p) ne-last var (y , ()) ne-last (app () y) (_ , β-beta) ne-last (app x y) (app a b , β-app₁ p) = ne-last x (a , p) ne-last (app x y) (app a b , β-app₂ p) = nf-last y (b , p) -- Proof that terms with no further derivation are in NF last-nf : ∀ {n} → (x : term n) → ¬ ∃[ y ] (x →β y) → norm x last-ne : ∀ {n y} → (x : term n) → ¬ ∃[ z ] (app x y →β z) → neut x last-nf (lam x) p = lam (last-nf x λ { (y , p₂) → p (lam y , β-lam p₂) }) last-nf (var x) p = gnd var last-nf (app x y) p = gnd (app (last-ne x λ { (z , p₁) → p (z , p₁) }) (last-nf y λ { (a , b) → p (app x a , β-app₂ b) })) last-ne {y = y} (lam x) p with p (subst₁ x y , β-beta) ... | () last-ne (var x) p = var last-ne {y = y} (app x z) p = app (last-ne x λ { (a , b) → p (app a y , β-app₁ b) }) (last-nf z λ { (a , b) → p (app (app x a) y , (β-app₁ (β-app₂ b))) }) const : ∀ {n} → contextD n const {zero} = ε const {suc n} = const ▸ base 0 -- Again because i messed up the renaming/substitution on ⊢D terms, i -- did not get to formalize the typing properly here. type-n : ∀ {n} → {x : term n} → norm x → ∃ (λ Γ → ∃ (λ T → Γ ⊢D x ∶ T)) type-e : ∀ {n} → {x : term n} → neut x → ∃ (λ Γ → ∃ (λ T → Γ ⊢D x ∶ T)) -- Here we compute inductively on the subterm, then "unload" the top of -- the context A and the result type B into the type A ⇒ B. type-n (lam x) = {! !} type-n (gnd x) = type-e x -- Here we create a context with fresh base types, assigning the matching -- one to the term. type-e (var {i}) = {! !} -- Here we compute inductively on both subterms: -- Γx ⊢D x ∶ Tx Γy ⊢D y ∶ Ty -- x is a neutral term so it has a type looking like -- T ⇒ A₁ ∧ T ⇒ A₁ ⇒ A₂ ∧ … -- We then simply extend it with An = Ty. This requires some proof -- rewriting with ∧ᵉ*. type-e (app x y) = {! !} -- Question 5 -- a) The definition of the conjunction in system F is: -- conjⁱ : Γ ⊢F x ∶ A → Γ ⊢F y ∶ B → Γ ⊢F (x , y) ∶ A ∧F B -- conjᵉʳ : Γ ⊢F x ∶ A ∧F B → Γ ⊢F π₀ x ∶ A -- conjᵉˡ : Γ ⊢F x : A ∧F B → Γ ⊢F π₁ x ∶ B -- The difference is that in system D, the conjunction is more of -- an intersection: if a single term has 2 type judgements, then -- it has a judgment for the intersection, whereas for system F -- it is a couple of 2 different terms.
//================================================================================================== /*! @file @copyright 2016 J.T.Lapreste Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt) */ //================================================================================================== #ifndef BOOST_SIMD_FUNCTION_DIV_INCLUDED #define BOOST_SIMD_FUNCTION_DIV_INCLUDED #if defined(DOXYGEN_ONLY) namespace boost { namespace simd { /*! @ingroup group-operator Perform the quotient of two parameters of the same type with or without options. @par Semantic For any value @c a and @c b of type @c T, @code T r = div(a, b{, option}); @endcode returns the quotient of @c a by @c b according to the option if there is no option the call is equivalent to divides(a, b), else option can be ceil, floor, fix, round, round2even (in the namespace booost::simd) and provide the same result as the calls divceil(a, b), divfloor(a, b), divfix(a, b), divround(a, b). @param a First parameter of the quotient @param b Second parameter of the quotient @param option is the option @return The quotient of the two parameters. **/ template<typename T> auto div(T const& a, T const& b); namespace functional { /*! @ingroup group-callable-operator Perform the quotient of two parameters of the same type. Function object tied to boost::simd::div @see boost::simd::div **/ const boost::dispatch::functor<tag::div_> div = {}; } } } #endif #include <boost/simd/function/scalar/div.hpp> #endif
""" periodic_porous script. """ import numpy as np from generate_mesh import MESHES_DIR, store_mesh_HDF5, line_points, \ rad_points, round_trip_connect, numpy_to_dolfin from utilities.plot import plot_edges, plot_faces from meshpy import triangle as tri from common import info import os import dolfin as df import matplotlib.pyplot as plt def description(**kwargs): info("") def method(Lx=6., Ly=4., Lx_inner=4., num_obstacles=32, rad=0.2, R=0.3, dx=0.05, seed=121, show=False, **kwargs): N = int(np.ceil(Lx/dx)) x_min, x_max = -Lx/2, Lx/2 y_min, y_max = -Ly/2, Ly/2 y = np.linspace(y_min, y_max, N).flatten() pts = np.zeros((num_obstacles, 2)) diam2 = 4*R**2 np.random.seed(seed) for i in range(num_obstacles): while True: pt = (np.random.rand(2)-0.5) * np.array([Lx_inner, Ly]) if i == 0: break dist = pts[:i, :] - np.outer(np.ones(i), pt) for j in range(len(dist)): if abs(dist[j, 1]) > Ly/2: dist[j, 1] = abs(dist[j, 1])-Ly dist2 = dist[:, 0]**2 + dist[:, 1]**2 if all(dist2 > diam2): break pts[i, :] = pt pts = pts[pts[:, 0].argsort(), :] obstacles = [tuple(row) for row in pts] line_segments_top = [] line_segments_btm = [] x_prev = x_min curve_segments_top = [] curve_segments_btm = [] interior_obstacles = [] exterior_obstacles = [] for x_c in obstacles: # Close to the top of the domain if x_c[1] > y_max-rad: # identify intersection theta = np.arcsin((y_max-x_c[1])/rad) rx = rad*np.cos(theta) x_left = x_c[0]-rx x_right = x_c[0]+rx line_segments_top.append(line_points((x_prev, y_max), (x_left, y_max), dx)) line_segments_btm.append(line_points((x_prev, y_min), (x_left, y_min), dx)) curve_btm = rad_points((x_c[0], x_c[1]-Ly), rad, dx, theta_start=np.pi-theta, theta_stop=theta)[1:-1] curve_top = rad_points(x_c, rad, dx, theta_start=np.pi-theta, theta_stop=2*np.pi+theta)[1:-1] curve_segments_btm.append(curve_btm) curve_segments_top.append(curve_top) x_prev = x_right exterior_obstacles.append(x_c) exterior_obstacles.append((x_c[0], x_c[1]-Ly)) # Close to the bottom of the domain elif x_c[1] < y_min+rad: # identify intersection theta = np.arcsin((-y_min+x_c[1])/rad) rx = rad*np.cos(theta) x_left = x_c[0]-rx x_right = x_c[0]+rx line_segments_top.append(line_points((x_prev, y_max), (x_left, y_max), dx)) line_segments_btm.append(line_points((x_prev, y_min), (x_left, y_min), dx)) curve_btm = rad_points(x_c, rad, dx, theta_start=np.pi+theta, theta_stop=-theta)[1:-1] curve_top = rad_points((x_c[0], x_c[1]+Ly), rad, dx, theta_start=np.pi+theta, theta_stop=2*np.pi-theta)[1:-1] curve_segments_btm.append(curve_btm) curve_segments_top.append(curve_top) x_prev = x_right exterior_obstacles.append(x_c) exterior_obstacles.append((x_c[0], x_c[1]+Ly)) else: interior_obstacles.append(x_c) line_segments_top.append(line_points((x_prev, y_max), (x_max, y_max), dx)) line_segments_btm.append(line_points((x_prev, y_min), (x_max, y_min), dx)) assert(len(line_segments_top) == len(curve_segments_top)+1) assert(len(line_segments_btm) == len(curve_segments_btm)+1) pts_top = list(line_segments_top[0]) for i in range(len(curve_segments_top)): pts_top.extend(curve_segments_top[i]) pts_top.extend(line_segments_top[i+1]) pts_top = pts_top[::-1] pts_btm = list(line_segments_btm[0]) for i in range(len(curve_segments_btm)): pts_btm.extend(curve_segments_btm[i]) pts_btm.extend(line_segments_btm[i+1]) y_side = y[1:-1] pts_right = list(zip(x_max*np.ones(N-2), y_side)) pts_left = list(zip(x_min*np.ones(N-2), y_side[::-1])) pts = pts_btm + pts_right + pts_top + pts_left edges = round_trip_connect(0, len(pts)-1) for interior_obstacle in interior_obstacles: pts_obstacle = rad_points(interior_obstacle, rad, dx)[1:] edges_obstacle = round_trip_connect(len(pts), len(pts)+len(pts_obstacle)-1) pts.extend(pts_obstacle) edges.extend(edges_obstacle) if show: plot_edges(pts, edges) mi = tri.MeshInfo() mi.set_points(pts) mi.set_facets(edges) mi.set_holes(interior_obstacles) max_area = 0.5*dx**2 mesh = tri.build(mi, max_volume=max_area, min_angle=25, allow_boundary_steiner=False) coords = np.array(mesh.points) faces = np.array(mesh.elements) # pp = [tuple(point) for point in mesh.points] # print "Number of points:", len(pp) # print "Number unique points:", len(set(pp)) if show: plot_faces(coords, faces) msh = numpy_to_dolfin(coords, faces) mesh_path = os.path.join( MESHES_DIR, "periodic_porous_Lx{}_Ly{}_rad{}_N{}_dx{}".format( Lx, Ly, rad, num_obstacles, dx)) store_mesh_HDF5(msh, mesh_path) obstacles_path = os.path.join( MESHES_DIR, "periodic_porous_Lx{}_Ly{}_rad{}_N{}_dx{}.dat".format( Lx, Ly, rad, num_obstacles, dx)) if len(exterior_obstacles) > 0 and len(interior_obstacles) > 0: all_obstacles = np.vstack((np.array(exterior_obstacles), np.array(interior_obstacles))) elif len(exterior_obstacles) > 0: all_obstacles = np.array(exterior_obstacles) else: all_obstacles = np.array(interior_obstacles) np.savetxt(obstacles_path, np.hstack((all_obstacles, np.ones((len(all_obstacles), 1))*rad))) if show: df.plot(msh) plt.show()
/- CONJUNCTION -/ variable (p q : Prop) -- `and.intro h1 h2` builds proof of `p ∧ q` using proofs `h1 : p` and `h2 : p` -- is described as the AND-INTRODUCTION rule\ example (hp : p) (hq : q) : p ∧ q := And.intro hp hq #check fun (hp : p) (hq : q) => And.intro hp hq -- `example` command states a theorem w/o naming or storing permanently - convinient for illustration /-left and right AND-ELIMINATION rules-/ -- `and.left h` creates proof of `p` from proof `h : p ∧ q` -- `and.right h` is proof of `q` example (h : p ∧ q) : p := And.left h example (h : p ∧ q) : q := And.right h example (h : p ∧ q) : q ∧ p := And.intro (And.right h) (And.left h) -- note: and-introduction and end-elimination are similar to pairing and projection operations for cartesian product. -- difference is given `hp : p` and `hq : q`: -- `And.intro hp hq` has type `p ∧ q : Prop` -- `Prod hp hq` has type `p × q : Type` -- similarity between ∧ and × is another instance of the Curry-Howard isomorphism tho treated separatedly in Lean. -- certain types in lean are STRUCTURES: defined w single conanical CONSTRUCTOR which builds an element of the type from a sequence of suitable arguments -- ie. For every `p q : Prop`, `p ∧ q` is an example -- canonical way to construct is to apply `And.intro` to suitable args `hp : p` amd `hq : q` -- lean lets us use anonymous constructor notation notation `⟨arg1, arg2, ...⟩` when relevant type is inductive type and can be inferred from context -- in particular, can often write `⟨hp, hq⟩` instead of `And.intro hp hq` variable (hp : p) (hq : q) #check (⟨hp, hq⟩ : p ∧ q) -- thus given shorthand syntax, can rewrite as variable (p q : Prop) example (h : p ∧ q) : q ∧ p := ⟨h.right, h.left⟩ 3
Formal statement is: lemma real_lim: fixes l::complex assumes "(f \<longlongrightarrow> l) F" and "\<not> trivial_limit F" and "eventually P F" and "\<And>a. P a \<Longrightarrow> f a \<in> \<real>" shows "l \<in> \<real>" Informal statement is: If $f$ converges to $l$ and $f$ is eventually real, then $l$ is real.
# Polynomials Some of the equations we've looked at so far include expressions that are actually *polynomials*; but what *is* a polynomial, and why should you care? A polynomial is an algebraic expression containing one or more *terms* that each meet some specific criteria. Specifically: - Each term can contain: - Numeric values that are coefficients or constants (for example 2, -5, <sup>1</sup>/<sub>7</sub>) - Variables (for example, x, y) - Non-negative integer exponents (for example <sup>2</sup>, <sup>64</sup>) - The terms can be combined using arithmetic operations - but **not** division by a variable. For example, the following expression is a polynomial: \begin{equation}12x^{3} + 2x - 16 \end{equation} When identifying the terms in a polynomial, it's important to correctly interpret the arithmetic addition and subtraction operators as the sign for the term that follows. For example, the polynomial above contains the following three terms: - 12x<sup>3</sup> - 2x - -16 The terms themselves include: - Two coefficients(12 and 2) and a constant (-16) - A variable (x) - An exponent (<sup>3</sup>) A polynomial that contains three terms is also known as a *trinomial*. Similarly, a polynomial with two terms is known as a *binomial* and a polynomial with only one term is known as a *monomial*. So why do we care? Well, polynomials have some useful properties that make them easy to work with. for example, if you multiply, add, or subtract a polynomial, the result is always another polynomial. ## Standard Form for Polynomials Techbnically, you can write the terms of a polynomial in any order; but the *standard form* for a polynomial is to start with the highest *degree* first and constants last. The degree of a term is the highest order (exponent) in the term, and the highest order in a polynomial determines the degree of the polynomial itself. For example, consider the following expression: \begin{equation}3x + 4xy^{2} - 3 + x^{3} \end{equation} To express this as a polynomial in the standard form, we need to re-order the terms like this: \begin{equation}x^{3} + 4xy^{2} + 3x - 3 \end{equation} ## Simplifying Polynomials We saw previously how you can simplify an equation by combining *like terms*. You can simplify polynomials in the same way. For example, look at the following polynomial: \begin{equation}x^{3} + 2x^{3} - 3x - x + 8 - 3 \end{equation} In this case, we can combine x<sup>3</sup> and 2x<sup>3</sup> by adding them to make 3x<sup>3</sup>. Then we can add -3x and -x (which is really just a shorthand way to say -1x) to get -4x, and then add 8 and -3 to get 5. Our simplified polynomial then looks like this: \begin{equation}3x^{3} - 4x + 5 \end{equation} We can use Python to compare the original and simplified polynomials to check them - using an arbitrary random value for ***x***: ```python from random import randint x = randint(1,100) (x**3 + 2*x**3 - 3*x - x + 8 - 3) == (3*x**3 - 4*x + 5) ``` True ## Adding Polynomials When you add two polynomials, the result is a polynomial. Here's an example: \begin{equation}(3x^{3} - 4x + 5) + (2x^{3} + 3x^{2} - 2x + 2) \end{equation} because this is an addition operation, you can simply add all of the like terms from both polynomials. To make this clear, let's first put the like terms together: \begin{equation}3x^{3} + 2x^{3} + 3x^{2} - 4x -2x + 5 + 2 \end{equation} This simplifies to: \begin{equation}5x^{3} + 3x^{2} - 6x + 7 \end{equation} We can verify this with Python: ```python from random import randint x = randint(1,100) (3*x**3 - 4*x + 5) + (2*x**3 + 3*x**2 - 2*x + 2) == 5*x**3 + 3*x**2 - 6*x + 7 ``` True ## Subtracting Polynomials Subtracting polynomials is similar to adding them but you need to take into account that one of the polynomials is a negative. Consider this expression: \begin{equation}(2x^{2} - 4x + 5) - (x^{2} - 2x + 2) \end{equation} The key to performing this calculation is to realize that the subtraction of the second polynomial is really an expression that adds -1(x<sup>2</sup> - 2x + 2); so you can use the distributive property to multiply each of the terms in the polynomial by -1 (which in effect simply reverses the sign for each term). So our expression becomes: \begin{equation}(2x^{2} - 4x + 5) + (-x^{2} + 2x - 2) \end{equation} Which we can solve as an addition problem. First place the like terms together: \begin{equation}2x^{2} + -x^{2} + -4x + 2x + 5 + -2 \end{equation} Which simplifies to: \begin{equation}x^{2} - 2x + 3 \end{equation} Let's check that with Python: ```python from random import randint x = randint(1,100) (2*x**2 - 4*x + 5) - (x**2 - 2*x + 2) == x**2 - 2*x + 3 ``` True ## Multiplying Polynomials To multiply two polynomials, you need to perform the following two steps: 1. Multiply each term in the first polynomial by each term in the second polynomial. 2. Add the results of the multiplication operations, combining like terms where possible. For example, consider this expression: \begin{equation}(x^{4} + 2)(2x^{2} + 3x - 3) \end{equation} Let's do the first step and multiply each term in the first polynomial by each term in the second polynomial. The first term in the first polynomial is x<sup>4</sup>, and the first term in the second polynomial is 2x<sup>2</sup>, so multiplying these gives us 2x<sup>6</sup>. Then we can multiply the first term in the first polynomial (x<sup>4</sup>) by the second term in the second polynomial (3x), which gives us 3x<sup>5</sup>, and so on until we've multipled all of the terms in the first polynomial by all of the terms in the second polynomial, which results in this: \begin{equation}2x^{6} + 3x^{5} - 3x^{4} + 4x^{2} + 6x - 6 \end{equation} We can verify a match between this result and the original expression this with the following Python code: ```python from random import randint x = randint(1,100) (x**4 + 2)*(2*x**2 + 3*x - 3) == 2*x**6 + 3*x**5 - 3*x**4 + 4*x**2 + 6*x - 6 ``` True ## Dividing Polynomials When you need to divide one polynomial by another, there are two approaches you can take depending on the number of terms in the divisor (the expression you're dividing by). ### Dividing Polynomials Using Simplification In the simplest case, division of a polynomial by a monomial, the operation is really just simplification of a fraction. For example, consider the following expression: \begin{equation}(4x + 6x^{2}) \div 2x \end{equation} This can also be written as: \begin{equation}\frac{4x + 6x^{2}}{2x} \end{equation} One approach to simplifying this fraction is to split it it into a separate fraction for each term in the dividend (the expression we're dividing), like this: \begin{equation}\frac{4x}{2x} + \frac{6x^{2}}{2x}\end{equation} Then we can simplify each fraction and add the results. For the first fraction, 2x goes into 4x twice, so the fraction simplifies to 2; and for the second, 6x<sup>2</sup> is 2x mutliplied by 3x. So our answer is 2 + 3x: \begin{equation}2 + 3x\end{equation} Let's use Python to compare the original fraction with the simplified result for an arbitrary value of ***x***: ```python from random import randint x = randint(1,100) (4*x + 6*x**2) / (2*x) == 2 + 3*x ``` True ### Dividing Polynomials Using Long Division Things get a little more complicated for divisors with more than one term. Suppose we have the following expression: \begin{equation}(x^{2} + 2x - 3) \div (x - 2) \end{equation} Another way of writing this is to use the long-division format, like this: \begin{equation} x - 2 |\overline{x^{2} + 2x - 3} \end{equation} We begin long-division by dividing the highest order divisor into the highest order dividend - so in this case we divide x into x<sup>2</sup>. X goes into x<sup>2</sup> x times, so we put an x on top and then multiply it through the divisor: \begin{equation} \;\;\;\;x \end{equation} \begin{equation}x - 2 |\overline{x^{2} + 2x - 3} \end{equation} \begin{equation} \;x^{2} -2x \end{equation} Now we'll subtract the remaining dividend, and then carry down the -3 that we haven't used to see what's left: \begin{equation} \;\;\;\;x \end{equation} \begin{equation}x - 2 |\overline{x^{2} + 2x - 3} \end{equation} \begin{equation}- (x^{2} -2x) \end{equation} \begin{equation}\;\;\;\;\;\overline{\;\;\;\;\;\;\;\;\;\;4x -3} \end{equation} OK, now we'll divide our highest order divisor into the highest order of the remaining dividend. In this case, x goes into 4x four times, so we'll add a 4 to the top line, multiply it through the divisor, and subtract the remaining dividend: \begin{equation} \;\;\;\;\;\;\;\;x + 4 \end{equation} \begin{equation}x - 2 |\overline{x^{2} + 2x - 3} \end{equation} \begin{equation}- (x^{2} -2x) \end{equation} \begin{equation}\;\;\;\;\;\overline{\;\;\;\;\;\;\;\;\;\;4x -3} \end{equation} \begin{equation}- (\;\;\;\;\;\;\;\;\;\;\;\;4x -8) \end{equation} \begin{equation}\;\;\;\;\;\overline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;5} \end{equation} We're now left with just 5, which we can't divide further by x - 2; so that's our remainder, which we'll add as a fraction. The solution to our division problem is: \begin{equation}x + 4 + \frac{5}{x-2} \end{equation} Once again, we can use Python to check our answer: ```python from random import randint x = randint(3,100) (x**2 + 2*x -3)/(x-2) == x + 4 + (5/(x-2)) ``` True ```python ```
# Copyright (c) Microsoft Corporation. All rights reserved. # Licensed under the MIT License. from numba import cuda from numba.cuda.cudadrv.error import CudaSupportError def get_number_gpus(): """Get the number of GPUs in the system. Returns: int: Number of GPUs. """ try: return len(cuda.gpus) except CudaSupportError: return 0 def clear_memory_all_gpus(): """Clear memory of all GPUs. """ try: for gpu in cuda.gpus: with gpu: cuda.current_context().deallocations.clear() except CudaSupportError: print("No CUDA available")
If $p$ is a prime number, then $p^k$ is an $n$th power if and only if $n$ divides $k$.
module Test.Parser import Test.Assertions import Idrlisp.Sexp import Idrlisp.Parser %default covering export test : IO () test = describe "Idrlisp.Parser" $ do describe "parseToEnd" $ do let parseSyn = parseToEnd {ty = SSyn ()} parseSyn "123" `shouldBe` Right (Num 123) parseSyn " \n\t ; comment \n 3.14 " `shouldBe` Right (Num 3.14) parseSyn "*foo-bar+baz" `shouldBe` Right (Sym "*foo-bar+baz") parseSyn (show "Hello, World!\n") `shouldBe` Right (Str "Hello, World!\n") parseSyn "()" `shouldBe` Right Nil parseSyn "(#t)" `shouldBe` Right (App [Bool True]) parseSyn "(#t #f)" `shouldBe` Right (App [Bool True, Bool False]) parseSyn "(#t #f . 0)" `shouldBe` Right ([Bool True, Bool False] :.: Num 0) parseSyn "(#t #f . 0 1)" `shouldSatisfy` isLeft parseSyn "(foo [bar baz])" `shouldBe` Right (App [Sym "foo", App [Sym "bar", Sym "baz"]]) parseSyn "`(foo ,bar ,@(hoge 'fuga))" `shouldBe` Right (Quasiquote (App [Sym "foo", Unquote (Sym "bar"), UnquoteSplicing (App [Sym "hoge", Quote (Sym "fuga")])])) parseToEnd {ty = List (SSyn ())} "123 () foo ; test \n \"bar\"" `shouldBe` Right [Num 123.0, Nil, Sym "foo", Str "bar"]
Require Import Crypto.Specific.Framework.RawCurveParameters. Require Import Crypto.Util.LetIn. (*** Modulus : 2^213 - 3 Base: 32 ***) Definition curve : CurveParameters := {| sz := 7%nat; base := 32; bitwidth := 32; s := 2^213; c := [(1, 3)]; carry_chains := None; a24 := None; coef_div_modulus := None; goldilocks := None; karatsuba := None; montgomery := true; freeze := Some false; ladderstep := false; mul_code := None; square_code := None; upper_bound_of_exponent_loose := None; upper_bound_of_exponent_tight := None; allowable_bit_widths := None; freeze_extra_allowable_bit_widths := None; modinv_fuel := None |}. Ltac extra_prove_mul_eq _ := idtac. Ltac extra_prove_square_eq _ := idtac.
[STATEMENT] lemma (in group) pow_int_mod_ord: assumes [simp]:"a \<in> carrier G" "ord a \<noteq> 0" shows "a [^] (n::int) = a [^] (n mod ord a)" [PROOF STATE] proof (prove) goal (1 subgoal): 1. a [^] n = a [^] (n mod int (ord a)) [PROOF STEP] proof - [PROOF STATE] proof (state) goal (1 subgoal): 1. a [^] n = a [^] (n mod int (ord a)) [PROOF STEP] obtain q r where d: "q = n div ord a" "r = n mod ord a" "n = q * ord a + r" [PROOF STATE] proof (prove) goal (1 subgoal): 1. (\<And>q r. \<lbrakk>q = n div int (ord a); r = n mod int (ord a); n = q * int (ord a) + r\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis [PROOF STEP] using mod_div_decomp [PROOF STATE] proof (prove) using this: (\<And>q r. \<lbrakk>q = ?a div ?b; r = ?a mod ?b; ?a = q * ?b + r\<rbrakk> \<Longrightarrow> ?thesis) \<Longrightarrow> ?thesis goal (1 subgoal): 1. (\<And>q r. \<lbrakk>q = n div int (ord a); r = n mod int (ord a); n = q * int (ord a) + r\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis [PROOF STEP] by blast [PROOF STATE] proof (state) this: q = n div int (ord a) r = n mod int (ord a) n = q * int (ord a) + r goal (1 subgoal): 1. a [^] n = a [^] (n mod int (ord a)) [PROOF STEP] hence "a [^] n = (a [^] int (ord a)) [^] q \<otimes> a [^] r" [PROOF STATE] proof (prove) using this: q = n div int (ord a) r = n mod int (ord a) n = q * int (ord a) + r goal (1 subgoal): 1. a [^] n = (a [^] int (ord a)) [^] q \<otimes> a [^] r [PROOF STEP] using assms(1) int_pow_mult int_pow_pow [PROOF STATE] proof (prove) using this: q = n div int (ord a) r = n mod int (ord a) n = q * int (ord a) + r a \<in> carrier G ?x \<in> carrier G \<Longrightarrow> ?x [^] (?i + ?j) = ?x [^] ?i \<otimes> ?x [^] ?j ?x \<in> carrier G \<Longrightarrow> (?x [^] ?n) [^] ?m = ?x [^] (?n * ?m) goal (1 subgoal): 1. a [^] n = (a [^] int (ord a)) [^] q \<otimes> a [^] r [PROOF STEP] by (metis mult_of_nat_commute) [PROOF STATE] proof (state) this: a [^] n = (a [^] int (ord a)) [^] q \<otimes> a [^] r goal (1 subgoal): 1. a [^] n = a [^] (n mod int (ord a)) [PROOF STEP] also [PROOF STATE] proof (state) this: a [^] n = (a [^] int (ord a)) [^] q \<otimes> a [^] r goal (1 subgoal): 1. a [^] n = a [^] (n mod int (ord a)) [PROOF STEP] have "\<dots> = \<one> [^] q \<otimes> a [^] r" [PROOF STATE] proof (prove) goal (1 subgoal): 1. (a [^] int (ord a)) [^] q \<otimes> a [^] r = \<one> [^] q \<otimes> a [^] r [PROOF STEP] by (simp add: int_pow_int) [PROOF STATE] proof (state) this: (a [^] int (ord a)) [^] q \<otimes> a [^] r = \<one> [^] q \<otimes> a [^] r goal (1 subgoal): 1. a [^] n = a [^] (n mod int (ord a)) [PROOF STEP] also [PROOF STATE] proof (state) this: (a [^] int (ord a)) [^] q \<otimes> a [^] r = \<one> [^] q \<otimes> a [^] r goal (1 subgoal): 1. a [^] n = a [^] (n mod int (ord a)) [PROOF STEP] have "\<dots> = a [^] r" [PROOF STATE] proof (prove) goal (1 subgoal): 1. \<one> [^] q \<otimes> a [^] r = a [^] r [PROOF STEP] by simp [PROOF STATE] proof (state) this: \<one> [^] q \<otimes> a [^] r = a [^] r goal (1 subgoal): 1. a [^] n = a [^] (n mod int (ord a)) [PROOF STEP] finally [PROOF STATE] proof (chain) picking this: a [^] n = a [^] r [PROOF STEP] show ?thesis [PROOF STATE] proof (prove) using this: a [^] n = a [^] r goal (1 subgoal): 1. a [^] n = a [^] (n mod int (ord a)) [PROOF STEP] using d(2) [PROOF STATE] proof (prove) using this: a [^] n = a [^] r r = n mod int (ord a) goal (1 subgoal): 1. a [^] n = a [^] (n mod int (ord a)) [PROOF STEP] by blast [PROOF STATE] proof (state) this: a [^] n = a [^] (n mod int (ord a)) goal: No subgoals! [PROOF STEP] qed
chapter \<open>Names as a unique datatype\<close> theory Name imports Main begin text \<open> I would like to model names as @{typ string}s. Unfortunately, there is no default order on lists, as there could be multiple reasonable implementations: e.g.\ lexicographic and point-wise. For both choices, users can import the corresponding instantiation. In Isabelle, only at most one implementation of a given type class for a given type may be present in the same theory. Consequently, I avoided importing a list ordering from the library, because it may cause conflicts with users who use another ordering. The general approach for these situations is to introduce a type copy. The full flexibility of strings (i.e.\ string manipulations) is only required where fresh names are being produced. Otherwise, only a linear order on terms is needed. Conveniently, Sternagel and Thiemann @{cite sternagel2015deriving} provide tooling to automatically generate such a lexicographic order. \<close> datatype name = Name (as_string: string) \<comment> \<open>Mostly copied from \<open>List_Lexorder\<close>\<close> instantiation name :: ord begin definition less_name where "xs < ys \<longleftrightarrow> (as_string xs, as_string ys) \<in> lexord {(u, v). (of_char u :: nat) < of_char v}" definition less_eq_name where "(xs :: name) \<le> ys \<longleftrightarrow> xs < ys \<or> xs = ys" instance .. end instance name :: order proof fix xs :: "name" show "xs \<le> xs" by (simp add: less_eq_name_def) next fix xs ys zs :: "name" assume "xs \<le> ys" and "ys \<le> zs" then show "xs \<le> zs" apply (auto simp add: less_eq_name_def less_name_def) apply (rule lexord_trans) apply (auto intro: transI) done next fix xs ys :: "name" assume "xs \<le> ys" and "ys \<le> xs" then show "xs = ys" apply (auto simp add: less_eq_name_def less_name_def) apply (rule lexord_irreflexive [THEN notE]) defer apply (rule lexord_trans) apply (auto intro: transI) done next fix xs ys :: "name" show "xs < ys \<longleftrightarrow> xs \<le> ys \<and> \<not> ys \<le> xs" apply (auto simp add: less_name_def less_eq_name_def) defer apply (rule lexord_irreflexive [THEN notE]) apply auto apply (rule lexord_irreflexive [THEN notE]) defer apply (rule lexord_trans) apply (auto intro: transI) done qed instance name :: linorder proof fix xs ys :: "name" have "(as_string xs, as_string ys) \<in> lexord {(u, v). (of_char u::nat) < of_char v} \<or> xs = ys \<or> (as_string ys, as_string xs) \<in> lexord {(u, v). (of_char u::nat) < of_char v}" by (metis (no_types, lifting) case_prodI lexord_linear linorder_neqE_nat mem_Collect_eq name.expand of_char_eq_iff) then show "xs \<le> ys \<or> ys \<le> xs" by (auto simp add: less_eq_name_def less_name_def) qed lemma less_name_code[code]: "Name xs < Name [] \<longleftrightarrow> False" "Name [] < Name (x # xs) \<longleftrightarrow> True" "Name (x # xs) < Name (y # ys) \<longleftrightarrow> (of_char x::nat) < of_char y \<or> x = y \<and> Name xs < Name ys" unfolding less_name_def by auto lemma le_name_code[code]: "Name (x # xs) \<le> Name [] \<longleftrightarrow> False" "Name [] \<le> Name (x # xs) \<longleftrightarrow> True" "Name (x # xs) \<le> Name (y # ys) \<longleftrightarrow> (of_char x::nat) < of_char y \<or> x = y \<and> Name xs \<le> Name ys" unfolding less_eq_name_def less_name_def by auto context begin qualified definition append :: "name \<Rightarrow> name \<Rightarrow> name" where "append v1 v2 = Name (as_string v1 @ as_string v2)" lemma name_append_less: assumes "xs \<noteq> Name []" shows "append ys xs > ys" proof - have "Name (ys @ xs) > Name ys" if "xs \<noteq> []" for xs ys using that proof (induction ys) case Nil thus ?case unfolding less_name_def by (cases xs) auto next case (Cons y ys) thus ?case unfolding less_name_def by auto qed with assms show ?thesis unfolding append_def by (cases xs, cases ys) auto qed end end
open import Common open import Global open import Projection open import Local open import Data.Fin open import Data.Product open import Data.Vec open import Relation.Binary.PropositionalEquality n = 4 Role = Fin n p : Role p = zero q : Role q = suc zero r : Role r = suc (suc zero) s : Role s = suc (suc (suc zero)) l : Label l = 0 l′ : Label l′ = 1 g₁ : Global n g₁ = msgSingle′ p q l endG lp : Local n lp = sendSingle q l endL g₁-proj-p-is-lp : project g₁ p ≡ lp g₁-proj-p-is-lp = refl lq : Local n lq = recvSingle p l endL g₁-proj-q-is-lq : project g₁ q ≡ lq g₁-proj-q-is-lq = refl p→q : Action n p→q = action′ p q l r→s : Action n r→s = action′ r s l′ g₂ : Global n g₂ = msgSingle′ r s l′ g₁ g₂′ : Global n g₂′ = msgSingle′ r s l′ endG g₁→end : g₁ - p→q →g endG g₁→end = →g-prefix g₂→g₁ : g₂ - r→s →g g₁ g₂→g₁ = →g-prefix g₂→g₂′ : g₂ - p→q →g g₂′ g₂→g₂′ = →g-cont g₁→end (λ ()) (λ ()) (λ ()) (λ ()) g₁-proj-p→end : (p , project g₁ p) - p→q →l (p , endL) g₁-proj-p→end = →l-send p refl λ () g₁-proj-q→end : (q , project g₁ q) - p→q →l (q , endL) g₁-proj-q→end = →l-recv q refl λ () g₂-proj-p→g₂′-proj-p : (p , project g₂ p) - p→q →l (p , project g₂′ p) g₂-proj-p→g₂′-proj-p = →l-send p refl λ () g₂-proj-q→g₂′-proj-q : (q , project g₂ q) - p→q →l (q , project g₂′ q) g₂-proj-q→g₂′-proj-q = →l-recv q refl λ () c₁ : Configuration n c₁ = lp ∷ lq ∷ endL ∷ endL ∷ [] cEnd : Configuration n cEnd = endL ∷ endL ∷ endL ∷ endL ∷ [] c₁→cEnd : c₁ - p→q →c cEnd c₁→cEnd = →c-comm c₁ (λ ()) refl refl refl g₁-proj-p→end g₁-proj-q→end g₁↔c₁ : g₁ ↔ c₁ g₁↔c₁ = record { isProj = refls } where refls : (p : Fin n) -> lookup c₁ p ≡ project g₁ p refls zero = refl refls (suc zero) = refl refls (suc (suc zero)) = refl refls (suc (suc (suc zero))) = refl
(* Title: HOL/Auth/n_german_on_ini.thy Author: Yongjian Li and Kaiqiang Duan, State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences Copyright 2016 State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences *) header{*The n_german Protocol Case Study*} theory n_german_on_ini imports n_german_base begin lemma iniImply_inv__1: assumes a1: "(f=inv__1 )" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__2: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__2 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__3: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__3 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__4: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__4 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__5: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__5 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__6: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__6 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__7: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__7 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__8: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__8 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__9: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__9 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__10: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__10 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__11: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__11 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__12: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__12 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__13: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__13 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__14: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__14 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__15: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__15 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__16: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__16 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__17: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__17 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__18: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__18 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__19: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__19 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__20: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__20 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__21: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__21 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__22: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__22 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__23: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__23 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__24: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__24 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__25: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__25 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__26: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__26 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__27: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__27 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__28: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__28 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__29: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__29 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__30: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__30 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__31: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__31 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__32: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__32 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__33: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__33 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__34: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__34 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__35: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__35 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__36: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__36 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__37: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__37 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__38: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__38 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__39: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__39 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__40: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__40 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__41: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__41 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__42: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__42 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__43: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__43 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__44: assumes a1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__44 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__45: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__45 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__46: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__46 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__47: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__47 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__48: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__48 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__49: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__49 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__50: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__50 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto lemma iniImply_inv__51: assumes a1: "(\<exists> p__Inv1 p__Inv2. p__Inv1\<le>N\<and>p__Inv2\<le>N\<and>p__Inv1~=p__Inv2\<and>f=inv__51 p__Inv1 p__Inv2)" and a2: "formEval (andList (allInitSpecs N)) s" shows "formEval f s" using a1 a2 by auto end
%% LyX 1.6.2 created this file. For more info, see http://www.lyx.org/. %% Do not edit unless you really know what you are doing. \documentclass[english]{article} \usepackage[T1]{fontenc} \usepackage[latin9]{inputenc} \usepackage{textcomp} \usepackage{relsize} \makeatletter %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands. \def\labnb{0} \usepackage{hyperref} \usepackage{ulem} \usepackage{latexsym} \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphics} \usepackage{lastpage} \usepackage{titling} \setlength{\droptitle}{-0.4in} \linespread{1.1} %%% HEADER \usepackage[head=32pt,top=1in,bottom=1in,left=1in,right=1in]{geometry} \usepackage{fancyhdr} \setlength{\headheight}{24pt} \pagestyle{fancy} \lhead{CE 191: CEE Systems Analysis \\ University of California, Berkeley} \rhead{Fall 2014 \\ Professor Scott Moura} \cfoot{Page \thepage\ of \pageref{LastPage}} \title{\Large Lab 2: Energy Portfolio Optimization} \author{Due: Friday 10/3 at 2:00pm} \date{} \renewcommand{\headrulewidth}{0.5pt} %\newcommand{\answer}[1]{\par\begin{center}\framebox{\parbox{5in}{{\bfseries \footnotesize Answer: }\textit{#1}}}\end{center}} \newcommand{\answer}[1]{} \newcommand{\inset}[2]{{\in\{{#1},\cdots,{#2}\} }} \newcounter{question} \setcounter{question}{1} \def\newquestion{\textbf{Question \arabic{section}.\arabic{question}\ \ }\stepcounter{question}} %\topmargin = -27 pt %\leftmargin = -0.5 in %\rightmargin= 1 in %\oddsidemargin = -0.10 in \textheight = 8.5 in \textwidth = 6.5in \setlength{\parindent}{0mm} \addtolength{\parskip}{0.5\baselineskip} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} \maketitle \thispagestyle{fancy} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Lab Overview} In this lab, you will learn to formulate a quadratic program to find a mix of energy supplies which minimizes the variability of the price of energy. Section \ref{sec:problem} provides a description of the full problem and the constraints. In Section \ref{sec:implementation}, you are asked to form the quadratic program, and implement it in MATLAB. Finally, in Section \ref{sec:addanalysis}, you will modify the quadratic program to analyze various scenarios. \textbf{Please remember to submit your MATLAB code (.m files in one ZIP file), and explain in the report how to run the code.} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Energy Portfolio Investment Problem}\label{sec:problem} The California Public Utilities Commission (CPUC) is charged with strategically planning its energy generation over the next several years to meet its growing energy demand. Currently, California generates 199 \textit{megawatt hours} (MWh) from a combination of eight sources. This collection, or mix, of energy sources is known as an \textit{energy portfolio}. The contributions of eight sources to California's current portfolio is listed in Table \ref{tbl:energymix}. \begin{table}[h] \caption{Current sources of energy to California, and percent contribution to the current energy mix. Source: \url{http://energyalmanac.ca.gov/electricity/total_system_power.html}} \begin{center} \begin{tabular}{|c || c|c|c|c|c|c|c|c|} \hline {\bfseries Source} & Coal & Hydro & Natural Gas & Nuclear & Biomass & Geo & Solar & Wind \\ \hline {\bfseries 2012 energy mix (\%)} & 7.5 & 8.3 & 43.4 & 9.0 & 2.3 & 4.4 & 0.9 & 6.3 \\ \hline \end{tabular} \end{center} \label{tbl:energymix} \end{table} By the year 2020, California must generate a peak of 225 MWh to meet its growing demand for energy. The expected price in 2020 in dollars per megawatt hour (USD/MWh) is given in Table 2. \begin{table}[h] \caption{Expected price of energy in California in the year 2020. Adopted from: Adopted from \url{http://www.eia.gov/forecasts/aeo/pdf/electricity_generation.pdf}} \begin{center} \begin{tabular}{|c || c|c|c|c|c|c|c|c|} \hline {\bfseries Source} & Coal & Hydro & Natural Gas & Nuclear & Biomass & Geo & Solar & Wind \\ \hline {\bfseries Expected Price (\$/MWh)} & 100 & 90 & 130 & 108 & 111 & 90 & 144 & 87 \\ \hline \end{tabular} \end{center} \label{tbl:energyprice} \end{table} Through technology improvements, California can expand its resources as required to meet future demands. However, the price of each energy source contains uncertainty. Namely, variations in fuel costs, technology development, and future environmental regulations in 2020 impose uncertainty on the expected prices listed in Table \ref{tbl:energyprice}. Suppose the standard deviation $\sigma$ of the prices for each source is given in Table \ref{tbl:std}\footnote{For simplicity, we are ignoring correlations in prices between sources.}. \begin{table}[h] \caption{Standard deviation of energy source prices in 2020.} \begin{center} \begin{tabular}{|c || c|c|c|c|c|c|c|c|} \hline {\bfseries Source} & Coal & Hydro & Natural Gas & Nuclear & Biomass & Geo & Solar & Wind \\ \hline {\bfseries $\sigma$ (\$/MWh)} & 22 & 30 & 15 & 20 & 30 & 36 & 32 & 40 \\ \hline \end{tabular} \end{center} \label{tbl:std} \end{table} The variance in price of an uncertain good (for example 1 MWh of electricity) can be used as a measure of the \textit{risk} of that good. Recall that variance is \begin{equation*} \textrm{var} = \sigma^{2}. \end{equation*} Portfolio theory assumes that for a given level of risk, planners prefer lower costs to higher ones. Conversely, for a given expected cost, planners prefer less risk to more risk. By combining various goods in a portfolio, it is possible to create a portfolio with lower risk than any of the goods individually. This is known as \textit{diversification}. The same concepts hold for stock market portfolios. To ensure competitive electricity rates, California must keep the expected cost of its energy portfolio under 100 USD/MWh. Therefore, California would like to determine an optimal energy portfolio. That is, determine the portfolio with the least risk for the given maximum expected cost. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Implementation}\label{sec:implementation} \begin{enumerate} \item Formulate a quadratic program (QP) that California can use to minimize the risk of obtaining its energy, while satisfying the maximum expected energy cost constraint described above. \begin{enumerate} \item Define your mathematical notation in a table. Be precise and organized. \item Using this notation, formulate (i) the objective function and (ii) all the constraints. \item Encode this formulation in matrices \texttt{Q, R, A, b}, where the QP is formulated as $\min \frac{1}{2} x^{T} Q x + R^{T} x$ subject to $A x \leq b$. Write down matrices \texttt{Q, R, A, b} in your report. \item Is the Hessian $Q$ positive definite, negative definite, positive semi-definite, negative semi-definite, or indefinite? Note: the answer would not be trivial if we assumed correlations exist between the standard deviations of energy prices. \end{enumerate} \item Solve the QP that you have formulated using MATLAB's \texttt{quadprog} command (read the documentation). In your report, provide \begin{itemize} \item the value of the objective function, i.e. the risk, \item the value of the decision variables at the optimum, \item a qualitative description the optimal solution, including the active constraints. \end{itemize} \end{enumerate} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Additional Analysis}\label{sec:addanalysis} The following questions study modifications to the original problem. Each question is independent from the other ones, i.e. the changes are not cumulative. Where applicable, provide (i) the objective function value, and (ii) the optimal decision variable values. \begin{enumerate} \setcounter{enumi}{2} \item A concerned and conservative member of the CPUC (yup, they went to Leland StanfUrd JR. University), who is not familiar with portfolio optimization suggests the safest plan is to apply the current energy portfolio mix (Table \ref{tbl:energymix}) to the year 2020. \textbf{Note:} The mix in Table 1 does not add to 100\%. In practice, California imports the remaining energy supply from out-of-state. Apply the same percentages to 2020 as 2012. The total energy supply will not add to 225 MWh. What is the expected risk and expected cost of this portfolio? Note this is a lower bound, because the remaining energy must be imported. Is there a safer (in the sense of less variance) portfolio with at least as small expected cost? Explain. \item The President of CPUC would like to know the minimal risk of each energy profile ranging in price 50 to 250 USD/MWh. Compute the minimal risk for each energy profile in this price range. \begin{enumerate} \item Summarize your results in a plot with max price [USD/MWh] on the $x-$axis and risk on the $y-$axis. Describe qualitatively the results. \item Describe qualitatively the mix of the lowest risk energy portfolio in this price range. How much does it cost? \end{enumerate} \textbf{Remark:} Ideally, one wishes to both minimize expected cost and minimize risk. This is a multi-objective optimization problem. However, you'll find there exists a tradeoff between these two objectives. To assess multiple objectives we often create the plot above. This is known as \textit{Pareto optimization}\footnote{\url{http://en.wikipedia.org/wiki/Multi-objective_optimization}}. \item By the year 2020, California must generate 225 MWh to meet its growing demand for energy. New information suggests that, due to resource limitations and future governmental regulations, the maximum energy supply of non-renewables sources in 2020 is constrained. The energy supply limits are given in Table \ref{tbl:limits}. Moreover, California has mandated a 33\% \textit{renewable portfolio standard} by 2020\footnote{\url{http://www.cpuc.ca.gov/PUC/energy/Renewables/index.htm}}, which includes wind, solar, biomass, and geothermal. Modify the original QP to include these additional constraints. \begin{enumerate} \item Formulate the appropriate constraints imposed by these limits, using the notation of Question 1. Describe any additional notation introduced. \item Solve the original QP with these additional constraints. How does the new solution compare with your results from Question 1? Which constraints are active? \end{enumerate} \begin{table}[h] \caption{Energy supply limits in 2020.} \begin{center} \begin{tabular}{|c || c|c|c|c|c|c|c|c|} \hline {\bfseries Source} & Coal & Hydro & Natural Gas & Nuclear & Biomass & Geo & Solar & Wind \\ \hline {\bfseries Limit (MWh)} & 40 & 50 & 150 & 35 & 10 & 15 & 200 & 50 \\ \hline \end{tabular} \end{center} \label{tbl:limits} \end{table} \end{enumerate} %%%%%%%%%%%%% \section*{Deliverables} Submit the following on bSpace. Zip your code. Be sure that the function files are named exactly as specified (including spelling and case), and make sure the function declaration is exactly as specified. \texttt{LASTNAME{\textunderscore}FIRSTNAME{\textunderscore}LAB2.PDF}\\ \texttt{LASTNAME{\textunderscore}FIRSTNAME{\textunderscore}LAB2.ZIP} which contains your respective Matlab files. \end{document}
function alpha_pq = moment_normalized ( n, x, y, p, q ) %*****************************************************************************80 % %% MOMENT_NORMALIZED computes a normalized moment of a polygon. % % Discussion: % % Alpha(P,Q) = Integral ( x, y in polygon ) x^p y^q dx dy / Area ( polygon ) % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 03 October 2012 % % Author: % % John Burkardt % % Reference: % % Carsten Steger, % On the calculation of arbitrary moments of polygons, % Technical Report FGBV-96-05, % Forschungsgruppe Bildverstehen, Informatik IX, % Technische Universitaet Muenchen, October 1996. % % Parameters: % % Input, integer N, the number of vertices of the polygon. % % Input, real X(N), Y(N), the vertex coordinates. % % Input, integer P, Q, the indices of the moment. % % Output, real ALPHA_PQ, the normalized moment Alpha(P,Q). % nu_pq = moment ( n, x, y, p, q ); nu_00 = moment ( n, x, y, 0, 0 ); alpha_pq = nu_pq / nu_00; return end
section \<open> Procedures \<close> theory ITree_Procedure imports ITree_Circus ITree_Hoare keywords "over" begin datatype (discs_sels) ('inp, 'outp) methop = Call_C 'inp | Return_C 'outp definition [lens_defs]: "Call = ctor_prism Call_C is_Call_C un_Call_C" definition [lens_defs]: "Return = ctor_prism Return_C (Not \<circ> is_Call_C) un_Return_C" record ('val, 'st) valst = vval :: 'val vst :: 'st type_synonym ('e, 'inp, 'outp, 'st) "procedure" = "('e, ('inp, 'st) valst, ('outp, 'st) valst) ktree" translations (type) "('e, 'inp, 'outp, 'st) procedure" <= (type) "('inp, 'st) valst \<Rightarrow> ('e, ('outp, 'st') valst) itree" definition procproc :: "(_, 'inp, 'outp, 'st::default) procedure \<Rightarrow> ('inp, 'outp) methop process" where "procproc P = process [\<leadsto>] (\<lambda> s. inp Call \<bind> (\<lambda> inp. P \<lparr> vval = inp, vst = s \<rparr> \<bind> (\<lambda> vst. outp Return (vval vst) \<bind> Ret)))" definition promote_proc :: "('e, 'inp, 'outp, 'ls) procedure \<Rightarrow> ('i \<Rightarrow> ('ls \<Longrightarrow> 's)) \<Rightarrow> ('e, 'i \<times> 'inp, 'outp, 's) procedure" where "promote_proc P a = (\<lambda> v. P \<lparr> vval = snd (vval v), vst = get\<^bsub>a (fst (vval v))\<^esub> (vst v) \<rparr> \<bind> (\<lambda> v'. Ret \<lparr> vval = vval v', vst = put\<^bsub>a (fst (vval v))\<^esub> (vst v) (vst v')\<rparr>))" lemma Call_wb_prism [simp, code_unfold]: "wb_prism Call" by (unfold_locales, auto simp add: lens_defs) lemma Return_wb_prism [simp, code_unfold]: "wb_prism Return" by (unfold_locales, auto simp add: lens_defs) definition "proc_ret e = (\<lambda> s. Ret \<lparr> vval = e s, vst = s \<rparr>)" definition "procedure" :: "('inp \<Rightarrow> 'st \<Rightarrow> ('e, ('outp, 'st) valst) itree) \<Rightarrow> ('e, 'inp, 'outp, 'st) procedure" where "procedure P = (\<lambda> vs. P (vval vs) (vst vs))" definition proc_call :: "('o \<Longrightarrow> 's) \<Rightarrow> ('e, 'i, 'o, 'ls::default) procedure \<Rightarrow> ('i, 's) expr \<Rightarrow> ('e, 's) htree" where "proc_call x P e = (\<lambda> s. P \<lparr> vval = e s, vst = default \<rparr> \<bind> (\<lambda> vs. Ret (put\<^bsub>x\<^esub> s (vval vs))))" definition exec_proc :: "(unit, 'inp, 'out, 'st::default) procedure \<Rightarrow> 'inp \<Rightarrow> (unit, 'out) itree" where "exec_proc P i = P \<lparr> vval = i, vst = default \<rparr> \<bind> (\<lambda> x. Ret (vval x))" syntax "_procedure" :: "pttrn \<Rightarrow> logic \<Rightarrow> logic" ("proc _./ _" [0, 20] 20) "_call" :: "svid \<Rightarrow> logic \<Rightarrow> logic \<Rightarrow> logic" ("_ := call _ _" [61, 0, 61] 61) "_return" :: "logic \<Rightarrow> logic" ("return") translations "_procedure x P" == "CONST procedure (\<lambda> x. P)" "_return e" == "CONST proc_ret (e)\<^sub>e" "_call x P e" == "CONST proc_call x P (e)\<^sub>e" ML_file \<open>ITree_Procedure.ML\<close> end
@init PyObject_TryConvert_AddRules("juliaaa.As", [ (Any, PyAs_ConvertRule_tryconvert), ]) PyAs_ConvertRule_tryconvert(o, ::Type{S}) where {S} = begin # get the type to = PyObject_GetAttrString(o, "type") isnull(to) && return -1 err = PyObject_Convert(to, Type) Py_DecRef(to) ism1(err) && return -1 t = takeresult(Type) # get the value vo = PyObject_GetAttrString(o, "value") isnull(vo) && return -1 err = PyObject_Convert(vo, t) Py_DecRef(vo) ism1(err) && return -1 v = takeresult(t) # convert putresult(tryconvert(S, v)) end
lemma netlimit_at_vector: fixes a :: "'a::real_normed_vector" shows "netlimit (at a) = a"
\section{Free Vibrations} \noindent Free damped vibrations, like in a massed spring system, are a common application of second order linear ODEs. In a massed spring system, there are three main forces acting on the mass that make up external forces. \begin{enumerate}[label=\arabic*)] \item Acceleration of The Mass -- Since acceleration is the 2nd derivative of position $y(t)$, and Newton's Second Law tells us that $F = ma$, the force from the acceleration of the mass is $my''$. \item Dampening -- We'll assume that this term is proportional to the velocity, $y'$, and a term $b$. So, the force from dampening is $by'$. \item Spring Stretch -- Hooke's Law tells us that the force from a spring is $ky$, where $k$ is some term that gives the spring's "stiffness" \end{enumerate} Since we assume that the net force is 0 (that's what free means), our equations is \begin{equation*} my'' + by' + ky = 0 \end{equation*} \noindent Extracting the coefficients and solving the auxiliary equation, \begin{equation*} mr^2 + br + k = 0 \implies r = \frac{-b \pm \sqrt{b^2 - 4mk}}{2m} \end{equation*} We will consider two cases. One in which there is no damping ($b = 0$), and one in which there is damping ($b > 0$). \input{./higherOrder/freeVibrs/freeUndamped.tex} \input{./higherOrder/freeVibrs/freeDamped.tex}
The CPS men objected to the mistreatment and abuse of patients and determined to improve conditions in the psychiatric wards . They wanted to show other attendants alternatives to violence when dealing with patients .
lemma restrict_space_sets_cong: "A = B \<Longrightarrow> sets M = sets N \<Longrightarrow> sets (restrict_space M A) = sets (restrict_space N B)"
# The Variational Quantum Eigensolver Algorithm ```python import numpy as np from VariationalForms import VariationalForms from qiskit import * from qiskit.visualization import * from qiskit.providers.aer import QasmSimulator, StatevectorSimulator, UnitarySimulator ``` ```python qasm_sim = QasmSimulator() state_sim = StatevectorSimulator() unit_sim = UnitarySimulator() vf = VariationalForms() ``` # Variational Forms ### Rotation Gates \begin{align} \mathbf{R_z(\theta) = e^{-i\frac{\theta}{2}\sigma_z}} \end{align} \begin{align} \mathbf{R_y(\phi) = e^{-i\frac{\phi}{2}\sigma_y}} \end{align} ## $R(\theta, \phi)$ $R(\theta, \phi)$ Rotation gate, where: $R(\theta, \phi) = $ ```python vf.draw(vf.R(0, 0)) ``` ```python vf.decompose(vf.R(0, 0)) ``` ## $R(\theta, \phi)^\dagger$ $R(\theta, \phi)^\dagger$ Rotation gate ```python vf.draw(vf.Rd(0, 0)) ``` ```python vf.decompose(vf.Rd(0, 0)) ``` ## $A(\theta, \phi)$ $A(\theta, \phi)$ 2 Qubit A gate. Preserves **Particle-Number Symmetry** and **Time-Reversal Symmetry** ```python vf.draw(vf.A(0, 0)) ``` ```python vf.decompose(vf.A(0, 0)) ``` ```python ``` Figure(748.797x204.68)
/- Copyright (c) 2018-2019 Minchao Wu. All rights reserved. Released under MIT license as described in the file LICENSE. Author: Minchao Wu -/ import defs data.list.perm .data open nnf tactic meta def frame_restriction : tactic unit := do intro `a >> `[simp] structure S4 (states : Type) extends kripke states := (refl : reflexive rel . frame_restriction) (trans : transitive rel . frame_restriction) instance inhabited_S4 : inhabited (S4 ℕ) := ⟨ { val := λ a b, tt, rel := λ a b, tt } ⟩ @[simp] def force {states : Type} (k : S4 states) : states → nnf → Prop | s (var n) := k.val n s | s (neg n) := ¬ k.val n s | s (and φ ψ) := force s φ ∧ force s ψ | s (or φ ψ) := force s φ ∨ force s ψ | s (box φ) := ∀ s', k.rel s s' → force s' φ | s (dia φ) := ∃ s', k.rel s s' ∧ force s' φ def sat {st} (k : S4 st) (s) (Γ : list nnf) : Prop := ∀ φ ∈ Γ, force k s φ def unsatisfiable (Γ : list nnf) : Prop := ∀ (st) (k : S4 st) s, ¬ sat k s Γ theorem unsat_singleton {φ} : unsatisfiable [φ] → ∀ (st) (k : S4 st) s, ¬ force k s φ := begin intros h _ _ _ hf, apply h, intros ψ hψ, rw list.mem_singleton at hψ, rw hψ, exact hf end theorem sat_of_empty {st} (k : S4 st) (s) : sat k s [] := λ φ h, absurd h $ list.not_mem_nil _ theorem ne_empty_of_unsat {Γ} (h : unsatisfiable Γ): Γ ≠ [] := begin intro heq, rw heq at h, apply h, apply sat_of_empty, exact nat, apply inhabited_S4.1, exact 0 end open tmodel @[simp] def minfo : Π m : tmodel, info | (cons i l ba) := i @[simp] def htk : Π m : tmodel, list nnf | (cons i l ba) := i.htk def hist : Π m : tmodel, list nnf | (cons i l ba) := i.id.h @[simp] def msig : Π m : tmodel, sig | (cons i l ba) := i.id.s @[simp] def manc : Π m : tmodel, list psig | (cons i l ba) := i.id.a def bhist : Π m : tmodel, list nnf | (cons i l ba) := i.id.b @[simp] def request : Π m : tmodel, list psig | (cons i l ba) := ba @[simp] def proper_request_box : Π m : tmodel, Prop | (cons i l ba) := ∀ rq : psig, rq ∈ ba → ∀ φ, (box φ ∈ i.htk ∨ box φ ∈ i.id.b) → box φ ∈ rq.b @[simp] def subset_request : Π m : tmodel, Prop | (cons i l ba) := ba ⊆ i.id.a @[simp] def tmodel_step_bhist : Π m : tmodel, Prop | m@(cons i l ba) := ∀ s ∈ l, ∀ φ, box φ ∈ i.id.b → box φ ∈ htk s @[simp] def tmodel_step_box : Π m : tmodel, Prop | m@(cons i l ba) := ∀ s ∈ l, ∀ φ, box φ ∈ i.htk → box φ ∈ htk s -- Can be strenghtened @[simp] def tmodel_dia : Π m : tmodel, Prop | m@(cons i l ba) := ∀ φ, dia φ ∈ i.htk → (∃ rq : psig, rq ∈ ba ∧ rq.d = φ) ∨ ∃ s ∈ l, φ ∈ htk s @[simp] def child : tmodel → tmodel → bool | s (cons i l ba) := s ∈ l inductive tc' {α : Type} (r : α → α → Prop) : α → α → Prop | base : ∀ a b, r a b → tc' a b | step : ∀ a b c, r a b → tc' b c → tc' a c theorem tc'.trans {α : Type} {r : α → α → Prop} {a b c : α} : tc' r a b → tc' r b c → tc' r a c := begin intros h₁ h₂, induction h₁, apply tc'.step, exact h₁_a_1, exact h₂, apply tc'.step, exact h₁_a_1, apply h₁_ih, exact h₂ end def desc : tmodel → tmodel → Prop := tc' (λ s m, child s m) theorem desc_not_nil : Π c i ba m, m = cons i [] ba → desc c m → false := begin intros c i ba m heq h, induction h, {rw heq at h_a_1, simp at h_a_1, exact h_a_1}, {apply h_ih, exact heq} end theorem desc_iff_eq_child_aux : Π i₁ i₂ s₁ s₂ l₁ l₂ m₁ m₂ m₃, m₁ = cons i₁ l₁ s₁ → m₂ = cons i₂ l₂ s₂ → l₁ = l₂ → (desc m₃ m₁ ↔ desc m₃ m₂) := begin intros i₁ i₂ s₁ s₂ l₁ l₂ m₁ m₂ m₃ heq₁ heq₂ heq, split, {intro hd, induction hd, {rw heq₁ at hd_a_1, simp at hd_a_1, rw heq at hd_a_1, apply tc'.base, rw heq₂, simp, exact hd_a_1}, {apply tc'.trans, apply tc'.base, exact hd_a_1, apply hd_ih, exact heq₁}}, {intro hd, induction hd, {rw heq₂ at hd_a_1, simp at hd_a_1, rw ←heq at hd_a_1, apply tc'.base, rw heq₁, simp, exact hd_a_1}, {apply tc'.trans, apply tc'.base, exact hd_a_1, apply hd_ih, exact heq₂}} end theorem eq_desc_of_eq_children {i₁ i₂ s₁ s₂ l c} : desc c (cons i₁ l s₁) = desc c (cons i₂ l s₂) := begin rw desc_iff_eq_child_aux, repeat {refl} end theorem desc_step : Π c i l ba, c ∈ l → desc c (cons i l ba) | c i [] ba h := absurd h $ list.not_mem_nil _ | c i (hd::tl) ba h := begin constructor, simp, cases h, left, exact h, right, exact h end theorem desc_ex : Π c i l ba, (∃ m ∈ l, desc c m) → desc c (cons i l ba) | c i [] ba h := begin rcases h with ⟨w, hmem, hw⟩, exact (absurd hmem $ list.not_mem_nil _) end | c i (hd::tl) ba h := begin rcases h with ⟨w, hmem, hw⟩, cases hw, {apply tc'.step, swap 3, {exact w}, {exact hw_a_1}, {apply tc'.base, simp, cases hmem, left, exact hmem, right, exact hmem}}, {apply tc'.step, exact hw_a_1, apply tc'.trans, exact hw_a_2, apply tc'.base, simp, exact hmem} end theorem ex_desc : Π c i l ba m, m = (cons i l ba) → desc c m → (c ∈ l ∨ ∃ m ∈ l, desc c m) := begin intros c i l ba m heq h, induction h, {left, rw heq at h_a_1, simp at h_a_1, exact h_a_1}, {cases h_ih heq, {right, split, split, exact h, apply tc'.base, exact h_a_1}, {rcases h with ⟨w, hmem, hw⟩, right, split, split, exact hmem, apply tc'.step, exact h_a_1, exact hw}} end theorem ex_desc' : Π c i l ba, desc c (cons i l ba) → (c ∈ l ∨ ∃ m ∈ l, desc c m) := begin intros c i l ba h, apply ex_desc, repeat {refl}, exact h end @[simp] def tmodel_anc : Π m : tmodel, Prop | m@(cons i l ba) := ∀ s rq, desc s m → rq ∈ request s → (rq ∈ manc m) ∨ (∃ d, desc d m ∧ some rq = msig d) structure ptmodel (m : tmodel) : Prop := (bhist : tmodel_step_bhist m) (sbox : tmodel_step_box m) (pdia : tmodel_dia m) (bdia : tmodel_anc m) (reqb : proper_request_box m) (sreq : subset_request m) def global_pt (m : tmodel) := ∀ s, desc s m → ptmodel s open subtype def model : Type := {m : tmodel // ptmodel m ∧ global_pt m} def rmodel : Type := {m : tmodel // ptmodel m} inductive reach_step : rmodel → rmodel → Prop | fwd_base (s : rmodel) (i l ba h) : s.1 ∈ l → reach_step ⟨(cons i l ba), h⟩ s | bwd_base (s : rmodel) (i l ba h) : (∃ rq ∈ ba, some rq = msig s.1) → reach_step ⟨(cons i l ba), h⟩ s theorem reach_step_box (s₁ s₂ φ) (h₁ : reach_step s₁ s₂) (h₂ : box φ ∈ htk s₁.1) : box φ ∈ htk s₂.1 := begin cases h₁, {cases s₂ with s₂ ps₂, cases s₂ with i₂ l₂ sg₂, simp, have := h₁_h.sbox, simp at this, simp at h₂, have hmem := this _ h₁_a _ h₂, simp at hmem, exact hmem }, {cases s₂ with s₂ ps₂, cases s₂ with i₂ l₂ sg₂, simp, rcases h₁_a with ⟨w,hmem,hw⟩, simp at hw, apply i₂.mhtk, have := i₂.id.ps₂, rw ←hw at this, have hneq : some w ≠ none, {intro heq, contradiction}, have hsub := this hneq, apply hsub, have := h₁_h.reqb, simp at this, simp at h₂, have hc := this w hmem φ (or.inl h₂), cases w, dsimp [bsig], exact hc} end inductive rtc {α : Type} (r : α → α → Prop) : α → α → Prop | refl : Π a, rtc a a | step : Π a b c, r a b → rtc b c → rtc a c theorem rtc.trans {α : Type} {r : α → α → Prop} {a b c : α} : rtc r a b → rtc r b c → rtc r a c := begin intros h₁ h₂, induction h₁, exact h₂, apply rtc.step, exact h₁_a_1, apply h₁_ih, exact h₂ end theorem rtc_step {α : Type} {r : α → α → Prop} {a b : α} (h : r a b) : rtc r a b := by apply rtc.step _ _ _ h; apply rtc.refl def reach (s₁ s₂ : rmodel) := rtc reach_step s₁ s₂ theorem refl_reach : Π s, reach s s := λ s, rtc.refl s theorem trans_reach : Π s₁ s₂ s₃, reach s₁ s₂ → reach s₂ s₃ → reach s₁ s₃ := λ s₁ s₂ s₃ h₁ h₂, rtc.trans h₁ h₂ @[simp] def builder (m : tmodel) : S4 {x : rmodel // x.1 = m ∨ desc x.1 m} := {val := λ v s, var v ∈ htk s.1.1, rel := λ s₁ s₂, reach s₁ s₂, refl := λ s, refl_reach s, trans := λ a b c, trans_reach a b c} open rtc theorem reach_box (s₁ s₂ φ) (h₁ : reach s₁ s₂) (h₂ : box φ ∈ htk s₁.1) : φ ∈ htk s₂.1 := begin induction h₁ with m m₁ m₂ m₃ h₁₂ h₂₃ ih, {cases m with tm hm, cases tm with i l sg, simp, apply i.hhtk.hbox, simp at h₂, exact h₂}, {apply ih, apply reach_step_box, exact h₁₂, exact h₂} end theorem reach_step_dia (s : rmodel) (rt : model) (φ) (h₁ : desc s.1 rt.1) (h₂ : manc rt.1 = []) (h₃ : dia φ ∈ htk s.1) : ∃ s', reach_step s s' ∧ φ ∈ htk s'.1 ∧ desc s'.1 rt.1 := begin cases s with s ps, cases s with i l sg, have := ps.pdia, simp at this, simp at h₃, have hc := this _ h₃, cases hc, {cases rt with rt prt, cases rt with irt lrt sgrt, rcases hc with ⟨w, hmem, hw⟩, have := prt.1.bdia, simp at this, simp at h₁, have hcaux := this _ w h₁, simp at hcaux, have hcc := hcaux hmem, simp at h₂, cases hcc, {rw h₂ at hcc, exfalso, apply list.not_mem_nil, exact hcc}, {rcases hcc with ⟨m, hml, hmr⟩, have pm := prt.2 m hml, split, split, swap 3, exact ⟨m, pm⟩, apply reach_step.bwd_base, split, split, exact hmem, simp, exact hmr, split, {cases m with im lm sgm, simp, apply im.mhtk, have := im.id.ps₁, simp at hmr, rw ←hmr at this, have hneq : some w ≠ none, {intro, contradiction}, have hmem := this hneq, cases w, dsimp [dsig] at hmem, rw ←hw, exact hmem_1 }, {exact hml} } }, {rcases hc with ⟨m, pml, pmr⟩, have hdm : desc m rt.1, {apply tc'.trans, apply tc'.base, swap 3, exact (⟨cons i l sg, ps⟩ : rmodel).val, simp, exact pml, exact h₁}, cases rt with rt prt, cases rt with irt lrt sgrt, have pm := prt.2 m hdm, split, split, swap 3, exact ⟨m, pm⟩, apply reach_step.fwd_base, exact pml, split, {exact pmr}, {exact hdm} } end theorem reach_dia (s : rmodel) (rt : model) (φ) (h₁ : desc s.1 rt.1) (h₂ : manc rt.1 = []) (h₃ : dia φ ∈ htk s.1) : ∃ s', reach s s' ∧ φ ∈ htk s'.1 ∧ desc s'.1 rt.1:= begin have := reach_step_dia s rt φ h₁ h₂ h₃, rcases this with ⟨w, hwl, hwr⟩, split, split, swap 3, exact w, apply rtc_step hwl, exact hwr end theorem reach_step_dia_root (s : rmodel) (rt : model) (φ) (h₁ : s.1 = rt.1) (h₂ : manc rt.1 = []) (h₃ : dia φ ∈ htk s.1) : ∃ s', reach_step s s' ∧ φ ∈ htk s'.1 ∧ desc s'.1 rt.1 := begin cases s with s ps, cases s with is ls sgs, have := ps.pdia, simp at this, simp at h₃, have hc := this _ h₃, cases hc, {have := ps.sreq, simp at this, rcases hc with ⟨w, hmw, hw⟩, have hmem := this hmw, cases rt with rt prt, rw ←h₁ at h₂, simp at h₂, rw h₂ at hmem, exfalso, apply list.not_mem_nil, exact hmem}, {cases rt with rt prt, rcases hc with ⟨w, hwl, hwr⟩, have ptw : ptmodel w, {apply prt.2, apply tc'.base, simp at h₁, rw ←h₁, simp, exact hwl}, split, split, swap 3, exact ⟨w, ptw⟩, apply reach_step.fwd_base, exact hwl, split, {exact hwr}, {apply tc'.base, simp, simp at h₁, rw ←h₁, simp, exact hwl} } end theorem reach_dia_root (s : rmodel) (rt : model) (φ) (h₁ : s.1 = rt.1) (h₂ : manc rt.1 = []) (h₃ : dia φ ∈ htk s.1) : ∃ s', reach s s' ∧ φ ∈ htk s'.1 ∧ desc s'.1 rt.1 := begin have := reach_step_dia_root s rt φ h₁ h₂ h₃, rcases this with ⟨w, hwl, hwr⟩, split, split, swap 3, exact w, apply rtc_step hwl, exact hwr end theorem good_model (m : model) (hrt : manc m.1 = []): Π (s : {x : rmodel // x.1 = m.1 ∨ desc x.1 m.1}) (φ : nnf), φ ∈ htk s.1.1 → force (builder m.1) s φ | s (var n) h := begin simp, exact h end | s (neg n) h := begin simp, intro hin, cases s with s ps, cases s with s pts, cases s with i l sg, have := i.hhtk.hno_contra, simp at hin, apply this hin, simp at h, exact h end | s (and φ ψ) h := begin split, {apply good_model, cases s with s ps, cases s with s pts, cases s with i l sg, have := i.hhtk.hand_left, simp, apply this, simp at h, exact h}, {apply good_model, cases s with s ps, cases s with s pts, cases s with i l sg, have := i.hhtk.hand_right, simp, apply this, simp at h, exact h} end | s (or φ ψ) h := begin cases s with s ps, cases s with s pts, cases s with i l sg, have := i.hhtk.hor, simp at h, have hc := this h, cases hc, {simp, left, apply good_model, simp, exact hc}, {simp, right, apply good_model, simp, exact hc} end | s (box φ) h := begin intros m hm, apply good_model, apply reach_box, exact hm, exact h end | s (dia φ) h := begin cases s with s ps, cases ps, {simp, simp at h, have := reach_dia_root _ _ _ ps hrt h, rcases this with ⟨s', hs'l, hs'm, hs'r⟩, split, split, exact hs'l, split, apply good_model, simp, exact hs'm, right, exact hs'r }, {simp, simp at h, have := reach_dia _ _ _ ps hrt h, rcases this with ⟨s', hs'l, hs'm, hs'r⟩, split, split, exact hs'l, split, apply good_model, simp, exact hs'm, right, exact hs'r} end
c------------------------------------------------------------------------ function ffsigiut(xx1,xx2,jpp,je1,je2) c------------------------------------------------------------------------ c c \int(dt) \int(du) ffsig *s/sh**3 *2*pi*alpha**2 *delta(uh+th+sh) c c----------------------------------------------------------------------- common /ar3/ x1(7),a1(7) include 'epos.incsem' include 'epos.inc' double precision tmin,tmax,t,sh2,sqrtq2s ig=3 s=engy**2 sh=s*xx1*xx2 ffsigiut=0. if(sh.le.4.*q2min)return sh2=dble(sh/2.) c tmin=sh/2-sqrt(sh*sh/4-q2min*sh) sqrtq2s=sqrt(dble(q2min*sh)) tmin=sh2-sqrt((sh2-sqrtq2s)*(sh2+sqrtq2s)) tmax=sh2 do i=1,ig do m=1,2 t=2d0*tmin/(1d0+tmin/tmax-dble(tgss(ig,i)*(2*m-3)) & *(1d0-tmin/tmax)) qq=sngl(t*(1d0-t/dble(sh))) ft=ffsigj(sngl(t),qq,xx1,xx2,jpp,je1,je2)/sh**3 * * (2*pi*pssalf(qq/qcdlam))**2 ffsigiut=ffsigiut+wgss(ig,i)*ft*sngl(t)**2 enddo enddo ffsigiut=ffsigiut * *0.5*sngl(1d0/tmin-1d0/tmax) * *2*pi*s * /2 !CS for parton pair return end c----------------------------------------------------------------------- function ffsigj(t,qt,x1,x2,jpp,je1,je2) c----------------------------------------------------------------------- c c \sum x1*f_i(x1,qt) * x2*f_k(x2,qt) * B_ik c c B_ik = psbori = contribution to Born xsection: c dsigmaBorn/d2pt/dy c = s/pi * delta(s+t+u) * 2*pi*alpha**2 /s**2 * B_ik c c qt = virtuality scale c x1, x2 = light cone momentum fractions c c x*f_j(x,qt) = function fparton(x,qt,j) c c----------------------------------------------------------------------- c jpp: type of Pomeron c 1 ... sea-sea c 2 ... val-sea c 3 ... sea-val c 4 ... val-val c 5 ... all c je = emission type c 0 ... no emissions c 1 ... emissions c 2 ... all c----------------------------------------------------------------------- include 'epos.incsem' include 'epos.inc' s=engy**2*x1*x2 if(jpp.ne.5)then ji1=mod(jpp+1,2)+1 ji2=(jpp+1)/2 sea1=pifpartone(x1,qt,-1,je1,ji1) g1= pifpartone(x1,qt, 0,je1,ji1) uv1= pifpartone(x1,qt, 1,je1,ji1) dv1= pifpartone(x1,qt, 2,je1,ji1) sea2=pifpartone(x2,qt,-1,je2,ji2) g2= pifpartone(x2,qt, 0,je2,ji2) uv2= pifpartone(x2,qt, 1,je2,ji2) dv2= pifpartone(x2,qt, 2,je2,ji2) else sea1=pifpartone(x1,qt,-1,je1,1)+pifpartone(x1,qt,-1,je1,2) g1= pifpartone(x1,qt, 0,je1,1)+pifpartone(x1,qt, 0,je1,2) uv1= pifpartone(x1,qt, 1,je1,1)+pifpartone(x1,qt, 1,je1,2) dv1= pifpartone(x1,qt, 2,je1,1)+pifpartone(x1,qt, 2,je1,2) sea2=pifpartone(x2,qt,-1,je2,1)+pifpartone(x2,qt,-1,je2,2) g2= pifpartone(x2,qt, 0,je2,1)+pifpartone(x2,qt, 0,je2,2) uv2= pifpartone(x2,qt, 1,je2,1)+pifpartone(x2,qt, 1,je2,2) dv2= pifpartone(x2,qt, 2,je2,1)+pifpartone(x2,qt, 2,je2,2) endif ffsigj= ffborn(s,t, g1*g2 !gg * ,(uv1+dv1+2.*naflav*sea1)*g2+g1*(uv2+dv2+2.*naflav*sea2) !gq * ,(uv1+sea1)*(uv2+sea2) !qq * +(dv1+sea1)*(dv2+sea2)+sea1*sea2*(naflav-1)*2. * ,(uv1+sea1)*sea2+(uv2+sea2)*sea1 !qa * +(dv1+sea1)*sea2+(dv2+sea2)*sea1+sea1*sea2*(naflav-2)*2. * ,dv1*uv2+dv2*uv1+(uv2+dv2)*sea1*(naflav-1)*2. !qqp * +(uv1+dv1)*sea2*(naflav-1)*2. * +sea1*sea2*naflav*(naflav-1)*4. *) end c----------------------------------------------------------------------- function ffsig(t,qt,x1,x2) !former psjy c----------------------------------------------------------------------- include 'epos.incsem' include 'epos.inc' s=engy**2*x1*x2 g1= pifpartone(x1,qt, 0,2,1)+pifpartone(x1,qt, 0,2,2) uv1= pifpartone(x1,qt, 1,2,1)+pifpartone(x1,qt, 1,2,2) dv1= pifpartone(x1,qt, 2,2,1)+pifpartone(x1,qt, 2,2,2) sea1=pifpartone(x1,qt,-1,2,1)+pifpartone(x1,qt,-1,2,2) g2= pifpartone(x2,qt, 0,2,1)+pifpartone(x2,qt, 0,2,2) uv2= pifpartone(x2,qt, 1,2,1)+pifpartone(x2,qt, 1,2,2) dv2= pifpartone(x2,qt, 2,2,1)+pifpartone(x2,qt, 2,2,2) sea2=pifpartone(x2,qt,-1,2,1)+pifpartone(x2,qt,-1,2,2) ffsig= ffborn(s,t, g1*g2 !gg * ,(uv1+dv1+2.*naflav*sea1)*g2+g1*(uv2+dv2+2.*naflav*sea2) !gq * ,(uv1+sea1)*(uv2+sea2) !qq * +(dv1+sea1)*(dv2+sea2)+sea1*sea2*(naflav-1)*2. * ,(uv1+sea1)*sea2+(uv2+sea2)*sea1 !qa * +(dv1+sea1)*sea2+(dv2+sea2)*sea1+sea1*sea2*(naflav-2)*2. * ,dv1*uv2+dv2*uv1+(uv2+dv2)*sea1*(naflav-1)*2. !qqp * +(uv1+dv1)*sea2*(naflav-1)*2. * +sea1*sea2*naflav*(naflav-1)*4. *) end c------------------------------------------------------------------------ function ffborn(s,t,gg,gq,qq,qa,qqp) c------------------------------------------------------------------------ ffborn= *( psbori(s,t,0,0,1)+psbori(s,s-t,0,0,1) * +psbori(s,t,0,0,2)+psbori(s,s-t,0,0,2)) /2. *gg !gg *+(psbori(s,t,0,1,1)+psbori(s,s-t,0,1,1)) *gq !gq *+(psbori(s,t,1,1,1)+psbori(s,s-t,1,1,1))/2. *qq !qq *+(psbori(s,t,1,-1,1)+psbori(s,s-t,1,-1,1)+psbori(s,t,1,-1,2)+ * psbori(s,s-t,1,-1,2)+psbori(s,t,1,-1,3)+psbori(s,s-t,1,-1,3)) !qa * *qa *+(psbori(s,t,1,2,1)+psbori(s,s-t,1,2,1)) *qqp !qq' end c----------------------------------------------------------------------- function pifpartone(xx,qq,j,je,ji) ! pol interpolation of partone c----------------------------------------------------------------------- include 'epos.incsem' include 'epos.inc' common/tabfptn/kxxmax,kqqmax,fptn(20,20,-1:2,0:2,2) real wi(3),wj(3) common /cpifpartone/npifpartone data npifpartone /0/ npifpartone=npifpartone+1 if(npifpartone.eq.1)call MakeFpartonTable qqmax=engy**2/4. xxmin=0.01/engy xxmax=1 xxk=1.+log(xx/xxmin)/log(xxmax/xxmin)*(kxxmax-1) qqk=1.+log(qq/q2min)/log(qqmax/q2min)*(kqqmax-1) kxx=int(xxk) kqq=int(qqk) if(kxx.lt.1)kxx=1 if(kqq.lt.1)kqq=1 if(kxx.gt.(kxxmax-2))kxx=kxxmax-2 if(kqq.gt.(kqqmax-2))kqq=kqqmax-2 wi(2)=xxk-kxx wi(3)=wi(2)*(wi(2)-1.)*.5 wi(1)=1.-wi(2)+wi(3) wi(2)=wi(2)-2.*wi(3) wj(2)=qqk-kqq wj(3)=wj(2)*(wj(2)-1.)*.5 wj(1)=1.-wj(2)+wj(3) wj(2)=wj(2)-2.*wj(3) pifpartone=0 do kx=1,3 do kq=1,3 pifpartone=pifpartone+fptn(kxx+kx-1,kqq+kq-1,j,je,ji) * *wi(kx)*wj(kq) enddo enddo end c----------------------------------------------------------------------- subroutine MakeFpartonTable c----------------------------------------------------------------------- include 'epos.incsem' include 'epos.inc' common/tabfptn/kxxmax,kqqmax,fptn(20,20,-1:2,0:2,2) write (*,'(a,$)')'(Fparton table' kxxmax=10 kqqmax=10 qqmax=engy**2/4. xxmin=0.01/engy xxmax=1 do ji=1,2 do je=0,2 write(*,'(a,$)')'.' do j=-1,2 do kxx=1,kxxmax xx=xxmin*(xxmax/xxmin)**((kxx-1.)/(kxxmax-1.)) do kqq=1,kqqmax qq=q2min*(qqmax/q2min)**((kqq-1.)/(kqqmax-1.)) fptn(kxx,kqq,j,je,ji)= fpartone(xx,qq,j,je,ji) enddo enddo enddo enddo enddo write (*,'(a,$)')'done)' end c------------------------------------------------------------------------ function fpartone(xx,qq,j,je,ji) !former pspdf0 (sha) c----------------------------------------------------------------------- c c parton distribution function for proton ( actually x*f(x) !!!!!!! ) c c xx = light cone momentum fraction c qq = virtuality scale c j = parton type c -1 ... sea (distribution function per flavor) c 0 ... g c 1 ... u c 2 ... d c je = emission type c 0 ... no emissions c 1 ... emissions c 2 ... all c ji = initial parton type c 1 ... sea (q et g) c 2 ... val c----------------------------------------------------------------------- double precision z,xmin,xm,zx,psuds common/ar3/ x1(7),a1(7) include 'epos.inc' include 'epos.incsem' fpartone=0 if(je.eq.1)goto888 c ...... f_0 * sudakov......... if(j.eq.0.and.ji.eq.1)then fpartone=fzeroGlu(xx,2,1) !hadron class 2, projectile side elseif((j.eq.1.or.j.eq.2).and.ji.eq.2)then fpartone=psdfh4(xx,q2min,0.,2,j) elseif(j.eq.-1.and.ji.eq.1)then fpartone=fzeroSea(xx,2,1) endif fpartone=fpartone*sngl(psuds(qq,j)/psuds(q2min,j)) if(je.eq.0)goto999 c......... integral f_0 E_qcd............ 888 continue xmin=dble(xx)/(1.d0-dble(q2ini/qq)) if(xmin.lt.1.d0)then dpd1=0. dpd2=0. xm=max(xmin,0.3d0) !numerical integration xm -> 1 do i=1,7 do m=1,2 zx=1.d0-(1.d0-xm)*(.5d0+(dble(m)-1.5d0)*dble(x1(i)))**.25d0 z=xx/zx gl=fzeroGlu(sngl(zx),2,1) uv=psdfh4(sngl(zx),q2min,0.,2,1) dv=psdfh4(sngl(zx),q2min,0.,2,2) sea=fzeroSea(sngl(zx),2,1) fz=0 if(j.eq.0)then if(ji.eq.1) * fz=gl *psevi(q2min,qq,z,1,1) * +sea*psevi(q2min,qq,z,2,1) !ccccc if(ji.eq.2) * fz=(uv+dv)*psevi(q2min,qq,z,2,1) elseif(j.eq.1.and.ji.eq.2)then fz=psevi(q2min,qq,z,3,2)*uv elseif(j.eq.2.and.ji.eq.2)then fz=psevi(q2min,qq,z,3,2)*dv elseif(j.eq.-1)then akns=psevi(q2min,qq,z,3,2) !nonsinglet contribution aks=(psevi(q2min,qq,z,2,2)-akns) !singlet contribution if(ji.eq.1) * fz=psevi(q2min,qq,z,1,2)*gl * +sea*aks+sea*akns !ccccc if(ji.eq.2) * fz=(uv+dv)*aks endif dpd1=dpd1+a1(i)*fz/sngl(zx)**2/sngl(1.d0-zx)**3 enddo enddo dpd1=dpd1*sngl(1.d0-xm)**4/8.*xx !numerical integration xmin -> xm if(xm.gt.xmin)then do i=1,7 do m=1,2 zx=xx+(xm-xx) & *((xmin-xx)/(xm-xx))**(.5d0-(dble(m)-1.5d0)*dble(x1(i))) z=xx/zx gl=fzeroGlu(sngl(zx),2,1) uv=psdfh4(sngl(zx),q2min,0.,2,1) dv=psdfh4(sngl(zx),q2min,0.,2,2) sea=fzeroSea(sngl(zx),2,1) fz=0 if(j.eq.0)then if(ji.eq.1) * fz=gl *psevi(q2min,qq,z,1,1) * +sea*psevi(q2min,qq,z,2,1) !ccccc if(ji.eq.2) * fz=(uv+dv)*psevi(q2min,qq,z,2,1) elseif(j.eq.1.and.ji.eq.2)then fz=psevi(q2min,qq,z,3,2)*uv elseif(j.eq.2.and.ji.eq.2)then fz=psevi(q2min,qq,z,3,2)*dv elseif(j.eq.-1)then akns=psevi(q2min,qq,z,3,2) !nonsinglet contribution aks=(psevi(q2min,qq,z,2,2)-akns) !singlet contribution if(ji.eq.1) * fz=psevi(q2min,qq,z,1,2)*gl * +sea*aks+sea*akns !ccccc if(ji.eq.2) * fz=(uv+dv)*aks endif dpd2=dpd2+a1(i)*fz*sngl((1.d0-xx/zx)/zx) enddo enddo dpd2=dpd2*sngl(log((xm-xx)/(xmin-xx))*.5d0*xx) endif fpartone=fpartone+dpd2+dpd1 endif 999 continue if(j.lt.0)fpartone=fpartone/naflav/2. return end c------------------------------------------------------------------------ function fparton(xx,qq,j) !former pspdf0 (sha) c----------------------------------------------------------------------- c c parton distribution function for proton ( actually x*f(x) !!!!!!! ) c c xx = light cone momentum fraction c qq = virtuality scale c j = parton type c -1 ... sea (dsistribution fuction per flavor) c 0 ... g c 1 ... u c 2 ... d c c----------------------------------------------------------------------- c (see pages 105 - 107 of our report) c c fparton(xx) = xx * f(xx) !!!!! c c f_j(xx,qq) = \sum_k \int(xx<x<1) dx/x f0_k(x) Eqcd_k_j(xx/x,qq) c c f0_k = fzeroGlu or fzeroSea c c Eqcd=E~qcd+delta*sudakov, E~qcd: at least one emission c c----------------------------------------------------------------------- double precision z,xmin,xm,zx,psuds common/ar3/ x1(7),a1(7) include 'epos.inc' include 'epos.incsem' c ...... f_0 * sudakov......... if(j.eq.0)then fparton=fzeroGlu(xx,2,1) elseif(j.eq.1.or.j.eq.2)then fparton=psdfh4(xx,q2min,0.,2,j) else fparton=fzeroSea(xx,2,1) endif fparton=fparton*sngl(psuds(qq,j)/psuds(q2min,j)) c......... integral f_0 E_qcd............ xmin=xx/(1.d0-dble(q2ini/qq)) if(xmin.lt.1.d0)then dpd1=0. dpd2=0. xm=max(xmin,.3d0) !numerical integration xm -> 1 do i=1,7 do m=1,2 zx=1.d0-(1.d0-xm)*(.5d0+(dble(m)-1.5d0)*dble(x1(i)))**.25d0 z=xx/zx gl=fzeroGlu(sngl(zx),2,1) uv=psdfh4(sngl(zx),q2min,0.,2,1) dv=psdfh4(sngl(zx),q2min,0.,2,2) sea=fzeroSea(sngl(zx),2,1) if(j.eq.0)then fz=psevi(q2min,qq,z,1,1)*gl * +(uv+dv+sea)*psevi(q2min,qq,z,2,1) elseif(j.eq.1)then fz=psevi(q2min,qq,z,3,2)*uv elseif(j.eq.2)then fz=psevi(q2min,qq,z,3,2)*dv else akns=psevi(q2min,qq,z,3,2) !nonsinglet contribution aks=(psevi(q2min,qq,z,2,2)-akns) !singlet contribution fz=(psevi(q2min,qq,z,1,2)*gl+(uv+dv+sea)*aks+sea*akns) endif dpd1=dpd1+a1(i)*fz/sngl(zx)**2/sngl(1.d0-zx)**3 enddo enddo dpd1=dpd1*sngl((1.d0-xm)**4/8.*xx) !numerical integration xmin -> xm if(xm.gt.xmin)then do i=1,7 do m=1,2 zx=xx+(xm-xx)*((xmin-xx)/(xm-xx)) * **(.5d0-(dble(m)-1.5)*dble(x1(i))) z=xx/zx gl=fzeroGlu(sngl(zx),2,1) uv=psdfh4(sngl(zx),q2min,0.,2,1) dv=psdfh4(sngl(zx),q2min,0.,2,2) sea=fzeroSea(sngl(zx),2,1) if(j.eq.0)then fz=psevi(q2min,qq,z,1,1)*gl+(uv+dv+sea)* * psevi(q2min,qq,z,2,1) elseif(j.eq.1)then fz=psevi(q2min,qq,z,3,2)*uv elseif(j.eq.2)then fz=psevi(q2min,qq,z,3,2)*dv else akns=psevi(q2min,qq,z,3,2) !nonsinglet contribution aks=(psevi(q2min,qq,z,2,2)-akns) !singlet contribution fz=(psevi(q2min,qq,z,1,2)*gl+(uv+dv+sea)*aks+sea*akns) endif dpd2=dpd2+a1(i)*fz*sngl((1.d0-xx/zx)/zx) enddo enddo dpd2=dpd2*sngl(log((xm-xx)/(xmin-xx))*.5d0*xx) endif fparton=fparton+dpd2+dpd1 endif if(j.lt.0)fparton=fparton/naflav/2. return end c------------------------------------------------------------------------ function fzeroGlu(z,k,ipt) c----------------------------------------------------------------------- c c x*f(x) c c f = F & EsoftGluon &=convolution c c F(x) = alpff(k)*x**betff(ipt)*(1-x)**alplea(k) c c EsoftGluon(x) = x**(-1-dels) * EsoftGluonTil(x) c c z - light cone x c k - hadron class c ipt - 1=proj 2=targ c----------------------------------------------------------------------- double precision xpmin,xp include 'epos.inc' common /ar3/ x1(7),a1(7) include 'epos.incsem' fzeroGlu=0. xpmin=z xpmin=xpmin**(1+betff(ipt)+dels) do i=1,7 do m=1,2 xp=(.5*(1.+xpmin+(2*m-3)*x1(i)*(1.-xpmin)))**(1./ * (1+betff(ipt)+dels)) zz=z/xp fzeroGlu=fzeroGlu+a1(i)*(1.-xp)**alplea(k)*EsoftGluonTil(zz) enddo enddo fzeroGlu=fzeroGlu*.5*(1.-xpmin)/(1+betff(ipt)+dels) fzeroGlu=fzeroGlu *alpff(k) *z**(-dels) end c------------------------------------------------------------------------ function fzeroSea(z,k,ipt) c----------------------------------------------------------------------- c c x*f(x) c c f = F & EsoftQuark &=convolution c c F(x) = alpff(k)*x**betff(ipt)*(1-x)**alplea(k) c c EsoftQuark(x) = x**(-1-dels) * EsoftQuarkTil(x) c c z - light cone x of the quark, c k - hadron class c----------------------------------------------------------------------- double precision xpmin,xp common /ar3/ x1(7),a1(7) include 'epos.inc' include 'epos.incsem' fzeroSea=0. xpmin=z xpmin=xpmin**(1+betff(ipt)+dels) do i=1,7 do m=1,2 xp=(.5*(1.+xpmin+(2*m-3)*x1(i)*(1.-xpmin)))**(1./ * (1+betff(ipt)+dels)) zz=z/xp fzeroSea=fzeroSea+a1(i)*(1.-xp)**alplea(k)*EsoftQuarkTil(zz) enddo enddo fzeroSea=fzeroSea*.5*(1.-xpmin)/(1+betff(ipt)+dels) fzeroSea=fzeroSea *alpff(k) *z**(-dels) end c------------------------------------------------------------------------ function EsoftGluonTil(zz) c----------------------------------------------------------------------- c EsoftGluon = zz^(-1-dels) * EsoftGluonTil c----------------------------------------------------------------------- include 'epos.inc' include 'epos.incsem' EsoftGluonTil=gamsoft*(1-glusea)*(1.-zz)**betpom end c------------------------------------------------------------------------ function EsoftQuarkTil(zz) c----------------------------------------------------------------------- c EsoftQuark = zz^(-1-dels) * EsoftQuarkTil c----------------------------------------------------------------------- double precision zmin,z common /ar3/ x1(7),a1(7) include 'epos.inc' include 'epos.incsem' EsoftQuarkTil=0. zmin=zz zmin=zmin**(1.+dels) do i=1,7 do m=1,2 z=(.5d0*(1.+zmin+(2*m-3)*x1(i)*(1.d0-zmin))) * **(1.d0/(1.d0+dels)) EsoftQuarkTil=EsoftQuarkTil+a1(i)*max(1.d-5,(1.d0-zz/z))**betpom * *(z**2+(1.-z)**2) enddo enddo EsoftQuarkTil=EsoftQuarkTil*1.5*(1.d0-zmin)/(1.+dels) !1.5=naflav/2 at Q0 EsoftQuarkTil=gamsoft*glusea*EsoftQuarkTil end c------------------------------------------------------------------------ function EsoftQZero(zz) ! former psftilf c----------------------------------------------------------------------- c c EsoftQuark = EsoftQZero * wsplit * z^(-1-dels) * gamsoft c c zz - ratio of the quark and pomeron light cone x (zz=x_G/x_P) c integration over quark to gluon light cone momentum ratio (z=x/x_G): c c EsoftQZero = int(dz) z^dels * (1-zz/z)^betpom * P_qG(z) c c----------------------------------------------------------------------- double precision zmin,z common /ar3/ x1(7),a1(7) include 'epos.incsem' EsoftQZero=0. zmin=zz zmin=zmin**(1.+dels) do i=1,7 do m=1,2 z=(.5d0*(1.+zmin+(2*m-3)*x1(i)*(1.d0-zmin))) * **(1.d0/(1.d0+dels)) EsoftQZero=EsoftQZero+a1(i)*max(1.d-5,(1.d0-zz/z))**betpom * *(z**2+(1.-z)**2) enddo enddo EsoftQZero=EsoftQZero*1.5*(1.d0-zmin)/(1.+dels) !1.5=naflav/2 at Q0 return end c------------------------------------------------------------------------ function ffsigi(qq,y0) !former psjx1 (sto) c------------------------------------------------------------------------ c c dsigma/dpt_jet = \int dy \int dx1 ffsig(x1,x2(x1)) c c x1=xplus, x2=xminus c x2=x2(x1) due to u+t+s=0 c ( s=x1*x2*spp, t/spp=-x1*xt*exp(-y)/2, u/spp=-x2*xt*exp(y)/2 ) c c qq = pt**2, xt=2.*sqrt(qq/s) c rapidity range: 0 to y0 c c ffsig = function ffsig(t,qq,x1,x2) c c----------------------------------------------------------------------- include 'epos.incsem' include 'epos.inc' double precision xx1,xx2,xt,ymax,ymin,y,xmin,xmax ig=3 ig1=3 s=engy**2 ffsigi=0. if(s.le.4.*qq)return if(qq.lt.q2min)return xt=2d0*sqrt(dble(qq)/dble(s)) ymax=min(dble(y0),log(1d0/xt+sqrt((1d0/xt-1d0)*(1d0/xt+1d0)))) ymin=-ymax !final result must be divided by 2 do i=1,ig do m=1,2 y=.5d0*(ymax+ymin+(ymin-ymax)*dble((2*m-3)*tgss(ig,i))) !for xx1-integration, use variable x=xx1-xt*exp(y)/2.,with xmin<x<xmax xmin=xt**2/2.d0/(2.d0-xt*exp(-y)) !condition x2<1 xmax=1.d0-xt*exp(y)/2.d0 !condition x1<1 fx=0. do i1=1,ig1 do m1=1,2 xx1=xt*exp(y)/2.d0+xmin*(xmax/xmin)**dble(.5 & +tgss(ig1,i1)*(m1-1.5)) xx2=xt*exp(-y)*xx1/(2.d0*xx1-xt*exp(y)) z=sngl(xx1*xx2) sh=z*s aa=1.-4.*qq/sh aa=max(1e-10,aa) t=sh/2.*(1.-sqrt(aa)) !formula in parton-parton cms ft=ffsig(t,qq,sngl(xx1),sngl(xx2)) fx=fx+wgss(ig1,i1)*ft/sh**2 enddo enddo fx=fx*0.5*sngl(log(xmax/xmin)) !dx/x=0.5*log(xmax/xmin)dt (gauss) ffsigi=ffsigi+wgss(ig,i)*fx enddo enddo ffsigi=ffsigi*0.5*sngl(ymax-ymin) !dy=0.5*(ymax-ymin)dt (gauss) * *2*pi*(2*pi*pssalf(qq/qcdlam))**2 !alpha = 2*pi*pssalf * *2*sqrt(qq) !d2pt=2*pi*pt*dpt * /2 ! y interval 2 * Delta_y * /2 ! condition t < sqrt(s)/2, ! since t > sqrt(s)/2 is automatically included, ! see psbori return end c------------------------------------------------------------------------ function psbori(s,t,j,l,n) c----------------------------------------------------------------------- c contribution to the born cross-section: c c dsigmaBorn/d2pt/dy = s/pi * delta(s+t+u) * 2*pi*alpha**2 /s**2 *psbori c c s - c.m. energy squared for the born scattering, c t - invariant variable for the born scattering |(p1-p3)**2|, c j - parton type at current end of the ladder (0 - g, 1,-1,2,... - q) c l - parton type at opposite end of the ladder (0 - g, 1,-1,2,... - q) c n - subprocess number c----------------------------------------------------------------------- include 'epos.incsem' psbori=0. u=s-t if(u.le.0.d0)return if(iabs(j).ne.4)then !light quarks and gluons if(n.eq.1)then if(j.eq.0.and.l.eq.0)then !gg->gg psbori=(3.-t*u/s**2+s*u/t**2+s*t/u**2)*4.5 elseif(j*l.eq.0)then !gq->gq psbori=(s**2+u**2)/t**2+(s/u+u/s)/2.25 elseif(j.eq.l)then !qq->qq psbori=((s**2+u**2)/t**2+(s**2+t**2)/u**2)/2.25 * -s**2/t/u/3.375 elseif(j.eq.-l)then !qq~->qq~ psbori=((s**2+u**2)/t**2+(u**2+t**2)/s**2)/2.25 * +u**2/t/s/3.375 else !qq'->qq' psbori=(s**2+u**2)/t**2/2.25 endif elseif(n.eq.2)then if(j.eq.0.and.l.eq.0)then !gg->qq~ psbori=.5*(t/u+u/t)-1.125*(t*t+u*u)/s**2 elseif(j.eq.-l)then !qq~->q'q'~ psbori=(t*t+u*u)/s**2/1.125 else psbori=0. endif elseif(n.eq.3)then if(j.ne.0.and.j.eq.-l)then !qq~->gg psbori=32./27.*(t/u+u/t)-(t*t+u*u)/s**2/.375 else psbori=0. endif c............ n=4 for photon product processes, make e_q**2 =2/9., c the average value of charge squared for all types of quarks. elseif(n.eq.4) then if(j.ne.0.and.j.eq.-l)then !qq~->g+gamma psbori=16*factgam*(u/t+t/u)/81. elseif (j*l.eq.0.and.j+l.ne.0) then !q(q~)g->q(q~)+gamma psbori=2*factgam*(u/s+s/u)/27. else psbori=0. endif ctp090305 temporary to avoid hard gamma which produce fragmentation problem in psahot psbori=0. !???????????? elseif(n.eq.5) then if(j.ne.0.and.j.eq.-l)then !qq~->gamma+gamma psbori=4*factgam*(t/u+u/t)/81. else psbori=0. endif ctp090305 temporary to avoid hard gamma which produce fragmentation problem in psahot psbori=0. !???????????? endif elseif(n.eq.1)then !c-quark if(l.eq.0)then !cg->cg xm=qcmass**2/s/u psbori=(s**2+u**2)/t**2+(s/u+u/s)/2.25 * -4.*qcmass**2/t+xm*(xm*t**2-t)/.5625+4.*qcmass**2*xm else !cq->cq psbori=(s**2+u**2)/t**2/2.25-qcmass**2/t/1.125 endif else psbori=0. endif return end c----------------------------------------------------------------------- double precision function om51p(sy,xh,yp,b,iqq) c----------------------------------------------------------------------- c om5p - chi~(x,y) c xh - fraction of the energy squared s for the pomeron; c yp - rapidity for the pomeron; c b - impact parameter between the pomeron ends; c iqq =-1 - 0+1+2+3+4, c iqq = 0 - soft pomeron, c iqq = 1 - gg, c iqq = 2 - qg, c iqq = 3 - gq, c iqq = 4 - qq, c iqq = 5 - soft(int)|b, c iqq = 6 - gg(int)|b, c iqq = 7 - soft(proj)|b, c iqq = 8 - gg(proj)|b, c iqq = 9 - qg(proj)|b, c iqq = 10 - total fro-uncut integrated, c iqq = 11 - total uncut integrated, c iqq = 12 - soft(int), c iqq = 13 - gg(int), c iqq = 14 - <b^2*soft(int)>, c iqq = 15 - <b^2*gg(int)>, c iqq = 16 - soft(proj-int), c iqq = 17 - gg(proj-int), c iqq = 18 - qg(proj-int), c iqq = 19 - <b^2*soft(proj)>, c iqq = 20 - <b^2*gg(proj)>, c iqq = 21 - <b^2*qg(proj)> c----------------------------------------------------------------------- double precision xh,yp!,coefom1,coefom2 common /psar7/ delx,alam3p,gam3p common /psar37/ coefom1,coefom2 include 'epos.inc' include 'epos.incsem' xp=dsqrt(xh)*exp(yp) if(xh.ne.0.d0)then xm=xh/xp else xm=0. endif rp=r2had(iclpro)+r2had(icltar)+slopom*log(max(1.,sy)) zb=exp(-b**2/(4.*.0389*rp)) rh=r2had(iclpro)+r2had(icltar) if(iqq.eq.0)then !soft c rp=r2hads(iclpro)+r2hads(icltar)+slopoms*log(max(1.,sy)) zb=exp(-b**2/(4.*.0389*rp)) om51p=chad(iclpro)*chad(icltar)*gamhads(iclpro) * *gamhads(icltar)*sy**dels*(xp*xm)**(-alppar)*zb/rp elseif(iqq.le.4)then !gg,qg,gq,qq om51p=psvin(sy,xp,xm,zb,iqq) elseif(iqq.eq.5)then !soft(int)|b c rh=alam3p+slopoms*log(max(1.,sy)) om51p=sy**dels*zb**(rp/rh)/rh elseif(iqq.eq.6)then !gg(int)|b om51p=psvin(sy,xp,xm,zb,14) elseif(iqq.eq.7)then !soft(proj)b c rh=r2hads(iclpro)+.5*alam3p+slopoms*log(max(1.,sy)) om51p=chad(iclpro)*gamhads(iclpro)*sy**dels * *xp**(-alppar)*zb**(rp/rh)/rh elseif(iqq.eq.8)then !gg(proj)b om51p=psvin(sy,xp,xm,zb,16) elseif(iqq.eq.9)then !qg(proj)b om51p=psvin(sy,xp,xm,zb,18) elseif(iqq.eq.10)then !total fro-uncut integrated om51p=0.d0 return elseif(iqq.eq.11)then !total uncut integrated om51p=psvin(sy,xp,xm,zb,9) c om51p=om51p+dble(coefom1)/2.d0*om51p**2+dble(coefom2)/6.d0*om51p**3 !!!!!!!!!! c if(om51p.gt.100.d0)om51p=100.d0 elseif(iqq.eq.12)then !soft(int) om51p=sy**dels*4.*.0389 elseif(iqq.eq.13)then !gg(int) om51p=psvin(sy,xp,xm,zb,5) elseif(iqq.eq.14)then !<b^2*soft(int)> c rh=alam3p+slopoms*log(max(1.,sy)) om51p=sy**dels*rh*(4.*.0389)**2 elseif(iqq.eq.15)then !<b^2*gg(int)> om51p=psvin(sy,xp,xm,zb,15) elseif(iqq.eq.16)then !soft(proj-int) om51p=chad(iclpro)*gamhads(iclpro)*sy**dels * *xp**(-alppar)*4.*.0389 elseif(iqq.eq.17)then !gg(proj-int) om51p=psvin(sy,xp,xm,zb,6) elseif(iqq.eq.18)then !qg(proj-int) om51p=psvin(sy,xp,xm,zb,7) elseif(iqq.eq.19)then !<b^2*soft(proj)> c rh=r2hads(iclpro)+.5*alam3p+slopoms*log(max(1.,sy)) om51p=chad(iclpro)*gamhads(iclpro)*sy**dels * *xp**(-alppar)*rh*(4.*.0389)**2 elseif(iqq.eq.20)then !<b^2*gg(proj)> om51p=psvin(sy,xp,xm,zb,17) elseif(iqq.eq.21)then !<b^2*qg(proj)> om51p=psvin(sy,xp,xm,zb,19) else om51p=0. call utstop("Unknown iqq in om51p !&") endif return end cc----------------------------------------------------------------------- c double precision function om2p(xh,yp,xprem0,xmrem0,b,iqq) cc----------------------------------------------------------------------- cc om2p - chi~(x,y) for cut pomeron cc xh - fraction of the energy squared s for the pomeron; cc yp - rapidity for the pomeron; cc xprem - x+ for the projectile remnant; cc xmrem - x- for the target remnant; cc b - impact parameter between the pomeron ends; cc iqq = 0 - total, cc iqq = 1 - 1-cut, cc iqq = 2 - Y+, cc iqq = -2 - Y-, cc iqq = 3 - 1-cut(soft), cc iqq = 4 - 1+(gg), cc iqq = 5 - 1+(qg), cc iqq = 6 - 1+(gq), cc iqq = 7 - 1+(difr) cc iqq = -7 - 1-(difr) cc----------------------------------------------------------------------- c double precision xh,yp,xprem0,xmrem0 c include 'epos.inc' c include 'epos.incsem' c c om2p=0.d0 c sy=xh*engy**2 c xprem=sngl(xprem0) c xmrem=sngl(xmrem0) c xp=dsqrt(xh)*dexp(yp) c if(xh.ne.0.d0)then c xm=xh/xp c else c xm=0. c endif c rp=r2had(iclpro)+r2had(icltar)+slopom*log(max(1.,sy)) c zb=exp(-b**2/(4.*.0389*rp)) c c if(iqq.eq.0)then c om2p=psvy(xp,xprem,xm,xmrem,b,2) c * +psvy(xp,xprem,xm,xmrem,b,-2) c * +psvy(xp,xprem,xm,xmrem,b,3) c * +psvy(xp,xprem,xm,xmrem,b,-3) c * +psvy(xp,xprem,xm,xmrem,b,9) c * +psvy(xp,xprem,xm,xmrem,b,-9) c * +psvx(xp,xprem,xm,xmrem,b,1) c * +psvx(xp,xprem,xm,xmrem,b,2) c * +psvx(xp,xprem,xm,xmrem,b,-2) c * +psvx(xp,xprem,xm,xmrem,b,6) c * +psvx(xp,xprem,xm,xmrem,b,-6) c om2p=om2p+(chad(iclpro)*chad(icltar)*gamhad(iclpro) c * *gamhad(icltar)*sy**dels*(xp*xm)**(-alppar)*zb/rp c * +psvin(sy,xp,xm,zb,1)+psvin(sy,xp,xm,zb,2) c * +psvin(sy,xp,xm,zb,3)+psvin(sy,xp,xm,zb,4)) c elseif(iqq.eq.1)then c om2p=psvy(xp,xprem,xm,xmrem,b,2)+psvy(xp,xprem,xm,xmrem,b,-2) c * +psvx(xp,xprem,xm,xmrem,b,1) c elseif(iqq.eq.2)then c om2p=psvy(xp,xprem,xm,xmrem,b,3) c * +psvx(xp,xprem,xm,xmrem,b,2) c elseif(iqq.eq.-2)then c om2p=psvy(xp,xprem,xm,xmrem,b,-3) c * +psvx(xp,xprem,xm,xmrem,b,-2) c elseif(iqq.eq.3)then c om2p=psvy(xp,xprem,xm,xmrem,b,4)+psvy(xp,xprem,xm,xmrem,b,-4) c * +psvx(xp,xprem,xm,xmrem,b,3) c elseif(iqq.eq.4)then c om2p=psvy(xp,xprem,xm,xmrem,b,5)+psvy(xp,xprem,xm,xmrem,b,7) c * +psvy(xp,xprem,xm,xmrem,b,-5)+psvy(xp,xprem,xm,xmrem,b,-7) c * +psvx(xp,xprem,xm,xmrem,b,4)+psvx(xp,xprem,xm,xmrem,b,-4) c elseif(iqq.eq.5)then c om2p=psvy(xp,xprem,xm,xmrem,b,6)+psvy(xp,xprem,xm,xmrem,b,-8) c * +psvx(xp,xprem,xm,xmrem,b,5) c elseif(iqq.eq.6)then c om2p=psvy(xp,xprem,xm,xmrem,b,-6)+psvy(xp,xprem,xm,xmrem,b,8) c * +psvx(xp,xprem,xm,xmrem,b,-5) c elseif(iqq.eq.7)then c om2p=psvy(xp,xprem,xm,xmrem,b,9) c * +psvx(xp,xprem,xm,xmrem,b,6) c elseif(iqq.eq.-7)then c om2p=psvy(xp,xprem,xm,xmrem,b,-9) c * +psvx(xp,xprem,xm,xmrem,b,-6) c else c stop'om2p-wrong iqq!!!' c endif c return c end c cc----------------------------------------------------------------------- c double precision function om3p(xh,yp,xleg,xprem,xmrem,xlrem c *,b1,b2,b12,iqq) cc----------------------------------------------------------------------- cc om3p - chi~(x,y) for cut pomeron (nuclear effects) cc xh - fraction of the energy squared s for the pomeron; cc yp - rapidity for the pomeron; cc xleg - x for the pomeron leg; cc xprem - x+ for the projectile remnant; cc xmrem - x- for the target remnant; cc xlrem - x for the leg remnant; cc b1 - impact parameter between the pomeron ends; cc b2 - impact parameter for the second pomeron end; cc iqq = 1 - uncut+, cc iqq = 2 - cut+, cc iqq = 3 - scr+, cc iqq = 4 - diffr+, cc iqq = 5 - uncut-, cc iqq = 6 - cut-, cc iqq = 7 - scr-, cc iqq = 8 - diff- cc iqq = 9 - uncut-h+, cc iqq = 10 - uncut-h-, cc iqq = 11 - uncut-YY+, cc iqq = 12 - uncut-YY-, cc----------------------------------------------------------------------- c double precision xh,yp,xleg,xprem,xmrem,xlrem c c om3p=0.d0 c return !!!!!!!!!!!!!!! cc if(iqq.ne.1.and.iqq.ne.5.and.iqq.ne.9.and.iqq.ne.10 cc *.and.iqq.ne.11.and.iqq.ne.12)return c cc$$$ xp=dsqrt(xh)*exp(yp) cc$$$ if(xh.ne.0.d0)then cc$$$ xm=xh/xp cc$$$ else cc$$$ xm=0.d0 cc$$$ endif cc$$$ cc$$$ return c end c cc----------------------------------------------------------------------- c double precision function om4p(xx1,xx2,xx3,xx4 c *,b12,b13,b14,b23,b24,b34,iqq) cc----------------------------------------------------------------------- cc om4p - chi for 2-leg contributions cc xx_i - x+- for pomeron ends; cc b_ij - impact parameter diff. between pomeron ends; cc iqq = 1 - uncut-H, cc iqq = 2 - uncut-YY+, cc iqq = 3 - uncut-YY- cc----------------------------------------------------------------------- c double precision xx1,xx2xx3,xx4 c om4p=0.d0 c return c end c cc------------------------------------------------------------------------ c function omi5pp(sy,xpp,xpm,z,iqq) !former psfsh1 cc----------------------------------------------------------------------- cc omi5pp - integrated semihard interaction eikonal cc sy - energy squared for the hard interaction, cc z - impact parameter factor, z=exp(-b**2/rp), cc iqq - type of the hard interaction: cc 0 - soft, 1 - gg, 2 - qg, 3 - gq cc----------------------------------------------------------------------- c common /ar3/ x1(7),a1(7) c common /ar9/ x9(3),a9(3) c include 'epos.inc' c include 'epos.incsem' c fsy(zsy)=zsy**dels !*(1.-1./zsy)**betpom c c omi5pp=0. c if(iclpro.eq.4.and.iqq.eq.2.or.icltar.eq.4.and.iqq.eq.3)then c spmin=4.*q2min+2.*qcmass**2 c elseif(iqq.ne.0)then c spmin=4.*q2min c else c spmin=0. c endif c if(sy.le.spmin)return c c rp=r2had(iclpro)+r2had(icltar)+slopom*log(max(1.,sy)) c alpq=(alppar+1.)/2. c if(iqq.eq.3)then c iclt=iclpro c iclp=icltar c else c iclp=iclpro c iclt=icltar c endif c c if(iqq.eq.0)then c xpmax=(1.-spmin/sy)**(1.+alplea(iclp)) c do i=1,3 c do m=1,2 c xp=1.-(xpmax*(.5+x9(i)*(m-1.5)))**(1./(1.+alplea(iclp))) c xmmax=(1.-spmin/sy/xp)**(1.+alplea(iclt)) c do i1=1,3 c do m1=1,2 c xm=1.-(xmmax*(.5+x9(i1)*(m1-1.5)))**(1./(1.+alplea(iclt))) c c sy1=sy*xp*xm c rh=r2had(iclpro)+r2had(icltar)+slopom*log(max(1.,sy1)) c omi5pp=omi5pp+a9(i)*a9(i1)*fsy(sy1)*xmmax*z**(rp/rh)/rh c * *(xp*xm)**(-alppar) c enddo c enddo c enddo c enddo c omi5pp=omi5pp*xpmax/(1.+alplea(iclp))/(1.+alplea(iclt)) c * *chad(iclpro)*chad(icltar)*gamhad(iclpro)*gamhad(icltar) c * *(xpp*xpm)**(1.-alppar)/4. c return c else c c xmin=(spmin/sy)**(delh-dels) c do i=1,3 c do m=1,2 c zh=(.5*(1.+xmin-(2*m-3)*x9(i)*(1.-xmin)))**(1./(delh-dels)) c if(iclpro.eq.4.and.iqq.eq.2.or.icltar.eq.4.and.iqq.eq.3)then c call psjti0(zh*sy,sgq,sgqb,4,0) c call psjti0(zh*sy,sqq,sqqb,4,1) c else c call psjti0(zh*sy,sgg,sggb,0,0) c call psjti0(zh*sy,sgq,sgqb,0,1) c call psjti0(zh*sy,sqq,sqqb,1,1) c call psjti0(zh*sy,sqaq,sqaqb,-1,1) c call psjti0(zh*sy,sqqp,sqqpb,1,2) c sqq=(sqq+sqaq+2.*(naflav-1)*sqqp)/naflav/2. c endif c c if(iqq.eq.1)then c stg=0. c do i1=1,3 c do m1=1,2 c xx=.5+x9(i1)*(m1-1.5) c xp=zh**xx c xm=zh/xp c c xp1max=(1.-xp)**(1.+alplea(iclp)) c xm1max=(1.-xm)**(1.+alplea(iclt)) c do i2=1,3 c do m2=1,2 c xp1=1.-(xp1max*(.5+x9(i2)*(m2-1.5))) c * **(1./(1.+alplea(iclp))) c do i3=1,3 c do m3=1,2 c xm1=1.-(xm1max*(.5+x9(i3)*(m3-1.5))) c * **(1./(1.+alplea(iclt))) c if(xp1.lt.xp.or.xm1.lt.xm)write (*,*)'xp1,xm1,xp,xm' c * ,xp1,xm1,xp,xm c c rh=r2had(iclpro)+r2had(icltar)+slopom c * *log(xp1*xm1/xp/xm) c glu1=(1.-xp/xp1)**betpom*(1.-glusea) c sea1=EsoftQZero(xp/xp1)*glusea c glu2=(1.-xm/xm1)**betpom*(1.-glusea) c sea2=EsoftQZero(xm/xm1)*glusea c stg=stg+a9(i1)*a9(i2)*a9(i3)*(glu1*glu2*sgg c * +(glu1*sea2+sea1*glu2)*sgq+sea1*sea2*sqq) c * *xp1max*xm1max*(xp1*xm1)**(dels-alppar) c * *z**(rp/rh)/rh c enddo c enddo c enddo c enddo c enddo c enddo c omi5pp=omi5pp-a9(i)*log(zh)*stg/zh**delh c c else c stq=0. c xpmin=zh**(dels+.5) c do i1=1,3 c do m1=1,2 c xp=(.5*(1.+xpmin-(2*m1-3)*x9(i1)*(1.-xpmin))) c * **(1./(dels+.5)) c xm=zh/xp c if(xp*xpp.lt..99999)then c uv1=psdfh4(xp*xpp,q2min,0.,iclp,1) c dv1=psdfh4(xp*xpp,q2min,0.,iclp,2) c xm1max=(1.-xm)**(1.+alplea(iclt)) c do i2=1,3 c do m2=1,2 c xm1=1.-(xm1max*(.5+x9(i2)*(m2-1.5))) c * **(1./(1.+alplea(iclt))) c c rh=r2had(iclpro)+r2had(icltar)+slopom*log(xm1/xm) c glu2=(1.-xm/xm1)**betpom*(1.-glusea) c sea2=EsoftQZero(xm/xm1)*glusea c stq=stq+a9(i1)*a9(i2)*(glu2*sgq+sea2*sqq)*(uv1+dv1) c * *z**(rp/rh)/rh*xm1max*xm1**(dels-alppar)/sqrt(xp) c * *((1.-xp)/(1.-xp*xpp))**(1.-alpq+alplea(iclp)) c enddo c enddo c endif c enddo c enddo c stq=stq*(1.-xpmin) c omi5pp=omi5pp+a9(i)*stq/zh**delh c endif c enddo c enddo c endif c c omi5pp=omi5pp*(1.-xmin)/(delh-dels) c if(iqq.eq.1)then c omi5pp=omi5pp*chad(iclp)*chad(iclt)*gamhad(iclp) c * *gamhad(iclt)*ffrr**2*(xpp*xpm)**(1.-alppar) c * /(1.+alplea(iclp))/(1.+alplea(iclt))*pi/8.*factk c else c omi5pp=omi5pp*chad(iclp)*chad(iclt)*ffrr*gamhad(iclt) c * *xpp**(1.-alpq)*xpm**(1.-alppar)/(.5+dels) c * /(1.+alplea(iclt))/16.*factk c endif c return c end c c------------------------------------------------------------------------ function om52pi(sy,xpp,xpm,iqq,je1,je2) !modified om51pp c----------------------------------------------------------------------- c sy - energy squared for the hard interaction c c iqq = 0 - sea-sea, c iqq = 1 - val-sea, c iqq = 2 - sea-val, c iqq = 3 - val-val, c c je = emission type c 0 ... no emissions c 1 ... emissions c else ... all c c already b-averaged (\int d2b /sigine*10) c----------------------------------------------------------------------- common /ar3/ x1(7),a1(7) common /psar7/ delx,alam3p,gam3p include 'epos.inc' include 'epos.incsem' if(iqq.lt.0.or.iqq.gt.3)stop'om52pi: unvalid iqq' om52pi=0. ef1=0 ef2=0 ef3=0 ef4=0 if( je1.ge.1 .and. je2.ge.1) ef1=1 if( je1.ge.1 .and.(je2.eq.0.or.je2.eq.2))ef2=1 if((je1.eq.0.or.je1.eq.2).and. je2.ge.1) ef3=1 if((je1.eq.0.or.je1.eq.2).and.(je2.eq.0.or.je2.eq.2))ef4=1 spmin=4.*q2min if(sy.le.spmin)goto999 if(iqq.eq.1)then iclv=iclpro ctp060829 icls=icltar elseif(iqq.eq.2)then ctp060829 icls=iclpro iclv=icltar endif delss=dels if(iqq.eq.3)delss=-0.5 xmin=spmin/sy xmin=xmin**(delh-delss) alpq=(alppar+1.)/2. c numerical integration over zh do i=1,7 do m=1,2 zh=(.5*(1.+xmin-(2*m-3)*x1(i)*(1.-xmin)))**(1./(delh-delss)) sgg= ef1 *pijet(2,q2min,q2min,zh*sy,0,0) * + (ef2+ef3)*pijet(1,q2min,q2min,zh*sy,0,0) * + ef4 *pijet(0,q2min,q2min,zh*sy,0,0) sgq= ef1 *pijet(2,q2min,q2min,zh*sy,0,1) * + (ef2+ef3)*pijet(1,q2min,q2min,zh*sy,0,1) * + ef4 *pijet(0,q2min,q2min,zh*sy,0,1) sqq= ef1 *pijet(2,q2min,q2min,zh*sy,1,1) * + (ef2+ef3)*pijet(1,q2min,q2min,zh*sy,1,1) * + ef4 *pijet(0,q2min,q2min,zh*sy,1,1) sqaq= ef1 *pijet(2,q2min,q2min,zh*sy,-1,1) * + (ef2+ef3)*pijet(1,q2min,q2min,zh*sy,-1,1) * + ef4 *pijet(0,q2min,q2min,zh*sy,-1,1) sqqp= ef1 *pijet(2,q2min,q2min,zh*sy,1,2) * + (ef2+ef3)*pijet(1,q2min,q2min,zh*sy,1,2) * + ef4 *pijet(0,q2min,q2min,zh*sy,1,2) sqqi=sqq sqq=(sqq+sqaq+2.*(naflav-1)*sqqp)/naflav/2. if(iqq.eq.0)then stg=0. do i1=1,7 do m1=1,2 xx=.5+x1(i1)*(m1-1.5) xp=zh**xx xm=zh/xp glu1=EsoftGluonTil(xp) sea1=EsoftQuarkTil(xp) glu2=EsoftGluonTil(xm) sea2=EsoftQuarkTil(xm) dstg= glu1*glu2*sgg * +(glu1*sea2+sea1*glu2)*sgq !ccccc * +sea1*sea2*sqq !ccccc stg=stg+a1(i1)*dstg enddo enddo om52pi=om52pi-a1(i)*log(zh)*stg/zh**delh elseif(iqq.eq.3)then stq=0. !int^1_(sqrt(z)) dx_p / x_p / sqrt(1-x_p) =int^(tmax)_(0) dt tmax=sqrt(1.-sqrt(zh)) !t=ln((1+sqrt(1-x_p))/(1-sqrt(1-x_p))) tmax=log((1.+tmax)/(1.-tmax)) if(tmax.gt.1.e-20)then do i1=1,7 do m1=1,2 t=tmax*(.5+x1(i1)*(m1-1.5)) z01=((1.d0-exp(-1.d0*t))/(1.d0+exp(-1.d0*t)))**2 xp=1.-z01 xm=zh/xp if(xp*xpp.le..9999.and.xm*xpm.le..9999 * .or.xm*xpp.le..9999.and.xp*xpm.le..9999)then stq=stq+a1(i1) * *(psharg(xp*xpp,xm*xpm,sqqi,sqqp,sqaq) * +psharg(xm*xpp,xp*xpm,sqqi,sqqp,sqaq)) * *max(1e-20,1.-xp)**(.5-alpq) * *max(1e-20,1.-xm)**(-alpq) * *xp**delss*xm**delss * *xpp**alppar/gamhad(iclpro) ! Eval * *xpm**alppar/gamhad(icltar) ! Eval endif enddo enddo stq=stq*tmax endif om52pi=om52pi+a1(i)*stq/zh**delh elseif(iqq.eq.1.or.iqq.eq.2)then stq=0. tmax=acos(sqrt(zh)) do i1=1,7 do m1=1,2 t=tmax*(.5+x1(i1)*(m1-1.5)) xp=cos(t)**2 xm=zh/xp if(xp*xpp.lt..99999)then uv1=psdfh4(xp*xpp,q2min,0.,iclv,1) ! Eval dv1=psdfh4(xp*xpp,q2min,0.,iclv,2) ! Eval glu2=EsoftGluonTil(xm) sea2=EsoftQuarkTil(xm) dstq=0 if(xp.ne.1.) * dstq=(glu2*sgq+sea2*sqq)*(uv1+dv1) * *(1.-xp*xpp)**(-1.+alpq-alplea(iclv)) ! Eval * *xp**(delss-.5)*(1.-xp)**(-alpq+.5) ! Eval *sqrt(1-x)/sqrt(x) * *xpp**alppar/gamhad(iclv) ! Eval stq=stq+a1(i1)*dstq endif enddo enddo stq=stq*tmax om52pi=om52pi+a1(i)*stq/zh**delh else stop'om52pi: unvalid iqq (2). ' endif enddo enddo om52pi=om52pi*(1.-xmin)/(delh-delss) if(iqq.eq.0)then om52pi=om52pi/4 elseif(iqq.eq.3)then om52pi=om52pi/4 * * utgam1(2.+alplea(iclpro)-alpq) ! Eval * /utgam1(1.+alplea(iclpro))/utgam1(1.-alpq) ! Eval * * utgam1(2.+alplea(icltar)-alpq) ! Eval * /utgam1(1.+alplea(icltar))/utgam1(1.-alpq) ! Eval * /xpp**alpq/xpm**alpq ! Eval elseif(iqq.le.2)then om52pi=om52pi/2 * *utgam1(2.+alplea(iclv)-alpq)/utgam1(1.+alplea(iclv)) ! Eval * /utgam1(1.-alpq) ! Eval * /xpp**alpq ! Eval endif 999 continue om52pi=om52pi*factk * .0390 /sigine*10 /2. end c------------------------------------------------------------------------ function psharg(zh1,zh2,sqq,sqqp,sqaq) c----------------------------------------------------------------------- include 'epos.incsem' include 'epos.inc' alpq=(alppar+1.)/2. if(zh1.le..9999.and.zh2.le..9999)then uv1=psdfh4(zh1,q2min,0.,iclpro,1) dv1=psdfh4(zh1,q2min,0.,iclpro,2) uv2=psdfh4(zh2,q2min,0.,icltar,1) dv2=psdfh4(zh2,q2min,0.,icltar,2) if(iclpro.eq.2.and.icltar.eq.2)then !proton fff=sqq*(uv1*uv2+dv1*dv2)+sqqp*(uv1*dv2+dv1*uv2) elseif(iclpro.eq.1.or.icltar.eq.1)then !pion fff=sqq*uv1*uv2+sqaq*dv1*dv2+sqqp*(uv1*dv2+dv1*uv2) elseif(iclpro.eq.3.or.icltar.eq.3)then !kaon fff=sqq*uv1*uv2+sqqp*(uv1*dv2+dv1*uv2+dv1*dv2) elseif(iclpro.eq.4.or.icltar.eq.4)then !J/psi fff=sqq*uv1*(uv2+dv2) else fff=0. call utstop("Projectile not know in psharg !&") endif psharg=fff * *(1.-zh1)**(-1.+alpq-alplea(iclpro)) * *(1.-zh2)**(-1.+alpq-alplea(icltar)) else psharg=0. endif return end c------------------------------------------------------------------------ function om51pp(sy,xpp,z,iqq) !former psfsh c----------------------------------------------------------------------- c om51pp - semihard interaction eikonal c sy - energy squared for the hard interaction, c z - impact parameter factor, z=exp(-b**2/rp), c iqq - type of the hard interaction: c 0 - gg, 1 - qg, 2 - gq, 3 - gg(int), 4 - gg(proj), 5 - qg(proj), c 6 - gg(int)|b=0, 7 - <b^2*gg(int)>, 8 - gg(proj)|b=0, c 9 - <b^2*gg(proj)>, 10 - qg(proj)|b=0, 11 - <b^2*qg(proj)> c----------------------------------------------------------------------- common /ar3/ x1(7),a1(7) common /psar7/ delx,alam3p,gam3p include 'epos.inc' include 'epos.incsem' om51pp=0. if(iqq.eq.0.or.iqq.eq.3.or.iqq.eq.4 *.or.iqq.eq.6.or.iqq.eq.7.or.iqq.eq.8.or.iqq.eq.9 *.or.iclpro.ne.4.and.(iqq.eq.1.or.iqq.eq.5 *.or.iqq.eq.10.or.iqq.eq.11) *.or.icltar.ne.4.and.iqq.eq.2)then spmin=4.*q2min else spmin=4.*q2min+2.*qcmass**2 endif if(sy.le.spmin)goto999 icls=iclpro if(iqq.eq.1.or.iqq.eq.5.or.iqq.eq.10.or.iqq.eq.11)then iclv=iclpro icls=icltar elseif(iqq.eq.2)then icls=iclpro iclv=icltar endif xmin=spmin/sy xmin=xmin**(delh-dels) rp=r2had(iclpro)+r2had(icltar)+slopom*log(max(1.,sy)) alpq=(alppar+1.)/2. c numerical integration over zh do i=1,7 do m=1,2 zh=(.5*(1.+xmin-(2*m-3)*x1(i)*(1.-xmin)))**(1./ * (delh-dels)) if(iqq.eq.0.or.iqq.eq.3.or.iqq.eq.4 * .or.iqq.eq.6.or.iqq.eq.7.or.iqq.eq.8.or.iqq.eq.9 * .or.iclpro.ne.4.and.(iqq.eq.1.or.iqq.eq.5 * .or.iqq.eq.10.or.iqq.eq.11) * .or.icltar.ne.4.and.iqq.eq.2)then call psjti0(zh*sy,sgg,sggb,0,0) !inclusive (sj) and born (sjb) call psjti0(zh*sy,sgq,sgqb,0,1) call psjti0(zh*sy,sqq,sqqb,1,1) call psjti0(zh*sy,sqaq,sqaqb,-1,1) call psjti0(zh*sy,sqqp,sqqpb,1,2) sqq=(sqq+sqaq+2.*(naflav-1)*sqqp)/naflav/2. c...........test....... c tgg= psjet(q2min,q2min,q2min,zh*sy,0,0,0) c * +2*psjet1(q2min,q2min,q2min,zh*sy,0,0,0) c * + psborn(q2min,q2min,q2min,zh*sy,0,0,0,1) c tgq= psjet(q2min,q2min,q2min,zh*sy,0,1,0) c * +2*psjet1(q2min,q2min,q2min,zh*sy,0,1,0) c * + psborn(q2min,q2min,q2min,zh*sy,0,1,0,1) c tqq= psjet(q2min,q2min,q2min,zh*sy,1,1,0) c * +2*psjet1(q2min,q2min,q2min,zh*sy,1,1,0) c * + psborn(q2min,q2min,q2min,zh*sy,1,1,0,1) c tqa= psjet(q2min,q2min,q2min,zh*sy,-1,1,0) c * +2*psjet1(q2min,q2min,q2min,zh*sy,-1,1,0) c * + psborn(q2min,q2min,q2min,zh*sy,-1,1,0,1) c tqqp= psjet(q2min,q2min,q2min,zh*sy,1,2,0) c * +2*psjet1(q2min,q2min,q2min,zh*sy,1,2,0) c * + psborn(q2min,q2min,q2min,zh*sy,1,2,0,1) c write(6,'(f12.2,3x,2f7.3,2(3x,2f7.3))') c * zh*sy,tgg,sgg, tgq,sgq, tqqp,sqqp c....................... else call psjti0(zh*sy,sgq,sgqb,4,0) call psjti0(zh*sy,sqq,sqqb,4,1) endif if(iqq.eq.0.or.iqq.eq.3.or.iqq.eq.4 * .or.iqq.eq.6.or.iqq.eq.7.or.iqq.eq.8.or.iqq.eq.9)then stg=0. do i1=1,7 do m1=1,2 xx=.5+x1(i1)*(m1-1.5) xp=zh**xx xm=zh/xp glu1=(1.-xp)**betpom*(1.-glusea) sea1=EsoftQZero(xp)*glusea glu2=(1.-xm)**betpom*(1.-glusea) sea2=EsoftQZero(xm)*glusea rh=0. if(iqq.eq.0)then rh=r2had(iclpro)+r2had(icltar)-slopom*log(zh) elseif(iqq.eq.3.or.iqq.eq.4)then rh=1. elseif(iqq.eq.6.or.iqq.eq.7)then rh=alam3p-slopom*log(zh) elseif(iqq.eq.8.or.iqq.eq.9)then rh=r2had(iclpro)+.5*alam3p-slopom*log(zh) endif dstg=(glu1*glu2*sgg+ * (glu1*sea2+sea1*glu2)*sgq+sea1*sea2*sqq) * *z**(rp/rh)/rh if(iqq.eq.7.or.iqq.eq.9)dstg=dstg*rh**2 stg=stg+a1(i1)*dstg enddo enddo om51pp=om51pp-a1(i)*log(zh)*stg/zh**delh else stq=0. tmax=acos(sqrt(zh)) do i1=1,7 do m1=1,2 t=tmax*(.5+x1(i1)*(m1-1.5)) xp=cos(t)**2 xm=zh/xp if(xp*xpp.lt..99999)then uv1=psdfh4(xp*xpp,q2min,0.,iclv,1) dv1=psdfh4(xp*xpp,q2min,0.,iclv,2) glu2=(1.-xm)**betpom*(1.-glusea) sea2=EsoftQZero(xm)*glusea rh=0. if(iqq.le.2)then rh=r2had(iclpro)+r2had(icltar)-slopom*log(xm) elseif(iqq.eq.5)then rh=1. elseif(iqq.le.10.or.iqq.le.11)then rh=r2had(iclpro)+.5*alam3p-slopom*log(xm) endif dstq=0 if(xp.ne.1.) * dstq=(glu2*sgq+sea2*sqq)*(uv1+dv1) * *z**(rp/rh)/rh * *(1.-xp*xpp)**(-1.+alpq-alplea(iclv)) * *xp**(dels-.5)*(1.-xp)**(-alpq+.5) if(iqq.eq.11)dstq=dstq*rh**2 stq=stq+a1(i1)*dstq endif enddo enddo stq=stq*tmax om51pp=om51pp+a1(i)*stq/zh**delh endif enddo enddo om51pp=om51pp*(1.-xmin)/(delh-dels)/sy**delh/2. if(iqq.eq.0)then om51pp=om51pp*chad(iclpro)*chad(icltar)*gamhad(iclpro) * *gamhad(icltar)*ffrr**2*pi elseif(iqq.eq.3)then om51pp=om51pp*ffrr**2*pi*4.*.0389 elseif(iqq.eq.6)then om51pp=om51pp*ffrr**2*pi elseif(iqq.eq.7)then om51pp=om51pp*ffrr**2*pi*(4.*.0389)**2 elseif(iqq.eq.4.or.iqq.eq.8.or.iqq.eq.9)then om51pp=om51pp*ffrr**2*pi*chad(iclpro)*gamhad(iclpro) if(iqq.eq.4)om51pp=om51pp*4.*.0389 if(iqq.eq.9)om51pp=om51pp*(4.*.0389)**2 elseif(iqq.le.2)then om51pp=om51pp*chad(iclpro)*chad(icltar)*ffrr*gamhad(icls) * *utgam1(2.+alplea(iclv)-alpq)/utgam1(1.+alplea(iclv)) * /utgam1(1.-alpq)/2./xpp**alpq elseif(iqq.eq.5.or.iqq.eq.10.or.iqq.eq.11)then om51pp=om51pp*chad(iclv)*ffrr * *utgam1(2.+alplea(iclv)-alpq)/utgam1(1.+alplea(iclv)) * /utgam1(1.-alpq)/2./xpp**alpq if(iqq.eq.5)om51pp=om51pp*4.*.0389 if(iqq.eq.11)om51pp=om51pp*(4.*.0389)**2 endif 999 continue end c------------------------------------------------------------------------------- subroutine epocrossc(niter,gtot,gprod,gabs,gcoh,gqel,gdd) c------------------------------------------------------------------------------- c epocrossc - nucleus-nucleus (nucleus-hydrogen) interaction cross sections c by calculation will real nuclear profiles and eikonal (simplified simulations) c gtot - total cross section c gprod - production cross section (all diffraction included) c gabs - cut Pomerons cross section (no diffraction at all) c gdd - proj (ionudi=2) or proj or targ (ionudi=0/3) excited diffraction c cross section c gcoh - coherent (elastic with respect to the projectile) cross section c (non excited diff proj if ionudi=2, non excited proj+targ if ionudi=0/3) c c Be careful : this function is not symmetric for gdd and gqel (only projectile c diffraction) in case of ionudi=2. c (target diffraction is not treated explicitely and contributes to c gprod, gdd, gcoh and gtot). c c WARNING : results are sure only in case of ionudi=1 (no substraction from c diffractive part) in particular for AA with A > 10 (nuclear diff c not well described). For pA seems to be OK with ionudi 2 and 3. c c code from QGSJET programs by S.Ostapchenko c------------------------------------------------------------------------------- include 'epos.inc' include 'epos.incems' common /cncl/xproj(mamx),yproj(mamx),zproj(mamx) * ,xtarg(mamx),ytarg(mamx),ztarg(mamx) common/geom/rmproj,rmtarg,bmax,bkmx dimension wabs(28),wdd(28),wcoh(28),wprod(28),wqel(28) & ,b0(28),ai(28) common /ar3/ x1(7),a1(7) double precision xgabs,xgdd,xgprod,xgcoh,xgqel call utpri('epocrs',ish,ishini,2) if(ish.ge.2)write(ifch,201)niter,bmax kollini=koll !koll modified do i=1,7 b0(15-i)=bmax*sqrt((1.+x1(i))/2.) b0(i)=bmax*sqrt((1.-x1(i))/2.) ai(i)=a1(i)*bmax**2*pi*5.05 !factor change cs ai(15-i)=ai(i) enddo if(maproj.gt.1.or.matarg.gt.1)then difn=max(difnuc(maproj),difnuc(matarg)) else difn=1. endif do i=1,7 tp=(1.+x1(i))/2. tm=(1.-x1(i))/2. b0(14+i)=bmax-log(tp)*difn b0(29-i)=bmax-log(tm)*difn ai(14+i)=a1(i)*b0(14+i)/tp*10.*difn*pi ai(29-i)=a1(i)*b0(29-i)/tm*10.*difn*pi enddo do i=1,28 wabs(i)=0. wdd(i)=0. wprod(i)=0. wcoh(i)=0. wqel(i)=0. enddo do nc=1,niter if(maproj.eq.1)then xproj(1)=0. yproj(1)=0. zproj(1)=0. else call conxyz('p',mamx,xproj,yproj,zproj,ypjtl-yhaha) endif if(matarg.eq.1)then xtarg(1)=0. ytarg(1)=0. ztarg(1)=0. else call conxyz('t',mamx,xtarg,ytarg,ztarg,yhaha) endif do i=1,28 call epogcr(b0(i),xgabs,xgdd,xgprod,xgcoh,xgqel) wabs(i)=wabs(i)+sngl(xgabs) wdd(i)=wdd(i)+sngl(xgdd) wprod(i)=wprod(i)+sngl(xgprod) wcoh(i)=wcoh(i)+sngl(xgcoh) wqel(i)=wqel(i)+sngl(xgqel) enddo enddo gabs=0. gdd=0. gcoh=0. gprod=0. gqel=0. do i=1,28 wabs(i)=wabs(i)/niter wdd(i)=wdd(i)/niter wcoh(i)=wcoh(i)/niter wprod(i)=wprod(i)/niter wqel(i)=wqel(i)/niter gabs=gabs+ai(i)*wabs(i) gdd=gdd+ai(i)*wdd(i) gcoh=gcoh+ai(i)*wcoh(i) gqel=gqel+ai(i)*wqel(i) gprod=gprod+ai(i)*wprod(i) enddo gtot=gprod+gcoh !total=all cut (with diff) + all uncut if(ish.ge.2)write (ifch,202)gtot,gprod,gabs,gdd,gcoh,gqel 201 format(2x,'epocrossc - A-B interaction cross sections,' *,' N of iter.:',i5,' bmax:',f5.2) 202 format(2x,'epocrossc: gtot=',e10.3,2x,'gprod=',e10.3,2x *,'gabs=',e10.3/4x,'gdd=',e10.3,2x,'gcoh=',e10.3,'gqel=',e10.3) koll=kollini call utprix('epocrs',ish,ishini,2) return end c------------------------------------------------------------------------------- subroutine epogcr(b,gabs,gdd,gprod,gcoh,gqel) c------------------------------------------------------------------------------- c epogcr - integrands (b-profiles) for nucleus-nucleus cross sections c b - impact parameter c code from QGSJET programs by S.Ostapchenko c------------------------------------------------------------------------------- include 'epos.inc' include 'epos.incems' include 'epos.incpar' common /cncl/xproj(mamx),yproj(mamx),zproj(mamx) * ,xtarg(mamx),ytarg(mamx),ztarg(mamx) common/geom/rmproj,rmtarg,bmax,bkmx common/scrangle/ phik3(kollmx),thetak3(kollmx) double precision vin,gabs,gdd,gprod,gcoh,fdd,gqel,fdt,vdt,vcu if(ish.ge.9)write (ifch,201)b gprod=1d0 gabs=1d0 gdd=1d0 fdd=1d0 fdt=1d0 bx=0 by=0 if(maproj.eq.1.and.matarg.eq.1)then if(b.gt.bkmx)then koll=0 else koll=1 bk(1)=b iproj(1)=1 itarg(1)=1 lproj(1)=1 ltarg(1)=1 lproj3(1)=1 ltarg3(1)=1 kproj3(1,1)=1 ktarg3(1,1)=1 kproj(1,1)=1 ktarg(1,1)=1 endif else bx=b by=0. koll=0 do i=1,maproj lproj(i)=0 lproj3(i)=0 enddo do j=1,matarg ltarg(j)=0 ltarg3(j)=0 enddo do 12 i=1,maproj do 11 j=1,matarg bij=sqrt((xproj(i)+bx-xtarg(j))**2+(yproj(i)+by-ytarg(j))**2) if(bij.gt.bkmx)goto 11 koll=koll+1 if(koll.gt.kollmx)call utstop('epogcr: kollmx too small&') bk(koll)=bij bkx(koll)=xproj(i)+bx-xtarg(j) bky(koll)=yproj(i)+by-ytarg(j) iproj(koll)=i itarg(koll)=j lproj(i)=lproj(i)+1 ltarg(j)=ltarg(j)+1 kproj(i,lproj(i))=koll ktarg(j,ltarg(j))=koll if(iscreen.ne.0.and.bij.le.bkmxndif)then if(zbrmax.gt.0..and.bij.gt.zbcut+zbrmax*rangen())goto 11 lproj3(i)=lproj3(i)+1 ltarg3(j)=ltarg3(j)+1 kproj3(i,lproj3(i))=koll ktarg3(j,ltarg3(j))=koll c define angle for anti-shadowing if(abs(bky(koll)).gt.1.e-6)then if(abs(bkx(koll)).gt.1.e-6)then phik3(koll)=atan(bky(koll)/bkx(koll)) else phik3(koll)=sign(0.5*pi,bky(koll)) endif elseif(bkx(koll).lt.0.)then phik3(koll)=pi endif if(bk(koll).gt.0.)then thetak3(koll)=atan(bglaubx/bk(koll)) else thetak3(koll)=0.5*pi endif endif 11 continue 12 continue endif if(koll.eq.0)then gabs=0d0 gdd=0d0 gprod=0d0 gcoh=0d0 gqel=0d0 goto 1000 endif if(iscreen.ne.0)call CalcScrPair(b) irea=-1 call GfunParK(irea) if(ionudi.eq.0 & .and.(maproj.ne.1.or.matarg.ne.1).and.nglevt.eq.0)then gabs=0d0 gdd=0d0 gprod=0d0 gcoh=0d0 gqel=0d0 goto 1000 endif call integom1(irea) do n=1,maproj call epov(n,vin,vcu,vdt) gprod=gprod*vin gabs=gabs*vcu fdd=fdd*(1.-rexdif(iclpro)) & **(1.+rexres(iclpro)*float(lproj(n)-1)) fdt=fdt*vdt enddo gprod=min(gprod,1.d0) gcoh=1d0-2d0*sqrt(gprod)+gprod gprod=1d0-gprod gabs=max(0d0,1d0-gabs) !cut (no diffraction) gdd=max(0d0,gprod-gabs) !diffractive part gqel=0d0 if(ionudi.eq.2.and.maproj+matarg.gt.2)then gqel=fdd*gdd !quasielastic = diffractive without excited proj. if(iLHC.eq.1)gqel=gqel-fdd*fdt*gdd !DPE counted as inelastic gdd=gdd-gqel !only excited projectile diffraction elseif(iLHC.ne.1)then gqel=fdd*fdt*gdd !quasielastic = diffractive without excited proj. or targ gdd=gdd-gqel !inelastic part due to excited diffraction endif 1000 continue if(ish.ge.9)write (ifch,202)gabs,gdd,gprod,gcoh,gqel,fdd,fdt 201 format(2x,'epogcr-integrands for nucleus-nucleus cross sections,' *,' b=',e10.3) 202 format(2x,'epogcr: gabs=',e10.3,2x,'gdd=',e10.3,2x,'gprod=',e10.3 *,2x,'gcoh=',e10.3,2x,'gqel=',e10.3,2x,'fdd=',e10.3,' fdt=',e10.3) return end c============================================================================= subroutine epov(n,vin,vcu,vdt) c epov - eikonal factors for nucleus-nucleus interaction c (used for cross-section calculation) c n - projectile nucleon indice c vin - all uncut pomerons c vcu - all uncut non diff pomerons c vdt - non diffractive excitation factor for target c code from QGSJET programs by S.Ostapchenko c---------------------------------------------------------------------------- include 'epos.inc' include 'epos.incems' common /cncl/xproj(mamx),yproj(mamx),zproj(mamx) * ,xtarg(mamx),ytarg(mamx),ztarg(mamx) double precision vvv2,vvv1,dv,vin,vcu,vdt,PhiExpoK,PhiExpoK2 if(ish.ge.9)write (ifch,201)xproj(n),yproj(n) vin=0.d0 vcu=0.d0 vvv1=1.d0 vvv2=1.d0 dv=1.d0 do m=1,lproj(n) k=kproj(n,m) vvv2=vvv2*max(0.d0,PhiExpoK2(k,1.d0,1.d0)) vvv1=vvv1*max(0.d0,PhiExpoK(k,1.d0,1.d0)) dv=dv*(1.-rexdif(icltar)) & **(1.+rexres(icltar)*float(ltarg(m)-1)) enddo vcu=vvv2 vin=vvv1 !exp(-2 * chi) vdt=dv if(ish.ge.9)write (ifch,202)vin,vcu,vdt if(ish.ge.9)write (ifch,203) 201 format(2x,'epov - eikonal factor: nucleon coordinates x=', *e10.3,2x,'y=',e10.3) 202 format(2x,'vin=',e10.3,2x,'vcu=',e10.3,2x,'vdt=',e10.3) 203 format(2x,'epov - end') return end c------------------------------------------------------------------------ subroutine psfz(iqq,gz2,b) c----------------------------------------------------------------------- c hadron-nucleus cross sections calculation c b - impact parameter squared C iqq - 1 = elastic cross section C 2 = inelastic cross section c----------------------------------------------------------------------- double precision PhiExpo include 'epos.inc' include 'epos.incems' include 'epos.incpar' common /ar3/ x1(7),a1(7) external pttcs,pprcs gz2=0. e1=exp(-1.) if(iomega.eq.2)then !no dif rs=r2had(iclpro)+r2had(icltar)+slopom*log(engy**2) else rs=r2had(iclpro)+r2had(icltar)+max(slopom,slopoms)*log(engy**2) & +gwidth*(r2had(iclpro)+r2had(icltar)) & +bmxdif(iclpro,icltar)/4./0.0389 endif rpom=4.*.0389*rs kollini=koll !koll modified in zzfz koll=1 if(iscreen.ne.0.and.(maproj.gt.1.or.matarg.gt.1))then call zzfz(zzp,zzt,kollth,b) koll=kollth else zzp=0. zzt=0. endif do i1=1,7 do m=1,2 z=.5+x1(i1)*(m-1.5) zv1=exp(-z) zv2=(e1*z) b1=sqrt(-rpom*log(zv1)) b2=sqrt(-rpom*log(zv2)) if(maproj.eq.1.and.matarg.eq.1)then cg1=1. cg2=1. elseif(matarg.eq.1)then cg1=ptrot(pprcs,b,b1) cg2=ptrot(pprcs,b,b2) else cg1=ptrot(pttcs,b,b1) cg2=ptrot(pttcs,b,b2) endif vv21=sngl(Phiexpo(zzp,zzt,1.,1.d0,1.d0,engy**2,b1)) vv22=sngl(Phiexpo(zzp,zzt,1.,1.d0,1.d0,engy**2,b2)) if(iqq.ne.1)then gz2=gz2+a1(i1)*(cg1*(1.-vv21)+cg2*(1.-vv22)/z) else vv11=sngl(Phiexpo(zzp,zzt,0.5,1.d0,1.d0,engy**2,b1)) vv12=sngl(Phiexpo(zzp,zzt,0.5,1.d0,1.d0,engy**2,b2)) gz2=gz2+a1(i1)*(cg1*(vv21-2.*vv11+1.) & +cg2*(vv22-2.*vv12+1.)/z) endif enddo enddo gz2=gz2*rpom*0.5 koll=kollini return end c------------------------------------------------------------------------ subroutine zzfz(zzp,zzt,kollth,b) c----------------------------------------------------------------------- c hadron-nucleus cross sections calculation c b - impact parameter squared C xsfct - 0.5 = total cross section C 1.0 = inelastic cross section c----------------------------------------------------------------------- common /psar50/ zznuc,b2xnuc include 'epos.inc' include 'epos.incems' include 'epos.incpar' common /ar3/ x1(7),a1(7) external pttcs,pprcs,pttzz,pprzz zzp=0. zzt=0. kollth=1 if(iscreen.eq.0.or.(maproj.eq.1.and.matarg.eq.1))return rs=r2had(iclpro)+r2had(icltar)+slopom*log(engy**2) rpom=4.*.0389*rs bgl2=2.*rpom*epscrp zzpp=epscrw*fscra(engy/egyscr) c caculate the radius where Z is saturated at epscrx to define the bases c of nuclear shadowing satrad=0. if(zzpp.gt.0.)satrad=-bgl2*log(epscrx/zzpp) bglx=zbrads*sqrt(max(0.1,satrad)) fzbrmax=1. if(zbrmax.gt.0)fzbrmax=zbrmax fzbcut=1. if(zbcut.gt.0)fzbcut=zbcut*bglx fzbrads=1. if(bglx.gt.0)fzbrads=bglx fnuc=1.2*fzbcut/fzbrads b2xnuc=bgl2+4.*fzbrmax*sqrt(float(maproj*matarg))*fnuc e1=exp(-1.) colp=0. colt=0. do i1=1,7 do m=1,2 z=.5+x1(i1)*(m-1.5) zv1=exp(-z) zv2=(e1*z) b1=sqrt(-rpom*log(zv1)) b2=sqrt(-rpom*log(zv2)) if(maproj.gt.1)then cg1=ptrot(pprcs,b,b1) cg2=ptrot(pprcs,b,b2) colnuc=a1(i1)*(cg1+cg2/z) colp=colp+colnuc rho=0.05 zznuc=epscrw*fscro(engy/egyscr,rho) zp1=ptrot(pprzz,b,b1) zp2=ptrot(pprzz,b,b2) zzp=zzp+a1(i1)*(zp1+zp2/z) endif if(matarg.gt.1)then cg1=ptrot(pttcs,b,b1) cg2=ptrot(pttcs,b,b2) colnuc=a1(i1)*(cg1+cg2/z) colt=colt+colnuc rho=0.05 zznuc=epscrw*fscro(engy/egyscr,rho) zt1=ptrot(pttzz,b,b1) zt2=ptrot(pttzz,b,b2) zzt=zzt+a1(i1)*(zt1+zt2/z) endif enddo enddo colp=sqrt(colp) colt=sqrt(colt) if(colp.gt.1.)then kollth=nint(max(1.,colp)) colp=fnuc*log(colp) zzp=sqrt(zzp) zzp=0.01*zzp*colp*bgl2 c saturation zzp=min(zzp,colp*epscrx) else zzp=0. endif if(colt.gt.1.)then kollth=nint(max(1.,kollth+colt)) colt=fnuc*log(colt) zzt=sqrt(zzt) zzt=0.01*zzt*colt*bgl2 c saturation zzt=min(zzt,colt*epscrx) else zzt=0. endif c zzp=zzp*2. !correction to have formula=MC c zzt=zzt*2. c print *,'ici',b,zzp,zzt,kollth,b2xnuc return end c------------------------------------------------------------------------ function ptgau(func,bm,ipt,iqq) c----------------------------------------------------------------------- c impact parameter integration for impact parameters <bm - c for nucleus-nucleus and hadron-nucleus cross-sections calculation c ipt=1 : projectile, ipt=2 : target c iqq=1 : elastic xsection, iqq=2 : inelastic cross section c----------------------------------------------------------------------- include 'epos.inc' common /ar3/ x1(7),a1(7) external func ptgau=0. do i=1,7 do m=1,2 b=bm*sqrt(.5+x1(i)*(m-1.5)) ptgau=ptgau+func(b,ipt,iqq)*a1(i) enddo enddo ptgau=ptgau*bm**2*pi*.5 return end c------------------------------------------------------------------------ function ptgau1(bm,ipt,iqq) c----------------------------------------------------------------------- c impact parameter integration for impact parameters >bm - c for hadron-nucleus cross-sections calculation c ipt=1 : projectile, ipt=2 : target c iqq=1 : elastic xsection, iqq=2 : inelastic cross section c----------------------------------------------------------------------- include 'epos.inc' common /ar5/ x5(2),a5(2) ptgau1=0. if(ipt.eq.1)then difn=difnuc(maproj) else difn=difnuc(matarg) endif do i=1,2 b=bm+x5(i)*difn ptgau1=ptgau1+ptfau(b,ipt,iqq)*a5(i)*exp(x5(i))*b*2.*pi*difn enddo return end c------------------------------------------------------------------------ function ptgau2(bm,iqq) c----------------------------------------------------------------------- c impact parameter integration for impact parameters >bm - c for nucleus-nucleus cross-sections calculation c iqq=1 : elastic xsection, iqq=2 : inelastic cross section c----------------------------------------------------------------------- include 'epos.inc' common /ar5/ x5(2),a5(2) ptgau2=0. difn=difnuc(maproj)+difnuc(matarg) do i=1,2 b=bm+x5(i)*difn ptgau2=ptgau2+ptfauAA(b,iqq)*a5(i)*exp(x5(i))*b*2.*pi*difn enddo return end c------------------------------------------------------------------------ function ptfau(b,ipt,iqq) c----------------------------------------------------------------------- c ptfau - integrands for hadron-nucleus cross-sections calculation c ipt=1 : projectile, ipt=2 : target c iqq=1 : elastic xsection, iqq=2 : inelastic cross section c----------------------------------------------------------------------- include 'epos.inc' common /psar35/ anorm,anormp call psfz(iqq,gz2,b) if(ipt.eq.1)then ptfau=1.-max(0.,(1.-anormp*gz2))**maproj else ptfau=1.-max(0.,(1.-anorm*gz2))**matarg endif return end c------------------------------------------------------------------------ function ptfauAA(b,iqq) c----------------------------------------------------------------------- c ptfau - integrands for hadron-nucleus cross-sections calculation c iqq=1 : elastic xsection, iqq=2 : inelastic cross section c----------------------------------------------------------------------- include 'epos.inc' common /ar3/ x1(7),a1(7) common /psar35/ anorm,anormp external pprcs ptfauAA=0. e1=exp(-1.) rs=r2had(iclpro)+r2had(icltar)+max(slopom,slopoms)*log(engy**2) & +gwidth*(r2had(iclpro)+r2had(icltar)) & +bmxdif(iclpro,icltar)/4./0.0389 rpom=4.*.0389*rs do i1=1,7 do m=1,2 z=.5+x1(i1)*(m-1.5) zv1=exp(-z) zv2=(e1*z) b1=sqrt(-rpom*log(zv1)) b2=sqrt(-rpom*log(zv2)) call psfz(iqq,gz21,b1) call psfz(iqq,gz22,b2) ptfau1=max(0.,(1.-anorm*gz21))**matarg ptfau2=max(0.,(1.-anorm*gz22))**matarg cg1=ptrot(pprcs,b,b1) cg2=ptrot(pprcs,b,b2) ptfauAA=ptfauAA+a1(i1)*(cg1*(1.-ptfau1)+cg2*(1.-ptfau2)/z) enddo enddo ptfauAA=ptfauAA*rpom/2. ptfauAA=1.-max(0.,(1.-anormp*ptfauAA))**maproj return end c------------------------------------------------------------------------ function ptrot(func,s,b) c----------------------------------------------------------------------- c convolution of nuclear profile functions (axial angle integration) c----------------------------------------------------------------------- common /ar8/ x2(4),a2 external func ptrot=0. do i=1,4 sb1=b**2+s**2-2.*b*s*(2.*x2(i)-1.) sb2=b**2+s**2-2.*b*s*(1.-2.*x2(i)) ptrot=ptrot+(func(sb1)+func(sb2)) enddo ptrot=ptrot*a2 return end c------------------------------------------------------------------------ function pttcs(b0) c----------------------------------------------------------------------- c ptt - nuclear profile function value at imp param squared b*difnuc**2 c----------------------------------------------------------------------- include 'epos.inc' common /psar34/ rrr,rrrm common /ar5/ x5(2),a5(2) common /ar9/ x9(3),a9(3) b=b0/difnuc(matarg)**2 pttcs=0. zm=rrrm**2-b if(zm.gt.4.*b)then zm=sqrt(zm) else zm=2.*sqrt(b) endif do i=1,3 z1=zm*(1.+x9(i))*0.5 z2=zm*(1.-x9(i))*0.5 quq=sqrt(b+z1**2)-rrr if (quq.lt.85.)pttcs=pttcs+a9(i)/(1.+exp(quq)) quq=sqrt(b+z2**2)-rrr if (quq.lt.85.)pttcs=pttcs+a9(i)/(1.+exp(quq)) enddo pttcs=pttcs*zm*0.5 dt=0. do i=1,2 z1=x5(i)+zm quq=sqrt(b+z1**2)-rrr-x5(i) if (quq.lt.85.)dt=dt+a5(i)/(exp(-x5(i))+exp(quq)) enddo pttcs=pttcs+dt return end c------------------------------------------------------------------------ function pttzz(b0) c----------------------------------------------------------------------- c ptt - nuclear Z function value at imp param squared b*difnuc**2 c----------------------------------------------------------------------- include 'epos.inc' include 'epos.incpar' common /psar34/ rrr,rrrm common /psar50/ zznuc,b2xnuc common /ar5/ x5(2),a5(2) common /ar9/ x9(3),a9(3) pttzz=0. b=b0/difnuc(matarg)**2 c absb=max(1.e-9,sqrt(b0)-zbcut) absb=max(1.e-9,sqrt(b0)) bsq=absb*absb zm=rrrm**2-b if(zm.gt.4.*b)then zm=sqrt(zm) else zm=2.*sqrt(b) endif do i=1,3 z1=zm*(1.+x9(i))*0.5 z2=zm*(1.-x9(i))*0.5 quq=sqrt(b+z1**2)-rrr if (quq.lt.85.)pttzz=pttzz+a9(i)/(1.+exp(quq)) quq=sqrt(b+z2**2)-rrr if (quq.lt.85.)pttzz=pttzz+a9(i)/(1.+exp(quq)) enddo pttzz=pttzz*zm*0.5 dt=0. do i=1,2 z1=x5(i)+zm quq=sqrt(b+z1**2)-rrr-x5(i) if (quq.lt.85.)dt=dt+a5(i)/(exp(-x5(i))+exp(quq)) enddo pttzz=max(0.,(pttzz+dt)-1.)*zznuc*exp(-bsq/2./b2xnuc) return end c------------------------------------------------------------------------ function pprcs(b0) c----------------------------------------------------------------------- c ppr - nuclear profile function value at imp param squared b*difnuc**2 c----------------------------------------------------------------------- include 'epos.inc' common /psar41/ rrrp,rrrmp common /ar5/ x5(2),a5(2) common /ar9/ x9(3),a9(3) b=b0/difnuc(maproj)**2 pprcs=0. zm=rrrmp**2-b if(zm.gt.4.*b)then zm=sqrt(zm) else zm=2.*sqrt(b) endif do i=1,3 z1=zm*(1.+x9(i))*0.5 z2=zm*(1.-x9(i))*0.5 quq=sqrt(b+z1**2)-rrrp if (quq.lt.85.)pprcs=pprcs+a9(i)/(1.+exp(quq)) quq=sqrt(b+z2**2)-rrrp if (quq.lt.85.)pprcs=pprcs+a9(i)/(1.+exp(quq)) enddo pprcs=pprcs*zm*0.5 dt=0. do i=1,2 z1=x5(i)+zm quq=sqrt(b+z1**2)-rrrp-x5(i) if (quq.lt.85.)dt=dt+a5(i)/(exp(-x5(i))+exp(quq)) enddo pprcs=pprcs+dt return end c------------------------------------------------------------------------ function pprzz(b0) c----------------------------------------------------------------------- c ppr - Z nuclear function value at imp param squared b*difnuc**2 c----------------------------------------------------------------------- include 'epos.inc' include 'epos.incpar' common /psar41/ rrrp,rrrmp common /psar50/ zznuc,b2xnuc common /ar5/ x5(2),a5(2) common /ar9/ x9(3),a9(3) pprzz=0. b=b0/difnuc(maproj)**2 c absb=max(1.e-9,sqrt(b0)-zbcut) absb=max(1.e-9,sqrt(b0)) bsq=absb*absb zm=rrrmp**2-b if(zm.gt.4.*b)then zm=sqrt(zm) else zm=2.*sqrt(b) endif do i=1,3 z1=zm*(1.+x9(i))*0.5 z2=zm*(1.-x9(i))*0.5 quq=sqrt(b+z1**2)-rrrp if (quq.lt.85.)pprzz=pprzz+a9(i)/(1.+exp(quq)) quq=sqrt(b+z2**2)-rrrp if (quq.lt.85.)pprzz=pprzz+a9(i)/(1.+exp(quq)) enddo pprzz=pprzz*zm*0.5 dt=0. do i=1,2 z1=x5(i)+zm quq=sqrt(b+z1**2)-rrrp-x5(i) if (quq.lt.85.)dt=dt+a5(i)/(exp(-x5(i))+exp(quq)) enddo pprzz=max(0.,(pprzz+dt)-1.)*zznuc*exp(-bsq/2./b2xnuc) return end c------------------------------------------------------------------------------ function pscrse(ek,mapr,matg,iqq) c------------------------------------------------------------------------------ c hadron-nucleus (hadron-proton) and nucl-nucl particle production cross section c ek - lab kinetic energy for the interaction c maproj - projec mass number c matarg - target mass number c iqq=1 - ela cross section c >2 - ine cross section (2 used for cut (changing iomega), 3 uses table, c 4 used for ine without table) c------------------------------------------------------------------------------ dimension wk(3),wa(3),wb(3) include 'epos.inc' common /psar33/ asect(7,4,7),asectn(7,7,7) common /psar34/ rrr,rrrm common /psar35/ anorm,anormp common /psar41/ rrrp,rrrmp external ptfau,ptfauAA pscrse=0. call idmass(1120,amt1) call idmass(1220,amt2) amtar=0.5*(amt1+amt2) if(matg.eq.1)amtar=amt1 if(mapr.eq.1)then call idmass(idproj,ampro) else ampro=amtar endif egy=ek+ampro c p=sqrt(max(0.,egy**2-ampro**2)) egy=sqrt( 2*egy*amtar+amtar**2+ampro**2 ) if(isetcs.le.1.or.iqq.ne.3)then maprojsave=maproj matargsave=matarg engysave=engy maproj=mapr matarg=matg engy=egy if(matg.eq.1.and.mapr.eq.1)then if(iqq.eq.1)then !sig ela call psfz(1,gz2,0.) else !sig ine call psfz(2,gz2,0.) endif gin=gz2*pi*10. elseif(mapr.eq.1)then rad=radnuc(matg) bm=rad+2. rrr=rad/difnuc(matg) rrrm=rrr+log(9.) anorm=1.5/pi/rrr**3/(1.+(pi/rrr)**2)/difnuc(matg)**2 if(iqq.ne.1)then gin=(ptgau(ptfau,bm,2,2)+ptgau1(bm,2,2))*10. !sig ine else gin=(ptgau(ptfau,bm,2,1)+ptgau1(bm,2,1))*10. !sig ela endif elseif(matg.eq.1)then rad=radnuc(mapr) bm=rad+2. rrrp=rad/difnuc(mapr) rrrmp=rrrp+log(9.) anormp=1.5/pi/rrrp**3/(1.+(pi/rrrp)**2)/difnuc(mapr)**2 if(iqq.ne.1)then gin=(ptgau(ptfau,bm,1,2)+ptgau1(bm,1,2))*10. !sig ine else gin=(ptgau(ptfau,bm,1,1)+ptgau1(bm,1,1))*10. !sig ela endif else rad=radnuc(matg)+1. radp=radnuc(mapr)+1. bm=rad+radp+2. rrr=rad/difnuc(matg) rrrm=rrr+log(9.) rrrp=radp/difnuc(mapr) rrrmp=rrrp+log(9.) anorm=1.5/pi/rrr**3/(1.+(pi/rrr)**2)/difnuc(matg)**2 anormp=1.5/pi/rrrp**3/(1.+(pi/rrrp)**2)/difnuc(mapr)**2 if(iqq.ne.1)then gin=(ptgau(ptfauAA,bm,2,2)+ptgau2(bm,2))*10. !sig ine else gin=(ptgau(ptfauAA,bm,2,1)+ptgau2(bm,1))*10. !sig ela endif endif pscrse=gin maproj=maprojsave matarg=matargsave engy=engysave else ye=log10(max(1.,egy/1.5))+1. je=min(5,int(ye)) wk(2)=ye-je wk(3)=wk(2)*(wk(2)-1.)*.5 wk(1)=1.-wk(2)+wk(3) wk(2)=wk(2)-2.*wk(3) ya=matg ya=log(ya)/.69315+1. ja=min(int(ya),4) wa(2)=ya-ja wa(3)=wa(2)*(wa(2)-1.)*.5 wa(1)=1.-wa(2)+wa(3) wa(2)=wa(2)-2.*wa(3) if(mapr.eq.1)then do i=1,3 do m=1,3 pscrse=pscrse+asect(je+i-1,iclpro,ja+m-1)*wk(i)*wa(m) enddo enddo else yb=mapr yb=log(yb)/.69315+1. jb=min(int(yb),4) wb(2)=yb-jb wb(3)=wb(2)*(wb(2)-1.)*.5 wb(1)=1.-wb(2)+wb(3) wb(2)=wb(2)-2.*wb(3) do i=1,3 do m=1,3 do n=1,3 pscrse=pscrse+asectn(je+i-1,jb+n-1,ja+m-1)*wk(i)*wa(m)*wb(n) enddo enddo enddo endif pscrse=exp(pscrse) endif return end c------------------------------------------------------------------------------ function eposcrse(ek,mapro,matar,id) c------------------------------------------------------------------------------ c inelastic cross section of epos c (id=0 corresponds to air) c ek - kinetic energy for the interaction c maproj - projec mass number (1<maproj<64) c matarg - target mass number (1<matarg<64) c------------------------------------------------------------------------------ include 'epos.inc' eposcrse=0. if(id.eq.0)then do k=1,3 mt=int(airanxs(k)) eposcrse=eposcrse+airwnxs(k)*pscrse(ek,mapro,mt,3) enddo else eposcrse=pscrse(ek,mapro,matar,3) endif return end c------------------------------------------------------------------------------ function eposinecrse(ek,mapro,matar,id) c------------------------------------------------------------------------------ c inelastic cross section of epos not using tabulated xs c (id=0 corresponds to air) c ek - kinetic energy for the interaction c maproj - projec mass number (1<maproj<64) c matarg - target mass number (1<matarg<64) c------------------------------------------------------------------------------ include 'epos.inc' eposinecrse=0. if(id.eq.0)then do k=1,3 mt=int(airanxs(k)) eposinecrse=eposinecrse+airwnxs(k)*pscrse(ek,mapro,mt,4) enddo else eposinecrse=pscrse(ek,mapro,matar,4) endif return end c------------------------------------------------------------------------------ function eposelacrse(ek,mapro,matar,id) c------------------------------------------------------------------------------ c elastic cross section of epos c (id=0 corresponds to air) c ek - kinetic energy for the interaction c maproj - projec mass number (1<maproj<64) c matarg - target mass number (1<matarg<64) c------------------------------------------------------------------------------ include 'epos.inc' eposelacrse=0. if(id.eq.0)then do k=1,3 mt=int(airanxs(k)) eposelacrse=eposelacrse+airwnxs(k)*pscrse(ek,mapro,mt,1) enddo else eposelacrse=pscrse(ek,mapro,matar,1) endif return end c------------------------------------------------------------------------------ function eposcutcrse(ek,mapro,matar,id) c------------------------------------------------------------------------------ c total cross section of epos c (id=0 corresponds to air) c ek - kinetic energy for the interaction c maproj - projec mass number (1<maproj<64) c matarg - target mass number (1<matarg<64) c------------------------------------------------------------------------------ include 'epos.inc' eposcutcrse=0. iomegasave=iomega iomega=2 if(id.eq.0)then do k=1,3 mt=int(airanxs(k)) eposcutcrse=eposcutcrse+airwnxs(k)*pscrse(ek,mapro,mt,2) enddo else eposcutcrse=pscrse(ek,mapro,matar,2) endif iomega=iomegasave return end c------------------------------------------------------------------------------ subroutine crseaaEpos(sigt,sigi,sigc,sige) c------------------------------------------------------------------------------ c nucleus-nucleus (hadron) cross section of epos from simplified (realistic) c simulations c (id=0 corresponds to air) c sigt = sig tot c sigi = sig inelastic (cut + projectile diffraction) c sigc = sig cut c sige = sig elastic (includes target diffraction) c------------------------------------------------------------------------------ include 'epos.inc' niter=20000 if(idtarg.eq.0)then sigt=0. sigc=0. sigi=0. sige=0. sigd=0. sigql=0. do k=1,3 matarg=int(airanxs(k)) call epocrossc(niter,xsigt,xsigi,xsigc,xsige,xsigql,xsigd) sigt=sigt+airwnxs(k)*xsigt sigi=sigi+airwnxs(k)*xsigi sigc=sigc+airwnxs(k)*xsigc sige=sige+airwnxs(k)*xsige sigd=sigd+airwnxs(k)*xsigd sigql=sigql+airwnxs(k)*xsigql enddo else call epocrossc(niter,sigt,sigi,sigc,sige,sigql,sigd) endif if(ionudi.ne.1)then sige=sige+sigql !add non-excited diffractive projectile to elastic sigi=sigi-sigql !do not count non-excited diffractive projectile in inelastic if(maproj+matarg.gt.2)then sigc=sigc+sigd*0.95 !for absorbtion cross section remove 5% of the !excited projectile diffractive cross section !which "looks like" non excited (approximation) endif endif end cc------------------------------------------------------------------------ c function pshard1(sy,xpp,xpm,z) cc----------------------------------------------------------------------- cc pshard - qq-pomeron eikonal cc sy - energy squared for the pomeron, cc xpp - lc+ for the pomeron, cc xpm - lc- for the pomeron cc----------------------------------------------------------------------- c common /ar3/ x1(7),a1(7) c common /ar9/ x9(3),a9(3) c include 'epos.inc' c include 'epos.incsem' c c pshard1=0. c if(iclpro.ne.4.and.icltar.ne.4)then c spmin=4.*q2min c else c spmin=4.*q2min+2.*qcmass**2 c endif c if(sy.le.spmin)return c c rp=r2had(iclpro)+r2had(icltar)+slopom*log(max(1.,sy)) c alpq=(alppar+1.)/2. c xmin=spmin/sy !min hard pomeron mass share c xminl=xmin**(delh+.5) c c do i=1,3 c do m=1,2 c zh=(.5*(1.+xminl-(2*m-3)*x9(i)*(1.-xminl)))**(1./(delh+.5)) c if(iclpro.ne.4.and.icltar.ne.4)then c call psjti0(zh*sy,sqq,sqqb,1,1) c call psjti0(zh*sy,sqqp,sqqpb,1,2) c call psjti0(zh*sy,sqaq,sqaqb,-1,1) c else c call psjti0(zh*sy,sqq,sqqb,4,1) c sqq=0. c sqaq=0. c endif c c stq=0. c do i1=1,3 c do m1=1,2 c xx=.5+x9(i1)*(m1-1.5) c xp=zh**xx c xm=zh/xp c if(xp*xpp.le..9999.and.xm*xpm.le..9999.or. c * xm*xpp.le..9999.and.xp*xpm.le..9999)then c stq=stq+a9(i1)*psharf(xp*xpp,xm*xpm,sqq,sqqp,sqaq) c * *(1.-xp)**(1.+alplea(iclpro)-alpq) c * *(1.-xm)**(1.+alplea(icltar)-alpq) c endif c enddo c enddo c pshard1=pshard1-a9(i)*stq/zh**(delh+0.5)*log(zh) c enddo c enddo c pshard1=pshard1*(1.-xminl)/(delh+.5)/4.*factk c **chad(iclpro)*chad(icltar)*(xpp*xpm)**(1.-alpq) c **z**(rp/(r2had(iclpro)+r2had(icltar))) c */(8.*pi*(r2had(iclpro)+r2had(icltar))) c return c end c c------------------------------------------------------------------------ function pshard(sy,xpp,xpm) c----------------------------------------------------------------------- c pshard - qq-pomeron eikonal c sy - energy squared for the pomeron, c xpp - lc+ for the pomeron, c xpm - lc- for the pomeron c----------------------------------------------------------------------- double precision z01 common /ar3/ x1(7),a1(7) include 'epos.inc' include 'epos.incsem' pshard=0. if(iclpro.ne.4.and.icltar.ne.4)then spmin=4.*q2min else spmin=4.*q2min+2.*qcmass**2 endif if(sy.le.spmin)return alpq=(alppar+1.)/2. xmin=spmin/sy !min hard pomeron mass share xminl=xmin**(delh+.5) do i=1,7 do m=1,2 zh=(.5*(1.+xminl-(2*m-3)*x1(i)*(1.-xminl)))**(1./(delh+.5)) if(iclpro.ne.4.and.icltar.ne.4)then call psjti0(zh*sy,sqq,sqqb,1,1) call psjti0(zh*sy,sqqp,sqqpb,1,2) call psjti0(zh*sy,sqaq,sqaqb,-1,1) else call psjti0(zh*sy,sqq,sqqb,4,1) sqqp=0. sqaq=0. endif stq=0. !int^1_(sqrt(z)) dx_p / x_p / sqrt(1-x_p) =int^(tmax)_(0) dt tmax=sqrt(1.-sqrt(zh)) !t=ln((1+sqrt(1-x_p))/(1-sqrt(1-x_p))) tmax=log((1.+tmax)/(1.-tmax)) if(tmax.gt.1.e-20)then do i1=1,7 do m1=1,2 t=tmax*(.5+x1(i1)*(m1-1.5)) z01=((1.d0-exp(-1.d0*t))/(1.d0+exp(-1.d0*t)))**2 xp=1.-z01 xm=zh/xp if(xp*xpp.le..9999.and.xm*xpm.le..9999.or. * xm*xpp.le..9999.and.xp*xpm.le..9999)then stq=stq+a1(i1)*(psharf(xp*xpp,xm*xpm,sqq,sqqp,sqaq)+ * psharf(xm*xpp,xp*xpm,sqq,sqqp,sqaq)) * *z01**(.5-alpq)/(1.-xm)**alpq endif enddo enddo stq=stq*tmax endif pshard=pshard+a1(i)*stq/zh**(delh+0.5) enddo enddo pshard=pshard*(1.-xminl)/(delh+.5)/4.* *utgam1(2.+alplea(iclpro)-alpq)/utgam1(1.+alplea(iclpro))/ *utgam1(1.-alpq)* *utgam1(2.+alplea(icltar)-alpq)/utgam1(1.+alplea(icltar))/ *utgam1(1.-alpq)* *chad(iclpro)*chad(icltar)/(8.*pi*(r2had(iclpro)+r2had(icltar)))* *(xpp*xpm)**(-alpq)/sy**delh return end c------------------------------------------------------------------------ function psharf(zh1,zh2,sqq,sqqp,sqaq) c----------------------------------------------------------------------- include 'epos.incsem' include 'epos.inc' alpq=(alppar+1.)/2. if(zh1.le..9999.and.zh2.le..9999)then uv1=psdfh4(zh1,q2min,0.,iclpro,1) dv1=psdfh4(zh1,q2min,0.,iclpro,2) uv2=psdfh4(zh2,q2min,0.,icltar,1) dv2=psdfh4(zh2,q2min,0.,icltar,2) if(iclpro.eq.2.and.icltar.eq.2)then !proton fff=sqq*(uv1*uv2+dv1*dv2)+sqqp*(uv1*dv2+dv1*uv2) elseif(iclpro.eq.1.or.icltar.eq.1)then !pion fff=sqq*uv1*uv2+sqaq*dv1*dv2+sqqp*(uv1*dv2+dv1*uv2) elseif(iclpro.eq.3.or.icltar.eq.3)then !kaon fff=sqq*uv1*uv2+sqqp*(uv1*dv2+dv1*uv2+dv1*dv2) elseif(iclpro.eq.4.or.icltar.eq.4)then !J/psi fff=sqq*uv1*(uv2+dv2) else fff=0. call utstop("Projectile not know in psharg !&") endif psharf=fff*(1.-zh1)**(-1.+alpq-alplea(iclpro))* * (1.-zh2)**(-1.+alpq-alplea(icltar)) else psharf=0. endif return end c------------------------------------------------------------------------ function psvin(sy,xpp,xpm,z,iqq) c----------------------------------------------------------------------- c psvin - contributions to the interaction eikonal c sy - energy squared for the hard interaction, c xpp - lc+ for the sh pomeron, c xpm - lc- for the sh pomeron, c z - impact parameter factor, z=exp(-b**2/4*rp), c iqq = 1 - gg, c iqq = 2 - qg, c iqq = 3 - gq, c iqq = 4 - qq, c iqq = 5 - gg(int), c iqq = 6 - gg(proj), c iqq = 7 - qg(proj), c iqq = 9 - total uncut-integrated, c iqq = 10 - total cut, c iqq = 14 - gg(int)|b=0, c iqq = 15 - <b^2*gg(int)>, c iqq = 16 - gg(proj)|b=0, c iqq = 17 - <b^2*gg(proj)>, c iqq = 18 - qg(proj)|b=0, c iqq = 19 - <b^2*qg(proj)> c----------------------------------------------------------------------- dimension wk(3),wi(3),wj(3),wz(3),fa(3) common /psar2/ edmax,epmax common /psar4/ fhgg(11,10,8),fhqg(11,10,80) *,fhgq(11,10,80),fhqq(11,10,80),fhgg0(11,10),fhgg1(11,10,4) *,fhqg1(11,10,40),fhgg01(11),fhgg02(11),fhgg11(11,4) *,fhgg12(11,4),fhqg11(11,10,4),fhqg12(11,10,4) *,ftoint(11,14,2,2,3) common /psar7/ delx,alam3p,gam3p include 'epos.inc' include 'epos.incsem' if(iqq.eq.3)then xp=xpm xm=xpp iclp=icltar iclt=iclpro else xp=xpp xm=xpm iclp=iclpro iclt=icltar endif rp=r2had(iclpro)+r2had(icltar)+slopom*log(max(1.,sy)) psvin=0. if(iqq.eq.1.or.iqq.eq.5.or.iqq.eq.6.or.iqq.eq.14 *.or.iqq.eq.15.or.iqq.eq.16.or.iqq.eq.17 *.or.iclpro.ne.4.and.(iqq.eq.2.or.iqq.eq.7 *.or.iqq.eq.18.or.iqq.eq.19) *.or.icltar.ne.4.and.iqq.eq.3 *.or.iclpro.ne.4.and.icltar.ne.4)then spmin=4.*q2min else spmin=4.*q2min+2.*qcmass**2 endif if(sy.le.spmin.and.(iqq.le.7.or.iqq.gt.13))return if(iqq.le.7.or.iqq.gt.13)then yl=log(sy/spmin)/log(epmax/2./spmin)*10.+1 k=int(yl) if(k.gt.9)k=9 wk(2)=yl-k wk(3)=wk(2)*(wk(2)-1.)*.5 wk(1)=1.-wk(2)+wk(3) wk(2)=wk(2)-2.*wk(3) if(iqq.ne.4)then !---------------- not 4 ------------------ if(iqq.eq.5)then if(k.eq.1)then psvin=max(0.,exp(fhgg01(k+1))*wk(2) * +exp(fhgg01(k+2))*wk(3)) else psvin=exp(fhgg01(k)*wk(1)+fhgg01(k+1)*wk(2) * +fhgg01(k+2)*wk(3)) endif psvin=psvin*factk*sy**delh return elseif(iqq.eq.15)then if(k.eq.1)then psvin=max(0.,exp(fhgg02(k+1))*wk(2) * +exp(fhgg02(k+2))*wk(3)) else psvin=exp(fhgg02(k)*wk(1)+fhgg02(k+1)*wk(2) * +fhgg02(k+2)*wk(3)) endif psvin=psvin*factk*sy**delh return elseif(iqq.eq.6)then if(k.eq.1)then psvin=max(0.,exp(fhgg11(k+1,iclpro))*wk(2) * +exp(fhgg11(k+2,iclpro))*wk(3)) else psvin=exp(fhgg11(k,iclpro)*wk(1)+fhgg11(k+1,iclpro)*wk(2) * +fhgg11(k+2,iclpro)*wk(3)) endif psvin=psvin*factk*sy**delh*xp**(-alppar) return elseif(iqq.eq.17)then if(k.eq.1)then psvin=max(0.,exp(fhgg12(k+1,iclpro))*wk(2) * +exp(fhgg12(k+2,iclpro))*wk(3)) else psvin=exp(fhgg12(k,iclpro)*wk(1)+fhgg12(k+1,iclpro)*wk(2) * +fhgg12(k+2,iclpro)*wk(3)) endif psvin=psvin*factk*sy**delh*xp**(-alppar) return elseif(iqq.eq.7.or.iqq.eq.19)then if(xp.lt..2)then xl=log(10.*xp)/log(2.)+5. else xl=5.*xp+5. endif i=int(xl) if(i.lt.1)i=1 if(i.eq.5)i=4 if(i.gt.8)i=8 wi(2)=xl-i wi(3)=wi(2)*(wi(2)-1.)*.5 wi(1)=1.-wi(2)+wi(3) wi(2)=wi(2)-2.*wi(3) do k1=1,3 fa(k1)=0. do i1=1,3 k2=k+k1-1 fhhh=0. if(iqq.eq.7)then fhhh=fhqg11(k2,i+i1-1,iclpro) elseif(iqq.eq.19)then fhhh=fhqg12(k2,i+i1-1,iclpro) endif fa(k1)=fa(k1)+fhhh*wi(i1) enddo enddo if(k.eq.1)then psvin=max(0.,exp(fa(2))*wk(2)+exp(fa(3))*wk(3)) else psvin=exp(fa(1)*wk(1)+fa(2)*wk(2)+fa(3)*wk(3)) endif psvin=psvin*factk*sy**delh return endif jz=int(10.*z) if(jz.gt.8)jz=8 if(jz.lt.1)jz=1 wz(2)=10.*z-jz wz(3)=wz(2)*(wz(2)-1.)*.5 wz(1)=1.-wz(2)+wz(3) wz(2)=wz(2)-2.*wz(3) if(iqq.eq.14)then do k1=1,3 k2=k+k1-1 fa(k1)=fhgg0(k2,jz)*wz(1)+fhgg0(k2,jz+1) * *wz(2)+fhgg0(k2,jz+2)*wz(3) enddo if(k.eq.1)then psvin=max(0.,exp(fa(2))*wk(2)+exp(fa(3))*wk(3)) else psvin=exp(fa(1)*wk(1)+fa(2)*wk(2)+fa(3)*wk(3)) endif psvin=psvin*z*factk*sy**delh elseif(iqq.eq.16)then do k1=1,3 k2=k+k1-1 fa(k1)=fhgg1(k2,jz,iclpro)*wz(1)+fhgg1(k2,jz+1,iclpro) * *wz(2)+fhgg1(k2,jz+2,iclpro)*wz(3) enddo if(k.eq.1)then psvin=max(0.,exp(fa(2))*wk(2)+exp(fa(3))*wk(3)) else psvin=exp(fa(1)*wk(1)+fa(2)*wk(2)+fa(3)*wk(3)) endif psvin=psvin*z*factk*sy**delh*xp**(-alppar) elseif(iqq.eq.18)then if(xp.lt..2)then xl=log(10.*xp)/log(2.)+5. else xl=5.*xp+5. endif i=int(xl) if(i.lt.1)i=1 if(i.eq.5)i=4 if(i.gt.8)i=8 wi(2)=xl-i wi(3)=wi(2)*(wi(2)-1.)*.5 wi(1)=1.-wi(2)+wi(3) wi(2)=wi(2)-2.*wi(3) do k1=1,3 fa(k1)=0. do i1=1,3 do l1=1,3 k2=k+k1-1 l2=jz+l1-1+10*(iclpro-1) fhhh=fhqg1(k2,i+i1-1,l2) fa(k1)=fa(k1)+fhhh*wi(i1)*wz(l1) enddo enddo enddo if(k.eq.1)then psvin=max(0.,exp(fa(2))*wk(2)+exp(fa(3))*wk(3)) else psvin=exp(fa(1)*wk(1)+fa(2)*wk(2)+fa(3)*wk(3)) endif psvin=psvin*z*factk*sy**delh elseif(iqq.eq.1)then !1111111111111111111111111111111111 do k1=1,3 k2=k+k1-1 iclpt=iclpro+4*(icltar-1) fa(k1)=fhgg(k2,jz,iclpt)*wz(1)+fhgg(k2,jz+1,iclpt) * *wz(2)+fhgg(k2,jz+2,iclpt)*wz(3) enddo if(k.eq.1)then psvin=max(0.,exp(fa(2))*wk(2)+exp(fa(3))*wk(3)) else psvin=exp(fa(1)*wk(1)+fa(2)*wk(2)+fa(3)*wk(3)) endif psvin=psvin*z*factk*sy**delh*(xp*xm)**(-alppar) else ! 2222222222222222222222 3333333333333333333333 .... if(xp.lt..2)then xl=log(10.*xp)/log(2.)+5. else xl=5.*xp+5. endif i=int(xl) if(i.lt.1)i=1 if(i.eq.5)i=4 if(i.gt.8)i=8 wi(2)=xl-i wi(3)=wi(2)*(wi(2)-1.)*.5 wi(1)=1.-wi(2)+wi(3) wi(2)=wi(2)-2.*wi(3) do k1=1,3 fa(k1)=0. do i1=1,3 do l1=1,3 k2=k+k1-1 fhhh=0. if(iqq.eq.2)then l2=jz+l1-1+10*(iclpro+4*(icltar-1)-1) fhhh=fhqg(k2,i+i1-1,l2) elseif(iqq.eq.3)then l2=jz+l1-1+10*(iclpro+4*(icltar-1)-1) fhhh=fhgq(k2,i+i1-1,l2) endif fa(k1)=fa(k1)+fhhh*wi(i1)*wz(l1) enddo enddo enddo if(k.eq.1)then psvin=max(0.,exp(fa(2))*wk(2)+exp(fa(3))*wk(3)) else psvin=exp(fa(1)*wk(1)+fa(2)*wk(2)+fa(3)*wk(3)) endif psvin=psvin*xm**(-alppar)*z*factk*sy**delh endif else ! ------------- 4444444444444444444 ----------------------- if(xp.lt..2)then xl1=log(10.*xp)/log(2.)+5. else xl1=5.*xp+5. endif i=max(1,int(xl1)) if(i.eq.5)i=4 i=min(8,i) wi(2)=xl1-i wi(3)=wi(2)*(wi(2)-1.)*.5 wi(1)=1.-wi(2)+wi(3) wi(2)=wi(2)-2.*wi(3) if(xm.lt..2)then xl2=log(10.*xm)/log(2.)+5. else xl2=5.*xm+5. endif j=max(1,int(xl2)) if(j.eq.5)j=4 j=min(8,j) wj(2)=xl2-j wj(3)=wj(2)*(wj(2)-1.)*.5 wj(1)=1.-wj(2)+wj(3) wj(2)=wj(2)-2.*wj(3) do k1=1,3 fa(k1)=0. do i1=1,3 do j1=1,3 k2=k+k1-1 j2=j+j1-1+10*(iclp+4*(iclt-1)-1) fa(k1)=fa(k1)+fhqq(k2,i+i1-1,j2)*wi(i1)*wj(j1) enddo enddo enddo if(k.eq.1)then psvin=max(0.,exp(fa(2))*wk(2)+exp(fa(3))*wk(3)) else psvin=exp(fa(1)*wk(1)+fa(2)*wk(2)+fa(3)*wk(3)) endif psvin=psvin*z**(rp/(r2had(iclpro)+r2had(icltar)))* * factk*sy**delh endif !-------------------------------------------- return endif yl=log(sy)/log(1.e8)*10.+1 k=max(1,int(yl)) k=min(k,9) !?????????????9 wk(2)=yl-k wk(3)=wk(2)*(wk(2)-1.)*.5 wk(1)=1.-wk(2)+wk(3) wk(2)=wk(2)-2.*wk(3) if(z.gt..1)then zz=10.*z+4 else zz=50.*z endif jz=min(12,int(zz)) if(jz.eq.0)jz=1 if(jz.eq.4)jz=3 wz(2)=zz-jz wz(3)=wz(2)*(wz(2)-1.)*.5 wz(1)=1.-wz(2)+wz(3) wz(2)=wz(2)-2.*wz(3) if(iqq.eq.9)then do k1=1,3 do l1=1,3 k2=k+k1-1 l2=jz+l1-1 psvin=psvin+ftoint(k2,l2,icdp,icdt,iclp)*wk(k1)*wz(l1) enddo enddo psvin=exp(psvin)*z endif return end c------------------------------------------------------------------------ function psbint(q1,q2,qqcut,ss,m1,l1,jdis) c----------------------------------------------------------------------- c psbint - born cross-section interpolation c q1 - virtuality cutoff at current end of the ladder; c q2 - virtuality cutoff at opposite end of the ladder; c qqcut - p_t cutoff for the born process; c s - total c.m. energy squared for the scattering, c m1 - parton type at current end of the ladder (0 - g, 1,-1,2,... - q) c l1 - parton type at opposite end of the ladder (0 - g, 1,-1,2,... - q) c----------------------------------------------------------------------- dimension wi(3),wk(3) common /psar2/ edmax,epmax common /psar21/ csbor(20,160,2) include 'epos.incsem' double precision psuds psbint=0. if(jdis.eq.0)then qq=max(q1,q2) else qq=max(q1/4.,q2) endif qq=max(qq,qqcut) if(iabs(m1).ne.4)then q2mass=0. if(m1.ne.0.and.m1.eq.l1)then m=2 l=2 elseif(m1.ne.0.and.m1.eq.-l1)then m=3 l=1 elseif(m1.ne.0.and.l1.ne.0.and.m1.ne.l1)then m=3 l=2 else m=min(1,iabs(m1))+1 l=min(1,iabs(l1))+1 endif else q2mass=qcmass**2 m=4 l=min(1,iabs(l1))+1 endif s=ss-q2mass spmin=4.*q2min+q2mass s2min=4.*qq+q2mass if(s.le.s2min)return p1=s/(1.+q2mass/s) if(p1.gt.4.*qq)then tmin=2.*qq/(1.+sqrt(1.-4.*qq/p1)) else tmin=2.*qq endif qmax=p1/4. tmax=p1/2. ml=20*(m-1)+80*(l-1) qli=log(qq/q2min)/log(qmax/q2min)*19.+1. sl=log(s/spmin)/log(epmax/2./spmin)*19.+1. k=int(sl) i=int(qli) if(k.lt.1)k=1 if(i.lt.1)i=1 if(k.gt.18)k=18 if(i.gt.18)i=18 wi(2)=qli-i wi(3)=wi(2)*(wi(2)-1.)*.5 wi(1)=1.-wi(2)+wi(3) wi(2)=wi(2)-2.*wi(3) wk(2)=sl-k wk(3)=wk(2)*(wk(2)-1.)*.5 wk(1)=1.-wk(2)+wk(3) wk(2)=wk(2)-2.*wk(3) do i1=1,3 do k1=1,3 psbint=psbint+csbor(i+i1-1,k+k1+ml-1,jdis+1) * *wi(i1)*wk(k1) enddo enddo psbint=exp(psbint)*(1./tmin-1./tmax) if(jdis.eq.0.and.qq.gt.q1)then psbint=psbint*sngl(psuds(qq,m1)/psuds(q1,m1)) elseif(jdis.eq.1.and.4.*qq.gt.q1)then psbint=psbint*sngl(psuds(4.*qq,m1)/psuds(q1,m1)) endif if(qq.gt.q2)psbint=psbint*sngl(psuds(qq,l1)/psuds(q2,l1)) return end c----------------------------------------------------------------------- function psborn(q1,q2,qqcut,s,j,l,jdis,md) c----------------------------------------------------------------------- c c hard 2->2 parton scattering born cross-section c including sudakov on both sides c c q1 - virtuality cutoff at current end of the ladder; c q2 - virtuality cutoff at opposite end of the ladder; c qqcut - p_t cutoff for the born process; c s - c.m. energy squared for the scattering; c j - parton type at current end of the ladder (0 - g, 1,2 etc. - q); c l - parton type at opposite end of the ladder (0 - g, 1,2 etc. - q). c----------------------------------------------------------------------- common /ar3/ x1(7),a1(7) double precision sud0,psbornd,psuds include 'epos.inc' include 'epos.incsem' psborn=0 if(jdis.eq.0)then qq=max(q1,q2) else qq=max(q1/4.,q2) endif qq=max(qq,qqcut) c if(j.ne.3)then !kkkkkkkkkk charm is 3 ??? if(j.ne.4)then j1=j q2mass=0. else j1=4 q2mass=qcmass**2 endif p1=s/(1.+q2mass/s) if(p1.gt.4.*qq)then tmin=2.*qq/(1.+sqrt(1.-4.*qq/p1)) else tmin=2.*qq ! return !tmin=2.*qq !kkkkkkk !????????????? tp why not ? endif tmax=p1/2. sud0=psuds(q1,j1)*psuds(q2,l) psbornd=0.d0 do i=1,7 do m=1,2 t=2.*tmin/(1.+tmin/tmax-x1(i)*(2*m-3) & *(1.-tmin/tmax)) qt=t*(1.-t/p1) if(qt.lt..999*qq.and.ish.ge.1)write(ifch,*)'psborn:qt,qq,q1,q2' & ,qq,qt,q1,q2 if(jdis.eq.0)then scale=qt else scale=qt*4. endif if(j1.eq.0.and.l.eq.0)then fb=ffborn(s,t, 1. , 0. , 0. , 0. , 0. ) !gg elseif(j1*l.eq.0)then fb=ffborn(s,t, 0. , 1. , 0. , 0. , 0.) !qg elseif(j1.eq.l)then fb=ffborn(s,t, 0. , 0. , 1. , 0. , 0.) !qq elseif(j1.eq.-l)then fb=ffborn(s,t, 0. , 0. , 0. , 1. , 0.) !qq else fb=ffborn(s,t, 0. , 0. , 0. , 0. , 1.) !qq endif fb=fb*pssalf(qt/qcdlam)**2 psbornd=psbornd+dble(a1(i)*fb)*dble(t)**2 & *psuds(scale,j1)*psuds(qt,l) enddo enddo psbornd=psbornd*dble(2.*pi**3)/dble(s)**2/sud0*2 * /2 !CS for parton pair if(md.eq.1)psbornd=psbornd*(1./tmin-1./tmax) psborn=sngl(psbornd) return end c------------------------------------------------------------------------ function psdgh(s,qq,long) c----------------------------------------------------------------------- c psdgh c s - energy squared for the interaction (hadron-hadron), c----------------------------------------------------------------------- common/ar3/ x1(7),a1(7) common /cnsta/ pi,pii,hquer,prom,piom,ainfin include 'epos.incsem' double precision psuds xd=qq/s if(long.eq.0)then psdgh=(psdfh4(xd,q2min,0.,2,1)/2.25+psdfh4(xd,q2min,0.,2,2)/9. * +psdfh4(xd,q2min,0.,2,3)/9.+ * 2.*(psdfh4(xd,q2min,0.,2,-1)+psdfh4(xd,q2min,0.,2,-2)+ * psdfh4(xd,q2min,0.,2,-3))/4.5) * *sngl(psuds(qq,1)/psuds(q2min,1))*4.*pi**2*alfe/qq else psdgh=0. endif dgh=0. if(long.eq.0)then s2min=qq/(1.-q2ini/qq) else s2min=4.*max(q2min,qcmass**2)+qq s2min=s2min/(1.-4.*q2ini/(s2min-qq)) endif xmin=s2min/s if(xmin.lt.1.)then do i=1,7 !numerical integration over z1 do m=1,2 if(long.eq.0)then z1=qq/s+(xmin-qq/s)*((1.-qq/s)/(xmin-qq/s)) * **(.5+(m-1.5)*x1(i)) else z1=.5*(1.+xmin+(2*m-3)*x1(i)*(1.-xmin)) endif call psdint(z1*s,qq,sds,sdn,sdb,sdt,sdr,1,long) call psdint(z1*s,qq,sdsg,sdng,sdbg,sdtg,sdrg,0,long) tu=psdfh4(z1,q2min,0.,2,1) td=psdfh4(z1,q2min,0.,2,2) ts=psdfh4(z1,q2min,0.,2,3) tg=psdfh4(z1,q2min,0.,2,0) tsea=2.*(psdfh4(z1,q2min,0.,2,-1)+psdfh4(z1,q2min,0.,2,-2) * +psdfh4(z1,q2min,0.,2,-3)) gy=sdn*(tu/2.25+td/9.+ts/9.+tsea/4.5)+sdtg*tg/4.5 * +sdt*(tu+td+ts+tsea)/4.5 dgh=dgh+a1(i)*gy*(1.-qq/s/z1) enddo enddo dgh=dgh*log((1.-qq/s)/(xmin-qq/s))*.5 endif psdgh=psdgh+dgh return end c------------------------------------------------------------------------ function psdh(s,qq,iclpro0,long) c----------------------------------------------------------------------- c pshard - hard quark-quark interaction cross-section c s - energy squared for the interaction (hadron-hadron), c iclpro0 - type of the primary hadron (nucleon) c----------------------------------------------------------------------- common /ar3/ x1(7),a1(7) include 'epos.incsem' include 'epos.inc' double precision psuds xd=qq/s qqs=q2min if(long.eq.0.and.(idisco.eq.0.or.idisco.eq.1))then psdh=(psdfh4(xd,qqs,0.,iclpro0,1)/2.25+ * psdfh4(xd,qqs,0.,iclpro0,2)/9.) * *sngl(psuds(qq,1)/psuds(qqs,1)) * *4.*pi**2*alfe/qq else psdh=0. endif dh=0. if(long.eq.0)then s2min=qq/(1.-q2ini/qq) else s2min=4.*max(q2min,qcmass**2)+qq s2min=s2min/(1.-4.*q2ini/(s2min-qq)) endif xmin=s2min/s if(xmin.lt.1.)then do i=1,7 !numerical integration over z1 do m=1,2 if(long.eq.0)then z1=qq/s+(xmin-qq/s)*((1.-qq/s)/(xmin-qq/s)) * **(.5+(m-1.5)*x1(i)) else z1=.5*(1.+xmin+(2*m-3)*x1(i)*(1.-xmin)) endif call psdint(z1*s,qq,sds,sdn,sdb,sdt,sdr,1,long) tu=psdfh4(z1,qqs,0.,iclpro0,1) td=psdfh4(z1,qqs,0.,iclpro0,2) gy=sdt*(tu+td)/4.5+sdn*(tu/2.25+td/9.) if(long.eq.0)then gy=gy*(1.-qq/s/z1) else gy=gy/z1 endif dh=dh+a1(i)*gy enddo enddo if(long.eq.0)then dh=dh*log((1.-qq/s)/(xmin-qq/s))*.5 else dh=dh*(1.-xmin)*.5 endif endif psdh=psdh+dh return end c------------------------------------------------------------------------ function psdsh(s,qq,iclpro0,dqsh,long) c----------------------------------------------------------------------- c psdsh - semihard interaction eikonal c s - energy squared for the interaction (hadron-hadron), c iclpro0 - hadron class, c z - impact parameter factor, z=exp(-b**2/rp), c iqq - type of the hard interaction (0 - gg, 1 - qg, 2 - gq) c----------------------------------------------------------------------- common /ar3/ x1(7),a1(7) include 'epos.inc' include 'epos.incsem' double precision psuds xd=qq/s if(long.eq.0.and.(idisco.eq.0.or.idisco.eq.1))then dqsh=fzeroSeaZZ(xd,iclpro0)/xd**dels * *ffrr*4.*pi*gamhad(iclpro0)/ * 4.5*sngl(psuds(qq,1)/psuds(q2min,1)) * *4.*pi**2*alfe/qq else dqsh=0. endif if(long.eq.0)then s2min=qq/(1.-q2ini/qq) else s2min=qq+4.*max(q2min,qcmass**2) endif xmin=s2min/s xmin=xmin**(delh-dels) dsh=0. if(xmin.lt.1.)then c numerical integration over z1 do i=1,7 do m=1,2 z1=(.5*(1.+xmin-(2*m-3)*x1(i)*(1.-xmin)))**(1./ * (delh-dels)) call psdint(z1*s,qq,sdsg,sdng,sdbg,sdtg,sdrg,0,long) call psdint(z1*s,qq,sdsq,sdnq,sdbq,sdtq,sdrq,1,long) dsh=dsh+a1(i)/z1**delh*(sdtg*fzeroGluZZ(z1,iclpro0) * +(sdtq+sdnq)*fzeroSeaZZ(z1,iclpro0)) enddo enddo dsh=dsh*(1.-xmin)/(delh-dels)/2. endif psdsh=dqsh+dsh*ffrr*4.*pi*gamhad(iclpro0)/4.5 !*ccorr(1,1,iclpro0) return end cc------------------------------------------------------------------------ c function psdsh1(s,qq,iclpro0,dqsh,long) cc----------------------------------------------------------------------- cc psdsh - semihard interaction eikonal cc s - energy squared for the interaction (hadron-hadron), cc iclpro0 - hadron class, cc z - impact parameter factor, z=exp(-b**2/rp), cc iqq - type of the hard interaction (0 - gg, 1 - qg, 2 - gq) cc----------------------------------------------------------------------- c common /ar3/ x1(7),a1(7) c include 'epos.inc' c include 'epos.incsem' cc double precision psuds c c psdsh1=0. !only for plotting in psaevp : not use any more c cc$$$ xd=qq/s cc$$$ write(ifch,*)'Psdsh1 for xd,qq',xd,qq cc$$$ if(long.eq.0.and.(idisco.eq.0.or.idisco.eq.1))then cc$$$ dqsh=psftist(xd)/4.5*sngl(psuds(qq,1)/psuds(q2min,1)) cc$$$ * *4.*pi**2*alfe/qq cc$$$ else cc$$$ dqsh=0. cc$$$ endif cc$$$ cc$$$ if(long.eq.0)then cc$$$ s2min=qq/(1.-q2ini/qq) cc$$$ else cc$$$ s2min=qq+4.*max(q2min,qcmass**2) cc$$$ endif cc$$$ xmin=s2min/s cc$$$ xmin=xmin**(delh-dels) cc$$$ dsh=0. cc$$$ if(xmin.lt.1.)then cc$$$c numerical integration over z1 cc$$$ do i=1,7 cc$$$ do m=1,2 cc$$$ z1=(.5*(1.+xmin-(2*m-3)*x1(i)*(1.-xmin)))**(1./ cc$$$ * (delh-dels)) cc$$$ call psdint(z1*s,qq,sdsg,sdng,sdbg,sdtg,sdrg,0,long) cc$$$ call psdint(z1*s,qq,sdsq,sdnq,sdbq,sdtq,sdrq,1,long) cc$$$ dsh=dsh+a1(i)/z1**delh*(sdtg*psftigt(z1) cc$$$ * +(sdtq+sdnq)*psftist(z1))*z1**dels cc$$$ enddo cc$$$ enddo cc$$$ dsh=dsh*(1.-xmin)/(delh-dels)/2. cc$$$ endif cc$$$ psdsh1=dqsh+dsh/4.5 c return c end c c------------------------------------------------------------------------ function psev0(q1,qq,xx,j) c----------------------------------------------------------------------- double precision xx,psuds,psev00 common /ar3/ x1(7),a1(7) include 'epos.incsem' psev0=0. psev00=0.d0 do i=1,7 do m=1,2 if(j.eq.1)then !g->q qi=2.*q1/(1.+q1/qq+(1.-q1/qq)*(2.*m-3.)*x1(i)) psev00=psev00+a1(i)*qi*psuds(qi,0)/psuds(qi,1) * /log(qi*(1.d0-xx)/qcdlam) else !q->g qi=(.5*(q1+qq+(q1-qq)*(2.*m-3.)*x1(i))) psev00=psev00+a1(i)/qi/psuds(qi,0)*psuds(qi,1) * /log(qi*(1.d0-xx)/qcdlam) endif enddo enddo if(j.eq.1)then psev00=psev00*(1.d0/q1-1.d0/qq)*psuds(qq,1)/psuds(qq,0)/2.d0 else psev00=psev00*(qq-q1)*psuds(qq,0)/psuds(qq,1)/2.d0 endif psev00=psev00/log(log(qq*(1.d0-xx)/qcdlam) & /log(q1*(1.d0-xx)/qcdlam)) psev0=sngl(psev00) return end c------------------------------------------------------------------------ function psev(q1,qq,xx,j,l,n) c------------------------------------------------------------------------ double precision xx,zmax,zmax1,zmin,zmin1,z,psuds,fk,fq &,fz1,fz2 common /ar3/ x1(7),a1(7) include 'epos.incsem' zmax=1.d0-q2ini/qq zmin=xx/zmax qmax=qq fz1=0.d0 fz2=0.d0 if(zmin.lt.zmax)then if(zmin.lt..1d0)then zmax1=min(.1d0,zmax) do i=1,7 do m=1,2 if(n.eq.2)then z=xx+(zmin-xx)*((zmax1-xx)/(zmin-xx))**(.5+(m-1.5)*x1(i)) elseif(j.eq.1)then z=zmin*(zmax1/zmin)**(.5+(m-1.5)*x1(i)) else z=(.5d0*(zmax1+zmin+(zmax1-zmin)*(2*m-3)*x1(i))) endif qmin=max(q2ini/(1.d0-xx/z),q2ini/(1.d0-z)) qmin=max(qmin,q1) do k=1,2 fq=0.d0 do i1=1,7 do m1=1,2 if(n.eq.2)then qi=qmin*(qmax/qmin)**(.5+x1(i1)*(m1-1.5)) else qi=(.5*(qmax+qmin+(qmax-qmin)*(2.*m1-3.)*x1(i1))) endif if(j.eq.3.and.k.eq.1)then fk=0.d0 else if(n.eq.2)then fk=dble(psevi0(q1,qi,xx/z,min(2,j),k)) else fk=dble(psevi(q1,qi,xx/z,j,k)/qi) endif endif qt=qi*(1.d0-z) fq=fq+a1(i1)*fk/psuds(qi,l-1)*pssalf(qt/qcdlam) enddo enddo if(n.eq.2)then fq=fq*log(qmax/qmin)*(1.d0-xx/z) elseif(j.eq.1)then fq=fq*(qmax-qmin) else fq=fq*(qmax-qmin)/z endif fz1=fz1+a1(i)*fq*psfap(z,k-1,l-1) enddo enddo enddo if(n.eq.2)then fz1=fz1*log((zmax1-xx)/(zmin-xx))/4. elseif(j.eq.1)then fz1=fz1*log(zmax1/zmin)/4. else fz1=fz1*(zmax1-zmin)/4. endif endif if(zmax.gt..1d0)then zmin1=max(.1d0,zmin) do i=1,7 do m=1,2 z=1.d0-(1.d0-zmax)*((1.d0-zmin1)/(1.d0-zmax))** * (.5+x1(i)*(m-1.5)) qmin=max(q2ini/(1.d0-z),q2ini/(1.d0-xx/z)) qmin=max(qmin,q1) do k=1,2 fq=0. do i1=1,7 do m1=1,2 if(n.eq.2)then qi=qmin*(qmax/qmin)**(.5+x1(i1)*(m1-1.5)) else qi=(.5*(qmax+qmin+(qmax-qmin)*(2.*m1-3.)*x1(i1))) endif if(j.eq.3.and.k.eq.1)then fk=0.d0 else if(n.eq.2)then fk=dble(psevi0(q1,qi,xx/z,min(2,j),k)) else fk=dble(psevi(q1,qi,xx/z,j,k)/qi) endif endif qt=qi*(1.d0-z) fq=fq+a1(i1)*fk/psuds(qi,l-1)*pssalf(qt/qcdlam) enddo enddo if(n.eq.2)then fq=fq*log(qmax/qmin) else fq=fq*(qmax-qmin) endif fz2=fz2+a1(i)*fq*psfap(z,k-1,l-1)*(1.d0/z-1.d0) enddo enddo enddo fz2=fz2*log((1.d0-zmin1)/(1.d0-zmax))/4. endif endif psev=sngl((fz1+fz2)*psuds(qq,l-1)) return end c------------------------------------------------------------------------ function psevi0(q1,qq,xx,m,l) c------------------------------------------------------------------------ double precision xx,xmax,psuds dimension wi(3),wj(3),wk(3) common /psar2/ edmax,epmax common /psar31/ evk0(21,21,54) include 'epos.inc' include 'epos.incsem' xmax=1.d0-2.d0*q2ini/epmax qmin=max(1.d0*q2min,q2ini/(1.d0-xx)) qm1=max(q1,qmin) if(qq.gt..5001*epmax.and.ish.ge.1)then write(ifch,*)'0-extrap.:q1,qq,epmax,xx,m,l:',q1,qq,epmax,xx,m,l c stop endif if(xx.ge.xmax.or.qq.le.1.000*qm1)then psevi0=0. c write (*,*)'xx,xmax,qq,qm1,qmin,q1',xx,xmax,qq,qm1,qmin,q1 return endif if(m.eq.l)then psevi0=1. else if(xx.lt..1d0)then yx=log(10.d0*xx)+13. k=int(yx) if(k.gt.11)k=11 if(k.lt.1)k=1 elseif(xx.lt..9d0)then yx=10.*xx+12. k=int(yx) if(k.gt.19)k=19 else yx=log(10.d0*(1.d0-xx))/log(10.d0*(1.d0-xmax))*6.+21 k=int(yx) if(k.gt.25)k=25 endif wk(2)=yx-k wk(3)=wk(2)*(wk(2)-1.)*.5 wk(1)=1.-wk(2)+wk(3) wk(2)=wk(2)-2.*wk(3) qli=log(qq/qmin)/log(.5*epmax/qmin)*20.+1. qlj=log(qm1/qmin)/log(qq/qmin)*20.+1. i=int(qli) if(i.gt.19)i=19 if(i.lt.1)i=1 wi(2)=qli-i wi(3)=wi(2)*(wi(2)-1.)*.5 wi(1)=1.-wi(2)+wi(3) wi(2)=wi(2)-2.*wi(3) j=int(qlj) if(j.lt.1)j=1 if(j.gt.19)j=19 wj(2)=qlj-j wj(3)=wj(2)*(wj(2)-1.)*.5 wj(1)=1.-wj(2)+wj(3) wj(2)=wj(2)-2.*wj(3) psevi0=0. do i1=1,3 do j1=1,3 do k1=1,3 psevi0=psevi0+evk0(i+i1-1,j+j1-1,k+k1-1+27*(m-1)) * *wi(i1)*wj(j1)*wk(k1) enddo enddo enddo psevi0=exp(psevi0) endif psevi0=psevi0*psfap(xx,m-1,l-1)*log(log(qq*(1.d0-xx)/qcdlam) */log(qm1*(1.d0-xx)/qcdlam))*sngl(psuds(qq,m-1)/psuds(q1,m-1))/4.5 return end c------------------------------------------------------------------------ function psevi(q1,qq,xx,m,l) c------------------------------------------------------------------------ c m l: 1 1 ... gluon -> gluon c 2 1 ... quark -> gluon c 1 2 ... gluon -> quark c 3 2 ... quark -> quark non singlet c 2 2 ... quark -> quark all c singlet = all - non singlet c----------------------------------------------------------------------- double precision xx,xmax,psuds dimension wi(3),wj(3),wk(3) common /psar2/ edmax,epmax common /psar32/ evk(21,21,135) include 'epos.inc' include 'epos.incsem' psevi=0. xmax=1.d0-2.d0*q2ini/epmax if(qq.gt..5001*epmax.and.ish.ge.1)then write(ifch,*)'1-extrap.:q1,qq,epmax,xx,m,l:',q1,qq,epmax,xx,m,l c stop endif qmin=max(1.d0*q2min,q2ini/(1.d0-xx)) qm1=max(q1,qmin) if(xx.ge.xmax.or.qq.le.1.0001*qm1)then return endif qmin1=max(1.d0*qmin,q2ini/(1.d0-dsqrt(xx))) if(qq.le.1.0001*qmin1)then psevi=psevi0(q1,qq,xx,min(m,2),l) return endif if(xx.lt..1d0)then yx=log(10.d0*xx)+13. k=int(yx) if(k.gt.11)k=11 if(k.lt.1)k=1 elseif(xx.lt..9d0)then yx=10.*xx+12. k=int(yx) if(k.gt.19)k=19 else yx=log(10.d0*(1.d0-xx))/log(10.d0*(1.d0-xmax))*6.+21 k=int(yx) if(k.gt.25)k=25 endif wk(2)=yx-k wk(3)=wk(2)*(wk(2)-1.)*.5 wk(1)=1.-wk(2)+wk(3) wk(2)=wk(2)-2.*wk(3) qli=log(qq/qmin)/log(.5*epmax/qmin)*20.+1. qlj=log(qm1/qmin)/log(qq/qmin)*20.+1. i=int(qli) if(i.lt.1)i=1 if(i.gt.19)i=19 wi(2)=qli-i wi(3)=wi(2)*(wi(2)-1.)*.5 wi(1)=1.-wi(2)+wi(3) wi(2)=wi(2)-2.*wi(3) j=int(qlj) if(j.lt.1)j=1 if(j.gt.19)j=19 wj(2)=qlj-j wj(3)=wj(2)*(wj(2)-1.)*.5 wj(1)=1.-wj(2)+wj(3) wj(2)=wj(2)-2.*wj(3) do i1=1,3 do j1=1,3 do k1=1,3 if(m.eq.3)then k2=k+k1-1+108 else k2=k+k1-1+27*(m-1)+54*(l-1) endif psevi=psevi+evk(i+i1-1,j+j1-1,k2) * *wi(i1)*wj(j1)*wk(k1) enddo enddo enddo psevi=exp(psevi)*psfap(xx,m-1,l-1)*log(log(qq*(1.d0-xx)/qcdlam) */log(qm1*(1.d0-xx)/qcdlam))/4.5 if(q1.lt.qm1)psevi=psevi*sngl(psuds(qm1,m-1)/psuds(q1,m-1)) return end c------------------------------------------------------------------------ function psjci(q1,s,l1) c----------------------------------------------------------------------- c psjci - inclusive ordered ladder cross-section interpolation for c-quark c q1 - virtuality cutoff at current end of the ladder c s - total c.m. energy squared for the ladder, c l1 - parton type at current end of the ladder (0-g, 1,2,etc.-q) c----------------------------------------------------------------------- dimension wi(3),wk(3) common /psar2/ edmax,epmax common /psar23/ cschar(20,20,2) include 'epos.incsem' psjci=0. q2mass=qcmass**2 spmin=4.*q2min+q2mass qq=q1 s2min=4.*qq+q2mass if(s.le.s2min)return smins=s2min/(1.-q2ini/q1) c if(s.le.smins)goto 1 if(s.le.smins.or.qq.le.q2min)goto 1 !??????? ctp070618 p1=s/(1.+q2mass/s) if(p1.gt.4.*qq)then tmin=2.*qq/(1.+sqrt(1.-4.*qq/p1)) else tmin=2.*qq endif tmax=p1/2. qmax=p1/4. l=min(1,iabs(l1))+1 qli=log(qq/q2min)/log(qmax/q2min)*19.+1. sl=log(s/spmin)/log(epmax/2./spmin)*19.+1. k=int(sl) i=int(qli) if(i.lt.1)i=1 if(k.gt.18)k=18 if(i.gt.18)i=18 wi(2)=qli-i wi(3)=wi(2)*(wi(2)-1.)*.5 wi(1)=1.-wi(2)+wi(3) wi(2)=wi(2)-2.*wi(3) wk(2)=sl-k wk(3)=wk(2)*(wk(2)-1.)*.5 wk(1)=1.-wk(2)+wk(3) wk(2)=wk(2)-2.*wk(3) do i1=1,3 do k1=1,3 psjci=psjci+cschar(i+i1-1,k+k1-1,l)*wi(i1)*wk(k1) enddo enddo psjci=exp(psjci)*(1./tmin-1./tmax) return 1 psjci=psbint(q2min,q1,0.,s,4,l1,0) return end c----------------------------------------------------------------------- function psjct(s,l) c----------------------------------------------------------------------- c psjct - unordered ladder cross-section for c-quark c s - c.m. energy squared for the scattering; c l - parton type at opposite end of the ladder (0 - g, 1,2 etc. - q). c----------------------------------------------------------------------- double precision xx,zmax,qmax,qmin,qi,zmin,fsj,z,s2,sj common /ar3/ x1(7),a1(7) include 'epos.inc' include 'epos.incsem' psjct=0. q2mass=qcmass**2 zmax=dble(s)/(dble(s)+dble(5.*q2mass)) qmax=zmax**2*dble(q2mass)/(1.d0-zmax) qmin=dble(q2min) if(qmax.lt.qmin.and.ish.ge.1)write(ifch,*)'psjct:qmin,qmax' * ,qmin,qmax do i=1,7 do m=1,2 qi=2.d0*qmin/(1.d0+qmin/qmax+dble((2*m-3)*x1(i)) * *(1.d0-qmin/qmax)) zmax=(2.d0/(1.d0+dsqrt(1.d0+4.d0*dble(q2mass)/qi)))**delh zmin=(5.d0*qi/dble(s))**delh fsj=0.d0 if(zmax.lt.zmin.and.ish.ge.1)write(ifch,*)'psjct:zmin,zmax' * ,zmin,zmax do i1=1,7 do m1=1,2 z=(.5d0*(zmax+zmin+dble((2*m1-3)*x1(i1)) * *(zmax-zmin)))**(1./delh) s2=z*dble(s)-qi xx=z sj=dble(psjti(sngl(qi),q2min,sngl(s2),0,l,0)*psfap(xx,1,0))*z fsj=fsj+dble(a1(i1))*sj*dble(pssalf(sngl(qi)/qcdlam))/z**delh enddo enddo fsj=fsj*(zmax-zmin) psjct=psjct+a1(i)*sngl(fsj*qi) enddo enddo psjct=psjct*sngl(1./qmin-1./qmax)/delh/4. return end c------------------------------------------------------------------------ function psjet1(q1,q2,qqcut,s,j,l,jdis) c----------------------------------------------------------------------- c psjet1 - ordered parton ladder cross-section c q1 - virtuality cutoff at current end of the ladder; c q2 - virtuality cutoff at opposite end of the ladder; c qqcut - p_t cutoff for the born process; c s - c.m. energy squared for the scattering; c j - parton type at current end of the ladder (0 - g, 1,2 etc. - q); c l - parton type at opposite end of the ladder (0 - g, 1,2 etc. - q). c----------------------------------------------------------------------- double precision xx,z,qq,xmax,xmin,s2min,smin,p1,q2ms,q2inis,xmin1 *,sh,qtmin,t,xmax1,fx1,fx2,psuds common /ar3/ x1(7),a1(7) common /ar9/ x9(3),a9(3) include 'epos.inc' include 'epos.incsem' psjet1=0. if(jdis.eq.0)then qq=dble(max(q1,q2)) elseif(jdis.eq.1)then qq=dble(max(q1/4.,q2)) else qq=dble(max(q1,q2/4.)) endif qq=max(qq,dble(qqcut)) if(l.ne.3)then q2mass=0. else q2mass=qcmass**2 endif s2min=dble(q2mass)+4.d0*qq if(jdis.eq.0.or.jdis.eq.2)then smin=s2min/(1.d0-dble(q2ini)/qq) else smin=s2min/(1.d0-dble(q2ini)/qq/4.d0) endif if(dble(s).le.smin)return q2ms=dble(q2mass)/dble(s) q2inis=dble(q2ini)/dble(s) p1=dble(s)/(1.d0+q2ms) if(jdis.eq.0.or.jdis.eq.2)then xmax=.5d0*(1.d0+q2ms)+dsqrt(.25d0*(1.d0-q2ms)**2-4.d0*q2inis) else xmax=.5d0*(1.+q2ms)+dsqrt(.25d0*(1.-q2ms)**2-q2inis) endif xmin=max(1.d0+q2ms-xmax,s2min/dble(s)) if(xmin.ge.xmax.and.ish.ge.1)then write(ifch,*)'jti1,xmin,xmax',xmin,xmax c return endif fx1=0.d0 fx2=0.d0 if(xmax.gt..8d0)then xmin1=max(xmin,.8d0) do i=1,3 do m=1,2 z=1.d0-(1.d0-xmax)*((1.d0-xmin1)/(1.d0-xmax))** * (.5d0+dble(x9(i)*(m-1.5))) sh=z*dble(s) xx=z p1=sh/(1.d0+dble(q2mass)/sh) if(jdis.eq.0.or.jdis.eq.2)then qtmin=max(qq,dble(q2ini)/(1.d0-z)) else qtmin=max(qq,dble(q2ini)/(1.d0-z)/4.d0) endif tmin=2.d0*dble(qtmin)/(1.d0+dsqrt(1.d0-4.d0*dble(qtmin)/p1)) tmax=p1/2.d0 ft=0. if(tmin.ge.tmax.and.ish.ge.1)write(ifch,*)'psjet1:tmin,tmax' * ,tmin,tmax do i1=1,3 do m1=1,2 t=2.d0*tmin/(1.d0+tmin/tmax-dble(x9(i1)*(2*m1-3)) & *(1.d0-tmin/tmax)) qt=sngl(t*(1.d0-t/p1)) c if(qt.lt.qtmin)write (*,*)'psjet1:qt,qq',qt,qq if(jdis.eq.0)then scale1=qt scale2=qt elseif(jdis.eq.1)then scale1=qt*4. scale2=qt elseif(jdis.eq.2)then scale1=qt scale2=qt*4. endif fb=0. do n=1,3 fb=fb+psjetj(q1,scale1,sngl(t),xx,sngl(sh),j,l,n) enddo ft=ft+a9(i1)*fb*pssalf(qt/qcdlam)**2*sngl(t**2 * *psuds(scale2,l)) enddo enddo fx1=fx1+dble(a9(i)*ft)*(1.d0/tmin-1.d0/tmax)/sh**2*(1.d0-z) enddo enddo fx1=fx1*dlog((1.d0-xmin1)/(1.d0-xmax)) endif if(xmin.lt..8d0)then xmax1=min(xmax,.8d0)**(-delh) xmin1=xmin**(-delh) do i=1,3 do m=1,2 z=(.5d0*(xmax1+xmin1+(xmin1-xmax1)*dble((2*m-3)*x9(i)))) * **(-1./delh) sh=z*dble(s) xx=z p1=sh/(1.d0+dble(q2mass)/sh) if(jdis.eq.0.or.jdis.eq.2)then qtmin=max(qq,dble(q2ini)/(1.d0-z)) else qtmin=max(qq,dble(q2ini)/(1.d0-z)/4.d0) endif tmin=2.d0*dble(qtmin)/(1.d0+dsqrt(1.d0-4.d0*dble(qtmin)/p1)) tmax=p1/2.d0 ft=0. if(tmin.ge.tmax.and.ish.ge.1)write(ifch,*)'psjet1:tmin,tmax' & ,tmin,tmax do i1=1,3 do m1=1,2 t=2.d0*tmin/(1.d0+tmin/tmax-dble(x9(i1)*(2*m1-3)) & *(1.d0-tmin/tmax)) qt=sngl(t*(1.d0-t/p1)) if(qt.lt.sngl(qtmin).and.ish.ge.1)write(ifch,*)'psjet1:qt,qq' & ,qt,qq if(jdis.eq.0)then scale1=qt scale2=qt elseif(jdis.eq.1)then scale1=qt*4. scale2=qt elseif(jdis.eq.2)then scale1=qt scale2=qt*4. endif fb=0. do n=1,3 fb=fb+psjetj(q1,scale1,sngl(t),xx,sngl(sh),j,l,n) enddo ft=ft+a9(i1)*fb*pssalf(qt/qcdlam)**2*sngl(t**2 * *psuds(scale2,l)) enddo enddo fx2=fx2+dble(a9(i)*ft)*(1.d0/tmin-1.d0/tmax)/sh**2*z**(1.+delh) enddo enddo fx2=fx2*(xmin1-xmax1)/dble(delh) endif psjet1=sngl((fx1+fx2)/psuds(q2,l))*pi**3*2 * /2 !CS for parton pair return end c----------------------------------------------------------------------- function psjet(q1,q2,qqcut,s,j,l,jdis) c----------------------------------------------------------------------- c parton ladder cross-section c with at least one emission on each side c c q1 - virtuality cutoff at current end of the ladder; c q2 - virtuality cutoff at opposite end of the ladder; c qqcut - p_t cutoff for the born process; c s - c.m. energy squared for the scattering; c j - parton type at current end of the ladder (0 - g, 1,2 etc. - q); c l - parton type at opposite end of the ladder (0 - g, 1,2 etc. - q). c----------------------------------------------------------------------- double precision xx1,xx2,qq,s2min,xmin,xmax,xmin1,xmax1,t,tmin *,tmax,sh,z,qtmin,ft,fx1,fx2 common /ar3/ x1(7),a1(7) common /ar9/ x9(3),a9(3) include 'epos.inc' include 'epos.incsem' common/ccctest/iiitest iiitest=0 psjet=0. if(jdis.eq.0)then qq=dble(max(q1,q2)) else qq=dble(max(q1/4.,q2)) endif qq=max(qq,dble(qqcut)) s2min=4.d0*qq if(dble(s).le.s2min/(1.d0-dble(q2ini)/qq)**2)return !kkkkkkk phi=acos(1.-54.*q2ini/s)/3. zmax=(1.+2.*cos(phi))**2/9. !kkkkkkk zmin=(1.-cos(phi)+sqrt(3.d0)*sin(phi))/3. !kkkkkkk zmin=max(zmin**2,sngl(s2min/dble(s))) if(zmin.gt.zmax.and.ish.ge.1)write(ifch,*)'psjet:zmin,zmax' * ,zmin,zmax zmin=zmin**(-delh) zmax=zmax**(-delh) do i=1,3 do m=1,2 z=dble(.5*(zmax+zmin+(zmin-zmax)*(2*m-3)*x9(i)))**(-1./delh) xmin=dsqrt(z) sh=z*dble(s) qtmin=max(qq,dble(q2ini)/(1.d0-dsqrt(z))) tmin=max(0.d0,1.d0-4.d0*qtmin/sh) tmin=2.d0*qtmin/(1.d0+dsqrt(tmin)) !kkkkkkk tmax=sh/2.d0 ft=0.d0 c if(tmin.gt.tmax)write (*,*)'psjet:tmin,tmax',tmin,tmax do i1=1,3 do m1=1,2 t=2.d0*tmin/(1.d0+tmin/tmax-dble(x9(i1)*(2*m1-3)) & *(1.d0-tmin/tmax)) qt=t*(1.d0-t/sh) c if(qt.lt.qtmin)write (*,*)'psjet:qt,qq',qt,qq xmax=1.d0-q2ini/qt xmin=max(dsqrt(z),z/xmax) !xm>xp !!! if(xmin.gt.xmax.and.ish.ge.1)write(ifch,*)'psjet:xmin,xmax' * ,xmin,xmax fx1=0.d0 fx2=0.d0 if(xmax.gt..8d0)then xmin1=max(xmin,.8d0) do i2=1,3 do m2=1,2 xx1=1.d0-(1.d0-xmax)*((1.d0-xmin1)/(1.d0-xmax))** * dble(.5+x9(i2)*(m2-1.5)) xx2=z/xx1 fb=0. fb=fb+psjeti(q1,q2,qt,sngl(t),xx1,xx2,sngl(sh) * ,j,l,jdis) * +psjeti(q1,q2,qt,sngl(t),xx2,xx1,sngl(sh) * ,j,l,jdis) fx1=fx1+dble(a9(i2)*fb)*(1.d0/xx1-1.d0) * *pssalf(qt/qcdlam)**2 enddo enddo fx1=fx1*dlog((1.d0-xmin1)/(1.d0-xmax)) endif if(xmin.lt..8d0)then xmax1=min(xmax,.8d0) do i2=1,3 do m2=1,2 xx1=xmin*(xmax1/xmin)**dble(.5+x9(i2)*(m2-1.5)) xx2=z/xx1 fb=0. fb=fb+psjeti(q1,q2,qt,sngl(t),xx1,xx2,sngl(sh) * ,j,l,jdis) * +psjeti(q1,q2,qt,sngl(t),xx2,xx1,sngl(sh) * ,j,l,jdis) fx2=fx2+dble(a9(i2))*fb*pssalf(qt/qcdlam)**2 enddo enddo fx2=fx2*dlog(xmax1/xmin) endif ft=ft+dble(a9(i1))*(fx1+fx2)*t**2 enddo enddo ft=ft*(1.d0/tmin-1.d0/tmax) psjet=psjet+a9(i)*sngl(ft*z**(1.+delh)/sh**2) enddo enddo psjet=psjet*(zmin-zmax)/delh*pi**3 * /2. !CS for parton pair return end c----------------------------------------------------------------------- function pijet(ii,qi,qq,sk,m1,l1) !polynomial interpol of jet CS c----------------------------------------------------------------------- c ii ..... type of CS (2 = bothside, 1 = oneside, 0 = no emission, Born) c qi ..... virtuality cutoff at current end of the ladder c qq ..... virtuality cutoff of Born c sk ..... energy squared for the scattering c m1,l1 .. parton types c----------------------------------------------------------------------- include 'epos.incsem' common/psar2/edmax,epmax common/tabcsjet/ksmax,iqmax,jqmax,csjet(0:2,2,20,20,20,3,2) real wi(3),wj(3),wk(3) common/cpijet/npijet data npijet/0/ npijet=npijet+1 if(npijet.eq.1)call MakeCSTable if(m1.ne.0.and.m1.eq.l1)then m=2 l=2 elseif(m1.ne.0.and.m1.eq.-l1)then m=3 l=1 elseif(m1.ne.0.and.l1.ne.0.and.m1.ne.l1)then m=3 l=2 else m=min(1,iabs(m1))+1 l=min(1,iabs(l1))+1 endif qqmin=min(qi,qq) qmax=sk/4. spmin=4.*q2min spmed=spmin*(epmax/2./spmin)**(1./(ksmax-1.)) if(sk.le.spmed)then kk=2 spmax=spmed else kk=1 spmax=epmax/2. endif qli=1.+log(qi/q2min)/log(qmax/q2min)*(iqmax-1) qlj=1.+log(qq/qqmin)/log(qmax/qqmin)*(jqmax-1) sl= 1.+log(sk/spmin)/log(spmax/spmin)*(ksmax-1) k=int(sl) i=int(qli) j=int(qlj) if(k.lt.1)k=1 if(j.lt.1)j=1 if(i.lt.1)i=1 if(k.gt.(ksmax-2))k=ksmax-2 if(i.gt.(iqmax-2))i=iqmax-2 if(j.gt.(jqmax-2))j=jqmax-2 wi(2)=qli-i wi(3)=wi(2)*(wi(2)-1.)*.5 wi(1)=1.-wi(2)+wi(3) wi(2)=wi(2)-2.*wi(3) wj(2)=qlj-j wj(3)=wj(2)*(wj(2)-1.)*.5 wj(1)=1.-wj(2)+wj(3) wj(2)=wj(2)-2.*wj(3) wk(2)=sl-k wk(3)=wk(2)*(wk(2)-1.)*.5 wk(1)=1.-wk(2)+wk(3) wk(2)=wk(2)-2.*wk(3) pijet=0 do i1=1,3 do j1=1,3 do k1=1,3 pijet=pijet+csjet(ii,kk,k+k1-1,i+i1-1,j+j1-1,m,l) * *wi(i1)*wj(j1)*wk(k1) enddo enddo enddo ! if(ii.eq.2)print*,' ' ! write(*,'(i2,f6.0,i2,3x,3(2f5.2,2x),f5.2)') !* ii,sk,k,(wk(kk1),csjet(ii,kk,k+kk1-1,1,1,m,l),kk1=1,3) ,pijet end c----------------------------------------------------------------------- subroutine MakeCSTable !tabulates psjet c----------------------------------------------------------------------- c last two indices of table: parton types c 1 1 ... gg c 1 2 ... gq c 2 1 ... qg c 2 2 ... qq c 3 1 ... qa c 3 2 ... qq' c----------------------------------------------------------------------- include 'epos.incsem' common/psar2/edmax,epmax common/tabcsjet/ksmax,iqmax,jqmax,csjet(0:2,2,20,20,20,3,2) write (*,'(a,$)')'(CS table' ksmax=10 iqmax=3 jqmax=3 spmin=4.*q2min do kk=1,2 if(kk.eq.1)then spmax=epmax/2. else !if(kk.eq.2) spmax=spmin*(epmax/2./spmin)**(1./(ksmax-1.)) endif do m=1,3 !parton type at upper end of the ladder write (*,'(a,$)')'.' do l=1,2 !parton type at lower end of the ladder m1=m-1 l1=l-1 if(m.eq.3.and.l.eq.1)l1=-m1 do k=1,ksmax sk=spmin*(spmax/spmin)**((k-1.)/(ksmax-1.)) qmax=sk/4. do i=1,iqmax qi=q2min*(qmax/q2min)**((i-1.)/(iqmax-1.)) do j=1,jqmax qq=qi*(qmax/qi)**((j-1.)/(jqmax-1.)) !write(*,'(i3,4f8.3,2i4,$)')j, qi,q2min,qq,sk,m1,l1 csjet(2,kk,k,i,j,m,l)= psjet(qi,q2min,qq,sk,m1,l1,0) csjet(1,kk,k,i,j,m,l)=psjet1(qi,q2min,qq,sk,m1,l1,0) csjet(0,kk,k,i,j,m,l)=psborn(qi,q2min,qq,sk,m1,l1,0,1) ! if(i.eq.1.and.j.eq.1.and.m.eq.1.and.l.eq.1) ! *write(*,'(2f8.2,f13.2,2i3,3x,i3,3f8.3)') ! * qi,qq,sk,m1,l1,k,csjet(2,kk,k,i,j,m,l) ! * ,csjet(1,kk,k,i,j,m,l),csjet(0,kk,k,i,j,m,l) enddo enddo enddo enddo enddo enddo write (*,'(a,$)')'done)' end c----------------------------------------------------------------------- function psjeti(q1,q2,qt,t,xx1,xx2,s,j,l,jdis) c----------------------------------------------------------------------- c c E~qcd_ji * E~qcd_lk * B_ik c c B_ik = psbori = contribution to Born xsection: c dsigmaBorn/d2pt/dy c = s/pi * delta(s+t+u) * 2*pi*alpha**2 /s**2 * B_ik c c E~qcd: at least one emission c c q1 - virtuality cutoff at current end of the ladder c q2 - virtuality cutoff at opposite end of the ladder c xx1 - feinman x for the first parton for the born process c xx2 - feinman x for the second parton for the born process c s - c.m. energy squared for the born scattering c t - invariant variable for the scattering |(p1-p3)**2|, c j - parton type at current end of the ladder (0 - g, 1,-1,2,... - q) c l - parton type at opposite end of the ladder (0 - g, 1,-1,2,... - q) c----------------------------------------------------------------------- c reminder c psevi: 1 1 ... gluon -> gluon c 2 1 ... quark -> gluon c 1 2 ... gluon -> quark c 3 2 ... quark -> quark non singlet c 2 2 ... quark -> quark all c singlet = all - non singlet c----------------------------------------------------------------------- double precision xx1,xx2 include 'epos.incsem' common/ccctest/iiitest if(jdis.eq.0)then scale=qt else scale=qt*4. endif if(j.eq.0.and.l.eq.0)then ! gluon-gluon ---> akg1=psevi(q1,scale,xx1,1,1) !gluon contribution akg2=psevi(q2,qt,xx2,1,1) !gluon contribution aks1=psevi(q1,scale,xx1,1,2)/naflav/2. !singlet contribution per quark aks2=psevi(q2,qt,xx2,1,2)/naflav/2. !singlet contribution per quark psjeti=ffborn(s,t,akg1*akg2 * ,(akg1*aks2+aks1*akg2)*naflav*2. !ccccc * ,aks1*aks2*naflav*2. * ,aks1*aks2*naflav*2. * ,aks1*aks2*naflav*2.*(naflav-1)*2. *) elseif(j.eq.0)then ! gluon-quark ---> akg1=psevi(q1,scale,xx1,1,1) !gluon contribution akg2=psevi(q2,qt,xx2,2,1) !gluon contribution aks1=psevi(q1,scale,xx1,1,2)/naflav/2. !singlet contribution akns2=psevi(q2,qt,xx2,3,2) !nonsinglet contribution aks2=(psevi(q2,qt,xx2,2,2)-akns2)/naflav/2. !singlet contribution psjeti=ffborn(s,t,akg1*akg2 * ,(akg1*(akns2+aks2*naflav*2.)+aks1*akg2*naflav*2.) * ,aks1*(akns2+aks2*naflav*2.) * ,aks1*(akns2+aks2*naflav*2.) * ,aks1*(akns2+aks2*naflav*2.)*(naflav-1)*2.) elseif(l.eq.0)then ! quark-gluon ---> akg1=psevi(q1,scale,xx1,2,1) !gluon contribution akg2=psevi(q2,qt,xx2,1,1) !gluon contribution akns1=psevi(q1,scale,xx1,3,2) !nonsinglet contribution aks1=(psevi(q1,scale,xx1,2,2)-akns1)/naflav/2. !singlet contribution aks2=psevi(q2,qt,xx2,1,2)/naflav/2. !singlet contribution psjeti=ffborn(s,t,akg1*akg2 * ,(akg2*(akns1+aks1*naflav*2.)+aks2*akg1*naflav*2.) * ,aks2*(akns1+aks1*naflav*2.) * ,aks2*(akns1+aks1*naflav*2.) * ,aks2*(akns1+aks1*naflav*2.)*(naflav-1)*2.) else ! quark-quark ---> akg1=psevi(q1,scale,xx1,2,1) !gluon contribution akg2=psevi(q2,qt,xx2,2,1) !gluon contribution akns1=psevi(q1,scale,xx1,3,2) !nonsinglet contribution aks1=(psevi(q1,scale,xx1,2,2)-akns1)/naflav/2.!singlet contribution akns2=psevi(q2,qt,xx2,3,2) !nonsinglet contribution aks2=(psevi(q2,qt,xx2,2,2)-akns2)/naflav/2.!singlet contribution if(j.eq.l)then psjeti=ffborn(s,t,akg1*akg2 * ,(akg2*(akns1+aks1*naflav*2.)+akg1*(akns2+aks2*naflav*2.)) * ,((akns1+aks1)*(akns2+aks2)+aks1*aks2*(2.*naflav-1.)) * ,(akns1*aks2+akns2*aks1+aks1*aks2*naflav*2.) * ,(akns1*aks2+akns2*aks1+aks1*aks2*naflav*2.)*(naflav-1)*2.) elseif(j.eq.-l)then psjeti=ffborn(s,t,akg1*akg2 * ,(akg2*(akns1+aks1*naflav*2.)+akg1*(akns2+aks2*naflav*2.)) * ,(akns1*aks2+akns2*aks1+aks1*aks2*naflav*2.) * ,((akns1+aks1)*(akns2+aks2)+aks1*aks2*(2.*naflav-1.)) * ,(akns1*aks2+akns2*aks1+aks1*aks2*naflav*2.)*(naflav-1)*2.) else !j.ne.l,-l psjeti=ffborn(s,t,akg1*akg2 * ,(akg2*(akns1+aks1*naflav*2.)+akg1*(akns2+aks2*naflav*2.)) * ,(akns1*aks2+akns2*aks1+aks1*aks2*naflav*2.) * ,(akns1*aks2+akns2*aks1+aks1*aks2*naflav*2.) * ,(akns1*akns2+akns1*aks2*(naflav-1)*2. * +akns2*aks1*(naflav-1)*2.+aks1*aks2*naflav*2.*(naflav-1)*2.)) endif endif return end c----------------------------------------------------------------------- function psjetj(q1,scale,t,xx,s,j,l,n) c----------------------------------------------------------------------- c psjetj - integrand for the ordered ladder cross-section c q1 - virtuality cutoff at current end of the ladder, c scale - born process scale, c t - invariant variable for the scattering |(p1-p3)**2|, c xx - feinman x for the first parton for the born process c s - c.m. energy squared for the born scattering, c j - parton type at current end of the ladder (0 - g, 1,-1,2,... - q) c l - parton type at opposite end of the ladder (0 - g, 1,-1,2,... - q) c n - subprocess number c----------------------------------------------------------------------- double precision xx include 'epos.incsem' m=min(1,iabs(j))+1 if(l.ne.3)then if(l.eq.0)then psjetj=psevi(q1,scale,xx,m,1)*(psbori(s,t,0,0,n)+ !gg * psbori(s,s-t,0,0,n))/2. * +psevi(q1,scale,xx,m,2)*(psbori(s,t,1,0,n)+ !qg * psbori(s,s-t,1,0,n)) elseif(j.eq.0)then aks=psevi(q1,scale,xx,1,2)/naflav/2. !singlet contribution per quark psjetj=psevi(q1,scale,xx,1,1)*(psbori(s,t,0,1,n)+ !gq * psbori(s,s-t,0,1,n)) * +aks*(psbori(s,t,1,1,n)+psbori(s,s-t,1,1,n))/2. !qq * +aks*(psbori(s,t,-1,1,n)+psbori(s,s-t,-1,1,n)) !qq~ * +aks*(psbori(s,t,1,2,n)+psbori(s,s-t,1,2,n))*(naflav-1)*2. !qq' else akg=psevi(q1,scale,xx,2,1) !gluon contribution akns=psevi(q1,scale,xx,3,2) !nonsinglet contribution aks=(psevi(q1,scale,xx,2,2)-akns)/naflav/2. !singlet contribution if(j.eq.l)then psjetj=akg*(psbori(s,t,0,1,n)+psbori(s,s-t,0,1,n)) !gq * +(akns+aks)*(psbori(s,t,1,1,n)+psbori(s,s-t,1,1,n))/2. !qq * +aks*(psbori(s,t,-1,1,n)+psbori(s,s-t,-1,1,n)) !qq~ * +aks*(psbori(s,t,1,2,n)+psbori(s,s-t,1,2,n))*(naflav-1)*2. !qq' elseif(j.eq.-l)then psjetj=akg*(psbori(s,t,0,1,n)+psbori(s,s-t,0,1,n)) !gq * +aks*(psbori(s,t,1,1,n)+psbori(s,s-t,1,1,n))/2. !qq * +(akns+aks)*(psbori(s,t,-1,1,n)+psbori(s,s-t,-1,1,n)) !qq~ * +aks*(psbori(s,t,1,2,n)+psbori(s,s-t,1,2,n))*(naflav-1)*2.!qq' else psjetj=akg*(psbori(s,t,0,1,n)+psbori(s,s-t,0,1,n)) !gq * +aks*(psbori(s,t,1,1,n)+psbori(s,s-t,1,1,n))/2. !qq * +aks*(psbori(s,t,-1,1,n)+psbori(s,s-t,-1,1,n)) !qq~ * +(akns+aks*(naflav-1)*2.)* * (psbori(s,t,1,2,n)+psbori(s,s-t,1,2,n)) !qq' endif endif elseif(n.eq.1)then p1=s/(1.+qcmass**2/s) psjetj=psevi(q1,scale,xx,m,1)*(psbori(s,t,4,0,n)+ !cg * psbori(s,p1-t,4,0,n)) * +psevi(q1,scale,xx,m,2)*(psbori(s,t,4,1,n)+ !cq * psbori(s,p1-t,4,1,n)) else psjetj=0. endif return end c------------------------------------------------------------------------ function psjti(q1,qqcut,s,m1,l1,jdis) c----------------------------------------------------------------------- c psjti - inclusive hard cross-section interpolation - for any ordering c in the ladder c q1 - virtuality cutoff at current end of the ladder c qqcut - p_t cutoff for the born process; c s - total c.m. energy squared for the ladder c m1 - parton type at current end of the ladder (0-g, 1,2,etc.-q) c l1 - parton type at opposite end of the ladder (0-g, 1,2,etc.-q) c----------------------------------------------------------------------- dimension wi(3),wj(3),wk(3) common /psar2/ edmax,epmax common /psar19/ cstot(20,20,240) include 'epos.incsem' psjti=0. c jdis1=jdis if(jdis.eq.0)then qqmin=q1 qmax=s/4. else qqmin=max(q2min,q1/4.) qmax=s endif qq=max(qqmin,qqcut) spmin=4.*q2min s2min=4.*qq if(s.le.s2min)return if(jdis.eq.0)then smins=s2min/(1.-q2ini/qq) else smins=s2min/(1.-q2ini/qq/4.) endif if(s.le.smins)goto 1 if(s.gt.4.*qq)then tmin=2.*qq/(1.+sqrt(1.-4.*qq/s)) else tmin=2.*qq endif tmax=s/2. if(m1.ne.0.and.m1.eq.l1)then m=2 l=2 elseif(m1.ne.0.and.m1.eq.-l1)then m=3 l=1 elseif(m1.ne.0.and.l1.ne.0.and.m1.ne.l1)then m=3 l=2 else m=min(1,iabs(m1))+1 l=min(1,iabs(l1))+1 endif ml=20*(m-1)+60*(l-1)+120*jdis qli=log(q1/q2min)/log(qmax/q2min)*19.+1. qlj=log(qq/qqmin)/log(s/4./qqmin)*19.+1. sl=log(s/spmin)/log(epmax/2./spmin)*19.+1. k=int(sl) i=int(qli) j=int(qlj) if(j.lt.1)j=1 if(i.lt.1)i=1 if(k.gt.18)k=18 if(i.gt.18)i=18 if(j.gt.18)j=18 wi(2)=qli-i wi(3)=wi(2)*(wi(2)-1.)*.5 wi(1)=1.-wi(2)+wi(3) wi(2)=wi(2)-2.*wi(3) wj(2)=qlj-j wj(3)=wj(2)*(wj(2)-1.)*.5 wj(1)=1.-wj(2)+wj(3) wj(2)=wj(2)-2.*wj(3) wk(2)=sl-k wk(3)=wk(2)*(wk(2)-1.)*.5 wk(1)=1.-wk(2)+wk(3) wk(2)=wk(2)-2.*wk(3) do i1=1,3 do j1=1,3 do k1=1,3 psjti=psjti+cstot(i+i1-1,j+j1-1,k+k1+ml-1) * *wi(i1)*wj(j1)*wk(k1) enddo enddo enddo psjti=exp(psjti)*(1./tmin-1./tmax) return 1 continue psjti=psbint(q1,q2min,qqcut,s,m1,l1,jdis) return end c------------------------------------------------------------------------ subroutine psjti0(ss,sj,sjb,m1,l1) c----------------------------------------------------------------------- c psjti0 - inclusive hard cross-section interpolation - c for minimal virtuality cutoff in the ladder c s - total c.m. energy squared for the ladder, c sj - inclusive jet cross-section, c sjb - born cross-section, c m1 - parton type at current end of the ladder (0-g, 1,2,etc.-q) c l1 - parton type at opposite end of the ladder (0-g, 1,2,etc.-q) c----------------------------------------------------------------------- dimension wk(3) common /psar2/ edmax,epmax common /psar22/ cstotzero(20,4,2),csborzer(20,4,2) include 'epos.incsem' sj=0. sjb=0. if(iabs(m1).ne.4)then q2mass=0. if(m1.ne.0.and.m1.eq.l1)then m=2 l=2 elseif(m1.ne.0.and.m1.eq.-l1)then m=3 l=1 elseif(m1.ne.0.and.l1.ne.0.and.m1.ne.l1)then m=3 l=2 else m=min(1,iabs(m1))+1 l=min(1,iabs(l1))+1 endif else q2mass=qcmass**2 m=4 l=min(1,iabs(l1))+1 endif s=ss-q2mass qq=q2min spmin=4.*qq+q2mass if(s.le.spmin)return p1=s/(1.+q2mass/s) if(p1.gt.4.*qq)then tmin=2.*qq/(1.+sqrt(1.-4.*qq/p1)) else tmin=2.*qq endif tmax=.5*p1 sl=log(s/spmin)/log(epmax/2./spmin)*19.+1. k=int(sl) if(k.gt.18)k=18 wk(2)=sl-k wk(3)=wk(2)*(wk(2)-1.)*.5 wk(1)=1.-wk(2)+wk(3) wk(2)=wk(2)-2.*wk(3) do k1=1,3 sj=sj+cstotzero(k+k1-1,m,l)*wk(k1) sjb=sjb+csborzer(k+k1-1,m,l)*wk(k1) enddo sjb=exp(sjb)*(1./tmin-1./tmax) sj=max(sjb,exp(sj)*(1./tmin-1./tmax)) return end c------------------------------------------------------------------------ function psjti1(q1,q2,qqcut,s,m1,l1,jdis) c----------------------------------------------------------------------- c psjti1 - inclusive hard cross-section interpolation - for strict order c in the ladder c q1 - virtuality cutoff at current end of the ladder c q2 - virtuality cutoff at opposite end of the ladder c qqcut - p_t cutoff for the born process; c s - total c.m. energy squared for the ladder, c m1 - parton type at current end of the ladder (0-g, 1,2,etc.-q) c l1 - parton type at opposite end of the ladder (0-g, 1,2,etc.-q) c----------------------------------------------------------------------- dimension wi(3),wj(3),wk(3) common /psar2/ edmax,epmax common /psar20/ csord(20,20,240) include 'epos.incsem' double precision psuds psjti1=0. if(jdis.eq.0)then qqmin=max(q1,q2) else qqmin=max(q1,q2/4.) endif qq=max(qqmin,qqcut) spmin=4.*q2min s2min=4.*qq if(s.le.s2min)return smins=s2min/(1.-q2ini/qq) if(s.le.smins)goto 1 if(s.gt.4.*qq)then tmin=2.*qq/(1.+sqrt(1.-4.*qq/s)) else tmin=2.*qq endif tmax=s/2. if(m1.ne.0.and.m1.eq.l1)then m=2 l=2 elseif(m1.ne.0.and.m1.eq.-l1)then m=3 l=1 elseif(m1.ne.0.and.l1.ne.0.and.m1.ne.l1)then m=3 l=2 else m=min(1,iabs(m1))+1 l=min(1,iabs(l1))+1 endif ml=20*(m-1)+60*(l-1)+120*jdis qli=log(q1/q2min)/log(s/4./q2min)*19.+1. qlj=log(qq/qqmin)/log(s/4./qqmin)*19.+1. sl=log(s/spmin)/log(epmax/2./spmin)*19.+1. k=int(sl) i=int(qli) j=int(qlj) if(j.lt.1)j=1 if(i.lt.1)i=1 if(k.gt.18)k=18 if(i.gt.18)i=18 if(j.gt.18)j=18 wi(2)=qli-i wi(3)=wi(2)*(wi(2)-1.)*.5 wi(1)=1.-wi(2)+wi(3) wi(2)=wi(2)-2.*wi(3) wj(2)=qlj-j wj(3)=wj(2)*(wj(2)-1.)*.5 wj(1)=1.-wj(2)+wj(3) wj(2)=wj(2)-2.*wj(3) wk(2)=sl-k wk(3)=wk(2)*(wk(2)-1.)*.5 wk(1)=1.-wk(2)+wk(3) wk(2)=wk(2)-2.*wk(3) do i1=1,3 do j1=1,3 do k1=1,3 k2=k+k1+ml-1 psjti1=psjti1+csord(i+i1-1,j+j1-1,k2) * *wi(i1)*wj(j1)*wk(k1) enddo enddo enddo psjti1=exp(psjti1)*(1./tmin-1./tmax) if(jdis.eq.0.and.qq.gt.q2)then psjti1=psjti1*sngl(psuds(qq,l1)/psuds(q2,l1)) elseif(jdis.eq.1.and.4.*qq.gt.q2)then psjti1=psjti1*sngl(psuds(4.*qq,l1)/psuds(q2,l1)) endif return 1 continue if(jdis.eq.0)then psjti1=psbint(q1,q2,qqcut,s,m1,l1,0) else psjti1=psbint(q2,q1,qqcut,s,l1,m1,1) endif return end c------------------------------------------------------------------------ function pspdfg(xx,qqs,qq,iclpro0,j) c----------------------------------------------------------------------- c pspdf - parton distribution function c qq - virtuality scale c qqs - initial virtuality for the input distributions c iclpro0 - hadron class c j - parton type c----------------------------------------------------------------------- double precision z common/ar3/ x1(7),a1(7) include 'epos.incsem' double precision psuds pspdfg=psdfh4(xx,qqs,0.,iclpro0,j) if(j.gt.0)pspdfg=pspdfg+psdfh4(xx,qqs,0.,iclpro0,-j) !+sea contr. pspdfg=pspdfg*sngl(psuds(qq,j)/psuds(qqs,j)) xmin=xx/(1.-q2ini/qq) if(xmin.ge.1.)return dpd1=0. dpd2=0. xm=max(xmin,.3) do i=1,7 !numerical integration over zx do m=1,2 zx=1.-(1.-xm)*(.5+(m-1.5)*x1(i))**.25 z=xx/zx if(j.eq.0)then aks=psevi(qqs,qq,z,2,1) !quark contribution akg=psevi(qqs,qq,z,1,1) !gluon contribution akns=0. else akg=psevi(qqs,qq,z,1,2)/naflav/2. !gluon contribution akns=psevi(qqs,qq,z,3,2) !nonsinglet contribution aks=(psevi(qqs,qq,z,2,2)-akns)/naflav/2. !quark contribution endif fz=akg*psdfh4(zx,qqs,0.,iclpro0,0) * +akns*psdfh4(zx,qqs,0.,iclpro0,j) * +aks*(psdfh4(zx,qqs,0.,iclpro0,1)+ * 2.*psdfh4(zx,qqs,0.,iclpro0,-1) * +psdfh4(zx,qqs,0.,iclpro0,2)+2.*psdfh4(zx,qqs,0.,iclpro0,-2) * +2.*psdfh4(zx,qqs,0.,iclpro0,-3)) if(j.gt.0)fz=fz+akns*psdfh4(zx,qqs,0.,iclpro0,-j) dpd1=dpd1+a1(i)*fz/zx**2/(1.-zx)**3 enddo enddo dpd1=dpd1*(1.-xm)**4/8.*xx if(xm.gt.xmin)then do i=1,7 !numerical integration do m=1,2 zx=xx+(xm-xx)*((xmin-xx)/(xm-xx))**(.5-(m-1.5)*x1(i)) z=xx/zx if(j.eq.0)then aks=psevi(qqs,qq,z,2,1) !quark contribution akg=psevi(qqs,qq,z,1,1) !gluon contribution akns=0. else akg=psevi(qqs,qq,z,1,2)/naflav/2. !gluon contribution akns=psevi(qqs,qq,z,3,2) !nonsinglet contribution aks=(psevi(qqs,qq,z,2,2)-akns)/naflav/2. !quark contribution endif fz=akg*psdfh4(zx,qqs,0.,iclpro0,0) * +akns*psdfh4(zx,qqs,0.,iclpro0,j) * +aks*(psdfh4(zx,qqs,0.,iclpro0,1) * +2.*psdfh4(zx,qqs,0.,iclpro0,-1) * +psdfh4(zx,qqs,0.,iclpro0,2)+2.*psdfh4(zx,qqs,0.,iclpro0,-2) * +2.*psdfh4(zx,qqs,0.,iclpro0,-3)) if(j.gt.0)fz=fz+akns*psdfh4(zx,qqs,0.,iclpro0,-j) dpd2=dpd2+a1(i)*fz*(1.-xx/zx)/zx enddo enddo dpd2=dpd2*log((xm-xx)/(xmin-xx))*.5*xx endif pspdfg=pspdfg+dpd2+dpd1 return end c----------------------------------------------------------------------- subroutine psaevp c----------------------------------------------------------------------- include 'epos.inc' include 'epos.incsem' qq=xpar1 jmod=nint(xpar2) iologb=1 if(jmod.eq.0)then !??????????????ttttttt write(*,*)"no more triple Pomeron, xpar2=0 in psaevp not accepted" write(*,*)"use xpar2=1 instead" jmod=1 endif do i=1,nrbins if(iologb.eq.0)then xx=xminim+(xmaxim-xminim)*(i-.5)/nrbins else xx=xminim*(xmaxim/xminim)**((i-.5)/nrbins) endif ar(i,1)=xx ar(i,2)=0. if(jmod.eq.0)then !evolution+matrix element +3P (ours) ww=qq/xx ar(i,3)=(psdh(ww,qq,2,0)+psdh(ww,qq,2,1) c * +psdsh1(ww,qq,2,dqsh,0)+psdsh1(ww,qq,2,dqsh,1) * )/(4.*pi**2*alfe)*qq elseif(jmod.eq.1)then !evolution+matrix element (ours) ww=qq/xx ar(i,3)=(psdh(ww,qq,2,0)+psdh(ww,qq,2,1)+ * psdsh(ww,qq,2,dqsh,0)+psdsh(ww,qq,2,dqsh,1) * )/(4.*pi**2*alfe)*qq elseif(jmod.eq.2)then !just evolution (grv) ar(i,3)=(pspdfg(xx,q2min,qq,2,1)/2.25+ * pspdfg(xx,q2min,qq,2,2)/9.+ * pspdfg(xx,q2min,qq,2,-1)*2./3.6+ * pspdfg(xx,q2min,qq,2,-3)*2./9.) if(naflav.eq.4)ar(i,3)=ar(i,3)+pspdfg(xx,q2min,qq,2,-4) * *2./2.25 elseif(jmod.eq.3)then !grv ar(i,3)=(psdfh4(xx,qq,0.,2,1)+2.*psdfh4(xx,qq,0.,2,-1))/2.25 * +(psdfh4(xx,qq,0.,2,2)+2.*psdfh4(xx,qq,0.,2,-2))/9. * +2.*psdfh4(xx,qq,0.,2,-3)/9. ! elseif(jmod.eq.4)then !just evolution (ours) ar(i,3)=(fparton(xx,qq,1)/2.25+fparton(xx,qq,2)/9.+ * fparton(xx,qq,-1)*6./4.5) !uv+dv+6*sea if(naflav.eq.4)ar(i,3)=ar(i,3)+fparton(xx,qq,-4)*2./2.25 elseif(jmod.eq.5)then !grv+res ww=qq/xx ar(i,3)=(psdgh(ww,qq,0)+psdgh(ww,qq,1) * )/(4.*pi**2*alfe)*qq endif ar(i,4)=0. enddo return end c------------------------------------------------------------------------ subroutine pscs(c,s) c----------------------------------------------------------------------- c pscs - cos (c) and sin (s) generation for uniformly distributed angle c----------------------------------------------------------------------- 1 s1=2.*rangen()-1. s2=2.*rangen()-1. s3=s1*s1+s2*s2 if(s3.gt.1.)goto 1 s3=sqrt(s3) c=s1/s3 s=s2/s3 return end c------------------------------------------------------------------------ subroutine psdefrot(ep,s0x,c0x,s0,c0) c----------------------------------------------------------------------- c psdefrot - determination of the parameters the spacial rotation to the c system for 4-vector ep c s0, c0 - sin and cos for the zx-rotation; c s0x, c0x - sin and cos for the xy-rotation c----------------------------------------------------------------------- dimension ep(4) c transverse momentum square for the current parton (ep) pt2=ep(3)**2+ep(4)**2 if(pt2.ne.0.)then pt=sqrt(pt2) c system rotation to get pt=0 - euler angles are determined (c0x = cos t c s0x = sin theta, c0 = cos phi, s0 = sin phi) c0x=ep(3)/pt s0x=ep(4)/pt c total momentum for the gluon pl=sqrt(pt2+ep(2)**2) s0=pt/pl c0=ep(2)/pl else c0x=1. s0x=0. pl=abs(ep(2)) s0=0. c0=ep(2)/pl endif ep(2)=pl ep(3)=0. ep(4)=0. return end c------------------------------------------------------------------------ subroutine psdeftr(s,ep,ey) c----------------------------------------------------------------------- c psdeftr - determination of the parameters for the lorentz transform to c rest frame system for 4-vector ep of mass squared s c----------------------------------------------------------------------- dimension ey(3) double precision ep(4) do i=1,3 if(ep(i+1).eq.0.d0)then ey(i)=1. else wp=ep(1)+ep(i+1) wm=ep(1)-ep(i+1) if(wp.gt.1.e-8.and.wm/wp.lt.1.e-8)then ww=s do l=1,3 if(l.ne.i)ww=ww+ep(l+1)**2 enddo wm=ww/wp elseif(wm.gt.1.e-8.and.wp/wm.lt.1.e-8)then ww=s do l=1,3 if(l.ne.i)ww=ww+ep(l+1)**2 enddo wp=ww/wm endif ey(i)=sqrt(wm/wp) ep(1)=wp*ey(i) ep(i+1)=0. endif enddo ep(1)=dsqrt(dble(s)) return end c------------------------------------------------------------------------ function psdfh4(xxx,qqs,qq,icq,iq) c------------------------------------------------------------------------ c psdfh4 - GRV structure functions c------------------------------------------------------------------------ common /psar8/ stmass ,amhadr(8),qcmass common /psar36/ alvc psdfh4=0. ! if(x.gt..99999)return x=min(xxx,0.99999) !warning ! but necessary for idraflx if(icq.eq.2)then if(qqs.le.0.232**2)return sq=log(log(qqs/.232**2)/log(.23/.232**2)) if(sq.le.0.)return if(iq.eq.0)then !gluon alg=.524 betg=1.088 aag=1.742-.93*sq bbg=-.399*sq**2 ag=7.486-2.185*sq bg=16.69-22.74*sq+5.779*sq*sq cg=-25.59+29.71*sq-7.296*sq*sq dg=2.792+2.215*sq+.422*sq*sq-.104*sq*sq*sq eg=.807+2.005*sq eeg=3.841+.361*sq psdfh4=(1.-x)**dg*(x**aag*(ag+bg*x+cg*x**2)*log(1./x)**bbg * +sq**alg*exp(-eg+sqrt(eeg*sq**betg*log(1./x)))) elseif(iq.eq.1.or.iq.eq.2)then !u_v or d_v aau=.59-.024*sq bbu=.131+.063*sq auu=2.284+.802*sq+.055*sq*sq au=-.449-.138*sq-.076*sq*sq bu=.213+2.669*sq-.728*sq*sq cu=8.854-9.135*sq+1.979*sq*sq du=2.997+.753*sq-.076*sq*sq uv=auu*x**aau*(1.-x)**du* * (1.+au*x**bbu+bu*x+cu*x**1.5) aad=.376 bbd=.486+.062*sq add=.371+.083*sq+.039*sq*sq ad=-.509+3.31*sq-1.248*sq*sq bd=12.41-10.52*sq+2.267*sq*sq ccd=6.373-6.208*sq+1.418*sq*sq dd=3.691+.799*sq-.071*sq*sq dv=add*x**aad*(1.-x)**dd* * (1.+ad*x**bbd+bd*x+ccd*x**1.5) if(iq.eq.1)then !u_v psdfh4=uv elseif(iq.eq.2)then !d_v psdfh4=dv endif elseif(iq.eq.-3)then !s_sea als=.914 bets=.577 aas=1.798-.596*sq as=-5.548+3.669*sqrt(sq)-.616*sq bs=18.92-16.73*sqrt(sq)+5.168*sq ds=6.379-.35*sq+.142*sq*sq es=3.981+1.638*sq ees=6.402 psdfh4=(1.-x)**ds*sq**als/log(1./x)**aas*(1.+as*sqrt(x) * +bs*x)*exp(-es+sqrt(ees*sq**bets*log(1./x))) elseif(iabs(iq).lt.3)then !u_sea or d_sea aadel=.409-.005*sq bbdel=.799+.071*sq addel=.082+.014*sq+.008*sq*sq adel=-38.07+36.13*sq-.656*sq*sq bdel=90.31-74.15*sq+7.645*sq*sq ccdel=0. ddel=7.486+1.217*sq-.159*sq*sq delv=addel*x**aadel*(1.-x)**ddel* * (1.+adel*x**bbdel+bdel*x+ccdel*x**1.5) alud=1.451 betud=.271 aaud=.41-.232*sq bbud=.534-.457*sq aud=.89-.14*sq bud=-.981 cud=.32+.683*sq dud=4.752+1.164*sq+.286*sq*sq eud=4.119+1.713*sq eeud=.682+2.978*sq udsea=(1.-x)**dud*(x**aaud*(aud+bud*x+cud*x**2) * *log(1./x)**bbud+sq**alud*exp(-eud+sqrt(eeud*sq**betud* * log(1./x)))) if(iq.eq.-1)then !u_sea psdfh4=(udsea-delv)/2. elseif(iq.eq.-2)then !d_sea psdfh4=(udsea+delv)/2. endif else psdfh4=0. endif elseif(icq.eq.1.or.icq.eq.3)then if(qqs.le.0.204**2)return sq=log(log(qqs/.204**2)/log(.26/.204**2)) if(sq.le.0.)return if(iq.eq.1.or.iq.eq.2)then aapi=.517-.02*sq api=-.037-.578*sq bpi=.241+.251*sq dpi=.383+.624*sq anorm=1.212+.498*sq+.009*sq**2 psdfh4=.5*anorm*x**aapi*(1.-x)**dpi* * (1.+api*sqrt(x)+bpi*x) elseif(iq.eq.0)then alfpi=.504 betpi=.226 aapi=2.251-1.339*sqrt(sq) api=2.668-1.265*sq+.156*sq**2 bbpi=0. bpi=-1.839+.386*sq cpi=-1.014+.92*sq-.101*sq**2 dpi=-.077+1.466*sq epi=1.245+1.833*sq eppi=.51+3.844*sq psdfh4=(1.-x)**dpi*(x**aapi*(api+bpi*sqrt(x)+cpi*x)* * log(1./x)**bbpi+sq**alfpi* * exp(-epi+sqrt(eppi*sq**betpi*log(1./x)))) elseif(iq.eq.-3)then alfpi=.823 betpi=.65 aapi=1.036-.709*sq api=-1.245+.713*sq bpi=5.58-1.281*sq dpi=2.746-.191*sq epi=5.101+1.294*sq eppi=4.854-.437*sq psdfh4=sq**alfpi/log(1./x)**aapi*(1.-x)**dpi* * (1.+api*sqrt(x)+bpi*x)* * exp(-epi+sqrt(eppi*sq**betpi*log(1./x))) elseif(iabs(iq).lt.3)then alfpi=1.147 betpi=1.241 aapi=.309-.134*sqrt(sq) api=.219-.054*sq bbpi=.893-.264*sqrt(sq) bpi=-.593+.24*sq cpi=1.1-.452*sq dpi=3.526+.491*sq epi=4.521+1.583*sq eppi=3.102 psdfh4=(1.-x)**dpi*(x**aapi*(api+bpi*sqrt(x)+cpi*x)* * log(1./x)**bbpi+sq**alfpi* * exp(-epi+sqrt(eppi*sq**betpi*log(1./x)))) else psdfh4=0. endif elseif(icq.eq.0)then if(qqs.le.0.204**2)return sq=log(log(qqs/.204**2)/log(.26/.204**2)) if(sq.le.0.)return if(iq.eq.0)then alfpi=.504 betpi=.226 aapi=2.251-1.339*sqrt(sq) api=2.668-1.265*sq+.156*sq**2 bbpi=0. bpi=-1.839+.386*sq cpi=-1.014+.92*sq-.101*sq**2 dpi=-.077+1.466*sq epi=1.245+1.833*sq eppi=.51+3.844*sq psdfh4=(1.-x)**dpi*(x**aapi*(api+bpi*sqrt(x)+cpi*x)* * log(1./x)**bbpi+sq**alfpi* * exp(-epi+sqrt(eppi*sq**betpi*log(1./x)))) * *.543 else alfpi=.823 betpi=.65 aapi=1.036-.709*sq api=-1.245+.713*sq bpi=5.58-1.281*sq dpi=2.746-.191*sq epi=5.101+1.294*sq eppi=4.854-.437*sq str=sq**alfpi/log(1./x)**aapi*(1.-x)**dpi* * (1.+api*sqrt(x)+bpi*x)* * exp(-epi+sqrt(eppi*sq**betpi*log(1./x))) if(iq.eq.3)then psdfh4=str*.543*2. else aapi=.517-.02*sq api=-.037-.578*sq bpi=.241+.251*sq dpi=.383+.624*sq anorm=1.212+.498*sq+.009*sq**2 val=.5*anorm*x**aapi*(1.-x)**dpi* * (1.+api*sqrt(x)+bpi*x) alfpi=1.147 betpi=1.241 aapi=.309-.134*sqrt(sq) api=.219-.054*sq bbpi=.893-.264*sqrt(sq) bpi=-.593+.24*sq cpi=1.1-.452*sq dpi=3.526+.491*sq epi=4.521+1.583*sq eppi=3.102 sea=(1.-x)**dpi*(x**aapi*(api+bpi*sqrt(x)+cpi*x)* * log(1./x)**bbpi+sq**alfpi* * exp(-epi+sqrt(eppi*sq**betpi*log(1./x)))) if(iq.eq.1)then psdfh4=(.836*(val+2.*sea)-.587*str) elseif(iq.eq.2)then psdfh4=(.25*(val+2.*sea)+.587*str) else psdfh4=0. endif endif endif psdfh4=psdfh4/(1.+qq/.59)**2 elseif(icq.eq.4)then if(qqs.le.qcmass**2)return sq=log(log(qqs/qcmass**2)/log(.23/qcmass**2)) if(sq.le.0.)return if(iq.eq.2)then psdfh4=x**3*(1.-x)**alvc*(alvc+3.)*(alvc+2.)*(alvc+1.) else aapi=.517-.02*sq api=-.037-.578*sq bpi=.241+.251*sq dpi=.383+.624*sq anorm=1.212+.498*sq+.009*sq**2 psdfh4=.5*anorm*x**aapi*(1.-x)**dpi* * (1.+api*sqrt(x)+bpi*x) endif else psdfh4=0. endif return end c------------------------------------------------------------------------ function psfap(x,j,l) c----------------------------------------------------------------------- c psfap - altarelli-parisi function (multiplied by x) c x - light cone momentum share value, c j - type of the parent parton (0-g;1,2,etc.-q) c l - type of the daughter parton (0-g;1,2,etc.-q) c----------------------------------------------------------------------- double precision x include 'epos.incsem' if(j.eq.0)then if(l.eq.0)then psfap=((1.d0-x)/x+x/(1.d0-x)+x*(1.d0-x))*6.d0 else psfap=(x**2+(1.d0-x)**2)*naflav endif else if(l.eq.0)then psfap=(1.d0+(1.d0-x)**2)/x/.75d0 else psfap=(x**2+1.d0)/(1.d0-x)/.75d0 endif endif return end cc------------------------------------------------------------------------ c function psgen(a1,a2) cc----------------------------------------------------------------------- cc psgen - x-values generation according to distribution cc x1^(-a1) x2^(-0.5) cc----------------------------------------------------------------------- c common/lept1/engy,elepti,elepto,angmue,icinpu c c aa=max(a1,a2) c1 continue c if(aa.lt.1.)then c x1=.5*rangen()**(1./(1.-aa)) c elseif(aa.eq.1.)then c x1=.5/engy**rangen() c else c x1=.5*(1.+rangen()*(engy**(aa-1.)-1.))**(1./(1.-aa)) c endif c if(x1.lt.1.e-7.or.x1.gt..999999)then c goto 1 c endif c if(rangen().lt..5)then c gb=x1**(aa-a1)*.5**aa/(1.-x1)**a2 c else c x1=1.-x1 c gb=(1.-x1)**(aa-a2)*.5**aa/x1**a1 c endif c if(rangen().gt.gb)goto 1 c psgen=x1 c return c end c c------------------------------------------------------------------------ function psidd(icc) c----------------------------------------------------------------------- c psidd - kink type decoder c----------------------------------------------------------------------- if(icc.eq.0)then !g psidd=9 elseif(iabs(icc).le.2)then !u,u~,d,d~ psidd=icc elseif(iabs(icc).eq.4)then !s,s~ psidd=icc/4*3 elseif(iabs(icc).gt.10)then !c,c~ etc. psidd=icc/10 elseif(icc.eq.3)then !ud psidd=1200 elseif(icc.eq.-3)then !u~d~ psidd=-1200 elseif(icc.eq.6)then !uu psidd=1100 elseif(icc.eq.-6)then !u~u~ psidd=-1100 elseif(icc.eq.7)then !dd psidd=2200 elseif(icc.eq.-7)then !d~d~ psidd=-2200 else psidd=0. write (*,*)'psidd?????????',icc endif return end cc------------------------------------------------------------------------ c function pslam(s,a,b) cc----------------------------------------------------------------------- cc kinematical function for two particle decay - maximal pt-value cc a - first particle mass squared, cc b - second particle mass squared, cc s - two particle invariant mass squared cc----------------------------------------------------------------------- c pslam=.25/s*(s+a-b)**2-a c return c end c c------------------------------------------------------------------------ function psjvrg1(qt,s,y0) c----------------------------------------------------------------------- common /ar3/ x1(7),a1(7) common /cnsta/ pi,pii,hquer,prom,piom,ainfin include 'epos.incsem' double precision xt,ymin,ymax,y,xmin,xmax,xx1,xx2 psjvrg1=0. if(s.le.4.*qt)return xt=2.d0*sqrt(dble(qt)/dble(s)) ymax=min(dble(y0),log(1d0/xt+sqrt((1d0/xt-1d0)*(1d0/xt+1d0)))) ymin=-ymax do i=1,7 do m=1,2 y=.5d0*(ymax+ymin+(ymin-ymax)*dble((2*m-3)*x1(i))) xmin=xt**2/2.d0/(2.d0-xt*exp(-y)) xmax=1.d0-xt*exp(y)/2.d0 fx=0. do i1=1,7 do m1=1,2 xx1=xt*exp(y)/2d0+xmin*(xmax/xmin)**dble(.5+x1(i1)*(m1-1.5)) xx2=xt*exp(-y)*xx1/(2.d0*xx1-xt*exp(y)) z=sngl(xx1*xx2) sh=z*s t=sngl(dble(sh)/2d0*(1d0 & -sqrt(max(0d0,1d0-4d0*dble(qt)/dble(sh))))) ft=psjvrx(t,qt,sngl(xx1),sngl(xx2),sh) fx=fx+a1(i1)*ft/sh**2 enddo enddo fx=fx*sngl(log(xmax/xmin)) psjvrg1=psjvrg1+a1(i)*fx enddo enddo psjvrg1=psjvrg1*sngl(ymax-ymin)*pi**3 **pssalf(qt/qcdlam)**2*sqrt(qt) return end c----------------------------------------------------------------------- function psjvrx(t,qt,xx1,xx2,s) c----------------------------------------------------------------------- include 'epos.incsem' g1=psdfh4(xx1,qt,0.,2,0) ub1=psdfh4(xx1,qt,0.,2,-1) u1=psdfh4(xx1,qt,0.,2,1)+ub1 db1=psdfh4(xx1,qt,0.,2,-2) d1=psdfh4(xx1,qt,0.,2,2)+db1 sb1=psdfh4(xx1,qt,0.,2,-3) s1=sb1 g2=psdfh4(xx2,qt,0.,2,0) ub2=psdfh4(xx2,qt,0.,2,-1) u2=psdfh4(xx2,qt,0.,2,1)+ub2 db2=psdfh4(xx2,qt,0.,2,-2) d2=psdfh4(xx2,qt,0.,2,2)+db2 sb2=psdfh4(xx2,qt,0.,2,-3) s2=sb2 psjvrx=g1*g2*(psbori(s,t,0,0,1)+psbori(s,s-t,0,0,1) *+psbori(s,t,0,0,2)+psbori(s,s-t,0,0,2))/2. *+(psbori(s,t,0,1,1)+psbori(s,s-t,0,1,1))* *(g2*(u1+ub1+d1+db1+s1+sb1)+g1*(u2+ub2+d2+db2+s2+sb2)) *+(psbori(s,t,1,1,1)+psbori(s,s-t,1,1,1))/2.* *(u1*u2+ub1*ub2+d1*d2+db1*db2+s1*s2+sb1*sb2) *+(psbori(s,t,1,-1,1)+psbori(s,s-t,1,-1,1)+psbori(s,t,1,-1,2)+ *psbori(s,s-t,1,-1,2)+psbori(s,t,1,-1,3)+psbori(s,s-t,1,-1,3))* *(u1*ub2+ub1*u2+d1*db2+db1*d2+s1*sb2+sb1*s2) *+(psbori(s,t,1,2,1)+psbori(s,s-t,1,2,1))* *((u1+ub1)*(d2+db2+s2+sb2)+(u2+ub2)*(d1+db1+s1+sb1)+ *(d1+db1)*(u2+ub2+s2+sb2)+(d2+db2)*(u1+ub1+s1+sb1)+ *(s1+sb1)*(u2+ub2+d2+db2)+(s2+sb2)*(u1+ub1+d1+db1)) return end c------------------------------------------------------------------------ function psjwo1(qt,s,y0) c----------------------------------------------------------------------- common /ar3/ x1(7),a1(7) common /cnsta/ pi,pii,hquer,prom,piom,ainfin double precision xt,ymax,ymin,y,xmin,xmax,xx1,xx2 include 'epos.incsem' psjwo1=0. if(s.le.4.*qt)return xt=2.d0*sqrt(dble(qt)/dble(s)) ymax=min(dble(y0),log(1d0/xt+sqrt((1d0/xt-1d0)*(1d0/xt+1d0)))) ymin=-ymax do i=1,7 do m=1,2 y=.5d0*(ymax+ymin+(ymin-ymax)*dble(2*m-3)*dble(x1(i))) xmin=xt**2/2.d0/(2.d0-xt*exp(-y)) xmax=1.d0-xt*exp(y)/2.d0 fx=0. do i1=1,7 do m1=1,2 xx1=xt*exp(y)/2.d0+xmin*(xmax/xmin)**dble(.5+x1(i1)*(m1-1.5)) xx2=xt*exp(-y)/(2.d0-xt*exp(y)/xx1) z=sngl(xx1*xx2) sh=z*s t=sngl(dble(sh)/2d0*(1d0-sqrt(1d0-4d0*dble(qt)/dble(sh)))) ft=psjwox(t,qt,sngl(xx1),sngl(xx2),sh) fx=fx+a1(i1)*ft/sh**2 enddo enddo fx=fx*log(xmax/xmin) psjwo1=psjwo1+a1(i)*fx enddo enddo psjwo1=psjwo1*sngl(ymax-ymin)*pi**3 **pssalf(qt/qcdlam)**2*sqrt(qt) return end c----------------------------------------------------------------------- function psjwox(t,qt,xx1,xx2,s) c----------------------------------------------------------------------- double precision x,scale,upv1,dnv1,sea1,str1,chm1,gl1, *upv2,dnv2,sea2,str2,chm2,gl2 scale=sqrt(qt) x=xx1 call strdo1(x,scale,upv1,dnv1,sea1,str1,chm1,gl1) x=xx2 call strdo1(x,scale,upv2,dnv2,sea2,str2,chm2,gl2) psjwox=gl1*gl2*(psbori(s,t,0,0,1)+psbori(s,s-t,0,0,1) *+psbori(s,t,0,0,2)+psbori(s,s-t,0,0,2)+psbori(s,t,0,0,3) *+psbori(s,s-t,0,0,3))/2. *+(psbori(s,t,0,1,1)+psbori(s,s-t,0,1,1) *+psbori(s,t,0,1,2)+psbori(s,s-t,0,1,2)+psbori(s,t,0,1,3) *+psbori(s,s-t,0,1,3))*(gl2*(upv1+dnv1+4.*sea1+2.*str1+2.*chm1)+ *gl1*(upv2+dnv2+4.*sea2+2.*str2+2.*chm2)) *+(psbori(s,t,1,1,1)+psbori(s,s-t,1,1,1) *+psbori(s,t,1,1,2)+psbori(s,s-t,1,1,2)+psbori(s,t,1,1,3)+ *psbori(s,s-t,1,1,3))/2.* *((upv1+sea1)*(upv2+sea2)+(dnv1+sea1)*(dnv2+sea2)+2.*sea1*sea2 *+2.*str1*str2+2.*chm1*chm2) *+(psbori(s,t,1,-1,1)+psbori(s,s-t,1,-1,1)+psbori(s,t,1,-1,2)+ *psbori(s,s-t,1,-1,2)+psbori(s,t,1,-1,3)+psbori(s,s-t,1,-1,3))* *((upv1+sea1)*sea2+sea1*(upv2+sea2)+(dnv1+sea1)*sea2+ *sea1*(dnv2+sea2)+2.*str1*str2+2.*chm1*chm2) *+(psbori(s,t,1,2,1) *+psbori(s,s-t,1,2,1)+psbori(s,t,1,2,2)+psbori(s,s-t,1,2,2) *+psbori(s,t,1,2,3)+psbori(s,s-t,1,2,3))* *(upv1*dnv2+upv2*dnv1+(upv1+dnv1)*(2.*sea2+2.*str2+2.*chm2)+ *(upv2+dnv2)*(2.*sea1+2.*str1+2.*chm1)+ *4.*sea1*(2.*sea2+2.*str2+2.*chm2)+2.*str1*(4.*sea2+2.*chm2)+ *2.*chm1*(4.*sea2+2.*str2)) return end c------------------------------------------------------------------------ subroutine pslcsh(wp1,wm1,wp2,wm2,samqt,amqpt) c----------------------------------------------------------------------- c pslcsh - sh pomeron lc momentum sharing between two strings c------------------------------------------------------------------------ double precision amqt(4),yqm(4),yqm1(4),xlp(4),xlm(4),am23,sx,y2 *,wp1,wp2,wm1,wm2,s,sq,psutz,yqmax,y,amjp,amjm,y1,s12,s34,x34,amqpt dimension samqt(4) include 'epos.inc' s=wp1*wm1 sq=dsqrt(s) do i=1,4 amqt(i)=dble(samqt(i)) yqm(i)=dlog(sq/amqt(i)*psutz(s,amqt(i)**2,(amqpt-amqt(i))**2)) enddo yqmax=max(yqm(1),yqm(2)) 1 y=yqmax*dble(rangen()) j=int(1.5+rangen()) if(y.gt.yqm(j))goto 1 amjp=amqt(j)*dexp(y) amjm=amqt(j)*dexp(-y) do i=3,4 am23=amqt(3-j)+amqt(7-i) sx=(am23+amjp)*(am23+amjm) yqm1(i)=dlog(sq/amqt(i)*psutz(s,amqt(i)**2,sx)) enddo yqmax1=max(yqm1(3),yqm1(4)) if(dble(rangen()).gt.yqmax1/max(yqm(3),yqm(4)))goto 1 y1=yqmax1*dble(rangen()) j1=int(3.5+rangen()) if(y1.gt.yqm1(j1))goto 1 amjp1=amqt(j1)*exp(y1) amjm1=amqt(j1)*exp(-y1) s12=(amqt(3-j)+amjp)*(amqt(3-j)+amjm) s34=(amqt(7-j1)+amjp1)*(amqt(7-j1)+amjm1) y2=dlog(sq/(amqt(3-j)+amjp)*psutz(s,s12,s34)) xlp(j)=amqt(j)/sq*dexp(y+y2) xlm(j)=amqt(j)/sq*dexp(-y-y2) xlp(3-j)=amqt(3-j)/sq*dexp(y2) xlm(3-j)=amqt(3-j)/sq*dexp(-y2) x34=1.-xlm(1)-xlm(2) xlm(7-j1)=x34/(1.+amjp1/amqt(7-j1)) xlm(j1)=x34-xlm(7-j1) c write (*,*)'xlc',xlp(1),xlp(2),xlm(3),xlm(4) if(dble(rangen()).gt.(xlp(1)*xlp(2)*xlm(3)*xlm(4))**(-alpqua)* *(xlp(j)*(1.d0-xlp(j))*xlm(j1)*(1.d0-xlm(j1))))goto 1 wp2=xlp(2)*wp1 wp1=xlp(1)*wp1 wm2=xlm(4)*wm1 wm1=xlm(3)*wm1 c write (*,*)'wp1,wm1,wp2,wm2',wp1,wm1,wp2,wm2 return end c------------------------------------------------------------------------ function psnorm(ep) c----------------------------------------------------------------------- c 4-vector squared calculation c----------------------------------------------------------------------- double precision sm2,ep(4) sm2=ep(1)**2 do i=1,3 sm2=sm2-ep(i+1)**2 enddo psnorm=sm2 return end c------------------------------------------------------------------------ subroutine psrotat(ep,s0x,c0x,s0,c0) c----------------------------------------------------------------------- c psrotat - spacial rotation to the lab. system for 4-vector ep c s0, c0 - sin and cos for the zx-rotation; c s0x, c0x - sin and cos for the xy-rotation c----------------------------------------------------------------------- dimension ep(4),ep1(3) ep1(3)=ep(4) ep1(2)=ep(2)*s0+ep(3)*c0 ep1(1)=ep(2)*c0-ep(3)*s0 ep(2)=ep1(1) ep(4)=ep1(2)*s0x+ep1(3)*c0x ep(3)=ep1(2)*c0x-ep1(3)*s0x return end cc------------------------------------------------------------------------ c subroutine psrotat1(ep,s0x,c0x,s0,c0) cc----------------------------------------------------------------------- cc psrotat - spacial rotation to the lab. system for 4-vector ep cc s0, c0 - sin and cos for the zx-rotation; cc s0x, c0x - sin and cos for the xy-rotation cc----------------------------------------------------------------------- c dimension ep(4),ep1(3) c c ep1(1)=ep(2) c ep1(3)=-ep(3)*s0x+ep(4)*c0x c ep1(2)=ep(3)*c0x+ep(4)*s0x c c ep(4)=ep1(3) c ep(3)=-ep1(1)*s0+ep1(2)*c0 c ep(2)=ep1(1)*c0+ep1(2)*s0 c return c end c c----------------------------------------------------------------------- function pssalf(qq) c----------------------------------------------------------------------- c pssalf - effective qcd coupling (alpha_s/2/pi) c----------------------------------------------------------------------- include "epos.incsem" pssalf=2./(11.-naflav/1.5)/log(qq) return end c------------------------------------------------------------------------ subroutine pstrans(ep,ey,jj) c----------------------------------------------------------------------- c pstrans - lorentz boosts according to the parameters ey ( determining c shift along the z,x,y-axis respectively (ey(1),ey(2),ey(3))) c jj=1 - inverse transformation to the lab. system; c jj=-1 - direct transformation c----------------------------------------------------------------------- dimension ey(3),ep(4) if(jj.eq.1)then c lorentz transform to lab. system according to 1/ey(i) parameters do i=1,3 if(ey(4-i).ne.1.)then wp=(ep(1)+ep(5-i))/ey(4-i) wm=(ep(1)-ep(5-i))*ey(4-i) ep(1)=.5*(wp+wm) ep(5-i)=.5*(wp-wm) endif enddo else c lorentz transform to lab. system according to ey(i) parameters do i=1,3 if(ey(i).ne.1.)then wp=(ep(1)+ep(i+1))*ey(i) wm=(ep(1)-ep(i+1))/ey(i) ep(1)=.5*(wp+wm) ep(i+1)=.5*(wp-wm) endif enddo endif return end c------------------------------------------------------------------------ double precision function psuds(q,m) c----------------------------------------------------------------------- c psuds - spacelike sudakov formfactor c q - maximal value of the effective momentum, c m - type of parton (0 - g, 1,2, etc. - q) c----------------------------------------------------------------------- dimension wi(3) common /psar15/ sudx(40,2) include 'epos.incsem' double precision dps,qlm,ffacs,qlm0,qlmi j=min(iabs(m),1)+1 if(q.gt.q2ini)then qli=log(q/q2min)*2.+1. i=int(qli) if(i.lt.1)i=1 if(i.gt.38)i=38 wi(2)=qli-i wi(3)=wi(2)*(wi(2)-1.)*.5 wi(1)=1.-wi(2)+wi(3) wi(2)=wi(2)-2.*wi(3) dps=0.d0 do i1=1,3 dps=dps+dble(sudx(i+i1-1,j)*wi(i1)) enddo qlm0=dble(log(q2ini/qcdlam)) qlm=dble(log(q/qcdlam)) qlmi=qlm-qlm0 !=log(q/q2ini) psuds=(qlm*log(qlm/qlm0)-qlmi) ffacs=(11.d0-dble(naflav)/1.5d0)/12.d0 if(j.eq.1)then psuds=(psuds-ffacs*log(qlm/qlm0) * +dps*(1.d0-dble(q2ini/q)))/ffacs else psuds=(psuds-log(qlm/qlm0)*.75d0 * +dps*(1.d0-dble(q2ini/q)))*4.d0/9.d0/ffacs endif psuds=exp(-psuds) else psuds=1.d0 endif return end c------------------------------------------------------------------------ function psudx(q,j) c----------------------------------------------------------------------- c psudx - part of the bspacelike sudakov formfactor c q - maximal value of the effective momentum, c j - type of parton (1 - g, 2 - q) c----------------------------------------------------------------------- common /ar3/ x1(7),a1(7) include 'epos.incsem' psudx=0. do i=1,7 do m=1,2 qt=.5*(q2ini+q-x1(i)*(2.*m-3.)*(q2ini-q)) if(j.eq.1)then zm=1.-qt/q dps=((11.-naflav/1.5)/12.-zm**2*(1.-naflav/12.)+ * (zm**3/3.-zm**4/4.)*(1.-naflav/3.))*q/qt else dps=(1.-qt/q/4.) endif psudx=psudx+a1(i)*dps/log(qt/qcdlam) enddo enddo psudx=psudx*.5 return end c------------------------------------------------------------------------ double precision function psutz(s,a,b) c----------------------------------------------------------------------- c psutz - kinematical function for two particle decay - light cone momen c share for the particle of mass squared a, c b - partner's mass squared, c s - two particle invariant mass c----------------------------------------------------------------------- double precision a1,b1,s1,x,dx,s,a,b a1=dsqrt(a) b1=dsqrt(b) s1=dsqrt(s) x=(1.d0+(a1-b1)*(a1+b1)/s)/2.d0 dx=(x-a1/s1)*(x+a1/s1) c x=.5*(1.+(a-b)/s) c dx=(x*x-a/s) if(dx.gt.0.d0)then x=x+dsqrt(dx) else x=a1/s1 endif psutz=min(0.999999999d0,x) return end c------------------------------------------------------------------------ block data ptdata c----------------------------------------------------------------------- c constants for numerical integration (gaussian weights) c----------------------------------------------------------------------- common /ar3/ x1(7),a1(7) common /ar4/ x4(2),a4(2) common /ar5/ x5(2),a5(2) common /ar8/ x2(4),a2 common /ar9/ x9(3),a9(3) data x1/.9862838,.9284349,.8272013,.6872929,.5152486, *.3191124,.1080549/ data a1/.03511946,.08015809,.1215186,.1572032, *.1855384,.2051985,.2152639/ data x2/.00960736,.0842652,.222215,.402455/ data a2/.392699/ data x4/ 0.339981,0.861136/ data a4/ 0.652145,0.347855/ data x5/.585786,3.41421/ data a5/.853553,.146447/ data x9/.93247,.661209,.238619/ data a9/.171324,.360762,.467914/ end c------------------------------------------------------------------------ subroutine strdo1(x,scale,upv,dnv,sea,str,chm,gl) c------------------------------------------------------------------------ c :::::::::::: duke owens set 1 :::::::::::::::::::::::::::: c------------------------------------------------------------------------ implicit double precision(a-h,o-z) double precision + f(5),a(6,5),b1(3,6,5) data q0,ql1/2.d0,.2d0/ data b1/3.d0,0.d0,0.d0,.419d0,.004383d0,-.007412d0, &3.46d0,.72432d0,-.065998d0,4.4d0,-4.8644d0,1.3274d0, &6*0.d0,1.d0, &0.d0,0.d0,.763d0,-.23696d0,.025836d0,4.d0,.62664d0,-.019163d0, &0.d0,-.42068d0,.032809d0,6*0.d0,1.265d0,-1.1323d0,.29268d0, &0.d0,-.37162d0,-.028977d0,8.05d0,1.5877d0,-.15291d0, &0.d0,6.3059d0,-.27342d0,0.d0,-10.543d0,-3.1674d0, &0.d0,14.698d0,9.798d0,0.d0,.13479d0,-.074693d0, &-.0355d0,-.22237d0,-.057685d0,6.3494d0,3.2649d0,-.90945d0, &0.d0,-3.0331d0,1.5042d0,0.d0,17.431d0,-11.255d0, &0.d0,-17.861d0,15.571d0,1.564d0,-1.7112d0,.63751d0, &0.d0,-.94892d0,.32505d0,6.d0,1.4345d0,-1.0485d0, &9.d0,-7.1858d0,.25494d0,0.d0,-16.457d0,10.947d0, &0.d0,15.261d0,-10.085d0/ wn=1.d0 s= log( log( max(q0,scale)/ql1)/ log(q0/ql1)) do 10 i=1,5 do 10 j=1,6 10 a(j,i)=b1(1,j,i)+s*(b1(2,j,i)+s*b1(3,j,i)) do 40 i=1,5 40 f(i)=a(1,i)*x**a(2,i)*(wn-x)**a(3,i)*(wn+x* & (a(4,i)+x*(a(5,i)+x*a(6,i)))) do 50 i=1,2 aa=wn+a(2,i)+a(3,i) 50 f(i)=f(i)*utgam2(aa)/((wn+a(2,i)*a(4,i)/aa) &*utgam2(a(2,i))*utgam2(wn+a(3,i))) upv=f(1)-f(2) dnv=f(2) sea=f(3)/6.d0 str=sea chm=f(4) gl =f(5) return end c------------------------------------------------------------------------ function fzeroGluZZ(z,k) ! former psftild c----------------------------------------------------------------------- c c fzeroGluZZComplete = fzeroGluZZ * z^(-1-dels) * gamsoft * gamhad c c A = 8*pi*s0*gampar*gamtilde c integration over semihard pomeron light cone momentum share xp==u c c fzeroGluZZ = (1-glusea) * engy^epszero c * int(du) u^(epszero-alppar+dels) (1-u)^alplea * (1-z/u)**betpom c c z - light cone x of the gluon, c k - hadron class c----------------------------------------------------------------------- double precision xpmin,xp include 'epos.inc' common /ar3/ x1(7),a1(7) include 'epos.incsem' fzeroGluZZ=0. xpmin=z xpmin=xpmin**(1.-alppar+dels+epszero) do i=1,7 do m=1,2 xp=(.5*(1.+xpmin+(2*m-3)*x1(i)*(1.-xpmin)))**(1./ * (1.-alppar+dels+epszero)) fzeroGluZZ=fzeroGluZZ+a1(i)*(1.-xp)**alplea(k)*(1.-z/xp)**betpom enddo enddo fzeroGluZZ= * fzeroGluZZ*.5*(1.-xpmin)/(1.-alppar+dels+epszero) * *(1.-glusea) *engy**epszero return end c------------------------------------------------------------------------ function fzeroSeaZZ(z,k) ! former psftile c----------------------------------------------------------------------- c c fzeroSeaZZComplete = fzeroSeaZZ * z^(-1-dels) * gamsoft * gamhad c c gamsoft = 8*pi*s0*gampar*gamtilde c integration over semihard pomeron light cone momentum share xp==u c c fzeroSeaZZ = glusea * engy^epszero c * int(du) u^(epszero-alppar+dels) (1-u)^alplea * EsoftQZero(z/u) c c z - light cone x of the quark, c k - hadron class c----------------------------------------------------------------------- double precision xpmin,xp common /ar3/ x1(7),a1(7) include 'epos.inc' include 'epos.incsem' fzeroSeaZZ=0. xpmin=z xpmin=xpmin**(1.-alppar+dels+epszero) do i=1,7 do m=1,2 xp=(.5*(1.+xpmin+(2*m-3)*x1(i)*(1.-xpmin)))**(1./ * (1.-alppar+dels+epszero)) zz=z/xp fzeroSeaZZ=fzeroSeaZZ+a1(i)*(1.-xp)**alplea(k)*EsoftQZero(zz) enddo enddo fzeroSeaZZ=fzeroSeaZZ*.5*(1.-xpmin)/(1.-alppar+dels+epszero) * *glusea *engy**epszero return end c######################################################################## c######################################################################## subroutine psaini c######################################################################## c######################################################################## c----------------------------------------------------------------------- c common initialization procedure c if isetcs = 0, alpD, betD, etc ... in inirj are not used and xkappa=1 c if isetcs = 1, alpD, betD, etc ... in inirj are not used but xkappa.ne.1 c if isetcs = 2, alpD, betD, xkappa, etc ... in inirj are used and c cross section from calculation in inics are read. c if epos.inics doesn't exist, it produces only the calculated part of it. c if isetcs = 3, alpD, betD, xkappa, etc ... in inirj are used and c cross section from simulation in inics are read. c if epos.inics doesn't exist, it produces the calculated AND the c simulated part of it both for ionudi=1 and 3. Only the values for c ionudi=1 (elastic for diffraction counted in xs) are always correct. c AA xs with ionudi=3 do not always correspond to MC simulations. c----------------------------------------------------------------------- include 'epos.inc' include 'epos.incpar' include 'epos.incsem' include 'epos.incems' logical lcalc!,lcalc2 c double precision om5p,xh,yh,v3pom(4),om2p dimension gamhad0(nclha),r2had0(nclha),chad0(nclha) *,alplea0(nclha),asect11(7,4,7),asect13(7,4,7),asect21(7,4,7) *,asect23(7,4,7),asect31(7,7,7),asect33(7,7,7) *,asect41(7,7,7),asect43(7,7,7)!,cgam(idxD) common /psar2/ edmax,epmax common /psar4/ fhgg(11,10,8),fhqg(11,10,80) *,fhgq(11,10,80),fhqq(11,10,80),fhgg0(11,10),fhgg1(11,10,4) *,fhqg1(11,10,40),fhgg01(11),fhgg02(11),fhgg11(11,4) *,fhgg12(11,4),fhqg11(11,10,4),fhqg12(11,10,4) *,ftoint(11,14,2,2,3) common /psar7/ delx,alam3p,gam3p common /psar9/ alpr common /psar15/ sudx(40,2) common /psar19/ cstot(20,20,240) common /psar20/ csord(20,20,240) common /psar21/ csbor(20,160,2) common /psar22/ cstotzero(20,4,2),csborzer(20,4,2) common /psar23/ cschar(20,20,2) common /psar25/ csdsi(21,21,104) common /psar27/ csds(21,26,4),csdt(21,26,2),csdr(21,26,2) common /psar33/ asect(7,4,7),asectn(7,7,7) common /psar34/ rrr,rrrm common /psar35/ anorm,anormp common /psar41/ rrrp,rrrmp common /psar36/ alvc common /psar37/ coefom1,coefom2 common /psar38/ vfro(11,14,3,2) common /psar39/ vnorm(11,14,3,2,2) c$$$ common /psar40/ coefxu1(idxD,nclha,10) c$$$ *,coefxu2(idxD,idxD,nclha,10),coefxc2(idxD,idxD,nclha,10) common/producetab/ producetables !used to link with CRMC logical producetables common /ar3/ x1(7),a1(7) common /testj/ ajeth(4),ajete(5),ajet0(7) parameter(nbkbin=40) common /kfitd/ xkappafit(nclegy,nclha,nclha,nbkbin),xkappa,bkbin common/geom/rmproj,rmtarg,bmax,bkmx character textini*38 external ptfau,ptfauAA call utpri('psaini',ish,ishini,4) c for fragmentation c ----------------- c number of flavors in fragmentation not less than active flavor in hard string nrflav=min(max(nrflav,naflav),nflavems) pmqu2=pmqu**2 difud=pmqd**2-pmqu2 difus=pmqs**2-pmqu2 difuuu=(pmqq+pmqu+pmqu)**2-pmqu2 difuud=(pudd*pmqq+pmqd+pmqu)**2-pmqu2 difuus=(puds*pmqq+pmqs+pmqu)**2-pmqu2 difudd=(pudd*pudd*pmqq+pmqd+pmqd)**2-pmqu2 difuds=(pudd*puds*pmqq+pmqs+pmqd)**2-pmqu2 difuss=(puds*puds*pmqq+pmqs+pmqs)**2-pmqu2 if(nrflav.gt.3)then difuc=pmqc**2-pmqu2 difuuc=(pudc*pmqq+pmqc+pmqu)**2-pmqu2 difudc=(pudd*pudc*pmqq+pmqc+pmqd)**2-pmqu2 difusc=(puds*pudc*pmqq+pmqc+pmqs)**2-pmqu2 difucc=(pudc*pudc*pmqq+pmqc+pmqs)**2-pmqu2 else difuc=0. difuuc=0. difudc=0. difusc=0. difucc=0. rstrac(1)=0. rstrac(2)=0. rstrac(3)=0. rstrac(4)=0. endif if(iappl.ne.6)then do i=1,4 ajeth(i)=0. enddo do i=1,5 ajete(i)=0. ajet0(i)=0. enddo ajet0(6)=0. ajet0(7)=0. if(isetcs.le.1)then !for Kfit bkbin=0.3 else bkbin=0.1 endif xkappa=1. edmax=edmaxi !1.e12 defined in epos-bas epmax=epmaxi !1.e12 defined in epos-bas c fix enhanced diagrams at minimum energy = 2.5 delx=1.5 !sqrt(egymin*egymin/exp(1.)) c arbitrary value for alam3p (not good if too small (infinite loop in rsh)) alam3p=0.5*(r2had(1)+r2had(2)+r2had(3)) !0.6 gam3p=.1 c interface to 'bas' c ---------------- dels=alppom-1. alpqua=(alppar+1.)/2. if(abs(alpqua).lt.1.e-6)call utstop('alpar should not be -1 !&') alpr=-2.+alpqua !x-exponent for remnant mass c omega coeffs c ---------------- coefom0=utgam1(1.+dels-alppar)*utgam1(1.+alplea(iclpro)) */utgam1(2.+alplea(iclpro)+dels-alppar) **utgam1(1.+dels-alppar)*utgam1(1.+alplea(icltar)) */utgam1(2.+alplea(icltar)+dels-alppar) coefom1=1.-utgam1(1.+dels-alppar)**2*utgam1(1.+alplea(iclpro)) */utgam1(1.+alplea(iclpro)+2.*(1.+dels-alppar)) **utgam1(1.+dels-alppar)**2*utgam1(1.+alplea(icltar)) */utgam1(1.+alplea(icltar)+2.*(1.+dels-alppar))/coefom0**2 coefom2=3.*coefom1-1. *+utgam1(1.+dels-alppar)**3*utgam1(1.+alplea(iclpro)) */utgam1(1.+alplea(iclpro)+3.*(1.+dels-alppar)) **utgam1(1.+dels-alppar)**3*utgam1(1.+alplea(icltar)) */utgam1(1.+alplea(icltar)+3.*(1.+dels-alppar))/coefom0**3 if(ish.ge.4)write(ifch,*)'coefom',coefom0,coefom1,coefom2,delx c soft pomeron: abbreviations c--------------------------------------- if(iappl.eq.1.or.iappl.eq.8.or.iappl.eq.9)then c--------------------------------------- c auxiliary constants: c--------------------------------------- stmass=.05 !string mass cutoff c--------------------------------------- c parton density normalization sq=log(log(q2min/.232**2)/log(.23/.232**2)) du=2.997+.753*sq-.076*sq*sq qnorm=0. do i=1,7 do m=1,2 xx=.5+x1(i)*(m-1.5) xxq=1.-xx**(1./(1.+du)) qnorm=qnorm+a1(i)*(psdfh4(xxq,q2min,0.,2,1)+ * psdfh4(xxq,q2min,0.,2,2))/(1.-xxq)**du enddo enddo qnorm=qnorm*.5/(1.+du) qnormp=qnorm ckkkkk----------------------------- c ffrr=(1.-qnorm)/4./pi/gamhad(2) c * *utgam1(2.+betpom-dels)/utgam1(1.-dels) c * /utgam1(1.+betpom)/utgam1(1.+alplea(2))/ c * utgam1(2.-alppar)*utgam1(3.+alplea(2)-alppar) c ffrr=(1.-qnorm)/4./pi/gamhad(2) c * *utgam1(2.+betpom-dels)/utgam1(1.-dels) c * /utgam1(1.+betpom) c write(6,*)'===========',ffrr ffrr=gamtil * /utgam1(1.+alplea(2))/ * utgam1(2.-alppar)*utgam1(3.+alplea(2)-alppar) gamsoft=ffrr*4.*pi ckkkkkkk------------------------------- if(ish.ge.4)write (ifch,*)'rr,qnorm',ffrr,qnorm sq=log(log(q2min/.232**2)/log(.25/.232**2)) dpi=.367+.563*sq qnorm=0. do i=1,7 do m=1,2 xx=.5+x1(i)*(m-1.5) xxq=1.-xx**(1./(1.+dpi)) qnorm=qnorm+a1(i)*(psdfh4(xxq,q2min,0.,1,1)+ * psdfh4(xxq,q2min,0.,1,2))/(1.-xxq)**dpi enddo enddo qnorm=qnorm*.5/(1.+dpi) cftmp=1./(1.-qnormp)*(1.-qnorm) * *utgam1(alplea(2)+1.)/utgam1(alplea(2)+3.-alppar) * /utgam1(alplea(1)+1.)*utgam1(alplea(1)+3.-alppar) gamhad(1)=gamhad(2)*cftmp if(gamhadsi(1).lt.0.)then gamhads(1)=gamhad(1) else gamhads(1)=gamhad(1)*gamhadsi(1) endif gamhad(1)=gamhads(1) if(ish.ge.4) * write (ifch,*)'gamhad(1),gamhads(1)',gamhad(1),gamhads(1) if(gamhadsi(2).lt.0.)then gamhads(2)=gamhad(2) else gamhads(2)=gamhad(2)*gamhadsi(2) endif gamhad(2)=gamhads(2) if(ish.ge.4) * write (ifch,*)'gamhad(2),gamhads(2)',gamhad(2),gamhads(2) qnorm=0. do i=1,7 do m=1,2 xx=.5+x1(i)*(m-1.5) xxq=1.-xx**(1./(1.+dpi)) qnorm=qnorm+a1(i)*(psdfh4(xxq,q2min,0.,1,1)+ * psdfh4(xxq,q2min,0.,1,2))/(1.-xxq)**dpi enddo enddo qnorm=qnorm*.5/(1.+dpi) cftmp=1./(1.-qnormp)*(1.-qnorm) * *utgam1(alplea(2)+1.)/utgam1(alplea(2)+3.-alppar) * /utgam1(alplea(3)+1.)*utgam1(alplea(3)+3.-alppar) gamhad(3)=gamhad(2)*cftmp if(gamhadsi(3).lt.0.)then gamhads(3)=gamhad(3) else gamhads(3)=gamhad(3)*gamhadsi(3) endif gamhad(3)=gamhads(3) if(ish.ge.4) * write (ifch,*)'gamhad(3),gamhads(3)',gamhad(3),gamhads(3) quamas=.35 gamhad(4)=gamhad(1)*(quamas/qcmass)**2 if(gamhadsi(4).lt.0.)then gamhads(4)=gamhad(4) else gamhads(4)=gamhad(4)*gamhadsi(4) endif gamhad(4)=gamhads(4) if(ish.ge.4) * write (ifch,*)'gamhad(4),gamhads(4)',gamhad(4),gamhads(4) gnorm=0. do i=1,7 do m=1,2 xx=.5+x1(i)*(m-1.5) xxg=xx**(1./(1.-dels)) gnorm=gnorm+a1(i)*(fzeroGluZZ(xxg,4)+fzeroSeaZZ(xxg,4)) enddo enddo gnorm=gnorm/(1.-dels)*2.*pi*gamhad(4)*ffrr alvc=6./(1.-gnorm)-4. if(ish.ge.4) write (ifch,*)'rr,qnorm,gnorm,alvc', * ffrr,qnorm,gnorm,alvc c write (*,*)'rr-c,qnorm,gnorm,alvc',ffrr,qnorm,gnorm,alvc endif c----------------------------------------------- c tabulation of inclusive jet cross sections c-------------------------------------------------- do i=1,40 qi=q2min*exp(.5*(i-1)) sudx(i,1)=psudx(qi,1) sudx(i,2)=psudx(qi,2) enddo if(ish.ge.4)write(ifch,*)'bare cross sections ...' call psaevc ccc call MakeCSTable inquire(file=fnii(1:nfnii),exist=lcalc) if(lcalc)then if(inicnt.eq.1)then write(ifmt,'(3a)')'read from ',fnii(1:nfnii),' ...' open(1,file=fnii(1:nfnii),status='old') read (1,*)qcdlam0,q2min0,q2ini0,naflav0,epmax0,pt2cut0 if(qcdlam0.ne.qcdlam)write(ifmt,'(a)')'initl: wrong qcdlam' if(q2min0 .ne.q2min )write(ifmt,'(a)')'initl: wrong q2min' if(q2ini0 .ne.q2ini )write(ifmt,'(a)')'initl: wrong q2ini' if(naflav0.ne.naflav)write(ifmt,'(a)')'initl: wrong naflav' if(epmax0 .ne.epmax )write(ifmt,'(a)')'initl: wrong epmax' if(pt2cut0 .ne.pt2cut )write(ifmt,'(a)')'initl: wrong pt2cut' if(qcdlam0.ne.qcdlam.or.q2min0 .ne.q2min .or.q2ini0 .ne.q2ini * .or.naflav0.ne.naflav.or.epmax0 .ne.epmax.or. pt2cut.ne.pt2cut0) * then write(ifmt,'(//a//)')' initl has to be reinitialized!!!' stop endif read (1,*)csbor,csord,cstot,cstotzero,csborzer close(1) endif goto 1 elseif(.not.producetables)then write(ifmt,*) "Missing epos.initl file !" write(ifmt,*) "Please correct the defined path ", &"or force production ..." stop endif write(ifmt,'(a)')'initl does not exist -> calculate tables ...' write (*,*)'Born xsection csbor' spmin=4.*q2min spminc=4.*q2min+qcmass**2 do m=1,4 !parton type at upper end of the ladder (1...4 - g,u,d,c) do k=1,20 if(m.ne.4)then sk=spmin*(epmax/2./spmin)**((k-1)/19.) p1=sk else sk=spminc*(epmax/2./spminc)**((k-1)/19.) p1=sk/(1.+qcmass**2/sk) endif qmax=p1/4. do i=1,20 qq=q2min*(qmax/q2min)**((i-1)/19.) do l=1,2 !parton type at lower end of the ladder k1=k+20*(m-1)+80*(l-1) m1=m-1 if(m.eq.3.and.l.eq.1)then !dd~ l1=-m1 else !du l1=l-1 endif !born cr.-sect. csbor(i,k1,1)=log(max(1.e-30,psborn(qq,qq,qq,sk,m1,l1,0,0))) if(m.ne.4)then csbor(i,k1,2)=log(max(1.e-30,psborn(4.*qq,qq,qq,sk,m1,l1,1,0))) endif enddo enddo enddo enddo write (*,*)'ordered jet xsection csord' do m=1,4 !parton type at upper end of the ladder do k=1,20 write (*,*)' m=',m,'/4 k=',k,'/20' if(m.ne.4)then sk=spmin*(epmax/2./spmin)**((k-1)/19.) !c.m. energy squared for the hard p1=sk else sk=spminc*(epmax/2./spminc)**((k-1)/19.) p1=sk/(1.+qcmass**2/sk) endif qmax=p1/4. tmax=p1/2. do i=1,20 !cross-sections initialization qi=q2min*(qmax/q2min)**((i-1)/19.) do j=1,20 qq=qi*(qmax/qi)**((j-1)/19.) if(p1.gt.4.*qq)then tmin=2.*qq/(1.+sqrt(1.-4.*qq/p1)) else tmin=2.*qq endif do l=1,2 !parton type at lower end of the ladder m1=m-1 if(m.eq.3.and.l.eq.1)then l1=-m1 else l1=l-1 endif if(m.ne.4)then k1=k+20*(m-1)+60*(l-1) if(k.eq.1.or.i.eq.20.or.j.eq.20)then csord(i,j,k1)=log(max(1.e-30,psborn(qi,qq,qq,sk,m1,l1,0,0))) csord(i,j,k1+120)= * log(max(1.e-30,psborn(4.*qq,qi,qq,sk,l1,m1,1,0))) else csord(i,j,k1)=log(psjet1(qi,qq,qq,sk,m1,l1,0) * /(1./tmin-1./tmax)+psborn(qi,qq,qq,sk,m1,l1,0,0)) csord(i,j,k1+120)=log(psjet1(qi,4.*qq,qq,sk,m1,l1,2) * /(1./tmin-1./tmax)+psborn(4.*qq,qi,qq,sk,l1,m1,1,0)) endif elseif(j.eq.1)then if(k.eq.1.or.i.eq.20)then cschar(i,k,l)=log(max(1.e-30,psborn(q2min,qi,qq,sk,m1,l1,0,0))) else cschar(i,k,l)=log(psjet1(qi,q2min,qq,sk,l1,m1,0) * /(1./tmin-1./tmax)+psborn(q2min,qi,qq,sk,m1,l1,0,0)) endif endif enddo enddo enddo enddo enddo write (ifmt,*)'tests:' write (ifmt,'(a,a)')' n-1 sk qi qj qq ' * ,' born born-i ord ord-i ' do k=1,7 sk=spmin*(epmax/2./spmin)**((k-1)/19.) if(k.ge.5)sk=spmin*1.5**(k-4) do n=1,2 if(n.eq.1)then qmax1=sk/4. qmax2=sk/4. else !if(n.eq.2)then qmax1=sk/4. qmax2=sk endif do i=1,3 qi=q2min*(qmax1/q2min)**((i-1)/3.) do j=1,3 qj=q2min*(qmax2/q2min)**((j-1)/3.) qqmax=sk/4. if(n.eq.1)then qqmin=max(qi,qj) else qqmin=max(qi,qj/4.) endif do lq=1,3 qq=qqmin*(qqmax/qqmin)**((lq-1)/3.) if(sk.gt.4.*qq)then tmin=2.*qq/(1.+sqrt(1.-4.*qq/sk)) else tmin=2.*qq endif tmax=sk/2. do m=1,1 !parton type at upper end of the ladder (1 do l=1,1 !parton type at lower end of the ladder (1 m1=m-1 if(m.eq.3.and.l.eq.1)then l1=-m1 else l1=l-1 endif a=psborn(qj,qi,qq,sk,l1,m1,n-1,0)*(1./tmin-1./tmax) b=psbint(qj,qi,qq,sk,l1,m1,n-1) c=psjet1(qi,qj,qq,sk,m1,l1,2*(n-1)) * +psborn(qj,qi,qq,sk,l1,m1,n-1,0)*(1./tmin-1./tmax) d=psjti1(qi,qj,qq,sk,m1,l1,n-1) write (ifmt,'(i3,4f9.1,3x,4f9.4)')n-1,sk,qi,qj,qq,a,b,c,d enddo enddo enddo enddo enddo enddo enddo write (*,*)'jet xsection cstot' do k=1,20 write (*,*)'k=',k,'/20' sk=spmin*(epmax/2./spmin)**((k-1)/19.) !c.m. energy squared for the hard qmax=sk/4. tmax=sk/2. do i=1,20 !cross-sections initialization do n=1,2 if(n.eq.1)then qi=q2min*(qmax/q2min)**((i-1)/19.) else qi=q2min*(4.*qmax/q2min)**((i-1)/19.) endif do j=1,20 if(n.eq.1)then qq=qi*(qmax/qi)**((j-1)/19.) else qq=max(q2min,qi/4.)*(qmax/max(q2min,qi/4.))** * ((j-1)/19.) endif if(sk.gt.4.*qq)then tmin=2.*qq/(1.+sqrt(1.-4.*qq/sk)) else tmin=2.*qq endif do m=1,3 !parton type at upper end of the ladder (1 do l=1,2 !parton type at lower end of the ladder (1 m1=m-1 if(m.eq.3.and.l.eq.1)then l1=-m1 else l1=l-1 endif k1=k+20*(m-1)+60*(l-1)+120*(n-1) if(k.eq.1.or.i.eq.20.or.j.eq.20)then cstot(i,j,k1)=log(max(1.e-30,psborn(qi,q2min,qq,sk,m1,l1,n-1,0))) else if(n.eq.1)then cstot(i,j,k1)=log((psjet(qi,q2min,qq,sk,m1,l1,0)+ * psjti1(qi,q2min,qq,sk,m1,l1,0)+ * psjti1(q2min,qi,qq,sk,l1,m1,0) * -psbint(qi,q2min,qq,sk,m1,l1,0))/(1./tmin-1./tmax)) else cstot(i,j,k1)=log((psjet(qi,q2min,qq,sk,m1,l1,1)+ * psjet1(qi,q2min,qq,sk,m1,l1,1)+ * psjti1(q2min,qi,qq,sk,l1,m1,1))/(1./tmin-1./tmax)) endif endif enddo enddo enddo enddo enddo enddo c total and born hard cross-sections logarithms for minimal cutoff c (q2min), interpolated in the psjti0 procedure spmin=4.*q2min spminc=4.*q2min+qcmass**2 do m=1,4 do l=1,2 m1=m-1 if(m.eq.3.and.l.eq.1)then l1=-m1 else l1=l-1 endif do k=1,20 if(m.ne.4)then sk=spmin*(epmax/2./spmin)**((k-1)/19.) !c.m. energy squared for the hard p1=sk qq=q2min else sk=spminc*(epmax/2./spminc)**((k-1)/19.) p1=sk/(1.+qcmass**2/sk) qq=q2min endif if(p1.gt.4.*qq)then tmin=2.*qq/(1.+sqrt(1.-4.*qq/p1)) else tmin=2.*qq endif tmax=p1/2. k1=k+20*(m-1)+80*(l-1) csborzer(k,m,l) * =log(max(1.e-30,psborn(q2min,q2min,qq,sk,m1,l1,0,0))) if(k.eq.1)then cstotzero(k,m,l)=csborzer(k,m,l) elseif(m.ne.4)then cstotzero(k,m,l)=log(psjti(q2min,qq,sk,m1,l1,0)/ * (1./tmin-1./tmax)) else smins=2.5*q2min*(1.+sqrt(1.+4.*qcmass**2/q2min)) if(sk.le.smins)then cstotzero(k,m,l)=log(psjci(q2min,sk,l1)/(1./tmin-1./tmax)) else cstotzero(k,m,l)=log((psjci(q2min,sk,l1)+psjct(sk,l1)) * /(1./tmin-1./tmax)) endif endif enddo enddo enddo write(ifmt,'(a)')'write to initl ...' open(1,file=fnii(1:nfnii),status='unknown') write (1,*)qcdlam,q2min,q2ini,naflav,epmax,pt2cut write (1,*)csbor,csord,cstot,cstotzero,csborzer,cschar close(1) 1 continue if(iappl.ne.8)goto 3 if(ish.ge.3)write(ifch,*)'dis cross sections ...' inquire(file=fnid(1:nfnid),exist=lcalc) if(lcalc)then if(inicnt.eq.1)then write(ifmt,'(3a)')'read from ',fnid(1:nfnid),' ...' open(1,file=fnid(1:nfnid),status='old') read (1,*)qcdlam0,q2min0,q2ini0,naflav0,epmax0,edmax0 if(qcdlam0.ne.qcdlam)write(ifmt,'(a)')'inidi: wrong qcdlam' if(q2min0 .ne.q2min )write(ifmt,'(a)')'inidi: wrong q2min' if(q2ini0 .ne.q2ini )write(ifmt,'(a)')'inidi: wrong q2ini' if(naflav0.ne.naflav)write(ifmt,'(a)')'inidi: wrong naflav' if(epmax0 .ne.epmax )write(ifmt,'(a)')'inidi: wrong epmax' if(edmax0 .ne.edmax )write(ifmt,'(a)')'inidi: wrong edmax' if(qcdlam0.ne.qcdlam.or.q2min0 .ne.q2min.or.q2ini0 .ne.q2ini * .or.naflav0.ne.naflav.or.epmax0 .ne.epmax * .or.edmax0 .ne.edmax)then write(ifmt,'(//a//)')' inidi has to be reinitialized!!!' stop endif read (1,*)csdsi,csds,csdt,csdr close(1) endif goto 3 elseif(.not.producetables)then write(ifmt,*) "Missing epos.inidi file !" write(ifmt,*) "Please correct the defined path ", &"or force production ..." stop endif write(ifmt,'(a)')'inidi does not exist -> calculate tables ...' do j=1,21 qq=q2min*exp(.5*(j-1)) !photon virtuality do m=1,2 !parton type at the end of the ladder q2mass=qcmass**2 s2min=4.*max(q2mass,q2min)+qq if(m.eq.2)s2min=s2min/(1.-4.*q2ini/(s2min-qq)) do k=1,26 write (*,*)'sin,j,m,k',j,m,k sk=s2min*(edmax/s2min)**(.04*(k-1)) !c.m. energy squared if(k.eq.26)sk=1.01*sk qmin=q2min if(m.eq.1)then qmax=(sk-qq)/4. else qmax=(sk-qq+sqrt((sk-qq)**2-16.*sk*q2ini))/8. endif do i=1,21 !cross-sections calculation qi=qmin*(qmax/qmin)**((i-1)/20.) tmax=.5*sk qtq=4.*max(q2mass,qi)/(sk-qq) if(qtq.lt.1.)then tmin=.5*sk*qtq/(1.+sqrt(1.-qtq)) else tmin=.5*sk endif do ilong=1,2 k1=k+26*(m-1)+52*(ilong-1) if(m.eq.1)then if(tmax.gt.1.01*tmin)then sij=psds(qi,qq,sk,m-1,ilong-1) if(sij.lt.0.)write (*,*)'qi,qq,sk,m,long,sij', * qi,qq,sk,m,ilong,sij csdsi(i,j,k1)=log(max(0.,sij)/(1./tmin-1./tmax) * +psdbor(qi,qq,sk,ilong-1)) else csdsi(i,j,k1)= * log(max(1.e-25,psdbor(qi,qq,sk,ilong-1))) endif else csdsi(i,j,k1)=psds(qi,qq,sk,m-1,ilong-1) endif enddo enddo enddo enddo enddo do j=1,21 qq=q2min*exp(.5*(j-1)) !photon virtuality s2min=max(4.*qq,16.*q2min) !pt2dis=qq do m=1,2 do k=1,26 do ilong=1,2 k1=k+26*(m-1)+52*(ilong-1) csds(j,k,m+2*(ilong-1))=csdsi(1,j,k1) enddo sk=(s2min+qq)*(edmax/(s2min+qq))**(.04*(k-1)) csdt(j,k,m)=psdres(qq,sk,s2min,m-1) csdr(j,k,m)=psdrga(qq,sk-qq,s2min,m-1) enddo enddo enddo write(ifmt,'(a)')'write to inidi ...' write(ifmt,'(a)')'write to inidi ...' open(1,file=fnid(1:nfnid),status='unknown') write (1,*)qcdlam,q2min,q2ini,naflav,epmax,edmax write (1,*)csdsi,csds,csdt,csdr close(1) 3 continue c--------------------------------------- c tabulation of semihard eikonals c--------------------------------------- !!!!!!!!! if(iappl.eq.1)then if(ish.ge.4)write(ifch,*)'semihard eikonals ...' 5 continue inquire(file=fnrj,exist=lcalc) if(lcalc)then if(inicnt.eq.1)then write(ifmt,'(3a)')'read from ',fnrj(1:nfnrj),' ...' open(1,file=fnrj(1:nfnrj),status='old') read (1,*)alpqua0,alplea0,alppom0,slopom0, * gamhad0,r2had0,chad0, * qcdlam0,q2min0,q2ini0,betpom0,glusea0,naflav0, * factk0,pt2cut0,gamtil0 if(alpqua0.ne.alpqua)write(ifmt,'(a,2f8.4)') * 'inirj: wrong alpqua',alpqua0,alpqua if(alppom0.ne.alppom)write(ifmt,'(a,2f8.4)') * 'inirj: wrong alppom',alppom0,alppom if(slopom0.ne.slopom)write(ifmt,'(a,2f8.4)') * 'inirj: wrong slopom',slopom0,slopom iii=2 if(gamhad0(iii).ne.gamhad(iii))write(ifmt,'(a,i1,a,2f8.4)') * 'inirj: wrong gamhad(',iii,')',gamhad0(iii),gamhad(iii) do iii=1,3 if(r2had0(iii) .ne.r2had(iii) )write(ifmt,'(a,i1,a,2f8.4)') * 'inirj: wrong r2had(',iii,')',r2had0(iii),r2had(iii) if(chad0(iii) .ne.chad(iii) )write(ifmt,'(a,i1,a,2f8.4)') * 'inirj: wrong chad(',iii,')',chad0(iii),chad(iii) if(alplea0(iii).ne.alplea0(iii))write(ifmt,'(a,i1,a,2f8.4)') * 'inirj: wrong alplea(',iii,')',alplea0(iii),alplea(iii) enddo if(qcdlam0.ne.qcdlam)write(ifmt,'(a,2f8.4)') * 'inirj: wrong qcdlam',qcdlam0,qcdlam if(q2min0 .ne.q2min )write(ifmt,'(a,2f8.4)') * 'inirj: wrong q2min',q2min0,q2min if(q2ini0 .ne.q2ini )write(ifmt,'(a,2f8.4)') * 'inirj: wrong q2ini',q2ini0,q2ini if(betpom0.ne.betpom)write(ifmt,'(a,2f8.4)') * 'inirj: wrong betpom',betpom0,betpom if(glusea0.ne.glusea)write(ifmt,'(a,2f8.4)') * 'inirj: wrong glusea',glusea0,glusea if(naflav0.ne.naflav)write(ifmt,'(a,2f8.4)') * 'inirj: wrong naflav',naflav0,naflav if(factk0 .ne.factk )write(ifmt,'(a,2f8.4)') * 'inirj: wrong factk', factk0,factk if(pt2cut0 .ne.pt2cut )write(ifmt,'(a,2f8.4)') * 'inirj: wrong pt2cut', pt2cut0,pt2cut if(gamtil0 .ne.gamtil )write(ifmt,'(a,2f8.4)') * 'inirj: wrong gamtil', gamtil0,gamtil if(alpqua0.ne.alpqua.or.alppom0.ne.alppom * .or.slopom0.ne.slopom.or.gamhad0(2).ne.gamhad(2) * .or.r2had0(1).ne.r2had(1).or.r2had0(2).ne.r2had(2) * .or.r2had0(3).ne.r2had(3) * .or.chad0(1).ne.chad(1).or.chad0(2).ne.chad(2) * .or.chad0(3).ne.chad(3) * .or.alplea0(1).ne.alplea(1).or.alplea0(2).ne.alplea(2) * .or.alplea0(3).ne.alplea(3) * .or.qcdlam0.ne.qcdlam.or.q2min0 .ne.q2min * .or.q2ini0 .ne.q2ini.or.gamtil0.ne.gamtil * .or.betpom0.ne.betpom.or.glusea0.ne.glusea.or.naflav0.ne.naflav * .or.factk0 .ne.factk .or.pt2cut0.ne.pt2cut)then write(ifmt,'(//a//)')' inirj has to be reinitialized!!!!' stop endif read(1,*)fhgg,fhqg,fhgq,fhqq,fhgg0,fhgg1,fhqg1 * ,fhgg01,fhgg02,fhgg11,fhgg12,fhqg11,fhqg12 * ,ftoint,vfro,vnorm,coefxu1,coefxu2,coefxc2 read(1,*)bkbin0,iclpro10,iclpro20,icltar10,icltar20,iclegy10 * ,iclegy20,egylow0,egymax0,iomega0,egyscr0,epscrw0,epscrp0 if(isetcs.gt.1)then textini=' ' if(iclpro10.ne.iclpro1)write(textini,'(a,2i8)') * 'inirj: wrong iclpro1 ',iclpro10,iclpro1 if(iclpro20.ne.iclpro2)write(textini,'(a,2i8)') * 'inirj: wrong iclpro2 ',iclpro20,iclpro2 if(icltar10.ne.icltar1)write(textini,'(a,2i8)') * 'inirj: wrong icltar1 ',icltar10,icltar1 if(icltar20.ne.icltar2)write(textini,'(a,2i8)') * 'inirj: wrong icltar2 ',icltar20,icltar2 if(iclegy10.ne.iclegy1)write(textini,'(a,2i8)') * 'inirj: wrong iclegy1 ',iclegy10,iclegy1 if(iclegy20.ne.iclegy2)write(textini,'(a,2i8)') * 'inirj: wrong iclegy2 ',iclegy20,iclegy2 if(iomega0.ne.iomega)write(textini,'(a,2i8)') * 'inirj: wrong iomega ',iomega0,iomega if(egylow0.ne.egylow)write(textini,'(a,2f8.4)') * 'inirj: wrong egylow ',egylow0,egylow if(egymax0.ne.egymax)write(textini,'(a,2f8.4)') * 'inirj: wrong egymax ',egymax0,egymax if(epscrw0.ne.epscrw)write(textini,'(a,2f8.4)') * 'inirj: wrong epscrw ',epscrw0,epscrw if(epscrp0.ne.epscrp)write(textini,'(a,2f8.4)') * 'inirj: wrong epscrp ',epscrp0,epscrp if(bkbin0.ne.bkbin)write(textini,'(a,2f8.4)') * 'inirj: wrong bkbin',bkbin0,bkbin if(textini.ne.' ')then write(ifmt,'(//10x,a//10x,a//)')textini, * 'inirj has to be reinitialized!!!!' stop endif do iiipro=iclpro1,iclpro2 do iiitar=icltar1,icltar2 do iiiegy=iclegy1,iclegy2 do iiib=1,nbkbin read(1,*)xkappafit(iiiegy,iiipro,iiitar,iiib) enddo xkappafit(iiiegy,iiipro,iiitar,nbkbin)=1. do iiib=2,nbkbin-1 if(xkappafit(iiiegy,iiipro,iiitar,iiib).lt.1.)then xkappafit(iiiegy,iiipro,iiitar,iiib)=max(1.,0.5* * (xkappafit(iiiegy,iiipro,iiitar,iiib-1) * +xkappafit(iiiegy,iiipro,iiitar,iiib+1))) endif enddo do iiidf=idxD0,idxD read(1,*)alpDs(iiidf,iiiegy,iiipro,iiitar), * alpDps(iiidf,iiiegy,iiipro,iiitar), * alpDpps(iiidf,iiiegy,iiipro,iiitar), * betDs(iiidf,iiiegy,iiipro,iiitar), * betDps(iiidf,iiiegy,iiipro,iiitar), * betDpps(iiidf,iiiegy,iiipro,iiitar), * gamDs(iiidf,iiiegy,iiipro,iiitar), * delDs(iiidf,iiiegy,iiipro,iiitar) enddo enddo enddo enddo endif close(1) endif goto 4 elseif(.not.producetables)then write(ifmt,*) "Missing epos.inirj file !" write(ifmt,*) "Please correct the defined path ", &"or force production ..." stop endif write(ifmt,'(a)')'inirj does not exist -> calculate tables ...' engysave=engy maprojsave=maproj matargsave=matarg iclpros=iclpro icltars=icltar spmin=4.*q2min spminc=4.*q2min+2.*qcmass**2 icltar=2 write(ifmt,'(a)')' tabulate om5 ...' do iy=1,11 sy=spmin*(epmax/2./spmin)**((iy-1)/10.) syc=spminc*(epmax/2./spminc)**((iy-1)/10.) iclpro=2 icltar=2 if(iy.eq.1)then fhgg01(iy)=-80. fhgg02(iy)=-80. else fhgg01(iy)=log(om51pp(sy,1.,1.,3)) fhgg02(iy)=log(om51pp(sy,1.,1.,7)) endif do iclpro=iclpro1,iclpro2 if(iy.eq.1)then fhgg11(iy,iclpro)=-80. fhgg12(iy,iclpro)=-80. else fhgg11(iy,iclpro)=log(om51pp(sy,1.,1.,4)) fhgg12(iy,iclpro)=log(om51pp(sy,1.,1.,9)) endif do ix=1,10 if(ix.le.5)then xp=.1*2.**(ix-5) else xp=.2*(ix-5) endif if(iy.eq.1)then fhqg11(iy,ix,iclpro)=-80. fhqg12(iy,ix,iclpro)=-80. elseif(iclpro.eq.4)then fhqg11(iy,ix,iclpro)=log(om51pp(syc,1.,1.,5)) fhqg12(iy,ix,iclpro)=log(om51pp(syc,1.,1.,11)) else fhqg11(iy,ix,iclpro)=log(om51pp(sy,xp,1.,5)) fhqg12(iy,ix,iclpro)=log(om51pp(sy,xp,1.,11)) endif enddo enddo do iz=1,10 z=.1*iz iclpro=2 icltar=2 if(iy.eq.1)then fhgg0(iy,iz)=-80. else fhgg0(iy,iz)=log(om51pp(sy,1.,z,6)/z) endif do iclpro=iclpro1,iclpro2 if(iy.eq.1)then fhgg1(iy,iz,iclpro)=-80. else fhgg1(iy,iz,iclpro)=log(om51pp(sy,1.,z,8)/z) endif do ix=1,10 if(ix.le.5)then xp=.1*2.**(ix-5) else xp=.2*(ix-5) endif if(iy.eq.1)then fhqg1(iy,ix,iz+10*(iclpro-1))=-80. elseif(iclpro.eq.4)then fhqg1(iy,ix,iz+10*(iclpro-1))=log(om51pp(syc,xp,z,10)/z) else fhqg1(iy,ix,iz+10*(iclpro-1))=log(om51pp(sy,xp,z,10)/z) endif enddo enddo enddo enddo do iclpro=iclpro1,iclpro2 !hadron type (1 - pion, 2 - nucleon, 3 - kaon, 4 - charm) do icltar=icltar1,icltar2 !hadron type (2 - nucleon) do iy=1,11 sy=spmin*(epmax/2./spmin)**((iy-1)/10.) syc=spminc*(epmax/2./spminc)**((iy-1)/10.) do iz=1,10 z=.1*iz if(iy.eq.1)then fhgg(iy,iz,iclpro+4*(icltar-1))=-80. else fhgg(iy,iz,iclpro+4*(icltar-1))=log(om51pp(sy,1.,z,0)/z) endif do ix=1,10 if(ix.le.5)then xp=.1*2.**(ix-5) else xp=.2*(ix-5) endif if(iy.eq.1)then fhqg(iy,ix,iz+10*(iclpro+4*(icltar-1)-1))=-80. fhgq(iy,ix,iz+10*(iclpro+4*(icltar-1)-1))=-80. else if(iclpro.ne.4)then syx=sy else syx=syc endif fhqg(iy,ix,iz+10*(iclpro+4*(icltar-1)-1))= * log(om51pp(syx,xp,z,1)/z) if(icltar.ne.4)then syx=sy else syx=syc endif fhgq(iy,ix,iz+10*(iclpro+4*(icltar-1)-1))= * log(om51pp(syx,xp,z,2)/z) endif enddo enddo do ix1=1,10 if(ix1.le.5)then xpph=.1*2.**(ix1-5) else xpph=.2*(ix1-5) endif do ix2=1,10 if(ix2.le.5)then xmm=.1*2.**(ix2-5) else xmm=.2*(ix2-5) endif if(iy.eq.1)then fhqq(iy,ix1,ix2+10*(iclpro+4*(icltar-1)-1))=-80. else if(iclpro.ne.4.and.icltar.ne.4)then syx=sy else syx=syc endif fhqq(iy,ix1,ix2+10*(iclpro+4*(icltar-1)-1))= * log(pshard(syx,xpph,xmm)) endif enddo enddo enddo enddo enddo if(isetcs.gt.1)then write(ifmt,'(a)')' tabulate fit parameters ...' engysave=engy do iclpro=iclpro1,iclpro2 !hadron type (1 - pion, 2 - nucleon, 3 - kaon, 4 - charm) do icltar=icltar1,icltar2 !hadron type (2 - nucleon) do iclegy=iclegy2,iclegy1,-1 call param enddo do iiclegy=iclegy2,iclegy1,-1 engy=egyfac**(iiclegy-1)*egylow call paramini(0) call Kfit(iiclegy) enddo enddo enddo engy=engysave endif write(ifmt,'(a)')' write to inirj ...' open(1,file=fnrj,status='unknown') write (1,*)alpqua,alplea,alppom,slopom,gamhad,r2had,chad, *qcdlam,q2min,q2ini,betpom,glusea,naflav,factk,pt2cut,gamtil write (1,*)fhgg,fhqg,fhgq,fhqq,fhgg0,fhgg1,fhqg1 *,fhgg01,fhgg02,fhgg11,fhgg12,fhqg11,fhqg12 *,ftoint,vfro,vnorm,coefxu1,coefxu2,coefxc2 write(1,*)bkbin,iclpro1,iclpro2,icltar1,icltar2,iclegy1,iclegy2 *,egylow,egymax,iomega,egyscr,epscrw,epscrp do iiipro=iclpro1,iclpro2 do iiitar=icltar1,icltar2 do iiiegy=iclegy1,iclegy2 do iiib=1,nbkbin write(1,*)xkappafit(iiiegy,iiipro,iiitar,iiib) enddo do iiidf=idxD0,idxD write(1,*)alpDs(iiidf,iiiegy,iiipro,iiitar), * alpDps(iiidf,iiiegy,iiipro,iiitar), * alpDpps(iiidf,iiiegy,iiipro,iiitar), * betDs(iiidf,iiiegy,iiipro,iiitar), * betDps(iiidf,iiiegy,iiipro,iiitar), * betDpps(iiidf,iiiegy,iiipro,iiitar), * gamDs(iiidf,iiiegy,iiipro,iiitar), * delDs(iiidf,iiiegy,iiipro,iiitar) enddo enddo enddo enddo close(1) engy=engysave maproj=maprojsave matarg=matargsave iclpro=iclpros icltar=icltars inicnt=1 goto 5 4 continue c-------------------------------------- c inelastic cross sections c--------------------------------------- if(isetcs.ge.2)then !-------------------- if(ish.ge.4)write(ifch,*)'cross sections ...' 6 continue inquire(file=fncs,exist=lcalc) if(lcalc)then if(inicnt.eq.1)then write(ifmt,'(3a)')'read from ',fncs(1:nfncs),' ...' open(1,file=fncs(1:nfncs),status='old') read (1,*)alpqua0,alplea0,alppom0,slopom0, * gamhad0,r2had0,chad0, * qcdlam0,q2min0,q2ini0,betpom0,glusea0,naflav0, * factk0,pt2cut0 if(alpqua0.ne.alpqua)write(ifmt,'(a,2f8.4)') * 'inics: wrong alpqua',alpqua0,alpqua if(alppom0.ne.alppom)write(ifmt,'(a,2f8.4)') * 'inics: wrong alppom',alppom0,alppom if(slopom0.ne.slopom)write(ifmt,'(a,2f8.4)') * 'inics: wrong slopom',slopom0,slopom iii=2 if(gamhad0(iii).ne.gamhad(iii))write(ifmt,'(a,i1,a,2f8.4)') * 'inics: wrong gamhad(',iii,')',gamhad0(iii),gamhad(iii) do iii=1,3 if(r2had0(iii) .ne.r2had(iii) )write(ifmt,'(a,i1,a,2f8.4)') * 'inics: wrong r2had(',iii,')',r2had0(iii),r2had(iii) if(chad0(iii) .ne.chad(iii) )write(ifmt,'(a,i1,a,2f8.4)') * 'inics: wrong chad(',iii,')',chad0(iii),chad(iii) if(alplea0(iii).ne.alplea0(iii))write(ifmt,'(a,i1,a,2f8.4)') * 'inics: wrong alplea(',iii,')',alplea0(iii),alplea(iii) enddo if(qcdlam0.ne.qcdlam)write(ifmt,'(a,2f8.4)') * 'inics: wrong qcdlam',qcdlam0,qcdlam if(q2min0 .ne.q2min )write(ifmt,'(a,2f8.4)') * 'inics: wrong q2min',q2min0,q2min if(q2ini0 .ne.q2ini )write(ifmt,'(a,2f8.4)') * 'inics: wrong q2ini',q2ini0,q2ini if(betpom0.ne.betpom)write(ifmt,'(a,2f8.4)') * 'inics: wrong betpom',betpom0,betpom if(glusea0.ne.glusea)write(ifmt,'(a,2f8.4)') * 'inics: wrong glusea',glusea0,glusea if(naflav0.ne.naflav)write(ifmt,'(a,2f8.4)') * 'inics: wrong naflav',naflav0,naflav if(factk0 .ne.factk )write(ifmt,'(a,2f8.4)') * 'inics: wrong factk', factk0,factk if(pt2cut0 .ne.pt2cut )write(ifmt,'(a,2f8.4)') * 'inics: wrong pt2cut', pt2cut0,pt2cut if(alpqua0.ne.alpqua.or.alppom0.ne.alppom * .or.slopom0.ne.slopom.or.gamhad0(2).ne.gamhad(2) * .or.r2had0(1).ne.r2had(1).or.r2had0(2).ne.r2had(2) * .or.r2had0(3).ne.r2had(3) * .or.chad0(1).ne.chad(1).or.chad0(2).ne.chad(2) * .or.chad0(3).ne.chad(3) * .or.alplea0(1).ne.alplea(1).or.alplea0(2).ne.alplea(2) * .or.alplea0(3).ne.alplea(3) * .or.qcdlam0.ne.qcdlam.or.q2min0 .ne.q2min * .or.q2ini0 .ne.q2ini * .or.betpom0.ne.betpom.or.glusea0.ne.glusea.or.naflav0.ne.naflav * .or.factk0 .ne.factk .or.pt2cut0.ne.pt2cut)then write(ifmt,'(//a//)')' inics has to be reinitialized!!!!' stop endif read(1,*)isetcs0,iclpro10,iclpro20,icltar10,icltar20,iclegy10 * ,iclegy20,egylow0,egymax0,iomega0,egyscr0,epscrw0,epscrp0 if(iclpro10.ne.iclpro1)write(ifmt,'(a,2i2)') * 'inics: wrong iclpro1',iclpro10,iclpro1 if(iclpro20.ne.iclpro2)write(ifmt,'(a,2i2)') * 'inics: wrong iclpro2',iclpro20,iclpro2 if(icltar10.ne.icltar1)write(ifmt,'(a,2i2)') * 'inics: wrong icltar1',icltar10,icltar1 if(icltar20.ne.icltar2)write(ifmt,'(a,2i2)') * 'inics: wrong icltar2',icltar20,icltar2 if(iclegy10.ne.iclegy1)write(ifmt,'(a,2i4)') * 'inics: wrong iclegy1',iclegy10,iclegy1 if(iclegy20.ne.iclegy2)write(ifmt,'(a,2i4)') * 'inics: wrong iclegy2',iclegy20,iclegy2 if(iomega0.ne.iomega)write(textini,'(a,2i8)') * 'inics: wrong iomega ',iomega0,iomega if(egylow0.ne.egylow)write(ifmt,'(a,2f8.4)') * 'inics: wrong egylow',egylow0,egylow if(egymax0.ne.egymax)write(ifmt,'(a,2f12.4)') * 'inics: wrong egymax',egymax0,egymax if(egyscr0.ne.egyscr)write(ifmt,'(a,2f8.4)') * 'inics: wrong egyscr ',egyscr0,egyscr if(epscrw0.ne.epscrw)write(ifmt,'(a,2f8.4)') * 'inics: wrong epscrw',epscrw0,epscrw if(epscrp0.ne.epscrp)write(ifmt,'(a,2f8.4)') * 'inics: wrong epscrp',epscrp0,epscrp if(isetcs0.lt.isetcs)write(ifmt,'(a,2f8.4)') * 'inics: wrong isetcs',isetcs0,isetcs if(iclpro10.ne.iclpro1.or.iclpro20.ne.iclpro2 * .or.icltar10.ne.icltar1.or.icltar20.ne.icltar2 * .or.iclegy10.ne.iclegy1.or.iclegy20.ne.iclegy2 * .or.egylow0.ne.egylow.or.egymax0.ne.egymax * .or.egyscr0.ne.egyscr.or.epscrw0.ne.epscrw.or.isetcs0.lt.isetcs * .or.epscrp0.ne.epscrp)then write(ifmt,'(//a//)')' inics has to be reinitialized!!!!' stop endif if(isetcs.eq.2)then if(ionudi.eq.1)then read (1,*)asect,asect13,asect21,asect23,asectn * ,asect33,asect41,asect43 else !ionudi=3 read (1,*)asect11,asect,asect21,asect23,asect31 * ,asectn,asect41,asect43 endif elseif(isetcs.eq.3)then if(ionudi.eq.1)then read (1,*)asect11,asect13,asect,asect23,asect31 * ,asect33,asectn,asect43 else !ionudi=3 read (1,*)asect11,asect13,asect21,asect,asect31 * ,asect33,asect41,asectn endif else write(ifmt,'(//a//)')' Wrong isetcs in psaini !!!!' endif close(1) endif goto 7 elseif(.not.producetables)then write(ifmt,*) "Missing epos.inics file !" write(ifmt,*) "Please correct the defined path ", &"or force production ..." stop endif ifradesave=ifrade iremnsave=iremn idprojsave=idproj idprojinsave=idprojin idtargsave=idtarg idtarginsave=idtargin laprojsave=laproj latargsave=latarg maprojsave=maproj matargsave=matarg icltarsave=icltar iclprosave=iclpro engysave=engy pnllsave=pnll elabsave=elab ecmssave=ecms iclegysave=iclegy nrevtsave=nrevt neventsave=nevent ntevtsave=ntevt isetcssave=isetcs noebinsave=noebin isigmasave=isigma bminimsave=bminim bmaximsave=bmaxim bimevtsave=bimevt bkmxndifsave=bkmxndif c fctrmxsave=fctrmx ionudisave=ionudi isetcs=2 isigma=1 noebin=1 idtarg=1120 idtargin=1120 bminim=0. bmaxim=10000. ifrade=0 !to save time, no fragmentation iremn=0 !to save time, simple remnants ionudi=3 !to have both ionudi=1 and 3 in tables write(ifmt,'(a)')'inics does not exist -> calculate tables ...' c initialize random numbers if(seedj.ne.0d0)then call ranfini(seedj,iseqsim,2) else stop 'seedi = 0 ... Please define it !' endif call aseed(2) laproj=-1 maproj=1 icltar=2 do iclpro=1,4 if(iclpro.lt.iclpro1.or.iclpro.gt.iclpro2)then do ie=1,7 do iia=1,7 asect11(ie,iclpro,iia)=0. asect21(ie,iclpro,iia)=0. asect13(ie,iclpro,iia)=0. asect23(ie,iclpro,iia)=0. enddo enddo else do ie=1,7 engy=1.5*10.**(ie-1) call paramini(0) bkmxndif=conbmxndif() if(ish.ge.1) & write(ifch,*)' calcul. ',ie,' (',iclpro,')',engy write(ifmt,*)' calcul. ',ie,' (',iclpro,')',engy sigine=0. do iia=1,7 matarg=2**(iia-1) if(matarg.eq.1)then !hadron-proton interaction c ine=cut+diff call psfz(2,gz2,0.) gin=gz2*pi*10. c cut iomegasave=iomega iomega=2 call psfz(2,gz2,0.) iomega=iomegasave gcut=gz2*pi*10. c diff difpart=gin-gcut c non excited projectile and target gqela=(1.-rexdif(iclpro))*(1.-rexdif(icltar))*difpart gin3=max(1.,gin-gqela) else call conini rad=radnuc(matarg) bm=rad+2. rrr=rad/difnuc(matarg) rrrm=rrr+log(9.) anorm=1.5/pi/rrr**3/(1.+(pi/rrr)**2)/difnuc(matarg)**2 c gela=(ptgau(ptfau,bm,2,1)+ptgau1(bm,2,1))*10. !sig_ela c in=cut+diff gcut=(ptgau(ptfau,bm,2,2)+ptgau1(bm,2,2))*10. !sig_in gin=gcut c cut iomegasave=iomega iomega=2 gcut=(ptgau(ptfau,bm,2,2)+ptgau1(bm,2,2))*10. !sig_cut iomega=iomegasave c diff difpart=gin-gcut c non excited projectile gqela=(1.-rexdif(iclpro)) & **(1.+rexres(iclpro)*float(matarg-1)**0.3) c non excited target gqela=gqela*(1.-rexdif(icltar)) gqela=gqela*difpart gin3=max(1.,gin-gqela) endif if(ish.ge.1)write (ifch,226)matarg,gin,gin3 226 format(2x,'psaini: hadron-nucleus (',i3,') cross sections:'/ * 4x,'gin,gin3=',2e10.3) write(ifmt,*)' matarg,gin,gin3:',matarg,gin,gin3 asect11(ie,iclpro,iia)=log(gin) asect13(ie,iclpro,iia)=log(gin3) enddo enddo if(isetcssave.ge.3)then if(iclpro.eq.1)then idprojin=120 elseif(iclpro.eq.2)then idprojin=1120 elseif(iclpro.eq.3)then idprojin=130 endif do ie=1,7 engy=1.5*10.**(ie-1) if(engy.le.egymin)engy=egymin if(engy.ge.egymax)engy=egymax write(ifmt,*)' simul. ',ie,' (',iclpro,')',engy if(ish.ge.1) & write(ifch,*)' simul. ',ie,' (',iclpro,')',engy do iia=1,7 matarg=2**(iia-1) latarg=min(1,matarg/2) c fctrmx=max(ftcrmxsave,float(matarg)) !to get stable pA and AA cross section, this number has to be large for large A ntevt=0 nrevt=0 pnll=-1. elab=-1. ecms=-1. ekin=-1. call conini call ainit nevent=50000 if(matarg.eq.1)nevent=1 call epocrossc(nevent,sigt,sigi,sigc,sige,sigql,sigd) c do not count non-excited diffractive projectile in inelastic sigi3=sigi-sigql if(ish.ge.1)write (ifch,228)matarg,sigi,sigi3 228 format(2x,'simul.: hadron-nucleus (',i3,') cross sections:'/ * 4x,'gin,gin3=',2e10.3) write(ifmt,*)' matarg,sigi,sigi3 :',matarg,sigi,sigi3 asect21(ie,iclpro,iia)=log(sigi) asect23(ie,iclpro,iia)=log(sigi3) c do n=1,nevent c ntry=0 c 222 ntevt=ntevt+1 c iret=0 c ntry=ntry+1 c bimevt=-1. c if(ntry.lt.10000)then cc if random sign for projectile, set it here c idproj=idprojin*(1-2*int(rangen()+0.5d0)) c call emsaaa(iret) c if(iret.gt.0)goto 222 c else c ntevt=ntry c endif c enddo c a=pi*bmax**2 c if(a.gt.0..and.ntevt.gt.0.)then c xs=anintine/float(ntevt)*a*10. c write(ifmt,*)' matarg,nevent,ntevt,bmax,xs :' c . ,matarg,anintine,ntevt,bmax,xs c write(ifch,*)' matarg,nevent,ntevt,bmax,xs :' c . ,matarg,anintine,ntevt,bmax,xs c asect2(ie,iclpro,iia)=log(xs) c else c write(ifmt,*)' Problem ? ',iclpro,matarg,bmax,ntevt c asect2(ie,iclpro,iia)=0. c endif enddo enddo else do ie=1,7 do iia=1,7 asect21(ie,iclpro,iia)=0. asect23(ie,iclpro,iia)=0. enddo enddo endif endif enddo idprojin=1120 iclpro=2 icltar=2 do ie=1,7 engy=1.5*10.**(ie-1) call paramini(0) bkmxndif=conbmxndif() if(ish.ge.1) & write(ifch,*)' calcul. AB ',ie,engy write(ifmt,*)' calcul. AB ',ie,engy do iia=1,7 maproj=2**(iia-1) laproj=max(1,maproj/2) do iib=1,7 matarg=2**(iib-1) latarg=max(1,matarg/2) sigine=0. if(matarg.eq.1.and.maproj.eq.1)then !proton-proton interaction c ine=cut+diff call psfz(2,gz2,0.) gin=gz2*pi*10. c cut iomegasave=iomega iomega=2 call psfz(2,gz2,0.) iomega=iomegasave gcut=gz2*pi*10. c diff difpart=gin-gcut c non excited projectile and target gqela=(1.-rexdif(iclpro))*(1.-rexdif(icltar))*difpart gin3=max(1.,gin-gqela) else call conini if(maproj.eq.1)then rad=radnuc(matarg) bm=rad+2. rrr=rad/difnuc(matarg) rrrm=rrr+log(9.) anorm=1.5/pi/rrr**3/(1.+(pi/rrr)**2)/difnuc(matarg)**2 c gela=(ptgau(ptfau,bm,2,1)+ptgau1(bm,2,1))*10. !sig_ela c in=cut+diff gcut=(ptgau(ptfau,bm,2,2)+ptgau1(bm,2,2))*10. !sig_in gin=gcut c cut iomegasave=iomega iomega=2 gcut=(ptgau(ptfau,bm,2,2)+ptgau1(bm,2,2))*10. !sig_cut iomega=iomegasave c diff difpart=gin-gcut c non excited projectile gqela=(1.-rexdif(iclpro)) & **(1.+rexres(iclpro)*float(matarg-1)**0.3) c non excited target gqela=gqela*(1.-rexdif(icltar))**(1.+float(matarg)**0.3) gqela=gqela*difpart gin3=max(1.,gin-gqela) elseif(matarg.eq.1)then radp=radnuc(maproj) bm=radp+2. rrrp=radp/difnuc(maproj) rrrmp=rrrp+log(9.) anormp=1.5/pi/rrrp**3/(1.+(pi/rrrp)**2)/difnuc(maproj)**2 c gtot=(ptgau(ptfau,bm,1,1)+ptgau1(bm,1,1))*10. !sig_in c in=cut+diff gcut=(ptgau(ptfau,bm,1,2)+ptgau1(bm,1,2))*10. !sig_in gin=gcut !in=cut+diff c cut iomegasave=iomega iomega=2 gcut=(ptgau(ptfau,bm,1,2)+ptgau1(bm,1,2))*10. !sig_cut iomega=iomegasave c diff difpart=gin-gcut c non excited projectile gqela=(1.-rexdif(iclpro))**(1.+float(maproj)**0.3) c non excited target gqela=gqela*(1.-rexdif(icltar)) & **(1.+rexres(icltar)*float(maproj-1)**0.3) gqela=gqela*difpart gin3=max(1.,gin-gqela) else rad=radnuc(matarg)+1. radp=radnuc(maproj)+1. bm=rad+radp+2. rrr=rad/difnuc(matarg) rrrm=rrr+log(9.) rrrp=radp/difnuc(maproj) rrrmp=rrrp+log(9.) anorm=1.5/pi/rrr**3/(1.+(pi/rrr)**2)/difnuc(matarg)**2 anormp=1.5/pi/rrrp**3/(1.+(pi/rrrp)**2)/difnuc(maproj)**2 c ine=cut+diff c gtot=(ptgau(ptfauAA,bm,2,1)+ptgau2(bm,1))*10. gcut=(ptgau(ptfauAA,bm,2,2)+ptgau2(bm,2))*10. c gin=gtot gin=gcut c cut iomegasave=iomega iomega=2 gcut=(ptgau(ptfauAA,bm,2,2)+ptgau2(bm,2))*10. !sig_cut iomega=iomegasave c diff difpart=gin-gcut c non excited projectile gqelap=(1.-rexdif(iclpro)) & **(1.+rexres(iclpro)*float(matarg-1)**0.3) gqelap=gqelap**(1.+float(maproj)**0.3) c non excited target gqelat=(1.-rexdif(icltar)) & **(1.+rexres(icltar)*float(maproj-1)**0.3) gqelat=gqelat**(1.+float(maproj)**0.3) gqela=gqelap*gqelat*difpart gin3=gin-gqela endif endif if(ish.ge.1)write (ifch,227)maproj,matarg,gin,gin3 227 format(2x,'psaini: nucleus-nucleus (',i3,'-',i3 * ,') cross sections:',/,4x,'gin,gin3=',2e10.3) write(ifmt,*)' maproj,matarg,gin,gin3 :' * ,maproj,matarg,gin,gin3 asect31(ie,iia,iib)=log(gin) asect33(ie,iia,iib)=log(gin3) enddo enddo enddo if(isetcssave.ge.3)then do ie=1,7 engy=1.5*10.**(ie-1) if(engy.le.egymin)engy=egymin if(engy.ge.egymax)engy=egymax write(ifmt,*)' AB xs ',ie,engy if(ish.ge.1) & write(ifch,*)' AB xs ',ie,engy do iia=1,7 maproj=2**(iia-1) laproj=max(1,maproj/2) do iib=1,7 matarg=2**(iib-1) latarg=max(1,matarg/2) c fctrmx=max(ftcrmxsave,float(max(maproj,matarg))) !to get stable pA and AA cross section, this number has to be large for large A ntevt=0 nrevt=0 pnll=-1. elab=-1. ecms=-1. ekin=-1. call conini call ainit nevent=10000 if(maproj+matarg.eq.2)nevent=1 call epocrossc(nevent,sigt,sigi,sigc,sige,sigql,sigd) c do not count non-excited diffractive projectile in inelastic sigi3=sigi-sigql if(ish.ge.1)write (ifch,229)maproj,matarg,sigi,sigi3 229 format(2x,'simul.: nucleus-nucleus (',i3,'-',i3 * ,') cross sections:',/,4x,'gin,gin3=',2e10.3) write(ifmt,*)' maproj,matarg,sigi,sigi3 :',maproj,matarg & ,sigi,sigi3 asect41(ie,iia,iib)=log(sigi) asect43(ie,iia,iib)=log(sigi3) c do n=1,nevent c ntry=0 c 223 ntevt=ntevt+1 c iret=0 c ntry=ntry+1 c bimevt=-1. c if(ntry.lt.10000)then c call emsaaa(iret) c if(iret.gt.0)goto 223 c else c ntevt=ntry c endif c enddo c a=pi*bmax**2 c if(a.gt.0..and.ntevt.gt.0.)then c xs=anintine/float(ntevt)*a*10. c write(ifmt,*)' maproj,matarg,nevent,ntevt,bmax,xs :' c & ,maproj,matarg,anintine,ntevt,bmax,xs c write(ifch,*)' maproj,matarg,nevent,ntevt,bmax,xs :' c & ,maproj,matarg,anintine,ntevt,bmax,xs c asect4(ie,iia,iib)=log(xs) c else c write(ifmt,*)' Problem ? ',maproj,matarg,bmax,ntevt c asect4(ie,iia,iib)=0. c endif enddo enddo enddo else do ie=1,7 do iia=1,7 do iib=1,7 asect41(ie,iia,iib)=0. asect43(ie,iia,iib)=0. enddo enddo enddo endif ifrade=ifradesave iremn=iremnsave idproj=idprojsave idprojin=idprojinsave idtarg=idtargsave idtargin=idtarginsave laproj=laprojsave latarg=latargsave maproj=maprojsave matarg=matargsave icltar=icltarsave iclpro=iclprosave engy=engysave pnll=pnllsave elab=elabsave ecms=ecmssave iclegy=iclegysave nrevt=nrevtsave nevent=neventsave ntevt=ntevtsave isetcs=isetcssave noebin=noebinsave isigma=isigmasave bminim=bminimsave bmaxim=bmaximsave bimevt=bimevtsave bkmxndif=bkmxndifsave ionudi=ionudisave c fctrmx=fctrmxsave inicnt=1 write(ifmt,'(a)')'write to inics ...' open(1,file=fncs,status='unknown') write (1,*)alpqua,alplea,alppom,slopom,gamhad,r2had,chad, *qcdlam,q2min,q2ini,betpom,glusea,naflav,factk,pt2cut write(1,*)isetcs,iclpro1,iclpro2,icltar1,icltar2,iclegy1,iclegy2 *,egylow,egymax,iomega,egyscr,epscrw,epscrp write (1,*)asect11,asect13,asect21,asect23 * ,asect31,asect33,asect41,asect43 close(1) goto 6 7 continue endif !----------isetcs.ge.2----------- endif call utprix('psaini',ish,ishini,4) return end cc----------------------------------------------------------------------- c function fjetxx(jpp,je1,je2) cc----------------------------------------------------------------------- cc almost exactly psjet, just with Eqcd replaced by fparton cc for testing cc gives indeed the same result as jetx cc so the integration seems correct cc----------------------------------------------------------------------- c double precision xx1,xx2,s2min,xmin,xmax,xmin1,xmax1,t,tmin c *,tmax,sh,z,qtmin,ft,fx1,fx2 c common /ar3/ x1(7),a1(7) c common /ar9/ x9(3),a9(3) c include 'epos.inc' c include 'epos.incsem' c c fjetxx=0. c s=engy*engy c s2min=4.d0*q2min c c zmin=s2min/dble(s) c zmax=1 c c zmin=zmin**(-delh) c zmax=zmax**(-delh) c do i=1,3 c do m=1,2 c z=dble(.5*(zmax+zmin+(zmin-zmax)*(2*m-3)*x9(i)))**(-1./delh) c xmin=dsqrt(z) c sh=z*dble(s) c qtmin=max(dble(q2min),dble(q2ini)/(1.d0-dsqrt(z))) c tmin=max(0.d0,1.d0-4.d0*qtmin/sh) c tmin=2.d0*qtmin/(1.d0+dsqrt(tmin)) c tmax=sh/2.d0 c ft=0.d0 c do i1=1,3 c do m1=1,2 c t=2.d0*tmin/(1.d0+tmin/tmax-dble(x9(i1)*(2*m1-3)) c & *(1.d0-tmin/tmax)) c qt=t*(1.d0-t/sh) c xmax=1.d0-q2ini/qt c xmin=max(dsqrt(z),z/xmax) !xm<xp !!! c if(xmin.gt.xmax.and.ish.ge.1)write(ifmt,*)'fjetxx:xmin,xmax' c * ,xmin,xmax c fx1=0.d0 c fx2=0.d0 c if(xmax.gt..8d0)then c xmin1=max(xmin,.8d0) c do i2=1,3 c do m2=1,2 c xx1=1.d0-(1.d0-xmax)*((1.d0-xmin1)/(1.d0-xmax))** c * dble(.5+x9(i2)*(m2-1.5)) c xx2=z/xx1 c fb=ffsigj(sngl(t),qt,sngl(xx1),sngl(xx2),jpp,je1,je2) c * +ffsigj(sngl(t),qt,sngl(xx2),sngl(xx1),jpp,je1,je2) c fx1=fx1+dble(a9(i2)*fb)*(1.d0/xx1-1.d0) c * *pssalf(qt/qcdlam)**2 c enddo c enddo c fx1=fx1*dlog((1.d0-xmin1)/(1.d0-xmax)) c endif c if(xmin.lt..8d0)then c xmax1=min(xmax,.8d0) c do i2=1,3 c do m2=1,2 c xx1=xmin*(xmax1/xmin)**dble(.5+x9(i2)*(m2-1.5)) c xx2=z/xx1 c c fb=0. c fb=fb c * +ffsigj(sngl(t),qt,sngl(xx1),sngl(xx2),jpp,je1,je2) c * +ffsigj(sngl(t),qt,sngl(xx2),sngl(xx1),jpp,je1,je2) c fx2=fx2+dble(a9(i2))*fb*pssalf(qt/qcdlam)**2 c enddo c enddo c fx2=fx2*dlog(xmax1/xmin) c endif c ft=ft+dble(a9(i1))*(fx1+fx2)*t**2 c enddo c enddo c ft=ft*(1.d0/tmin-1.d0/tmax) c fjetxx=fjetxx+a9(i)*sngl(ft*z**(1.+delh)/sh**2) c * /z ! ffsig = xp f xm f sigma c enddo c enddo c fjetxx=fjetxx*(zmin-zmax)/delh*pi**3 c ! * /2. !??????????????? kkkkkkkkk c return c end c c
# This file is generated. Do not modify it by hand. ## @type x : raw|complex|logical "!" <- function (x) .Primitive("!") "&" <- function (e1, e2) .Primitive("&") "*" <- function (e1, e2) .Primitive("*") "+" <- function (e1, e2) .Primitive("+") "-" <- function (e1, e2) .Primitive("-") "<" <- function (e1, e2) .Primitive("<") ">" <- function (e1, e2) .Primitive(">") "^" <- function (e1, e2) .Primitive("^") ## @type recursive : logical c <- function (..., recursive = FALSE) .Primitive("c") I <- function (x) { structure(x, class = unique(c("AsIs", oldClass(x)))) } ## @type save : character q <- function (save = "default", status = 0, runLast = TRUE) .Internal(quit(save, status, runLast)) t <- function (x) UseMethod("t") "|" <- function (e1, e2) .Primitive("|") "!=" <- function (e1, e2) .Primitive("!=") "%%" <- function (e1, e2) .Primitive("%%") ## @type pkg : character ## @type name : character "::" <- function (pkg, name) { pkg <- as.character(substitute(pkg)) name <- as.character(substitute(name)) getExportedValue(pkg, name) } "<=" <- function (e1, e2) .Primitive("<=") "==" <- function (e1, e2) .Primitive("==") ">=" <- function (e1, e2) .Primitive(">=") ## @type simplify : logical by <- function (data, INDICES, FUN, ..., simplify = TRUE) UseMethod("by") ## @type reset : logical ## @type verbose : logical gc <- function (verbose = getOption("verbose"), reset = FALSE) { res <- .Internal(gc(verbose, reset)) res <- matrix(res, 2L, 7L, dimnames = list(c("Ncells", "Vcells"), c("used", "(Mb)", "gc trigger", "(Mb)", "limit (Mb)", "max used", "(Mb)"))) if (all(is.na(res[, 5L]))) res[, -5L] else res } gl <- function (n, k, length = n * k, labels = seq_len(n), ordered = FALSE) { f <- rep_len(rep.int(seq_len(n), rep.int(k, n)), length) levels(f) <- as.character(labels) class(f) <- c(if (ordered) "ordered", "factor") f } ## @type z : complex Im <- function (z) .Primitive("Im") ls <- function (name, pos = -1L, envir = as.environment(pos), all.names = FALSE, pattern) { if (!missing(name)) { pos <- tryCatch(name, error = function(e) e) if (inherits(pos, "error")) { name <- substitute(name) if (!is.character(name)) name <- deparse(name) warning(gettextf("%s converted to character string", sQuote(name)), domain = NA) pos <- name } } all.names <- .Internal(ls(envir, all.names)) if (!missing(pattern)) { if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != length(grep("]", pattern, fixed = TRUE))) { if (pattern == "[") { pattern <- "\\[" warning("replaced regular expression pattern '[' by '\\\\['") } else if (length(grep("[^\\\\]\\[<-", pattern))) { pattern <- sub("\\[<-", "\\\\\\[<-", pattern) warning("replaced '[<-' by '\\\\[<-' in regular expression pattern") } } grep(pattern, all.names, value = TRUE) } else all.names } ## @type x : complex qr <- function (x, ...) UseMethod("qr") ## @type z : complex Re <- function (z) .Primitive("Re") ## @type list : character rm <- function (..., list = character(), pos = -1, envir = as.environment(pos), inherits = FALSE) { dots <- match.call(expand.dots = FALSE)$... if (length(dots) && !all(sapply(dots, function(x) is.symbol(x) || is.character(x)))) stop("... must contain names or character strings") names <- sapply(dots, as.character) if (length(names) == 0L) names <- character() list <- .Primitive("c")(list, names) .Internal(remove(list, envir, inherits)) } ## @type y : complex ## @type x : complex "%*%" <- function (x, y) .Primitive("%*%") "%o%" <- function (X, Y) outer(X, Y) "%x%" <- function (X, Y) kronecker(X, Y) ## @type name : character ## @type pkg : character ":::" <- function (pkg, name) { pkg <- as.character(substitute(pkg)) name <- as.character(substitute(name)) get(name, envir = asNamespace(pkg), inherits = FALSE) } ## @type x : complex abs <- function (x) .Primitive("abs") ## @type na.rm : logical ## @return logical all <- function (..., na.rm = FALSE) .Primitive("all") ## @type na.rm : logical ## @return logical any <- function (..., na.rm = FALSE) .Primitive("any") ## @type z : complex Arg <- function (z) .Primitive("Arg") ## @type file : character ## @type labels : character ## @type sep : character ## @type append : logical|character ## @type fill : numeric|logical cat <- function (..., file = "", sep = " ", fill = FALSE, labels = NULL, append = FALSE) { if (is.character(file)) if (file == "") file <- stdout() else if (substring(file, 1L, 1L) == "|") { file <- pipe(substring(file, 2L), "w") on.exit(close(file)) } else { file <- file(file, ifelse(append, "a", "w")) on.exit(close(file)) } .Internal(cat(list(...), file, sep, fill, labels, append)) } ## @type as.factor : logical col <- function (x, as.factor = FALSE) { if (as.factor) { labs <- colnames(x, do.NULL = FALSE, prefix = "") res <- factor(.Internal(col(dim(x))), labels = labs) dim(res) <- dim(x) res } else .Internal(col(dim(x))) } ## @type x : complex cos <- function (x) .Primitive("cos") ## @type x : numeric cut <- function (x, ...) UseMethod("cut") ## @type x : logical|numeric ## @return numeric det <- function (x, ...) { z <- determinant(x, logarithm = TRUE, ...) c(z$sign * exp(z$modulus)) } dim <- function (x) .Primitive("dim") ## @type no.. : logical ## @type full.names : logical ## @type include.dirs : logical ## @type ignore.case : logical ## @type recursive : logical ## @type path : character ## @type all.files : logical ## @return character dir <- function (path = ".", pattern = NULL, all.files = FALSE, full.names = FALSE, recursive = FALSE, ignore.case = FALSE, include.dirs = FALSE, no.. = FALSE) .Internal(list.files(path, pattern, all.files, full.names, recursive, ignore.case, include.dirs, no..)) ## @type x : complex exp <- function (x) .Primitive("exp") ## @type envir : character ## @type pos : character ## @type x : character get <- function (x, pos = -1L, envir = as.environment(pos), mode = "any", inherits = TRUE) .Internal(get(x, envir, mode, inherits)) ## @type x : complex ## @type base : complex log <- function (x, base = exp(1)) .Primitive("log") Map <- function (f, ...) { f <- match.fun(f) mapply(FUN = f, ..., SIMPLIFY = FALSE) } ## @type na.rm : logical max <- function (..., na.rm = FALSE) .Primitive("max") ## @return numeric|character min <- function (..., na.rm = FALSE) .Primitive("min") ## @type z : complex Mod <- function (z) .Primitive("Mod") raw <- function (length = 0L) .Internal(vector("raw", length)) rep <- function (x, ...) .Primitive("rep") rev <- function (x) UseMethod("rev") rle <- function (x) { if (!is.vector(x) && !is.list(x)) stop("'x' must be a vector of an atomic type") n <- length(x) if (n == 0L) return(structure(list(lengths = integer(), values = x), class = "rle")) y <- x[-1L] != x[-n] i <- c(which(y | is.na(y)), n) structure(list(lengths = diff(c(0L, i)), values = x[i]), class = "rle") } ## @type as.factor : logical row <- function (x, as.factor = FALSE) { if (as.factor) { labs <- rownames(x, do.NULL = FALSE, prefix = "") res <- factor(.Internal(row(dim(x))), labels = labs) dim(res) <- dim(x) res } else .Internal(row(dim(x))) } seq <- function (...) UseMethod("seq") ## @type x : complex sin <- function (x) .Primitive("sin") ## @type na.rm : logical sum <- function (..., na.rm = FALSE) .Primitive("sum") ## @type LINPACK : logical ## @type nu : complex ## @type x : complex ## @type nv : complex svd <- function (x, nu = min(n, p), nv = min(n, p), LINPACK = FALSE) { x <- as.matrix(x) if (any(!is.finite(x))) stop("infinite or missing values in 'x'") dx <- dim(x) n <- dx[1L] p <- dx[2L] if (!n || !p) stop("a dimension is zero") La.res <- La.svd(x, nu, nv) res <- list(d = La.res$d) if (nu) res$u <- La.res$u if (nv) { if (is.complex(x)) res$v <- Conj(t(La.res$vt)) else res$v <- t(La.res$vt) } res } ## @type x : complex tan <- function (x) .Primitive("tan") ## @type silent : logical try <- function (expr, silent = FALSE) { tryCatch(expr, error = function(e) { call <- conditionCall(e) if (!is.null(call)) { if (identical(call[[1L]], quote(doTryCatch))) call <- sys.call(-4L) dcall <- deparse(call)[1L] prefix <- paste("Error in", dcall, ": ") LONG <- 75L msg <- conditionMessage(e) sm <- strsplit(msg, "\n")[[1L]] w <- 14L + nchar(dcall, type = "w") + nchar(sm[1L], type = "w") if (is.na(w)) w <- 14L + nchar(dcall, type = "b") + nchar(sm[1L], type = "b") if (w > LONG) prefix <- paste0(prefix, "\n ") } else prefix <- "Error : " msg <- paste0(prefix, conditionMessage(e), "\n") .Internal(seterrmessage(msg[1L])) if (!silent && identical(getOption("show.error.messages"), TRUE)) { cat(msg, file = stderr()) .Internal(printDeferredWarnings()) } invisible(structure(msg, class = "try-error", condition = e)) }) } ## @type open : character ## @type description : character ## @type encoding : character unz <- function (description, filename, open = "", encoding = getOption("encoding")) .Internal(unz(paste(description, filename, sep = ":"), open, encoding)) ## @type description : character ## @type open : character ## @type encoding : character ## @type blocking : logical url <- function (description, open = "", blocking = TRUE, encoding = getOption("encoding")) .Internal(url(description, open, blocking, encoding)) ## @type x : raw|complex|logical ## @type y : raw|complex|logical xor <- function (x, y) { (x | y) & !(x & y) } "%in%" <- function (x, table) match(x, table, nomatch = 0L) > 0L ## @type x : complex acos <- function (x) .Primitive("acos") ## @type x : complex asin <- function (x) .Primitive("asin") ## @type complete : logical ## @type flag : logical asS3 <- function (object, flag = TRUE, complete = TRUE) .Internal(setS4Object(object, !as.logical(flag), complete)) ## @type flag : logical ## @type complete : logical asS4 <- function (object, flag = TRUE, complete = TRUE) .Internal(setS4Object(object, flag, complete)) ## @type x : complex atan <- function (x) .Primitive("atan") attr <- function (x, which, exact = FALSE) .Primitive("attr") ## @type b : numeric ## @type a : numeric beta <- function (a, b) .Internal(beta(a, b)) body <- function (fun = sys.function(sys.parent())) { if (is.character(fun)) fun <- get(fun, mode = "function", envir = parent.frame()) .Internal(body(fun)) } ## @type name : character call <- function (name, ...) .Primitive("call") ## @type x : logical|numeric chol <- function (x, ...) UseMethod("chol") ## @type z : complex Conj <- function (z) .Primitive("Conj") ## @type x : complex cosh <- function (x) .Primitive("cosh") date <- function () .Internal(date()) dget <- function (file) eval(parse(file = file)) diag <- function (x = 1, nrow, ncol) { if (is.matrix(x)) { if (nargs() > 1L) stop("'nrow' or 'ncol' cannot be specified when 'x' is a matrix") if ((m <- min(dim(x))) == 0L) return(vector(typeof(x), 0L)) y <- c(x)[1 + 0L:(m - 1L) * (dim(x)[1L] + 1)] nms <- dimnames(x) if (is.list(nms) && !any(sapply(nms, is.null)) && identical((nm <- nms[[1L]][seq_len(m)]), nms[[2L]][seq_len(m)])) names(y) <- nm return(y) } if (is.array(x) && length(dim(x)) != 1L) stop("'x' is an array, but not one-dimensional.") if (missing(x)) n <- nrow else if (length(x) == 1L && nargs() == 1L) { n <- as.integer(x) x <- 1 } else n <- length(x) if (!missing(nrow)) n <- nrow if (missing(ncol)) ncol <- n .Internal(diag(x, n, ncol)) } ## @type x : numeric diff <- function (x, ...) UseMethod("diff") ## @type file : character ## @type control : character dput <- function (x, file = "", control = c("keepNA", "keepInteger", "showAttributes")) { if (is.character(file)) if (nzchar(file)) { file <- file(file, "wt") on.exit(close(file)) } else file <- stdout() opts <- .deparseOpts(control) if (isS4(x)) { clx <- class(x) cat("new(\"", clx, "\"\n", file = file, sep = "") for (n in .slotNames(clx)) { cat(" ,", n, "= ", file = file) dput(slot(x, n), file = file, control = control) } cat(")\n", file = file) invisible() } else .Internal(dput(x, file, opts)) } drop <- function (x) .Internal(drop(x)) ## @return character dump <- function (list, file = "dumpdata.R", append = FALSE, control = "all", envir = parent.frame(), evaluate = TRUE) { if (is.character(file)) { ex <- sapply(list, exists, envir = envir) if (!any(ex)) return(invisible(character())) if (nzchar(file)) { file <- file(file, ifelse(append, "a", "w")) on.exit(close(file), add = TRUE) } else file <- stdout() } opts <- .deparseOpts(control) .Internal(dump(list, file, envir, opts, evaluate)) } eval <- function (expr, envir = parent.frame(), enclos = if (is.list(envir) || is.pairlist(envir)) parent.frame() else baseenv()) .Internal(eval(expr, envir, enclos)) ## @type description : character ## @type encoding : character ## @type open : character ## @type blocking : logical fifo <- function (description, open = "", blocking = FALSE, encoding = getOption("encoding")) .Internal(fifo(description, open, blocking, encoding)) ## @type description : character ## @type encoding : character ## @type raw : raw|logical|character ## @type open : character ## @type blocking : logical file <- function (description = "", open = "", blocking = TRUE, encoding = getOption("encoding"), raw = FALSE) .Internal(file(description, open, blocking, encoding, raw)) ## @type right : logical Find <- function (f, x, right = FALSE, nomatch = NULL) { f <- match.fun(f) if ((pos <- Position(f, x, right, nomatch = 0L)) > 0L) x[[pos]] else nomatch } ## @type invert : logical ## @type value : integer ## @type pattern : character ## @type fixed : logical|character ## @type useBytes : logical ## @type x : character ## @type perl : logical ## @return logical|integer|character grep <- function (pattern, x, ignore.case = FALSE, perl = FALSE, value = FALSE, fixed = FALSE, useBytes = FALSE, invert = FALSE) { if (!is.character(x)) x <- structure(as.character(x), names = names(x)) .Internal(grep(as.character(pattern), x, ignore.case, value, perl, fixed, useBytes, invert)) } ## @type replacement : character ## @type x : character ## @type fixed : logical|character ## @type pattern : character ## @type perl : logical ## @type useBytes : logical gsub <- function (pattern, replacement, x, ignore.case = FALSE, perl = FALSE, fixed = FALSE, useBytes = FALSE) { if (!is.character(x)) x <- as.character(x) .Internal(gsub(as.character(pattern), as.character(replacement), x, ignore.case, perl, fixed, useBytes)) } is.R <- function () exists("version") && !is.null(vl <- version$language) && vl == "R" isS4 <- function (object) .Primitive("isS4") list <- function (...) .Primitive("list") load <- function (file, envir = parent.frame(), verbose = FALSE) { if (is.character(file)) { con <- gzfile(file) on.exit(close(con)) magic <- readChar(con, 5L, useBytes = TRUE) if (!length(magic)) stop("empty (zero-byte) input file") if (!grepl("RD[AX]2\n", magic)) { if (grepl("RD[ABX][12]\r", magic)) stop("input has been corrupted, with LF replaced by CR") warning(sprintf("file %s has magic number '%s'\n", sQuote(basename(file)), gsub("[\n\r]*", "", magic)), " ", "Use of save versions prior to 2 is deprecated", domain = NA, call. = FALSE) return(.Internal(load(file, envir))) } } else if (inherits(file, "connection")) { con <- if (inherits(file, "gzfile") || inherits(file, "gzcon")) file else gzcon(file) } else stop("bad 'file' argument") if (verbose) cat("Loading objects:\n") .Internal(loadFromConn2(con, envir, verbose)) } ## @type x : complex log2 <- function (x) .Primitive("log2") ## @type base : complex ## @type x : complex logb <- function (x, base = exp(1)) if (missing(base)) log(x) else log(x, base) mean <- function (x, ...) UseMethod("mean") ## @type x : character ## @type envir : character mget <- function (x, envir = as.environment(-1L), mode = "any", ifnotfound, inherits = FALSE) .Internal(mget(x, envir, mode, if (missing(ifnotfound)) list(function(x) stop(gettextf("value for %s not found", sQuote(x)), call. = FALSE)) else ifnotfound, inherits)) mode <- function (x) { if (is.expression(x)) return("expression") if (is.call(x)) return(switch(deparse(x[[1L]])[1L], `(` = "(", "call")) if (is.name(x)) "name" else switch(tx <- typeof(x), double = , integer = "numeric", closure = , builtin = , special = "function", tx) } NCOL <- function (x) if (length(d <- dim(x)) > 1L) d[2L] else 1L ## @type type : character ## @type x : numeric norm <- function (x, type = c("O", "I", "F", "M", "2")) { if (identical("2", type)) { svd(x, nu = 0L, nv = 0L)$d[1L] } else .Internal(La_dlange(x, type)) } NROW <- function (x) if (length(d <- dim(x))) d[1L] else length(x) open <- function (con, ...) UseMethod("open") ## @type encoding : character ## @type description : character ## @type open : character pipe <- function (description, open = "", encoding = getOption("encoding")) .Internal(pipe(description, open, encoding)) ## @return numeric|character pmax <- function (..., na.rm = FALSE) { elts <- list(...) if (length(elts) == 0L) stop("no arguments") if (all(vapply(elts, function(x) is.atomic(x) && !is.object(x), NA))) { mmm <- .Internal(pmax(na.rm, ...)) } else { mmm <- elts[[1L]] attr(mmm, "dim") <- NULL has.na <- FALSE for (each in elts[-1L]) { attr(each, "dim") <- NULL l1 <- length(each) l2 <- length(mmm) if (l2 < l1) { if (l2 && l1%%l2) warning("an argument will be fractionally recycled") mmm <- rep(mmm, length.out = l1) } else if (l1 && l1 < l2) { if (l2%%l1) warning("an argument will be fractionally recycled") each <- rep(each, length.out = l2) } nas <- cbind(is.na(mmm), is.na(each)) if (has.na || (has.na <- any(nas))) { mmm[nas[, 1L]] <- each[nas[, 1L]] each[nas[, 2L]] <- mmm[nas[, 2L]] } change <- mmm < each change <- change & !is.na(change) mmm[change] <- each[change] if (has.na && !na.rm) mmm[nas[, 1L] | nas[, 2L]] <- NA } } mostattributes(mmm) <- attributes(elts[[1L]]) mmm } ## @return numeric|character pmin <- function (..., na.rm = FALSE) { elts <- list(...) if (length(elts) == 0L) stop("no arguments") if (all(vapply(elts, function(x) is.atomic(x) && !is.object(x), NA))) { mmm <- .Internal(pmin(na.rm, ...)) } else { mmm <- elts[[1L]] attr(mmm, "dim") <- NULL has.na <- FALSE for (each in elts[-1L]) { attr(each, "dim") <- NULL l1 <- length(each) l2 <- length(mmm) if (l2 < l1) { if (l2 && l1%%l2) warning("an argument will be fractionally recycled") mmm <- rep(mmm, length.out = l1) } else if (l1 && l1 < l2) { if (l2%%l1) warning("an argument will be fractionally recycled") each <- rep(each, length.out = l2) } nas <- cbind(is.na(mmm), is.na(each)) if (has.na || (has.na <- any(nas))) { mmm[nas[, 1L]] <- each[nas[, 1L]] each[nas[, 2L]] <- mmm[nas[, 2L]] } change <- mmm > each change <- change & !is.na(change) mmm[change] <- each[change] if (has.na && !na.rm) mmm[nas[, 1L] | nas[, 2L]] <- NA } } mostattributes(mmm) <- attributes(elts[[1L]]) mmm } ## @type na.rm : logical prod <- function (..., na.rm = FALSE) .Primitive("prod") ## @type complete : logical qr.Q <- function (qr, complete = FALSE, Dvec) { if (!is.qr(qr)) stop("argument is not a QR decomposition") dqr <- dim(qr$qr) n <- dqr[1L] cmplx <- mode(qr$qr) == "complex" if (missing(Dvec)) Dvec <- rep.int(if (cmplx) 1 + (0+0i) else 1, if (complete) n else min(dqr)) D <- if (complete) diag(Dvec, n) else { ncols <- min(dqr) diag(Dvec[seq_len(ncols)], nrow = n, ncol = ncols) } qr.qy(qr, D) } ## @type complete : logical qr.R <- function (qr, complete = FALSE, ...) { if (!is.qr(qr)) stop("argument is not a QR decomposition") if (!missing(...)) warning(sprintf(ngettext(length(list(...)), "extra argument %s will be disregarded", "extra arguments %s will be disregarded"), paste(sQuote(names(list(...))), collapse = ", ")), domain = NA) R <- qr$qr if (!complete) R <- R[seq.int(min(dim(R))), , drop = FALSE] R[row(R) > col(R)] <- 0 R } ## @type ncol : complex ## @type complete : logical qr.X <- function (qr, complete = FALSE, ncol = if (complete) nrow(R) else min(dim(R))) { if (!is.qr(qr)) stop("argument is not a QR decomposition") pivoted <- !identical(qr$pivot, ip <- seq_along(qr$pivot)) R <- qr.R(qr, complete = TRUE) if (pivoted && ncol < length(qr$pivot)) stop("need larger value of 'ncol' as pivoting occurred") cmplx <- mode(R) == "complex" p <- as.integer(dim(R)[2L]) if (is.na(p)) stop("invalid NCOL(R)") if (ncol < p) R <- R[, seq_len(ncol), drop = FALSE] else if (ncol > p) { tmp <- diag(if (!cmplx) 1 else 1 + (0+0i), nrow(R), ncol) tmp[, seq_len(p)] <- R R <- tmp } res <- qr.qy(qr, R) cn <- colnames(res) if (pivoted) { res[, qr$pivot] <- res[, ip] if (!is.null(cn)) colnames(res)[qr$pivot] <- cn[ip] } res } ## @type save : character quit <- function (save = "default", status = 0, runLast = TRUE) .Internal(quit(save, status, runLast)) ## @type ties.method : character ## @type x : complex|logical|character rank <- function (x, na.last = TRUE, ties.method = c("average", "first", "random", "max", "min")) { nas <- is.na(x) nm <- names(x) ties.method <- match.arg(ties.method) if (is.factor(x)) x <- as.integer(x) xx <- x[!nas] y <- switch(ties.method, average = , min = , max = .Internal(rank(xx, length(xx), ties.method)), first = sort.list(sort.list(xx)), random = sort.list(order(xx, stats::runif(sum(!nas))))) if (!is.na(na.last) && any(nas)) { yy <- integer(length(x)) storage.mode(yy) <- storage.mode(y) yy <- NA NAkeep <- (na.last == "keep") if (NAkeep || na.last) { yy[!nas] <- y if (!NAkeep) yy[nas] <- (length(y) + 1L):length(yy) } else { len <- sum(nas) yy[!nas] <- y + len yy[nas] <- 1L:len } y <- yy names(y) <- nm } else names(y) <- nm[!nas] y } save <- function (..., list = character(), file = stop("'file' must be specified"), ascii = FALSE, version = NULL, envir = parent.frame(), compress = !ascii, compression_level, eval.promises = TRUE, precheck = TRUE) { opts <- getOption("save.defaults") if (missing(compress) && !is.null(opts$compress)) compress <- opts$compress if (missing(compression_level) && !is.null(opts$compression_level)) compression_level <- opts$compression_level if (missing(ascii) && !is.null(opts$ascii)) ascii <- opts$ascii if (missing(version)) version <- opts$version if (!is.null(version) && version < 2) warning("Use of save versions prior to 2 is deprecated", domain = NA) names <- as.character(substitute(list(...)))[-1L] if (missing(list) && !length(names)) warning("nothing specified to be save()d") list <- c(list, names) if (!is.null(version) && version == 1) .Internal(save(list, file, ascii, version, envir, eval.promises)) else { if (precheck) { ok <- unlist(lapply(list, exists, envir = envir)) if (!all(ok)) { n <- sum(!ok) stop(sprintf(ngettext(n, "object %s not found", "objects %s not found"), paste(sQuote(list[!ok]), collapse = ", ")), domain = NA) } } if (is.character(file)) { if (!nzchar(file)) stop("'file' must be non-empty string") if (!is.character(compress)) { if (!is.logical(compress)) stop("'compress' must be logical or character") compress <- if (compress) "gzip" else "no compression" } con <- switch(compress, bzip2 = { if (!missing(compression_level)) bzfile(file, "wb", compression = compression_level) else bzfile(file, "wb") }, xz = { if (!missing(compression_level)) xzfile(file, "wb", compression = compression_level) else xzfile(file, "wb", compression = 9) }, gzip = { if (!missing(compression_level)) gzfile(file, "wb", compression = compression_level) else gzfile(file, "wb") }, `no compression` = file(file, "wb"), stop(gettextf("'compress = \"%s\"' is invalid", compress))) on.exit(close(con)) } else if (inherits(file, "connection")) con <- file else stop("bad file argument") if (isOpen(con) && summary(con)$text != "binary") stop("can only save to a binary connection") .Internal(saveToConn(list, con, ascii, version, envir, eval.promises)) } } scan <- function (file = "", what = double(), nmax = -1L, n = -1L, sep = "", quote = if (identical(sep, "\n")) "" else "'\"", dec = ".", skip = 0L, nlines = 0L, na.strings = "NA", flush = FALSE, fill = FALSE, strip.white = FALSE, quiet = FALSE, blank.lines.skip = TRUE, multi.line = TRUE, comment.char = "", allowEscapes = FALSE, fileEncoding = "", encoding = "unknown", text, skipNul = FALSE) { na.strings <- as.character(na.strings) if (!missing(n)) { if (missing(nmax)) nmax <- n/pmax(length(what), 1L) else stop("either specify 'nmax' or 'n', but not both.") } if (missing(file) && !missing(text)) { file <- textConnection(text, encoding = "UTF-8") encoding <- "UTF-8" on.exit(close(file)) } if (is.character(file)) if (file == "") file <- stdin() else { file <- if (nzchar(fileEncoding)) file(file, "r", encoding = fileEncoding) else file(file, "r") on.exit(close(file)) } if (!inherits(file, "connection")) stop("'file' must be a character string or connection") .Internal(scan(file, what, nmax, sep, dec, quote, skip, nlines, na.strings, flush, fill, strip.white, quiet, blank.lines.skip, multi.line, comment.char, allowEscapes, encoding, skipNul)) } seek <- function (con, ...) UseMethod("seek") ## @type x : numeric sign <- function (x) .Primitive("sign") ## @type x : complex sinh <- function (x) .Primitive("sinh") ## @type type : character ## @type file : character ## @type split : logical ## @type append : logical sink <- function (file = NULL, append = FALSE, type = c("output", "message"), split = FALSE) { type <- match.arg(type) if (type == "message") { if (is.null(file)) file <- stderr() else if (!inherits(file, "connection") || !isOpen(file)) stop("'file' must be NULL or an already open connection") if (split) stop("cannot split the message connection") .Internal(sink(file, FALSE, TRUE, FALSE)) } else { closeOnExit <- FALSE if (is.null(file)) file <- -1L else if (is.character(file)) { file <- file(file, ifelse(append, "a", "w")) closeOnExit <- TRUE } else if (!inherits(file, "connection")) stop("'file' must be NULL, a connection or a character string") .Internal(sink(file, closeOnExit, FALSE, split)) } } ## @optional x sort <- function (x, decreasing = FALSE, ...) { if (!is.logical(decreasing) || length(decreasing) != 1L) stop("'decreasing' must be a length-1 logical vector.\nDid you intend to set 'partial'?") UseMethod("sort") } ## @type x : complex sqrt <- function (x) .Primitive("sqrt") ## @type call. : logical stop <- function (..., call. = TRUE, domain = NULL) { args <- list(...) if (length(args) == 1L && inherits(args[[1L]], "condition")) { cond <- args[[1L]] if (nargs() > 1L) warning("additional arguments ignored in stop()") message <- conditionMessage(cond) call <- conditionCall(cond) .Internal(.signalCondition(cond, message, call)) .Internal(.dfltStop(message, call)) } else .Internal(stop(call., .makeMessage(..., domain = domain))) } ## @type x : complex tanh <- function (x) .Primitive("tanh") with <- function (data, expr, ...) UseMethod("with") ## @type x : complex acosh <- function (x) .Primitive("acosh") addNA <- function (x, ifany = FALSE) { if (!is.factor(x)) x <- factor(x) if (ifany & !anyNA(x)) return(x) ll <- levels(x) if (!anyNA(ll)) ll <- c(ll, NA) factor(x, levels = ll, exclude = NULL) } ## @type x : character ## @type pattern : character ## @type costs : numeric ## @type value : integer ## @type max.distance : integer ## @type useBytes : logical ## @type fixed : logical agrep <- function (pattern, x, max.distance = 0.1, costs = NULL, ignore.case = FALSE, value = FALSE, fixed = TRUE, useBytes = FALSE) { pattern <- as.character(pattern) if (!is.character(x)) x <- as.character(x) costs <- as.integer(.amatch_costs(costs)) bounds <- .amatch_bounds(max.distance) .Internal(agrep(pattern, x, ignore.case, value, costs, bounds, useBytes, fixed)) } alist <- function (...) as.list(sys.call())[-1L] anyNA <- function (x) .Primitive("anyNA") ## @type perm : complex|character aperm <- function (a, perm, ...) UseMethod("aperm") apply <- function (X, MARGIN, FUN, ...) { FUN <- match.fun(FUN) dl <- length(dim(X)) if (!dl) stop("dim(X) must have a positive length") if (is.object(X)) X <- if (dl == 2L) as.matrix(X) else as.array(X) d <- dim(X) dn <- dimnames(X) ds <- seq_len(dl) if (is.character(MARGIN)) { if (is.null(dnn <- names(dn))) stop("'X' must have named dimnames") MARGIN <- match(MARGIN, dnn) if (anyNA(MARGIN)) stop("not all elements of 'MARGIN' are names of dimensions") } s.call <- ds[-MARGIN] s.ans <- ds[MARGIN] d.call <- d[-MARGIN] d.ans <- d[MARGIN] dn.call <- dn[-MARGIN] dn.ans <- dn[MARGIN] d2 <- prod(d.ans) if (d2 == 0L) { newX <- array(vector(typeof(X), 1L), dim = c(prod(d.call), 1L)) ans <- FUN(if (length(d.call) < 2L) newX[, 1] else array(newX[, 1L], d.call, dn.call), ...) return(if (is.null(ans)) ans else if (length(d.ans) < 2L) ans[1L][-1L] else array(ans, d.ans, dn.ans)) } newX <- aperm(X, c(s.call, s.ans)) dim(newX) <- c(prod(d.call), d2) ans <- vector("list", d2) if (length(d.call) < 2L) { if (length(dn.call)) dimnames(newX) <- c(dn.call, list(NULL)) for (i in 1L:d2) { tmp <- FUN(newX[, i], ...) if (!is.null(tmp)) ans[[i]] <- tmp } } else for (i in 1L:d2) { tmp <- FUN(array(newX[, i], d.call, dn.call), ...) if (!is.null(tmp)) ans[[i]] <- tmp } ans.list <- is.recursive(ans[[1L]]) l.ans <- length(ans[[1L]]) ans.names <- names(ans[[1L]]) if (!ans.list) ans.list <- any(unlist(lapply(ans, length)) != l.ans) if (!ans.list && length(ans.names)) { all.same <- vapply(ans, function(x) identical(names(x), ans.names), NA) if (!all(all.same)) ans.names <- NULL } len.a <- if (ans.list) d2 else length(ans <- unlist(ans, recursive = FALSE)) if (length(MARGIN) == 1L && len.a == d2) { names(ans) <- if (length(dn.ans[[1L]])) dn.ans[[1L]] return(ans) } if (len.a == d2) return(array(ans, d.ans, dn.ans)) if (len.a && len.a%%d2 == 0L) { if (is.null(dn.ans)) dn.ans <- vector(mode = "list", length(d.ans)) dn.ans <- c(list(ans.names), dn.ans) return(array(ans, c(len.a%/%d2, d.ans), if (!all(vapply(dn.ans, is.null, NA))) dn.ans)) } return(ans) } ## @type dimnames : complex|character ## @type dim : integer array <- function (data = NA, dim = length(data), dimnames = NULL) { if (is.atomic(data) && !is.object(data)) return(.Internal(array(data, dim, dimnames))) data <- as.vector(data) if (is.object(data)) { dim <- as.integer(dim) if (!length(dim)) stop("'dims' cannot be of length 0") vl <- prod(dim) if (length(data) != vl) { if (vl > .Machine$integer.max) stop("'dim' specifies too large an array") data <- rep_len(data, vl) } if (length(dim)) dim(data) <- dim if (is.list(dimnames) && length(dimnames)) dimnames(data) <- dimnames data } else .Internal(array(data, dim, dimnames)) } ## @type x : complex as.qr <- function (x) stop("you cannot be serious", domain = NA) ## @type x : complex asinh <- function (x) .Primitive("asinh") ## @type x : complex ## @type y : complex atan2 <- function (y, x) .Internal(atan2(y, x)) ## @type x : complex atanh <- function (x) .Primitive("atanh") ## @type deparse.level : integer cbind <- function (..., deparse.level = 1) .Internal(cbind(deparse.level, ...)) class <- function (x) .Primitive("class") close <- function (con, ...) UseMethod("close") ## @type x : complex cospi <- function (x) .Primitive("cospi") ## @type text : character debug <- function (fun, text = "", condition = NULL) .Internal(debug(fun, text, condition)) ## @type value : numeric "dim<-" <- function (x, value) .Primitive("dim<-") eigen <- function (x, symmetric, only.values = FALSE, EISPACK = FALSE) { x <- as.matrix(x) n <- nrow(x) if (!n) stop("0 x 0 matrix") if (n != ncol(x)) stop("non-square matrix in 'eigen'") n <- as.integer(n) if (is.na(n)) stop("invalid nrow(x)") complex.x <- is.complex(x) if (!all(is.finite(x))) stop("infinite or missing values in 'x'") if (missing(symmetric)) symmetric <- isSymmetric.matrix(x) if (symmetric) { z <- if (!complex.x) .Internal(La_rs(x, only.values)) else .Internal(La_rs_cmplx(x, only.values)) ord <- rev(seq_along(z$values)) } else { z <- if (!complex.x) .Internal(La_rg(x, only.values)) else .Internal(La_rg_cmplx(x, only.values)) ord <- sort.list(Mod(z$values), decreasing = TRUE) } return(list(values = z$values[ord], vectors = if (!only.values) z$vectors[, ord, drop = FALSE])) } evalq <- function (expr, envir = parent.frame(), enclos = if (is.list(envir) || is.pairlist(envir)) parent.frame() else baseenv()) .Internal(eval(substitute(expr), envir, enclos)) ## @type x : complex expm1 <- function (x) .Primitive("expm1") ## @type x : complex floor <- function (x) .Primitive("floor") flush <- function (con) UseMethod("flush") force <- function (x) x ## @type x : numeric gamma <- function (x) .Primitive("gamma") getwd <- function () .Internal(getwd()) ## @type x : character ## @type fixed : logical|character ## @type perl : logical ## @type pattern : character ## @type useBytes : logical grepl <- function (pattern, x, ignore.case = FALSE, perl = FALSE, fixed = FALSE, useBytes = FALSE) { if (!is.character(x)) x <- as.character(x) .Internal(grepl(as.character(pattern), x, ignore.case, FALSE, perl, fixed, useBytes, FALSE)) } ## @type allowNonCompressed : logical ## @type level : integer gzcon <- function (con, level = 6, allowNonCompressed = TRUE) .Internal(gzcon(con, level, allowNonCompressed)) ## @type toRaw : raw|logical|character ## @type x : raw|character ## @type mark : logical ## @type from : character ## @type sub : character ## @type to : character iconv <- function (x, from = "", to = "", sub = NA, mark = TRUE, toRaw = FALSE) { if (!(is.character(x) || (is.list(x) && is.null(oldClass(x))))) x <- as.character(x) .Internal(iconv(x, from, to, as.character(sub), mark, toRaw)) } is.na <- function (x) .Primitive("is.na") ## @type x : complex is.qr <- function (x) inherits(x, "qr") kappa <- function (z, ...) UseMethod("kappa") ## @type a : numeric ## @type b : numeric lbeta <- function (a, b) .Internal(lbeta(a, b)) local <- function (expr, envir = new.env()) eval.parent(substitute(eval(quote(expr), envir))) log10 <- function (x) .Primitive("log10") ## @type x : complex log1p <- function (x) .Primitive("log1p") ## @type nomatch : integer match <- function (x, table, nomatch = NA_integer_, incomparables = NULL) .Internal(match(x, table, nomatch, incomparables)) merge <- function (x, y, ...) UseMethod("merge") names <- function (x) .Primitive("names") nargs <- function () .Primitive("nargs") ## @type type : character ## @type allowNA : logical ## @type x : character nchar <- function (x, type = "chars", allowNA = FALSE) .Internal(nchar(x, type, allowNA)) ## @type decreasing : logical order <- function (..., na.last = TRUE, decreasing = FALSE) { z <- list(...) if (any(unlist(lapply(z, is.object)))) { z <- lapply(z, function(x) if (is.object(x)) xtfrm(x) else x) if (!is.na(na.last)) return(do.call("order", c(z, na.last = na.last, decreasing = decreasing))) } else if (!is.na(na.last)) { if (length(z) == 1L && is.factor(zz <- z[[1L]]) && nlevels(zz) < 1e+05) return(.Internal(radixsort(zz, na.last, decreasing))) else return(.Internal(order(na.last, decreasing, ...))) } if (any(diff(l.z <- vapply(z, length, 1L)) != 0L)) stop("argument lengths differ") ans <- vapply(z, is.na, rep.int(NA, l.z[1L])) ok <- if (is.matrix(ans)) !apply(ans, 1, any) else !any(ans) if (all(!ok)) return(integer()) z[[1L]][!ok] <- NA ans <- do.call("order", c(z, decreasing = decreasing)) keep <- seq_along(ok)[ok] ans[ans %in% keep] } outer <- function (X, Y, FUN = "*", ...) { if (is.array(X)) { dX <- dim(X) nx <- dimnames(X) no.nx <- is.null(nx) } else { dX <- length(X) no.nx <- is.null(names(X)) if (!no.nx) nx <- list(names(X)) } if (is.array(Y)) { dY <- dim(Y) ny <- dimnames(Y) no.ny <- is.null(ny) } else { dY <- length(Y) no.ny <- is.null(names(Y)) if (!no.ny) ny <- list(names(Y)) } if (is.character(FUN) && FUN == "*") { if (!missing(...)) stop("using ... with FUN = \"*\" is an error") robj <- as.vector(X) %*% t(as.vector(Y)) dim(robj) <- c(dX, dY) } else { FUN <- match.fun(FUN) Y <- rep(Y, rep.int(length(X), length(Y))) if (length(X)) X <- rep(X, times = ceiling(length(Y)/length(X))) robj <- FUN(X, Y, ...) dim(robj) <- c(dX, dY) } if (!(no.nx && no.ny)) { if (no.nx) nx <- vector("list", length(dX)) else if (no.ny) ny <- vector("list", length(dY)) dimnames(robj) <- c(nx, ny) } robj } parse <- function (file = "", n = NULL, text = NULL, prompt = "?", keep.source = getOption("keep.source"), srcfile = NULL, encoding = "unknown") { keep.source <- isTRUE(keep.source) if (!is.null(text)) { if (length(text) == 0L) return(expression()) if (missing(srcfile)) { srcfile <- "<text>" if (keep.source) srcfile <- srcfilecopy(srcfile, text) } file <- stdin() } else { if (is.character(file)) { if (file == "") { file <- stdin() if (missing(srcfile)) srcfile <- "<stdin>" } else { filename <- file file <- file(filename, "r") if (missing(srcfile)) srcfile <- filename if (keep.source) { text <- readLines(file, warn = FALSE) if (!length(text)) text <- "" close(file) file <- stdin() srcfile <- srcfilecopy(filename, text, file.info(filename)[1, "mtime"], isFile = TRUE) } else on.exit(close(file)) } } } .Internal(parse(file, n, text, prompt, srcfile, encoding)) } ## @type sep : character ## @type collapse : character ## @return character paste <- function (..., sep = " ", collapse = NULL) .Internal(paste(list(...), sep, collapse)) print <- function (x, ...) UseMethod("print") qr.qy <- function (qr, y) { if (!is.qr(qr)) stop("argument is not a QR decomposition") if (is.complex(qr$qr)) return(.Internal(qr_qy_cmplx(qr, as.matrix(y), FALSE))) if (isTRUE(attr(qr, "useLAPACK"))) return(.Internal(qr_qy_real(qr, as.matrix(y), FALSE))) n <- as.integer(nrow(qr$qr)) if (is.na(n)) stop("invalid nrow(qr$qr)") k <- as.integer(qr$rank) ny <- as.integer(NCOL(y)) if (is.na(ny)) stop("invalid NCOL(y)") storage.mode(y) <- "double" if (NROW(y) != n) stop("'qr' and 'y' must have the same number of rows") .Fortran(.F_dqrqy, as.double(qr$qr), n, k, as.double(qr$qraux), y, ny, qy = y)$qy } quote <- function (expr) .Primitive("quote") ## @type na.rm : logical range <- function (..., na.rm = FALSE) .Primitive("range") ## @type deparse.level : integer rbind <- function (..., deparse.level = 1) .Internal(rbind(deparse.level, ...)) ## @type triangular : logical ## @type norm : complex|character rcond <- function (x, norm = c("O", "I", "1"), triangular = FALSE, ...) { norm <- match.arg(norm) stopifnot(is.matrix(x)) if ({ d <- dim(x) d[1L] != d[2L] }) return(rcond(qr.R(qr(if (d[1L] < d[2L]) t(x) else x)), norm = norm, ...)) if (is.complex(x)) { if (triangular) .Internal(La_ztrcon(x, norm)) else .Internal(La_zgecon(x, norm)) } else { if (triangular) .Internal(La_dtrcon(x, norm)) else .Internal(La_dgecon(x, norm)) } } round <- function (x, digits = 0) .Primitive("round") ## @type x : numeric ## @type center : complex|logical ## @type scale : complex|logical scale <- function (x, center = TRUE, scale = TRUE) UseMethod("scale") ## @return character setwd <- function (dir) .Internal(setwd(dir)) ## @type x : complex sinpi <- function (x) .Primitive("sinpi") "/" <- function (e1, e2) .Primitive("/") ## @type a : complex ## @type b : complex solve <- function (a, b, ...) UseMethod("solve") ## @type drop : logical split <- function (x, f, drop = FALSE, ...) UseMethod("split") stdin <- function () .Internal(stdin()) ## @type check.margin : logical sweep <- function (x, MARGIN, STATS, FUN = "-", check.margin = TRUE, ...) { FUN <- match.fun(FUN) dims <- dim(x) if (check.margin) { dimmargin <- dims[MARGIN] dimstats <- dim(STATS) lstats <- length(STATS) if (lstats > prod(dimmargin)) { warning("STATS is longer than the extent of 'dim(x)[MARGIN]'") } else if (is.null(dimstats)) { cumDim <- c(1L, cumprod(dimmargin)) upper <- min(cumDim[cumDim >= lstats]) lower <- max(cumDim[cumDim <= lstats]) if (lstats && (upper%%lstats != 0L || lstats%%lower != 0L)) warning("STATS does not recycle exactly across MARGIN") } else { dimmargin <- dimmargin[dimmargin > 1L] dimstats <- dimstats[dimstats > 1L] if (length(dimstats) != length(dimmargin) || any(dimstats != dimmargin)) warning("length(STATS) or dim(STATS) do not match dim(x)[MARGIN]") } } perm <- c(MARGIN, seq_along(dims)[-MARGIN]) FUN(x, aperm(array(STATS, dims[perm]), order(perm)), ...) } table <- function (..., exclude = if (useNA == "no") c(NA, NaN), useNA = c("no", "ifany", "always"), dnn = list.names(...), deparse.level = 1) { list.names <- function(...) { l <- as.list(substitute(list(...)))[-1L] nm <- names(l) fixup <- if (is.null(nm)) seq_along(l) else nm == "" dep <- vapply(l[fixup], function(x) switch(deparse.level + 1, "", if (is.symbol(x)) as.character(x) else "", deparse(x, nlines = 1)[1L]), "") if (is.null(nm)) dep else { nm[fixup] <- dep nm } } if (!missing(exclude) && is.null(exclude)) useNA <- "always" useNA <- match.arg(useNA) args <- list(...) if (!length(args)) stop("nothing to tabulate") if (length(args) == 1L && is.list(args[[1L]])) { args <- args[[1L]] if (length(dnn) != length(args)) dnn <- if (!is.null(argn <- names(args))) argn else paste(dnn[1L], seq_along(args), sep = ".") } bin <- 0L lens <- NULL dims <- integer() pd <- 1L dn <- NULL for (a in args) { if (is.null(lens)) lens <- length(a) else if (length(a) != lens) stop("all arguments must have the same length") cat <- if (is.factor(a)) { if (any(is.na(levels(a)))) a else { if (is.null(exclude) && useNA != "no") addNA(a, ifany = (useNA == "ifany")) else { if (useNA != "no") a <- addNA(a, ifany = (useNA == "ifany")) ll <- levels(a) a <- factor(a, levels = ll[!(ll %in% exclude)], exclude = if (useNA == "no") NA) } } } else { a <- factor(a, exclude = exclude) if (useNA != "no") addNA(a, ifany = (useNA == "ifany")) else a } nl <- length(ll <- levels(cat)) dims <- c(dims, nl) if (prod(dims) > .Machine$integer.max) stop("attempt to make a table with >= 2^31 elements") dn <- c(dn, list(ll)) bin <- bin + pd * (as.integer(cat) - 1L) pd <- pd * nl } names(dn) <- dnn bin <- bin[!is.na(bin)] if (length(bin)) bin <- bin + 1L y <- array(tabulate(bin, pd), dims, dimnames = dn) class(y) <- "table" y } ## @type x : complex tanpi <- function (x) .Primitive("tanpi") ## @optional tracer, at, signature, print, exit trace <- function (what, tracer, exit, at, print, signature, where = topenv(parent.frame()), edit = FALSE) { needsAttach <- nargs() > 1L && !.isMethodsDispatchOn() if (needsAttach) { ns <- try(loadNamespace("methods")) if (isNamespace(ns)) message("(loaded the methods namespace)", domain = NA) else stop("tracing functions requires the 'methods' package, but unable to load the 'methods' namespace") } else if (nargs() == 1L) return(.primTrace(what)) tState <- tracingState(FALSE) on.exit(tracingState(tState)) call <- sys.call() call[[1L]] <- quote(methods::.TraceWithMethods) call$where <- where value <- eval.parent(call) on.exit() tracingState(tState) value } ## @type x : complex trunc <- function (x, ...) .Primitive("trunc") union <- function (x, y) unique(c(as.vector(x), as.vector(y))) units <- function (x) UseMethod("units") ## @type useNames : logical ## @type arr.ind : logical ## @type x : logical which <- function (x, arr.ind = FALSE, useNames = TRUE) { wh <- .Internal(which(x)) if (arr.ind && !is.null(d <- dim(x))) arrayInd(wh, d, dimnames(x), useNames = useNames) else wh } write <- function (x, file = "data", ncolumns = if (is.character(x)) 1 else 5, append = FALSE, sep = " ") cat(x, file = file, sep = c(rep.int(sep, ncolumns - 1), "\n"), append = append) xtfrm <- function (x) .Primitive("xtfrm") "+.Date" <- function (e1, e2) { coerceTimeUnit <- function(x) as.vector(round(switch(attr(x, "units"), secs = x/86400, mins = x/1440, hours = x/24, days = x, weeks = 7 * x))) if (nargs() == 1) return(e1) if (inherits(e1, "Date") && inherits(e2, "Date")) stop("binary + is not defined for \"Date\" objects") if (inherits(e1, "difftime")) e1 <- coerceTimeUnit(e1) if (inherits(e2, "difftime")) e2 <- coerceTimeUnit(e2) structure(unclass(e1) + unclass(e2), class = "Date") } "-.Date" <- function (e1, e2) { coerceTimeUnit <- function(x) as.vector(round(switch(attr(x, "units"), secs = x/86400, mins = x/1440, hours = x/24, days = x, weeks = 7 * x))) if (!inherits(e1, "Date")) stop("can only subtract from \"Date\" objects") if (nargs() == 1) stop("unary - is not defined for \"Date\" objects") if (inherits(e2, "Date")) return(difftime(e1, e2, units = "days")) if (inherits(e2, "difftime")) e2 <- coerceTimeUnit(e2) if (!is.null(attr(e2, "class"))) stop("can only subtract numbers from \"Date\" objects") structure(unclass(as.Date(e1)) - e2, class = "Date") } "[.AsIs" <- function (x, i, ...) I(NextMethod("[")) "[.Date" <- function (x, ..., drop = TRUE) { cl <- oldClass(x) class(x) <- NULL val <- NextMethod("[") class(val) <- cl val } ## @type costs : numeric ## @type x : character ## @type fixed : logical ## @type useBytes : logical ## @type pattern : character ## @type max.distance : integer agrepl <- function (pattern, x, max.distance = 0.1, costs = NULL, ignore.case = FALSE, fixed = TRUE, useBytes = FALSE) { pattern <- as.character(pattern) if (!is.character(x)) x <- as.character(x) costs <- as.integer(.amatch_costs(costs)) bounds <- .amatch_bounds(max.distance) .Internal(agrepl(pattern, x, ignore.case, FALSE, costs, bounds, useBytes, fixed)) } append <- function (x, values, after = length(x)) { lengx <- length(x) if (!after) c(values, x) else if (after >= lengx) c(x, values) else c(x[1L:after], values, x[(after + 1L):lengx]) } as.raw <- function (x) .Primitive("as.raw") assign <- function (x, value, pos = -1, envir = as.environment(pos), inherits = FALSE, immediate = TRUE) .Internal(assign(x, value, envir, inherits)) ## @type warn.conflicts : logical ## @type pos : integer ## @type name : character attach <- function (what, pos = 2L, name = deparse(substitute(what)), warn.conflicts = TRUE) { checkConflicts <- function(env) { dont.mind <- c("last.dump", "last.warning", ".Last.value", ".Random.seed", ".Last.lib", ".onDetach", ".packageName", ".noGenerics", ".required", ".no_S3_generics", ".requireCachedGenerics") sp <- search() for (i in seq_along(sp)) { if (identical(env, as.environment(i))) { db.pos <- i break } } ob <- objects(db.pos, all.names = TRUE) if (.isMethodsDispatchOn()) { these <- ob[substr(ob, 1L, 6L) == ".__T__"] gen <- gsub(".__T__(.*):([^:]+)", "\\1", these) from <- gsub(".__T__(.*):([^:]+)", "\\2", these) gen <- gen[from != ".GlobalEnv"] ob <- ob[!(ob %in% gen)] } ipos <- seq_along(sp)[-c(db.pos, match(c("Autoloads", "CheckExEnv"), sp, 0L))] for (i in ipos) { obj.same <- match(objects(i, all.names = TRUE), ob, nomatch = 0L) if (any(obj.same > 0L)) { same <- ob[obj.same] same <- same[!(same %in% dont.mind)] Classobjs <- grep("^\\.__", same) if (length(Classobjs)) same <- same[-Classobjs] same.isFn <- function(where) vapply(same, exists, NA, where = where, mode = "function", inherits = FALSE) same <- same[same.isFn(i) == same.isFn(db.pos)] if (length(same)) { pkg <- if (sum(sp == sp[i]) > 1L) sprintf("%s (pos = %d)", sp[i], i) else sp[i] message(.maskedMsg(same, pkg, by = i < db.pos), domain = NA) } } } } if (pos == 1L) { warning("*** 'pos=1' is not possible; setting 'pos=2' for now.\n", "*** Note that 'pos=1' will give an error in the future") pos <- 2L } if (is.character(what) && (length(what) == 1L)) { if (!file.exists(what)) stop(gettextf("file '%s' not found", what), domain = NA) if (missing(name)) name <- paste0("file:", what) value <- .Internal(attach(NULL, pos, name)) load(what, envir = as.environment(pos)) } else value <- .Internal(attach(what, pos, name)) if (warn.conflicts && !exists(".conflicts.OK", envir = value, inherits = FALSE)) { checkConflicts(value) } if (length(ls(envir = value, all.names = TRUE)) && .isMethodsDispatchOn()) methods:::cacheMetaData(value, TRUE) invisible(value) } ## @type which : character "attr<-" <- function (x, which, value) .Primitive("attr<-") ## @return integer bitwOr <- function (a, b) .Internal(bitwiseOr(a, b)) bquote <- function (expr, where = parent.frame()) { unquote <- function(e) if (is.pairlist(e)) as.pairlist(lapply(e, unquote)) else if (length(e) <= 1L) e else if (e[[1L]] == as.name(".")) eval(e[[2L]], where) else as.call(lapply(e, unquote)) unquote(substitute(expr)) } ## @type compression : integer ## @type description : character ## @type open : character ## @type encoding : character bzfile <- function (description, open = "", encoding = getOption("encoding"), compression = 9) .Internal(bzfile(description, open, encoding, compression)) c.Date <- function (..., recursive = FALSE) structure(c(unlist(lapply(list(...), unclass))), class = "Date") ## @optional fun callCC <- function (fun) { value <- NULL delayedAssign("throw", return(value)) fun(function(v) { value <<- v throw }) } chartr <- function (old, new, x) { if (!is.character(x)) x <- as.character(x) .Internal(chartr(old, new, x)) } ## @type n : numeric ## @type k : integer choose <- function (n, k) .Internal(choose(n, k)) ## @type x : complex cummax <- function (x) .Primitive("cummax") ## @type x : complex cummin <- function (x) .Primitive("cummin") ## @type x : complex cumsum <- function (x) .Primitive("cumsum") detach <- function (name, pos = 2L, unload = FALSE, character.only = FALSE, force = FALSE) { if (!missing(name)) { if (!character.only) name <- substitute(name) pos <- if (is.numeric(name)) name else { if (!is.character(name)) name <- deparse(name) match(name, search()) } if (is.na(pos)) stop("invalid 'name' argument") } packageName <- search()[[pos]] if (!grepl("^package:", packageName)) return(invisible(.Internal(detach(pos)))) pkgname <- sub("^package:", "", packageName) for (pkg in search()[-1L]) { if (grepl("^package:", pkg) && exists(".Depends", pkg, inherits = FALSE) && pkgname %in% get(".Depends", pkg, inherits = FALSE)) if (force) warning(gettextf("package %s is required by %s, which may no longer work correctly", sQuote(pkgname), sQuote(sub("^package:", "", pkg))), call. = FALSE, domain = NA) else stop(gettextf("package %s is required by %s so will not be detached", sQuote(pkgname), sQuote(sub("^package:", "", pkg))), call. = FALSE, domain = NA) } env <- as.environment(pos) libpath <- attr(env, "path") hook <- getHook(packageEvent(pkgname, "detach")) for (fun in rev(hook)) try(fun(pkgname, libpath)) ns <- .getNamespace(pkgname) if (!is.null(ns) && exists(".onDetach", mode = "function", where = ns, inherits = FALSE)) { .onDetach <- get(".onDetach", mode = "function", pos = ns, inherits = FALSE) if (!is.null(libpath)) { res <- tryCatch(.onDetach(libpath), error = identity) if (inherits(res, "error")) { warning(gettextf("%s failed in %s() for '%s', details:\n call: %s\n error: %s", ".onDetach", "detach", pkgname, deparse(conditionCall(res))[1L], conditionMessage(res)), call. = FALSE, domain = NA) } } } else if (exists(".Last.lib", mode = "function", where = pos, inherits = FALSE)) { .Last.lib <- get(".Last.lib", mode = "function", pos = pos, inherits = FALSE) if (!is.null(libpath)) { res <- tryCatch(.Last.lib(libpath), error = identity) if (inherits(res, "error")) { warning(gettextf("%s failed in %s() for '%s', details:\n call: %s\n error: %s", ".Last.lib", "detach", pkgname, deparse(conditionCall(res))[1L], conditionMessage(res)), call. = FALSE, domain = NA) } } } .Internal(detach(pos)) if (pkgname %in% loadedNamespaces()) { if (unload) { tryCatch(unloadNamespace(pkgname), error = function(e) warning(gettextf("%s namespace cannot be unloaded:\n ", sQuote(pkgname)), conditionMessage(e), call. = FALSE, domain = NA)) } } else { if (.isMethodsDispatchOn() && methods:::.hasS4MetaData(env)) methods:::cacheMetaData(env, FALSE) .Internal(lazyLoadDBflush(paste0(libpath, "/R/", pkgname, ".rdb"))) } invisible() } "diag<-" <- function (x, value) { dx <- dim(x) if (length(dx) != 2L) stop("only matrix diagonals can be replaced") len.i <- min(dx) len.v <- length(value) if (len.v != 1L && len.v != len.i) stop("replacement diagonal has wrong length") if (len.i) { i <- seq_len(len.i) x[cbind(i, i)] <- value } x } ## @type length : integer double <- function (length = 0L) .Internal(vector("double", length)) ## @type x : character dQuote <- function (x) { if (!length(x)) return(character()) before <- after <- "\"" q <- getOption("useFancyQuotes") if (!is.null(q)) { if (identical(q, TRUE)) { li <- l10n_info() if (li$"UTF-8") q <- "UTF-8" if (!is.null(li$codepage) && li$codepage > 0L) { if (li$codepage >= 1250L && li$codepage <= 1258L || li$codepage == 874L) { before <- "\x93" after <- "\x94" } else { z <- iconv(c("“", "”"), "UTF-8", "") before <- z[1L] after <- z[2L] } } } if (identical(q, "TeX")) { before <- "``" after <- "''" } if (identical(q, "UTF-8")) { before <- "“" after <- "”" } if (is.character(q) && length(q) >= 4L) { before <- q[3L] after <- q[4L] } Encoding(before) <- Encoding(after) <- "unknown" } paste0(before, x, after) } eapply <- function (env, FUN, ..., all.names = FALSE, USE.NAMES = TRUE) { FUN <- match.fun(FUN) .Internal(eapply(env, FUN, all.names, USE.NAMES)) } exists <- function (x, where = -1, envir = if (missing(frame)) as.environment(where) else sys.frame(frame), frame, mode = "any", inherits = TRUE) .Internal(exists(x, envir, mode, inherits)) factor <- function (x = character(), levels, labels = levels, exclude = NA, ordered = is.ordered(x), nmax = NA) { if (is.null(x)) x <- character() nx <- names(x) if (missing(levels)) { y <- unique(x, nmax = nmax) ind <- sort.list(y) y <- as.character(y) levels <- unique(y[ind]) } force(ordered) exclude <- as.vector(exclude, typeof(x)) x <- as.character(x) levels <- levels[is.na(match(levels, exclude))] f <- match(x, levels) if (!is.null(nx)) names(f) <- nx nl <- length(labels) nL <- length(levels) if (!any(nl == c(1L, nL))) stop(gettextf("invalid 'labels'; length %d should be 1 or %d", nl, nL), domain = NA) levels(f) <- if (nl == nL) as.character(labels) else paste0(labels, seq_along(levels)) class(f) <- c(if (ordered) "ordered", "factor") f } Filter <- function (f, x) { ind <- as.logical(unlist(lapply(x, f))) x[!is.na(ind) & ind] } ## @type x : numeric format <- function (x, ...) UseMethod("format") gcinfo <- function (verbose) .Internal(gcinfo(verbose)) ## @type description : character ## @type open : character ## @type encoding : character ## @type compression : integer gzfile <- function (description, open = "", encoding = getOption("encoding"), compression = 6) .Internal(gzfile(description, open, encoding, compression)) ## @type test : logical ifelse <- function (test, yes, no) { if (is.atomic(test)) { if (typeof(test) != "logical") storage.mode(test) <- "logical" if (length(test) == 1 && is.null(attributes(test))) { if (is.na(test)) return(NA) else if (test) { if (length(yes) == 1 && is.null(attributes(yes))) return(yes) } else if (length(no) == 1 && is.null(attributes(no))) return(no) } } else test <- if (isS4(test)) as(test, "logical") else as.logical(test) ans <- test ok <- !(nas <- is.na(test)) if (any(test[ok])) ans[test & ok] <- rep(yes, length.out = length(ans))[test & ok] if (any(!test[ok])) ans[!test & ok] <- rep(no, length.out = length(ans))[!test & ok] ans[nas] <- NA ans } is.nan <- function (x) .Primitive("is.nan") is.raw <- function (x) .Primitive("is.raw") isatty <- function (con) { if (!inherits(con, "terminal")) FALSE else .Internal(isatty(con)) } ## @type rw : character isOpen <- function (con, rw = "") { rw <- pmatch(rw, c("read", "write"), 0L) .Internal(isOpen(con, rw)) } ## @type x : raw|complex|logical isTRUE <- function (x) identical(TRUE, x) ## @type factor : numeric ## @type x : numeric ## @type amount : numeric ## @return numeric jitter <- function (x, factor = 1, amount = NULL) { if (length(x) == 0L) return(x) if (!is.numeric(x)) stop("'x' must be numeric") z <- diff(r <- range(x[is.finite(x)])) if (z == 0) z <- abs(r[1L]) if (z == 0) z <- 1 if (is.null(amount)) { d <- diff(xx <- unique(sort.int(round(x, 3 - floor(log10(z)))))) d <- if (length(d)) min(d) else if (xx != 0) xx/10 else z/10 amount <- factor/5 * abs(d) } else if (amount == 0) amount <- factor * (z/50) x + stats::runif(length(x), -amount, amount) } julian <- function (x, ...) UseMethod("julian") ## @type nu : complex ## @type nv : complex ## @type x : complex La.svd <- function (x, nu = min(n, p), nv = min(n, p)) { if (!is.logical(x) && !is.numeric(x) && !is.complex(x)) stop("argument to 'La.svd' must be numeric or complex") if (any(!is.finite(x))) stop("infinite or missing values in 'x'") x <- as.matrix(x) n <- nrow(x) p <- ncol(x) if (!n || !p) stop("a dimension is zero") zero <- if (is.complex(x)) 0 + (0+0i) else 0 if (nu || nv) { np <- min(n, p) if (nu <= np && nv <= np) { jobu <- "S" u <- matrix(zero, n, np) vt <- matrix(zero, np, p) nu0 <- nv0 <- np } else { jobu <- "A" u <- matrix(zero, n, n) vt <- matrix(zero, p, p) nu0 <- n nv0 <- p } } else { jobu <- "N" u <- matrix(zero, 1L, 1L) vt <- matrix(zero, 1L, 1L) } res <- if (is.complex(x)) .Internal(La_svd_cmplx(jobu, x, double(min(n, p)), u, vt)) else .Internal(La_svd(jobu, x, double(min(n, p)), u, vt)) res <- res[c("d", if (nu) "u", if (nv) "vt")] if (nu && nu < nu0) res$u <- res$u[, seq_len(min(n, nu)), drop = FALSE] if (nv && nv < nv0) res$vt <- res$vt[seq_len(min(p, nv)), , drop = FALSE] res } labels <- function (object, ...) UseMethod("labels") lapply <- function (X, FUN, ...) { FUN <- match.fun(FUN) if (!is.vector(X) || is.object(X)) X <- as.list(X) .Internal(lapply(X, FUN)) } length <- function (x) .Primitive("length") levels <- function (x) UseMethod("levels") ## @type x : numeric lgamma <- function (x) .Primitive("lgamma") ## @type SIMPLIFY : logical|character ## @type USE.NAMES : logical|character mapply <- function (FUN, ..., MoreArgs = NULL, SIMPLIFY = TRUE, USE.NAMES = TRUE) { FUN <- match.fun(FUN) dots <- list(...) answer <- .Internal(mapply(FUN, dots, MoreArgs)) if (USE.NAMES && length(dots)) { if (is.null(names1 <- names(dots[[1L]])) && is.character(dots[[1L]])) names(answer) <- dots[[1L]] else if (!is.null(names1)) names(answer) <- names1 } if (!identical(SIMPLIFY, FALSE) && length(answer)) simplify2array(answer, higher = (SIMPLIFY == "array")) else answer } matrix <- function (data = NA, nrow = 1, ncol = 1, byrow = FALSE, dimnames = NULL) { if (is.object(data) || !is.atomic(data)) data <- as.vector(data) .Internal(matrix(data, nrow, ncol, byrow, dimnames, missing(nrow), missing(ncol))) } ## @type value : character "mode<-" <- function (x, value) { if (storage.mode(x) == value) return(x) if (is.factor(x)) stop("invalid to change the storage mode of a factor") mde <- paste0("as.", value) atr <- attributes(x) isSingle <- !is.null(attr(x, "Csingle")) setSingle <- value == "single" x <- eval(call(mde, x), parent.frame()) attributes(x) <- atr if (setSingle != isSingle) attr(x, "Csingle") <- if (setSingle) TRUE x } ## @return complex|character months <- function (x, abbreviate) UseMethod("months") Negate <- function (f) { f <- match.fun(f) function(...) !f(...) } ## @type x : character nzchar <- function (x) .Primitive("nzchar") ## @type collapse : character paste0 <- function (..., collapse = NULL) .Internal(paste0(list(...), collapse)) ## @return integer pmatch <- function (x, table, nomatch = NA_integer_, duplicates.ok = FALSE) .Internal(pmatch(as.character(x), as.character(table), nomatch, duplicates.ok)) ## @type x : numeric pretty <- function (x, ...) UseMethod("pretty") qr.qty <- function (qr, y) { if (!is.qr(qr)) stop("argument is not a QR decomposition") if (is.complex(qr$qr)) return(.Internal(qr_qy_cmplx(qr, as.matrix(y), TRUE))) if (isTRUE(attr(qr, "useLAPACK"))) return(.Internal(qr_qy_real(qr, as.matrix(y), TRUE))) n <- as.integer(nrow(qr$qr)) if (is.na(n)) stop("invalid nrow(qr$qr)") k <- as.integer(qr$rank) ny <- as.integer(NCOL(y)) if (is.na(ny)) stop("invalid NCOL(y)") if (NROW(y) != n) stop("'qr' and 'y' must have the same number of rows") storage.mode(y) <- "double" .Fortran(.F_dqrqty, as.double(qr$qr), n, k, as.double(qr$qraux), y, ny, qty = y)$qty } R.home <- function (component = "home") { rh <- .Internal(R.home()) switch(component, home = rh, bin = if (.Platform$OS.type == "windows" && nzchar(p <- .Platform$r_arch)) file.path(rh, component, p) else file.path(rh, component), share = if (nzchar(p <- Sys.getenv("R_SHARE_DIR"))) p else file.path(rh, component), doc = if (nzchar(p <- Sys.getenv("R_DOC_DIR"))) p else file.path(rh, component), include = if (nzchar(p <- Sys.getenv("R_INCLUDE_DIR"))) p else file.path(rh, component), modules = if (nzchar(p <- .Platform$r_arch)) file.path(rh, component, p) else file.path(rh, component), file.path(rh, component)) } ## @type how : character ## @type classes : character rapply <- function (object, f, classes = "ANY", deflt = NULL, how = c("unlist", "replace", "list"), ...) { if (typeof(object) != "list") stop("'object' must be a list") how <- match.arg(how) res <- .Internal(rapply(object, f, classes, deflt, how)) if (how == "unlist") unlist(res, recursive = TRUE) else res } Recall <- function (...) .Internal(Recall(...)) ## @type accumulate : logical ## @type right : logical Reduce <- function (f, x, init, right = FALSE, accumulate = FALSE) { mis <- missing(init) len <- length(x) if (len == 0L) return(if (mis) NULL else init) f <- match.fun(f) if (!is.vector(x) || is.object(x)) x <- as.list(x) ind <- seq_len(len) if (mis) { if (right) { init <- x[[len]] ind <- ind[-len] } else { init <- x[[1L]] ind <- ind[-1L] } } if (!accumulate) { if (right) { for (i in rev(ind)) init <- f(x[[i]], init) } else { for (i in ind) init <- f(init, x[[i]]) } init } else { len <- length(ind) + 1L out <- vector("list", len) if (mis) { if (right) { out[[len]] <- init for (i in rev(ind)) { init <- f(x[[i]], init) out[[i]] <- init } } else { out[[1L]] <- init for (i in ind) { init <- f(init, x[[i]]) out[[i]] <- init } } } else { if (right) { out[[len]] <- init for (i in rev(ind)) { init <- f(x[[i]], init) out[[i]] <- init } } else { for (i in ind) { out[[i]] <- init init <- f(init, x[[i]]) } out[[len]] <- init } } if (all(vapply(out, length, 1) == 1L)) out <- unlist(out, recursive = FALSE) out } } ## @type list : character remove <- function (..., list = character(), pos = -1, envir = as.environment(pos), inherits = FALSE) { dots <- match.call(expand.dots = FALSE)$... if (length(dots) && !all(sapply(dots, function(x) is.symbol(x) || is.character(x)))) stop("... must contain names or character strings") names <- sapply(dots, as.character) if (length(names) == 0L) names <- character() list <- .Primitive("c")(list, names) .Internal(remove(list, envir, inherits)) } ## @type x : numeric rowsum <- function (x, group, reorder = TRUE, ...) UseMethod("rowsum") ## @return integer sample <- function (x, size, replace = FALSE, prob = NULL) { if (length(x) == 1L && is.numeric(x) && x >= 1) { if (missing(size)) size <- x sample.int(x, size, replace, prob) } else { if (missing(size)) size <- length(x) x[sample.int(length(x), size, replace, prob)] } } sapply <- function (X, FUN, ..., simplify = TRUE, USE.NAMES = TRUE) { FUN <- match.fun(FUN) answer <- lapply(X = X, FUN = FUN, ...) if (USE.NAMES && is.character(X) && is.null(names(answer))) names(answer) <- X if (!identical(simplify, FALSE) && length(answer)) simplify2array(answer, higher = (simplify == "array")) else answer } search <- function () .Internal(search()) signif <- function (x, digits = 6) .Primitive("signif") ## @type length : integer single <- function (length = 0L) structure(vector("double", length), Csingle = TRUE) source <- function (file, local = FALSE, echo = verbose, print.eval = echo, verbose = getOption("verbose"), prompt.echo = getOption("prompt"), max.deparse.length = 150, chdir = FALSE, encoding = getOption("encoding"), continue.echo = getOption("continue"), skip.echo = 0, keep.source = getOption("keep.source")) { envir <- if (isTRUE(local)) { parent.frame() } else if (identical(local, FALSE)) { .GlobalEnv } else if (is.environment(local)) { local } else stop("'local' must be TRUE, FALSE or an environment") have_encoding <- !missing(encoding) && encoding != "unknown" if (!missing(echo)) { if (!is.logical(echo)) stop("'echo' must be logical") if (!echo && verbose) { warning("'verbose' is TRUE, 'echo' not; ... coercing 'echo <- TRUE'") echo <- TRUE } } if (verbose) { cat("'envir' chosen:") print(envir) } ofile <- file from_file <- FALSE srcfile <- NULL if (is.character(file)) { if (identical(encoding, "unknown")) { enc <- utils::localeToCharset() encoding <- enc[length(enc)] } else enc <- encoding if (length(enc) > 1L) { encoding <- NA owarn <- options("warn") options(warn = 2) for (e in enc) { if (is.na(e)) next zz <- file(file, encoding = e) res <- tryCatch(readLines(zz, warn = FALSE), error = identity) close(zz) if (!inherits(res, "error")) { encoding <- e break } } options(owarn) } if (is.na(encoding)) stop("unable to find a plausible encoding") if (verbose) cat(gettextf("encoding = \"%s\" chosen", encoding), "\n", sep = "") if (file == "") { file <- stdin() srcfile <- "<stdin>" } else { filename <- file file <- file(filename, "r", encoding = encoding) on.exit(close(file)) if (isTRUE(keep.source)) { lines <- readLines(file, warn = FALSE) on.exit() close(file) srcfile <- srcfilecopy(filename, lines, file.info(filename)[1, "mtime"], isFile = TRUE) } else { from_file <- TRUE srcfile <- filename } loc <- utils::localeToCharset()[1L] encoding <- if (have_encoding) switch(loc, `UTF-8` = "UTF-8", `ISO8859-1` = "latin1", "unknown") else "unknown" } } else { lines <- readLines(file, warn = FALSE) if (isTRUE(keep.source)) srcfile <- srcfilecopy(deparse(substitute(file)), lines) else srcfile <- deparse(substitute(file)) } exprs <- if (!from_file) { if (length(lines)) .Internal(parse(stdin(), n = -1, lines, "?", srcfile, encoding)) else expression() } else .Internal(parse(file, n = -1, NULL, "?", srcfile, encoding)) on.exit() if (from_file) close(file) Ne <- length(exprs) if (verbose) cat("--> parsed", Ne, "expressions; now eval(.)ing them:\n") if (chdir) { if (is.character(ofile)) { isURL <- length(grep("^(ftp|http|file)://", ofile)) > 0L if (isURL) warning("'chdir = TRUE' makes no sense for a URL") if (!isURL && (path <- dirname(ofile)) != ".") { owd <- getwd() if (is.null(owd)) stop("cannot 'chdir' as current directory is unknown") on.exit(setwd(owd), add = TRUE) setwd(path) } } else { warning("'chdir = TRUE' makes no sense for a connection") } } if (echo) { sd <- "\"" nos <- "[^\"]*" oddsd <- paste0("^", nos, sd, "(", nos, sd, nos, sd, ")*", nos, "$") trySrcLines <- function(srcfile, showfrom, showto) { lines <- tryCatch(suppressWarnings(getSrcLines(srcfile, showfrom, showto)), error = function(e) e) if (inherits(lines, "error")) character() else lines } } yy <- NULL lastshown <- 0 srcrefs <- attr(exprs, "srcref") for (i in seq_len(Ne + echo)) { tail <- i > Ne if (!tail) { if (verbose) cat("\n>>>> eval(expression_nr.", i, ")\n\t\t =================\n") ei <- exprs[i] } if (echo) { nd <- 0 srcref <- if (tail) attr(exprs, "wholeSrcref") else if (i <= length(srcrefs)) srcrefs[[i]] if (!is.null(srcref)) { if (i == 1) lastshown <- min(skip.echo, srcref[3L] - 1) if (lastshown < srcref[3L]) { srcfile <- attr(srcref, "srcfile") dep <- trySrcLines(srcfile, lastshown + 1, srcref[3L]) if (length(dep)) { leading <- if (tail) length(dep) else srcref[1L] - lastshown lastshown <- srcref[3L] while (length(dep) && length(grep("^[[:blank:]]*$", dep[1L]))) { dep <- dep[-1L] leading <- leading - 1L } dep <- paste0(rep.int(c(prompt.echo, continue.echo), c(leading, length(dep) - leading)), dep, collapse = "\n") nd <- nchar(dep, "c") } else srcref <- NULL } } if (is.null(srcref)) { if (!tail) { dep <- substr(paste(deparse(ei, control = "showAttributes"), collapse = "\n"), 12L, 1000000L) dep <- paste0(prompt.echo, gsub("\n", paste0("\n", continue.echo), dep)) nd <- nchar(dep, "c") - 1L } } if (nd) { do.trunc <- nd > max.deparse.length dep <- substr(dep, 1L, if (do.trunc) max.deparse.length else nd) cat("\n", dep, if (do.trunc) paste(if (length(grep(sd, dep)) && length(grep(oddsd, dep))) " ...\" ..." else " ....", "[TRUNCATED] "), "\n", sep = "") } } if (!tail) { yy <- withVisible(eval(ei, envir)) i.symbol <- mode(ei[[1L]]) == "name" if (!i.symbol) { curr.fun <- ei[[1L]][[1L]] if (verbose) { cat("curr.fun:") utils::str(curr.fun) } } if (verbose >= 2) { cat(".... mode(ei[[1L]])=", mode(ei[[1L]]), "; paste(curr.fun)=") utils::str(paste(curr.fun)) } if (print.eval && yy$visible) { if (isS4(yy$value)) methods::show(yy$value) else print(yy$value) } if (verbose) cat(" .. after ", sQuote(deparse(ei, control = c("showAttributes", "useSource"))), "\n", sep = "") } } invisible(yy) } ## @type x : character sQuote <- function (x) { if (!length(x)) return(character()) before <- after <- "'" q <- getOption("useFancyQuotes") if (!is.null(q)) { if (identical(q, TRUE)) { li <- l10n_info() if (li$"UTF-8") q <- "UTF-8" if (!is.null(li$codepage) && li$codepage > 0L) { if (li$codepage >= 1250L && li$codepage <= 1258L || li$codepage == 874L) { before <- "\x91" after <- "\x92" } else { z <- iconv(c("‘", "’"), "UTF-8", "") before <- z[1L] after <- z[2L] } } } if (identical(q, "TeX")) { before <- "`" after <- "'" } if (identical(q, "UTF-8")) { before <- "‘" after <- "’" } if (is.character(q) && length(q) >= 4L) { before <- q[1L] after <- q[2L] } Encoding(before) <- Encoding(after) <- "unknown" } paste0(before, x, after) } srcref <- function (srcfile, lloc) { stopifnot(inherits(srcfile, "srcfile"), length(lloc) %in% c(4L, 6L, 8L)) if (length(lloc) == 4) lloc <- c(lloc, lloc[c(2, 4)]) if (length(lloc) == 6) lloc <- c(lloc, lloc[c(1, 3)]) structure(as.integer(lloc), srcfile = srcfile, class = "srcref") } stderr <- function () .Internal(stderr()) stdout <- function () .Internal(stdout()) ## @type base : integer ## @type x : character ## @return integer strtoi <- function (x, base = 0L) .Internal(strtoi(as.character(x), as.integer(base))) subset <- function (x, ...) UseMethod("subset") ## @type stop : integer ## @type start : integer ## @type x : character ## @return character substr <- function (x, start, stop) { if (!is.character(x)) x <- as.character(x) .Internal(substr(x, as.integer(start), as.integer(stop))) } switch <- function (EXPR, ...) .Primitive("switch") ## @type intern : logical|character ## @type ignore.stderr : logical ## @type wait : logical ## @type input : character ## @type command : character ## @type ignore.stdout : logical system <- function (command, intern = FALSE, ignore.stdout = FALSE, ignore.stderr = FALSE, wait = TRUE, input = NULL, show.output.on.console = TRUE, minimized = FALSE, invisible = TRUE) { if (!missing(show.output.on.console) || !missing(minimized) || !missing(invisible)) message("arguments 'show.output.on.console', 'minimized' and 'invisible' are for Windows only") if (!is.logical(intern) || is.na(intern)) stop("'intern' must be TRUE or FALSE") if (!is.logical(ignore.stdout) || is.na(ignore.stdout)) stop("'ignore.stdout' must be TRUE or FALSE") if (!is.logical(ignore.stderr) || is.na(ignore.stderr)) stop("'ignore.stderr' must be TRUE or FALSE") if (!is.logical(wait) || is.na(wait)) stop("'wait' must be TRUE or FALSE") if (ignore.stdout) command <- paste(command, ">/dev/null") if (ignore.stderr) command <- paste(command, "2>/dev/null") if (!is.null(input)) { if (!is.character(input)) stop("'input' must be a character vector or 'NULL'") f <- tempfile() on.exit(unlink(f)) writeLines(input, f) command <- paste(command, "<", shQuote(f)) } if (!wait && !intern) command <- paste(command, "&") .Internal(system(command, intern)) } tapply <- function (X, INDEX, FUN = NULL, ..., simplify = TRUE) { FUN <- if (!is.null(FUN)) match.fun(FUN) if (!is.list(INDEX)) INDEX <- list(INDEX) nI <- length(INDEX) if (!nI) stop("'INDEX' is of length zero") namelist <- vector("list", nI) names(namelist) <- names(INDEX) extent <- integer(nI) nx <- length(X) one <- 1L group <- rep.int(one, nx) ngroup <- one for (i in seq_along(INDEX)) { index <- as.factor(INDEX[[i]]) if (length(index) != nx) stop("arguments must have same length") namelist[[i]] <- levels(index) extent[i] <- nlevels(index) group <- group + ngroup * (as.integer(index) - one) ngroup <- ngroup * nlevels(index) } if (is.null(FUN)) return(group) ans <- lapply(X = split(X, group), FUN = FUN, ...) index <- as.integer(names(ans)) if (simplify && all(unlist(lapply(ans, length)) == 1L)) { ansmat <- array(dim = extent, dimnames = namelist) ans <- unlist(ans, recursive = FALSE) } else { ansmat <- array(vector("list", prod(extent)), dim = extent, dimnames = namelist) } if (length(index)) { names(ans) <- NULL ansmat[index] <- ans } ansmat } topenv <- function (envir = parent.frame(), matchThisEnv = getOption("topLevelEnvironment")) { while (!identical(envir, emptyenv())) { nm <- attributes(envir)[["names", exact = TRUE]] if ((is.character(nm) && length(grep("^package:", nm))) || identical(envir, matchThisEnv) || identical(envir, .GlobalEnv) || identical(envir, baseenv()) || .Internal(isNamespaceEnv(envir)) || exists(".packageName", envir = envir, inherits = FALSE)) return(envir) else envir <- parent.env(envir) } return(.GlobalEnv) } typeof <- function (x) .Internal(typeof(x)) unique <- function (x, incomparables = FALSE, ...) UseMethod("unique") ## @type force : logical ## @type recursive : logical ## @type x : character unlink <- function (x, recursive = FALSE, force = FALSE) .Internal(unlink(as.character(x), recursive, force)) ## @type recursive : logical ## @type use.names : logical unlist <- function (x, recursive = TRUE, use.names = TRUE) { if (.Internal(islistfactor(x, recursive))) { lv <- unique(.Internal(unlist(lapply(x, levels), recursive, FALSE))) nm <- if (use.names) names(.Internal(unlist(x, recursive, use.names))) res <- .Internal(unlist(lapply(x, as.character), recursive, FALSE)) res <- match(res, lv) structure(res, levels = lv, names = nm, class = "factor") } else .Internal(unlist(x, recursive, use.names)) } ## @type force : logical unname <- function (obj, force = FALSE) { if (!is.null(names(obj))) names(obj) <- NULL if (!is.null(dimnames(obj)) && (force || !is.data.frame(obj))) dimnames(obj) <- NULL obj } vapply <- function (X, FUN, FUN.VALUE, ..., USE.NAMES = TRUE) { FUN <- match.fun(FUN) if (!is.vector(X) || is.object(X)) X <- as.list(X) .Internal(vapply(X, FUN, FUN.VALUE, USE.NAMES)) } ## @type length : integer ## @type mode : character vector <- function (mode = "logical", length = 0L) .Internal(vector(mode, length)) within <- function (data, expr, ...) UseMethod("within") ## @type description : character ## @type encoding : character ## @type open : character ## @type compression : integer xzfile <- function (description, open = "", encoding = getOption("encoding"), compression = 6) .Internal(xzfile(description, open, encoding, compression)) "%/%" <- function (e1, e2) .Primitive("%/%") "[[.Date" <- function (x, ..., drop = TRUE) { cl <- oldClass(x) class(x) <- NULL val <- NextMethod("[[") class(val) <- cl val } as.call <- function (x) .Primitive("as.call") as.Date <- function (x, ...) UseMethod("as.Date") as.list <- function (x, ...) UseMethod("as.list") as.name <- function (x) .Internal(as.vector(x, "symbol")) as.null <- function (x, ...) UseMethod("as.null") baseenv <- function () .Primitive("baseenv") besselI <- function (x, nu, expon.scaled = FALSE) { .Internal(besselI(x, nu, 1 + as.logical(expon.scaled))) } besselJ <- function (x, nu) .Internal(besselJ(x, nu)) besselK <- function (x, nu, expon.scaled = FALSE) { .Internal(besselK(x, nu, 1 + as.logical(expon.scaled))) } besselY <- function (x, nu) .Internal(besselY(x, nu)) ## @return integer bitwAnd <- function (a, b) .Internal(bitwiseAnd(a, b)) ## @type a : numeric bitwNot <- function (a) .Internal(bitwiseNot(a)) ## @return integer bitwXor <- function (a, b) .Internal(bitwiseXor(a, b)) ## @type text : character browser <- function (text = "", condition = NULL, expr = TRUE, skipCalls = 0L) .Primitive("browser") ## @type x : complex ceiling <- function (x) .Primitive("ceiling") ## @type value : character "class<-" <- function (x, value) .Primitive("class<-") ## @type dims : integer ## @type x : complex|logical ## @type na.rm : logical colSums <- function (x, na.rm = FALSE, dims = 1L) { if (is.data.frame(x)) x <- as.matrix(x) if (!is.array(x) || length(dn <- dim(x)) < 2L) stop("'x' must be an array of at least two dimensions") if (dims < 1L || dims > length(dn) - 1L) stop("invalid 'dims'") n <- prod(dn[1L:dims]) dn <- dn[-(1L:dims)] z <- if (is.complex(x)) .Internal(colSums(Re(x), n, prod(dn), na.rm)) + (0+1i) * .Internal(colSums(Im(x), n, prod(dn), na.rm)) else .Internal(colSums(x, n, prod(dn), na.rm)) if (length(dn) > 1L) { dim(z) <- dn dimnames(z) <- dimnames(x)[-(1L:dims)] } else names(z) <- dimnames(x)[[dims + 1]] z } comment <- function (x) .Internal(comment(x)) ## @type imaginary : numeric ## @type length.out : numeric ## @type modulus : numeric ## @type argument : numeric ## @type real : numeric complex <- function (length.out = 0L, real = numeric(), imaginary = numeric(), modulus = 1, argument = 0) { if (missing(modulus) && missing(argument)) { .Internal(complex(length.out, real, imaginary)) } else { n <- max(length.out, length(argument), length(modulus)) rep_len(modulus, n) * exp((0+1i) * rep_len(argument, n)) } } ## @type x : complex ## @return numeric cumprod <- function (x) .Primitive("cumprod") ## @type width.cutoff : integer ## @type nlines : complex ## @type backtick : logical ## @type control : character deparse <- function (expr, width.cutoff = 60L, backtick = mode(expr) %in% c("call", "expression", "(", "function"), control = c("keepInteger", "showAttributes", "keepNA"), nlines = -1L) .Internal(deparse(expr, width.cutoff, backtick, .deparseOpts(control), nlines)) ## @type x : numeric digamma <- function (x) .Primitive("digamma") ## @type path : character ## @return character dirname <- function (path) .Internal(dirname(path)) do.call <- function (what, args, quote = FALSE, envir = parent.frame()) { if (!is.list(args)) stop("second argument must be a list") if (quote) args <- lapply(args, enquote) .Internal(do.call(what, args, envir)) } enquote <- function (cl) as.call(list(as.name("quote"), cl)) formals <- function (fun = sys.function(sys.parent())) { if (is.character(fun)) fun <- get(fun, mode = "function", envir = parent.frame()) .Internal(formals(fun)) } ## @return character formatC <- function (x, digits = NULL, width = NULL, format = NULL, flag = "", mode = NULL, big.mark = "", big.interval = 3L, small.mark = "", small.interval = 5L, decimal.mark = ".", preserve.width = "individual", zero.print = NULL, drop0trailing = FALSE) { if (is.object(x)) { x <- unclass(x) warning("class of 'x' was discarded") } format.char <- function(x, width, flag) { if (is.null(width)) width <- 0L else if (width < 0L) { flag <- "-" width <- -width } format.default(x, width = width, justify = if (flag == "-") "left" else "right") } blank.chars <- function(no) vapply(no + 1L, function(n) paste(character(n), collapse = " "), "") if (!(n <- length(x))) return("") if (is.null(mode)) mode <- storage.mode(x) else if (any(mode == c("double", "real", "integer"))) { if (mode == "real") mode <- "double" storage.mode(x) <- mode } else if (mode != "character") stop("'mode' must be \"double\" (\"real\"), \"integer\" or \"character\"") if (mode == "character" || (!is.null(format) && format == "s")) { if (mode != "character") { warning("coercing argument to \"character\" for format=\"s\"") x <- as.character(x) } return(format.char(x, width = width, flag = flag)) } if (missing(format) || is.null(format)) format <- if (mode == "integer") "d" else "g" else { if (any(format == c("f", "e", "E", "g", "G", "fg"))) { if (mode == "integer") mode <- storage.mode(x) <- "double" } else if (format == "d") { if (mode != "integer") mode <- storage.mode(x) <- "integer" } else stop("'format' must be one of {\"f\",\"e\",\"E\",\"g\",\"G\", \"fg\", \"s\"}") } some.special <- !all(Ok <- is.finite(x)) if (some.special) { rQ <- as.character(x[!Ok]) rQ[is.na(rQ)] <- "NA" x[!Ok] <- as.vector(0, mode = mode) } if (is.null(width) && is.null(digits)) width <- 1L if (is.null(digits)) digits <- if (mode == "integer") 2L else 4L else if (digits < 0L) digits <- 6L else { maxDigits <- if (format != "f") 50L else ceiling(-(.Machine$double.neg.ulp.digits + .Machine$double.min.exp)/log2(10)) if (digits > maxDigits) { warning(gettextf("'digits' reduced to %d", maxDigits), domain = NA) digits <- maxDigits } } if (is.null(width)) width <- digits + 1L else if (width == 0L) width <- digits i.strlen <- pmax(abs(as.integer(width)), if (format == "fg" || format == "f") { xEx <- as.integer(floor(log10(abs(x + ifelse(x == 0, 1, 0))))) as.integer(x < 0 | flag != "") + digits + if (format == "f") { 2L + pmax(xEx, 0L) } else { pmax(xEx, digits, digits + (-xEx) + 1L) + ifelse(flag != "", nchar(flag, "b"), 0L) + 1L } } else rep.int(digits + 8L, n)) flag <- as.character(flag) nf <- strsplit(flag, "")[[1L]] if (!all(nf %in% c("0", "+", "-", " ", "#"))) stop("'flag' can contain only '0+- #'") if (digits > 0 && any(nf == "#")) digits <- -digits attr(x, "Csingle") <- NULL r <- .Internal(formatC(x, as.character(mode), width, digits, as.character(format), as.character(flag), i.strlen)) if (some.special) r[!Ok] <- format.char(rQ, width = width, flag = flag) if (big.mark != "" || small.mark != "" || decimal.mark != "." || !is.null(zero.print) || drop0trailing) r <- prettyNum(r, big.mark = big.mark, big.interval = big.interval, small.mark = small.mark, small.interval = small.interval, decimal.mark = decimal.mark, preserve.width = preserve.width, zero.print = zero.print, drop0trailing = drop0trailing, is.cmplx = FALSE) if (!is.null(x.atr <- attributes(x))) attributes(r) <- x.atr r } ## @type on : logical gc.time <- function (on = TRUE) .Primitive("gc.time") ## @type hookName : character getHook <- function (hookName) { if (exists(hookName, envir = .userHooksEnv, inherits = FALSE)) get(hookName, envir = .userHooksEnv, inherits = FALSE) else list() } gettext <- function (..., domain = NULL) { args <- lapply(list(...), as.character) .Internal(gettext(domain, unlist(args))) } ## @type pattern : raw|character ## @type all : logical ## @type offset : integer ## @type invert : logical ## @type x : raw ## @type fixed : logical ## @type value : logical grepRaw <- function (pattern, x, offset = 1L, ignore.case = FALSE, value = FALSE, fixed = FALSE, all = FALSE, invert = FALSE) { if (!is.raw(pattern)) pattern <- charToRaw(as.character(pattern)) if (!is.raw(x)) x <- charToRaw(as.character(x)) .Internal(grepRaw(pattern, x, offset, ignore.case, fixed, value, all, invert)) } ## @type length : integer integer <- function (length = 0L) .Internal(vector("integer", length)) is.call <- function (x) .Primitive("is.call") is.list <- function (x) .Primitive("is.list") "is.na<-" <- function (x, value) UseMethod("is.na<-") is.name <- function (x) .Primitive("is.symbol") is.null <- function (x) .Primitive("is.null") ISOdate <- function (year, month, day, hour = 12, min = 0, sec = 0, tz = "GMT") ISOdatetime(year, month, day, hour, min, sec, tz) ## @type n : numeric ## @type k : integer lchoose <- function (n, k) .Internal(lchoose(n, k)) ## @return logical library <- function (package, help, pos = 2, lib.loc = NULL, character.only = FALSE, logical.return = FALSE, warn.conflicts = TRUE, quietly = FALSE, verbose = getOption("verbose")) { testRversion <- function(pkgInfo, pkgname, pkgpath) { if (is.null(built <- pkgInfo$Built)) stop(gettextf("package %s has not been installed properly\n", sQuote(pkgname)), call. = FALSE, domain = NA) R_version_built_under <- as.numeric_version(built$R) if (R_version_built_under < "3.0.0") stop(gettextf("package %s was built before R 3.0.0: please re-install it", sQuote(pkgname)), call. = FALSE, domain = NA) current <- getRversion() if (length(Rdeps <- pkgInfo$Rdepends2)) { for (dep in Rdeps) if (length(dep) > 1L) { target <- dep$version res <- if (is.character(target)) { do.call(dep$op, list(as.numeric(R.version[["svn rev"]]), as.numeric(sub("^r", "", dep$version)))) } else { do.call(dep$op, list(current, as.numeric_version(target))) } if (!res) stop(gettextf("This is R %s, package %s needs %s %s", current, sQuote(pkgname), dep$op, target), call. = FALSE, domain = NA) } } if (R_version_built_under > current) warning(gettextf("package %s was built under R version %s", sQuote(pkgname), as.character(built$R)), call. = FALSE, domain = NA) platform <- built$Platform r_arch <- .Platform$r_arch if (.Platform$OS.type == "unix") { if (!nzchar(r_arch) && length(grep("\\w", platform)) && !testPlatformEquivalence(platform, R.version$platform)) stop(gettextf("package %s was built for %s", sQuote(pkgname), platform), call. = FALSE, domain = NA) } else { if (nzchar(platform) && !grepl("mingw", platform)) stop(gettextf("package %s was built for %s", sQuote(pkgname), platform), call. = FALSE, domain = NA) } if (nzchar(r_arch) && file.exists(file.path(pkgpath, "libs")) && !file.exists(file.path(pkgpath, "libs", r_arch))) stop(gettextf("package %s is not installed for 'arch = %s'", sQuote(pkgname), r_arch), call. = FALSE, domain = NA) } checkLicense <- function(pkg, pkgInfo, pkgPath) { L <- tools:::analyze_license(pkgInfo$DESCRIPTION["License"]) if (!L$is_empty && !L$is_verified) { site_file <- path.expand(file.path(R.home("etc"), "licensed.site")) if (file.exists(site_file) && pkg %in% readLines(site_file)) return() personal_file <- path.expand("~/.R/licensed") if (file.exists(personal_file)) { agreed <- readLines(personal_file) if (pkg %in% agreed) return() } else agreed <- character() if (!interactive()) stop(gettextf("package %s has a license that you need to accept in an interactive session", sQuote(pkg)), domain = NA) lfiles <- file.path(pkgpath, c("LICENSE", "LICENCE")) lfiles <- lfiles[file.exists(lfiles)] if (length(lfiles)) { message(gettextf("package %s has a license that you need to accept after viewing", sQuote(pkg)), domain = NA) readline("press RETURN to view license") encoding <- pkgInfo$DESCRIPTION["Encoding"] if (is.na(encoding)) encoding <- "" if (encoding == "latin1") encoding <- "cp1252" file.show(lfiles[1L], encoding = encoding) } else { message(gettextf("package %s has a license that you need to accept:\naccording to the DESCRIPTION file it is", sQuote(pkg)), domain = NA) message(pkgInfo$DESCRIPTION["License"], domain = NA) } choice <- menu(c("accept", "decline"), title = paste("License for", sQuote(pkg))) if (choice != 1) stop(gettextf("license for package %s not accepted", sQuote(package)), domain = NA, call. = FALSE) dir.create(dirname(personal_file), showWarnings = FALSE) writeLines(c(agreed, pkg), personal_file) } } checkNoGenerics <- function(env, pkg) { nenv <- env ns <- .getNamespace(as.name(pkg)) if (!is.null(ns)) nenv <- asNamespace(ns) if (exists(".noGenerics", envir = nenv, inherits = FALSE)) TRUE else { length(objects(env, pattern = "^\\.__T", all.names = TRUE)) == 0L } } checkConflicts <- function(package, pkgname, pkgpath, nogenerics, env) { dont.mind <- c("last.dump", "last.warning", ".Last.value", ".Random.seed", ".Last.lib", ".onDetach", ".packageName", ".noGenerics", ".required", ".no_S3_generics", ".Depends", ".requireCachedGenerics") sp <- search() lib.pos <- match(pkgname, sp) ob <- objects(lib.pos, all.names = TRUE) if (!nogenerics) { these <- ob[substr(ob, 1L, 6L) == ".__T__"] gen <- gsub(".__T__(.*):([^:]+)", "\\1", these) from <- gsub(".__T__(.*):([^:]+)", "\\2", these) gen <- gen[from != package] ob <- ob[!(ob %in% gen)] } fst <- TRUE ipos <- seq_along(sp)[-c(lib.pos, match(c("Autoloads", "CheckExEnv"), sp, 0L))] for (i in ipos) { obj.same <- match(objects(i, all.names = TRUE), ob, nomatch = 0L) if (any(obj.same > 0)) { same <- ob[obj.same] same <- same[!(same %in% dont.mind)] Classobjs <- grep("^\\.__", same) if (length(Classobjs)) same <- same[-Classobjs] same.isFn <- function(where) vapply(same, exists, NA, where = where, mode = "function", inherits = FALSE) same <- same[same.isFn(i) == same.isFn(lib.pos)] not.Ident <- function(ch, TRAFO = identity, ...) vapply(ch, function(.) !identical(TRAFO(get(., i)), TRAFO(get(., lib.pos)), ...), NA) if (length(same)) same <- same[not.Ident(same)] if (length(same) && identical(sp[i], "package:base")) same <- same[not.Ident(same, ignore.environment = TRUE)] if (length(same)) { if (fst) { fst <- FALSE packageStartupMessage(gettextf("\nAttaching package: %s\n", sQuote(package)), domain = NA) } msg <- .maskedMsg(same, pkg = sQuote(sp[i]), by = i < lib.pos) packageStartupMessage(msg, domain = NA) } } } } if (verbose && quietly) message("'verbose' and 'quietly' are both true; being verbose then ..") if (!missing(package)) { if (is.null(lib.loc)) lib.loc <- .libPaths() lib.loc <- lib.loc[file.info(lib.loc)$isdir %in% TRUE] if (!character.only) package <- as.character(substitute(package)) if (length(package) != 1L) stop("'package' must be of length 1") if (is.na(package) || (package == "")) stop("invalid package name") pkgname <- paste("package", package, sep = ":") newpackage <- is.na(match(pkgname, search())) if (newpackage) { pkgpath <- find.package(package, lib.loc, quiet = TRUE, verbose = verbose) if (length(pkgpath) == 0L) { txt <- if (length(lib.loc)) gettextf("there is no package called %s", sQuote(package)) else gettext("no library trees found in 'lib.loc'") if (logical.return) { warning(txt, domain = NA) return(FALSE) } else stop(txt, domain = NA) } which.lib.loc <- normalizePath(dirname(pkgpath), "/", TRUE) pfile <- system.file("Meta", "package.rds", package = package, lib.loc = which.lib.loc) if (!nzchar(pfile)) stop(gettextf("%s is not a valid installed package", sQuote(package)), domain = NA) pkgInfo <- readRDS(pfile) testRversion(pkgInfo, package, pkgpath) if (!package %in% c("datasets", "grDevices", "graphics", "methods", "splines", "stats", "stats4", "tcltk", "tools", "utils") && isTRUE(getOption("checkPackageLicense", FALSE))) checkLicense(package, pkgInfo, pkgpath) if (is.character(pos)) { npos <- match(pos, search()) if (is.na(npos)) { warning(gettextf("%s not found on search path, using pos = 2", sQuote(pos)), domain = NA) pos <- 2 } else pos <- npos } .getRequiredPackages2(pkgInfo, quietly = quietly) deps <- unique(names(pkgInfo$Depends)) if (packageHasNamespace(package, which.lib.loc)) { tt <- try({ ns <- loadNamespace(package, c(which.lib.loc, lib.loc)) env <- attachNamespace(ns, pos = pos, deps) }) if (inherits(tt, "try-error")) if (logical.return) return(FALSE) else stop(gettextf("package or namespace load failed for %s", sQuote(package)), call. = FALSE, domain = NA) else { on.exit(detach(pos = pos)) nogenerics <- !.isMethodsDispatchOn() || checkNoGenerics(env, package) if (warn.conflicts && !exists(".conflicts.OK", envir = env, inherits = FALSE)) checkConflicts(package, pkgname, pkgpath, nogenerics, ns) on.exit() if (logical.return) return(TRUE) else return(invisible(.packages())) } } else stop(gettextf("package %s does not have a namespace and should be re-installed", sQuote(package)), domain = NA) } if (verbose && !newpackage) warning(gettextf("package %s already present in search()", sQuote(package)), domain = NA) } else if (!missing(help)) { if (!character.only) help <- as.character(substitute(help)) pkgName <- help[1L] pkgPath <- find.package(pkgName, lib.loc, verbose = verbose) docFiles <- c(file.path(pkgPath, "Meta", "package.rds"), file.path(pkgPath, "INDEX")) if (file.exists(vignetteIndexRDS <- file.path(pkgPath, "Meta", "vignette.rds"))) docFiles <- c(docFiles, vignetteIndexRDS) pkgInfo <- vector("list", 3L) readDocFile <- function(f) { if (basename(f) %in% "package.rds") { txt <- readRDS(f)$DESCRIPTION if ("Encoding" %in% names(txt)) { to <- if (Sys.getlocale("LC_CTYPE") == "C") "ASCII//TRANSLIT" else "" tmp <- try(iconv(txt, from = txt["Encoding"], to = to)) if (!inherits(tmp, "try-error")) txt <- tmp else warning("'DESCRIPTION' has an 'Encoding' field and re-encoding is not possible", call. = FALSE) } nm <- paste0(names(txt), ":") formatDL(nm, txt, indent = max(nchar(nm, "w")) + 3) } else if (basename(f) %in% "vignette.rds") { txt <- readRDS(f) if (is.data.frame(txt) && nrow(txt)) cbind(basename(gsub("\\.[[:alpha:]]+$", "", txt$File)), paste(txt$Title, paste0(rep.int("(source", NROW(txt)), ifelse(txt$PDF != "", ", pdf", ""), ")"))) else NULL } else readLines(f) } for (i in which(file.exists(docFiles))) pkgInfo[[i]] <- readDocFile(docFiles[i]) y <- list(name = pkgName, path = pkgPath, info = pkgInfo) class(y) <- "packageInfo" return(y) } else { if (is.null(lib.loc)) lib.loc <- .libPaths() db <- matrix(character(), nrow = 0L, ncol = 3L) nopkgs <- character() for (lib in lib.loc) { a <- .packages(all.available = TRUE, lib.loc = lib) for (i in sort(a)) { file <- system.file("Meta", "package.rds", package = i, lib.loc = lib) title <- if (file != "") { txt <- readRDS(file) if (is.list(txt)) txt <- txt$DESCRIPTION if ("Encoding" %in% names(txt)) { to <- if (Sys.getlocale("LC_CTYPE") == "C") "ASCII//TRANSLIT" else "" tmp <- try(iconv(txt, txt["Encoding"], to, "?")) if (!inherits(tmp, "try-error")) txt <- tmp else warning("'DESCRIPTION' has an 'Encoding' field and re-encoding is not possible", call. = FALSE) } txt["Title"] } else NA if (is.na(title)) title <- " ** No title available ** " db <- rbind(db, cbind(i, lib, title)) } if (length(a) == 0L) nopkgs <- c(nopkgs, lib) } dimnames(db) <- list(NULL, c("Package", "LibPath", "Title")) if (length(nopkgs) && !missing(lib.loc)) { pkglist <- paste(sQuote(nopkgs), collapse = ", ") msg <- sprintf(ngettext(length(nopkgs), "library %s contains no packages", "libraries %s contain no packages"), pkglist) warning(msg, domain = NA) } y <- list(header = NULL, results = db, footer = NULL) class(y) <- "libraryIQR" return(y) } if (logical.return) TRUE else invisible(.packages()) } licence <- function () { cat("\nThis software is distributed under the terms of the GNU General\n") cat("Public License, either Version 2, June 1991 or Version 3, June 2007.\n") cat("The terms of version 2 of the license are in a file called COPYING\nwhich you should have received with\n") cat("this software and which can be displayed by RShowDoc(\"COPYING\").\n") cat("Version 3 of the license can be displayed by RShowDoc(\"GPL-3\").\n") cat("\n") cat("Copies of both versions 2 and 3 of the license can be found\n") cat("at http://www.R-project.org/Licenses/.\n") cat("\n") cat("A small number of files (the API header files listed in\n") cat("R_DOC_DIR/COPYRIGHTS) are distributed under the\n") cat("LESSER GNU GENERAL PUBLIC LICENSE, version 2.1 or later.\n") cat("This can be displayed by RShowDoc(\"LGPL-2.1\"),\n") cat("or obtained at the URI given.\n") cat("Version 3 of the license can be displayed by RShowDoc(\"LGPL-3\").\n") cat("\n") cat("'Share and Enjoy.'\n\n") } license <- function () { cat("\nThis software is distributed under the terms of the GNU General\n") cat("Public License, either Version 2, June 1991 or Version 3, June 2007.\n") cat("The terms of version 2 of the license are in a file called COPYING\nwhich you should have received with\n") cat("this software and which can be displayed by RShowDoc(\"COPYING\").\n") cat("Version 3 of the license can be displayed by RShowDoc(\"GPL-3\").\n") cat("\n") cat("Copies of both versions 2 and 3 of the license can be found\n") cat("at http://www.R-project.org/Licenses/.\n") cat("\n") cat("A small number of files (the API header files listed in\n") cat("R_DOC_DIR/COPYRIGHTS) are distributed under the\n") cat("LESSER GNU GENERAL PUBLIC LICENSE, version 2.1 or later.\n") cat("This can be displayed by RShowDoc(\"LGPL-2.1\"),\n") cat("or obtained at the URI given.\n") cat("Version 3 of the license can be displayed by RShowDoc(\"LGPL-3\").\n") cat("\n") cat("'Share and Enjoy.'\n\n") } ## @type length : integer logical <- function (length = 0L) .Internal(vector("logical", length)) ## @type ties.method : character max.col <- function (m, ties.method = c("random", "first", "last")) { ties.method <- match.arg(ties.method) tieM <- which(ties.method == eval(formals()[["ties.method"]])) .Internal(max.col(as.matrix(m), tieM)) } ## @type appendLF : logical|character message <- function (..., domain = NULL, appendLF = TRUE) { args <- list(...) cond <- if (length(args) == 1L && inherits(args[[1L]], "condition")) { if (nargs() > 1L) warning("additional arguments ignored in message()") args[[1L]] } else { msg <- .makeMessage(..., domain = domain, appendLF = appendLF) call <- sys.call() simpleMessage(msg, call) } defaultHandler <- function(c) { cat(conditionMessage(c), file = stderr(), sep = "") } withRestarts({ signalCondition(cond) defaultHandler(cond) }, muffleMessage = function() NULL) invisible() } missing <- function (x) .Primitive("missing") ## @type value : character "names<-" <- function (x, value) .Primitive("names<-") new.env <- function (hash = TRUE, parent = parent.frame(), size = 29L) .Internal(new.env(hash, parent, size)) nlevels <- function (x) length(levels(x)) ## @type obj : character noquote <- function (obj) { if (!inherits(obj, "noquote")) class(obj) <- c(attr(obj, "class"), "noquote") obj } ## @type length : integer numeric <- function (length = 0L) .Internal(vector("double", length)) objects <- function (name, pos = -1L, envir = as.environment(pos), all.names = FALSE, pattern) { if (!missing(name)) { pos <- tryCatch(name, error = function(e) e) if (inherits(pos, "error")) { name <- substitute(name) if (!is.character(name)) name <- deparse(name) warning(gettextf("%s converted to character string", sQuote(name)), domain = NA) pos <- name } } all.names <- .Internal(ls(envir, all.names)) if (!missing(pattern)) { if ((ll <- length(grep("[", pattern, fixed = TRUE))) && ll != length(grep("]", pattern, fixed = TRUE))) { if (pattern == "[") { pattern <- "\\[" warning("replaced regular expression pattern '[' by '\\\\['") } else if (length(grep("[^\\\\]\\[<-", pattern))) { pattern <- sub("\\[<-", "\\\\\\[<-", pattern) warning("replaced '[<-' by '\\\\[<-' in regular expression pattern") } } grep(pattern, all.names, value = TRUE) } else all.names } on.exit <- function (expr = NULL, add = FALSE) .Primitive("on.exit") options <- function (...) .Internal(options(...)) ordered <- function (x, ...) factor(x, ..., ordered = TRUE) qr.coef <- function (qr, y) { if (!is.qr(qr)) stop("first argument must be a QR decomposition") n <- as.integer(nrow(qr$qr)) if (is.na(n)) stop("invalid nrow(qr$qr)") p <- as.integer(ncol(qr$qr)) if (is.na(p)) stop("invalid ncol(qr$qr)") k <- as.integer(qr$rank) if (is.na(k)) stop("invalid ncol(qr$rank)") im <- is.matrix(y) if (!im) y <- as.matrix(y) ny <- as.integer(ncol(y)) if (is.na(ny)) stop("invalid ncol(y)") if (p == 0L) return(if (im) matrix(0, p, ny) else numeric()) ix <- if (p > n) c(seq_len(n), rep(NA, p - n)) else seq_len(p) if (is.complex(qr$qr)) { coef <- matrix(NA_complex_, nrow = p, ncol = ny) coef[qr$pivot, ] <- .Internal(qr_coef_cmplx(qr, y))[ix, ] return(if (im) coef else c(coef)) } if (isTRUE(attr(qr, "useLAPACK"))) { coef <- matrix(NA_real_, nrow = p, ncol = ny) coef[qr$pivot, ] <- .Internal(qr_coef_real(qr, y))[ix, ] return(if (im) coef else c(coef)) } if (k == 0L) return(if (im) matrix(NA, p, ny) else rep.int(NA, p)) storage.mode(y) <- "double" if (nrow(y) != n) stop("'qr' and 'y' must have the same number of rows") z <- .Fortran(.F_dqrcf, as.double(qr$qr), n, k, as.double(qr$qraux), y, ny, coef = matrix(0, nrow = k, ncol = ny), info = integer(1L), NAOK = TRUE)[c("coef", "info")] if (z$info) stop("exact singularity in 'qr.coef'") if (k < p) { coef <- matrix(NA_real_, nrow = p, ncol = ny) coef[qr$pivot[seq_len(k)], ] <- z$coef } else coef <- z$coef if (!is.null(nam <- colnames(qr$qr))) if (k < p) rownames(coef)[qr$pivot] <- nam else rownames(coef) <- nam if (im && !is.null(nam <- colnames(y))) colnames(coef) <- nam if (im) coef else drop(coef) } readBin <- function (con, what, n = 1L, size = NA_integer_, signed = TRUE, endian = .Platform$endian) { if (is.character(con)) { con <- file(con, "rb") on.exit(close(con)) } swap <- endian != .Platform$endian if (!is.character(what) || is.na(what) || length(what) != 1L || !any(what == c("numeric", "double", "integer", "int", "logical", "complex", "character", "raw"))) what <- typeof(what) .Internal(readBin(con, what, n, size, signed, swap)) } readRDS <- function (file, refhook = NULL) { if (is.character(file)) { con <- gzfile(file, "rb") on.exit(close(con)) } else if (inherits(file, "connection")) con <- file else stop("bad 'file' argument") .Internal(unserializeFromConn(con, refhook)) } regexec <- function (pattern, text, ignore.case = FALSE, fixed = FALSE, useBytes = FALSE) .Internal(regexec(pattern, text, ignore.case, fixed, useBytes)) ## @return logical|integer|character regexpr <- function (pattern, text, ignore.case = FALSE, perl = FALSE, fixed = FALSE, useBytes = FALSE) { if (!is.character(text)) text <- as.character(text) .Internal(regexpr(as.character(pattern), text, ignore.case, perl, fixed, useBytes)) } rep.int <- function (x, times) .Internal(rep.int(x, times)) ## @type length.out : integer rep_len <- function (x, length.out) .Internal(rep_len(x, length.out)) ## @optional list replace <- function (x, list, values) { x[list] <- values x } require <- function (package, lib.loc = NULL, quietly = FALSE, warn.conflicts = TRUE, character.only = FALSE) { if (!character.only) package <- as.character(substitute(package)) loaded <- paste("package", package, sep = ":") %in% search() if (!loaded) { if (!quietly) packageStartupMessage(gettextf("Loading required package: %s", package), domain = NA) value <- tryCatch(library(package, lib.loc = lib.loc, character.only = TRUE, logical.return = TRUE, warn.conflicts = warn.conflicts, quietly = quietly), error = function(e) e) if (inherits(value, "error")) { if (!quietly) { msg <- conditionMessage(value) cat("Failed with error: ", sQuote(msg), "\n", file = stderr(), sep = "") .Internal(printDeferredWarnings()) } return(invisible(FALSE)) } if (!value) return(invisible(FALSE)) } else value <- TRUE invisible(value) } ## @type normal.kind : character ## @type kind : character ## @return complex|character RNGkind <- function (kind = NULL, normal.kind = NULL) { kinds <- c("Wichmann-Hill", "Marsaglia-Multicarry", "Super-Duper", "Mersenne-Twister", "Knuth-TAOCP", "user-supplied", "Knuth-TAOCP-2002", "L'Ecuyer-CMRG", "default") n.kinds <- c("Buggy Kinderman-Ramage", "Ahrens-Dieter", "Box-Muller", "user-supplied", "Inversion", "Kinderman-Ramage", "default") do.set <- length(kind) > 0L if (do.set) { if (!is.character(kind) || length(kind) > 1L) stop("'kind' must be a character string of length 1 (RNG to be used).") if (is.na(i.knd <- pmatch(kind, kinds) - 1L)) stop(gettextf("'%s' is not a valid abbreviation of an RNG", kind), domain = NA) if (i.knd == length(kinds) - 1L) i.knd <- -1L } else i.knd <- NULL if (!is.null(normal.kind)) { if (!is.character(normal.kind) || length(normal.kind) != 1L) stop("'normal.kind' must be a character string of length 1") normal.kind <- pmatch(normal.kind, n.kinds) - 1L if (is.na(normal.kind)) stop(gettextf("'%s' is not a valid choice", normal.kind), domain = NA) if (normal.kind == 0L) warning("buggy version of Kinderman-Ramage generator used", domain = NA) if (normal.kind == length(n.kinds) - 1L) normal.kind <- -1L } r <- 1L + .Internal(RNGkind(i.knd, normal.kind)) r <- c(kinds[r[1L]], n.kinds[r[2L]]) if (do.set || !is.null(normal.kind)) invisible(r) else r } ## @type na.rm : logical ## @type x : complex|logical ## @type dims : integer rowSums <- function (x, na.rm = FALSE, dims = 1L) { if (is.data.frame(x)) x <- as.matrix(x) if (!is.array(x) || length(dn <- dim(x)) < 2L) stop("'x' must be an array of at least two dimensions") if (dims < 1L || dims > length(dn) - 1L) stop("invalid 'dims'") p <- prod(dn[-(1L:dims)]) dn <- dn[1L:dims] z <- if (is.complex(x)) .Internal(rowSums(Re(x), prod(dn), p, na.rm)) + (0+1i) * .Internal(rowSums(Im(x), prod(dn), p, na.rm)) else .Internal(rowSums(x, prod(dn), p, na.rm)) if (length(dn) > 1L) { dim(z) <- dn dimnames(z) <- dimnames(x)[1L:dims] } else names(z) <- dimnames(x)[[1L]] z } ## @type file : character ## @type ascii : logical ## @type compress : logical saveRDS <- function (object, file = "", ascii = FALSE, version = NULL, compress = TRUE, refhook = NULL) { if (is.character(file)) { if (file == "") stop("'file' must be non-empty string") mode <- if (ascii) "w" else "wb" con <- if (identical(compress, "bzip2")) bzfile(file, mode) else if (identical(compress, "xz")) xzfile(file, mode) else if (compress) gzfile(file, mode) else file(file, mode) on.exit(close(con)) } else if (inherits(file, "connection")) { if (!missing(compress)) warning("'compress' is ignored unless 'file' is a file name") con <- file } else stop("bad 'file' argument") .Internal(serializeToConn(object, con, ascii, version, refhook)) } seq.int <- function (from, to, by, length.out, along.with, ...) .Primitive("seq.int") ## @type length.out : complex seq_len <- function (length.out) .Primitive("seq_len") setdiff <- function (x, y) { x <- as.vector(x) y <- as.vector(y) unique(if (length(x) || length(y)) x[match(x, y, 0L) == 0L] else x) } ## @type hookName : character setHook <- function (hookName, value, action = c("append", "prepend", "replace")) { action <- match.arg(action) old <- getHook(hookName) new <- switch(action, append = c(old, value), prepend = c(value, old), replace = if (is.null(value) || is.list(value)) value else list(value)) if (length(new)) assign(hookName, new, envir = .userHooksEnv, inherits = FALSE) else if (exists(hookName, envir = .userHooksEnv, inherits = FALSE)) remove(list = hookName, envir = .userHooksEnv, inherits = FALSE) invisible() } ## @type string : character ## @type type : character ## @return character shQuote <- function (string, type = c("sh", "csh", "cmd")) { cshquote <- function(x) { xx <- strsplit(x, "'", fixed = TRUE)[[1L]] paste(paste0("'", xx, "'"), collapse = "\"'\"") } if (missing(type) && .Platform$OS.type == "windows") type <- "cmd" type <- match.arg(type) if (type == "cmd") { paste0("\"", gsub("\"", "\\\\\"", string), "\"") } else { if (!length(string)) return("") has_single_quote <- grep("'", string) if (!length(has_single_quote)) return(paste0("'", string, "'")) if (type == "sh") paste0("\"", gsub("([\"$`\\])", "\\\\\\1", string), "\"") else { if (!length(grep("([$`])", string))) { paste0("\"", gsub("([\"!\\])", "\\\\\\1", string), "\"") } else vapply(string, cshquote, "") } } } ## @type drop : logical "split<-" <- function (x, f, drop = FALSE, ..., value) UseMethod("split<-") ## @type fmt : character sprintf <- function (fmt, ...) .Internal(sprintf(fmt, ...)) ## @type encoding : character ## @type filename : character srcfile <- function (filename, encoding = getOption("encoding"), Enc = "unknown") { stopifnot(is.character(filename), length(filename) == 1L) e <- new.env(hash = FALSE, parent = emptyenv()) e$wd <- getwd() e$filename <- filename e$timestamp <- file.info(filename)[1, "mtime"] if (identical(encoding, "unknown")) encoding <- "native.enc" e$encoding <- encoding e$Enc <- Enc class(e) <- "srcfile" return(e) } ## @type x : character ## @type width : integer ## @return character strtrim <- function (x, width) { if (!is.character(x)) x <- as.character(x) .Internal(strtrim(x, width)) } ## @type prefix : character ## @type width : integer ## @type indent : integer ## @type x : character ## @type exdent : integer ## @type initial : character ## @type simplify : logical|character strwrap <- function (x, width = 0.9 * getOption("width"), indent = 0, exdent = 0, prefix = "", simplify = TRUE, initial = prefix) { if (!is.character(x)) x <- as.character(x) indentString <- paste(rep.int(" ", indent), collapse = "") exdentString <- paste(rep.int(" ", exdent), collapse = "") y <- list() UB <- TRUE if (all(Encoding(x) == "UTF-8")) UB <- FALSE else { enc <- Encoding(x) %in% c("latin1", "UTF-8") if (length(enc)) x[enc] <- enc2native(x[enc]) } z <- lapply(strsplit(x, "\n[ \t\n]*\n", perl = TRUE, useBytes = UB), strsplit, "[ \t\n]", perl = TRUE, useBytes = UB) for (i in seq_along(z)) { yi <- character() for (j in seq_along(z[[i]])) { words <- z[[i]][[j]] nc <- nchar(words, type = "w") if (anyNA(nc)) { nc0 <- nchar(words, type = "b") nc[is.na(nc)] <- nc0[is.na(nc)] } if (any(nc == 0L)) { zLenInd <- which(nc == 0L) zLenInd <- zLenInd[!(zLenInd %in% (grep("[.?!][)\"']{0,1}$", words, perl = TRUE, useBytes = TRUE) + 1L))] if (length(zLenInd)) { words <- words[-zLenInd] nc <- nc[-zLenInd] } } if (!length(words)) { yi <- c(yi, "", initial) next } currentIndex <- 0L lowerBlockIndex <- 1L upperBlockIndex <- integer() lens <- cumsum(nc + 1L) first <- TRUE maxLength <- width - nchar(initial, type = "w") - indent while (length(lens)) { k <- max(sum(lens <= maxLength), 1L) if (first) { first <- FALSE maxLength <- width - nchar(prefix, type = "w") - exdent } currentIndex <- currentIndex + k if (nc[currentIndex] == 0L) upperBlockIndex <- c(upperBlockIndex, currentIndex - 1L) else upperBlockIndex <- c(upperBlockIndex, currentIndex) if (length(lens) > k) { if (nc[currentIndex + 1L] == 0L) { currentIndex <- currentIndex + 1L k <- k + 1L } lowerBlockIndex <- c(lowerBlockIndex, currentIndex + 1L) } if (length(lens) > k) lens <- lens[-seq_len(k)] - lens[k] else lens <- NULL } nBlocks <- length(upperBlockIndex) s <- paste0(c(initial, rep.int(prefix, nBlocks - 1L)), c(indentString, rep.int(exdentString, nBlocks - 1L))) initial <- prefix for (k in seq_len(nBlocks)) s[k] <- paste0(s[k], paste(words[lowerBlockIndex[k]:upperBlockIndex[k]], collapse = " ")) yi <- c(yi, s, prefix) } y <- if (length(yi)) c(y, list(yi[-length(yi)])) else c(y, "") } if (simplify) y <- as.character(unlist(y)) y } summary <- function (object, ...) UseMethod("summary") ## @type command : character ## @type stdout : character ## @type wait : logical ## @type args : character ## @type input : character ## @type stderr : character ## @type env : character ## @type stdin : character system2 <- function (command, args = character(), stdout = "", stderr = "", stdin = "", input = NULL, env = character(), wait = TRUE, minimized = FALSE, invisible = TRUE) { if (!missing(minimized) || !missing(invisible)) message("arguments 'minimized' and 'invisible' are for Windows only") if (!is.logical(wait) || is.na(wait)) stop("'wait' must be TRUE or FALSE") intern <- FALSE command <- paste(c(env, shQuote(command), args), collapse = " ") if (is.null(stdout)) stdout <- FALSE if (is.null(stderr)) stderr <- FALSE if (isTRUE(stderr)) { if (!isTRUE(stdout)) warning("setting stdout = TRUE") stdout <- TRUE } if (identical(stdout, FALSE)) command <- paste(command, ">/dev/null") else if (isTRUE(stdout)) intern <- TRUE else if (is.character(stdout)) { if (length(stdout) != 1L) stop("'stdout' must be of length 1") if (nzchar(stdout)) { command <- if (identical(stdout, stderr)) paste(command, ">", shQuote(stdout), "2>&1") else command <- paste(command, ">", shQuote(stdout)) } } if (identical(stderr, FALSE)) command <- paste(command, "2>/dev/null") else if (isTRUE(stderr)) { command <- paste(command, "2>&1") } else if (is.character(stderr)) { if (length(stderr) != 1L) stop("'stderr' must be of length 1") if (nzchar(stderr) && !identical(stdout, stderr)) command <- paste(command, "2>", shQuote(stderr)) } if (!is.null(input)) { if (!is.character(input)) stop("'input' must be a character vector or 'NULL'") f <- tempfile() on.exit(unlink(f)) writeLines(input, f) command <- paste(command, "<", shQuote(f)) } else if (nzchar(stdin)) command <- paste(command, "<", stdin) if (!wait && !intern) command <- paste(command, "&") .Internal(system(command, intern)) } tempdir <- function () .Internal(tempdir()) ## @type x : character ## @return character tolower <- function (x) { if (!is.character(x)) x <- as.character(x) .Internal(tolower(x)) } ## @type x : character ## @return character toupper <- function (x) { if (!is.character(x)) x <- as.character(x) .Internal(toupper(x)) } unclass <- function (x) .Primitive("unclass") undebug <- function (fun) .Internal(undebug(fun)) ## @type value : character "units<-" <- function (x, value) UseMethod("units<-") ## @type drop : logical unsplit <- function (value, f, drop = FALSE) { len <- length(if (is.list(f)) f[[1L]] else f) if (is.data.frame(value[[1L]])) { x <- value[[1L]][rep(NA, len), , drop = FALSE] rownames(x) <- unsplit(lapply(value, rownames), f, drop = drop) } else x <- value[[1L]][rep(NA, len)] split(x, f, drop = drop) <- value x } untrace <- function (what, signature = NULL, where = topenv(parent.frame())) { MethodsDispatchOn <- .isMethodsDispatchOn() if (MethodsDispatchOn) { tState <- tracingState(FALSE) on.exit(tracingState(tState)) } if (!MethodsDispatchOn) return(.primUntrace(what)) call <- sys.call() call[[1L]] <- quote(methods::.TraceWithMethods) call$where <- where call$untrace <- TRUE value <- eval.parent(call) on.exit() tracingState(tState) invisible(value) } ## @type noBreaks. : logical ## @type call. : logical ## @type immediate. : logical ## @return character warning <- function (..., call. = TRUE, immediate. = FALSE, noBreaks. = FALSE, domain = NULL) { args <- list(...) if (length(args) == 1L && inherits(args[[1L]], "condition")) { cond <- args[[1L]] if (nargs() > 1L) cat(gettext("additional arguments ignored in warning()"), "\n", sep = "", file = stderr()) message <- conditionMessage(cond) call <- conditionCall(cond) withRestarts({ .Internal(.signalCondition(cond, message, call)) .Internal(.dfltWarn(message, call)) }, muffleWarning = function() NULL) invisible(message) } else .Internal(warning(call., immediate., noBreaks., .makeMessage(..., domain = domain))) } "+.POSIXt" <- function (e1, e2) { coerceTimeUnit <- function(x) as.vector(switch(attr(x, "units"), secs = x, mins = 60 * x, hours = 60 * 60 * x, days = 60 * 60 * 24 * x, weeks = 60 * 60 * 24 * 7 * x)) if (nargs() == 1) return(e1) if (inherits(e1, "POSIXt") && inherits(e2, "POSIXt")) stop("binary '+' is not defined for \"POSIXt\" objects") if (inherits(e1, "POSIXlt")) e1 <- as.POSIXct(e1) if (inherits(e2, "POSIXlt")) e2 <- as.POSIXct(e2) if (inherits(e1, "difftime")) e1 <- coerceTimeUnit(e1) if (inherits(e2, "difftime")) e2 <- coerceTimeUnit(e2) .POSIXct(unclass(e1) + unclass(e2), check_tzones(e1, e2)) } "-.POSIXt" <- function (e1, e2) { coerceTimeUnit <- function(x) as.vector(switch(attr(x, "units"), secs = x, mins = 60 * x, hours = 60 * 60 * x, days = 60 * 60 * 24 * x, weeks = 60 * 60 * 24 * 7 * x)) if (!inherits(e1, "POSIXt")) stop("can only subtract from \"POSIXt\" objects") if (nargs() == 1) stop("unary '-' is not defined for \"POSIXt\" objects") if (inherits(e2, "POSIXt")) return(difftime(e1, e2)) if (inherits(e2, "difftime")) e2 <- coerceTimeUnit(e2) if (!is.null(attr(e2, "class"))) stop("can only subtract numbers from \"POSIXt\" objects") e1 <- as.POSIXct(e1) .POSIXct(unclass(e1) - e2, attr(e1, "tzone")) } ## @type drop : logical "[.factor" <- function (x, ..., drop = FALSE) { y <- NextMethod("[") attr(y, "contrasts") <- attr(x, "contrasts") attr(y, "levels") <- attr(x, "levels") class(y) <- oldClass(x) lev <- levels(x) if (drop) factor(y, exclude = if (anyNA(levels(x))) NULL else NA) else y } "[.listof" <- function (x, i, ...) structure(NextMethod("["), class = class(x)) "[<-.Date" <- function (x, ..., value) { if (!length(value)) return(x) value <- unclass(as.Date(value)) cl <- oldClass(x) class(x) <- NULL x <- NextMethod(.Generic) class(x) <- cl x } ## @type unique : logical ## @type functions : logical ## @type max.names : complex ## @return character all.vars <- function (expr, functions = FALSE, max.names = -1L, unique = TRUE) .Internal(all.names(expr, functions, max.names, unique)) ## @type .dimnames : character ## @type .dim : integer ## @type useNames : logical arrayInd <- function (ind, .dim, .dimnames = NULL, useNames = FALSE) { m <- length(ind) rank <- length(.dim) wh1 <- ind - 1L ind <- 1L + wh1%%.dim[1L] dnms <- if (useNames) { list(.dimnames[[1L]][ind], if (any(nzchar(nd <- names(.dimnames)))) nd else if (rank == 2L) c("row", "col") else paste0("dim", seq_len(rank))) } ind <- matrix(ind, nrow = m, ncol = rank, dimnames = dnms) if (rank >= 2L) { denom <- 1L for (i in 2L:rank) { denom <- denom * .dim[i - 1L] nextd1 <- wh1%/%denom ind[, i] <- 1L + nextd1%%.dim[i] } } storage.mode(ind) <- "integer" ind } as.array <- function (x, ...) UseMethod("as.array") as.table <- function (x, ...) UseMethod("as.table") autoload <- function (name, package, reset = FALSE, ...) { if (!reset && exists(name, envir = .GlobalEnv, inherits = FALSE)) stop("an object with that name already exists") m <- match.call() m[[1L]] <- as.name("list") newcall <- eval(m, parent.frame()) newcall <- as.call(c(as.name("autoloader"), newcall)) newcall$reset <- NULL if (is.na(match(package, .Autoloaded))) assign(".Autoloaded", c(package, .Autoloaded), envir = .AutoloadEnv) do.call("delayedAssign", list(name, newcall, .GlobalEnv, .AutoloadEnv)) invisible() } ## @type path : character ## @return character basename <- function (path) .Internal(basename(path)) ## @type internal : logical builtins <- function (internal = FALSE) .Internal(builtins(internal)) ## @type upper : logical ## @type x : character casefold <- function (x, upper = FALSE) if (upper) toupper(x) else tolower(x) ## @type size : complex ## @type LINPACK : logical chol2inv <- function (x, size = NCOL(x), LINPACK = FALSE) .Internal(La_chol2inv(x, size)) ## @type na.rm : logical ## @type x : complex|logical ## @type dims : integer ## @return complex colMeans <- function (x, na.rm = FALSE, dims = 1L) { if (is.data.frame(x)) x <- as.matrix(x) if (!is.array(x) || length(dn <- dim(x)) < 2L) stop("'x' must be an array of at least two dimensions") if (dims < 1L || dims > length(dn) - 1L) stop("invalid 'dims'") n <- prod(dn[1L:dims]) dn <- dn[-(1L:dims)] z <- if (is.complex(x)) .Internal(colMeans(Re(x), n, prod(dn), na.rm)) + (0+1i) * .Internal(colMeans(Im(x), n, prod(dn), na.rm)) else .Internal(colMeans(x, n, prod(dn), na.rm)) if (length(dn) > 1L) { dim(z) <- dn dimnames(z) <- dimnames(x)[-(1L:dims)] } else names(z) <- dimnames(x)[[dims + 1]] z } ## @type do.NULL : logical colnames <- function (x, do.NULL = TRUE, prefix = "col") { if (is.data.frame(x) && do.NULL) return(names(x)) dn <- dimnames(x) if (!is.null(dn[[2L]])) dn[[2L]] else { nc <- NCOL(x) if (do.NULL) NULL else if (nc > 0L) paste0(prefix, seq_len(nc)) else character() } } ## @type breaks : complex ## @type start.on.monday : logical ## @type labels : integer cut.Date <- function (x, breaks, labels = NULL, start.on.monday = TRUE, right = FALSE, ...) { if (!inherits(x, "Date")) stop("'x' must be a date-time object") x <- as.Date(x) if (inherits(breaks, "Date")) { breaks <- sort(as.Date(breaks)) } else if (is.numeric(breaks) && length(breaks) == 1L) { } else if (is.character(breaks) && length(breaks) == 1L) { by2 <- strsplit(breaks, " ", fixed = TRUE)[[1L]] if (length(by2) > 2L || length(by2) < 1L) stop("invalid specification of 'breaks'") valid <- pmatch(by2[length(by2)], c("days", "weeks", "months", "years", "quarters")) if (is.na(valid)) stop("invalid specification of 'breaks'") start <- as.POSIXlt(min(x, na.rm = TRUE)) if (valid == 1L) incr <- 1L if (valid == 2L) { start$mday <- start$mday - start$wday if (start.on.monday) start$mday <- start$mday + ifelse(start$wday > 0L, 1L, -6L) start$isdst <- -1L incr <- 7L } if (valid == 3L) { start$mday <- 1L start$isdst <- -1L end <- as.POSIXlt(max(x, na.rm = TRUE)) step <- ifelse(length(by2) == 2L, as.integer(by2[1L]), 1L) end <- as.POSIXlt(end + (31 * step * 86400)) end$mday <- 1L end$isdst <- -1L breaks <- as.Date(seq(start, end, breaks)) } else if (valid == 4L) { start$mon <- 0L start$mday <- 1L start$isdst <- -1L end <- as.POSIXlt(max(x, na.rm = TRUE)) step <- ifelse(length(by2) == 2L, as.integer(by2[1L]), 1L) end <- as.POSIXlt(end + (366 * step * 86400)) end$mon <- 0L end$mday <- 1L end$isdst <- -1L breaks <- as.Date(seq(start, end, breaks)) } else if (valid == 5L) { qtr <- rep(c(0L, 3L, 6L, 9L), each = 3L) start$mon <- qtr[start$mon + 1L] start$mday <- 1L start$isdst <- -1L maxx <- max(x, na.rm = TRUE) end <- as.POSIXlt(maxx) step <- ifelse(length(by2) == 2L, as.integer(by2[1L]), 1L) end <- as.POSIXlt(end + (93 * step * 86400)) end$mon <- qtr[end$mon + 1L] end$mday <- 1L end$isdst <- -1L breaks <- as.Date(seq(start, end, paste(step * 3L, "months"))) lb <- length(breaks) if (maxx < breaks[lb - 1]) breaks <- breaks[-lb] } else { start <- as.Date(start) if (length(by2) == 2L) incr <- incr * as.integer(by2[1L]) maxx <- max(x, na.rm = TRUE) breaks <- seq(start, maxx + incr, breaks) breaks <- breaks[seq_len(1L + max(which(breaks <= maxx)))] } } else stop("invalid specification of 'breaks'") res <- cut(unclass(x), unclass(breaks), labels = labels, right = right, ...) if (is.null(labels)) { levels(res) <- as.character(if (is.numeric(breaks)) x[!duplicated(res)] else breaks[-length(breaks)]) } res } ## @type units : character difftime <- function (time1, time2, tz, units = c("auto", "secs", "mins", "hours", "days", "weeks")) { if (missing(tz)) { time1 <- as.POSIXct(time1) time2 <- as.POSIXct(time2) } else { time1 <- as.POSIXct(time1, tz = tz) time2 <- as.POSIXct(time2, tz = tz) } z <- unclass(time1) - unclass(time2) attr(z, "tzone") <- NULL units <- match.arg(units) if (units == "auto") { if (all(is.na(z))) units <- "secs" else { zz <- min(abs(z), na.rm = TRUE) if (is.na(zz) || zz < 60) units <- "secs" else if (zz < 3600) units <- "mins" else if (zz < 86400) units <- "hours" else units <- "days" } } switch(units, secs = .difftime(z, units = "secs"), mins = .difftime(z/60, units = "mins"), hours = .difftime(z/3600, units = "hours"), days = .difftime(z/86400, units = "days"), weeks = .difftime(z/(7 * 86400), units = "weeks")) } dimnames <- function (x) .Primitive("dimnames") ## @type local : logical ## @type x : character ## @type now : logical dyn.load <- function (x, local = TRUE, now = TRUE, ...) .Internal(dyn.load(x, as.logical(local), as.logical(now), "")) emptyenv <- function () .Primitive("emptyenv") ## @type x : character enc2utf8 <- function (x) .Primitive("enc2utf8") ## @type x : character ## @return character Encoding <- function (x) .Internal(Encoding(x)) ## @type indent : integer ## @type style : character ## @type width : integer ## @optional y formatDL <- function (x, y, style = c("table", "list"), width = 0.9 * getOption("width"), indent = NULL) { if (is.list(x)) { if (length(x) == 2L && diff(vapply(x, length, 1L)) == 0L) { y <- x[[2L]] x <- x[[1L]] } else stop("incorrect value for 'x'") } else if (is.matrix(x)) { if (NCOL(x) == 2L) { y <- x[, 2L] x <- x[, 1L] } else stop("incorrect value for 'x'") } else if (missing(y) && !is.null(nms <- names(x))) { y <- x x <- nms } else if (length(x) != length(y)) stop("'x' and 'y' must have the same length") x <- as.character(x) if (!length(x)) return(x) y <- as.character(y) style <- match.arg(style) if (is.null(indent)) indent <- switch(style, table = width/3, list = width/9) if (indent > 0.5 * width) stop("incorrect values of 'indent' and 'width'") indentString <- paste(rep.int(" ", indent), collapse = "") if (style == "table") { i <- (nchar(x, type = "w") > indent - 3L) if (any(i)) x[i] <- paste0(x[i], "\n", indentString) i <- !i if (any(i)) x[i] <- formatC(x[i], width = indent, flag = "-") y <- lapply(strwrap(y, width = width - indent, simplify = FALSE), paste, collapse = paste0("\n", indentString)) r <- paste0(x, unlist(y)) } else if (style == "list") { y <- strwrap(paste0(x, ": ", y), exdent = indent, width = width, simplify = FALSE) r <- unlist(lapply(y, paste, collapse = "\n")) } r } ## @type fmt : character gettextf <- function (fmt, ..., domain = NULL) sprintf(gettext(fmt, domain = domain), ...) gregexpr <- function (pattern, text, ignore.case = FALSE, perl = FALSE, fixed = FALSE, useBytes = FALSE) { if (!is.character(text)) text <- as.character(text) .Internal(gregexpr(as.character(pattern), text, ignore.case, perl, fixed, useBytes)) } identity <- function (x) x ## @type what : character ## @type which : logical inherits <- function (x, what, which = FALSE) .Internal(inherits(x, what, which)) is.array <- function (x) .Primitive("is.array") is.table <- function (x) inherits(x, "table") kappa.lm <- function (z, ...) kappa.qr(z$qr, ...) ## @optional z kappa.qr <- function (z, ...) { qr <- z$qr R <- qr[1L:min(dim(qr)), , drop = FALSE] R[lower.tri(R)] <- 0 .kappa_tri(R, ...) } lazyLoad <- function (filebase, envir = parent.frame(), filter) { fun <- function(db) { vals <- db$vals vars <- db$vars expr <- quote(lazyLoadDBfetch(key, datafile, compressed, envhook)) .Internal(makeLazy(vars, vals, expr, db, envir)) } lazyLoadDBexec(filebase, fun, filter) } ## @type value : integer "length<-" <- function (x, value) .Primitive("length<-") ## @type value : complex|character "levels<-" <- function (x, value) .Primitive("levels<-") list2env <- function (x, envir = NULL, parent = parent.frame(), hash = (length(x) > 100), size = max(29L, length(x))) { if (is.null(envir)) envir <- new.env(hash = hash, parent = parent, size = size) .Internal(list2env(x, envir)) } ## @type n : integer ngettext <- function (n, msg1, msg2, domain = NULL) .Internal(ngettext(n, msg1, msg2, domain)) oldClass <- function (x) .Primitive("oldClass") Ops.Date <- function (e1, e2) { if (nargs() == 1) stop(gettextf("unary %s not defined for \"Date\" objects", .Generic), domain = NA) boolean <- switch(.Generic, `<` = , `>` = , `==` = , `!=` = , `<=` = , `>=` = TRUE, FALSE) if (!boolean) stop(gettextf("%s not defined for \"Date\" objects", .Generic), domain = NA) if (is.character(e1)) e1 <- as.Date(e1) if (is.character(e2)) e2 <- as.Date(e2) NextMethod(.Generic) } packBits <- function (x, type = c("raw", "integer")) { type <- match.arg(type) .Internal(packBits(x, type)) } pairlist <- function (...) as.pairlist(list(...)) pmax.int <- function (..., na.rm = FALSE) .Internal(pmax(na.rm, ...)) pmin.int <- function (..., na.rm = FALSE) .Internal(pmin(na.rm, ...)) polyroot <- function (z) .Internal(polyroot(z)) ## @type right : logical ## @optional f Position <- function (f, x, right = FALSE, nomatch = NA_integer_) { ind <- if (right) rev(seq_along(x)) else seq_along(x) for (i in ind) if (f(x[[i]])) return(i) nomatch } print.by <- function (x, ..., vsep) { d <- dim(x) dn <- dimnames(x) dnn <- names(dn) if (missing(vsep)) vsep <- paste(rep.int("-", 0.75 * getOption("width")), collapse = "") lapply(X = seq_along(x), FUN = function(i, x, vsep, ...) { if (i != 1L && !is.null(vsep)) cat(vsep, "\n") ii <- i - 1L for (j in seq_along(dn)) { iii <- ii%%d[j] + 1L ii <- ii%/%d[j] cat(dnn[j], ": ", dn[[j]][iii], "\n", sep = "") } print(x[[i]], ...) }, x, vsep, ...) invisible(x) } prmatrix <- function (x, rowlab = dn[[1]], collab = dn[[2]], quote = TRUE, right = FALSE, na.print = NULL, ...) { x <- as.matrix(x) dn <- dimnames(x) .Internal(prmatrix(x, rowlab, collab, quote, right, na.print)) } ## @type x : numeric ## @type deriv : integer psigamma <- function (x, deriv = 0L) .Internal(psigamma(x, deriv)) pushBack <- function (data, connection, newLine = TRUE, encoding = c("", "bytes", "UTF-8")) { if (length(encoding) > 1) encoding <- encoding[1] if (nchar(encoding)) encoding <- match.arg(encoding) type <- match(encoding, c("", "bytes", "UTF-8")) .Internal(pushBack(data, connection, newLine, type)) } qr.resid <- function (qr, y) { if (!is.qr(qr)) stop("argument is not a QR decomposition") if (is.complex(qr$qr)) stop("not implemented for complex 'qr'") if (isTRUE(attr(qr, "useLAPACK"))) stop("not supported for LAPACK QR") k <- as.integer(qr$rank) if (k == 0) return(y) n <- as.integer(nrow(qr$qr)) if (is.na(n)) stop("invalid nrow(qr$qr)") ny <- as.integer(NCOL(y)) if (is.na(ny)) stop("invalid NCOL(y)") if (NROW(y) != n) stop("'qr' and 'y' must have the same number of rows") storage.mode(y) <- "double" .Fortran(.F_dqrrsd, as.double(qr$qr), n, k, as.double(qr$qraux), y, ny, rsd = y)$rsd } qr.solve <- function (a, b, tol = 1e-07) { if (!is.qr(a)) a <- qr(a, tol = tol) nc <- ncol(a$qr) nr <- nrow(a$qr) if (a$rank != min(nc, nr)) stop("singular matrix 'a' in solve") if (missing(b)) { if (nc != nr) stop("only square matrices can be inverted") b <- diag(1, nc) } res <- qr.coef(a, b) res[is.na(res)] <- 0 res } ## @return complex|character quarters <- function (x, abbreviate) UseMethod("quarters") ## @return raw|numeric|character rawShift <- function (x, n) .Internal(rawShift(x, n)) read.dcf <- function (file, fields = NULL, all = FALSE, keep.white = NULL) { if (is.character(file)) { file <- gzfile(file) on.exit(close(file)) } if (!inherits(file, "connection")) stop("'file' must be a character string or connection") if (!all) return(.Internal(readDCF(file, fields, keep.white))) .assemble_things_into_a_data_frame <- function(tags, vals, nums) { tf <- factor(tags, levels = unique(tags)) cnts <- table(nums, tf) out <- array(NA_character_, dim = dim(cnts), dimnames = list(NULL, levels(tf))) if (all(cnts <= 1L)) { out[cbind(nums, tf)] <- vals out <- as.data.frame(out, stringsAsFactors = FALSE) } else { levs <- colSums(cnts > 1L) == 0L if (any(levs)) { inds <- tf %in% levels(tf)[levs] out[cbind(nums[inds], tf[inds])] <- vals[inds] } out <- as.data.frame(out, stringsAsFactors = FALSE) for (l in levels(tf)[!levs]) { out[[l]] <- rep.int(list(NA_character_), nrow(cnts)) i <- tf == l out[[l]][unique(nums[i])] <- split(vals[i], nums[i]) } } out } ctype <- Sys.getlocale("LC_CTYPE") on.exit(Sys.setlocale("LC_CTYPE", ctype), add = TRUE) Sys.setlocale("LC_CTYPE", "C") lines <- readLines(file) ind <- grep("^[^[:blank:]][^:]*$", lines) if (length(ind)) { lines <- strtrim(lines[ind], 0.7 * getOption("width")) stop(gettextf("Invalid DCF format.\nRegular lines must have a tag.\nOffending lines start with:\n%s", paste0(" ", lines, collapse = "\n")), domain = NA) } line_is_not_empty <- !grepl("^[[:space:]]*$", lines) nums <- cumsum(diff(c(FALSE, line_is_not_empty) > 0L) > 0L) nums <- nums[line_is_not_empty] lines <- lines[line_is_not_empty] line_is_escaped_blank <- grepl("^[[:space:]]+\\.[[:space:]]*$", lines) if (any(line_is_escaped_blank)) lines[line_is_escaped_blank] <- "" line_has_tag <- grepl("^[^[:blank:]][^:]*:", lines) ind <- which(!line_has_tag[which(diff(nums) > 0L) + 1L]) if (length(ind)) { lines <- strtrim(lines[ind], 0.7 * getOption("width")) stop(gettextf("Invalid DCF format.\nContinuation lines must not start a record.\nOffending lines start with:\n%s", paste0(" ", lines, collapse = "\n")), domain = NA) } lengths <- rle(cumsum(line_has_tag))$lengths pos <- cumsum(lengths) tags <- sub(":.*", "", lines[line_has_tag]) lines[line_has_tag] <- sub("[^:]*:[[:space:]]*", "", lines[line_has_tag]) foldable <- rep.int(is.na(match(tags, keep.white)), lengths) lines[foldable] <- sub("^[[:space:]]*", "", lines[foldable]) lines[foldable] <- sub("[[:space:]]*$", "", lines[foldable]) vals <- mapply(function(from, to) paste(lines[from:to], collapse = "\n"), c(1L, pos[-length(pos)] + 1L), pos) out <- .assemble_things_into_a_data_frame(tags, vals, nums[pos]) if (!is.null(fields)) out <- out[fields] out } ## @type con : raw|character ## @type useBytes : complex|logical ## @type nchars : integer|character readChar <- function (con, nchars, useBytes = FALSE) { if (is.character(con)) { con <- file(con, "rb") on.exit(close(con)) } .Internal(readChar(con, as.integer(nchars), useBytes)) } ## @type prompt : character ## @return character readline <- function (prompt = "") .Internal(readline(prompt)) ## @optional x rep.Date <- function (x, ...) { y <- NextMethod() structure(y, class = "Date") } ## @type na.rm : logical ## @type dims : integer ## @type x : complex|logical ## @return complex rowMeans <- function (x, na.rm = FALSE, dims = 1L) { if (is.data.frame(x)) x <- as.matrix(x) if (!is.array(x) || length(dn <- dim(x)) < 2L) stop("'x' must be an array of at least two dimensions") if (dims < 1L || dims > length(dn) - 1L) stop("invalid 'dims'") p <- prod(dn[-(1L:dims)]) dn <- dn[1L:dims] z <- if (is.complex(x)) .Internal(rowMeans(Re(x), prod(dn), p, na.rm)) + (0+1i) * .Internal(rowMeans(Im(x), prod(dn), p, na.rm)) else .Internal(rowMeans(x, prod(dn), p, na.rm)) if (length(dn) > 1L) { dim(z) <- dn dimnames(z) <- dimnames(x)[1L:dims] } else names(z) <- dimnames(x)[[1L]] z } ## @type do.NULL : logical rownames <- function (x, do.NULL = TRUE, prefix = "row") { dn <- dimnames(x) if (!is.null(dn[[1L]])) dn[[1L]] else { nr <- NROW(x) if (do.NULL) NULL else if (nr > 0L) paste0(prefix, seq_len(nr)) else character() } } ## @type length.out : integer seq.Date <- function (from, to, by, length.out = NULL, along.with = NULL, ...) { if (missing(from)) stop("'from' must be specified") if (!inherits(from, "Date")) stop("'from' must be a \"Date\" object") if (length(as.Date(from)) != 1L) stop("'from' must be of length 1") if (!missing(to)) { if (!inherits(to, "Date")) stop("'to' must be a \"Date\" object") if (length(as.Date(to)) != 1L) stop("'to' must be of length 1") } if (!missing(along.with)) { length.out <- length(along.with) } else if (!is.null(length.out)) { if (length(length.out) != 1L) stop("'length.out' must be of length 1") length.out <- ceiling(length.out) } status <- c(!missing(to), !missing(by), !is.null(length.out)) if (sum(status) != 2L) stop("exactly two of 'to', 'by' and 'length.out' / 'along.with' must be specified") if (missing(by)) { from <- unclass(as.Date(from)) to <- unclass(as.Date(to)) res <- seq.int(from, to, length.out = length.out) return(structure(res, class = "Date")) } if (length(by) != 1L) stop("'by' must be of length 1") valid <- 0L if (inherits(by, "difftime")) { by <- switch(attr(by, "units"), secs = 1/86400, mins = 1/1440, hours = 1/24, days = 1, weeks = 7) * unclass(by) } else if (is.character(by)) { by2 <- strsplit(by, " ", fixed = TRUE)[[1L]] if (length(by2) > 2L || length(by2) < 1L) stop("invalid 'by' string") valid <- pmatch(by2[length(by2)], c("days", "weeks", "months", "quarters", "years")) if (is.na(valid)) stop("invalid string for 'by'") if (valid <= 2L) { by <- c(1, 7)[valid] if (length(by2) == 2L) by <- by * as.integer(by2[1L]) } else by <- if (length(by2) == 2L) as.integer(by2[1L]) else 1 } else if (!is.numeric(by)) stop("invalid mode for 'by'") if (is.na(by)) stop("'by' is NA") if (valid <= 2L) { from <- unclass(as.Date(from)) if (!is.null(length.out)) res <- seq.int(from, by = by, length.out = length.out) else { to0 <- unclass(as.Date(to)) res <- seq.int(0, to0 - from, by) + from } res <- structure(res, class = "Date") } else { r1 <- as.POSIXlt(from) if (valid == 5L) { if (missing(to)) { yr <- seq.int(r1$year, by = by, length.out = length.out) } else { to0 <- as.POSIXlt(to) yr <- seq.int(r1$year, to0$year, by) } r1$year <- yr res <- as.Date(r1) } else { if (valid == 4L) by <- by * 3 if (missing(to)) { mon <- seq.int(r1$mon, by = by, length.out = length.out) } else { to0 <- as.POSIXlt(to) mon <- seq.int(r1$mon, 12 * (to0$year - r1$year) + to0$mon, by) } r1$mon <- mon res <- as.Date(r1) } } if (!missing(to)) { to <- as.Date(to) res <- if (by > 0) res[res <= to] else res[res >= to] } res } ## @type nvec : integer sequence <- function (nvec) unlist(lapply(nvec, seq_len)) ## @type seed : integer ## @type normal.kind : character ## @type kind : character set.seed <- function (seed, kind = NULL, normal.kind = NULL) { kinds <- c("Wichmann-Hill", "Marsaglia-Multicarry", "Super-Duper", "Mersenne-Twister", "Knuth-TAOCP", "user-supplied", "Knuth-TAOCP-2002", "L'Ecuyer-CMRG", "default") n.kinds <- c("Buggy Kinderman-Ramage", "Ahrens-Dieter", "Box-Muller", "user-supplied", "Inversion", "Kinderman-Ramage", "default") if (length(kind)) { if (!is.character(kind) || length(kind) > 1L) stop("'kind' must be a character string of length 1 (RNG to be used).") if (is.na(i.knd <- pmatch(kind, kinds) - 1L)) stop(gettextf("'%s' is not a valid abbreviation of an RNG", kind), domain = NA) if (i.knd == length(kinds) - 1L) i.knd <- -1L } else i.knd <- NULL if (!is.null(normal.kind)) { if (!is.character(normal.kind) || length(normal.kind) != 1L) stop("'normal.kind' must be a character string of length 1") normal.kind <- pmatch(normal.kind, n.kinds) - 1L if (is.na(normal.kind)) stop(gettextf("'%s' is not a valid choice", normal.kind), domain = NA) if (normal.kind == 0L) stop("buggy version of Kinderman-Ramage generator is not allowed", domain = NA) if (normal.kind == length(n.kinds) - 1L) normal.kind <- -1L } .Internal(set.seed(seed, i.knd, normal.kind)) } setequal <- function (x, y) { x <- as.vector(x) y <- as.vector(y) all(c(match(x, y, 0L) > 0L, match(y, x, 0L) > 0L)) } solve.qr <- function (a, b, ...) { if (!is.qr(a)) stop("this is the \"qr\" method for the generic function solve()") nc <- ncol(a$qr) nr <- nrow(a$qr) if (a$rank != min(nc, nr)) if (a$rank != nc) stop("singular matrix 'a' in 'solve'") if (missing(b)) { if (nc != nr) stop("only square matrices can be inverted") b <- diag(1, nc) } res <- qr.coef(a, b) res[is.na(res)] <- 0 res } ## @type method : character ## @type index.return : logical ## @type x : complex|logical|character ## @type decreasing : logical sort.int <- function (x, partial = NULL, na.last = NA, decreasing = FALSE, method = c("shell", "quick"), index.return = FALSE) { if (isfact <- is.factor(x)) { if (index.return) stop("'index.return' only for non-factors") lev <- levels(x) nlev <- nlevels(x) isord <- is.ordered(x) x <- c(x) } else if (!is.atomic(x)) stop("'x' must be atomic") if (has.na <- any(ina <- is.na(x))) { nas <- x[ina] x <- x[!ina] } if (index.return && !is.na(na.last)) stop("'index.return' only for 'na.last = NA'") if (!is.null(partial)) { if (index.return || decreasing || isfact || !missing(method)) stop("unsupported options for partial sorting") if (!all(is.finite(partial))) stop("non-finite 'partial'") y <- if (length(partial) <= 10L) { partial <- .Internal(qsort(partial, FALSE)) .Internal(psort(x, partial)) } else if (is.double(x)) .Internal(qsort(x, FALSE)) else .Internal(sort(x, FALSE)) } else if (isfact && missing(method) && nlev < 1e+05) { o <- sort.list(x, decreasing = decreasing, method = "radix") y <- x[o] } else { nms <- names(x) method <- if (is.numeric(x)) match.arg(method) else "shell" switch(method, quick = { if (!is.null(nms)) { if (decreasing) x <- -x y <- .Internal(qsort(x, TRUE)) if (decreasing) y$x <- -y$x names(y$x) <- nms[y$ix] if (!index.return) y <- y$x } else { if (decreasing) x <- -x y <- .Internal(qsort(x, index.return)) if (decreasing) if (index.return) y$x <- -y$x else y <- -y } }, shell = { if (index.return || !is.null(nms)) { o <- sort.list(x, decreasing = decreasing) y <- if (index.return) list(x = x[o], ix = o) else x[o] } else y <- .Internal(sort(x, decreasing)) }) } if (!is.na(na.last) && has.na) y <- if (!na.last) c(nas, y) else c(y, nas) if (isfact) y <- (if (isord) ordered else factor)(y, levels = seq_len(nlev), labels = lev) y } ## @type usetz : logical ## @type tz : character ## @type format : complex|character ## @type x : character strftime <- function (x, format = "", tz = "", usetz = FALSE, ...) format(as.POSIXlt(x, tz = tz), format = format, usetz = usetz, ...) strptime <- function (x, format, tz = "") { y <- .Internal(strptime(as.character(x), format, tz)) names(y$year) <- names(x) y } strsplit <- function (x, split, fixed = FALSE, perl = FALSE, useBytes = FALSE) .Internal(strsplit(x, as.character(split), fixed, perl, useBytes)) ## @type stop : integer ## @type x : character ## @type value : character ## @type start : integer "substr<-" <- function (x, start, stop, value) .Internal(`substr<-`(x, as.integer(start), as.integer(stop), value)) sys.call <- function (which = 0L) .Internal(sys.call(which)) Sys.Date <- function () as.Date(as.POSIXlt(Sys.time())) ## @type paths : character ## @type dirmark : logical ## @return character Sys.glob <- function (paths, dirmark = FALSE) .Internal(Sys.glob(path.expand(paths), dirmark)) Sys.info <- function () .Internal(Sys.info()) Sys.time <- function () .POSIXct(.Internal(Sys.time())) ## @return integer tabulate <- function (bin, nbins = max(1L, bin, na.rm = TRUE)) { if (!is.numeric(bin) && !is.factor(bin)) stop("'bin' must be numeric or a factor") if (typeof(bin) != "integer") bin <- as.integer(bin) if (nbins > .Machine$integer.max) stop("attempt to make a table with >= 2^31 elements") nbins <- as.integer(nbins) if (is.na(nbins)) stop("invalid value of 'nbins'") .Internal(tabulate(bin, nbins)) } ## @type tmpdir : character ## @type fileext : character ## @type pattern : character ## @return character tempfile <- function (pattern = "file", tmpdir = tempdir(), fileext = "") .Internal(tempfile(pattern, tmpdir, fileext)) toString <- function (x, ...) UseMethod("toString") tracemem <- function (x) .Primitive("tracemem") ## @type x : numeric trigamma <- function (x) .Primitive("trigamma") truncate <- function (con, ...) UseMethod("truncate") tryCatch <- function (expr, ..., finally) { tryCatchList <- function(expr, names, parentenv, handlers) { nh <- length(names) if (nh > 1L) tryCatchOne(tryCatchList(expr, names[-nh], parentenv, handlers[-nh]), names[nh], parentenv, handlers[[nh]]) else if (nh == 1L) tryCatchOne(expr, names, parentenv, handlers[[1L]]) else expr } tryCatchOne <- function(expr, name, parentenv, handler) { doTryCatch <- function(expr, name, parentenv, handler) { .Internal(.addCondHands(name, list(handler), parentenv, environment(), FALSE)) expr } value <- doTryCatch(return(expr), name, parentenv, handler) if (is.null(value[[1L]])) { msg <- .Internal(geterrmessage()) call <- value[[2L]] cond <- simpleError(msg, call) } else cond <- value[[1L]] value[[3L]](cond) } if (!missing(finally)) on.exit(finally) handlers <- list(...) classes <- names(handlers) parentenv <- parent.frame() if (length(classes) != length(handlers)) stop("bad handler specification") tryCatchList(expr, classes, parentenv, handlers) } warnings <- function (...) { if (!exists("last.warning", envir = baseenv())) return() last.warning <- get("last.warning", envir = baseenv()) if (!(n <- length(last.warning))) return() structure(last.warning, dots = list(...), class = "warnings") } ## @return complex|character weekdays <- function (x, abbreviate) UseMethod("weekdays") writeBin <- function (object, con, size = NA_integer_, endian = .Platform$endian, useBytes = FALSE) { swap <- endian != .Platform$endian if (!is.vector(object) || mode(object) == "list") stop("can only write vector objects") if (is.character(con)) { con <- file(con, "wb") on.exit(close(con)) } .Internal(writeBin(object, con, size, swap, useBytes)) } ## @type digits : integer ## @type x : complex zapsmall <- function (x, digits = getOption("digits")) { if (length(digits) == 0L) stop("invalid 'digits'") if (all(ina <- is.na(x))) return(x) mx <- max(abs(x[!ina])) round(x, digits = if (mx > 0) max(0L, digits - log10(mx)) else digits) } "!.hexmode" <- function (a) as.hexmode(bitwNot(as.hexmode(a))) "!.octmode" <- function (a) as.octmode(bitwNot(as.octmode(a))) "$.DLLInfo" <- function (x, name) getNativeSymbolInfo(as.character(name), PACKAGE = x) "&.hexmode" <- function (a, b) as.hexmode(bitwAnd(as.hexmode(a), as.hexmode(b))) "&.octmode" <- function (a, b) as.octmode(bitwAnd(as.octmode(a), as.octmode(b))) ## @optional i "[.hexmode" <- function (x, i) { cl <- oldClass(x) y <- NextMethod("[") oldClass(y) <- cl y } "[.noquote" <- function (x, ...) { attr <- attributes(x) r <- unclass(x)[...] attributes(r) <- c(attributes(r), attr[is.na(match(names(attr), c("dim", "dimnames", "names")))]) r } ## @optional i "[.octmode" <- function (x, i) { cl <- oldClass(x) y <- NextMethod("[") oldClass(y) <- cl y } "[.POSIXct" <- function (x, ..., drop = TRUE) { cl <- oldClass(x) class(x) <- NULL val <- NextMethod("[") class(val) <- cl attr(val, "tzone") <- attr(x, "tzone") val } "[.POSIXlt" <- function (x, ..., drop = TRUE) { val <- lapply(X = x, FUN = "[", ..., drop = drop) attributes(val) <- attributes(x) val } "[[.factor" <- function (x, ...) { y <- NextMethod("[[") attr(y, "contrasts") <- attr(x, "contrasts") attr(y, "levels") <- attr(x, "levels") class(y) <- oldClass(x) y } all.equal <- function (target, current, ...) UseMethod("all.equal") ## @type max.names : complex ## @type functions : logical ## @type unique : logical ## @return character all.names <- function (expr, functions = TRUE, max.names = -1L, unique = FALSE) .Internal(all.names(expr, functions, max.names, unique)) as.double <- function (x, ...) .Primitive("as.double") as.factor <- function (x) { if (is.factor(x)) x else if (!is.object(x) && is.integer(x)) { levels <- sort(unique.default(x)) f <- match(x, levels) levels(f) <- as.character(levels) class(f) <- "factor" f } else factor(x) } as.matrix <- function (x, ...) UseMethod("as.matrix") as.single <- function (x, ...) UseMethod("as.single") as.symbol <- function (x) .Internal(as.vector(x, "symbol")) ## @type mode : character ## @return raw|numeric|character as.vector <- function (x, mode = "any") .Internal(as.vector(x, mode)) ## @type upper.tri : logical ## @type transpose : logical ## @type k : complex backsolve <- function (r, x, k = ncol(r), upper.tri = TRUE, transpose = FALSE) { r <- as.matrix(r) x.mat <- is.matrix(x) if (!x.mat) x <- as.matrix(x) z <- .Internal(backsolve(r, x, k, upper.tri, transpose)) if (x.mat) z else drop(z) } c.noquote <- function (..., recursive = FALSE) structure(NextMethod("c"), class = "noquote") c.POSIXct <- function (..., recursive = FALSE) .POSIXct(c(unlist(lapply(list(...), unclass)))) c.POSIXlt <- function (..., recursive = FALSE) as.POSIXlt(do.call("c", lapply(list(...), as.POSIXct))) ## @type length : integer character <- function (length = 0L) .Internal(vector("character", length)) ## @return integer charmatch <- function (x, table, nomatch = NA_integer_) .Internal(charmatch(as.character(x), as.character(table), nomatch)) charToRaw <- function (x) .Internal(charToRaw(x)) ## @type value : character "comment<-" <- function (x, value) .Internal(`comment<-`(x, value)) conflicts <- function (where = search(), detail = FALSE) { if (length(where) < 1L) stop("argument 'where' of length 0") z <- vector(length(where), mode = "list") names(z) <- where for (i in seq_along(where)) z[[i]] <- objects(pos = where[i]) all <- unlist(z, use.names = FALSE) dups <- duplicated(all) dups <- all[dups] if (detail) { for (i in where) z[[i]] <- z[[i]][match(dups, z[[i]], 0L)] z[vapply(z, function(x) length(x) == 0L, NA)] <- NULL z } else dups } ## @type y : complex ## @type x : complex crossprod <- function (x, y = NULL) .Internal(crossprod(x, y)) ## @type text : character debugonce <- function (fun, text = "", condition = NULL) .Internal(debugonce(fun, text, condition)) ## @type lag : integer ## @type x : numeric ## @type differences : integer diff.Date <- function (x, lag = 1L, differences = 1L, ...) { ismat <- is.matrix(x) xlen <- if (ismat) dim(x)[1L] else length(x) if (length(lag) != 1L || length(differences) > 1L || lag < 1L || differences < 1L) stop("'lag' and 'differences' must be integers >= 1") if (lag * differences >= xlen) return(structure(numeric(), class = "difftime", units = "days")) r <- x i1 <- -seq_len(lag) if (ismat) for (i in seq_len(differences)) r <- r[i1, , drop = FALSE] - r[-nrow(r):-(nrow(r) - lag + 1L), , drop = FALSE] else for (i in seq_len(differences)) r <- r[i1] - r[-length(r):-(length(r) - lag + 1L)] r } dontCheck <- function (x) x ## @type x : numeric factorial <- function (x) gamma(x + 1) ## @type copy.mode : logical ## @type overwrite : logical ## @type from : character ## @type to : character ## @type recursive : logical ## @type copy.date : logical file.copy <- function (from, to, overwrite = recursive, recursive = FALSE, copy.mode = TRUE, copy.date = FALSE) { if (!(nf <- length(from))) return(logical()) if (!(nt <- length(to))) stop("no files to copy to") if (nt == 1 && isTRUE(file.info(to)$isdir)) { if (recursive && to %in% from) stop("attempt to copy a directory to itself") if (.Platform$OS.type == "windows") { from <- gsub("/", "\\", from, fixed = TRUE) to <- gsub("/", "\\", to, fixed = TRUE) } return(.Internal(file.copy(from, to, overwrite, recursive, copy.mode, copy.date))) } else if (nf > nt) stop("more 'from' files than 'to' files") else if (recursive) warning("'recursive' will be ignored as 'to' is not a single existing directory") if (nt > nf) from <- rep_len(from, length.out = nt) okay <- file.exists(from) if (!overwrite) okay[file.exists(to)] <- FALSE if (any(from[okay] %in% to[okay])) stop("file can not be copied both 'from' and 'to'") if (any(okay)) { okay[okay] <- file.create(to[okay]) if (any(okay)) { okay[okay] <- file.append(to[okay], from[okay]) if (copy.mode || copy.date) { fi <- file.info(from[okay]) if (copy.mode) Sys.chmod(to[okay], fi$mode, TRUE) if (copy.date) Sys.setFileTime(to[okay], fi$mtime) } } } okay } file.info <- function (...) { res <- .Internal(file.info(fn <- c(...))) res$mtime <- .POSIXct(res$mtime) res$ctime <- .POSIXct(res$ctime) res$atime <- .POSIXct(res$atime) class(res) <- "data.frame" attr(res, "row.names") <- fn res } ## @type to : character ## @type from : character file.link <- function (from, to) { if (!(length(from))) stop("no files to link from") if (!(nt <- length(to))) stop("no files to link to") .Internal(file.link(from, to)) } file.path <- function (..., fsep = .Platform$file.sep) .Internal(file.path(list(...), fsep)) ## @type encoding : character ## @type header : complex|character file.show <- function (..., header = rep("", nfiles), title = "R Information", delete.file = FALSE, pager = getOption("pager"), encoding = "") { files <- path.expand(c(...)) nfiles <- length(files) if (nfiles == 0L) return(invisible(NULL)) if (l10n_info()[["UTF-8"]] && encoding == "UTF-8") encoding <- "" if (l10n_info()[["Latin-1"]] && encoding == "latin1") encoding <- "" if (!is.na(encoding) && encoding != "") { for (i in seq_along(files)) { f <- files[i] tf <- tempfile() tmp <- readLines(f, warn = FALSE) tmp2 <- try(iconv(tmp, encoding, "", "byte")) if (inherits(tmp2, "try-error")) file.copy(f, tf) else writeLines(tmp2, tf) files[i] <- tf if (delete.file) unlink(f) } delete.file <- TRUE } if (is.function(pager)) pager(files, header = header, title = title, delete.file = delete.file) else .Internal(file.show(files, header, title, delete.file, pager)) } "formals<-" <- function (fun, envir = environment(fun), value) { bd <- body(fun) as.function(c(value, if (is.null(bd) || is.list(bd)) list(bd) else bd), envir) } ## @type on : logical gctorture <- function (on = TRUE) .Internal(gctorture(on)) ## @type x : character getOption <- function (x, default = NULL) { if (missing(default)) return(options(x)[[1L]]) if (x %in% names(options())) options(x)[[1L]] else default } globalenv <- function () .Primitive("globalenv") iconvlist <- function () { int <- .Internal(iconv(NULL, "", "", "", TRUE, FALSE)) if (length(int)) return(sort.int(int)) icfile <- system.file("iconvlist", package = "utils") if (!nchar(icfile, type = "bytes")) stop("'iconvlist' is not available on this system") ext <- readLines(icfile) if (!length(ext)) stop("'iconvlist' is not available on this system") cnt <- grep("//$", ext) if (length(cnt)/length(ext) > 0.5) { ext <- grep("//$", ext, value = TRUE) ext <- sub("//$", "", ext) } sort.int(unlist(strsplit(ext, "[[:space:]]"))) } ## @type num.eq : complex|logical ## @type attrib.as.set : logical ## @type ignore.environment : logical ## @type single.NA : numeric|logical ## @type ignore.bytecode : logical ## @return logical identical <- function (x, y, num.eq = TRUE, single.NA = TRUE, attrib.as.set = TRUE, ignore.bytecode = TRUE, ignore.environment = FALSE) .Internal(identical(x, y, num.eq, single.NA, attrib.as.set, ignore.bytecode, ignore.environment)) ## @optional x intersect <- function (x, y) { y <- as.vector(y) unique(y[match(as.vector(x), y, 0L)]) } intToBits <- function (x) .Internal(intToBits(x)) ## @type multiple : logical|character ## @return complex|character intToUtf8 <- function (x, multiple = FALSE) .Internal(intToUtf8(x, multiple)) invisible <- function (x) .Primitive("invisible") is.atomic <- function (x) .Primitive("is.atomic") is.double <- function (x) .Primitive("is.double") is.factor <- function (x) inherits(x, "factor") is.finite <- function (x) .Primitive("is.finite") ## @type PACKAGE : character ## @type symbol : character is.loaded <- function (symbol, PACKAGE = "", type = "") .Internal(is.loaded(symbol, PACKAGE, type)) is.matrix <- function (x) .Primitive("is.matrix") is.object <- function (x) .Primitive("is.object") is.single <- function (x) .Primitive("is.single") is.symbol <- function (x) .Primitive("is.symbol") ## @type mode : character is.vector <- function (x, mode = "any") .Internal(is.vector(x, mode)) isRestart <- function (x) inherits(x, "restart") l10n_info <- function () .Internal(l10n_info()) ## @type path : character ## @type full.names : logical ## @type recursive : logical ## @return character list.dirs <- function (path = ".", full.names = TRUE, recursive = TRUE) .Internal(list.dirs(path, full.names, recursive)) ## @type diag : logical lower.tri <- function (x, diag = FALSE) { x <- as.matrix(x) if (diag) row(x) >= col(x) else row(x) > col(x) } ## @type choices : character ## @type several.ok : logical ## @type arg : character match.arg <- function (arg, choices, several.ok = FALSE) { if (missing(choices)) { formal.args <- formals(sys.function(sys.parent())) choices <- eval(formal.args[[deparse(substitute(arg))]]) } if (is.null(arg)) return(choices[1L]) else if (!is.character(arg)) stop("'arg' must be NULL or a character vector") if (!several.ok) { if (identical(arg, choices)) return(arg[1L]) if (length(arg) > 1L) stop("'arg' must be of length 1") } else if (length(arg) == 0L) stop("'arg' must be of length >= 1") i <- pmatch(arg, choices, nomatch = 0L, duplicates.ok = TRUE) if (all(i == 0L)) stop(gettextf("'arg' should be one of %s", paste(dQuote(choices), collapse = ", ")), domain = NA) i <- i[i > 0L] if (!several.ok && length(i) > 1) stop("there is more than one match in 'match.arg'") choices[i] } ## @type FUN : character ## @type descend : logical match.fun <- function (FUN, descend = TRUE) { if (is.function(FUN)) return(FUN) if (!(is.character(FUN) && length(FUN) == 1L || is.symbol(FUN))) { FUN <- eval.parent(substitute(substitute(FUN))) if (!is.symbol(FUN)) stop(gettextf("'%s' is not a function, character or symbol", deparse(FUN)), domain = NA) } envir <- parent.frame(2) if (descend) FUN <- get(as.character(FUN), mode = "function", envir = envir) else { FUN <- get(as.character(FUN), mode = "any", envir = envir) if (!is.function(FUN)) stop(gettextf("found non-function '%s'", FUN), domain = NA) } return(FUN) } Math.Date <- function (x, ...) stop(gettextf("%s not defined for \"Date\" objects", .Generic), domain = NA) mean.Date <- function (x, ...) structure(mean(unclass(x), ...), class = "Date") ## @type x : complex|character ## @type is.cmplx : complex|logical|character ## @type drop0trailing : logical ## @type preserve.width : character ## @type decimal.mark : numeric|character ## @type big.mark : character ## @type small.mark : character ## @type zero.print : logical|character ## @return complex|character prettyNum <- function (x, big.mark = "", big.interval = 3L, small.mark = "", small.interval = 5L, decimal.mark = ".", preserve.width = c("common", "individual", "none"), zero.print = NULL, drop0trailing = FALSE, is.cmplx = NA, ...) { if (!is.character(x)) { is.cmplx <- is.complex(x) x <- sapply(X = x, FUN = format, ...) } nMark <- big.mark == "" && small.mark == "" && decimal.mark == "." nZero <- is.null(zero.print) && !drop0trailing if (nMark && nZero) return(x) if (!is.null(zero.print) && any(i0 <- as.numeric(x) == 0)) { if (length(zero.print) > 1L) stop("'zero.print' has length > 1") if (is.logical(zero.print)) zero.print <- if (zero.print) "0" else " " if (!is.character(zero.print)) stop("'zero.print' must be character, logical or NULL") blank.chars <- function(no) vapply(no + 1L, function(n) paste(character(n), collapse = " "), "") nz <- nchar(zero.print, "c") nc <- nchar(x[i0], "c") ind0 <- regexpr("0", x[i0], fixed = TRUE) substr(x[i0], ind0, (i1 <- ind0 + nz - 1L)) <- zero.print substr(x[i0], ind0 + nz, nc) <- blank.chars(nc - i1) } if (nMark && !drop0trailing) return(x) if (is.na(is.cmplx)) { ina <- is.na(x) | x == "NA" is.cmplx <- if (all(ina)) FALSE else length(grep("[0-9].*[-+][0-9].*i$", x)) > 0 } if (is.cmplx) { z.sp <- strsplit(sub("([0-9] *)([-+])( *[0-9])", "\\1::\\2::\\3", x), "::", fixed = TRUE) i3 <- vapply(z.sp, length, 0L) == 3L if (any(i3)) { z.sp <- z.sp[i3] z.im <- sapply(z.sp, `[[`, 3L) has.i <- grep("i$", z.im) z.im[has.i] <- sub("i$", "", z.im[has.i]) r <- lapply(list(sapply(z.sp, `[[`, 1L), z.im), function(.) prettyNum(., big.mark = big.mark, big.interval = big.interval, small.mark = small.mark, small.interval = small.interval, decimal.mark = decimal.mark, preserve.width = preserve.width, zero.print = zero.print, drop0trailing = drop0trailing, is.cmplx = FALSE, ...)) r[[2]][has.i] <- paste0(r[[2]][has.i], "i") x[i3] <- paste0(r[[1]], sapply(z.sp, `[[`, 2L), r[[2]]) } return(x) } preserve.width <- match.arg(preserve.width) x.sp <- strsplit(x, ".", fixed = TRUE) revStr <- function(cc) sapply(lapply(strsplit(cc, NULL), rev), paste, collapse = "") B. <- sapply(x.sp, `[`, 1L) A. <- sapply(x.sp, `[`, 2) if (any(iN <- is.na(A.))) A.[iN] <- "" if (nzchar(big.mark) && length(i.big <- grep(paste0("[0-9]{", big.interval + 1L, ",}"), B.))) { B.[i.big] <- revStr(gsub(paste0("([0-9]{", big.interval, "})\\B"), paste0("\\1", revStr(big.mark)), revStr(B.[i.big]))) } if (nzchar(small.mark) && length(i.sml <- grep(paste0("[0-9]{", small.interval + 1L, ",}"), A.))) { A.[i.sml] <- gsub(paste0("([0-9]{", small.interval, "}\\B)"), paste0("\\1", small.mark), A.[i.sml]) } if (drop0trailing) { a <- A.[!iN] if (length(hasE <- grep("e", a, fixed = TRUE))) { a[hasE] <- sub("e[+-]0+$", "", a[hasE]) a[-hasE] <- sub("0+$", "", a[-hasE]) } else a <- sub("0+$", "", a) A.[!iN] <- a iN <- !nzchar(A.) } A. <- paste0(B., c(decimal.mark, "")[iN + 1L], A.) if (preserve.width != "none") { nnc <- nchar(A., "c") d.len <- nnc - nchar(x, "c") if (any(ii <- d.len > 0L)) { switch(preserve.width, individual = { A.[ii] <- sapply(which(ii), function(i) sub(sprintf("^ {1,%d}", d.len[i]), "", A.[i])) }, common = { A. <- format(A., justify = "right") }) } } attributes(A.) <- attributes(x) class(A.) <- NULL A. } ## @type prefix : character ## @type digits : complex print.rle <- function (x, digits = getOption("digits"), prefix = "", ...) { if (is.null(digits)) digits <- getOption("digits") cat("", "Run Length Encoding\n", " lengths:", sep = prefix) utils::str(x$lengths) cat("", " values :", sep = prefix) utils::str(x$values, digits.d = digits) invisible(x) } proc.time <- function () .Primitive("proc.time") qr.fitted <- function (qr, y, k = qr$rank) { if (!is.qr(qr)) stop("argument is not a QR decomposition") if (is.complex(qr$qr)) stop("not implemented for complex 'qr'") if (isTRUE(attr(qr, "useLAPACK"))) stop("not supported for LAPACK QR") n <- as.integer(nrow(qr$qr)) if (is.na(n)) stop("invalid nrow(qr$qr)") k <- as.integer(k) if (k > qr$rank) stop("'k' is too large") ny <- as.integer(NCOL(y)) if (is.na(ny)) stop("invalid NCOL(y)") if (NROW(y) != n) stop("'qr' and 'y' must have the same number of rows") storage.mode(y) <- "double" .Fortran(.F_dqrxb, as.double(qr$qr), n, k, as.double(qr$qraux), y, ny, xb = y)$xb } R.Version <- function () .Internal(Version()) rawToBits <- function (x) .Internal(rawToBits(x)) ## @type multiple : logical|character ## @return raw|numeric|character rawToChar <- function (x, multiple = FALSE) .Internal(rawToChar(x, multiple)) ## @type n : complex ## @type encoding : character ## @type warn : logical ## @type skipNul : logical ## @type con : character ## @type ok : logical readLines <- function (con = stdin(), n = -1L, ok = TRUE, warn = TRUE, encoding = "unknown", skipNul = FALSE) { if (is.character(con)) { con <- file(con, "r") on.exit(close(con)) } .Internal(readLines(con, n, ok, warn, encoding, skipNul)) } ## @type n : complex ## @type simplify : logical|character replicate <- function (n, expr, simplify = "array") sapply(integer(n), eval.parent(substitute(function(...) expr)), simplify = simplify) row.names <- function (x) UseMethod("row.names") seq_along <- function (along.with) .Primitive("seq_along") ## @type connection : raw ## @type xdr : logical ## @type ascii : logical ## @return raw serialize <- function (object, connection, ascii = FALSE, xdr = TRUE, version = NULL, refhook = NULL) { if (!is.null(connection)) { if (!inherits(connection, "connection")) stop("'connection' must be a connection") if (missing(ascii)) ascii <- summary(connection)$text == "text" } if (!ascii && inherits(connection, "sockconn")) .Internal(serializeb(object, connection, xdr, version, refhook)) else { if (!isTRUE(ascii) && !xdr) ascii <- NA .Internal(serialize(object, connection, ascii, version, refhook)) } } ## @type decreasing : logical sort.list <- function (x, partial = NULL, na.last = TRUE, decreasing = FALSE, method = c("shell", "quick", "radix")) { if (missing(method) && is.factor(x) && nlevels(x) < 1e+05) method <- "radix" method <- match.arg(method) if (!is.atomic(x)) stop("'x' must be atomic for 'sort.list'\nHave you called 'sort' on a list?") if (!is.null(partial)) .NotYetUsed("partial != NULL") if (method == "quick") { if (is.factor(x)) x <- as.integer(x) if (is.numeric(x)) return(sort(x, na.last = na.last, decreasing = decreasing, method = "quick", index.return = TRUE)$ix) else stop("method = \"quick\" is only for numeric 'x'") } if (method == "radix") { if (!typeof(x) == "integer") stop("method = \"radix\" is only for integer 'x'") if (is.na(na.last)) return(.Internal(radixsort(x[!is.na(x)], TRUE, decreasing))) else return(.Internal(radixsort(x, na.last, decreasing))) } if (is.na(na.last)) .Internal(order(TRUE, decreasing, x[!is.na(x)])) else .Internal(order(na.last, decreasing, x)) } stopifnot <- function (...) { n <- length(ll <- list(...)) if (n == 0L) return(invisible()) mc <- match.call() for (i in 1L:n) if (!(is.logical(r <- ll[[i]]) && !anyNA(r) && all(r))) { ch <- deparse(mc[[i + 1]], width.cutoff = 60L) if (length(ch) > 1L) ch <- paste(ch[1L], "....") stop(sprintf(ngettext(length(r), "%s is not TRUE", "%s are not all TRUE"), ch), call. = FALSE, domain = NA) } invisible() } structure <- function (.Data, ...) { attrib <- list(...) if (length(attrib)) { specials <- c(".Dim", ".Dimnames", ".Names", ".Tsp", ".Label") replace <- c("dim", "dimnames", "names", "tsp", "levels") m <- match(names(attrib), specials) ok <- (!is.na(m) & m) names(attrib)[ok] <- replace[m[ok]] if ("factor" %in% attrib[["class", exact = TRUE]] && typeof(.Data) == "double") storage.mode(.Data) <- "integer" attributes(.Data) <- c(attributes(.Data), attrib) } return(.Data) } ## @return character substring <- function (text, first, last = 1000000L) { if (!is.character(text)) text <- as.character(text) n <- max(lt <- length(text), length(first), length(last)) if (lt && lt < n) text <- rep_len(text, length.out = n) .Internal(substr(text, as.integer(first), as.integer(last))) } sys.calls <- function () .Internal(sys.calls()) ## @type paths : character ## @type use_umask : logical Sys.chmod <- function (paths, mode = "0777", use_umask = TRUE) .Internal(Sys.chmod(paths, as.octmode(mode), use_umask)) sys.frame <- function (which = 0L) .Internal(sys.frame(which)) Sys.sleep <- function (time) .Internal(Sys.sleep(time)) Sys.umask <- function (mode = NA) .Internal(Sys.umask(if (is.na(mode)) NA_integer_ else as.octmode(mode))) Sys.which <- function (names) { res <- character(length(names)) names(res) <- names which <- "/usr/bin/which" if (!nzchar(which)) { warning("'which' was not found on this platform") return(res) } for (i in seq_along(names)) { if (is.na(names[i])) { res[i] <- NA next } ans <- suppressWarnings(system(paste(which, shQuote(names[i])), intern = TRUE, ignore.stderr = TRUE)) if (grepl("solaris", R.version$os)) { tmp <- strsplit(ans[1], " ", fixed = TRUE)[[1]] if (identical(tmp[1:3], c("no", i, "in"))) ans <- "" } res[i] <- if (length(ans)) ans[1] else "" if (!file.exists(res[i])) res[i] <- "" } res } t.default <- function (x) .Internal(t.default(x)) ## @type max.lines : complex ## @type x : integer traceback <- function (x = NULL, max.lines = getOption("deparse.max.lines")) { if (is.null(x) && (exists(".Traceback", envir = baseenv()))) x <- get(".Traceback", envir = baseenv()) else if (is.numeric(x)) x <- .Internal(traceback(x)) n <- length(x) if (n == 0L) cat(gettext("No traceback available"), "\n") else { for (i in 1L:n) { label <- paste0(n - i + 1L, ": ") m <- length(x[[i]]) if (!is.null(srcref <- attr(x[[i]], "srcref"))) { srcfile <- attr(srcref, "srcfile") x[[i]][m] <- paste0(x[[i]][m], " at ", basename(srcfile$filename), "#", srcref[1L]) } if (m > 1) label <- c(label, rep(substr(" ", 1L, nchar(label, type = "w")), m - 1L)) if (is.numeric(max.lines) && max.lines > 0L && max.lines < m) { cat(paste0(label[1L:max.lines], x[[i]][1L:max.lines]), sep = "\n") cat(label[max.lines + 1L], " ...\n") } else cat(paste0(label, x[[i]]), sep = "\n") } } invisible(x) } transform <- function (`_data`, ...) UseMethod("transform") unix.time <- function (expr, gcFirst = TRUE) { ppt <- function(y) { if (!is.na(y[4L])) y[1L] <- y[1L] + y[4L] if (!is.na(y[5L])) y[2L] <- y[2L] + y[5L] y[1L:3L] } if (!exists("proc.time")) return(rep(NA_real_, 5L)) if (gcFirst) gc(FALSE) time <- proc.time() on.exit(cat("Timing stopped at:", ppt(proc.time() - time), "\n")) expr new.time <- proc.time() on.exit() structure(new.time - time, class = "proc_time") } ## @type diag : logical upper.tri <- function (x, diag = FALSE) { x <- as.matrix(x) if (diag) row(x) <= col(x) else row(x) < col(x) } ## @type generic : character UseMethod <- function (generic, object) .Primitive("UseMethod") utf8ToInt <- function (x) .Internal(utf8ToInt(x)) ## @type SIMPLIFY : logical|character ## @type USE.NAMES : logical|character ## @type vectorize.args : character ## @return function Vectorize <- function (FUN, vectorize.args = arg.names, SIMPLIFY = TRUE, USE.NAMES = TRUE) { arg.names <- as.list(formals(FUN)) arg.names[["..."]] <- NULL arg.names <- names(arg.names) vectorize.args <- as.character(vectorize.args) if (!length(vectorize.args)) return(FUN) if (!all(vectorize.args %in% arg.names)) stop("must specify names of formal arguments for 'vectorize'") FUNV <- function() { args <- lapply(as.list(match.call())[-1L], eval, parent.frame()) names <- if (is.null(names(args))) character(length(args)) else names(args) dovec <- names %in% vectorize.args do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]), SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES)) } formals(FUNV) <- formals(FUN) FUNV } ## @type x : numeric ## @return integer which.max <- function (x) .Internal(which.max(x)) ## @type x : numeric ## @return integer which.min <- function (x) .Internal(which.min(x)) ## @type keep.white : character ## @type indent : integer ## @type width : integer ## @type file : character ## @type append : logical|character write.dcf <- function (x, file = "", append = FALSE, indent = 0.1 * getOption("width"), width = 0.9 * getOption("width"), keep.white = NULL) { if (file == "") file <- stdout() else if (is.character(file)) { file <- file(file, ifelse(append, "a", "w")) on.exit(close(file)) } if (!inherits(file, "connection")) stop("'file' must be a character string or connection") escape_paragraphs <- function(s) gsub("\n \\.([^\n])", "\n .\\1", gsub("\n[ \t]*\n", "\n .\n ", s, perl = TRUE, useBytes = TRUE), perl = TRUE, useBytes = TRUE) fmt <- function(tag, val, fold = TRUE) { s <- if (fold) formatDL(rep.int(tag, length(val)), val, style = "list", width = width, indent = indent) else { sprintf("%s: %s", tag, gsub("\n([^[:blank:]])", "\n \\1", val)) } escape_paragraphs(s) } if (!is.data.frame(x)) x <- as.data.frame(x, stringsAsFactors = FALSE) nmx <- names(x) out <- matrix("", nrow(x), ncol(x)) foldable <- is.na(match(nmx, keep.white)) for (j in seq_along(x)) { xj <- x[[j]] if (is.atomic(xj)) { i <- !is.na(xj) out[i, j] <- fmt(nmx[j], xj[i], foldable[j]) } else { nmxj <- nmx[j] fold <- foldable[j] i <- !vapply(xj, function(s) (length(s) == 1L) && is.na(s), NA) out[i, j] <- vapply(xj[i], function(s) { paste(fmt(nmxj, s, fold), collapse = "\n") }, "") } } out <- t(out) is_not_empty <- c(out != "") eor <- character(sum(is_not_empty)) if (length(eor)) { eor[diff(c(col(out))[is_not_empty]) >= 1L] <- "\n" } writeLines(paste0(c(out[is_not_empty]), eor), file) } ## @type nchars : integer|character ## @type object : character ## @type eos : character ## @type con : raw|character ## @type useBytes : complex|logical writeChar <- function (object, con, nchars = nchar(object, type = "chars"), eos = "", useBytes = FALSE) { if (!is.character(object)) stop("can only write character objects") if (is.character(con)) { con <- file(con, "wb") on.exit(close(con)) } .Internal(writeChar(object, con, as.integer(nchars), eos, useBytes)) } "|.hexmode" <- function (a, b) as.hexmode(bitwOr(as.hexmode(a), as.hexmode(b))) "|.octmode" <- function (a, b) as.octmode(bitwOr(as.octmode(a), as.octmode(b))) "*.difftime" <- function (e1, e2) { if (inherits(e1, "difftime") && inherits(e2, "difftime")) stop("both arguments of * cannot be \"difftime\" objects") if (inherits(e2, "difftime")) { tmp <- e1 e1 <- e2 e2 <- tmp } .difftime(e2 * unclass(e1), attr(e1, "units")) } "[.difftime" <- function (x, ..., drop = TRUE) { cl <- oldClass(x) class(x) <- NULL val <- NextMethod("[") class(val) <- cl attr(val, "units") <- attr(x, "units") val } "[.warnings" <- function (x, ...) structure(NextMethod("["), class = "warnings") ## @type value : character "[<-.factor" <- function (x, ..., value) { lx <- levels(x) cx <- oldClass(x) if (is.factor(value)) value <- levels(value)[value] m <- match(value, lx) if (any(is.na(m) & !is.na(value))) warning("invalid factor level, NA generated") class(x) <- NULL x[...] <- m attr(x, "levels") <- lx class(x) <- cx x } "[[.POSIXct" <- function (x, ..., drop = TRUE) { cl <- oldClass(x) class(x) <- NULL val <- NextMethod("[[") class(val) <- cl attr(val, "tzone") <- attr(x, "tzone") val } ## @type dot : logical ## @type method : character ## @type use.classes : logical ## @type names.arg : character ## @type strict : logical ## @return character abbreviate <- function (names.arg, minlength = 4L, use.classes = TRUE, dot = FALSE, strict = FALSE, method = c("left.kept", "both.sides")) { if (minlength <= 0L) return(rep.int("", length(names.arg))) names.arg <- sub("^ +", "", sub(" +$", "", as.character(names.arg))) dups <- duplicated(names.arg) old <- names.arg if (any(dups)) names.arg <- names.arg[!dups] x <- names.arg if (strict) { x[] <- .Internal(abbreviate(x, minlength, use.classes)) } else { method <- match.arg(method) if (method == "both.sides") chRev <- function(x) sapply(lapply(strsplit(x, NULL), rev), paste, collapse = "") dup2 <- rep.int(TRUE, length(names.arg)) these <- names.arg repeat { ans <- .Internal(abbreviate(these, minlength, use.classes)) x[dup2] <- ans if (!any(dup2 <- duplicated(x))) break if (method == "both.sides") { x[dup2] <- chRev(.Internal(abbreviate(chRev(names.arg[dup2]), minlength, use.classes))) if (!any(dup2 <- duplicated(x))) break } minlength <- minlength + 1 dup2 <- dup2 | match(x, x[dup2], 0L) these <- names.arg[dup2] } } if (any(dups)) x <- x[match(old, names.arg)] if (dot) { chgd <- x != old x[chgd] <- paste0(x[chgd], ".") } names(x) <- old x } ## @type x : complex as.complex <- function (x, ...) .Primitive("as.complex") as.hexmode <- function (x) { if (inherits(x, "hexmode")) return(x) if (is.double(x) && (x == as.integer(x))) x <- as.integer(x) if (is.integer(x)) return(structure(x, class = "hexmode")) if (is.character(x)) { z <- strtoi(x, 16L) if (!any(is.na(z) | z < 0)) return(structure(z, class = "hexmode")) } stop("'x' cannot be coerced to class \"hexmode\"") } as.integer <- function (x, ...) .Primitive("as.integer") as.logical <- function (x, ...) .Primitive("as.logical") as.numeric <- function (x, ...) .Primitive("as.double") as.octmode <- function (x) { if (inherits(x, "octmode")) return(x) if (is.double(x) && x == as.integer(x)) x <- as.integer(x) if (is.integer(x)) return(structure(x, class = "octmode")) if (is.character(x)) { z <- strtoi(x, 8L) if (!any(is.na(z) | z < 0)) return(structure(z, class = "octmode")) } stop("'x' cannot be coerced to class \"octmode\"") } as.ordered <- function (x) if (is.ordered(x)) x else ordered(x) as.POSIXct <- function (x, tz = "", ...) UseMethod("as.POSIXct") as.POSIXlt <- function (x, tz = "", ...) UseMethod("as.POSIXlt") attributes <- function (obj) .Primitive("attributes") autoloader <- function (name, package, ...) { name <- paste0(name, "") rm(list = name, envir = .AutoloadEnv, inherits = FALSE) m <- match.call() m$name <- NULL m[[1L]] <- as.name("library") eval(m, .GlobalEnv) autoload(name, package, reset = TRUE, ...) where <- match(paste("package", package, sep = ":"), search()) if (exists(name, where = where, inherits = FALSE)) eval(as.name(name), as.environment(where)) else stop(gettextf("autoloader did not find '%s' in '%s'", name, package), domain = NA) } ## @type a : numeric ## @type n : integer bitwShiftL <- function (a, n) .Internal(bitwiseShiftL(a, n)) ## @type n : integer ## @type a : numeric ## @return integer bitwShiftR <- function (a, n) .Internal(bitwiseShiftR(a, n)) ## @type simplify : logical by.default <- function (data, INDICES, FUN, ..., simplify = TRUE) { dd <- as.data.frame(data) if (length(dim(data))) by(dd, INDICES, FUN, ..., simplify = simplify) else { if (!is.list(INDICES)) { IND <- vector("list", 1L) IND[[1L]] <- INDICES names(IND) <- deparse(substitute(INDICES))[1L] } else IND <- INDICES FUNx <- function(x) FUN(dd[x, ], ...) nd <- nrow(dd) structure(eval(substitute(tapply(seq_len(nd), IND, FUNx, simplify = simplify)), dd), call = match.call(), class = "by") } } ## @type value : character "colnames<-" <- function (x, value) { if (is.data.frame(x)) { names(x) <- value } else { dn <- dimnames(x) if (is.null(dn)) { if (is.null(value)) return(x) if ((nd <- length(dim(x))) < 2L) stop("attempt to set 'colnames' on an object with less than two dimensions") dn <- vector("list", nd) } if (length(dn) < 2L) stop("attempt to set 'colnames' on an object with less than two dimensions") if (is.null(value)) dn[2L] <- list(NULL) else dn[[2L]] <- value dimnames(x) <- dn } x } ## @type breaks : complex ## @type start.on.monday : logical ## @type labels : integer cut.POSIXt <- function (x, breaks, labels = NULL, start.on.monday = TRUE, right = FALSE, ...) { if (!inherits(x, "POSIXt")) stop("'x' must be a date-time object") x <- as.POSIXct(x) if (inherits(breaks, "POSIXt")) { breaks <- sort(as.POSIXct(breaks)) } else if (is.numeric(breaks) && length(breaks) == 1L) { } else if (is.character(breaks) && length(breaks) == 1L) { by2 <- strsplit(breaks, " ", fixed = TRUE)[[1L]] if (length(by2) > 2L || length(by2) < 1L) stop("invalid specification of 'breaks'") valid <- pmatch(by2[length(by2)], c("secs", "mins", "hours", "days", "weeks", "months", "years", "DSTdays", "quarters")) if (is.na(valid)) stop("invalid specification of 'breaks'") start <- as.POSIXlt(min(x, na.rm = TRUE)) incr <- 1 if (valid > 1L) { start$sec <- 0L incr <- 60 } if (valid > 2L) { start$min <- 0L incr <- 3600 } if (valid > 3L) { start$hour <- 0L start$isdst <- -1L incr <- 86400 } if (valid == 5L) { start$mday <- start$mday - start$wday if (start.on.monday) start$mday <- start$mday + ifelse(start$wday > 0L, 1L, -6L) incr <- 7 * 86400 } if (valid == 8L) incr <- 25 * 3600 if (valid == 6L) { start$mday <- 1L end <- as.POSIXlt(max(x, na.rm = TRUE)) step <- ifelse(length(by2) == 2L, as.integer(by2[1L]), 1L) end <- as.POSIXlt(end + (31 * step * 86400)) end$mday <- 1L end$isdst <- -1L breaks <- seq(start, end, breaks) } else if (valid == 7L) { start$mon <- 0L start$mday <- 1L end <- as.POSIXlt(max(x, na.rm = TRUE)) step <- ifelse(length(by2) == 2L, as.integer(by2[1L]), 1L) end <- as.POSIXlt(end + (366 * step * 86400)) end$mon <- 0L end$mday <- 1L end$isdst <- -1L breaks <- seq(start, end, breaks) } else if (valid == 9L) { qtr <- rep(c(0L, 3L, 6L, 9L), each = 3L) start$mon <- qtr[start$mon + 1L] start$mday <- 1L maxx <- max(x, na.rm = TRUE) end <- as.POSIXlt(maxx) step <- ifelse(length(by2) == 2L, as.integer(by2[1L]), 1L) end <- as.POSIXlt(end + (93 * step * 86400)) end$mon <- qtr[end$mon + 1L] end$mday <- 1L end$isdst <- -1L breaks <- seq(start, end, paste(step * 3, "months")) lb <- length(breaks) if (maxx < breaks[lb - 1]) breaks <- breaks[-lb] } else { if (length(by2) == 2L) incr <- incr * as.integer(by2[1L]) maxx <- max(x, na.rm = TRUE) breaks <- seq(start, maxx + incr, breaks) breaks <- breaks[seq_len(1 + max(which(breaks <= maxx)))] } } else stop("invalid specification of 'breaks'") res <- cut(unclass(x), unclass(breaks), labels = labels, right = right, ...) if (is.null(labels)) { levels(res) <- as.character(if (is.numeric(breaks)) x[!duplicated(res)] else breaks[-length(breaks)]) } res } data.class <- function (x) { if (length(cl <- oldClass(x))) cl[1L] else { l <- length(dim(x)) if (l == 2L) "matrix" else if (l) "array" else mode(x) } } ## @type stringsAsFactors : logical|character ## @type row.names : integer|character ## @type check.names : logical data.frame <- function (..., row.names = NULL, check.rows = FALSE, check.names = TRUE, stringsAsFactors = default.stringsAsFactors()) { data.row.names <- if (check.rows && is.null(row.names)) function(current, new, i) { if (is.character(current)) new <- as.character(new) if (is.character(new)) current <- as.character(current) if (anyDuplicated(new)) return(current) if (is.null(current)) return(new) if (all(current == new) || all(current == "")) return(new) stop(gettextf("mismatch of row names in arguments of 'data.frame', item %d", i), domain = NA) } else function(current, new, i) { if (is.null(current)) { if (anyDuplicated(new)) { warning(gettextf("some row.names duplicated: %s --> row.names NOT used", paste(which(duplicated(new)), collapse = ",")), domain = NA) current } else new } else current } object <- as.list(substitute(list(...)))[-1L] mirn <- missing(row.names) mrn <- is.null(row.names) x <- list(...) n <- length(x) if (n < 1L) { if (!mrn) { if (is.object(row.names) || !is.integer(row.names)) row.names <- as.character(row.names) if (anyNA(row.names)) stop("row names contain missing values") if (anyDuplicated(row.names)) stop(gettextf("duplicate row.names: %s", paste(unique(row.names[duplicated(row.names)]), collapse = ", ")), domain = NA) } else row.names <- integer() return(structure(list(), names = character(), row.names = row.names, class = "data.frame")) } vnames <- names(x) if (length(vnames) != n) vnames <- character(n) no.vn <- !nzchar(vnames) vlist <- vnames <- as.list(vnames) nrows <- ncols <- integer(n) for (i in seq_len(n)) { xi <- if (is.character(x[[i]]) || is.list(x[[i]])) as.data.frame(x[[i]], optional = TRUE, stringsAsFactors = stringsAsFactors) else as.data.frame(x[[i]], optional = TRUE) nrows[i] <- .row_names_info(xi) ncols[i] <- length(xi) namesi <- names(xi) if (ncols[i] > 1L) { if (length(namesi) == 0L) namesi <- seq_len(ncols[i]) if (no.vn[i]) vnames[[i]] <- namesi else vnames[[i]] <- paste(vnames[[i]], namesi, sep = ".") } else { if (length(namesi)) vnames[[i]] <- namesi else if (no.vn[[i]]) { tmpname <- deparse(object[[i]])[1L] if (substr(tmpname, 1L, 2L) == "I(") { ntmpn <- nchar(tmpname, "c") if (substr(tmpname, ntmpn, ntmpn) == ")") tmpname <- substr(tmpname, 3L, ntmpn - 1L) } vnames[[i]] <- tmpname } } if (mirn && nrows[i] > 0L) { rowsi <- attr(xi, "row.names") nc <- nchar(rowsi, allowNA = FALSE) nc <- nc[!is.na(nc)] if (length(nc) && any(nc)) row.names <- data.row.names(row.names, rowsi, i) } nrows[i] <- abs(nrows[i]) vlist[[i]] <- xi } nr <- max(nrows) for (i in seq_len(n)[nrows < nr]) { xi <- vlist[[i]] if (nrows[i] > 0L && (nr%%nrows[i] == 0L)) { xi <- unclass(xi) fixed <- TRUE for (j in seq_along(xi)) { xi1 <- xi[[j]] if (is.vector(xi1) || is.factor(xi1)) xi[[j]] <- rep(xi1, length.out = nr) else if (is.character(xi1) && inherits(xi1, "AsIs")) xi[[j]] <- structure(rep(xi1, length.out = nr), class = class(xi1)) else if (inherits(xi1, "Date") || inherits(xi1, "POSIXct")) xi[[j]] <- rep(xi1, length.out = nr) else { fixed <- FALSE break } } if (fixed) { vlist[[i]] <- xi next } } stop(gettextf("arguments imply differing number of rows: %s", paste(unique(nrows), collapse = ", ")), domain = NA) } value <- unlist(vlist, recursive = FALSE, use.names = FALSE) vnames <- unlist(vnames[ncols > 0L]) noname <- !nzchar(vnames) if (any(noname)) vnames[noname] <- paste("Var", seq_along(vnames), sep = ".")[noname] if (check.names) vnames <- make.names(vnames, unique = TRUE) names(value) <- vnames if (!mrn) { if (length(row.names) == 1L && nr != 1L) { if (is.character(row.names)) row.names <- match(row.names, vnames, 0L) if (length(row.names) != 1L || row.names < 1L || row.names > length(vnames)) stop("'row.names' should specify one of the variables") i <- row.names row.names <- value[[i]] value <- value[-i] } else if (!is.null(row.names) && length(row.names) != nr) stop("row names supplied are of the wrong length") } else if (!is.null(row.names) && length(row.names) != nr) { warning("row names were found from a short variable and have been discarded") row.names <- NULL } if (is.null(row.names)) row.names <- .set_row_names(nr) else { if (is.object(row.names) || !is.integer(row.names)) row.names <- as.character(row.names) if (anyNA(row.names)) stop("row names contain missing values") if (anyDuplicated(row.names)) stop(gettextf("duplicate row.names: %s", paste(unique(row.names[duplicated(row.names)]), collapse = ", ")), domain = NA) } attr(value, "row.names") <- row.names attr(value, "class") <- "data.frame" value } "dimnames<-" <- function (x, value) .Primitive("dimnames<-") ## @type showWarnings : logical ## @type path : character ## @type recursive : logical dir.create <- function (path, showWarnings = TRUE, recursive = FALSE, mode = "0777") .Internal(dir.create(path, showWarnings, recursive, as.octmode(mode))) droplevels <- function (x, ...) UseMethod("droplevels") duplicated <- function (x, incomparables = FALSE, ...) UseMethod("duplicated") ## @type x : character dyn.unload <- function (x) .Internal(dyn.unload(x)) ## @type x : character enc2native <- function (x) .Primitive("enc2native") ## @type value : character ## @type x : character "Encoding<-" <- function (x, value) .Internal(setEncoding(x, value)) expression <- function (...) .Primitive("expression") ## @type wait : complex ## @type step : integer ## @type inhibit_release : logical gctorture2 <- function (step, wait = step, inhibit_release = FALSE) .Internal(gctorture2(step, wait, inhibit_release)) getElement <- function (object, name) { if (isS4(object)) slot(object, name) else object[[name, exact = TRUE]] } ## @type x : complex is.complex <- function (x) .Primitive("is.complex") is.element <- function (el, set) match(el, set, 0L) > 0L is.integer <- function (x) .Primitive("is.integer") is.logical <- function (x) .Primitive("is.logical") is.numeric <- function (x) .Primitive("is.numeric") is.ordered <- function (x) inherits(x, "ordered") isdebugged <- function (fun) .Internal(isdebugged(fun)) isSeekable <- function (con) .Internal(isSeekable(con)) La_version <- function () .Internal(La_version()) ## @type x : numeric lfactorial <- function (x) lgamma(x + 1) ## @type path : character ## @type ignore.case : logical ## @type full.names : logical ## @type include.dirs : logical ## @type no.. : logical ## @type all.files : logical ## @type recursive : logical ## @return character list.files <- function (path = ".", pattern = NULL, all.files = FALSE, full.names = FALSE, recursive = FALSE, ignore.case = FALSE, include.dirs = FALSE, no.. = FALSE) .Internal(list.files(path, pattern, all.files, full.names, recursive, ignore.case, include.dirs, no..)) ## @return character make.names <- function (names, unique = FALSE, allow_ = TRUE) { names <- as.character(names) names2 <- .Internal(make.names(names, allow_)) if (unique) { o <- order(names != names2) names2[o] <- make.unique(names2[o]) } names2 } mat.or.vec <- function (nr, nc) if (nc == 1L) numeric(nr) else matrix(0, nr, nc) ## @type expand.dots : logical match.call <- function (definition = NULL, call = sys.call(sys.parent()), expand.dots = TRUE) .Internal(match.call(definition, call, expand.dots)) mem.limits <- function (nsize = NA, vsize = NA) .Defunct("gc") ## @type generic : character NextMethod <- function (generic = NULL, object = NULL, ...) .Internal(NextMethod(generic, object, ...)) ## @type value : character "oldClass<-" <- function (x, value) .Primitive("oldClass<-") OlsonNames <- function () { if (.Platform$OS.type == "windows") tzdir <- Sys.getenv("TZDIR", file.path(R.home("share"), "zoneinfo")) else { tzdirs <- c(Sys.getenv("TZDIR"), file.path(R.home("share"), "zoneinfo"), "/usr/share/zoneinfo", "/usr/share/lib/zoneinfo", "/usr/lib/zoneinfo", "/usr/local/etc/zoneinfo", "/etc/zoneinfo", "/usr/etc/zoneinfo") tzdirs <- tzdirs[file.exists(tzdirs)] if (!length(tzdirs)) { warning("no Olson database found") return(character()) } else tzdir <- tzdirs[1] } x <- list.files(tzdir, recursive = TRUE) grep("^[ABCDEFGHIJKLMNOPQRSTUVWXYZ]", x, value = TRUE) } Ops.factor <- function (e1, e2) { ok <- switch(.Generic, `==` = , `!=` = TRUE, FALSE) if (!ok) { warning(.Generic, " not meaningful for factors") return(rep.int(NA, max(length(e1), if (!missing(e2)) length(e2)))) } nas <- is.na(e1) | is.na(e2) noNA.levels <- function(f) { r <- levels(f) if (any(ina <- is.na(r))) { n <- " NA " while (n %in% r) n <- paste(n, ".") r[ina] <- n } r } if (nzchar(.Method[1L])) { l1 <- noNA.levels(e1) e1 <- l1[e1] } if (nzchar(.Method[2L])) { l2 <- noNA.levels(e2) e2 <- l2[e2] } if (all(nzchar(.Method)) && (length(l1) != length(l2) || !all(sort.int(l2) == sort.int(l1)))) stop("level sets of factors are different") value <- NextMethod(.Generic) value[nas] <- NA value } Ops.POSIXt <- function (e1, e2) { if (nargs() == 1) stop(gettextf("unary '%s' not defined for \"POSIXt\" objects", .Generic), domain = NA) boolean <- switch(.Generic, `<` = , `>` = , `==` = , `!=` = , `<=` = , `>=` = TRUE, FALSE) if (!boolean) stop(gettextf("'%s' not defined for \"POSIXt\" objects", .Generic), domain = NA) if (inherits(e1, "POSIXlt") || is.character(e1)) e1 <- as.POSIXct(e1) if (inherits(e2, "POSIXlt") || is.character(e2)) e2 <- as.POSIXct(e2) check_tzones(e1, e2) NextMethod(.Generic) } parent.env <- function (env) .Internal(parent.env(env)) ## @type x : integer pos.to.env <- function (x) .Primitive("pos.to.env") print.AsIs <- function (x, ...) { cl <- oldClass(x) oldClass(x) <- cl[cl != "AsIs"] NextMethod("print") invisible(x) } print.Date <- function (x, max = NULL, ...) { if (is.null(max)) max <- getOption("max.print", 9999L) if (max < length(x)) { print(format(x[seq_len(max)]), max = max, ...) cat(" [ reached getOption(\"max.print\") -- omitted", length(x) - max, "entries ]\n") } else print(format(x), max = max, ...) invisible(x) } prop.table <- function (x, margin = NULL) { if (length(margin)) sweep(x, margin, margin.table(x, margin), "/", check.margin = FALSE) else x/sum(x) } ## @type x : complex ## @type LAPACK : logical qr.default <- function (x, tol = 1e-07, LAPACK = FALSE, ...) { x <- as.matrix(x) if (is.complex(x)) return(structure(.Internal(La_qr_cmplx(x)), class = "qr")) if (LAPACK) return(structure(.Internal(La_qr(x)), useLAPACK = TRUE, class = "qr")) p <- as.integer(ncol(x)) if (is.na(p)) stop("invalid ncol(x)") n <- as.integer(nrow(x)) if (is.na(n)) stop("invalid nrow(x)") if (1 * n * p > 2147483647) stop("too large a matrix for LINPACK") storage.mode(x) <- "double" res <- .Fortran(.F_dqrdc2, qr = x, n, n, p, as.double(tol), rank = integer(1L), qraux = double(p), pivot = as.integer(seq_len(p)), double(2L * p))[c(1, 6, 7, 8)] if (!is.null(cn <- colnames(x))) colnames(res$qr) <- cn[res$pivot] class(res) <- "qr" res } ## @type invert : logical ## @type x : character regmatches <- function (x, m, invert = FALSE) { if (length(x) != length(m)) stop(gettextf("%s and %s must have the same length", sQuote("x"), sQuote("m")), domain = NA) ili <- is.list(m) useBytes <- if (ili) any(unlist(lapply(m, attr, "useBytes"))) else any(attr(m, "useBytes")) if (useBytes) { asc <- iconv(x, "latin1", "ASCII") ind <- is.na(asc) | (asc != x) if (any(ind)) Encoding(x[ind]) <- "bytes" } if (!ili && !invert) { so <- m[ind <- (!is.na(m) & (m > -1L))] eo <- so + attr(m, "match.length")[ind] - 1L return(substring(x[ind], so, eo)) } y <- if (invert) { Map(function(u, so, ml) { if ((n <- length(so)) == 1L) { if (is.na(so)) return(character()) else if (so == -1L) return(u) } beg <- if (n > 1L) { eo <- so + ml - 1L if (any(eo[-n] >= so[-1L])) stop(gettextf("need non-overlapping matches for %s", sQuote("invert = TRUE")), domain = NA) c(1L, eo + 1L) } else { c(1L, so + ml) } end <- c(so - 1L, nchar(u)) substring(u, beg, end) }, x, m, if (ili) lapply(m, attr, "match.length") else attr(m, "match.length"), USE.NAMES = FALSE) } else { Map(function(u, so, ml) { if (length(so) == 1L) { if (is.na(so) || (so == -1L)) return(character()) } substring(u, so, so + ml - 1L) }, x, m, lapply(m, attr, "match.length"), USE.NAMES = FALSE) } names(y) <- names(x) y } rep.factor <- function (x, ...) { y <- NextMethod() structure(y, class = class(x), levels = levels(x)) } retracemem <- function (x, previous = NULL) .Primitive("retracemem") ## @type vstr : complex|character ## @optional vstr RNGversion <- function (vstr) { vnum <- as.numeric(strsplit(vstr, ".", fixed = TRUE)[[1L]]) if (length(vnum) < 2L) stop("malformed version string") if (vnum[1L] == 0 && vnum[2L] < 99) RNGkind("Wichmann-Hill", "Buggy Kinderman-Ramage") else if (vnum[1L] == 0 || vnum[1L] == 1 && vnum[2L] <= 6) RNGkind("Marsaglia-Multicarry", "Buggy Kinderman-Ramage") else RNGkind("Mersenne-Twister", "Inversion") } round.Date <- function (x, ...) { cl <- oldClass(x) class(x) <- NULL val <- NextMethod() class(val) <- cl val } ## @type value : character "rownames<-" <- function (x, value) { if (is.data.frame(x)) { row.names(x) <- value } else { dn <- dimnames(x) if (is.null(dn)) { if (is.null(value)) return(x) if ((nd <- length(dim(x))) < 1L) stop("attempt to set 'rownames' on an object with no dimensions") dn <- vector("list", nd) } if (length(dn) < 1L) stop("attempt to set 'rownames' on an object with no dimensions") if (is.null(value)) dn[1L] <- list(NULL) else dn[[1L]] <- value dimnames(x) <- dn } x } sample.int <- function (n, size = n, replace = FALSE, prob = NULL) { if (!replace && is.null(prob) && n > 1e+07 && size <= n/2) .Internal(sample2(n, size)) else .Internal(sample(n, size, replace, prob)) } save.image <- function (file = ".RData", version = NULL, ascii = FALSE, compress = !ascii, safe = TRUE) { if (!is.character(file) || file == "") stop("'file' must be non-empty string") opts <- getOption("save.image.defaults") if (is.null(opts)) opts <- getOption("save.defaults") if (missing(safe) && !is.null(opts$safe)) safe <- opts$safe if (missing(ascii) && !is.null(opts$ascii)) ascii <- opts$ascii if (missing(compress) && !is.null(opts$compress)) compress <- opts$compress if (missing(version)) version <- opts$version if (safe) { outfile <- paste0(file, "Tmp") i <- 0 while (file.exists(outfile)) { i <- i + 1 outfile <- paste0(file, "Tmp", i) } } else outfile <- file on.exit(file.remove(outfile)) save(list = ls(envir = .GlobalEnv, all.names = TRUE), file = outfile, version = version, ascii = ascii, compress = compress, envir = .GlobalEnv, precheck = FALSE) if (safe) if (!file.rename(outfile, file)) { on.exit() stop(gettextf("image could not be renamed and is left in %s", outfile), domain = NA) } on.exit() } ## @type length.out : integer seq.POSIXt <- function (from, to, by, length.out = NULL, along.with = NULL, ...) { if (missing(from)) stop("'from' must be specified") if (!inherits(from, "POSIXt")) stop("'from' must be a \"POSIXt\" object") cfrom <- as.POSIXct(from) if (length(cfrom) != 1L) stop("'from' must be of length 1") tz <- attr(cfrom, "tzone") if (!missing(to)) { if (!inherits(to, "POSIXt")) stop("'to' must be a \"POSIXt\" object") if (length(as.POSIXct(to)) != 1) stop("'to' must be of length 1") } if (!missing(along.with)) { length.out <- length(along.with) } else if (!is.null(length.out)) { if (length(length.out) != 1L) stop("'length.out' must be of length 1") length.out <- ceiling(length.out) } status <- c(!missing(to), !missing(by), !is.null(length.out)) if (sum(status) != 2L) stop("exactly two of 'to', 'by' and 'length.out' / 'along.with' must be specified") if (missing(by)) { from <- unclass(cfrom) to <- unclass(as.POSIXct(to)) res <- seq.int(from, to, length.out = length.out) return(.POSIXct(res, tz)) } if (length(by) != 1L) stop("'by' must be of length 1") valid <- 0L if (inherits(by, "difftime")) { by <- switch(attr(by, "units"), secs = 1, mins = 60, hours = 3600, days = 86400, weeks = 7 * 86400) * unclass(by) } else if (is.character(by)) { by2 <- strsplit(by, " ", fixed = TRUE)[[1L]] if (length(by2) > 2L || length(by2) < 1L) stop("invalid 'by' string") valid <- pmatch(by2[length(by2)], c("secs", "mins", "hours", "days", "weeks", "months", "years", "DSTdays", "quarters")) if (is.na(valid)) stop("invalid string for 'by'") if (valid <= 5L) { by <- c(1, 60, 3600, 86400, 7 * 86400)[valid] if (length(by2) == 2L) by <- by * as.integer(by2[1L]) } else by <- if (length(by2) == 2L) as.integer(by2[1L]) else 1 } else if (!is.numeric(by)) stop("invalid mode for 'by'") if (is.na(by)) stop("'by' is NA") if (valid <= 5L) { from <- unclass(as.POSIXct(from)) if (!is.null(length.out)) res <- seq.int(from, by = by, length.out = length.out) else { to0 <- unclass(as.POSIXct(to)) res <- seq.int(0, to0 - from, by) + from } return(.POSIXct(res, tz)) } else { r1 <- as.POSIXlt(from) if (valid == 7L) { if (missing(to)) { yr <- seq.int(r1$year, by = by, length.out = length.out) } else { to <- as.POSIXlt(to) yr <- seq.int(r1$year, to$year, by) } r1$year <- yr } else if (valid %in% c(6L, 9L)) { if (valid == 9L) by <- by * 3 if (missing(to)) { mon <- seq.int(r1$mon, by = by, length.out = length.out) } else { to0 <- as.POSIXlt(to) mon <- seq.int(r1$mon, 12 * (to0$year - r1$year) + to0$mon, by) } r1$mon <- mon } else if (valid == 8L) { if (!missing(to)) { length.out <- 2L + floor((unclass(as.POSIXct(to)) - unclass(as.POSIXct(from)))/86400) } r1$mday <- seq.int(r1$mday, by = by, length.out = length.out) } r1$isdst <- -1L res <- as.POSIXct(r1) if (!missing(to)) { to <- as.POSIXct(to) res <- if (by > 0) res[res <= to] else res[res >= to] } res } } split.Date <- function (x, f, drop = FALSE, ...) { y <- split.default(as.integer(x), f, drop = drop) for (i in seq_along(y)) class(y[[i]]) <- "Date" y } substitute <- function (expr, env) .Primitive("substitute") sys.frames <- function () .Internal(sys.frames()) ## @type names : logical ## @type unset : character ## @type x : character ## @return character Sys.getenv <- function (x = NULL, unset = "", names = NA) { if (is.null(x)) { x <- strsplit(.Internal(Sys.getenv(character(), "")), "=", fixed = TRUE) v <- n <- character(LEN <- length(x)) for (i in 1L:LEN) { n[i] <- x[[i]][1L] v[i] <- paste(x[[i]][-1L], collapse = "=") } if (!identical(names, FALSE)) v <- structure(v, names = n) v[sort.list(n)] } else { v <- .Internal(Sys.getenv(as.character(x), as.character(unset))) if (isTRUE(names) || (length(x) > 1L && !identical(names, FALSE))) structure(v, names = x) else v } } Sys.getpid <- function () .Internal(Sys.getpid()) sys.nframe <- function () .Internal(sys.nframe()) sys.parent <- function (n = 1L) .Internal(sys.parent(n)) Sys.setenv <- function (...) { x <- list(...) nm <- names(x) if (is.null(nm) || "" %in% nm) stop("all arguments must be named") .Internal(Sys.setenv(nm, as.character(unlist(x)))) } sys.source <- function (file, envir = baseenv(), chdir = FALSE, keep.source = getOption("keep.source.pkgs")) { if (!(is.character(file) && file.exists(file))) stop(gettextf("'%s' is not an existing file", file)) keep.source <- as.logical(keep.source) oop <- options(keep.source = keep.source, topLevelEnvironment = as.environment(envir)) on.exit(options(oop)) if (keep.source) { lines <- readLines(file, warn = FALSE) srcfile <- srcfilecopy(file, lines, file.info(file)[1, "mtime"], isFile = TRUE) exprs <- parse(text = lines, srcfile = srcfile, keep.source = TRUE) } else exprs <- parse(n = -1, file = file, srcfile = NULL, keep.source = FALSE) if (length(exprs) == 0L) return(invisible()) if (chdir && (path <- dirname(file)) != ".") { owd <- getwd() if (is.null(owd)) stop("cannot 'chdir' as current directory is unknown") on.exit(setwd(owd), add = TRUE) setwd(path) } for (i in seq_along(exprs)) eval(exprs[i], envir) invisible() } sys.status <- function () list(sys.calls = sys.calls(), sys.parents = sys.parents(), sys.frames = sys.frames()) ## @type x : complex ## @type y : complex tcrossprod <- function (x, y = NULL) .Internal(tcrossprod(x, y)) trunc.Date <- function (x, ...) round(x - 0.4999999) untracemem <- function (x) .Primitive("untracemem") writeLines <- function (text, con = stdout(), sep = "\n", useBytes = FALSE) { if (is.character(con)) { con <- file(con, "w") on.exit(close(con)) } .Internal(writeLines(text, con, sep, useBytes)) } xtfrm.AsIs <- function (x) { if (length(cl <- class(x)) > 1) oldClass(x) <- cl[-1L] NextMethod("xtfrm") } xtfrm.Date <- function (x) as.numeric(x) xtfrm.Surv <- function (x) if (ncol(x) == 2L) order(x[, 1L], x[, 2L]) else order(x[, 1L], x[, 2L], x[, 3L]) "[<-.POSIXct" <- function (x, ..., value) { if (!length(value)) return(x) value <- unclass(as.POSIXct(value)) cl <- oldClass(x) tz <- attr(x, "tzone") class(x) <- NULL x <- NextMethod(.Generic) class(x) <- cl attr(x, "tzone") <- tz x } ## @optional i "[<-.POSIXlt" <- function (x, i, value) { if (!length(value)) return(x) value <- unclass(as.POSIXlt(value)) cl <- oldClass(x) class(x) <- NULL for (n in names(x)) x[[n]][i] <- value[[n]] class(x) <- cl x } ## @type value : character "[[<-.factor" <- function (x, ..., value) { lx <- levels(x) cx <- oldClass(x) if (is.factor(value)) value <- levels(value)[value] m <- match(value, lx) if (any(is.na(m) & !is.na(value))) warning("invalid factor level, NA generated") class(x) <- NULL x[[...]] <- m attr(x, "levels") <- lx class(x) <- cx x } ## @type perm : complex|character ## @type keep.class : logical aperm.table <- function (a, perm = NULL, resize = TRUE, keep.class = TRUE, ...) { r <- aperm.default(a, perm, resize = resize) if (keep.class) class(r) <- class(a) r } ## @type tim : numeric|character ## @type units : character ## @type format : character as.difftime <- function (tim, format = "%X", units = "auto") { if (inherits(tim, "difftime")) return(tim) if (is.character(tim)) { difftime(strptime(tim, format = format), strptime("0:0:0", format = "%X"), units = units) } else { if (!is.numeric(tim)) stop("'tim' is not character or numeric") if (units == "auto") stop("need explicit units for numeric conversion") if (!(units %in% c("secs", "mins", "hours", "days", "weeks"))) stop("invalid units specified") structure(tim, units = units, class = "difftime") } } as.function <- function (x, ...) UseMethod("as.function") as.pairlist <- function (x) .Internal(as.vector(x, "pairlist")) asNamespace <- function (ns, base.OK = TRUE) { if (is.character(ns) || is.name(ns)) ns <- getNamespace(ns) if (!isNamespace(ns)) stop("not a namespace") else if (!base.OK && isBaseNamespace(ns)) stop("operation not allowed on base namespace") else ns } browserText <- function (n = 1L) .Internal(browserText(n)) ## @type target : character ## @type input : character ## @return character char.expand <- function (input, target, nomatch = stop("no match")) { if (length(input) != 1L) stop("'input' must have length 1") if (!(is.character(input) && is.character(target))) stop("'input' and 'target' must be character vectors") y <- .Internal(charmatch(input, target, NA_integer_)) if (anyNA(y)) eval(nomatch) target[y] } ## @type trailingOnly : logical ## @return character commandArgs <- function (trailingOnly = FALSE) { args <- .Internal(commandArgs()) if (trailingOnly) { m <- match("--args", args, 0L) if (m) args[-seq_len(m)] else character() } else args } Cstack_info <- function () .Internal(Cstack_info()) ## @type right : logical ## @type labels : integer ## @type include.lowest : logical ## @type ordered_result : logical ## @type breaks : complex ## @type x : numeric ## @type dig.lab : complex cut.default <- function (x, breaks, labels = NULL, include.lowest = FALSE, right = TRUE, dig.lab = 3L, ordered_result = FALSE, ...) { if (!is.numeric(x)) stop("'x' must be numeric") if (length(breaks) == 1L) { if (is.na(breaks) || breaks < 2L) stop("invalid number of intervals") nb <- as.integer(breaks + 1) dx <- diff(rx <- range(x, na.rm = TRUE)) if (dx == 0) { dx <- abs(rx[1L]) breaks <- seq.int(rx[1L] - dx/1000, rx[2L] + dx/1000, length.out = nb) } else { breaks <- seq.int(rx[1L], rx[2L], length.out = nb) breaks[c(1L, nb)] <- c(rx[1L] - dx/1000, rx[2L] + dx/1000) } } else nb <- length(breaks <- sort.int(as.double(breaks))) if (anyDuplicated(breaks)) stop("'breaks' are not unique") codes.only <- FALSE if (is.null(labels)) { for (dig in dig.lab:max(12L, dig.lab)) { ch.br <- formatC(0 + breaks, digits = dig, width = 1L) if (ok <- all(ch.br[-1L] != ch.br[-nb])) break } labels <- if (ok) paste0(if (right) "(" else "[", ch.br[-nb], ",", ch.br[-1L], if (right) "]" else ")") else paste("Range", seq_len(nb - 1L), sep = "_") if (ok && include.lowest) { if (right) substr(labels[1L], 1L, 1L) <- "[" else substring(labels[nb - 1L], nchar(labels[nb - 1L], "c")) <- "]" } } else if (is.logical(labels) && !labels) codes.only <- TRUE else if (length(labels) != nb - 1L) stop("lengths of 'breaks' and 'labels' differ") code <- .bincode(x, breaks, right, include.lowest) if (codes.only) code else factor(code, seq_along(labels), labels, ordered = ordered_result) } data.matrix <- function (frame, rownames.force = NA) { if (!is.data.frame(frame)) return(as.matrix(frame)) d <- dim(frame) rn <- if (rownames.force %in% FALSE) NULL else if (rownames.force %in% TRUE) row.names(frame) else { if (.row_names_info(frame) <= 0L) NULL else row.names(frame) } for (i in seq_len(d[2L])) { xi <- frame[[i]] if (is.integer(xi) || is.numeric(xi)) next if (is.logical(xi) || is.factor(xi)) { frame[[i]] <- as.integer(xi) next } frame[[i]] <- if (isS4(xi)) methods::as(xi, "numeric") else as.numeric(xi) } intOK <- all(unlist(lapply(frame, is.integer))) x <- matrix(if (intOK) NA_integer_ else NA_real_, nrow = d[1L], ncol = d[2L], dimnames = list(rn, names(frame))) for (i in seq_len(d[2L])) x[, i] <- frame[[i]] x } ## @type x : logical|numeric ## @type logarithm : logical determinant <- function (x, logarithm = TRUE, ...) UseMethod("determinant") ## @type x : numeric ## @type differences : integer ## @type lag : integer diff.POSIXt <- function (x, lag = 1L, differences = 1L, ...) { ismat <- is.matrix(x) r <- if (inherits(x, "POSIXlt")) as.POSIXct(x) else x xlen <- if (ismat) dim(x)[1L] else length(r) if (length(lag) != 1L || length(differences) > 1L || lag < 1L || differences < 1L) stop("'lag' and 'differences' must be integers >= 1") if (lag * differences >= xlen) return(.difftime(numeric(), "secs")) i1 <- -seq_len(lag) if (ismat) for (i in seq_len(differences)) r <- r[i1, , drop = FALSE] - r[-nrow(r):-(nrow(r) - lag + 1), , drop = FALSE] else for (i in seq_len(differences)) r <- r[i1] - r[-length(r):-(length(r) - lag + 1L)] r } env.profile <- function (env) .Internal(env.profile(env)) environment <- function (fun = NULL) .Internal(environment(fun)) eval.parent <- function (expr, n = 1) { p <- parent.frame(n + 1) eval(expr, p) } ## @type KEEP.OUT.ATTRS : logical ## @type stringsAsFactors : logical|character expand.grid <- function (..., KEEP.OUT.ATTRS = TRUE, stringsAsFactors = TRUE) { nargs <- length(args <- list(...)) if (!nargs) return(as.data.frame(list())) if (nargs == 1L && is.list(a1 <- args[[1L]])) nargs <- length(args <- a1) if (nargs == 0L) return(as.data.frame(list())) cargs <- vector("list", nargs) iArgs <- seq_len(nargs) nmc <- paste0("Var", iArgs) nm <- names(args) if (is.null(nm)) nm <- nmc else if (any(ng0 <- nzchar(nm))) nmc[ng0] <- nm[ng0] names(cargs) <- nmc rep.fac <- 1L d <- sapply(args, length) if (KEEP.OUT.ATTRS) { dn <- vector("list", nargs) names(dn) <- nmc } orep <- prod(d) if (orep == 0L) { for (i in iArgs) cargs[[i]] <- args[[i]][FALSE] } else { for (i in iArgs) { x <- args[[i]] if (KEEP.OUT.ATTRS) dn[[i]] <- paste0(nmc[i], "=", if (is.numeric(x)) format(x) else x) nx <- length(x) orep <- orep/nx x <- x[rep.int(rep.int(seq_len(nx), rep.int(rep.fac, nx)), orep)] if (stringsAsFactors && !is.factor(x) && is.character(x)) x <- factor(x, levels = unique(x)) cargs[[i]] <- x rep.fac <- rep.fac * nx } } if (KEEP.OUT.ATTRS) attr(cargs, "out.attrs") <- list(dim = d, dimnames = dn) rn <- .set_row_names(as.integer(prod(d))) structure(cargs, class = "data.frame", row.names = rn) } ## @return integer file.access <- function (names, mode = 0) { res <- .Internal(file.access(names, mode)) names(res) <- names res } ## @type file1 : character ## @type file2 : character ## @return logical|character file.append <- function (file1, file2) .Internal(file.append(file1, file2)) file.choose <- function (new = FALSE) .Internal(file.choose(new)) ## @type showWarnings : logical ## @return logical|character file.create <- function (..., showWarnings = TRUE) .Internal(file.create(c(...), showWarnings)) file.exists <- function (...) .Internal(file.exists(c(...))) file.remove <- function (...) .Internal(file.remove(c(...))) ## @type from : character ## @type to : character file.rename <- function (from, to) .Internal(file.rename(from, to)) findRestart <- function (name, cond = NULL) { i <- 1L repeat { r <- .Internal(.getRestart(i)) if (is.null(r)) return(NULL) else if (name == r[[1L]] && (is.null(cond) || is.null(r$test) || r$test(cond))) return(r) else i <- i + 1L } } ## @type x : numeric format.AsIs <- function (x, width = 12, ...) { if (is.character(x)) return(format.default(x, ...)) if (is.null(width)) width = 12L n <- length(x) rvec <- rep.int(NA_character_, n) for (i in seq_len(n)) { y <- x[[i]] cl <- oldClass(y) if (m <- match("AsIs", cl, 0L)) oldClass(y) <- cl[-m] rvec[i] <- toString(y, width = width, ...) } dim(rvec) <- dim(x) dimnames(rvec) <- dimnames(x) format.default(rvec, justify = "right") } format.Date <- function (x, ...) { xx <- format(as.POSIXlt(x), ...) names(xx) <- names(x) xx } ## @type digits : complex format.info <- function (x, digits = NULL, nsmall = 0L) .Internal(format.info(x, digits, nsmall)) ## @type pv : numeric ## @type na.form : character ## @return character format.pval <- function (pv, digits = max(1L, getOption("digits") - 2L), eps = .Machine$double.eps, na.form = "NA", ...) { if ((has.na <- any(ina <- is.na(pv)))) pv <- pv[!ina] r <- character(length(is0 <- pv < eps)) if (any(!is0)) { rr <- pv <- pv[!is0] expo <- floor(log10(ifelse(pv > 0, pv, 1e-50))) fixp <- expo >= -3 | (expo == -4 & digits > 1) if (any(fixp)) rr[fixp] <- format(pv[fixp], digits = digits, ...) if (any(!fixp)) rr[!fixp] <- format(pv[!fixp], digits = digits, ...) r[!is0] <- rr } if (any(is0)) { digits <- max(1L, digits - 2L) if (any(!is0)) { nc <- max(nchar(rr, type = "w")) if (digits > 1L && digits + 6L > nc) digits <- max(1L, nc - 7L) sep <- if (digits == 1L && nc <= 6L) "" else " " } else sep <- if (digits == 1) "" else " " r[is0] <- paste("<", format(eps, digits = digits, ...), sep = sep) } if (has.na) { rok <- r r <- character(length(ina)) r[!ina] <- rok r[ina] <- na.form } r } getRversion <- function () package_version(R.version) getSrcLines <- function (srcfile, first, last) { if (first > last) return(character()) if (inherits(srcfile, "srcfilealias")) srcfile <- srcfile$original if (inherits(srcfile, "srcfilecopy")) { if (is.null(srcfile$fixedNewlines)) { lines <- srcfile$lines if (any(grepl("\n", lines, fixed = TRUE))) srcfile$lines <- unlist(strsplit(sub("$", "\n", as.character(lines)), "\n")) srcfile$fixedNewlines <- TRUE } last <- min(last, length(srcfile$lines)) if (first > last) return(character()) else return(srcfile$lines[first:last]) } if (!.isOpen(srcfile)) on.exit(close(srcfile)) conn <- open(srcfile, first) lines <- readLines(conn, n = last - first + 1L, warn = FALSE) if (!is.null(Enc <- srcfile$Enc) && !(Enc %in% c("unknown", "native.enc"))) lines <- iconv(lines, "", Enc) srcfile$line <- first + length(lines) return(lines) } ## @type sep : character ## @type lex.order : logical interaction <- function (..., drop = FALSE, sep = ".", lex.order = FALSE) { args <- list(...) narg <- length(args) if (narg < 1L) stop("No factors specified") if (narg == 1L && is.list(args[[1L]])) { args <- args[[1L]] narg <- length(args) } for (i in narg:1L) { f <- as.factor(args[[i]])[, drop = drop] l <- levels(f) if1 <- as.integer(f) - 1L if (i == narg) { ans <- if1 lvs <- l } else { if (lex.order) { ll <- length(lvs) ans <- ans + ll * if1 lvs <- paste(rep(l, each = ll), rep(lvs, length(l)), sep = sep) } else { ans <- ans * length(l) + if1 lvs <- paste(rep(l, length(lvs)), rep(lvs, each = length(l)), sep = sep) } if (anyDuplicated(lvs)) { ulvs <- unique(lvs) while ((i <- anyDuplicated(flv <- match(lvs, ulvs)))) { lvs <- lvs[-i] ans[ans + 1L == i] <- match(flv[i], flv[1:(i - 1)]) - 1L ans[ans + 1L > i] <- ans[ans + 1L > i] - 1L } lvs <- ulvs } if (drop) { olvs <- lvs lvs <- lvs[sort(unique(ans + 1L))] ans <- match(olvs[ans + 1L], lvs) - 1L } } } structure(as.integer(ans + 1L), levels = lvs, class = "factor") } interactive <- function () .Primitive("interactive") ## @optional x inverse.rle <- function (x, ...) { if (is.null(le <- x$lengths) || is.null(v <- x$values) || length(le) != length(v)) stop("invalid 'rle' structure") rep.int(v, le) } is.function <- function (x) .Primitive("is.function") is.infinite <- function (x) .Primitive("is.infinite") is.language <- function (x) .Primitive("is.language") is.pairlist <- function (x) .Primitive("is.pairlist") ## @type na.rm : logical ## @type strictly : logical ## @type x : raw|complex|logical|character ## @return logical is.unsorted <- function (x, na.rm = FALSE, strictly = FALSE) { if (length(x) <= 1L) return(FALSE) if (!na.rm && anyNA(x)) return(NA) if (na.rm && any(ii <- is.na(x))) x <- x[!ii] .Internal(is.unsorted(x, strictly)) } isNamespace <- function (ns) .Internal(isNamespaceEnv(ns)) ISOdatetime <- function (year, month, day, hour, min, sec, tz = "") { if (min(sapply(list(year, month, day, hour, min, sec), length)) == 0L) .POSIXct(numeric(), tz = tz) else { x <- paste(year, month, day, hour, min, sec, sep = "-") as.POSIXct(strptime(x, "%Y-%m-%d-%H-%M-%OS", tz = tz), tz = tz) } } isSymmetric <- function (object, ...) UseMethod("isSymmetric") julian.Date <- function (x, origin = as.Date("1970-01-01"), ...) { if (length(origin) != 1L) stop("'origin' must be of length one") structure(unclass(x) - unclass(origin), origin = origin) } ## @type sym : character lockBinding <- function (sym, env) { if (is.character(sym)) sym <- as.name(sym) .Internal(lockBinding(sym, env)) } ## @return character make.unique <- function (names, sep = ".") .Internal(make.unique(names, sep)) ## @optional x Math.factor <- function (x, ...) { stop(.Generic, " not meaningful for factors") } ## @optional x Math.POSIXt <- function (x, ...) { stop(gettextf("'%s' not defined for \"POSIXt\" objects", .Generic), domain = NA) } ## @type from : raw|character ## @type type : character ## @return raw|character memCompress <- function (from, type = c("gzip", "bzip2", "xz", "none")) { if (is.character(from)) from <- charToRaw(paste(from, collapse = "\n")) else if (!is.raw(from)) stop("'from' must be raw or character") type <- match(match.arg(type), c("none", "gzip", "bzip2", "xz")) .Internal(memCompress(from, type)) } months.Date <- function (x, abbreviate = FALSE) format(x, ifelse(abbreviate, "%b", "%B")) Ops.ordered <- function (e1, e2) { ok <- switch(.Generic, `<` = , `>` = , `<=` = , `>=` = , `==` = , `!=` = TRUE, FALSE) if (!ok) { warning(sprintf("'%s' is not meaningful for ordered factors", .Generic)) return(rep.int(NA, max(length(e1), if (!missing(e2)) length(e2)))) } if (.Generic %in% c("==", "!=")) return(NextMethod(.Generic)) nas <- is.na(e1) | is.na(e2) ord1 <- FALSE ord2 <- FALSE if (nzchar(.Method[1L])) { l1 <- levels(e1) ord1 <- TRUE } if (nzchar(.Method[2L])) { l2 <- levels(e2) ord2 <- TRUE } if (all(nzchar(.Method)) && (length(l1) != length(l2) || !all(l2 == l1))) stop("level sets of factors are different") if (ord1 && ord2) { e1 <- as.integer(e1) e2 <- as.integer(e2) } else if (!ord1) { e1 <- match(e1, l2) e2 <- as.integer(e2) } else if (!ord2) { e2 <- match(e2, l1) e1 <- as.integer(e1) } value <- get(.Generic, mode = "function")(e1, e2) value[nas] <- NA value } ## @type path : character path.expand <- function (path) .Internal(path.expand(path)) print.table <- function (x, digits = getOption("digits"), quote = FALSE, na.print = "", zero.print = "0", justify = "none", ...) { d <- dim(x) if (any(d == 0)) { cat("< table of extent", paste(d, collapse = " x "), ">\n") return(invisible(x)) } xx <- format(unclass(x), digits = digits, justify = justify) if (any(ina <- is.na(x))) xx[ina] <- na.print if (zero.print != "0" && any(i0 <- !ina & x == 0)) xx[i0] <- zero.print if (is.numeric(x) || is.complex(x)) print(xx, quote = quote, right = TRUE, ...) else print(xx, quote = quote, ...) invisible(x) } rep.POSIXct <- function (x, ...) { y <- NextMethod() .POSIXct(y, attr(x, "tzone")) } rep.POSIXlt <- function (x, ...) { y <- lapply(X = x, FUN = rep, ...) attributes(y) <- attributes(x) y } rev.default <- function (x) if (length(x)) x[length(x):1L] else x ## @type value : complex|character "row.names<-" <- function (x, value) UseMethod("row.names<-") searchpaths <- function () { s <- search() paths <- lapply(seq_along(s), function(i) attr(as.environment(i), "path")) paths[[length(s)]] <- system.file() m <- grep("^package:", s) if (length(m)) paths[-m] <- as.list(s[-m]) unlist(paths) } ## @type length.out : complex ## @type by : complex seq.default <- function (from = 1, to = 1, by = ((to - from)/(length.out - 1)), length.out = NULL, along.with = NULL, ...) { if ((One <- nargs() == 1L) && !missing(from)) { lf <- length(from) return(if (mode(from) == "numeric" && lf == 1L) { if (!is.finite(from)) stop("'from' cannot be NA, NaN or infinite") 1L:from } else if (lf) 1L:lf else integer()) } if (!missing(along.with)) { length.out <- length(along.with) if (One) return(if (length.out) seq_len(length.out) else integer()) } else if (!missing(length.out)) { len <- length(length.out) if (!len) stop("argument 'length.out' must be of length 1") if (len > 1L) { warning("first element used of 'length.out' argument") length.out <- length.out[1L] } length.out <- ceiling(length.out) } if (!missing(...)) warning(sprintf(ngettext(length(list(...)), "extra argument %s will be disregarded", "extra arguments %s will be disregarded"), paste(sQuote(names(list(...))), collapse = ", ")), domain = NA) if (!missing(from) && length(from) != 1L) stop("'from' must be of length 1") if (!missing(to) && length(to) != 1L) stop("'to' must be of length 1") if (!missing(from) && !is.finite(from)) stop("'from' cannot be NA, NaN or infinite") if (!missing(to) && !is.finite(to)) stop("'to' cannot be NA, NaN or infinite") if (is.null(length.out)) if (missing(by)) from:to else { del <- to - from if (del == 0 && to == 0) return(to) n <- del/by if (!(length(n) && is.finite(n))) { if (length(by) && by == 0 && length(del) && del == 0) return(from) stop("invalid (to - from)/by in seq(.)") } if (n < 0L) stop("wrong sign in 'by' argument") if (n > .Machine$integer.max) stop("'by' argument is much too small") dd <- abs(del)/max(abs(to), abs(from)) if (dd < 100 * .Machine$double.eps) return(from) if (is.integer(del) && is.integer(by)) { n <- as.integer(n) from + (0L:n) * by } else { n <- as.integer(n + 1e-10) x <- from + (0L:n) * by if (by > 0) pmin(x, to) else pmax(x, to) } } else if (!is.finite(length.out) || length.out < 0L) stop("length must be non-negative number") else if (length.out == 0L) integer() else if (One) seq_len(length.out) else if (missing(by)) { if (missing(to)) to <- from + length.out - 1L if (missing(from)) from <- to - length.out + 1L if (length.out > 2L) if (from == to) rep.int(from, length.out) else as.vector(c(from, from + seq_len(length.out - 2L) * by, to)) else as.vector(c(from, to))[seq_len(length.out)] } else if (missing(to)) from + (0L:(length.out - 1L)) * by else if (missing(from)) to - ((length.out - 1L):0L) * by else stop("too many arguments") } simpleError <- function (message, call = NULL) { class <- c("simpleError", "error", "condition") structure(list(message = as.character(message), call = call), class = class) } ## @type type : character sink.number <- function (type = c("output", "message")) { type <- match.arg(type) .Internal(sink.number(type != "message")) } slice.index <- function (x, MARGIN) { d <- dim(x) if (is.null(d)) d <- length(x) n <- length(d) if ((length(MARGIN) > 1L) || (MARGIN < 1L) || (MARGIN > n)) stop("incorrect value for 'MARGIN'") if (any(d == 0L)) return(array(integer(), d)) y <- rep.int(rep.int(1L:d[MARGIN], prod(d[seq_len(MARGIN - 1L)]) * rep.int(1L, d[MARGIN])), prod(d[seq.int(from = MARGIN + 1L, length.out = n - MARGIN)])) dim(y) <- d y } srcfilecopy <- function (filename, lines, timestamp = Sys.time(), isFile = FALSE) { stopifnot(is.character(filename), length(filename) == 1L) e <- new.env(parent = emptyenv()) if (any(grepl("\n", lines, fixed = TRUE))) lines <- unlist(strsplit(sub("$", "\n", as.character(lines)), "\n")) e$filename <- filename e$wd <- getwd() e$isFile <- isFile e$lines <- as.character(lines) e$fixedNewlines <- TRUE e$timestamp <- timestamp e$Enc <- "unknown" class(e) <- c("srcfilecopy", "srcfile") return(e) } ## @type first : integer ## @type value : character ## @type text : character ## @type last : integer "substring<-" <- function (text, first, last = 1000000L, value) .Internal(`substr<-`(text, as.integer(first), as.integer(last), value)) sys.on.exit <- function () .Internal(sys.on.exit()) sys.parents <- function () .Internal(sys.parents()) ## @type lib.loc : character ## @type mustWork : logical ## @type package : character ## @return character system.file <- function (..., package = "base", lib.loc = NULL, mustWork = FALSE) { if (nargs() == 0L) return(file.path(.Library, "base")) if (length(package) != 1L) stop("'package' must be of length 1") packagePath <- find.package(package, lib.loc, quiet = TRUE) ans <- if (length(packagePath)) { FILES <- file.path(packagePath, ...) present <- file.exists(FILES) if (any(present)) FILES[present] else "" } else "" if (mustWork && identical(ans, "")) stop("no file found") ans } system.time <- function (expr, gcFirst = TRUE) { ppt <- function(y) { if (!is.na(y[4L])) y[1L] <- y[1L] + y[4L] if (!is.na(y[5L])) y[2L] <- y[2L] + y[5L] y[1L:3L] } if (!exists("proc.time")) return(rep(NA_real_, 5L)) if (gcFirst) gc(FALSE) time <- proc.time() on.exit(cat("Timing stopped at:", ppt(proc.time() - time), "\n")) expr new.time <- proc.time() on.exit() structure(new.time - time, class = "proc_time") } ## @type connection : raw unserialize <- function (connection, refhook = NULL) { if (typeof(connection) != "raw" && !is.character(connection) && !inherits(connection, "connection")) stop("'connection' must be a connection") .Internal(unserialize(connection, refhook)) } within.list <- function (data, expr, ...) { parent <- parent.frame() e <- evalq(environment(), data, parent) eval(substitute(expr), e) l <- as.list(e) l <- l[!sapply(l, is.null)] nD <- length(del <- setdiff(names(data), (nl <- names(l)))) data[nl] <- l if (nD) data[del] <- if (nD == 1) NULL else vector("list", nD) data } withVisible <- function (x) .Internal(withVisible(x)) xor.hexmode <- function (a, b) as.hexmode(bitwXor(as.hexmode(a), as.hexmode(b))) xor.octmode <- function (a, b) as.octmode(bitwXor(as.octmode(a), as.octmode(b))) ## @type name : character "$.data.frame" <- function (x, name) { a <- x[[name]] if (!is.null(a)) return(a) a <- x[[name, exact = FALSE]] if (!is.null(a) && getOption("warnPartialMatchDollar", default = FALSE)) { names <- names(x) warning(gettextf("Partial match of '%s' to '%s' in data frame", name, names[pmatch(name, names)])) } return(a) } ## @type i : numeric|logical|character ## @type j : numeric|logical|character ## @type drop : logical "[.data.frame" <- function (x, i, j, drop = if (missing(i)) TRUE else length(cols) == 1) { mdrop <- missing(drop) Narg <- nargs() - (!mdrop) has.j <- !missing(j) if (!all(names(sys.call()) %in% c("", "drop")) && !isS4(x)) warning("named arguments other than 'drop' are discouraged") if (Narg < 3L) { if (!mdrop) warning("'drop' argument will be ignored") if (missing(i)) return(x) if (is.matrix(i)) return(as.matrix(x)[i]) nm <- names(x) if (is.null(nm)) nm <- character() if (!is.character(i) && anyNA(nm)) { names(nm) <- names(x) <- seq_along(x) y <- NextMethod("[") cols <- names(y) if (anyNA(cols)) stop("undefined columns selected") cols <- names(y) <- nm[cols] } else { y <- NextMethod("[") cols <- names(y) if (!is.null(cols) && anyNA(cols)) stop("undefined columns selected") } if (anyDuplicated(cols)) names(y) <- make.unique(cols) attr(y, "row.names") <- .row_names_info(x, 0L) attr(y, "class") <- oldClass(x) return(y) } if (missing(i)) { if (drop && !has.j && length(x) == 1L) return(.subset2(x, 1L)) nm <- names(x) if (is.null(nm)) nm <- character() if (has.j && !is.character(j) && anyNA(nm)) { names(nm) <- names(x) <- seq_along(x) y <- .subset(x, j) cols <- names(y) if (anyNA(cols)) stop("undefined columns selected") cols <- names(y) <- nm[cols] } else { y <- if (has.j) .subset(x, j) else x cols <- names(y) if (anyNA(cols)) stop("undefined columns selected") } if (drop && length(y) == 1L) return(.subset2(y, 1L)) if (anyDuplicated(cols)) names(y) <- make.unique(cols) nrow <- .row_names_info(x, 2L) if (drop && !mdrop && nrow == 1L) return(structure(y, class = NULL, row.names = NULL)) else { attr(y, "class") <- oldClass(x) attr(y, "row.names") <- .row_names_info(x, 0L) return(y) } } xx <- x cols <- names(xx) x <- vector("list", length(x)) x <- .Internal(copyDFattr(xx, x)) oldClass(x) <- attr(x, "row.names") <- NULL if (has.j) { nm <- names(x) if (is.null(nm)) nm <- character() if (!is.character(j) && anyNA(nm)) names(nm) <- names(x) <- seq_along(x) x <- x[j] cols <- names(x) if (drop && length(x) == 1L) { if (is.character(i)) { rows <- attr(xx, "row.names") i <- pmatch(i, rows, duplicates.ok = TRUE) } xj <- .subset2(.subset(xx, j), 1L) return(if (length(dim(xj)) != 2L) xj[i] else xj[i, , drop = FALSE]) } if (anyNA(cols)) stop("undefined columns selected") if (!is.null(names(nm))) cols <- names(x) <- nm[cols] nxx <- structure(seq_along(xx), names = names(xx)) sxx <- match(nxx[j], seq_along(xx)) } else sxx <- seq_along(x) rows <- NULL if (is.character(i)) { rows <- attr(xx, "row.names") i <- pmatch(i, rows, duplicates.ok = TRUE) } for (j in seq_along(x)) { xj <- xx[[sxx[j]]] x[[j]] <- if (length(dim(xj)) != 2L) xj[i] else xj[i, , drop = FALSE] } if (drop) { n <- length(x) if (n == 1L) return(x[[1L]]) if (n > 1L) { xj <- x[[1L]] nrow <- if (length(dim(xj)) == 2L) dim(xj)[1L] else length(xj) drop <- !mdrop && nrow == 1L } else drop <- FALSE } if (!drop) { if (is.null(rows)) rows <- attr(xx, "row.names") rows <- rows[i] if ((ina <- anyNA(rows)) | (dup <- anyDuplicated(rows))) { if (!dup && is.character(rows)) dup <- "NA" %in% rows if (ina) rows[is.na(rows)] <- "NA" if (dup) rows <- make.unique(as.character(rows)) } if (has.j && anyDuplicated(nm <- names(x))) names(x) <- make.unique(nm) if (is.null(rows)) rows <- attr(xx, "row.names")[i] attr(x, "row.names") <- rows oldClass(x) <- oldClass(xx) } x } as.character <- function (x, ...) .Primitive("as.character") as.Date.date <- function (x, ...) { if (inherits(x, "date")) { x <- (x - 3653) return(structure(x, class = "Date")) } else stop(gettextf("'%s' is not a \"date\" object", deparse(substitute(x)))) } as.list.Date <- function (x, ...) lapply(seq_along(x), function(i) x[i]) "attributes<-" <- function (obj, value) .Primitive("attributes<-") ## @type what : character ## @return logical capabilities <- function (what = NULL) { z <- .Internal(capabilities()) if (!is.null(what)) z <- z[match(what, names(z), 0L)] if (.Platform$OS.type == "windows") return(z) nas <- names(z[is.na(z)]) if (any(nas %in% c("X11", "jpeg", "png", "tiff"))) { z[nas] <- tryCatch(.Internal(capabilitiesX11()), error = function(e) FALSE) } z } check_tzones <- function (...) { tzs <- unique(sapply(list(...), function(x) { y <- attr(x, "tzone") if (is.null(y)) "" else y[1L] })) tzs <- tzs[tzs != ""] if (length(tzs) > 1L) warning("'tzone' attributes are inconsistent") if (length(tzs)) tzs[1L] else NULL } ## @type tol : numeric ## @type LINPACK : logical ## @type x : logical|numeric chol.default <- function (x, pivot = FALSE, LINPACK = FALSE, tol = -1, ...) { if (is.complex(x)) stop("complex matrices not permitted at present") .Internal(La_chol(as.matrix(x), pivot, tol)) } contributors <- function () { outFile <- tempfile() outConn <- file(outFile, open = "w") writeLines(paste0("R is a project which is attempting to provide a ", "modern piece of\nstatistical software for the ", "GNU suite of software.\n\n", "The current R is the result of a collaborative ", "effort with\ncontributions from all over the ", "world.\n\n"), outConn) writeLines(readLines(file.path(R.home("doc"), "AUTHORS")), outConn) writeLines("", outConn) writeLines(readLines(file.path(R.home("doc"), "THANKS")), outConn) close(outConn) file.show(outFile, delete.file = TRUE) } ## @type lag : integer ## @type differences : integer ## @type x : numeric diff.default <- function (x, lag = 1L, differences = 1L, ...) { ismat <- is.matrix(x) xlen <- if (ismat) dim(x)[1L] else length(x) if (length(lag) != 1L || length(differences) > 1L || lag < 1L || differences < 1L) stop("'lag' and 'differences' must be integers >= 1") if (lag * differences >= xlen) return(x[0L]) r <- unclass(x) i1 <- -seq_len(lag) if (ismat) for (i in seq_len(differences)) r <- r[i1, , drop = FALSE] - r[-nrow(r):-(nrow(r) - lag + 1L), , drop = FALSE] else for (i in seq_len(differences)) r <- r[i1] - r[-length(r):-(length(r) - lag + 1L)] class(r) <- oldClass(x) r } ## @return character encodeString <- function (x, width = 0L, quote = "", na.encode = TRUE, justify = c("left", "right", "centre", "none")) { at <- attributes(x) x <- as.character(x) attributes(x) <- at oldClass(x) <- NULL justify <- match(match.arg(justify), c("left", "right", "centre", "none")) - 1L .Internal(encodeString(x, width, quote, justify, na.encode)) } ## @type from : character ## @type to : character ## @return logical|character file.symlink <- function (from, to) { if (!(length(from))) stop("no files to link from") if (!(nt <- length(to))) stop("no files/directory to link to") if (nt == 1 && file.exists(to) && file.info(to)$isdir) to <- file.path(to, basename(from)) .Internal(file.symlink(from, to)) } ## @type lib.loc : character ## @type verbose : logical ## @type package : character ## @type quiet : logical find.package <- function (package = NULL, lib.loc = NULL, quiet = FALSE, verbose = getOption("verbose")) { if (is.null(package) && is.null(lib.loc) && !verbose) { return(path.package()) } if (length(package) == 1L && package %in% c("base", "tools", "utils", "grDevices", "graphics", "stats", "datasets", "methods", "grid", "parallel", "splines", "stats4", "tcltk")) return(file.path(.Library, package)) use_loaded <- FALSE if (is.null(package)) package <- .packages() if (is.null(lib.loc)) { use_loaded <- TRUE lib.loc <- .libPaths() } if (!length(package)) return(character()) bad <- character() out <- character() for (pkg in package) { paths <- character() for (lib in lib.loc) { dirs <- list.files(lib, pattern = paste0("^", pkg, "$"), full.names = TRUE) paths <- c(paths, dirs[file.info(dirs)$isdir & file.exists(file.path(dirs, "DESCRIPTION"))]) } if (use_loaded && pkg %in% loadedNamespaces()) { dir <- if (pkg == "base") system.file() else getNamespaceInfo(pkg, "path") paths <- c(dir, paths) } if (length(paths) && file.exists(file.path(paths[1], "dummy_for_check"))) { bad <- c(bad, pkg) next } if (length(paths)) { paths <- unique(paths) valid_package_version_regexp <- .standard_regexps()$valid_package_version db <- lapply(paths, function(p) { pfile <- file.path(p, "Meta", "package.rds") info <- if (file.exists(pfile)) readRDS(pfile)$DESCRIPTION[c("Package", "Version")] else { info <- tryCatch(read.dcf(file.path(p, "DESCRIPTION"), c("Package", "Version"))[1, ], error = identity) if (inherits(info, "error") || (length(info) != 2L) || anyNA(info)) c(Package = NA, Version = NA) else info } }) db <- do.call("rbind", db) ok <- (apply(!is.na(db), 1L, all) & (db[, "Package"] == pkg) & (grepl(valid_package_version_regexp, db[, "Version"]))) paths <- paths[ok] } if (length(paths) == 0L) { bad <- c(bad, pkg) next } if (length(paths) > 1L) { paths <- paths[1L] if (verbose) warning(gettextf("package %s found more than once,\nusing the one found in %s", sQuote(pkg), sQuote(paths)), domain = NA) } out <- c(out, paths) } if (!quiet && length(bad)) { if (length(out) == 0L) { if (length(bad) == 1L) { stop(gettextf("there is no package called %s", sQuote(pkg)), domain = NA) } else { stop(ngettext(length(bad), "there is no package called", "there are no packages called"), " ", paste(sQuote(bad), collapse = ", "), domain = NA) } } for (pkg in bad) warning(gettextf("there is no package called %s", sQuote(pkg)), domain = NA) } out } ## @type rightmost.closed : logical ## @type vec : numeric ## @type all.inside : logical ## @type x : numeric findInterval <- function (x, vec, rightmost.closed = FALSE, all.inside = FALSE) { if (anyNA(vec)) stop("'vec' contains NAs") if (is.unsorted(vec)) stop("'vec' must be sorted non-decreasingly") .Internal(findInterval(as.double(vec), as.double(x), rightmost.closed, all.inside)) } ## @type transpose : logical ## @type k : complex ## @type upper.tri : logical forwardsolve <- function (l, x, k = ncol(l), upper.tri = FALSE, transpose = FALSE) { l <- as.matrix(l) x.mat <- is.matrix(x) if (!x.mat) x <- as.matrix(x) z <- .Internal(backsolve(l, x, k, upper.tri, transpose)) if (x.mat) z else drop(z) } ## @type name : character getNamespace <- function (name) { ns <- .Internal(getRegisteredNamespace(as.name(name))) if (!is.null(ns)) ns else tryCatch(loadNamespace(name), error = function(e) stop(e)) } is.character <- function (x) .Primitive("is.character") is.primitive <- function (x) switch(typeof(x), special = , builtin = TRUE, FALSE) is.recursive <- function (x) .Primitive("is.recursive") isIncomplete <- function (con) .Internal(isIncomplete(con)) margin.table <- function (x, margin = NULL) { if (!is.array(x)) stop("'x' is not an array") if (length(margin)) { z <- apply(x, margin, sum) dim(z) <- dim(x)[margin] dimnames(z) <- dimnames(x)[margin] } else return(sum(x)) class(z) <- oldClass(x) z } ## @type na.rm : logical mean.default <- function (x, trim = 0, na.rm = FALSE, ...) { if (!is.numeric(x) && !is.complex(x) && !is.logical(x)) { warning("argument is not numeric or logical: returning NA") return(NA_real_) } if (na.rm) x <- x[!is.na(x)] if (!is.numeric(trim) || length(trim) != 1L) stop("'trim' must be numeric of length one") n <- length(x) if (trim > 0 && n) { if (is.complex(x)) stop("trimmed means are not defined for complex data") if (anyNA(x)) return(NA_real_) if (trim >= 0.5) return(stats::median(x, na.rm = FALSE)) lo <- floor(n * trim) + 1 hi <- n + 1 - lo x <- sort.int(x, partial = unique(c(lo, hi)))[lo:hi] } .Internal(mean(x)) } mean.POSIXct <- function (x, ...) .POSIXct(mean(unclass(x), ...), attr(x, "tzone")) mean.POSIXlt <- function (x, ...) as.POSIXlt(mean(as.POSIXct(x), ...)) open.srcfile <- function (con, line, ...) { srcfile <- con oldline <- srcfile$line if (!is.null(oldline) && oldline > line) close(srcfile) conn <- srcfile$conn if (is.null(conn)) { if (!is.null(srcfile$wd)) { olddir <- setwd(srcfile$wd) on.exit(setwd(olddir)) } timestamp <- file.info(srcfile$filename)[1, "mtime"] if (!is.null(srcfile$timestamp) && !is.na(srcfile$timestamp) && (is.na(timestamp) || timestamp != srcfile$timestamp)) warning(gettextf("Timestamp of %s has changed", sQuote(srcfile$filename)), call. = FALSE, domain = NA) if (is.null(srcfile$encoding)) encoding <- getOption("encoding") else encoding <- srcfile$encoding srcfile$conn <- conn <- file(srcfile$filename, open = "rt", encoding = encoding) srcfile$line <- 1L oldline <- 1L } else if (!isOpen(conn)) { open(conn, open = "rt") srcfile$line <- 1 oldline <- 1L } if (oldline < line) { readLines(conn, line - oldline, warn = FALSE) srcfile$line <- line } invisible(conn) } Ops.difftime <- function (e1, e2) { coerceTimeUnit <- function(x) { switch(attr(x, "units"), secs = x, mins = 60 * x, hours = 60 * 60 * x, days = 60 * 60 * 24 * x, weeks = 60 * 60 * 24 * 7 * x) } if (nargs() == 1) { switch(.Generic, `+` = { }, `-` = { e1[] <- -unclass(e1) }, stop(gettextf("unary '%s' not defined for \"difftime\" objects", .Generic), domain = NA, call. = FALSE)) return(e1) } boolean <- switch(.Generic, `<` = , `>` = , `==` = , `!=` = , `<=` = , `>=` = TRUE, FALSE) if (boolean) { if (inherits(e1, "difftime") && inherits(e2, "difftime")) { e1 <- coerceTimeUnit(e1) e2 <- coerceTimeUnit(e2) } NextMethod(.Generic) } else if (.Generic == "+" || .Generic == "-") { if (inherits(e1, "difftime") && !inherits(e2, "difftime")) return(structure(NextMethod(.Generic), units = attr(e1, "units"), class = "difftime")) if (!inherits(e1, "difftime") && inherits(e2, "difftime")) return(structure(NextMethod(.Generic), units = attr(e2, "units"), class = "difftime")) u1 <- attr(e1, "units") if (attr(e2, "units") == u1) { structure(NextMethod(.Generic), units = u1, class = "difftime") } else { e1 <- coerceTimeUnit(e1) e2 <- coerceTimeUnit(e2) structure(NextMethod(.Generic), units = "secs", class = "difftime") } } else { stop(gettextf("'%s' not defined for \"difftime\" objects", .Generic), domain = NA) } } ## @type pkgname : character ## @type event : character ## @optional pkgname packageEvent <- function (pkgname, event = c("onLoad", "attach", "detach", "onUnload")) { event <- match.arg(event) pkgname <- strsplit(pkgname, "_", fixed = TRUE)[[1L]][1L] paste("UserHook", pkgname, event, sep = "::") } "parent.env<-" <- function (env, value) .Internal(`parent.env<-`(env, value)) parent.frame <- function (n = 1) .Internal(parent.frame(n)) ## @type package : character ## @type quiet : logical path.package <- function (package = NULL, quiet = FALSE) { if (is.null(package)) package <- .packages() if (length(package) == 0L) return(character()) s <- search() searchpaths <- lapply(seq_along(s), function(i) attr(as.environment(i), "path")) searchpaths[[length(s)]] <- system.file() pkgs <- paste("package", package, sep = ":") pos <- match(pkgs, s) if (any(m <- is.na(pos))) { if (!quiet) { if (all(m)) stop("none of the packages are loaded") else warning(sprintf(ngettext(as.integer(sum(m)), "package %s is not loaded", "packages %s are not loaded"), paste(package[m], collapse = ", ")), domain = NA) } pos <- pos[!m] } unlist(searchpaths[pos], use.names = FALSE) } ## @type quote : logical ## @type max.levels : integer print.factor <- function (x, quote = FALSE, max.levels = NULL, width = getOption("width"), ...) { ord <- is.ordered(x) if (length(x) == 0L) cat(if (ord) "ordered" else "factor", "(0)\n", sep = "") else { xx <- x class(xx) <- NULL levels(xx) <- NULL xx[] <- as.character(x) print(xx, quote = quote, ...) } maxl <- if (is.null(max.levels)) TRUE else max.levels if (maxl) { n <- length(lev <- encodeString(levels(x), quote = ifelse(quote, "\"", ""))) colsep <- if (ord) " < " else " " T0 <- "Levels: " if (is.logical(maxl)) maxl <- { width <- width - (nchar(T0, "w") + 3L + 1L + 3L) lenl <- cumsum(nchar(lev, "w") + nchar(colsep, "w")) if (n <= 1L || lenl[n] <= width) n else max(1L, which.max(lenl > width) - 1L) } drop <- n > maxl cat(if (drop) paste(format(n), ""), T0, paste(if (drop) c(lev[1L:max(1, maxl - 1)], "...", if (maxl > 1) lev[n]) else lev, collapse = colsep), "\n", sep = "") } invisible(x) } print.listof <- function (x, ...) { nn <- names(x) ll <- length(x) if (length(nn) != ll) nn <- paste("Component", seq.int(ll)) for (i in seq_len(ll)) { cat(nn[i], ":\n") print(x[[i]], ...) cat("\n") } invisible(x) } print.srcref <- function (x, useSource = TRUE, ...) { cat(as.character(x, useSource = useSource), sep = "\n") invisible(x) } ## @type path : character ## @return logical readRenviron <- function (path) .Internal(readRenviron(path)) ## @type x : character ## @type invert : logical "regmatches<-" <- function (x, m, invert = FALSE, value) { if (!length(x)) return(x) ili <- is.list(m) if (!ili && invert && any(m == -1L)) { y <- rep_len(list(character()), length(x)) y[m > -1L] <- as.list(regmatches(x, m, FALSE)) } else { y <- regmatches(x, m, !invert) } if (!ili && !invert) { value <- as.character(value) if (anyNA(value)) stop("missing replacement values are not allowed") pos <- which(sapply(y, length) == 2L) np <- length(pos) nv <- length(value) if (np != nv) { if (!nv) stop("must have replacement values for matches") value <- rep_len(value, np) } y <- y[pos] x[pos] <- paste0(sapply(y, `[`, 1L), value, sapply(y, `[`, 2L)) return(x) } value <- lapply(value, as.character) if (anyNA(value)) stop("missing replacement values are not allowed") if (!length(value)) stop("value does not provide any replacement values") value <- rep_len(value, length(x)) y <- if (invert) { Map(function(u, v) { nu <- length(u) nv <- length(v) if (nv != (nu + 1L)) { if (!nv) stop("must have replacements for non-matches") v <- rep_len(v, nu + 1L) } paste0(v, c(u, ""), collapse = "") }, y, value, USE.NAMES = FALSE) } else { Map(function(u, v) { nu <- length(u) nv <- length(v) if (nv != (nu - 1L)) { if (!nv) stop("must have replacements for matches") v <- rep_len(v, nu - 1L) } paste0(u, c(v, ""), collapse = "") }, y, value, USE.NAMES = FALSE) } y <- unlist(y) names(y) <- names(x) y } round.POSIXt <- function (x, units = c("secs", "mins", "hours", "days")) { if (is.numeric(units) && units == 0) units <- "secs" units <- match.arg(units) x <- as.POSIXct(x) x <- x + switch(units, secs = 0.5, mins = 30, hours = 1800, days = 43200) trunc.POSIXt(x, units = units) } ## @type transient : logical setTimeLimit <- function (cpu = Inf, elapsed = Inf, transient = FALSE) .Internal(setTimeLimit(cpu, elapsed, transient)) ## @type write : logical ## @type timeout : numeric socketSelect <- function (socklist, write = FALSE, timeout = NULL) { if (is.null(timeout)) timeout <- -1 else if (timeout < 0) stop("'timeout' must be NULL or a non-negative number") if (length(write) < length(socklist)) write <- rep_len(write, length(socklist)) .Internal(sockSelect(socklist, write, timeout)) } ## @type x : complex|logical|character ## @type decreasing : logical sort.default <- function (x, decreasing = FALSE, na.last = NA, ...) { if (is.object(x)) x[order(x, na.last = na.last, decreasing = decreasing)] else sort.int(x, na.last = na.last, decreasing = decreasing, ...) } ## @type x : complex|logical|character ## @type decreasing : logical sort.POSIXlt <- function (x, decreasing = FALSE, na.last = NA, ...) x[order(as.POSIXct(x), na.last = na.last, decreasing = decreasing)] ## @type filename : character srcfilealias <- function (filename, srcfile) { stopifnot(is.character(filename), length(filename) == 1L) e <- new.env(parent = emptyenv()) e$filename <- filename e$original <- srcfile class(e) <- c("srcfilealias", "srcfile") return(e) } storage.mode <- function (x) switch(tx <- typeof(x), closure = , builtin = , special = "function", tx) ## @optional na.rm Summary.Date <- function (..., na.rm) { ok <- switch(.Generic, max = , min = , range = TRUE, FALSE) if (!ok) stop(gettextf("%s not defined for \"Date\" objects", .Generic), domain = NA) val <- NextMethod(.Generic) class(val) <- oldClass(list(...)[[1L]]) val } sys.function <- function (which = 0L) .Internal(sys.function(which)) ## @type paths : character Sys.readlink <- function (paths) .Internal(Sys.readlink(paths)) ## @type location : logical|character ## @return character Sys.timezone <- function (location = TRUE) { tz <- Sys.getenv("TZ", names = FALSE) if (!location || nzchar(tz)) return(Sys.getenv("TZ", unset = NA_character_)) lt <- normalizePath("/etc/localtime") if (grepl(pat <- "^/usr/share/zoneinfo/", lt)) sub(pat, "", lt) else NA_character_ } ## @type x : character ## @return logical Sys.unsetenv <- function (x) .Internal(Sys.unsetenv(as.character(x))) t.data.frame <- function (x) { x <- as.matrix(x) NextMethod("t") } tracingState <- function (on = NULL) .Internal(traceOnOff(on)) trunc.POSIXt <- function (x, units = c("secs", "mins", "hours", "days"), ...) { units <- match.arg(units) x <- as.POSIXlt(x) if (length(x$sec)) switch(units, secs = { x$sec <- trunc(x$sec) }, mins = { x$sec[] <- 0 }, hours = { x$sec[] <- 0 x$min[] <- 0L }, days = { x$sec[] <- 0 x$min[] <- 0L x$hour[] <- 0L x$isdst[] <- -1L }) x } ## @type fromLast : logical ## @type MARGIN : integer unique.array <- function (x, incomparables = FALSE, MARGIN = 1, fromLast = FALSE, ...) { if (!identical(incomparables, FALSE)) .NotYetUsed("incomparables != FALSE") dx <- dim(x) ndim <- length(dx) if (length(MARGIN) > ndim || any(MARGIN > ndim)) stop(gettextf("MARGIN = %d is invalid for dim = %d", MARGIN, dx), domain = NA) collapse <- (ndim > 1L) && (prod(dx[-MARGIN]) > 1L) temp <- if (collapse) apply(x, MARGIN, function(x) paste(x, collapse = "\r")) else x args <- rep(alist(a = ), ndim) names(args) <- NULL args[[MARGIN]] <- !duplicated.default(temp, fromLast = fromLast, ...) do.call("[", c(list(x), args, list(drop = FALSE))) } with.default <- function (data, expr, ...) eval(substitute(expr), data, enclos = parent.frame()) withRestarts <- function (expr, ...) { docall <- function(fun, args) { if ((is.character(fun) && length(fun) == 1L) || is.name(fun)) fun <- get(as.character(fun), envir = parent.frame(), mode = "function") do.call("fun", lapply(args, enquote)) } makeRestart <- function(name = "", handler = function(...) NULL, description = "", test = function(c) TRUE, interactive = NULL) { structure(list(name = name, exit = NULL, handler = handler, description = description, test = test, interactive = interactive), class = "restart") } makeRestartList <- function(...) { specs <- list(...) names <- names(specs) restarts <- vector("list", length(specs)) for (i in seq_along(specs)) { spec <- specs[[i]] name <- names[i] if (is.function(spec)) restarts[[i]] <- makeRestart(handler = spec) else if (is.character(spec)) restarts[[i]] <- makeRestart(description = spec) else if (is.list(spec)) restarts[[i]] <- docall("makeRestart", spec) else stop("not a valid restart specification") restarts[[i]]$name <- name } restarts } withOneRestart <- function(expr, restart) { doWithOneRestart <- function(expr, restart) { restart$exit <- environment() .Internal(.addRestart(restart)) expr } restartArgs <- doWithOneRestart(return(expr), restart) docall(restart$handler, restartArgs) } withRestartList <- function(expr, restarts) { nr <- length(restarts) if (nr > 1L) withOneRestart(withRestartList(expr, restarts[-nr]), restarts[[nr]]) else if (nr == 1L) withOneRestart(expr, restarts[[1L]]) else expr } restarts <- makeRestartList(...) if (length(restarts) == 0L) expr else if (length(restarts) == 1L) withOneRestart(expr, restarts[[1L]]) else withRestartList(expr, restarts) } xtfrm.factor <- function (x) as.integer(x) "[.simple.list" <- function (x, i, ...) structure(NextMethod("["), class = class(x)) ## @type exact : logical "[[.data.frame" <- function (x, ..., exact = TRUE) { na <- nargs() - (!missing(exact)) if (!all(names(sys.call()) %in% c("", "exact"))) warning("named arguments other than 'exact' are discouraged") if (na < 3L) (function(x, i, exact) if (is.matrix(i)) as.matrix(x)[[i]] else .subset2(x, i, exact = exact))(x, ..., exact = exact) else { col <- .subset2(x, ..2, exact = exact) i <- if (is.character(..1)) pmatch(..1, row.names(x), duplicates.ok = TRUE) else ..1 col[[i, exact = exact]] } } ## @type check.attributes : logical ## @return logical all.equal.raw <- function (target, current, ..., check.attributes = TRUE) { if (!is.logical(check.attributes)) stop(gettextf("'%s' must be logical", "check.attributes"), domain = NA) msg <- if (check.attributes) attr.all.equal(target, current, ...) if (data.class(target) != data.class(current)) { msg <- c(msg, paste0("target is ", data.class(target), ", current is ", data.class(current))) return(msg) } lt <- length(target) lc <- length(current) if (lt != lc) { if (!is.null(msg)) msg <- msg[-grep("\\bLengths\\b", msg)] msg <- c(msg, paste0("Lengths (", lt, ", ", lc, ") differ (comparison on first ", ll <- min(lt, lc), " components)")) ll <- seq_len(ll) target <- target[ll] current <- current[ll] } nas <- is.na(target) nasc <- is.na(current) if (any(nas != nasc)) { msg <- c(msg, paste("'is.NA' value mismatch:", sum(nasc), "in current", sum(nas), "in target")) return(msg) } ne <- !nas & (target != current) if (!any(ne) && is.null(msg)) TRUE else if (sum(ne) == 1L) c(msg, paste("1 element mismatch")) else if (sum(ne) > 1L) c(msg, paste(sum(ne), "element mismatches")) else msg } anyDuplicated <- function (x, incomparables = FALSE, ...) UseMethod("anyDuplicated") anyNA.POSIXlt <- function (x) anyNA(as.POSIXct(x)) ## @type perm : complex|character aperm.default <- function (a, perm = NULL, resize = TRUE, ...) .Internal(aperm(a, perm, resize)) ## @type optional : logical ## @type row.names : character as.data.frame <- function (x, row.names = NULL, optional = FALSE, ...) { if (is.null(x)) return(as.data.frame(list())) UseMethod("as.data.frame") } as.Date.dates <- function (x, ...) { if (inherits(x, "dates")) { z <- attr(x, "origin") x <- trunc(as.numeric(x)) if (length(z) == 3L && is.numeric(z)) x <- x + as.numeric(as.Date(paste(z[3L], z[1L], z[2L], sep = "/"))) return(structure(x, class = "Date")) } else stop(gettextf("'%s' is not a \"dates\" object", deparse(substitute(x)))) } as.expression <- function (x, ...) UseMethod("as.expression") ## @type simplify : logical ## @optional FUN by.data.frame <- function (data, INDICES, FUN, ..., simplify = TRUE) { if (!is.list(INDICES)) { IND <- vector("list", 1L) IND[[1L]] <- INDICES names(IND) <- deparse(substitute(INDICES))[1L] } else IND <- INDICES FUNx <- function(x) FUN(data[x, , drop = FALSE], ...) nd <- nrow(data) structure(eval(substitute(tapply(seq_len(nd), IND, FUNx, simplify = simplify)), data), call = match.call(), class = "by") } clearPushBack <- function (connection) .Internal(clearPushBack(connection)) close.srcfile <- function (con, ...) { srcfile <- con conn <- srcfile$conn if (is.null(conn)) return() else { close(conn) rm(list = c("conn", "line"), envir = srcfile) } } conditionCall <- function (c) UseMethod("conditionCall") delayedAssign <- function (x, value, eval.env = parent.frame(1), assign.env = parent.frame(1)) .Internal(delayedAssign(x, substitute(value), eval.env, assign.env)) "environment<-" <- function (fun, value) .Primitive("environment<-") ## @type x : numeric format.factor <- function (x, ...) format(structure(as.character(x), names = names(x), dim = dim(x), dimnames = dimnames(x)), ...) ## @type doStop : logical getCallingDLL <- function (f = sys.function(-1), doStop = FALSE) { e <- environment(f) if (!isNamespace(e)) { if (doStop) stop("function is not in a namespace, so cannot locate associated DLL") else return(NULL) } if (is.null(env <- e$.__NAMESPACE__.)) env <- baseenv() if (exists("DLLs", envir = env) && length(env$DLLs)) return(env$DLLs[[1L]]) else { if (doStop) stop("looking for DLL for native routine call, but no DLLs in namespace of call") else NULL } NULL } ## @type what : complex getConnection <- function (what) .Internal(getConnection(what)) geterrmessage <- function () .Internal(geterrmessage()) getLoadedDLLs <- function () .Internal(getLoadedDLLs()) icuSetCollate <- function (...) .Internal(icuSetCollate(...)) importIntoEnv <- function (impenv, impnames, expenv, expnames) { exports <- getNamespaceInfo(expenv, "exports") ex <- .Internal(ls(exports, TRUE)) if (!all(expnames %in% ex)) { miss <- expnames[!expnames %in% ex] if (all(grepl("^\\.__C__", miss))) { miss <- sub("^\\.__C__", "", miss) stop(sprintf(ngettext(length(miss), "class %s is not exported by 'namespace:%s'", "classes %s are not exported by 'namespace:%s'"), paste(paste0("\"", miss, "\""), collapse = ", "), getNamespaceName(expenv)), call. = FALSE, domain = NA) } else { stop(sprintf(ngettext(length(miss), "object %s is not exported by 'namespace:%s'", "objects %s are not exported by 'namespace:%s'"), paste(sQuote(miss), collapse = ", "), getNamespaceName(expenv)), call. = FALSE, domain = NA) } } expnames <- unlist(lapply(expnames, get, envir = exports, inherits = FALSE)) if (is.null(impnames)) impnames <- character() if (is.null(expnames)) expnames <- character() .Internal(importIntoEnv(impenv, impnames, expenv, expnames)) } invokeRestart <- function (r, ...) { if (!isRestart(r)) { res <- findRestart(r) if (is.null(res)) stop(gettextf("no 'restart' '%s' found", as.character(r)), domain = NA) r <- res } .Internal(.invokeRestart(r, list(...))) } is.data.frame <- function (x) inherits(x, "data.frame") is.expression <- function (x) .Primitive("is.expression") is.na.POSIXlt <- function (x) is.na(as.POSIXct(x)) julian.POSIXt <- function (x, origin = as.POSIXct("1970-01-01", tz = "GMT"), ...) { origin <- as.POSIXct(origin) if (length(origin) != 1L) stop("'origin' must be of length one") res <- difftime(as.POSIXct(x), origin, units = "days") structure(res, origin = origin) } ## @type norm : complex|character ## @type exact : logical ## @type method : character kappa.default <- function (z, exact = FALSE, norm = NULL, method = c("qr", "direct"), ...) { method <- match.arg(method) z <- as.matrix(z) norm <- if (!is.null(norm)) match.arg(norm, c("2", "1", "O", "I")) else "2" if (exact && norm == "2") { s <- svd(z, nu = 0, nv = 0)$d max(s)/min(s[s > 0]) } else { if (exact) warning(gettextf("norm '%s' currently always uses exact = FALSE", norm)) d <- dim(z) if (method == "qr" || d[1L] != d[2L]) kappa.qr(qr(if (d[1L] < d[2L]) t(z) else z), exact = FALSE, norm = norm, ...) else .kappa_tri(z, exact = FALSE, norm = norm, ...) } } library.dynam <- function (chname, package, lib.loc, verbose = getOption("verbose"), file.ext = .Platform$dynlib.ext, ...) { dll_list <- .dynLibs() if (missing(chname) || !nzchar(chname)) return(dll_list) package lib.loc r_arch <- .Platform$r_arch chname1 <- paste0(chname, file.ext) for (pkg in find.package(package, lib.loc, verbose = verbose)) { DLLpath <- if (nzchar(r_arch)) file.path(pkg, "libs", r_arch) else file.path(pkg, "libs") file <- file.path(DLLpath, chname1) if (file.exists(file)) break else file <- "" } if (file == "") if (.Platform$OS.type == "windows") stop(gettextf("DLL %s not found: maybe not installed for this architecture?", sQuote(chname)), domain = NA) else stop(gettextf("shared object %s not found", sQuote(chname1)), domain = NA) file <- file.path(normalizePath(DLLpath, "/", TRUE), chname1) ind <- vapply(dll_list, function(x) x[["path"]] == file, NA) if (length(ind) && any(ind)) { if (verbose) if (.Platform$OS.type == "windows") message(gettextf("DLL %s already loaded", sQuote(chname1)), domain = NA) else message(gettextf("shared object '%s' already loaded", sQuote(chname1)), domain = NA) return(invisible(dll_list[[seq_along(dll_list)[ind]]])) } if (.Platform$OS.type == "windows") { PATH <- Sys.getenv("PATH") Sys.setenv(PATH = paste(gsub("/", "\\\\", DLLpath), PATH, sep = ";")) on.exit(Sys.setenv(PATH = PATH)) } if (verbose) message(gettextf("now dyn.load(\"%s\") ...", file), domain = NA) dll <- if ("DLLpath" %in% names(list(...))) dyn.load(file, ...) else dyn.load(file, DLLpath = DLLpath, ...) .dynLibs(c(dll_list, list(dll))) invisible(dll) } ## @type partial : logical ## @type lib.loc : character ## @type package : character ## @optional package loadNamespace <- function (package, lib.loc = NULL, keep.source = getOption("keep.source.pkgs"), partial = FALSE, versionCheck = NULL) { package <- as.character(package)[[1L]] dynGet <- function(name, notFound = stop(gettextf("%s not found", name), domain = NA)) { n <- sys.nframe() while (n > 1) { n <- n - 1 env <- sys.frame(n) if (exists(name, envir = env, inherits = FALSE)) return(get(name, envir = env, inherits = FALSE)) } notFound } loading <- dynGet("__NameSpacesLoading__", NULL) if (match(package, loading, 0L)) stop("cyclic namespace dependency detected when loading ", sQuote(package), ", already loading ", paste(sQuote(loading), collapse = ", "), domain = NA) "__NameSpacesLoading__" <- c(package, loading) ns <- .Internal(getRegisteredNamespace(as.name(package))) if (!is.null(ns)) { if (length(z <- versionCheck) == 3L) { current <- getNamespaceVersion(ns) if (!do.call(z$op, list(as.numeric_version(current), z$version))) stop(gettextf("namespace %s %s is already loaded, but %s %s is required", sQuote(package), current, z$op, z$version), domain = NA) } ns } else { runHook <- function(hookname, env, libname, pkgname) { if (exists(hookname, envir = env, inherits = FALSE)) { fun <- get(hookname, envir = env, inherits = FALSE) res <- tryCatch(fun(libname, pkgname), error = identity) if (inherits(res, "error")) { stop(gettextf("%s failed in %s() for '%s', details:\n call: %s\n error: %s", hookname, "loadNamespace", pkgname, deparse(conditionCall(res))[1L], conditionMessage(res)), call. = FALSE, domain = NA) } } } runUserHook <- function(pkgname, pkgpath) { hooks <- getHook(packageEvent(pkgname, "onLoad")) for (fun in hooks) try(fun(pkgname, pkgpath)) } makeNamespace <- function(name, version = NULL, lib = NULL) { impenv <- new.env(parent = .BaseNamespaceEnv, hash = TRUE) attr(impenv, "name") <- paste("imports", name, sep = ":") env <- new.env(parent = impenv, hash = TRUE) name <- as.character(as.name(name)) version <- as.character(version) info <- new.env(hash = TRUE, parent = baseenv()) assign(".__NAMESPACE__.", info, envir = env) assign("spec", c(name = name, version = version), envir = info) setNamespaceInfo(env, "exports", new.env(hash = TRUE, parent = baseenv())) dimpenv <- new.env(parent = baseenv(), hash = TRUE) attr(dimpenv, "name") <- paste("lazydata", name, sep = ":") setNamespaceInfo(env, "lazydata", dimpenv) setNamespaceInfo(env, "imports", list(base = TRUE)) setNamespaceInfo(env, "path", normalizePath(file.path(lib, name), "/", TRUE)) setNamespaceInfo(env, "dynlibs", NULL) setNamespaceInfo(env, "S3methods", matrix(NA_character_, 0L, 3L)) assign(".__S3MethodsTable__.", new.env(hash = TRUE, parent = baseenv()), envir = env) .Internal(registerNamespace(name, env)) env } sealNamespace <- function(ns) { namespaceIsSealed <- function(ns) environmentIsLocked(ns) ns <- asNamespace(ns, base.OK = FALSE) if (namespaceIsSealed(ns)) stop(gettextf("namespace %s is already sealed in 'loadNamespace'", sQuote(getNamespaceName(ns))), call. = FALSE, domain = NA) lockEnvironment(ns, TRUE) lockEnvironment(parent.env(ns), TRUE) } addNamespaceDynLibs <- function(ns, newlibs) { dynlibs <- getNamespaceInfo(ns, "dynlibs") setNamespaceInfo(ns, "dynlibs", c(dynlibs, newlibs)) } bindTranslations <- function(pkgname, pkgpath) { std <- c("compiler", "foreign", "grDevices", "graphics", "grid", "methods", "parallel", "splines", "stats", "stats4", "tcltk", "tools", "utils") popath <- if (pkgname %in% std) .popath else file.path(pkgpath, "po") if (!file.exists(popath)) return() bindtextdomain(pkgname, popath) bindtextdomain(paste("R", pkgname, sep = "-"), popath) } assignNativeRoutines <- function(dll, lib, env, nativeRoutines) { if (length(nativeRoutines) == 0L) return(NULL) if (nativeRoutines$useRegistration) { fixes <- nativeRoutines$registrationFixes routines <- getDLLRegisteredRoutines.DLLInfo(dll, addNames = FALSE) lapply(routines, function(type) { lapply(type, function(sym) { varName <- paste0(fixes[1L], sym$name, fixes[2L]) if (exists(varName, envir = env)) warning(gettextf("failed to assign RegisteredNativeSymbol for %s to %s since %s is already defined in the %s namespace", sym$name, varName, varName, sQuote(package)), domain = NA) else assign(varName, sym, envir = env) }) }) } symNames <- nativeRoutines$symbolNames if (length(symNames) == 0L) return(NULL) symbols <- getNativeSymbolInfo(symNames, dll, unlist = FALSE, withRegistrationInfo = TRUE) lapply(seq_along(symNames), function(i) { varName <- names(symNames)[i] origVarName <- symNames[i] if (exists(varName, envir = env)) if (origVarName != varName) warning(gettextf("failed to assign NativeSymbolInfo for %s to %s since %s is already defined in the %s namespace", origVarName, varName, varName, sQuote(package)), domain = NA) else warning(gettextf("failed to assign NativeSymbolInfo for %s since %s is already defined in the %s namespace", origVarName, varName, sQuote(package)), domain = NA) else assign(varName, symbols[[origVarName]], envir = env) }) symbols } pkgpath <- find.package(package, lib.loc, quiet = TRUE) if (length(pkgpath) == 0L) stop(gettextf("there is no package called %s", sQuote(package)), domain = NA) bindTranslations(package, pkgpath) package.lib <- dirname(pkgpath) package <- basename(pkgpath) if (!packageHasNamespace(package, package.lib)) { hasNoNamespaceError <- function(package, package.lib, call = NULL) { class <- c("hasNoNamespaceError", "error", "condition") msg <- gettextf("package %s does not have a namespace", sQuote(package)) structure(list(message = msg, package = package, package.lib = package.lib, call = call), class = class) } stop(hasNoNamespaceError(package, package.lib)) } nsInfoFilePath <- file.path(pkgpath, "Meta", "nsInfo.rds") nsInfo <- if (file.exists(nsInfoFilePath)) readRDS(nsInfoFilePath) else parseNamespaceFile(package, package.lib, mustExist = FALSE) pkgInfoFP <- file.path(pkgpath, "Meta", "package.rds") if (file.exists(pkgInfoFP)) { pkgInfo <- readRDS(pkgInfoFP) version <- pkgInfo$DESCRIPTION["Version"] vI <- pkgInfo$Imports if (is.null(built <- pkgInfo$Built)) stop(gettextf("package %s has not been installed properly\n", sQuote(basename(pkgpath))), call. = FALSE, domain = NA) R_version_built_under <- as.numeric_version(built$R) if (R_version_built_under < "3.0.0") stop(gettextf("package %s was built before R 3.0.0: please re-install it", sQuote(basename(pkgpath))), call. = FALSE, domain = NA) dependsMethods <- "methods" %in% names(pkgInfo$Depends) if (dependsMethods) loadNamespace("methods") if (length(z <- versionCheck) == 3L && !do.call(z$op, list(as.numeric_version(version), z$version))) stop(gettextf("namespace %s %s is being loaded, but %s %s is required", sQuote(package), version, z$op, z$version), domain = NA) } ns <- makeNamespace(package, version = version, lib = package.lib) on.exit(.Internal(unregisterNamespace(package))) for (i in nsInfo$imports) { if (is.character(i)) namespaceImport(ns, loadNamespace(i, c(lib.loc, .libPaths()), versionCheck = vI[[i]]), from = package) else namespaceImportFrom(ns, loadNamespace(j <- i[[1L]], c(lib.loc, .libPaths()), versionCheck = vI[[j]]), i[[2L]], from = package) } for (imp in nsInfo$importClasses) namespaceImportClasses(ns, loadNamespace(j <- imp[[1L]], c(lib.loc, .libPaths()), versionCheck = vI[[j]]), imp[[2L]], from = package) for (imp in nsInfo$importMethods) namespaceImportMethods(ns, loadNamespace(j <- imp[[1L]], c(lib.loc, .libPaths()), versionCheck = vI[[j]]), imp[[2L]], from = package) "__LoadingNamespaceInfo__" <- list(libname = package.lib, pkgname = package) env <- asNamespace(ns) assign(".packageName", package, envir = env) codename <- strsplit(package, "_", fixed = TRUE)[[1L]][1L] codeFile <- file.path(pkgpath, "R", codename) if (file.exists(codeFile)) { res <- try(sys.source(codeFile, env, keep.source = keep.source)) if (inherits(res, "try-error")) stop(gettextf("unable to load R code in package %s", sQuote(package)), call. = FALSE, domain = NA) } if (partial) return(ns) dbbase <- file.path(pkgpath, "R", "sysdata") if (file.exists(paste0(dbbase, ".rdb"))) lazyLoad(dbbase, env) dbbase <- file.path(pkgpath, "data", "Rdata") if (file.exists(paste0(dbbase, ".rdb"))) lazyLoad(dbbase, getNamespaceInfo(ns, "lazydata")) registerS3methods(nsInfo$S3methods, package, env) dlls <- list() dynLibs <- nsInfo$dynlibs for (i in seq_along(dynLibs)) { lib <- dynLibs[i] dlls[[lib]] <- library.dynam(lib, package, package.lib) assignNativeRoutines(dlls[[lib]], lib, env, nsInfo$nativeRoutines[[lib]]) if (!is.null(names(nsInfo$dynlibs)) && names(nsInfo$dynlibs)[i] != "") assign(names(nsInfo$dynlibs)[i], dlls[[lib]], envir = env) setNamespaceInfo(env, "DLLs", dlls) } addNamespaceDynLibs(env, nsInfo$dynlibs) Sys.setenv(`_R_NS_LOAD_` = package) on.exit(Sys.unsetenv("_R_NS_LOAD_"), add = TRUE) runHook(".onLoad", env, package.lib, package) exports <- nsInfo$exports for (p in nsInfo$exportPatterns) exports <- c(ls(env, pattern = p, all.names = TRUE), exports) if (.isMethodsDispatchOn() && methods:::.hasS4MetaData(ns) && !identical(package, "methods")) { methods:::cacheMetaData(ns, TRUE, ns) for (p in nsInfo$exportPatterns) { expp <- ls(ns, pattern = p, all.names = TRUE) newEx <- !(expp %in% exports) if (any(newEx)) exports <- c(expp[newEx], exports) } expClasses <- nsInfo$exportClasses pClasses <- character() aClasses <- methods:::getClasses(ns) classPatterns <- nsInfo$exportClassPatterns if (!length(classPatterns)) classPatterns <- nsInfo$exportPatterns for (p in classPatterns) { pClasses <- c(aClasses[grep(p, aClasses)], pClasses) } pClasses <- unique(pClasses) if (length(pClasses)) { good <- vapply(pClasses, methods:::isClass, NA, where = ns) if (!any(good) && length(nsInfo$exportClassPatterns)) warning(gettextf("'exportClassPattern' specified in 'NAMESPACE' but no matching classes in package %s", sQuote(package)), call. = FALSE, domain = NA) expClasses <- c(expClasses, pClasses[good]) } if (length(expClasses)) { missingClasses <- !vapply(expClasses, methods:::isClass, NA, where = ns) if (any(missingClasses)) stop(gettextf("in package %s classes %s were specified for export but not defined", sQuote(package), paste(expClasses[missingClasses], collapse = ", ")), domain = NA) expClasses <- paste0(methods:::classMetaName(""), expClasses) } allGenerics <- unique(c(methods:::.getGenerics(ns), methods:::.getGenerics(parent.env(ns)))) expMethods <- nsInfo$exportMethods addGenerics <- expMethods[is.na(match(expMethods, exports))] if (length(addGenerics)) { nowhere <- sapply(addGenerics, function(what) !exists(what, mode = "function", envir = ns)) if (any(nowhere)) { warning(gettextf("no function found corresponding to methods exports from %s for: %s", sQuote(package), paste(sQuote(sort(unique(addGenerics[nowhere]))), collapse = ", ")), domain = NA, call. = FALSE) addGenerics <- addGenerics[!nowhere] } if (length(addGenerics)) { addGenerics <- addGenerics[sapply(addGenerics, function(what) !is.primitive(get(what, mode = "function", envir = ns)))] ok <- sapply(addGenerics, methods:::.findsGeneric, ns) if (!all(ok)) { bad <- sort(unique(addGenerics[!ok])) msg <- ngettext(length(bad), "Function found when exporting methods from the namespace %s which is not S4 generic: %s", "Functions found when exporting methods from the namespace %s which are not S4 generic: %s", domain = "R-base") stop(sprintf(msg, sQuote(package), paste(sQuote(bad), collapse = ", ")), domain = NA, call. = FALSE) } else if (any(ok > 1L)) addGenerics <- addGenerics[ok < 2L] } exports <- c(exports, addGenerics) } expTables <- character() if (length(allGenerics)) { expMethods <- unique(c(expMethods, exports[!is.na(match(exports, allGenerics))])) missingMethods <- !(expMethods %in% allGenerics) if (any(missingMethods)) stop(gettextf("in %s methods for export not found: %s", sQuote(package), paste(expMethods[missingMethods], collapse = ", ")), domain = NA) tPrefix <- methods:::.TableMetaPrefix() allMethodTables <- unique(c(methods:::.getGenerics(ns, tPrefix), methods:::.getGenerics(parent.env(ns), tPrefix))) needMethods <- (exports %in% allGenerics) & !(exports %in% expMethods) if (any(needMethods)) expMethods <- c(expMethods, exports[needMethods]) pm <- allGenerics[!(allGenerics %in% expMethods)] if (length(pm)) { prim <- logical(length(pm)) for (i in seq_along(prim)) { f <- methods:::getFunction(pm[[i]], FALSE, FALSE, ns) prim[[i]] <- is.primitive(f) } expMethods <- c(expMethods, pm[prim]) } for (i in seq_along(expMethods)) { mi <- expMethods[[i]] if (!(mi %in% exports) && exists(mi, envir = ns, mode = "function", inherits = FALSE)) exports <- c(exports, mi) pattern <- paste0(tPrefix, mi, ":") ii <- grep(pattern, allMethodTables, fixed = TRUE) if (length(ii)) { if (length(ii) > 1L) { warning(gettextf("multiple methods tables found for %s", sQuote(mi)), call. = FALSE, domain = NA) ii <- ii[1L] } expTables[[i]] <- allMethodTables[ii] } else { warning(gettextf("failed to find metadata object for %s", sQuote(mi)), call. = FALSE, domain = NA) } } } else if (length(expMethods)) stop(gettextf("in package %s methods %s were specified for export but not defined", sQuote(package), paste(expMethods, collapse = ", ")), domain = NA) exports <- unique(c(exports, expClasses, expTables)) } if (length(exports)) { stoplist <- c(".__NAMESPACE__.", ".__S3MethodsTable__.", ".packageName", ".First.lib", ".onLoad", ".onAttach", ".conflicts.OK", ".noGenerics") exports <- exports[!exports %in% stoplist] } namespaceExport(ns, exports) sealNamespace(ns) runUserHook(package, pkgpath) on.exit() Sys.unsetenv("_R_NS_LOAD_") ns } } Math.difftime <- function (x, ...) { switch(.Generic, abs = , sign = , floor = , ceiling = , trunc = , round = , signif = { units <- attr(x, "units") .difftime(NextMethod(), units) }, stop(gettextf("'%s' not defined for \"difftime\" objects", .Generic), domain = NA)) } mean.difftime <- function (x, ...) .difftime(mean(unclass(x), ...), attr(x, "units")) ## @type from : raw|character ## @type type : character ## @type asChar : logical|character memDecompress <- function (from, type = c("unknown", "gzip", "bzip2", "xz", "none"), asChar = FALSE) { type <- match(match.arg(type), c("none", "gzip", "bzip2", "xz", "unknown")) ans <- .Internal(memDecompress(from, type)) if (asChar) rawToChar(ans) else ans } merge.default <- function (x, y, ...) merge(as.data.frame(x), as.data.frame(y), ...) months.POSIXt <- function (x, abbreviate = FALSE) { format(x, ifelse(abbreviate, "%b", "%B")) } names.POSIXlt <- function (x) names(x$year) ## @type path : character ## @type mustWork : logical normalizePath <- function (path, winslash = "\\", mustWork = NA) .Internal(normalizePath(path.expand(path), winslash, mustWork)) ## @type max : complex ## @type print.gap : integer ## @type digits : complex ## @type right : logical ## @type quote : logical|character ## @type useSource : logical ## @type na.print : character print.default <- function (x, digits = NULL, quote = TRUE, na.print = NULL, print.gap = NULL, right = FALSE, max = NULL, useSource = TRUE, ...) { noOpt <- missing(digits) && missing(quote) && missing(na.print) && missing(print.gap) && missing(right) && missing(max) && missing(useSource) && missing(...) .Internal(print.default(x, digits, quote, na.print, print.gap, right, max, useSource, noOpt)) } print.DLLInfo <- function (x, ...) { tmp <- as.data.frame.list(x[c("name", "path", "dynamicLookup")]) names(tmp) <- c("DLL name", "Filename", "Dynamic lookup") write.dcf(tmp, ...) invisible(x) } print.hexmode <- function (x, ...) { print(format(x), ...) invisible(x) } print.noquote <- function (x, ...) { if (!is.null(cl <- attr(x, "class"))) { cl <- cl[cl != "noquote"] attr(x, "class") <- (if (length(cl)) cl else NULL) } print(x, quote = FALSE, ...) } print.octmode <- function (x, ...) { print(format(x), ...) invisible(x) } print.POSIXct <- function (x, ...) { max.print <- getOption("max.print", 9999L) if (max.print < length(x)) { print(format(x[seq_len(max.print)], usetz = TRUE), ...) cat(" [ reached getOption(\"max.print\") -- omitted", length(x) - max.print, "entries ]\n") } else print(format(x, usetz = TRUE), ...) invisible(x) } print.POSIXlt <- function (x, ...) { max.print <- getOption("max.print", 9999L) if (max.print < length(x)) { print(format(x[seq_len(max.print)], usetz = TRUE), ...) cat(" [ reached getOption(\"max.print\") -- omitted", length(x) - max.print, "entries ]\n") } else print(format(x, usetz = TRUE), ...) invisible(x) } print.restart <- function (x, ...) { cat(paste("<restart:", x[[1L]], ">\n")) invisible(x) } print.srcfile <- function (x, ...) { cat(x$filename, "\n") invisible(x) } ## @optional x quarters.Date <- function (x, ...) { x <- (as.POSIXlt(x)$mon)%/%3L paste0("Q", x + 1L) } ## @type finite : logical ## @type na.rm : logical range.default <- function (..., na.rm = FALSE, finite = FALSE) { x <- c(..., recursive = TRUE) if (is.numeric(x)) { if (finite) x <- x[is.finite(x)] else if (na.rm) x <- x[!is.na(x)] return(c(min(x), max(x))) } c(min(x, na.rm = na.rm), max(x, na.rm = na.rm)) } ## @type open : character ## @type object : raw|character rawConnection <- function (object, open = "r") { .Internal(rawConnection(deparse(substitute(object)), object, open)) } reg.finalizer <- function (e, f, onexit = FALSE) .Internal(reg.finalizer(e, f, onexit)) ## @type center : complex|logical ## @type x : numeric ## @type scale : complex|logical scale.default <- function (x, center = TRUE, scale = TRUE) { x <- as.matrix(x) nc <- ncol(x) if (is.logical(center)) { if (center) { center <- colMeans(x, na.rm = TRUE) x <- sweep(x, 2L, center, check.margin = FALSE) } } else if (is.numeric(center) && (length(center) == nc)) x <- sweep(x, 2L, center, check.margin = FALSE) else stop("length of 'center' must equal the number of columns of 'x'") if (is.logical(scale)) { if (scale) { f <- function(v) { v <- v[!is.na(v)] sqrt(sum(v^2)/max(1, length(v) - 1L)) } scale <- apply(x, 2L, f) x <- sweep(x, 2L, scale, "/", check.margin = FALSE) } } else if (is.numeric(scale) && length(scale) == nc) x <- sweep(x, 2L, scale, "/", check.margin = FALSE) else stop("length of 'scale' must equal the number of columns of 'x'") if (is.numeric(center)) attr(x, "scaled:center") <- center if (is.numeric(scale)) attr(x, "scaled:scale") <- scale x } simpleMessage <- function (message, call = NULL) structure(list(message = message, call = call), class = c("simpleMessage", "message", "condition")) simpleWarning <- function (message, call = NULL) { class <- c("simpleWarning", "warning", "condition") structure(list(message = as.character(message), call = call), class = class) } ## @type tol : complex ## @type b : complex ## @type a : complex ## @type LINPACK : logical solve.default <- function (a, b, tol = .Machine$double.eps, LINPACK = FALSE, ...) { if (is.complex(a) || (!missing(b) && is.complex(b))) { a <- as.matrix(a) if (missing(b)) { b <- diag(1 + (0+0i), nrow(a)) colnames(b) <- rownames(a) } return(.Internal(La_solve_cmplx(a, b))) } if (is.qr(a)) { warning("solve.default called with a \"qr\" object: use 'qr.solve'") return(solve.qr(a, b, tol)) } a <- as.matrix(a) if (missing(b)) { b <- diag(1, nrow(a)) colnames(b) <- rownames(a) } .Internal(La_solve(a, b, tol)) } ## @type drop : logical split.default <- function (x, f, drop = FALSE, sep = ".", ...) { if (!missing(...)) .NotYetUsed(deparse(...), error = FALSE) if (is.list(f)) f <- interaction(f, drop = drop, sep = sep) else if (!is.factor(f)) f <- as.factor(f) else if (drop) f <- factor(f) storage.mode(f) <- "integer" if (is.null(attr(x, "class"))) return(.Internal(split(x, f))) lf <- levels(f) y <- vector("list", length(lf)) names(y) <- lf ind <- .Internal(split(seq_along(x), f)) for (k in lf) y[[k]] <- x[ind[[k]]] y } split.POSIXct <- function (x, f, drop = FALSE, ...) lapply(split.default(as.double(x), f, drop = drop), .POSIXct, tz = attr(x, "tzone")) ## @type subset : logical subset.matrix <- function (x, subset, select, drop = FALSE, ...) { if (missing(select)) vars <- TRUE else { nl <- as.list(1L:ncol(x)) names(nl) <- colnames(x) vars <- eval(substitute(select), nl, parent.frame()) } if (missing(subset)) subset <- TRUE else if (!is.logical(subset)) stop("'subset' must be logical") x[subset & !is.na(subset), vars, drop = drop] } summary.table <- function (object, ...) { if (!inherits(object, "table")) stop(gettextf("'object' must inherit from class %s", dQuote("table")), domain = NA) n.cases <- sum(object) n.vars <- length(dim(object)) y <- list(n.vars = n.vars, n.cases = n.cases) if (n.vars > 1) { m <- vector("list", length = n.vars) relFreqs <- object/n.cases for (k in 1L:n.vars) m[[k]] <- apply(relFreqs, k, sum) expected <- apply(do.call("expand.grid", m), 1L, prod) * n.cases statistic <- sum((c(object) - expected)^2/expected) lm <- vapply(m, length, 1L) parameter <- prod(lm) - 1L - sum(lm - 1L) y <- c(y, list(statistic = statistic, parameter = parameter, approx.ok = all(expected >= 5), p.value = stats::pchisq(statistic, parameter, lower.tail = FALSE), call = attr(object, "call"))) } class(y) <- "summary.table" y } ## @type category : character ## @return character Sys.getlocale <- function (category = "LC_ALL") { category <- match(category, c("LC_ALL", "LC_COLLATE", "LC_CTYPE", "LC_MONETARY", "LC_NUMERIC", "LC_TIME", "LC_MESSAGES", "LC_PAPER", "LC_MEASUREMENT")) if (is.na(category)) stop("invalid 'category' argument") .Internal(Sys.getlocale(category)) } ## @type category : character ## @type locale : character ## @return character Sys.setlocale <- function (category = "LC_ALL", locale = "") { category <- match(category, c("LC_ALL", "LC_COLLATE", "LC_CTYPE", "LC_MONETARY", "LC_NUMERIC", "LC_TIME", "LC_MESSAGES", "LC_PAPER", "LC_MEASUREMENT")) if (is.na(category)) stop("invalid 'category' argument") .Internal(Sys.setlocale(category, locale)) } ## @type MARGIN : integer ## @type fromLast : logical unique.matrix <- function (x, incomparables = FALSE, MARGIN = 1, fromLast = FALSE, ...) { if (!identical(incomparables, FALSE)) .NotYetUsed("incomparables != FALSE") dx <- dim(x) ndim <- length(dx) if (length(MARGIN) > ndim || any(MARGIN > ndim)) stop(gettextf("MARGIN = %d is invalid for dim = %d", MARGIN, dx), domain = NA) collapse <- (ndim > 1L) && (prod(dx[-MARGIN]) > 1L) temp <- if (collapse) apply(x, MARGIN, function(x) paste(x, collapse = "\r")) else x args <- rep(alist(a = ), ndim) names(args) <- NULL args[[MARGIN]] <- !duplicated.default(temp, fromLast = fromLast, ...) do.call("[", c(list(x), args, list(drop = FALSE))) } ## @type sym : character unlockBinding <- function (sym, env) { if (is.character(sym)) sym <- as.name(sym) .Internal(unlockBinding(sym, env)) } weekdays.Date <- function (x, abbreviate = FALSE) format(x, ifelse(abbreviate, "%a", "%A")) xtfrm.default <- function (x) if (is.numeric(x)) unclass(x) else as.vector(rank(x, ties.method = "min", na.last = "keep")) xtfrm.POSIXct <- function (x) as.numeric(x) xtfrm.POSIXlt <- function (x) as.double(x) ## @type value : complex ## @type name : character ## @optional name "$<-.data.frame" <- function (x, name, value) { cl <- oldClass(x) class(x) <- NULL nrows <- .row_names_info(x, 2L) if (!is.null(value)) { N <- NROW(value) if (N > nrows) stop(sprintf(ngettext(N, "replacement has %d row, data has %d", "replacement has %d rows, data has %d"), N, nrows), domain = NA) if (N < nrows) if (N > 0L && (nrows%%N == 0L) && length(dim(value)) <= 1L) value <- rep(value, length.out = nrows) else stop(sprintf(ngettext(N, "replacement has %d row, data has %d", "replacement has %d rows, data has %d"), N, nrows), domain = NA) if (is.atomic(value) && !is.null(names(value))) names(value) <- NULL } x[[name]] <- value class(x) <- cl return(x) } ## @type i : numeric|logical|character ## @type j : numeric|logical|character ## @type value : complex "[<-.data.frame" <- function (x, i, j, value) { if (!all(names(sys.call()) %in% c("", "value"))) warning("named arguments are discouraged") nA <- nargs() if (nA == 4L) { has.i <- !missing(i) has.j <- !missing(j) } else if (nA == 3L) { if (is.atomic(value) && !is.null(names(value))) names(value) <- NULL if (missing(i) && missing(j)) { i <- j <- NULL has.i <- has.j <- FALSE if (is.null(value)) return(x[logical()]) } else { if (is.numeric(i) && is.matrix(i) && ncol(i) == 2) { index <- rep.int(FALSE, prod(dim(x))) dim(index) <- dim(x) tryCatch(index[i] <- TRUE, error = function(e) stop(conditionMessage(e), call. = FALSE)) o <- order(i[, 2], i[, 1]) N <- length(value) if (length(o)%%N != 0L) warning("number of items to replace is not a multiple of replacement length") if (N < length(o)) value <- rep(value, length.out = length(o)) value <- value[o] i <- index } if (is.logical(i) && is.matrix(i) && all(dim(i) == dim(x))) { nreplace <- sum(i, na.rm = TRUE) if (!nreplace) return(x) N <- length(value) if (N > 1L && N < nreplace && (nreplace%%N) == 0L) value <- rep(value, length.out = nreplace) if (N > 1L && (length(value) != nreplace)) stop("'value' is the wrong length") n <- 0L nv <- nrow(x) for (v in seq_len(dim(i)[2L])) { thisvar <- i[, v, drop = TRUE] nv <- sum(thisvar, na.rm = TRUE) if (nv) { if (is.matrix(x[[v]])) x[[v]][thisvar, ] <- if (N > 1L) value[n + seq_len(nv)] else value else x[[v]][thisvar] <- if (N > 1L) value[n + seq_len(nv)] else value } n <- n + nv } return(x) } if (is.matrix(i)) stop("unsupported matrix index in replacement") j <- i i <- NULL has.i <- FALSE has.j <- TRUE } } else { stop("need 0, 1, or 2 subscripts") } if (has.j && length(j) == 0L) return(x) cl <- oldClass(x) class(x) <- NULL new.cols <- NULL nvars <- length(x) nrows <- .row_names_info(x, 2L) if (has.i && length(i)) { rows <- NULL if (anyNA(i)) stop("missing values are not allowed in subscripted assignments of data frames") if (char.i <- is.character(i)) { rows <- attr(x, "row.names") ii <- match(i, rows) nextra <- sum(new.rows <- is.na(ii)) if (nextra > 0L) { ii[new.rows] <- seq.int(from = nrows + 1L, length.out = nextra) new.rows <- i[new.rows] } i <- ii } if (all(i >= 0L) && (nn <- max(i)) > nrows) { if (is.null(rows)) rows <- attr(x, "row.names") if (!char.i) { nrr <- (nrows + 1L):nn if (inherits(value, "data.frame") && (dim(value)[1L]) >= length(nrr)) { new.rows <- attr(value, "row.names")[seq_along(nrr)] repl <- duplicated(new.rows) | match(new.rows, rows, 0L) if (any(repl)) new.rows[repl] <- nrr[repl] } else new.rows <- nrr } x <- xpdrows.data.frame(x, rows, new.rows) rows <- attr(x, "row.names") nrows <- length(rows) } iseq <- seq_len(nrows)[i] if (anyNA(iseq)) stop("non-existent rows not allowed") } else iseq <- NULL if (has.j) { if (anyNA(j)) stop("missing values are not allowed in subscripted assignments of data frames") if (is.character(j)) { if ("" %in% j) stop("column name \"\" cannot match any column") jj <- match(j, names(x)) nnew <- sum(is.na(jj)) if (nnew > 0L) { n <- is.na(jj) jj[n] <- nvars + seq_len(nnew) new.cols <- j[n] } jseq <- jj } else if (is.logical(j) || min(j) < 0L) jseq <- seq_along(x)[j] else { jseq <- j if (max(jseq) > nvars) { new.cols <- paste0("V", seq.int(from = nvars + 1L, to = max(jseq))) if (length(new.cols) != sum(jseq > nvars)) stop("new columns would leave holes after existing columns") if (is.list(value) && !is.null(vnm <- names(value))) { p <- length(jseq) if (length(vnm) < p) vnm <- rep_len(vnm, p) new.cols <- vnm[jseq > nvars] } } } } else jseq <- seq_along(x) if (anyDuplicated(jseq)) stop("duplicate subscripts for columns") n <- length(iseq) if (n == 0L) n <- nrows p <- length(jseq) m <- length(value) if (!is.list(value)) { if (p == 1L) { N <- NROW(value) if (N > n) stop(sprintf(ngettext(N, "replacement has %d row, data has %d", "replacement has %d rows, data has %d"), N, n), domain = NA) if (N < n && N > 0L) if (n%%N == 0L && length(dim(value)) <= 1L) value <- rep(value, length.out = n) else stop(sprintf(ngettext(N, "replacement has %d row, data has %d", "replacement has %d rows, data has %d"), N, nrows), domain = NA) if (!is.null(names(value))) names(value) <- NULL value <- list(value) } else { if (m < n * p && (m == 0L || (n * p)%%m)) stop(sprintf(ngettext(m, "replacement has %d item, need %d", "replacement has %d items, need %d"), m, n * p), domain = NA) value <- matrix(value, n, p) value <- split(value, col(value)) } dimv <- c(n, p) } else { value <- unclass(value) lens <- vapply(value, NROW, 1L) for (k in seq_along(lens)) { N <- lens[k] if (n != N && length(dim(value[[k]])) == 2L) stop(sprintf(ngettext(N, "replacement element %d is a matrix/data frame of %d row, need %d", "replacement element %d is a matrix/data frame of %d rows, need %d"), k, N, n), domain = NA) if (N > 0L && N < n && n%%N) stop(sprintf(ngettext(N, "replacement element %d has %d row, need %d", "replacement element %d has %d rows, need %d"), k, N, n), domain = NA) if (N > 0L && N < n) value[[k]] <- rep(value[[k]], length.out = n) if (N > n) { warning(sprintf(ngettext(N, "replacement element %d has %d row to replace %d rows", "replacement element %d has %d rows to replace %d rows"), k, N, n), domain = NA) value[[k]] <- value[[k]][seq_len(n)] } } dimv <- c(n, length(value)) } nrowv <- dimv[1L] if (nrowv < n && nrowv > 0L) { if (n%%nrowv == 0L) value <- value[rep_len(seq_len(nrowv), n), , drop = FALSE] else stop(sprintf(ngettext(nrowv, "%d row in value to replace %d rows", "%d rows in value to replace %d rows"), nrowv, n), domain = NA) } else if (nrowv > n) warning(sprintf(ngettext(nrowv, "replacement data has %d row to replace %d rows", "replacement data has %d rows to replace %d rows"), nrowv, n), domain = NA) ncolv <- dimv[2L] jvseq <- seq_len(p) if (ncolv < p) jvseq <- rep_len(seq_len(ncolv), p) else if (ncolv > p) { warning(sprintf(ngettext(ncolv, "provided %d variable to replace %d variables", "provided %d variables to replace %d variables"), ncolv, p), domain = NA) new.cols <- new.cols[seq_len(p)] } if (length(new.cols)) { nm <- names(x) rows <- .row_names_info(x, 0L) a <- attributes(x) a["names"] <- NULL x <- c(x, vector("list", length(new.cols))) attributes(x) <- a names(x) <- c(nm, new.cols) attr(x, "row.names") <- rows } if (has.i) for (jjj in seq_len(p)) { jj <- jseq[jjj] vjj <- value[[jvseq[[jjj]]]] if (jj <= nvars) { if (length(dim(x[[jj]])) != 2L) x[[jj]][iseq] <- vjj else x[[jj]][iseq, ] <- vjj } else { x[[jj]] <- vjj[FALSE] if (length(dim(vjj)) == 2L) { length(x[[j]]) <- nrows * ncol(vjj) dim(x[[j]]) <- c(nrows, ncol(vjj)) x[[jj]][iseq, ] <- vjj } else { length(x[[j]]) <- nrows x[[jj]][iseq] <- vjj } } } else if (p > 0L) for (jjj in p:1L) { o <- order(jseq) jseq <- jseq[o] jvseq <- jvseq[o] jj <- jseq[jjj] v <- value[[jvseq[[jjj]]]] if (nrows > 0L && !length(v)) length(v) <- nrows x[[jj]] <- v if (!is.null(v) && is.atomic(x[[jj]]) && !is.null(names(x[[jj]]))) names(x[[jj]]) <- NULL } if (length(new.cols) > 0L) { new.cols <- names(x) if (anyDuplicated(new.cols)) names(x) <- make.unique(new.cols) } class(x) <- cl x } ## @type check.attributes : logical ## @type use.names : logical|integer|character ## @return logical all.equal.list <- function (target, current, ..., check.attributes = TRUE, use.names = TRUE) { if (!is.logical(check.attributes)) stop(gettextf("'%s' must be logical", "check.attributes"), domain = NA) if (!is.logical(use.names)) stop(gettextf("'%s' must be logical", "use.names"), domain = NA) msg <- if (check.attributes) attr.all.equal(target, current, ...) target <- unclass(target) current <- unclass(current) if (!is.list(target) && !is.vector(target)) return(c(msg, "target is not list-like")) if (!is.list(current) && !is.vector(current)) return(c(msg, "current is not list-like")) if ((n <- length(target)) != length(current)) { if (!is.null(msg)) msg <- msg[-grep("\\bLengths\\b", msg)] n <- min(n, length(current)) msg <- c(msg, paste("Length mismatch: comparison on first", n, "components")) } iseq <- seq_len(n) if (use.names) use.names <- (length(nt <- names(target)[iseq]) == n && length(nc <- names(current)[iseq]) == n) for (i in iseq) { mi <- all.equal(target[[i]], current[[i]], check.attributes = check.attributes, use.names = use.names, ...) if (is.character(mi)) msg <- c(msg, paste0("Component ", if (use.names && nt[i] == nc[i]) dQuote(nt[i]) else i, ": ", mi)) } if (is.null(msg)) TRUE else msg } as.Date.factor <- function (x, ...) as.Date(as.character(x), ...) as.environment <- function (x) .Primitive("as.environment") as.list.factor <- function (x, ...) { res <- vector("list", length(x)) for (i in seq_along(x)) res[[i]] <- x[i] res } ## @type check.attributes : logical ## @type check.names : logical attr.all.equal <- function (target, current, ..., check.attributes = TRUE, check.names = TRUE) { if (!is.logical(check.attributes)) stop(gettextf("'%s' must be logical", "check.attributes"), domain = NA) if (!is.logical(check.names)) stop(gettextf("'%s' must be logical", "check.names"), domain = NA) msg <- NULL if (mode(target) != mode(current)) msg <- paste0("Modes: ", mode(target), ", ", mode(current)) if (length(target) != length(current)) msg <- c(msg, paste0("Lengths: ", length(target), ", ", length(current))) ax <- attributes(target) ay <- attributes(current) if (check.names) { nx <- names(target) ny <- names(current) if ((lx <- length(nx)) | (ly <- length(ny))) { ax$names <- ay$names <- NULL if (lx && ly) { if (is.character(m <- all.equal.character(nx, ny, check.attributes = check.attributes))) msg <- c(msg, paste("Names:", m)) } else if (lx) msg <- c(msg, "names for target but not for current") else msg <- c(msg, "names for current but not for target") } } else { ax[["names"]] <- NULL ay[["names"]] <- NULL } if (check.attributes && (length(ax) || length(ay))) { nx <- names(ax) ny <- names(ay) if (length(nx)) ax <- ax[order(nx)] if (length(ny)) ay <- ay[order(ny)] tt <- all.equal(ax, ay, ..., check.attributes = check.attributes) if (is.character(tt)) msg <- c(msg, paste("Attributes: <", tt, ">")) } msg } bindtextdomain <- function (domain, dirname = NULL) .Internal(bindtextdomain(domain, dirname)) dim.data.frame <- function (x) c(.row_names_info(x, 2L), length(x)) findPackageEnv <- function (info) { if (info %in% search()) return(as.environment(info)) message(gettextf("Attempting to load the environment %s", sQuote(info)), domain = NA) pkg <- substr(info, 9L, 1000L) if (require(pkg, character.only = TRUE, quietly = TRUE)) return(as.environment(info)) message("Specified environment not found: using '.GlobalEnv' instead") .GlobalEnv } ## @type big.mark : complex ## @type small.mark : complex ## @type trim : complex|logical ## @type digits : complex ## @type nsmall : complex ## @type big.interval : complex ## @type na.encode : complex|logical|character ## @type scientific : complex|logical ## @type x : numeric ## @type justify : character format.default <- function (x, trim = FALSE, digits = NULL, nsmall = 0L, justify = c("left", "right", "centre", "none"), width = NULL, na.encode = TRUE, scientific = NA, big.mark = "", big.interval = 3L, small.mark = "", small.interval = 5L, decimal.mark = ".", zero.print = NULL, drop0trailing = FALSE, ...) { justify <- match.arg(justify) adj <- match(justify, c("left", "right", "centre", "none")) - 1L if (is.list(x)) { if (missing(trim)) trim <- TRUE if (missing(justify)) justify <- "none" res <- lapply(X = x, FUN = function(xx, ...) format.default(unlist(xx), ...), trim = trim, digits = digits, nsmall = nsmall, justify = justify, width = width, na.encode = na.encode, scientific = scientific, big.mark = big.mark, big.interval = big.interval, small.mark = small.mark, small.interval = small.interval, decimal.mark = decimal.mark, zero.print = zero.print, drop0trailing = drop0trailing, ...) sapply(res, paste, collapse = ", ") } else { switch(mode(x), `NULL` = "NULL", character = .Internal(format(x, trim, digits, nsmall, width, adj, na.encode, scientific)), call = , expression = , `function` = , `(` = deparse(x), raw = as.character(x), { prettyNum(.Internal(format(x, trim, digits, nsmall, width, 3L, na.encode, scientific)), big.mark = big.mark, big.interval = big.interval, small.mark = small.mark, small.interval = small.interval, decimal.mark = decimal.mark, zero.print = zero.print, drop0trailing = drop0trailing, is.cmplx = is.complex(x), preserve.width = if (trim) "individual" else "common") }) } } ## @type upper.case : logical ## @type width : integer format.hexmode <- function (x, width = NULL, upper.case = FALSE, ...) { isna <- is.na(x) y <- as.integer(x[!isna]) fmt0 <- if (upper.case) "X" else "x" fmt <- if (!is.null(width)) paste0("%0", width, fmt0) else paste0("%", fmt0) ans <- rep.int(NA_character_, length(x)) ans0 <- sprintf(fmt, y) if (is.null(width) && length(y) > 1L) { nc <- max(nchar(ans0)) ans0 <- sprintf(paste0("%0", nc, fmt0), y) } ans[!isna] <- ans0 dim(ans) <- dim(x) dimnames(ans) <- dimnames(x) names(ans) <- names(x) ans } ## @type width : integer format.octmode <- function (x, width = NULL, ...) { isna <- is.na(x) y <- as.integer(x[!isna]) fmt <- if (!is.null(width)) paste0("%0", width, "o") else "%o" ans <- rep.int(NA_character_, length(x)) ans0 <- sprintf(fmt, y) if (is.null(width) && length(y) > 1L) { nc <- max(nchar(ans0)) ans0 <- sprintf(paste0("%0", nc, "o"), y) } ans[!isna] <- ans0 dim(ans) <- dim(x) dimnames(ans) <- dimnames(x) names(ans) <- names(x) ans } ## @type x : character ## @type format : complex|character ## @type tz : character ## @type usetz : logical format.POSIXct <- function (x, format = "", tz = "", usetz = FALSE, ...) { if (!inherits(x, "POSIXct")) stop("wrong class") if (missing(tz) && !is.null(tzone <- attr(x, "tzone"))) tz <- tzone structure(format.POSIXlt(as.POSIXlt(x, tz), format, usetz, ...), names = names(x)) } ## @type usetz : logical ## @type x : character ## @type format : complex|character format.POSIXlt <- function (x, format = "", usetz = FALSE, ...) { if (!inherits(x, "POSIXlt")) stop("wrong class") if (format == "") { times <- unlist(unclass(x)[1L:3L]) secs <- x$sec secs <- secs[!is.na(secs)] np <- getOption("digits.secs") if (is.null(np)) np <- 0L else np <- min(6L, np) if (np >= 1L) for (i in seq_len(np) - 1L) if (all(abs(secs - round(secs, i)) < 1e-06)) { np <- i break } format <- if (all(times[!is.na(times)] == 0)) "%Y-%m-%d" else if (np == 0L) "%Y-%m-%d %H:%M:%S" else paste0("%Y-%m-%d %H:%M:%OS", np) } y <- .Internal(format.POSIXlt(x, format, usetz)) names(y) <- names(x$year) y } ## @optional e getCallingDLLe <- function (e) { if (is.null(env <- e$.__NAMESPACE__.)) env <- baseenv() if (exists("DLLs", envir = env) && length(env$DLLs)) return(env$DLLs[[1L]]) NULL } is.environment <- function (x) .Primitive("is.environment") ## @optional value "is.na<-.factor" <- function (x, value) { lx <- levels(x) cx <- oldClass(x) class(x) <- NULL x[value] <- NA structure(x, levels = lx, class = cx) } labels.default <- function (object, ...) { if (length(d <- dim(object))) { nt <- dimnames(object) if (is.null(nt)) nt <- vector("list", length(d)) for (i in seq_along(d)) if (!length(nt[[i]])) nt[[i]] <- as.character(seq_len(d[i])) } else { nt <- names(object) if (!length(nt)) nt <- as.character(seq_along(object)) } nt } ## @optional fun lazyLoadDBexec <- function (filebase, fun, filter) { glue <- function(..., sep = " ", collapse = NULL) .Internal(paste(list(...), sep, collapse)) readRDS <- function(file) { halt <- function(message) .Internal(stop(TRUE, message)) gzfile <- function(description, open) .Internal(gzfile(description, open, "", 6)) close <- function(con) .Internal(close(con, "rw")) if (!is.character(file)) halt("bad file name") con <- gzfile(file, "rb") on.exit(close(con)) .Internal(unserializeFromConn(con, baseenv())) } `parent.env<-` <- function(env, value) .Internal(`parent.env<-`(env, value)) existsInFrame <- function(x, env) .Internal(exists(x, env, "any", FALSE)) getFromFrame <- function(x, env) .Internal(get(x, env, "any", FALSE)) set <- function(x, value, env) .Internal(assign(x, value, env, FALSE)) environment <- function() .Internal(environment(NULL)) mkenv <- function() .Internal(new.env(TRUE, baseenv(), 29L)) mapfile <- glue(filebase, "rdx", sep = ".") datafile <- glue(filebase, "rdb", sep = ".") env <- mkenv() map <- readRDS(mapfile) vars <- names(map$variables) rvars <- names(map$references) compressed <- map$compressed for (i in seq_along(rvars)) set(rvars[i], map$references[[i]], env) envenv <- mkenv() envhook <- function(n) { if (existsInFrame(n, envenv)) getFromFrame(n, envenv) else { e <- mkenv() set(n, e, envenv) key <- getFromFrame(n, env) data <- lazyLoadDBfetch(key, datafile, compressed, envhook) if (is.null(data$enclos)) parent.env(e) <- emptyenv() else parent.env(e) <- data$enclos vars <- names(data$bindings) for (i in seq_along(vars)) set(vars[i], data$bindings[[i]], e) if (!is.null(data$attributes)) attributes(e) <- data$attributes if (!is.null(data$isS4) && data$isS4) .Internal(setS4Object(e, TRUE, TRUE)) if (!is.null(data$locked) && data$locked) .Internal(lockEnvironment(e, FALSE)) e } } if (!missing(filter)) { use <- filter(vars) vars <- vars[use] vals <- map$variables[use] use <- NULL } else vals <- map$variables res <- fun(environment()) map <- NULL vars <- NULL vals <- NULL rvars <- NULL mapfile <- NULL readRDS <- NULL res } length.POSIXlt <- function (x) length(x[[1L]]) levels.default <- function (x) attr(x, "levels") memory.profile <- function () .Internal(memory.profile()) Ops.data.frame <- function (e1, e2 = NULL) { isList <- function(x) !is.null(x) && is.list(x) unary <- nargs() == 1L lclass <- nzchar(.Method[1L]) rclass <- !unary && (nzchar(.Method[2L])) value <- list() rn <- NULL FUN <- get(.Generic, envir = parent.frame(), mode = "function") f <- if (unary) quote(FUN(left)) else quote(FUN(left, right)) lscalar <- rscalar <- FALSE if (lclass && rclass) { nr <- .row_names_info(e1, 2L) if (.row_names_info(e1) > 0L) rn <- attr(e1, "row.names") cn <- names(e1) if (any(dim(e2) != dim(e1))) stop(.Generic, " only defined for equally-sized data frames") } else if (lclass) { nr <- .row_names_info(e1, 2L) if (.row_names_info(e1) > 0L) rn <- attr(e1, "row.names") cn <- names(e1) rscalar <- length(e2) <= 1L if (isList(e2)) { if (rscalar) e2 <- e2[[1L]] else if (length(e2) != ncol(e1)) stop(gettextf("list of length %d not meaningful", length(e2)), domain = NA) } else { if (!rscalar) e2 <- split(rep_len(as.vector(e2), prod(dim(e1))), rep.int(seq_len(ncol(e1)), rep.int(nrow(e1), ncol(e1)))) } } else { nr <- .row_names_info(e2, 2L) if (.row_names_info(e2) > 0L) rn <- attr(e2, "row.names") cn <- names(e2) lscalar <- length(e1) <= 1L if (isList(e1)) { if (lscalar) e1 <- e1[[1L]] else if (length(e1) != ncol(e2)) stop(gettextf("list of length %d not meaningful", length(e1)), domain = NA) } else { if (!lscalar) e1 <- split(rep_len(as.vector(e1), prod(dim(e2))), rep.int(seq_len(ncol(e2)), rep.int(nrow(e2), ncol(e2)))) } } for (j in seq_along(cn)) { left <- if (!lscalar) e1[[j]] else e1 right <- if (!rscalar) e2[[j]] else e2 value[[j]] <- eval(f) } if (.Generic %in% c("+", "-", "*", "/", "%%", "%/%")) { names(value) <- cn data.frame(value, row.names = rn, check.names = FALSE, check.rows = FALSE) } else matrix(unlist(value, recursive = FALSE, use.names = FALSE), nrow = nr, dimnames = list(rn, cn)) } ## @type n : complex ## @type x : numeric ## @type high.u.bias : numeric ## @type u5.bias : numeric ## @type shrink.sml : numeric ## @type eps.correct : integer ## @type min.n : complex ## @optional x pretty.default <- function (x, n = 5, min.n = n%/%3, shrink.sml = 0.75, high.u.bias = 1.5, u5.bias = 0.5 + 1.5 * high.u.bias, eps.correct = 0, ...) { x <- x[is.finite(x <- as.numeric(x))] if (!length(x)) return(x) z <- .Internal(pretty(min(x), max(x), n, min.n, shrink.sml, c(high.u.bias, u5.bias), eps.correct)) s <- seq.int(z$l, z$u, length.out = z$n + 1) if (!eps.correct && z$n) { delta <- diff(range(z$l, z$u))/z$n if (any(small <- abs(s) < 1e-14 * delta)) s[small] <- 0 } s } print.difftime <- function (x, digits = getOption("digits"), ...) { if (is.array(x) || length(x) > 1L) { cat("Time differences in ", attr(x, "units"), "\n", sep = "") y <- unclass(x) attr(y, "units") <- NULL print(y) } else cat("Time difference of ", format(unclass(x), digits = digits), " ", attr(x, "units"), "\n", sep = "") invisible(x) } ## @type useSource : logical print.function <- function (x, useSource = TRUE, ...) .Internal(print.function(x, useSource, ...)) print.warnings <- function (x, ...) { if (n <- length(x)) { cat(ngettext(n, "Warning message:\n", "Warning messages:\n")) msgs <- names(x) for (i in seq_len(n)) { ind <- if (n == 1L) "" else paste0(i, ": ") out <- if (length(x[[i]])) { temp <- deparse(x[[i]], width.cutoff = 50L, nlines = 2L) sm <- strsplit(msgs[i], "\n")[[1L]] nl <- if (nchar(ind, "w") + nchar(temp[1L], "w") + nchar(sm[1L], "w") <= 75L) " " else "\n " paste(ind, "In ", temp[1L], if (length(temp) > 1L) " ...", " :", nl, msgs[i], sep = "") } else paste0(ind, msgs[i]) do.call("cat", c(list(out), attr(x, "dots"), fill = TRUE)) } } invisible(x) } pushBackLength <- function (connection) .Internal(pushBackLength(connection)) restartFormals <- function (r) formals(r$handler) ## @type na.rm : logical ## @type x : numeric rowsum.default <- function (x, group, reorder = TRUE, na.rm = FALSE, ...) { if (!is.numeric(x)) stop("'x' must be numeric") if (length(group) != NROW(x)) stop("incorrect length for 'group'") if (anyNA(group)) warning("missing values for 'group'") ugroup <- unique(group) if (reorder) ugroup <- sort(ugroup, na.last = TRUE, method = "quick") .Internal(rowsum_matrix(x, group, ugroup, na.rm, as.character(ugroup))) } ## @type higher : logical simplify2array <- function (x, higher = TRUE) { if (length(common.len <- unique(unlist(lapply(x, length)))) > 1L) return(x) if (common.len == 1L) unlist(x, recursive = FALSE) else if (common.len > 1L) { n <- length(x) r <- as.vector(unlist(x, recursive = FALSE)) if (higher && length(c.dim <- unique(lapply(x, dim))) == 1 && is.numeric(c.dim <- c.dim[[1L]]) && prod(d <- c(c.dim, n)) == length(r)) { iN1 <- is.null(n1 <- dimnames(x[[1L]])) n2 <- names(x) dnam <- if (!(iN1 && is.null(n2))) c(if (iN1) rep.int(list(n1), length(c.dim)) else n1, list(n2)) array(r, dim = d, dimnames = dnam) } else if (prod(d <- c(common.len, n)) == length(r)) array(r, dim = d, dimnames = if (!(is.null(n1 <- names(x[[1L]])) & is.null(n2 <- names(x)))) list(n1, n2)) else x } else x } "/.difftime" <- function (e1, e2) { if (inherits(e2, "difftime")) stop("second argument of / cannot be a \"difftime\" object") .difftime(unclass(e1)/e2, attr(e1, "units")) } ## @type value : character "storage.mode<-" <- function (x, value) .Primitive("storage.mode<-") ## @type subset : logical ## @optional x subset.default <- function (x, subset, ...) { if (!is.logical(subset)) stop("'subset' must be logical") x[subset & !is.na(subset)] } Summary.factor <- function (..., na.rm) stop(.Generic, " not meaningful for factors") summary.matrix <- function (object, ...) { summary.data.frame(as.data.frame.matrix(object), ...) } summary.srcref <- function (object, useSource = FALSE, ...) { cat(as.character(object, useSource = useSource), sep = "\n") invisible(object) } ## @type name : character ## @type quiet : logical sys.load.image <- function (name, quiet) { if (file.exists(name)) { load(name, envir = .GlobalEnv) if (!quiet) message("[Previously saved workspace restored]", "\n") } } Sys.localeconv <- function () .Internal(Sys.localeconv()) ## @type name : character sys.save.image <- function (name) { closeAllConnections() save.image(name) } textConnection <- function (object, open = "r", local = FALSE, encoding = c("", "bytes", "UTF-8")) { env <- if (local) parent.frame() else .GlobalEnv type <- match(match.arg(encoding), c("", "bytes", "UTF-8")) nm <- deparse(substitute(object)) if (length(nm) != 1) stop("argument 'object' must deparse to a single character string") .Internal(textConnection(nm, object, open, env, type)) } ## @type nmax : complex ## @type fromLast : logical unique.default <- function (x, incomparables = FALSE, fromLast = FALSE, nmax = NA, ...) { if (is.factor(x)) { z <- .Internal(unique(x, incomparables, fromLast, min(length(x), nlevels(x) + 1L))) return(factor(z, levels = seq_len(nlevels(x)), labels = levels(x), ordered = is.ordered(x))) } z <- .Internal(unique(x, incomparables, fromLast, nmax)) if (inherits(x, "POSIXct")) structure(z, class = class(x), tzone = attr(x, "tzone")) else if (inherits(x, "Date")) structure(z, class = class(x)) else z } unique.POSIXlt <- function (x, incomparables = FALSE, ...) x[!duplicated(x, incomparables, ...)] units.difftime <- function (x) attr(x, "units") xtfrm.difftime <- function (x) as.numeric(x) ## @type j : numeric|logical|character ## @type i : numeric|logical|character ## @type value : complex "[[<-.data.frame" <- function (x, i, j, value) { if (!all(names(sys.call()) %in% c("", "value"))) warning("named arguments are discouraged") cl <- oldClass(x) class(x) <- NULL nrows <- .row_names_info(x, 2L) if (is.atomic(value) && !is.null(names(value))) names(value) <- NULL if (nargs() < 4L) { nc <- length(x) if (!is.null(value)) { N <- NROW(value) if (N > nrows) stop(sprintf(ngettext(N, "replacement has %d row, data has %d", "replacement has %d rows, data has %d"), N, nrows), domain = NA) if (N < nrows) if (N > 0L && (nrows%%N == 0L) && length(dim(value)) <= 1L) value <- rep(value, length.out = nrows) else stop(sprintf(ngettext(N, "replacement has %d row, data has %d", "replacement has %d rows, data has %d"), N, nrows), domain = NA) } x[[i]] <- value if (length(x) > nc) { nc <- length(x) if (names(x)[nc] == "") names(x)[nc] <- paste0("V", nc) names(x) <- make.unique(names(x)) } class(x) <- cl return(x) } if (missing(i) || missing(j)) stop("only valid calls are x[[j]] <- value or x[[i,j]] <- value") rows <- attr(x, "row.names") nvars <- length(x) if (n <- is.character(i)) { ii <- match(i, rows) n <- sum(new.rows <- is.na(ii)) if (n > 0L) { ii[new.rows] <- seq.int(from = nrows + 1L, length.out = n) new.rows <- i[new.rows] } i <- ii } if (all(i >= 0L) && (nn <- max(i)) > nrows) { if (n == 0L) { nrr <- (nrows + 1L):nn if (inherits(value, "data.frame") && (dim(value)[1L]) >= length(nrr)) { new.rows <- attr(value, "row.names")[seq_len(nrr)] repl <- duplicated(new.rows) | match(new.rows, rows, 0L) if (any(repl)) new.rows[repl] <- nrr[repl] } else new.rows <- nrr } x <- xpdrows.data.frame(x, rows, new.rows) rows <- attr(x, "row.names") nrows <- length(rows) } iseq <- seq_len(nrows)[i] if (anyNA(iseq)) stop("non-existent rows not allowed") if (is.character(j)) { if ("" %in% j) stop("column name \"\" cannot match any column") jseq <- match(j, names(x)) if (anyNA(jseq)) stop(gettextf("replacing element in non-existent column: %s", j[is.na(jseq)]), domain = NA) } else if (is.logical(j) || min(j) < 0L) jseq <- seq_along(x)[j] else { jseq <- j if (max(jseq) > nvars) stop(gettextf("replacing element in non-existent column: %s", jseq[jseq > nvars]), domain = NA) } if (length(iseq) > 1L || length(jseq) > 1L) stop("only a single element should be replaced") x[[jseq]][[iseq]] <- value class(x) <- cl x } ## @return logical|integer|character addTaskCallback <- function (f, data = NULL, name = character()) { if (!is.function(f)) stop("handler must be a function") val <- .Call(.C_R_addTaskCallback, f, data, !missing(data), as.character(name)) val + 1L } as.Date.default <- function (x, ...) { if (inherits(x, "Date")) return(x) if (is.logical(x) && all(is.na(x))) return(structure(as.numeric(x), class = "Date")) stop(gettextf("do not know how to convert '%s' to class %s", deparse(substitute(x)), dQuote("Date")), domain = NA) } as.Date.numeric <- function (x, origin, ...) { if (missing(origin)) stop("'origin' must be supplied") as.Date(origin, ...) + x } ## @type tz : character as.Date.POSIXct <- function (x, tz = "UTC", ...) { if (tz == "UTC") { z <- floor(unclass(x)/86400) attr(z, "tzone") <- NULL structure(z, class = "Date") } else as.Date(as.POSIXlt(x, tz = tz)) } as.Date.POSIXlt <- function (x, ...) .Internal(POSIXlt2Date(x)) as.list.default <- function (x, ...) if (typeof(x) == "list") x else .Internal(as.vector(x, "list")) as.list.POSIXct <- function (x, ...) { nms <- names(x) names(x) <- NULL y <- lapply(seq_along(x), function(i) x[i]) names(y) <- nms y } as.null.default <- function (x, ...) NULL as.POSIXct.Date <- function (x, ...) .POSIXct(unclass(x) * 86400) as.POSIXlt.Date <- function (x, ...) .Internal(Date2POSIXlt(x)) attachNamespace <- function (ns, pos = 2L, depends = NULL) { runHook <- function(hookname, env, libname, pkgname) { if (exists(hookname, envir = env, inherits = FALSE)) { fun <- get(hookname, envir = env, inherits = FALSE) res <- tryCatch(fun(libname, pkgname), error = identity) if (inherits(res, "error")) { stop(gettextf("%s failed in %s() for '%s', details:\n call: %s\n error: %s", hookname, "attachNamespace", nsname, deparse(conditionCall(res))[1L], conditionMessage(res)), call. = FALSE, domain = NA) } } } runUserHook <- function(pkgname, pkgpath) { hook <- getHook(packageEvent(pkgname, "attach")) for (fun in hook) try(fun(pkgname, pkgpath)) } ns <- asNamespace(ns, base.OK = FALSE) nsname <- getNamespaceName(ns) nspath <- getNamespaceInfo(ns, "path") attname <- paste("package", nsname, sep = ":") if (attname %in% search()) stop("namespace is already attached") env <- attach(NULL, pos = pos, name = attname) on.exit(.Internal(detach(pos))) attr(env, "path") <- nspath exports <- getNamespaceExports(ns) importIntoEnv(env, exports, ns, exports) dimpenv <- getNamespaceInfo(ns, "lazydata") dnames <- ls(dimpenv, all.names = TRUE) .Internal(importIntoEnv(env, dnames, dimpenv, dnames)) if (length(depends)) assign(".Depends", depends, env) Sys.setenv(`_R_NS_LOAD_` = nsname) on.exit(Sys.unsetenv("_R_NS_LOAD_"), add = TRUE) runHook(".onAttach", ns, dirname(nspath), nsname) lockEnvironment(env, TRUE) runUserHook(nsname, nspath) on.exit() Sys.unsetenv("_R_NS_LOAD_") invisible(env) } ## @type sym : character ## @return logical bindingIsActive <- function (sym, env) { if (is.character(sym)) sym <- as.name(sym) .Internal(bindingIsActive(sym, env)) } ## @type sym : character bindingIsLocked <- function (sym, env) { if (is.character(sym)) sym <- as.name(sym) .Internal(bindingIsLocked(sym, env)) } browserSetDebug <- function (n = 1L) .Internal(browserSetDebug(n)) computeRestarts <- function (cond = NULL) { val <- NULL i <- 1L repeat { r <- .Internal(.getRestart(i)) if (is.null(r)) return(val) else if (is.null(cond) || is.null(r$test) || r$test(cond)) val <- c(val, list(r)) i <- i + 1L } } environmentName <- function (env) .Internal(environmentName(env)) format.difftime <- function (x, ...) paste(format(unclass(x), ...), units(x)) ## @optional value "is.na<-.default" <- function (x, value) { x[value] <- NA x } is.numeric.Date <- function (x) FALSE isBaseNamespace <- function (ns) identical(ns, .BaseNamespaceEnv) ## @type key : character ## @type compressed : logical lazyLoadDBfetch <- function (key, file, compressed, hook) .Primitive("lazyLoadDBfetch") ## @type value : integer ## @optional value "length<-.factor" <- function (x, value) { cl <- class(x) levs <- levels(x) x <- NextMethod() structure(x, levels = levs, class = cl) } ## @type value : complex|character "levels<-.factor" <- function (x, value) { xlevs <- levels(x) if (is.list(value)) { nlevs <- rep.int(names(value), lapply(value, length)) value <- unlist(value) m <- match(value, xlevs, nomatch = 0L) xlevs[m] <- nlevs[m > 0L] } else { if (length(xlevs) > length(value)) stop("number of levels differs") nlevs <- xlevs <- as.character(value) nlevs <- nlevs[!is.na(nlevs)] } nlevs <- unique(nlevs) at <- attributes(x) at$levels <- nlevs y <- match(xlevs[x], nlevs) attributes(y) <- at y } ## @type bindings : logical lockEnvironment <- function (env, bindings = FALSE) .Internal(lockEnvironment(env, bindings)) Math.data.frame <- function (x, ...) { mode.ok <- vapply(x, function(x) is.numeric(x) || is.complex(x), NA) if (all(mode.ok)) { x[] <- lapply(X = x, FUN = .Generic, ...) return(x) } else { vnames <- names(x) if (is.null(vnames)) vnames <- seq_along(x) stop("non-numeric variable in data frame: ", vnames[!mode.ok]) } } "names<-.POSIXlt" <- function (x, value) { names(x$year) <- value x } namespaceExport <- function (ns, vars) { namespaceIsSealed <- function(ns) environmentIsLocked(ns) if (namespaceIsSealed(ns)) stop("cannot add to exports of a sealed namespace") ns <- asNamespace(ns, base.OK = FALSE) if (length(vars)) { addExports <- function(ns, new) { exports <- getNamespaceInfo(ns, "exports") expnames <- names(new) intnames <- new objs <- .Internal(ls(exports, TRUE)) ex <- expnames %in% objs if (any(ex)) warning(sprintf(ngettext(sum(ex), "previous export '%s' is being replaced", "previous exports '%s' are being replaced"), paste(sQuote(expnames[ex]), collapse = ", ")), call. = FALSE, domain = NA) for (i in seq_along(new)) assign(expnames[i], intnames[i], envir = exports) } makeImportExportNames <- function(spec) { old <- as.character(spec) new <- names(spec) if (is.null(new)) new <- old else { change <- !nzchar(new) new[change] <- old[change] } names(old) <- new old } new <- makeImportExportNames(unique(vars)) undef <- new[!new %in% .Internal(ls(ns, TRUE))] undef <- undef[!vapply(undef, exists, NA, envir = ns)] if (length(undef)) { undef <- do.call("paste", as.list(c(undef, sep = ", "))) stop(gettextf("undefined exports: %s", undef), domain = NA) } if (.isMethodsDispatchOn()) .mergeExportMethods(new, ns) addExports(ns, new) } } namespaceImport <- function (self, ..., from = NULL) for (ns in list(...)) namespaceImportFrom(self, asNamespace(ns), from = from) ## @type strict : numeric|logical ## @type x : numeric|character numeric_version <- function (x, strict = TRUE) .make_numeric_version(x, strict, .standard_regexps()$valid_numeric_version) ## @type blocking : logical ## @type open : character open.connection <- function (con, open = "r", blocking = TRUE, ...) .Internal(open(con, open, blocking)) ## @type strict : numeric|logical ## @type x : numeric|character package_version <- function (x, strict = TRUE) { if (is.list(x) && all(c("major", "minor") %in% names(x))) return(R_system_version(paste(x[c("major", "minor")], collapse = "."))) .make_numeric_version(x, strict, .standard_regexps()$valid_package_version, "package_version") } print.condition <- function (x, ...) { msg <- conditionMessage(x) call <- conditionCall(x) cl <- class(x)[1L] if (!is.null(call)) cat("<", cl, " in ", deparse(call), ": ", msg, ">\n", sep = "") else cat("<", cl, ": ", msg, ">\n", sep = "") invisible(x) } print.proc_time <- function (x, ...) { print(summary(x, ...)) invisible(x) } ## @type sep : character ## @type base : character provideDimnames <- function (x, sep = "", base = list(LETTERS)) { dx <- dim(x) dnx <- dimnames(x) if (new <- is.null(dnx)) dnx <- vector("list", length(dx)) k <- length(M <- vapply(base, length, 1L)) for (i in which(vapply(dnx, is.null, NA))) { ii <- 1L + (i - 1L)%%k ss <- seq_len(dx[i]) - 1L dnx[[i]] <- make.unique(base[[ii]][1L + (ss%%M[ii])], sep = sep) new <- TRUE } if (new) dimnames(x) <- dnx x } ## @optional x quarters.POSIXt <- function (x, ...) { x <- (as.POSIXlt(x)$mon)%/%3 paste0("Q", x + 1) } ## @type where : numeric ## @type origin : character ## @type rw : character seek.connection <- function (con, where = NA, origin = "start", rw = "", ...) { origin <- pmatch(origin, c("start", "current", "end")) rw <- pmatch(rw, c("read", "write"), 0L) if (is.na(origin)) stop("'origin' must be one of 'start', 'current' or 'end'") .Internal(seek(con, as.double(where), origin, rw)) } ## @type all : logical showConnections <- function (all = FALSE) { set <- getAllConnections() if (!all) set <- set[set > 2L] ans <- matrix("", length(set), 7L) for (i in seq_along(set)) ans[i, ] <- unlist(summary.connection(set[i])) rownames(ans) <- set colnames(ans) <- c("description", "class", "mode", "text", "isopen", "can read", "can write") if (!all) ans[ans[, 5L] == "opened", , drop = FALSE] else ans[, , drop = FALSE] } signalCondition <- function (cond) { if (!inherits(cond, "condition")) cond <- simpleCondition(cond) msg <- conditionMessage(cond) call <- conditionCall(cond) .Internal(.signalCondition(cond, msg, call)) } simpleCondition <- function (message, call = NULL) { class <- c("simpleCondition", "condition") structure(list(message = as.character(message), call = call), class = class) } ## @type drop : logical "split<-.default" <- function (x, f, drop = FALSE, ..., value) { ix <- split(seq_along(x), f, drop = drop, ...) n <- length(value) j <- 0 for (i in ix) { j <- j%%n + 1 x[i] <- value[[j]] } x } standardGeneric <- function (f, fdef) .Primitive("standardGeneric") ## @type digits : complex summary.default <- function (object, ..., digits = max(3L, getOption("digits") - 3L)) { if (is.factor(object)) return(summary.factor(object, ...)) else if (is.matrix(object)) return(summary.matrix(object, digits = digits, ...)) value <- if (is.logical(object)) c(Mode = "logical", { tb <- table(object, exclude = NULL) if (!is.null(n <- dimnames(tb)[[1L]]) && any(iN <- is.na(n))) dimnames(tb)[[1L]][iN] <- "NA's" tb }) else if (is.numeric(object)) { nas <- is.na(object) object <- object[!nas] qq <- stats::quantile(object) qq <- signif(c(qq[1L:3L], mean(object), qq[4L:5L]), digits) names(qq) <- c("Min.", "1st Qu.", "Median", "Mean", "3rd Qu.", "Max.") if (any(nas)) c(qq, `NA's` = sum(nas)) else qq } else if (is.recursive(object) && !is.language(object) && (n <- length(object))) { sumry <- array("", c(n, 3L), list(names(object), c("Length", "Class", "Mode"))) ll <- numeric(n) for (i in 1L:n) { ii <- object[[i]] ll[i] <- length(ii) cls <- oldClass(ii) sumry[i, 2L] <- if (length(cls)) cls[1L] else "-none-" sumry[i, 3L] <- mode(ii) } sumry[, 1L] <- format(as.integer(ll)) sumry } else c(Length = length(object), Class = class(object), Mode = mode(object)) class(value) <- c("summaryDefault", "table") value } Summary.ordered <- function (..., na.rm) { ok <- switch(.Generic, max = , min = , range = TRUE, FALSE) if (!ok) stop(gettextf("'%s' not defined for ordered factors", .Generic), domain = NA) args <- list(...) levl <- lapply(args, levels) levset <- levl[[1]] if (!all(vapply(args, is.ordered, NA)) || !all(sapply(levl, identical, levset))) stop(gettextf("'%s' is only meaningful for ordered factors if all arguments have the same level sets", .Generic)) codes <- lapply(args, as.integer) ind <- do.call(.Generic, c(codes, na.rm = na.rm)) ordered(levset[ind], levels = levset) } ## @optional na.rm Summary.POSIXct <- function (..., na.rm) { ok <- switch(.Generic, max = , min = , range = TRUE, FALSE) if (!ok) stop(gettextf("'%s' not defined for \"POSIXt\" objects", .Generic), domain = NA) args <- list(...) tz <- do.call("check_tzones", args) val <- NextMethod(.Generic) class(val) <- oldClass(args[[1L]]) attr(val, "tzone") <- tz val } Summary.POSIXlt <- function (..., na.rm) { ok <- switch(.Generic, max = , min = , range = TRUE, FALSE) if (!ok) stop(gettextf("'%s' not defined for \"POSIXt\" objects", .Generic), domain = NA) args <- list(...) tz <- do.call("check_tzones", args) args <- lapply(args, as.POSIXct) val <- do.call(.Generic, c(args, na.rm = na.rm)) as.POSIXlt(.POSIXct(val, tz)) } summary.srcfile <- function (object, ...) { cat(utils:::.normalizePath(object$filename, object$wd), "\n") if (inherits(object$timestamp, "POSIXt")) cat("Timestamp: ", format(object$timestamp, usetz = TRUE), "\n", sep = "") cat("Encoding: \"", object$encoding, "\"", sep = "") if (!is.null(object$Enc) && object$Enc != object$encoding && object$Enc != "unknown") cat(", re-encoded to \"", object$Enc, "\"", sep = "") cat("\n") invisible(object) } ## @type path : character Sys.setFileTime <- function (path, time) { if (!is.character(path) || length(path) != 1L) stop("invalid 'path' argument") time <- as.POSIXct(time) if (is.na(time)) stop("invalid 'time' argument") .Internal(setFileTime(path, time)) } unloadNamespace <- function (ns) { runHook <- function(hookname, env, ...) { if (exists(hookname, envir = env, inherits = FALSE)) { fun <- get(hookname, envir = env, inherits = FALSE) res <- tryCatch(fun(...), error = identity) if (inherits(res, "error")) { warning(gettextf("%s failed in %s() for '%s', details:\n call: %s\n error: %s", hookname, "unloadNamespace", nsname, deparse(conditionCall(res))[1L], conditionMessage(res)), call. = FALSE, domain = NA) } } } ns <- asNamespace(ns, base.OK = FALSE) nsname <- getNamespaceName(ns) pos <- match(paste("package", nsname, sep = ":"), search()) if (!is.na(pos)) detach(pos = pos) users <- getNamespaceUsers(ns) if (length(users)) stop(gettextf("namespace %s is imported by %s so cannot be unloaded", sQuote(getNamespaceName(ns)), paste(sQuote(users), collapse = ", ")), domain = NA) nspath <- getNamespaceInfo(ns, "path") hook <- getHook(packageEvent(nsname, "onUnload")) for (fun in rev(hook)) try(fun(nsname, nspath)) runHook(".onUnload", ns, nspath) .Internal(unregisterNamespace(nsname)) if (.isMethodsDispatchOn() && methods:::.hasS4MetaData(ns)) methods:::cacheMetaData(ns, FALSE, ns) .Internal(lazyLoadDBflush(paste0(nspath, "/R/", nsname, ".rdb"))) invisible() } weekdays.POSIXt <- function (x, abbreviate = FALSE) { format(x, ifelse(abbreviate, "%a", "%A")) } ## @type check.attributes : logical ## @return logical|character all.equal.factor <- function (target, current, ..., check.attributes = TRUE) { if (!inherits(target, "factor")) return("'target' is not a factor") if (!inherits(current, "factor")) return("'current' is not a factor") msg <- if (check.attributes) attr.all.equal(target, current, ...) n <- all.equal(as.character(target), as.character(current), check.attributes = check.attributes, ...) if (is.character(n)) msg <- c(msg, n) if (is.null(msg)) TRUE else msg } ## @type scale : numeric ## @type tolerance : numeric ## @optional scale all.equal.POSIXt <- function (target, current, ..., tolerance = 0.001, scale) { target <- as.POSIXct(target) current <- as.POSIXct(current) check_tzones(target, current) attr(target, "tzone") <- attr(current, "tzone") <- NULL all.equal.numeric(target, current, ..., tolerance = tolerance, scale = 1) } as.array.default <- function (x, ...) { if (is.array(x)) return(x) n <- names(x) dim(x) <- length(x) if (length(n)) dimnames(x) <- list(n) return(x) } as.data.frame.ts <- function (x, ...) { if (is.matrix(x)) as.data.frame.matrix(x, ...) else as.data.frame.vector(x, ...) } as.list.function <- function (x, ...) c(formals(x), list(body(x))) as.POSIXct.dates <- function (x, ...) { if (inherits(x, "dates")) { z <- attr(x, "origin") x <- as.numeric(x) * 86400 if (length(z) == 3L && is.numeric(z)) x <- x + as.numeric(ISOdate(z[3L], z[1L], z[2L], 0)) return(.POSIXct(x)) } else stop(gettextf("'%s' is not a \"dates\" object", deparse(substitute(x)))) } as.POSIXlt.dates <- function (x, ...) as.POSIXlt(as.POSIXct(x), ...) as.table.default <- function (x, ...) { if (is.table(x)) return(x) else if (is.array(x) || is.numeric(x)) { x <- as.array(x) if (any(dim(x) == 0L)) stop("cannot coerce to a table") structure(class = c("table", oldClass(x)), provideDimnames(x)) } else stop("cannot coerce to a table") } ## @type mode : character ## @return numeric|character as.vector.factor <- function (x, mode = "any") { if (mode == "list") as.list(x) else if (mode == "any" || mode == "character" || mode == "logical") as.vector(levels(x)[x], mode) else as.vector(unclass(x), mode) } browserCondition <- function (n = 1L) .Internal(browserCondition(n)) ## @type deparse.level : integer cbind.data.frame <- function (..., deparse.level = 1) data.frame(..., check.names = FALSE) ## @type type : character close.connection <- function (con, type = "rw", ...) .Internal(close(con, type)) conditionMessage <- function (c) UseMethod("conditionMessage") ## @type fromLast : logical duplicated.array <- function (x, incomparables = FALSE, MARGIN = 1L, fromLast = FALSE, ...) { if (!identical(incomparables, FALSE)) .NotYetUsed("incomparables != FALSE") dx <- dim(x) ndim <- length(dx) if (length(MARGIN) > ndim || any(MARGIN > ndim)) stop(gettextf("MARGIN = %d is invalid for dim = %d", MARGIN, dx), domain = NA) collapse <- (ndim > 1L) && (prod(dx[-MARGIN]) > 1L) temp <- if (collapse) apply(x, MARGIN, function(x) paste(x, collapse = "\r")) else x res <- duplicated.default(temp, fromLast = fromLast, ...) dim(res) <- dim(temp) dimnames(res) <- dimnames(temp) res } flush.connection <- function (con) .Internal(flush(con)) getExportedValue <- function (ns, name) { getInternalExportName <- function(name, ns) { exports <- getNamespaceInfo(ns, "exports") if (exists(name, envir = exports, inherits = FALSE)) get(get(name, envir = exports, inherits = FALSE), envir = ns) else { ld <- getNamespaceInfo(ns, "lazydata") if (exists(name, envir = ld, inherits = FALSE)) get(name, envir = ld, inherits = FALSE) else stop(gettextf("'%s' is not an exported object from 'namespace:%s'", name, getNamespaceName(ns)), call. = FALSE, domain = NA) } } ns <- asNamespace(ns) if (isBaseNamespace(ns)) get(name, envir = ns, inherits = FALSE) else getInternalExportName(name, ns) } getNamespaceInfo <- function (ns, which) { ns <- asNamespace(ns, base.OK = FALSE) info <- get(".__NAMESPACE__.", envir = ns, inherits = FALSE) get(which, envir = info, inherits = FALSE) } ## @return character getNamespaceName <- function (ns) { ns <- asNamespace(ns) if (isBaseNamespace(ns)) "base" else getNamespaceInfo(ns, "spec")["name"] } is.na.data.frame <- function (x) { y <- if (length(x)) { do.call("cbind", lapply(x, "is.na")) } else matrix(FALSE, length(row.names(x)), 0) if (.row_names_info(x) > 0L) rownames(y) <- row.names(x) y } loadedNamespaces <- function () ls(.Internal(getNamespaceRegistry()), all.names = TRUE) ## @type all.x : logical ## @type sort : logical ## @type all : logical ## @type suffixes : character ## @type all.y : logical merge.data.frame <- function (x, y, by = intersect(names(x), names(y)), by.x = by, by.y = by, all = FALSE, all.x = all, all.y = all, sort = TRUE, suffixes = c(".x", ".y"), incomparables = NULL, ...) { fix.by <- function(by, df) { if (is.null(by)) by <- numeric() by <- as.vector(by) nc <- ncol(df) if (is.character(by)) { poss <- c("row.names", names(df)) if (any(bad <- !charmatch(by, poss, 0L))) stop(ngettext(sum(bad), "'by' must specify a uniquely valid column", "'by' must specify uniquely valid columns"), domain = NA) by <- match(by, poss) - 1L } else if (is.numeric(by)) { if (any(by < 0L) || any(by > nc)) stop("'by' must match numbers of columns") } else if (is.logical(by)) { if (length(by) != nc) stop("'by' must match number of columns") by <- seq_along(by)[by] } else stop("'by' must specify one or more columns as numbers, names or logical") if (any(bad <- is.na(by))) stop(ngettext(sum(bad), "'by' must specify a uniquely valid column", "'by' must specify uniquely valid columns"), domain = NA) unique(by) } nx <- nrow(x <- as.data.frame(x)) ny <- nrow(y <- as.data.frame(y)) if (nx >= 2^31 || ny >= 2^31) stop("long vectors are not supported") by.x <- fix.by(by.x, x) by.y <- fix.by(by.y, y) if ((l.b <- length(by.x)) != length(by.y)) stop("'by.x' and 'by.y' specify different numbers of columns") if (l.b == 0L) { nm <- nm.x <- names(x) nm.y <- names(y) has.common.nms <- any(cnm <- nm.x %in% nm.y) if (has.common.nms) { names(x)[cnm] <- paste0(nm.x[cnm], suffixes[1L]) cnm <- nm.y %in% nm names(y)[cnm] <- paste0(nm.y[cnm], suffixes[2L]) } if (nx == 0L || ny == 0L) { res <- cbind(x[FALSE, ], y[FALSE, ]) } else { ij <- expand.grid(seq_len(nx), seq_len(ny)) res <- cbind(x[ij[, 1L], , drop = FALSE], y[ij[, 2L], , drop = FALSE]) } } else { if (any(by.x == 0L)) { x <- cbind(Row.names = I(row.names(x)), x) by.x <- by.x + 1L } if (any(by.y == 0L)) { y <- cbind(Row.names = I(row.names(y)), y) by.y <- by.y + 1L } row.names(x) <- NULL row.names(y) <- NULL if (l.b == 1L) { bx <- x[, by.x] if (is.factor(bx)) bx <- as.character(bx) by <- y[, by.y] if (is.factor(by)) by <- as.character(by) } else { if (!is.null(incomparables)) stop("'incomparables' is supported only for merging on a single column") bx <- x[, by.x, drop = FALSE] by <- y[, by.y, drop = FALSE] names(bx) <- names(by) <- paste0("V", seq_len(ncol(bx))) bz <- do.call("paste", c(rbind(bx, by), sep = "\r")) bx <- bz[seq_len(nx)] by <- bz[nx + seq_len(ny)] } comm <- match(bx, by, 0L) bxy <- bx[comm > 0L] xinds <- match(bx, bxy, 0L, incomparables) yinds <- match(by, bxy, 0L, incomparables) if (nx > 0L && ny > 0L) m <- .Internal(merge(xinds, yinds, all.x, all.y)) else m <- list(xi = integer(), yi = integer(), x.alone = seq_len(nx), y.alone = seq_len(ny)) nm <- nm.x <- names(x)[-by.x] nm.by <- names(x)[by.x] nm.y <- names(y)[-by.y] ncx <- ncol(x) if (all.x) all.x <- (nxx <- length(m$x.alone)) > 0L if (all.y) all.y <- (nyy <- length(m$y.alone)) > 0L lxy <- length(m$xi) has.common.nms <- any(cnm <- nm.x %in% nm.y) if (has.common.nms && nzchar(suffixes[1L])) nm.x[cnm] <- paste0(nm.x[cnm], suffixes[1L]) x <- x[c(m$xi, if (all.x) m$x.alone), c(by.x, seq_len(ncx)[-by.x]), drop = FALSE] names(x) <- c(nm.by, nm.x) if (all.y) { ya <- y[m$y.alone, by.y, drop = FALSE] names(ya) <- nm.by xa <- x[rep.int(NA_integer_, nyy), nm.x, drop = FALSE] names(xa) <- nm.x x <- rbind(x, cbind(ya, xa)) } if (has.common.nms && nzchar(suffixes[2L])) { cnm <- nm.y %in% nm nm.y[cnm] <- paste0(nm.y[cnm], suffixes[2L]) } y <- y[c(m$yi, if (all.x) rep.int(1L, nxx), if (all.y) m$y.alone), -by.y, drop = FALSE] if (all.x) { zap <- (lxy + 1L):(lxy + nxx) for (i in seq_along(y)) { if (is.matrix(y[[1]])) y[[1]][zap, ] <- NA else is.na(y[[i]]) <- zap } } if (has.common.nms) names(y) <- nm.y nm <- c(names(x), names(y)) if (any(d <- duplicated(nm))) if (sum(d) > 1L) warning("column names ", paste(sQuote(nm[d]), collapse = ", "), " are duplicated in the result", domain = NA) else warning("column name ", sQuote(nm[d]), " is duplicated in the result", domain = NA) res <- cbind(x, y) if (sort) res <- res[if (all.x || all.y) do.call("order", x[, seq_len(l.b), drop = FALSE]) else sort.list(bx[m$xi]), , drop = FALSE] } attr(res, "row.names") <- .set_row_names(nrow(res)) res } "mostattributes<-" <- function (obj, value) { if (length(value)) { if (!is.list(value)) stop("'value' must be a list") if (h.nam <- !is.na(inam <- match("names", names(value)))) { n1 <- value[[inam]] value <- value[-inam] } if (h.dim <- !is.na(idin <- match("dim", names(value)))) { d1 <- value[[idin]] value <- value[-idin] } if (h.dmn <- !is.na(idmn <- match("dimnames", names(value)))) { dn1 <- value[[idmn]] value <- value[-idmn] } attributes(obj) <- value dm <- attr(obj, "dim") L <- length(if (is.list(obj)) unclass(obj) else obj) if (h.dim && L == prod(d1)) attr(obj, "dim") <- dm <- d1 if (h.dmn && !is.null(dm)) { ddn <- sapply(dn1, length) if (all((dm == ddn)[ddn > 0])) attr(obj, "dimnames") <- dn1 } if (h.nam && is.null(dm) && L == length(n1)) attr(obj, "names") <- n1 } obj } open.srcfilecopy <- function (con, line, ...) { srcfile <- con oldline <- srcfile$line if (!is.null(oldline) && oldline > line) close(srcfile) conn <- srcfile$conn if (is.null(conn)) { srcfile$conn <- conn <- textConnection(srcfile$lines, open = "r") srcfile$line <- 1L oldline <- 1L } else if (!isOpen(conn)) { open(conn, open = "r") srcfile$line <- 1L oldline <- 1L } if (oldline < line) { readLines(conn, line - oldline, warn = FALSE) srcfile$line <- line } invisible(conn) } print.connection <- function (x, ...) { print(unlist(summary(x))) invisible(x) } ## @type right : logical ## @type digits : complex ## @type row.names : logical|character ## @type quote : logical print.data.frame <- function (x, ..., digits = NULL, quote = FALSE, right = TRUE, row.names = TRUE) { n <- length(row.names(x)) if (length(x) == 0L) { cat(gettextf("data frame with 0 columns and %d rows\n", n)) } else if (n == 0L) { print.default(names(x), quote = FALSE) cat(gettext("<0 rows> (or 0-length row.names)\n")) } else { m <- as.matrix(format.data.frame(x, digits = digits, na.encode = FALSE)) if (!isTRUE(row.names)) dimnames(m)[[1L]] <- if (identical(row.names, FALSE)) rep.int("", n) else row.names print(m, ..., quote = quote, right = right) } invisible(x) } print.libraryIQR <- function (x, ...) { s <- format(x) if (!length(s)) { message("no packages found") } else { outFile <- tempfile("RlibraryIQR") writeLines(s, outFile) file.show(outFile, delete.file = TRUE, title = gettext("R packages available")) } invisible(x) } ## @type strict : numeric|logical ## @type x : numeric|character R_system_version <- function (x, strict = TRUE) .make_numeric_version(x, strict, .standard_regexps()$valid_R_system_version, c("R_system_version", "package_version")) ## @type deparse.level : integer rbind.data.frame <- function (..., deparse.level = 1) { match.names <- function(clabs, nmi) { if (identical(clabs, nmi)) NULL else if (length(nmi) == length(clabs) && all(nmi %in% clabs)) { m <- pmatch(nmi, clabs, 0L) if (any(m == 0L)) stop("names do not match previous names") m } else stop("names do not match previous names") } Make.row.names <- function(nmi, ri, ni, nrow) { if (nzchar(nmi)) { if (ni == 0L) character() else if (ni > 1L) paste(nmi, ri, sep = ".") else nmi } else if (nrow > 0L && identical(ri, seq_len(ni))) as.integer(seq.int(from = nrow + 1L, length.out = ni)) else ri } allargs <- list(...) allargs <- allargs[vapply(allargs, length, 1L) > 0L] if (length(allargs)) { nr <- vapply(allargs, function(x) if (is.data.frame(x)) .row_names_info(x, 2L) else if (is.list(x)) length(x[[1L]]) else length(x), 1L) if (any(nr > 0L)) allargs <- allargs[nr > 0L] else return(allargs[[1L]]) } n <- length(allargs) if (n == 0L) return(structure(list(), class = "data.frame", row.names = integer())) nms <- names(allargs) if (is.null(nms)) nms <- character(n) cl <- NULL perm <- rows <- rlabs <- vector("list", n) nrow <- 0L value <- clabs <- NULL all.levs <- list() for (i in seq_len(n)) { xi <- allargs[[i]] nmi <- nms[i] if (is.matrix(xi)) allargs[[i]] <- xi <- as.data.frame(xi) if (inherits(xi, "data.frame")) { if (is.null(cl)) cl <- oldClass(xi) ri <- attr(xi, "row.names") ni <- length(ri) if (is.null(clabs)) clabs <- names(xi) else { if (length(xi) != length(clabs)) stop("numbers of columns of arguments do not match") pi <- match.names(clabs, names(xi)) if (!is.null(pi)) perm[[i]] <- pi } rows[[i]] <- seq.int(from = nrow + 1L, length.out = ni) rlabs[[i]] <- Make.row.names(nmi, ri, ni, nrow) nrow <- nrow + ni if (is.null(value)) { value <- unclass(xi) nvar <- length(value) all.levs <- vector("list", nvar) has.dim <- logical(nvar) facCol <- logical(nvar) ordCol <- logical(nvar) for (j in seq_len(nvar)) { xj <- value[[j]] if (!is.null(levels(xj))) { all.levs[[j]] <- levels(xj) facCol[j] <- TRUE } else facCol[j] <- is.factor(xj) ordCol[j] <- is.ordered(xj) has.dim[j] <- length(dim(xj)) == 2L } } else for (j in seq_len(nvar)) { xij <- xi[[j]] if (is.null(pi) || is.na(jj <- pi[[j]])) jj <- j if (facCol[jj]) { if (length(lij <- levels(xij))) { all.levs[[jj]] <- unique(c(all.levs[[jj]], lij)) ordCol[jj] <- ordCol[jj] & is.ordered(xij) } else if (is.character(xij)) all.levs[[jj]] <- unique(c(all.levs[[jj]], xij)) } } } else if (is.list(xi)) { ni <- range(vapply(xi, length, 1L)) if (ni[1L] == ni[2L]) ni <- ni[1L] else stop("invalid list argument: all variables should have the same length") rows[[i]] <- ri <- as.integer(seq.int(from = nrow + 1L, length.out = ni)) nrow <- nrow + ni rlabs[[i]] <- Make.row.names(nmi, ri, ni, nrow) if (length(nmi <- names(xi)) > 0L) { if (is.null(clabs)) clabs <- nmi else { if (length(xi) != length(clabs)) stop("numbers of columns of arguments do not match") pi <- match.names(clabs, nmi) if (!is.null(pi)) perm[[i]] <- pi } } } else if (length(xi)) { rows[[i]] <- nrow <- nrow + 1L rlabs[[i]] <- if (nzchar(nmi)) nmi else as.integer(nrow) } } nvar <- length(clabs) if (nvar == 0L) nvar <- max(vapply(allargs, length, 1L)) if (nvar == 0L) return(structure(list(), class = "data.frame", row.names = integer())) pseq <- seq_len(nvar) if (is.null(value)) { value <- list() value[pseq] <- list(logical(nrow)) all.levs <- vector("list", nvar) has.dim <- logical(nvar) facCol <- logical(nvar) ordCol <- logical(nvar) } names(value) <- clabs for (j in pseq) if (length(lij <- all.levs[[j]])) value[[j]] <- factor(as.vector(value[[j]]), lij, ordered = ordCol[j]) if (any(has.dim)) { rmax <- max(unlist(rows)) for (i in pseq[has.dim]) if (!inherits(xi <- value[[i]], "data.frame")) { dn <- dimnames(xi) rn <- dn[[1L]] if (length(rn) > 0L) length(rn) <- rmax pi <- dim(xi)[2L] length(xi) <- rmax * pi value[[i]] <- array(xi, c(rmax, pi), list(rn, dn[[2L]])) } } for (i in seq_len(n)) { xi <- unclass(allargs[[i]]) if (!is.list(xi)) if (length(xi) != nvar) xi <- rep(xi, length.out = nvar) ri <- rows[[i]] pi <- perm[[i]] if (is.null(pi)) pi <- pseq for (j in pseq) { jj <- pi[j] xij <- xi[[j]] if (has.dim[jj]) { value[[jj]][ri, ] <- xij rownames(value[[jj]])[ri] <- rownames(xij) } else { value[[jj]][ri] <- if (is.factor(xij)) as.vector(xij) else xij if (!is.null(nm <- names(xij))) names(value[[jj]])[ri] <- nm } } } rlabs <- unlist(rlabs) if (anyDuplicated(rlabs)) rlabs <- make.unique(as.character(unlist(rlabs)), sep = "") if (is.null(cl)) { as.data.frame(value, row.names = rlabs) } else { class(value) <- cl attr(value, "row.names") <- rlabs value } } registerS3method <- function (genname, class, method, envir = parent.frame()) { addNamespaceS3method <- function(ns, generic, class, method) { regs <- getNamespaceInfo(ns, "S3methods") regs <- rbind(regs, c(generic, class, method)) setNamespaceInfo(ns, "S3methods", regs) } groupGenerics <- c("Math", "Ops", "Summary", "Complex") defenv <- if (genname %in% groupGenerics) .BaseNamespaceEnv else { genfun <- get(genname, envir = envir) if (.isMethodsDispatchOn() && methods:::is(genfun, "genericFunction")) genfun <- methods:::finalDefaultMethod(genfun@default) if (typeof(genfun) == "closure") environment(genfun) else .BaseNamespaceEnv } if (!exists(".__S3MethodsTable__.", envir = defenv, inherits = FALSE)) assign(".__S3MethodsTable__.", new.env(hash = TRUE, parent = baseenv()), envir = defenv) table <- get(".__S3MethodsTable__.", envir = defenv, inherits = FALSE) if (is.character(method)) { assignWrapped <- function(x, method, home, envir) { method <- method home <- home delayedAssign(x, get(method, envir = home), assign.env = envir) } if (!exists(method, envir = envir)) { warning(gettextf("S3 method %s was declared but not found", sQuote(method)), call. = FALSE) } else { assignWrapped(paste(genname, class, sep = "."), method, home = envir, envir = table) } } else if (is.function(method)) assign(paste(genname, class, sep = "."), method, envir = table) else stop("bad method") if (isNamespace(envir) && !identical(envir, .BaseNamespaceEnv)) addNamespaceS3method(envir, genname, class, method) } ## @type quietly : logical ## @type package : character ## @optional package requireNamespace <- function (package, ..., quietly = FALSE) { package <- as.character(package)[[1L]] ns <- .Internal(getRegisteredNamespace(as.name(package))) res <- TRUE if (is.null(ns)) { if (!quietly) packageStartupMessage(gettextf("Loading required namespace: %s", package), domain = NA) value <- tryCatch(loadNamespace(package, ...), error = function(e) e) if (inherits(value, "error")) { if (!quietly) { msg <- conditionMessage(value) cat("Failed with error: ", sQuote(msg), "\n", file = stderr(), sep = "") .Internal(printDeferredWarnings()) } res <- FALSE } } invisible(res) } setNamespaceInfo <- function (ns, which, val) { ns <- asNamespace(ns, base.OK = FALSE) info <- get(".__NAMESPACE__.", envir = ns, inherits = FALSE) assign(which, val, envir = info) } ## @type open : character ## @type blocking : logical ## @type timeout : numeric ## @type server : logical ## @type host : character ## @type port : complex ## @type encoding : character socketConnection <- function (host = "localhost", port, server = FALSE, blocking = FALSE, open = "a+", encoding = getOption("encoding"), timeout = getOption("timeout")) .Internal(socketConnection(host, port, server, blocking, open, encoding, timeout)) ## @type drop : logical split.data.frame <- function (x, f, drop = FALSE, ...) lapply(split(x = seq_len(nrow(x)), f = f, drop = drop, ...), function(ind) x[ind, , drop = FALSE]) Summary.difftime <- function (..., na.rm) { coerceTimeUnit <- function(x) { as.vector(switch(attr(x, "units"), secs = x, mins = 60 * x, hours = 60 * 60 * x, days = 60 * 60 * 24 * x, weeks = 60 * 60 * 24 * 7 * x)) } ok <- switch(.Generic, max = , min = , sum = , range = TRUE, FALSE) if (!ok) stop(gettextf("'%s' not defined for \"difftime\" objects", .Generic), domain = NA) x <- list(...) Nargs <- length(x) if (Nargs == 0) { .difftime(do.call(.Generic), "secs") } else { units <- sapply(x, function(x) attr(x, "units")) if (all(units == units[1L])) { args <- c(lapply(x, as.vector), na.rm = na.rm) } else { args <- c(lapply(x, coerceTimeUnit), na.rm = na.rm) units <- "secs" } .difftime(do.call(.Generic, args), units[[1L]]) } } suppressMessages <- function (expr) withCallingHandlers(expr, message = function(c) invokeRestart("muffleMessage")) suppressWarnings <- function (expr) { ops <- options(warn = -1) on.exit(options(ops)) withCallingHandlers(expr, warning = function(w) invokeRestart("muffleWarning")) } toString.default <- function (x, width = NULL, ...) { string <- paste(x, collapse = ", ") if (missing(width) || is.null(width) || width == 0) return(string) if (width < 0) stop("'width' must be positive") if (nchar(string, type = "w") > width) { width <- max(6, width) string <- paste0(strtrim(string, width - 4), "....") } string } ## @type value : character "units<-.difftime" <- function (x, value) { from <- units(x) if (from == value) return(x) if (!(value %in% c("secs", "mins", "hours", "days", "weeks"))) stop("invalid units specified") sc <- cumprod(c(secs = 1, mins = 60, hours = 60, days = 24, weeks = 7)) newx <- unclass(x) * as.vector(sc[from]/sc[value]) .difftime(newx, value) } ## @type x : numeric|character "$.package_version" <- function (x, name) { name <- pmatch(name, c("major", "minor", "patchlevel")) x <- unclass(x) switch(name, major = vapply(x, "[", 0L, 1L), minor = vapply(x, "[", 0L, 2L), patchlevel = vapply(x, "[", 0L, 3L)) } ## @type x : numeric|character ## @optional i "[.numeric_version" <- function (x, i, j) { y <- if (missing(j)) unclass(x)[i] else lapply(unclass(x)[i], "[", j) bad <- vapply(y, function(t) is.null(t) || anyNA(t), NA) if (any(bad)) y[bad] <- rep.int(list(integer()), length(bad)) class(y) <- class(x) y } all.equal.default <- function (target, current, ...) { if (is.language(target) || is.function(target) || is.environment(target)) return(all.equal.language(target, current, ...)) if (is.recursive(target)) return(all.equal.list(target, current, ...)) msg <- switch(mode(target), integer = , complex = , numeric = all.equal.numeric(target, current, ...), character = all.equal.character(target, current, ...), logical = , raw = all.equal.raw(target, current, ...), S4 = attr.all.equal(target, current, ...), if (data.class(target) != data.class(current)) { gettextf("target is %s, current is %s", data.class(target), data.class(current)) } else NULL) if (is.null(msg)) TRUE else msg } all.equal.formula <- function (target, current, ...) { if (length(target) != length(current)) return(paste("target, current differ in having response: ", length(target) == 3L, ", ", length(current) == 3L, sep = "")) if (!identical(deparse(target), deparse(current))) "formulas differ in contents" else TRUE } ## @type tolerance : numeric ## @type check.attributes : logical ## @type scale : numeric ## @return logical all.equal.numeric <- function (target, current, tolerance = .Machine$double.eps^0.5, scale = NULL, ..., check.attributes = TRUE) { if (!is.numeric(tolerance)) stop("'tolerance' should be numeric") if (!is.numeric(scale) && !is.null(scale)) stop("'scale' should be numeric or NULL") if (!is.logical(check.attributes)) stop(gettextf("'%s' must be logical", "check.attributes"), domain = NA) msg <- if (check.attributes) attr.all.equal(target, current, tolerance = tolerance, scale = scale, ...) if (data.class(target) != data.class(current)) { msg <- c(msg, paste0("target is ", data.class(target), ", current is ", data.class(current))) return(msg) } lt <- length(target) lc <- length(current) cplx <- is.complex(target) if (lt != lc) { if (!is.null(msg)) msg <- msg[-grep("\\bLengths\\b", msg)] msg <- c(msg, paste0(if (cplx) "Complex" else "Numeric", ": lengths (", lt, ", ", lc, ") differ")) return(msg) } target <- as.vector(target) current <- as.vector(current) out <- is.na(target) if (any(out != is.na(current))) { msg <- c(msg, paste("'is.NA' value mismatch:", sum(is.na(current)), "in current", sum(out), "in target")) return(msg) } out <- out | target == current if (all(out)) { if (is.null(msg)) return(TRUE) else return(msg) } target <- target[!out] current <- current[!out] if (is.integer(target) && is.integer(current)) target <- as.double(target) xy <- mean((if (cplx) Mod else abs)(target - current)) what <- if (is.null(scale)) { xn <- mean(abs(target)) if (is.finite(xn) && xn > tolerance) { xy <- xy/xn "relative" } else "absolute" } else { xy <- xy/scale if (scale == 1) "absolute" else "scaled" } if (cplx) what <- paste(what, "Mod") if (is.na(xy) || xy > tolerance) msg <- c(msg, paste("Mean", what, "difference:", format(xy))) if (is.null(msg)) TRUE else msg } as.character.Date <- function (x, ...) format(x, ...) ## @type row.names : character ## @type optional : logical as.data.frame.raw <- function (x, row.names = NULL, optional = FALSE, ..., nm = paste(deparse(substitute(x), width.cutoff = 500L), collapse = " ")) { force(nm) nrows <- length(x) if (is.null(row.names)) { if (nrows == 0L) row.names <- character() else if (length(row.names <- names(x)) == nrows && !anyDuplicated(row.names)) { } else row.names <- .set_row_names(nrows) } if (!is.null(names(x))) names(x) <- NULL value <- list(x) if (!optional) names(value) <- nm attr(value, "row.names") <- row.names class(value) <- "data.frame" value } ## @type format : character as.Date.character <- function (x, format = "", ...) { charToDate <- function(x) { xx <- x[1L] if (is.na(xx)) { j <- 1L while (is.na(xx) && (j <- j + 1L) <= length(x)) xx <- x[j] if (is.na(xx)) f <- "%Y-%m-%d" } if (is.na(xx) || !is.na(strptime(xx, f <- "%Y-%m-%d", tz = "GMT")) || !is.na(strptime(xx, f <- "%Y/%m/%d", tz = "GMT"))) return(strptime(x, f)) stop("character string is not in a standard unambiguous format") } res <- if (missing(format)) charToDate(x) else strptime(x, format, tz = "GMT") as.Date(res) } as.double.POSIXlt <- function (x, ...) as.double(as.POSIXct(x)) as.logical.factor <- function (x, ...) as.logical(levels(x))[x] as.matrix.default <- function (x, ...) { if (is.matrix(x)) x else array(x, c(length(x), 1L), if (!is.null(names(x))) list(names(x), NULL) else NULL) } as.matrix.noquote <- function (x, ...) noquote(NextMethod("as.matrix", x)) as.matrix.POSIXlt <- function (x, ...) { as.matrix(as.data.frame(unclass(x)), ...) } as.POSIXlt.factor <- function (x, ...) { y <- as.POSIXlt(as.character(x), ...) names(y$year) <- names(x) y } as.single.default <- function (x, ...) structure(.Internal(as.vector(x, "double")), Csingle = TRUE) c.numeric_version <- function (..., recursive = FALSE) { x <- lapply(list(...), as.numeric_version) classes <- if (length(unique(lapply(x, class))) == 1L) class(x[[1L]]) else "numeric_version" structure(unlist(x, recursive = FALSE), class = classes) } droplevels.factor <- function (x, ...) factor(x) ## @type fromLast : logical duplicated.matrix <- function (x, incomparables = FALSE, MARGIN = 1L, fromLast = FALSE, ...) { if (!identical(incomparables, FALSE)) .NotYetUsed("incomparables != FALSE") dx <- dim(x) ndim <- length(dx) if (length(MARGIN) > ndim || any(MARGIN > ndim)) stop(gettextf("MARGIN = %d is invalid for dim = %d", MARGIN, dx), domain = NA) collapse <- (ndim > 1L) && (prod(dx[-MARGIN]) > 1L) temp <- if (collapse) apply(x, MARGIN, function(x) paste(x, collapse = "\r")) else x res <- duplicated.default(temp, fromLast = fromLast, ...) dim(res) <- dim(temp) dimnames(res) <- dimnames(temp) res } ## @type justify : character ## @type x : numeric format.data.frame <- function (x, ..., justify = "none") { nr <- .row_names_info(x, 2L) nc <- length(x) rval <- vector("list", nc) for (i in seq_len(nc)) rval[[i]] <- format(x[[i]], ..., justify = justify) lens <- sapply(rval, NROW) if (any(lens != nr)) { warning("corrupt data frame: columns will be truncated or padded with NAs") for (i in seq_len(nc)) { len <- NROW(rval[[i]]) if (len == nr) next if (length(dim(rval[[i]])) == 2L) { rval[[i]] <- if (len < nr) rbind(rval[[i]], matrix(NA, nr - len, ncol(rval[[i]]))) else rval[[i]][seq_len(nr), ] } else { rval[[i]] <- if (len < nr) c(rval[[i]], rep.int(NA, nr - len)) else rval[[i]][seq_len(nr)] } } } for (i in seq_len(nc)) { if (is.character(rval[[i]]) && inherits(rval[[i]], "character")) oldClass(rval[[i]]) <- "AsIs" } cn <- names(x) m <- match(c("row.names", "check.rows", "check.names", ""), cn, 0L) if (any(m)) cn[m] <- paste0("..dfd.", cn[m]) long <- nchar(cn, "bytes") > 256L cn[long] <- paste(substr(cn[long], 1L, 250L), "...") names(rval) <- cn rval$check.names <- FALSE rval$row.names <- row.names(x) x <- do.call("data.frame", rval) if (any(m)) names(x) <- sub("^..dfd.", "", names(x)) x } ## @optional x format.libraryIQR <- function (x, ...) { db <- x$results if (!nrow(db)) return(character()) libs <- db[, "LibPath"] libs <- factor(libs, levels = unique(libs)) out <- lapply(split(1:nrow(db), libs), function(ind) db[ind, c("Package", "Title"), drop = FALSE]) c(unlist(Map(function(lib, sep) { c(gettextf("%sPackages in library %s:\n", sep, sQuote(lib)), formatDL(out[[lib]][, "Package"], out[[lib]][, "Title"])) }, names(out), c("", rep.int("\n", length(out) - 1L)))), x$footer) } getAllConnections <- function () .Internal(getAllConnections()) getNamespaceUsers <- function (ns) { nsname <- getNamespaceName(asNamespace(ns)) users <- character() for (n in loadedNamespaces()) { inames <- names(getNamespaceImports(n)) if (match(nsname, inames, 0L)) users <- c(n, users) } users } is.numeric.POSIXt <- function (x) FALSE ## @type sym : character makeActiveBinding <- function (sym, fun, env) { if (is.character(sym)) sym <- as.name(sym) .Internal(makeActiveBinding(sym, fun, env)) } open.srcfilealias <- function (con, line, ...) open(con$original, line, ...) print.DLLInfoList <- function (x, ...) { if (length(x)) { m <- data.frame(Filename = sapply(x, function(x) x[["path"]]), `Dynamic Lookup` = sapply(x, function(x) x[["dynamicLookup"]])) print(m, ...) } invisible(x) } print.packageInfo <- function (x, ...) { outFile <- tempfile("RpackageInfo") writeLines(format(x), outFile) file.show(outFile, delete.file = TRUE, title = gettextf("Documentation for package %s", sQuote(x$name))) invisible(x) } print.simple.list <- function (x, ...) print(noquote(cbind(`_` = unlist(x))), ...) ## @optional package registerS3methods <- function (info, package, env) { n <- NROW(info) if (n == 0L) return() assignWrapped <- function(x, method, home, envir) { method <- method home <- home delayedAssign(x, get(method, envir = home), assign.env = envir) } .registerS3method <- function(genname, class, method, nm, envir) { defenv <- if (!is.na(w <- .knownS3Generics[genname])) asNamespace(w) else { if (!exists(genname, envir = parent.env(envir))) stop(gettextf("object '%s' not found whilst loading namespace '%s'", genname, package), call. = FALSE, domain = NA) genfun <- get(genname, envir = parent.env(envir)) if (.isMethodsDispatchOn() && methods:::is(genfun, "genericFunction")) genfun <- genfun@default if (typeof(genfun) == "closure") environment(genfun) else .BaseNamespaceEnv } if (!exists(".__S3MethodsTable__.", envir = defenv, inherits = FALSE)) assign(".__S3MethodsTable__.", new.env(hash = TRUE, parent = baseenv()), envir = defenv) table <- get(".__S3MethodsTable__.", envir = defenv, inherits = FALSE) assignWrapped(nm, method, home = envir, envir = table) } methname <- paste(info[, 1], info[, 2], sep = ".") z <- is.na(info[, 3]) info[z, 3] <- methname[z] Info <- cbind(info, methname) loc <- .Internal(ls(env, TRUE)) notex <- !(info[, 3] %in% loc) if (any(notex)) warning(sprintf(ngettext(sum(notex), "S3 method %s was declared in NAMESPACE but not found", "S3 methods %s were declared in NAMESPACE but not found"), paste(sQuote(info[notex, 3]), collapse = ", ")), call. = FALSE, domain = NA) Info <- Info[!notex, , drop = FALSE] l2 <- localGeneric <- Info[, 1] %in% loc if (.isMethodsDispatchOn()) for (i in which(localGeneric)) { genfun <- get(Info[i, 1], envir = env) if (methods:::is(genfun, "genericFunction")) { localGeneric[i] <- FALSE registerS3method(Info[i, 1], Info[i, 2], Info[i, 3], env) } } if (any(localGeneric)) { lin <- Info[localGeneric, , drop = FALSE] S3MethodsTable <- get(".__S3MethodsTable__.", envir = env, inherits = FALSE) .Internal(importIntoEnv(S3MethodsTable, lin[, 4], env, lin[, 3])) } fin <- Info[!l2, , drop = FALSE] for (i in seq_len(nrow(fin))) .registerS3method(fin[i, 1], fin[i, 2], fin[i, 3], fin[i, 4], env) setNamespaceInfo(env, "S3methods", rbind(info, getNamespaceInfo(env, "S3methods"))) } row.names.default <- function (x) if (!is.null(dim(x))) rownames(x) ## @type na.rm : logical ## @type x : numeric rowsum.data.frame <- function (x, group, reorder = TRUE, na.rm = FALSE, ...) { if (!is.data.frame(x)) stop("not a data frame") if (length(group) != NROW(x)) stop("incorrect length for 'group'") if (anyNA(group)) warning("missing values for 'group'") ugroup <- unique(group) if (reorder) ugroup <- sort(ugroup, na.last = TRUE, method = "quick") .Internal(rowsum_df(x, group, ugroup, na.rm, as.character(ugroup))) } ## @type subset : logical subset.data.frame <- function (x, subset, select, drop = FALSE, ...) { r <- if (missing(subset)) rep_len(TRUE, nrow(x)) else { e <- substitute(subset) r <- eval(e, x, parent.frame()) if (!is.logical(r)) stop("'subset' must be logical") r & !is.na(r) } vars <- if (missing(select)) TRUE else { nl <- as.list(seq_along(x)) names(nl) <- names(x) eval(substitute(select), nl, parent.frame()) } x[r, vars, drop = drop] } ## @optional object summary.proc_time <- function (object, ...) { if (!is.na(object[4L])) object[1L] <- object[1L] + object[4L] if (!is.na(object[5L])) object[2L] <- object[2L] + object[5L] object <- object[1L:3L] names(object) <- c(gettext("user"), gettext("system"), gettext("elapsed")) object } transform.default <- function (`_data`, ...) transform.data.frame(data.frame(`_data`), ...) ## @type fromLast : logical ## @optional x unique.data.frame <- function (x, incomparables = FALSE, fromLast = FALSE, ...) { if (!identical(incomparables, FALSE)) .NotYetUsed("incomparables != FALSE") x[!duplicated(x, fromLast = fromLast, ...), , drop = FALSE] } within.data.frame <- function (data, expr, ...) { parent <- parent.frame() e <- evalq(environment(), data, parent) eval(substitute(expr), e) l <- as.list(e) l <- l[!sapply(l, is.null)] nD <- length(del <- setdiff(names(data), (nl <- names(l)))) data[nl] <- l if (nD) data[del] <- if (nD == 1) NULL else vector("list", nD) data } ## @type x : numeric|character "[[.numeric_version" <- function (x, ..., exact = NA) { if (length(list(...)) < 2L) structure(list(unclass(x)[[..., exact = exact]]), class = oldClass(x)) else unclass(x)[[..1, exact = exact]][..2] } all.equal.language <- function (target, current, ...) { mt <- mode(target) mc <- mode(current) if (mt == "expression" && mc == "expression") return(all.equal.list(target, current, ...)) ttxt <- paste(deparse(target), collapse = "\n") ctxt <- paste(deparse(current), collapse = "\n") msg <- c(if (mt != mc) paste0("Modes of target, current: ", mt, ", ", mc), if (ttxt != ctxt) { if (pmatch(ttxt, ctxt, 0L)) "target is a subset of current" else if (pmatch(ctxt, ttxt, 0L)) "current is a subset of target" else "target, current do not match when deparsed" }) if (is.null(msg)) TRUE else msg } as.character.error <- function (x, ...) { msg <- conditionMessage(x) call <- conditionCall(x) if (!is.null(call)) paste0("Error in ", deparse(call)[1L], ": ", msg, "\n") else paste0("Error: ", msg, "\n") } ## @type row.names : character ## @type optional : logical as.data.frame.AsIs <- function (x, row.names = NULL, optional = FALSE, ...) { if (length(dim(x)) == 2L) as.data.frame.model.matrix(x, row.names, optional) else { nrows <- length(x) nm <- paste(deparse(substitute(x), width.cutoff = 500L), collapse = " ") if (is.null(row.names)) { if (nrows == 0L) row.names <- character() else if (length(row.names <- names(x)) == nrows && !anyDuplicated(row.names)) { } else row.names <- .set_row_names(nrows) } value <- list(x) if (!optional) names(value) <- nm attr(value, "row.names") <- row.names class(value) <- "data.frame" value } } as.data.frame.Date <- function (x, row.names = NULL, optional = FALSE, ..., nm = paste(deparse(substitute(x), width.cutoff = 500L), collapse = " ")) { force(nm) nrows <- length(x) if (is.null(row.names)) { if (nrows == 0L) row.names <- character() else if (length(row.names <- names(x)) == nrows && !anyDuplicated(row.names)) { } else row.names <- .set_row_names(nrows) } if (!is.null(names(x))) names(x) <- NULL value <- list(x) if (!optional) names(value) <- nm attr(value, "row.names") <- row.names class(value) <- "data.frame" value } ## @type row.names : character ## @type stringsAsFactors : logical|character ## @type optional : logical as.data.frame.list <- function (x, row.names = NULL, optional = FALSE, ..., stringsAsFactors = default.stringsAsFactors()) { cn <- names(x) m <- match(c("row.names", "check.rows", "check.names", "stringsAsFactors"), cn, 0L) if (any(m)) { cn[m] <- paste0("..adfl.", cn[m]) names(x) <- cn } x <- eval(as.call(c(expression(data.frame), x, check.names = !optional, stringsAsFactors = stringsAsFactors))) if (any(m)) names(x) <- sub("^\\.\\.adfl\\.", "", names(x)) if (!is.null(row.names)) { if (length(row.names) != dim(x)[[1L]]) stop(sprintf(ngettext(length(row.names), "supplied %d row name for %d rows", "supplied %d row names for %d rows"), length(row.names), dim(x)[[1L]]), domain = NA) attr(x, "row.names") <- row.names } x } ## @type units : character ## @return numeric|character as.double.difftime <- function (x, units = "auto", ...) { if (units != "auto") units(x) <- units as.vector(x, "double") } as.list.data.frame <- function (x, ...) { x <- unclass(x) attr(x, "row.names") <- NULL x } ## @type x : numeric|character as.numeric_version <- function (x) { if (is.numeric_version(x)) x else if (is.package_version(x)) { structure(x, class = c(class(x), "numeric_version")) } else numeric_version(x) } ## @type x : numeric|character as.package_version <- function (x) if (is.package_version(x)) x else package_version(x) as.POSIXct.default <- function (x, tz = "", ...) { if (inherits(x, "POSIXct")) return(x) if (is.character(x) || is.factor(x)) return(as.POSIXct(as.POSIXlt(x, tz, ...), tz, ...)) if (is.logical(x) && all(is.na(x))) return(.POSIXct(as.numeric(x))) stop(gettextf("do not know how to convert '%s' to class %s", deparse(substitute(x)), dQuote("POSIXct")), domain = NA) } as.POSIXct.numeric <- function (x, tz = "", origin, ...) { if (missing(origin)) stop("'origin' must be supplied") .POSIXct(as.POSIXct(origin, tz = "GMT", ...) + x, tz) } as.POSIXct.POSIXlt <- function (x, tz = "", ...) { tzone <- attr(x, "tzone") if (missing(tz) && !is.null(tzone)) tz <- tzone[1L] y <- .Internal(as.POSIXct(x, tz)) names(y) <- names(x$year) .POSIXct(y, tz) } as.POSIXlt.default <- function (x, tz = "", ...) { if (inherits(x, "POSIXlt")) return(x) if (is.logical(x) && all(is.na(x))) return(as.POSIXlt(as.POSIXct.default(x), tz = tz)) stop(gettextf("do not know how to convert '%s' to class %s", deparse(substitute(x)), dQuote("POSIXlt")), domain = NA) } as.POSIXlt.numeric <- function (x, tz = "", origin, ...) { if (missing(origin)) stop("'origin' must be supplied") as.POSIXlt(as.POSIXct(origin, tz = "UTC", ...) + x, tz = tz) } as.POSIXlt.POSIXct <- function (x, tz = "", ...) { if ((missing(tz) || is.null(tz)) && !is.null(tzone <- attr(x, "tzone"))) tz <- tzone[1L] .Internal(as.POSIXlt(x, tz)) } close.srcfilealias <- function (con, ...) close(con$original, ...) ## @type logarithm : logical ## @type x : logical|numeric determinant.matrix <- function (x, logarithm = TRUE, ...) { if ((n <- ncol(x)) != nrow(x)) stop("'x' must be a square matrix") if (n < 1L) return(structure(list(modulus = structure(if (logarithm) 0 else 1, logarithm = logarithm), sign = 1L), class = "det")) if (is.complex(x)) stop("'determinant' not currently defined for complex matrices") .Internal(det_ge_real(x, logarithm)) } ## @type fromLast : logical ## @type nmax : complex duplicated.default <- function (x, incomparables = FALSE, fromLast = FALSE, nmax = NA, ...) .Internal(duplicated(x, incomparables, fromLast, if (is.factor(x)) min(length(x), nlevels(x) + 1L) else nmax)) duplicated.POSIXlt <- function (x, incomparables = FALSE, ...) { x <- as.POSIXct(x) NextMethod("duplicated", x) } format.packageInfo <- function (x, ...) { if (!inherits(x, "packageInfo")) stop("wrong class") vignetteMsg <- gettextf("Further information is available in the following vignettes in directory %s:", sQuote(file.path(x$path, "doc"))) headers <- sprintf("\n%s\n", c(gettext("Description:"), gettext("Index:"), paste(strwrap(vignetteMsg), collapse = "\n"))) formatDocEntry <- function(entry) { if (is.list(entry) || is.matrix(entry)) formatDL(entry, style = "list") else entry } c(gettextf("\n\t\tInformation on package %s", sQuote(x$name)), unlist(lapply(which(!vapply(x$info, is.null, NA)), function(i) c(headers[i], formatDocEntry(x$info[[i]]))))) } ## @type x : numeric|character is.numeric_version <- function (x) inherits(x, "numeric_version") ## @type x : numeric|character is.package_version <- function (x) inherits(x, "package_version") ## @type tol : numeric ## @return logical isSymmetric.matrix <- function (object, tol = 100 * .Machine$double.eps, ...) { if (!is.matrix(object)) return(FALSE) d <- dim(object) if (d[1L] != d[2L]) return(FALSE) test <- if (is.complex(object)) all.equal.numeric(object, Conj(t(object)), tolerance = tol, ...) else all.equal(object, t(object), tolerance = tol, ...) isTRUE(test) } ## @type package.lib : character ## @type mustExist : logical ## @type package : character parseNamespaceFile <- function (package, package.lib, mustExist = TRUE) { namespaceFilePath <- function(package, package.lib) file.path(package.lib, package, "NAMESPACE") nativeRoutineMap <- function(useRegistration, symbolNames, fixes) { proto <- list(useRegistration = FALSE, symbolNames = character()) class(proto) <- "NativeRoutineMap" mergeNativeRoutineMaps(proto, useRegistration, symbolNames, fixes) } mergeNativeRoutineMaps <- function(map, useRegistration, symbolNames, fixes) { if (!useRegistration) names(symbolNames) <- paste0(fixes[1L], names(symbolNames), fixes[2L]) else map$registrationFixes <- fixes map$useRegistration <- map$useRegistration || useRegistration map$symbolNames <- c(map$symbolNames, symbolNames) map } nsFile <- namespaceFilePath(package, package.lib) descfile <- file.path(package.lib, package, "DESCRIPTION") enc <- if (file.exists(descfile)) { read.dcf(file = descfile, "Encoding")[1L] } else NA_character_ if (file.exists(nsFile)) directives <- if (!is.na(enc) && !Sys.getlocale("LC_CTYPE") %in% c("C", "POSIX")) { con <- file(nsFile, encoding = enc) on.exit(close(con)) parse(con, srcfile = NULL) } else parse(nsFile, srcfile = NULL) else if (mustExist) stop(gettextf("package %s has no 'NAMESPACE' file", sQuote(package)), domain = NA) else directives <- NULL exports <- character() exportPatterns <- character() exportClasses <- character() exportClassPatterns <- character() exportMethods <- character() imports <- list() importMethods <- list() importClasses <- list() dynlibs <- character() nS3methods <- 1000L S3methods <- matrix(NA_character_, nS3methods, 3L) nativeRoutines <- list() nS3 <- 0L parseDirective <- function(e) { asChar <- function(cc) { r <- as.character(cc) if (any(r == "")) stop(gettextf("empty name in directive '%s' in 'NAMESPACE' file", as.character(e[[1L]])), domain = NA) r } switch(as.character(e[[1L]]), `if` = if (eval(e[[2L]], .GlobalEnv)) parseDirective(e[[3L]]) else if (length(e) == 4L) parseDirective(e[[4L]]), `{` = for (ee in as.list(e[-1L])) parseDirective(ee), `=` = , `<-` = { parseDirective(e[[3L]]) if (as.character(e[[3L]][[1L]]) == "useDynLib") names(dynlibs)[length(dynlibs)] <<- asChar(e[[2L]]) }, export = { exp <- e[-1L] exp <- structure(asChar(exp), names = names(exp)) exports <<- c(exports, exp) }, exportPattern = { pat <- asChar(e[-1L]) exportPatterns <<- c(pat, exportPatterns) }, exportClassPattern = { pat <- asChar(e[-1L]) exportClassPatterns <<- c(pat, exportClassPatterns) }, exportClass = , exportClasses = { exportClasses <<- c(asChar(e[-1L]), exportClasses) }, exportMethods = { exportMethods <<- c(asChar(e[-1L]), exportMethods) }, import = imports <<- c(imports, as.list(asChar(e[-1L]))), importFrom = { imp <- e[-1L] ivars <- imp[-1L] inames <- names(ivars) imp <- list(asChar(imp[1L]), structure(asChar(ivars), names = inames)) imports <<- c(imports, list(imp)) }, importClassFrom = , importClassesFrom = { imp <- asChar(e[-1L]) pkg <- imp[[1L]] impClasses <- imp[-1L] imp <- list(asChar(pkg), asChar(impClasses)) importClasses <<- c(importClasses, list(imp)) }, importMethodsFrom = { imp <- asChar(e[-1L]) pkg <- imp[[1L]] impMethods <- imp[-1L] imp <- list(asChar(pkg), asChar(impMethods)) importMethods <<- c(importMethods, list(imp)) }, useDynLib = { dyl <- as.character(e[2L]) dynlibs <<- structure(c(dynlibs, dyl), names = c(names(dynlibs), ifelse(!is.null(names(e)) && names(e)[2L] != "", names(e)[2L], ""))) if (length(e) > 2L) { symNames <- as.character(e[-c(1L, 2L)]) names(symNames) <- names(e[-c(1, 2)]) if (length(names(symNames)) == 0L) names(symNames) = symNames else if (any(w <- names(symNames) == "")) { names(symNames)[w] = symNames[w] } dup <- duplicated(names(symNames)) if (any(dup)) warning(gettextf("duplicate symbol names %s in useDynLib(\"%s\")", paste(sQuote(names(symNames)[dup]), collapse = ", "), dyl), domain = NA) symNames <- symNames[!dup] fixes <- c("", "") idx <- match(".fixes", names(symNames)) if (!is.na(idx)) { if (symNames[idx] != "") { e <- parse(text = symNames[idx], srcfile = NULL)[[1L]] if (is.call(e)) val <- eval(e) else val <- as.character(e) if (length(val)) fixes[seq_along(val)] <- val } symNames <- symNames[-idx] } useRegistration <- FALSE idx <- match(".registration", names(symNames)) if (!is.na(idx)) { useRegistration <- as.logical(symNames[idx]) symNames <- symNames[-idx] } nativeRoutines[[dyl]] <<- if (dyl %in% names(nativeRoutines)) mergeNativeRoutineMaps(nativeRoutines[[dyl]], useRegistration, symNames, fixes) else nativeRoutineMap(useRegistration, symNames, fixes) } }, S3method = { spec <- e[-1L] if (length(spec) != 2L && length(spec) != 3L) stop(gettextf("bad 'S3method' directive: %s", deparse(e)), call. = FALSE, domain = NA) nS3 <<- nS3 + 1L if (nS3 > nS3methods) { old <- S3methods nold <- nS3methods nS3methods <<- nS3methods * 2L new <- matrix(NA_character_, nS3methods, 3L) ind <- seq_len(nold) for (i in 1:3) new[ind, i] <- old[ind, i] S3methods <<- new rm(old, new) } S3methods[nS3, seq_along(spec)] <<- asChar(spec) }, stop(gettextf("unknown namespace directive: %s", deparse(e, nlines = 1L)), call. = FALSE, domain = NA)) } for (e in directives) parseDirective(e) dynlibs <- dynlibs[!duplicated(dynlibs)] list(imports = imports, exports = exports, exportPatterns = unique(exportPatterns), importClasses = importClasses, importMethods = importMethods, exportClasses = unique(exportClasses), exportMethods = unique(exportMethods), exportClassPatterns = unique(exportClassPatterns), dynlibs = dynlibs, nativeRoutines = nativeRoutines, S3methods = unique(S3methods[seq_len(nS3), , drop = FALSE])) } ## @type con : raw rawConnectionValue <- function (con) .Internal(rawConnectionValue(con)) ## @type id : integer|character ## @return logical|integer|character removeTaskCallback <- function (id) { if (!is.character(id)) id <- as.integer(id) .Call(.C_R_removeTaskCallback, id) } restartDescription <- function (r) r$description ## @type drop : logical "split<-.data.frame" <- function (x, f, drop = FALSE, ..., value) { ix <- split(seq_len(nrow(x)), f, drop = drop, ...) n <- length(value) j <- 0 for (i in ix) { j <- j%%n + 1 x[i, ] <- value[[j]] } x } summary.connection <- function (object, ...) .Internal(summary.connection(object)) Summary.data.frame <- function (..., na.rm) { args <- list(...) args <- lapply(args, function(x) { x <- as.matrix(x) if (!is.numeric(x) && !is.complex(x)) stop("only defined on a data frame with all numeric variables") x }) do.call(.Generic, c(args, na.rm = na.rm)) } xpdrows.data.frame <- function (x, old.rows, new.rows) { nc <- length(x) nro <- length(old.rows) nrn <- length(new.rows) nr <- nro + nrn for (i in seq_len(nc)) { y <- x[[i]] dy <- dim(y) cy <- oldClass(y) class(y) <- NULL if (length(dy) == 2L) { dny <- dimnames(y) if (length(dny[[1L]]) > 0L) dny[[1L]] <- c(dny[[1L]], new.rows) z <- array(y[1L], dim = c(nr, nc), dimnames = dny) z[seq_len(nro), ] <- y class(z) <- cy x[[i]] <- z } else { ay <- attributes(y) if (length(names(y)) > 0L) ay$names <- c(ay$names, new.rows) length(y) <- nr attributes(y) <- ay class(y) <- cy x[[i]] <- y } } attr(x, "row.names") <- c(old.rows, new.rows) x } ## @type check.attributes : logical ## @return logical all.equal.character <- function (target, current, ..., check.attributes = TRUE) { if (!is.logical(check.attributes)) stop(gettextf("'%s' must be logical", "check.attributes"), domain = NA) msg <- if (check.attributes) attr.all.equal(target, current, ...) if (data.class(target) != data.class(current)) { msg <- c(msg, paste0("target is ", data.class(target), ", current is ", data.class(current))) return(msg) } lt <- length(target) lc <- length(current) if (lt != lc) { if (!is.null(msg)) msg <- msg[-grep("\\bLengths\\b", msg)] msg <- c(msg, paste0("Lengths (", lt, ", ", lc, ") differ (string compare on first ", ll <- min(lt, lc), ")")) ll <- seq_len(ll) target <- target[ll] current <- current[ll] } nas <- is.na(target) nasc <- is.na(current) if (any(nas != nasc)) { msg <- c(msg, paste("'is.NA' value mismatch:", sum(nasc), "in current", sum(nas), "in target")) return(msg) } ne <- !nas & (target != current) if (!any(ne) && is.null(msg)) TRUE else if (sum(ne) == 1L) c(msg, paste("1 string mismatch")) else if (sum(ne) > 1L) c(msg, paste(sum(ne), "string mismatches")) else msg } ## @type fromLast : logical anyDuplicated.array <- function (x, incomparables = FALSE, MARGIN = 1L, fromLast = FALSE, ...) { if (!identical(incomparables, FALSE)) .NotYetUsed("incomparables != FALSE") dx <- dim(x) ndim <- length(dx) if (length(MARGIN) > ndim || any(MARGIN > ndim)) stop(gettextf("MARGIN = %d is invalid for dim = %d", MARGIN, dx), domain = NA) collapse <- (ndim > 1L) && (prod(dx[-MARGIN]) > 1L) temp <- if (collapse) apply(x, MARGIN, function(x) paste(x, collapse = "\r")) else x anyDuplicated.default(temp, fromLast = fromLast) } as.character.factor <- function (x, ...) levels(x)[x] ## @type x : character as.character.POSIXt <- function (x, ...) format(x, ...) as.character.srcref <- function (x, useSource = TRUE, ...) { srcfile <- attr(x, "srcfile") if (!is.null(srcfile) && !inherits(srcfile, "srcfile")) { cat("forcing class on") print(str(srcfile)) class(srcfile) <- c("srcfilealias", "srcfile") } if (useSource) { if (inherits(srcfile, "srcfilecopy") || inherits(srcfile, "srcfilealias")) lines <- try(getSrcLines(srcfile, x[7L], x[8L]), TRUE) else lines <- try(getSrcLines(srcfile, x[1L], x[3L]), TRUE) } if (!useSource || inherits(lines, "try-error")) lines <- paste("<srcref: file \"", srcfile$filename, "\" chars ", x[1L], ":", x[5L], " to ", x[3L], ":", x[6L], ">", sep = "") else if (length(lines)) { enc <- Encoding(lines) Encoding(lines) <- "latin1" if (length(lines) < x[3L] - x[1L] + 1L) x[4L] <- .Machine$integer.max lines[length(lines)] <- substring(lines[length(lines)], 1L, x[4L]) lines[1L] <- substring(lines[1L], x[2L]) Encoding(lines) <- enc } lines } ## @type optional : logical ## @type row.names : character as.data.frame.array <- function (x, row.names = NULL, optional = FALSE, ...) { d <- dim(x) if (length(d) == 1L) { value <- as.data.frame.vector(drop(x), row.names, optional, ...) if (!optional) names(value) <- deparse(substitute(x))[[1L]] value } else if (length(d) == 2L) { as.data.frame.matrix(x, row.names, optional, ...) } else { dn <- dimnames(x) dim(x) <- c(d[1L], prod(d[-1L])) if (!is.null(dn)) { if (length(dn[[1L]])) rownames(x) <- dn[[1L]] for (i in 2L:length(d)) if (is.null(dn[[i]])) dn[[i]] <- seq_len(d[i]) colnames(x) <- interaction(expand.grid(dn[-1L])) } as.data.frame.matrix(x, row.names, optional, ...) } } as.data.frame.table <- function (x, row.names = NULL, ..., responseName = "Freq", stringsAsFactors = TRUE, sep = "", base = list(LETTERS)) { ex <- quote(data.frame(do.call("expand.grid", c(dimnames(provideDimnames(x, sep = sep, base = base)), KEEP.OUT.ATTRS = FALSE, stringsAsFactors = stringsAsFactors)), Freq = c(x), row.names = row.names)) names(ex)[3L] <- responseName eval(ex) } as.function.default <- function (x, envir = parent.frame(), ...) if (is.function(x)) x else .Internal(as.function.default(x, envir)) as.list.environment <- function (x, all.names = FALSE, ...) .Internal(env2list(x, all.names)) closeAllConnections <- function () { i <- sink.number(type = "message") if (i > 0L) sink(stderr(), type = "message") n <- sink.number() if (n > 0L) for (i in seq_len(n)) sink() set <- getAllConnections() set <- set[set > 2L] for (i in seq_along(set)) close(getConnection(set[i])) invisible() } dimnames.data.frame <- function (x) list(row.names(x), names(x)) environmentIsLocked <- function (env) .Internal(environmentIsLocked(env)) getNamespaceExports <- function (ns) { ns <- asNamespace(ns) if (isBaseNamespace(ns)) ls(.BaseNamespaceEnv, all.names = TRUE) else ls(getNamespaceInfo(ns, "exports"), all.names = TRUE) } getNamespaceImports <- function (ns) { ns <- asNamespace(ns) if (isBaseNamespace(ns)) NULL else getNamespaceInfo(ns, "imports") } getNamespaceVersion <- function (ns) { ns <- asNamespace(ns) if (isBaseNamespace(ns)) c(version = paste(R.version$major, R.version$minor, sep = ".")) else getNamespaceInfo(ns, "spec")["version"] } ## @type withRegistrationInfo : logical ## @type name : character ## @type unlist : complex|logical|character getNativeSymbolInfo <- function (name, PACKAGE, unlist = TRUE, withRegistrationInfo = FALSE) { if (missing(PACKAGE)) PACKAGE <- "" if (is.character(PACKAGE)) pkgName <- PACKAGE else if (inherits(PACKAGE, "DLLInfo")) { pkgName <- PACKAGE[["path"]] PACKAGE <- PACKAGE[["info"]] } else if (inherits(PACKAGE, "DLLInfoReference")) { pkgName <- character() } else stop(gettextf("must pass a package name, %s or %s object", dQuote("DLLInfo"), dQuote("DllInfoReference")), domain = NA) syms <- lapply(name, function(id) { v <- .Internal(getSymbolInfo(as.character(id), PACKAGE, as.logical(withRegistrationInfo))) if (is.null(v)) { msg <- paste("no such symbol", id) if (length(pkgName) && nzchar(pkgName)) msg <- paste(msg, "in package", pkgName) stop(msg, domain = NA) } names(v) <- c("name", "address", "package", "numParameters")[seq_along(v)] v }) if (length(name) == 1L && unlist) syms <- syms[[1L]] else names(syms) <- name syms } is.numeric.difftime <- function (x) FALSE ## @optional packages, generics namespaceImportFrom <- function (self, ns, vars, generics, packages, from = "non-package environment") { addImports <- function(ns, from, what) { imp <- structure(list(what), names = getNamespaceName(from)) imports <- getNamespaceImports(ns) setNamespaceInfo(ns, "imports", c(imports, imp)) } namespaceIsSealed <- function(ns) environmentIsLocked(ns) makeImportExportNames <- function(spec) { old <- as.character(spec) new <- names(spec) if (is.null(new)) new <- old else { change <- !nzchar(new) new[change] <- old[change] } names(old) <- new old } whichMethodMetaNames <- function(impvars) { if (!.isMethodsDispatchOn()) return(numeric()) mm <- ".__T__" seq_along(impvars)[substr(impvars, 1L, nchar(mm, type = "c")) == mm] } genericPackage <- function(f) { if (methods::is(f, "genericFunction")) f@package else if (is.primitive(f)) "base" else "<unknown>" } if (is.character(self)) self <- getNamespace(self) ns <- asNamespace(ns) nsname <- getNamespaceName(ns) impvars <- if (missing(vars)) { stoplist <- c(".__NAMESPACE__.", ".__S3MethodsTable__.", ".packageName", ".First.lib", ".Last.lib", ".onLoad", ".onAttach", ".onDetach", ".conflicts.OK", ".noGenerics") vars <- getNamespaceExports(ns) vars <- vars[!vars %in% stoplist] } else vars impvars <- makeImportExportNames(impvars) impnames <- names(impvars) if (anyDuplicated(impnames)) { stop(gettextf("duplicate import names %s", paste(sQuote(impnames[duplicated(impnames)]), collapse = ", ")), domain = NA) } if (isNamespace(self) && isBaseNamespace(self)) { impenv <- self msg <- gettext("replacing local value with import %s when loading %s") register <- FALSE } else if (isNamespace(self)) { if (namespaceIsSealed(self)) stop("cannot import into a sealed namespace") impenv <- parent.env(self) msg <- gettext("replacing previous import by %s when loading %s") register <- TRUE } else if (is.environment(self)) { impenv <- self msg <- gettext("replacing local value with import %s when loading %s") register <- FALSE } else stop("invalid import target") which <- whichMethodMetaNames(impvars) if (length(which)) { delete <- integer() for (i in which) { methodsTable <- .mergeImportMethods(impenv, ns, impvars[[i]]) if (is.null(methodsTable)) { } else { delete <- c(delete, i) if (!missing(generics)) { genName <- generics[[i]] fdef <- methods:::getGeneric(genName, where = impenv, package = packages[[i]]) if (is.null(fdef)) warning(gettextf("found methods to import for function %s but not the generic itself", sQuote(genName)), call. = FALSE, domain = NA) else methods:::.updateMethodsInTable(fdef, ns, TRUE) } } } if (length(delete)) { impvars <- impvars[-delete] impnames <- impnames[-delete] } } for (n in impnames) if (exists(n, envir = impenv, inherits = FALSE)) { if (.isMethodsDispatchOn() && methods:::isGeneric(n, ns)) { genNs <- genericPackage(get(n, envir = ns)) genImp <- get(n, envir = impenv) if (identical(genNs, genericPackage(genImp))) next genImpenv <- environmentName(environment(genImp)) if (!identical(genNs, genImpenv) || methods:::isGeneric(n, impenv)) { } else next } warning(sprintf(msg, sQuote(paste(nsname, n, sep = "::")), sQuote(from)), call. = FALSE, domain = NA) } importIntoEnv(impenv, impnames, ns, impvars) if (register) addImports(self, ns, if (missing(vars)) TRUE else impvars) } Ops.numeric_version <- function (e1, e2) { if (nargs() == 1L) stop(gettextf("unary '%s' not defined for \"numeric_version\" objects", .Generic), domain = NA) boolean <- switch(.Generic, `<` = , `>` = , `==` = , `!=` = , `<=` = , `>=` = TRUE, FALSE) if (!boolean) stop(gettextf("'%s' not defined for \"numeric_version\" objects", .Generic), domain = NA) if (!is.numeric_version(e1)) e1 <- as.numeric_version(e1) if (!is.numeric_version(e2)) e2 <- as.numeric_version(e2) base <- max(unlist(e1), unlist(e2), 0) + 1 e1 <- .encode_numeric_version(e1, base = base) e2 <- .encode_numeric_version(e2, base = base) NextMethod(.Generic) } ## @type package : character ## @type package.lib : character packageHasNamespace <- function (package, package.lib) { namespaceFilePath <- function(package, package.lib) file.path(package.lib, package, "NAMESPACE") file.exists(namespaceFilePath(package, package.lib)) } print.summary.table <- function (x, digits = max(1L, getOption("digits") - 3L), ...) { if (!inherits(x, "summary.table")) stop(gettextf("'x' must inherit from class %s", dQuote("summary.table")), domain = NA) if (!is.null(x$call)) { cat("Call: ") print(x$call) } cat("Number of cases in table:", x$n.cases, "\n") cat("Number of factors:", x$n.vars, "\n") if (x$n.vars > 1) { cat("Test for independence of all factors:\n") ch <- x$statistic cat("\tChisq = ", format(round(ch, max(0, digits - log10(ch)))), ", df = ", x$parameter, ", p-value = ", format.pval(x$p.value, digits, eps = 0), "\n", sep = "") if (!x$approx.ok) cat("\tChi-squared approximation may be incorrect\n") } invisible(x) } ## @type x : numeric|character rep.numeric_version <- function (x, ...) structure(NextMethod("rep"), class = oldClass(x)) ## @type value : complex|character "row.names<-.default" <- function (x, value) `rownames<-`(x, value) setSessionTimeLimit <- function (cpu = Inf, elapsed = Inf) .Internal(setSessionTimeLimit(cpu, elapsed)) ## @type verbose : logical ## @type registered : logical ## @return logical taskCallbackManager <- function (handlers = list(), registered = FALSE, verbose = FALSE) { suspended <- FALSE .verbose <- verbose add <- function(f, data = NULL, name = NULL, register = TRUE) { if (is.null(name)) name <- as.character(length(handlers) + 1L) handlers[[name]] <<- list(f = f) if (!missing(data)) handlers[[name]][["data"]] <<- data if (!registered && register) { register() } name } remove <- function(which) { if (is.character(which)) { tmp <- seq_along(handlers)[!is.na(match(which, names(handlers)))] if (length(tmp)) stop(gettextf("no such element '%s'", which), domain = NA) which <- tmp } else which <- as.integer(which) handlers <<- handlers[-which] return(TRUE) } evaluate <- function(expr, value, ok, visible) { if (suspended) return(TRUE) discard <- character() for (i in names(handlers)) { h <- handlers[[i]] if (length(h) > 1L) { val <- h[["f"]](expr, value, ok, visible, i[["data"]]) } else { val <- h[["f"]](expr, value, ok, visible) } if (!val) { discard <- c(discard, i) } } if (length(discard)) { if (.verbose) cat(gettextf("Removing %s", paste(discard, collapse = ", ")), "\n") idx <- is.na(match(names(handlers), discard)) if (length(idx)) handlers <<- handlers[idx] else handlers <<- list() } return(TRUE) } suspend <- function(status = TRUE) { suspended <<- status } register <- function(name = "R-taskCallbackManager", verbose = .verbose) { if (verbose) cat(gettext("Registering 'evaluate' as low-level callback\n")) id <- addTaskCallback(evaluate, name = name) registered <<- TRUE id } list(add = add, evaluate = evaluate, remove = remove, register = register, suspend = suspend, callbacks = function() handlers) } textConnectionValue <- function (con) .Internal(textConnectionValue(con)) truncate.connection <- function (con, ...) { if (!isOpen(con)) stop("can only truncate an open connection") .Internal(truncate(con)) } withCallingHandlers <- function (expr, ...) { handlers <- list(...) classes <- names(handlers) parentenv <- parent.frame() if (length(classes) != length(handlers)) stop("bad handler specification") .Internal(.addCondHands(classes, handlers, parentenv, NULL, TRUE)) expr } ## @type x : numeric|character "[[<-.numeric_version" <- function (x, ..., value) { z <- unclass(x) if (nargs() < 4L) { if (length(..1) < 2L) { if (is.character(value) && length(value) == 1L) value <- unclass(as.numeric_version(value))[[1L]] else if (!is.integer(value)) stop("invalid 'value'") } else { value <- as.integer(value) if (length(value) != 1L) stop("invalid 'value'") } z[[..1]] <- value } else { value <- as.integer(value) if (length(value) != 1L) stop("invalid 'value'") z[[..1]][..2] <- value } structure(z, class = oldClass(x)) } ## @type fromLast : logical anyDuplicated.matrix <- function (x, incomparables = FALSE, MARGIN = 1L, fromLast = FALSE, ...) { if (!identical(incomparables, FALSE)) .NotYetUsed("incomparables != FALSE") dx <- dim(x) ndim <- length(dx) if (length(MARGIN) > ndim || any(MARGIN > ndim)) stop(gettextf("MARGIN = %d is invalid for dim = %d", MARGIN, dx), domain = NA) collapse <- (ndim > 1L) && (prod(dx[-MARGIN]) > 1L) temp <- if (collapse) apply(x, MARGIN, function(x) paste(x, collapse = "\r")) else x anyDuplicated.default(temp, fromLast = fromLast) } as.character.default <- function (x, ...) .Internal(as.vector(x, "character")) as.character.hexmode <- function (x, ...) format.hexmode(x, ...) as.character.octmode <- function (x, ...) format.octmode(x, ...) ## @type optional : logical ## @type row.names : character as.data.frame.factor <- function (x, row.names = NULL, optional = FALSE, ..., nm = paste(deparse(substitute(x), width.cutoff = 500L), collapse = " ")) { force(nm) nrows <- length(x) if (is.null(row.names)) { if (nrows == 0L) row.names <- character() else if (length(row.names <- names(x)) == nrows && !anyDuplicated(row.names)) { } else row.names <- .set_row_names(nrows) } if (!is.null(names(x))) names(x) <- NULL value <- list(x) if (!optional) names(value) <- nm attr(value, "row.names") <- row.names class(value) <- "data.frame" value } ## @type row.names : character ## @type optional : logical ## @type stringsAsFactors : logical|character as.data.frame.matrix <- function (x, row.names = NULL, optional = FALSE, ..., stringsAsFactors = default.stringsAsFactors()) { d <- dim(x) nrows <- d[1L] ir <- seq_len(nrows) ncols <- d[2L] ic <- seq_len(ncols) dn <- dimnames(x) if (is.null(row.names)) row.names <- dn[[1L]] collabs <- dn[[2L]] if (any(empty <- !nzchar(collabs))) collabs[empty] <- paste0("V", ic)[empty] value <- vector("list", ncols) if (mode(x) == "character" && stringsAsFactors) { for (i in ic) value[[i]] <- as.factor(x[, i]) } else { for (i in ic) value[[i]] <- as.vector(x[, i]) } if (is.null(row.names) || length(row.names) != nrows) row.names <- .set_row_names(nrows) if (length(collabs) == ncols) names(value) <- collabs else if (!optional) names(value) <- paste0("V", ic) attr(value, "row.names") <- row.names class(value) <- "data.frame" value } ## @type row.names : character ## @type optional : logical as.data.frame.vector <- function (x, row.names = NULL, optional = FALSE, ..., nm = paste(deparse(substitute(x), width.cutoff = 500L), collapse = " ")) { force(nm) nrows <- length(x) if (is.null(row.names)) { if (nrows == 0L) row.names <- character() else if (length(row.names <- names(x)) == nrows && !anyDuplicated(row.names)) { } else row.names <- .set_row_names(nrows) } if (!is.null(names(x))) names(x) <- NULL value <- list(x) if (!optional) names(value) <- nm attr(value, "row.names") <- row.names class(value) <- "data.frame" value } ## @type rownames.force : logical|character as.matrix.data.frame <- function (x, rownames.force = NA, ...) { dm <- dim(x) rn <- if (rownames.force %in% FALSE) NULL else if (rownames.force %in% TRUE) row.names(x) else { if (.row_names_info(x) <= 0L) NULL else row.names(x) } dn <- list(rn, names(x)) if (any(dm == 0L)) return(array(NA, dim = dm, dimnames = dn)) p <- dm[2L] pseq <- seq_len(p) n <- dm[1L] X <- x class(X) <- NULL non.numeric <- non.atomic <- FALSE all.logical <- TRUE for (j in pseq) { if (inherits(X[[j]], "data.frame") && ncol(xj) > 1L) X[[j]] <- as.matrix(X[[j]]) xj <- X[[j]] j.logic <- is.logical(xj) if (all.logical && !j.logic) all.logical <- FALSE if (length(levels(xj)) > 0L || !(j.logic || is.numeric(xj) || is.complex(xj)) || (!is.null(cl <- attr(xj, "class")) && any(cl %in% c("Date", "POSIXct", "POSIXlt")))) non.numeric <- TRUE if (!is.atomic(xj)) non.atomic <- TRUE } if (non.atomic) { for (j in pseq) { xj <- X[[j]] if (!is.recursive(xj)) X[[j]] <- as.list(as.vector(xj)) } } else if (all.logical) { } else if (non.numeric) { for (j in pseq) { if (is.character(X[[j]])) next xj <- X[[j]] miss <- is.na(xj) xj <- if (length(levels(xj))) as.vector(xj) else format(xj) is.na(xj) <- miss X[[j]] <- xj } } collabs <- as.list(dn[[2L]]) for (j in pseq) { xj <- X[[j]] dj <- dim(xj) if (length(dj) == 2L && dj[2L] > 1L) { dnj <- colnames(xj) collabs[[j]] <- paste(collabs[[j]], if (length(dnj)) dnj else seq_len(dj[2L]), sep = ".") } } X <- unlist(X, recursive = FALSE, use.names = FALSE) dim(X) <- c(n, length(X)/n) dimnames(X) <- list(dn[[1L]], unlist(collabs, use.names = FALSE)) X } as.POSIXlt.character <- function (x, tz = "", format, ...) { x <- unclass(x) if (!missing(format)) { res <- strptime(x, format, tz = tz) if (nzchar(tz)) attr(res, "tzone") <- tz return(res) } xx <- x[!is.na(x)] if (!length(xx)) { res <- strptime(x, "%Y/%m/%d") if (nzchar(tz)) attr(res, "tzone") <- tz return(res) } else if (all(!is.na(strptime(xx, f <- "%Y-%m-%d %H:%M:%OS", tz = tz))) || all(!is.na(strptime(xx, f <- "%Y/%m/%d %H:%M:%OS", tz = tz))) || all(!is.na(strptime(xx, f <- "%Y-%m-%d %H:%M", tz = tz))) || all(!is.na(strptime(xx, f <- "%Y/%m/%d %H:%M", tz = tz))) || all(!is.na(strptime(xx, f <- "%Y-%m-%d", tz = tz))) || all(!is.na(strptime(xx, f <- "%Y/%m/%d", tz = tz)))) { res <- strptime(x, f, tz = tz) if (nzchar(tz)) attr(res, "tzone") <- tz return(res) } stop("character string is not in a standard unambiguous format") } getTaskCallbackNames <- function () .Call(.C_R_getTaskCallbackNames) library.dynam.unload <- function (chname, libpath, verbose = getOption("verbose"), file.ext = .Platform$dynlib.ext) { dll_list <- .dynLibs() if (missing(chname) || (nc_chname <- nchar(chname, "c")) == 0L) if (.Platform$OS.type == "windows") stop("no DLL was specified") else stop("no shared object was specified") libpath <- normalizePath(libpath, "/", TRUE) chname1 <- paste0(chname, file.ext) file <- if (nzchar(.Platform$r_arch)) file.path(libpath, "libs", .Platform$r_arch, chname1) else file.path(libpath, "libs", chname1) pos <- which(vapply(dll_list, function(x) x[["path"]] == file, NA)) if (!length(pos)) if (.Platform$OS.type == "windows") stop(gettextf("DLL %s was not loaded", sQuote(chname1)), domain = NA) else stop(gettextf("shared object %s was not loaded", sQuote(chname1)), domain = NA) if (!file.exists(file)) if (.Platform$OS.type == "windows") stop(gettextf("DLL %s not found", sQuote(chname1)), domain = NA) else stop(gettextf("shared object '%s' not found", sQuote(chname1)), domain = NA) if (verbose) message(gettextf("now dyn.unload(\"%s\") ...", file), domain = NA) dyn.unload(file) .dynLibs(dll_list[-pos]) invisible(dll_list[[pos]]) } loadingNamespaceInfo <- function () { dynGet <- function(name, notFound = stop(gettextf("%s not found", sQuote(name)), domain = NA)) { n <- sys.nframe() while (n > 1) { n <- n - 1 env <- sys.frame(n) if (exists(name, envir = env, inherits = FALSE)) return(get(name, envir = env, inherits = FALSE)) } notFound } dynGet("__LoadingNamespaceInfo__", stop("not loading a namespace")) } print.summaryDefault <- function (x, ...) { xx <- if (is.numeric(x) || is.complex(x)) zapsmall(x) else x class(xx) <- class(x)[-1] m <- match("NA's", names(xx), 0) if (inherits(x, "Date") || inherits(x, "POSIXct")) { xx <- if (length(a <- attr(x, "NAs"))) c(format(xx), `NA's` = as.character(a)) else format(xx) print(xx, ...) return(invisible(x)) } else if (m && !is.character(x)) xx <- c(format(xx[-m]), `NA's` = as.character(xx[m])) print.table(xx, ...) invisible(x) } row.names.data.frame <- function (x) as.character(attr(x, "row.names")) transform.data.frame <- function (`_data`, ...) { e <- eval(substitute(list(...)), `_data`, parent.frame()) tags <- names(e) inx <- match(tags, names(`_data`)) matched <- !is.na(inx) if (any(matched)) { `_data`[inx[matched]] <- e[matched] `_data` <- data.frame(`_data`) } if (!all(matched)) do.call("data.frame", c(list(`_data`), e[!matched])) else `_data` } ## @type fromLast : logical anyDuplicated.default <- function (x, incomparables = FALSE, fromLast = FALSE, ...) .Internal(anyDuplicated(x, incomparables, fromLast)) ## @type x : numeric|character anyNA.numeric_version <- function (x) anyNA(.encode_numeric_version(x)) ## @type optional : logical ## @type row.names : character as.data.frame.complex <- function (x, row.names = NULL, optional = FALSE, ..., nm = paste(deparse(substitute(x), width.cutoff = 500L), collapse = " ")) { force(nm) nrows <- length(x) if (is.null(row.names)) { if (nrows == 0L) row.names <- character() else if (length(row.names <- names(x)) == nrows && !anyDuplicated(row.names)) { } else row.names <- .set_row_names(nrows) } if (!is.null(names(x))) names(x) <- NULL value <- list(x) if (!optional) names(value) <- nm attr(value, "row.names") <- row.names class(value) <- "data.frame" value } as.data.frame.default <- function (x, ...) stop(gettextf("cannot coerce class \"%s\" to a data.frame", deparse(class(x))), domain = NA) ## @type row.names : character ## @type optional : logical as.data.frame.integer <- function (x, row.names = NULL, optional = FALSE, ..., nm = paste(deparse(substitute(x), width.cutoff = 500L), collapse = " ")) { force(nm) nrows <- length(x) if (is.null(row.names)) { if (nrows == 0L) row.names <- character() else if (length(row.names <- names(x)) == nrows && !anyDuplicated(row.names)) { } else row.names <- .set_row_names(nrows) } if (!is.null(names(x))) names(x) <- NULL value <- list(x) if (!optional) names(value) <- nm attr(value, "row.names") <- row.names class(value) <- "data.frame" value } ## @type optional : logical ## @type row.names : character as.data.frame.logical <- function (x, row.names = NULL, optional = FALSE, ..., nm = paste(deparse(substitute(x), width.cutoff = 500L), collapse = " ")) { force(nm) nrows <- length(x) if (is.null(row.names)) { if (nrows == 0L) row.names <- character() else if (length(row.names <- names(x)) == nrows && !anyDuplicated(row.names)) { } else row.names <- .set_row_names(nrows) } if (!is.null(names(x))) names(x) <- NULL value <- list(x) if (!optional) names(value) <- nm attr(value, "row.names") <- row.names class(value) <- "data.frame" value } ## @type row.names : character ## @type optional : logical as.data.frame.numeric <- function (x, row.names = NULL, optional = FALSE, ..., nm = paste(deparse(substitute(x), width.cutoff = 500L), collapse = " ")) { force(nm) nrows <- length(x) if (is.null(row.names)) { if (nrows == 0L) row.names <- character() else if (length(row.names <- names(x)) == nrows && !anyDuplicated(row.names)) { } else row.names <- .set_row_names(nrows) } if (!is.null(names(x))) names(x) <- NULL value <- list(x) if (!optional) names(value) <- nm attr(value, "row.names") <- row.names class(value) <- "data.frame" value } ## @type optional : logical ## @type row.names : character as.data.frame.ordered <- function (x, row.names = NULL, optional = FALSE, ..., nm = paste(deparse(substitute(x), width.cutoff = 500L), collapse = " ")) { force(nm) nrows <- length(x) if (is.null(row.names)) { if (nrows == 0L) row.names <- character() else if (length(row.names <- names(x)) == nrows && !anyDuplicated(row.names)) { } else row.names <- .set_row_names(nrows) } if (!is.null(names(x))) names(x) <- NULL value <- list(x) if (!optional) names(value) <- nm attr(value, "row.names") <- row.names class(value) <- "data.frame" value } as.data.frame.POSIXct <- function (x, row.names = NULL, optional = FALSE, ..., nm = paste(deparse(substitute(x), width.cutoff = 500L), collapse = " ")) { force(nm) nrows <- length(x) if (is.null(row.names)) { if (nrows == 0L) row.names <- character() else if (length(row.names <- names(x)) == nrows && !anyDuplicated(row.names)) { } else row.names <- .set_row_names(nrows) } if (!is.null(names(x))) names(x) <- NULL value <- list(x) if (!optional) names(value) <- nm attr(value, "row.names") <- row.names class(value) <- "data.frame" value } as.data.frame.POSIXlt <- function (x, row.names = NULL, optional = FALSE, ...) { value <- as.data.frame.POSIXct(as.POSIXct(x), row.names, optional, ...) if (!optional) names(value) <- deparse(substitute(x))[[1L]] value } as.expression.default <- function (x, ...) .Internal(as.vector(x, "expression")) "dimnames<-.data.frame" <- function (x, value) { d <- dim(x) if (!is.list(value) || length(value) != 2L) stop("invalid 'dimnames' given for data frame") value[[1L]] <- as.character(value[[1L]]) value[[2L]] <- as.character(value[[2L]]) if (d[[1L]] != length(value[[1L]]) || d[[2L]] != length(value[[2L]])) stop("invalid 'dimnames' given for data frame") row.names(x) <- value[[1L]] names(x) <- value[[2L]] x } droplevels.data.frame <- function (x, except = NULL, ...) { ix <- vapply(x, is.factor, NA) if (!is.null(except)) ix[except] <- FALSE x[ix] <- lapply(x[ix], factor) x } ## @type fromLast : logical duplicated.data.frame <- function (x, incomparables = FALSE, fromLast = FALSE, ...) { if (!identical(incomparables, FALSE)) .NotYetUsed("incomparables != FALSE") if (length(x) != 1L) duplicated(do.call("paste", c(x, sep = "\r")), fromLast = fromLast) else duplicated(x[[1L]], fromLast = fromLast, ...) } format.summaryDefault <- function (x, ...) { xx <- if (is.numeric(x) || is.complex(x)) zapsmall(x) else x class(xx) <- class(x)[-1] m <- match("NA's", names(x), 0) if (inherits(x, "Date") || inherits(x, "POSIXct")) { if (length(a <- attr(x, "NAs"))) c(format(xx, ...), `NA's` = as.character(a)) else format(xx) } else if (m && !is.character(x)) xx <- c(format(xx[-m], ...), `NA's` = as.character(xx[m])) else format(xx, ...) } ## @type x : numeric|character is.na.numeric_version <- function (x) is.na(.encode_numeric_version(x)) ## @type appendLF : logical|character packageStartupMessage <- function (..., domain = NULL, appendLF = TRUE) { call <- sys.call() msg <- .makeMessage(..., domain = domain, appendLF = appendLF) message(.packageStartupMessage(msg, call)) } ## @type x : numeric|character print.numeric_version <- function (x, ...) { y <- as.character(x) if (!length(y)) writeLines(gettext("<0 elements>")) else print(noquote(ifelse(is.na(y), NA_character_, sQuote(y))), ...) invisible(x) } ## @type x : numeric|character xtfrm.numeric_version <- function (x) .encode_numeric_version(x) as.character.condition <- function (x, ...) { msg <- conditionMessage(x) call <- conditionCall(x) cl <- class(x)[1L] if (!is.null(call)) paste0(cl, " in ", deparse(call)[1L], ": ", msg, "\n") else paste0(cl, ": ", msg, "\n") } ## @type row.names : character ## @type optional : logical as.data.frame.difftime <- function (x, row.names = NULL, optional = FALSE, ..., nm = paste(deparse(substitute(x), width.cutoff = 500L), collapse = " ")) { force(nm) nrows <- length(x) if (is.null(row.names)) { if (nrows == 0L) row.names <- character() else if (length(row.names <- names(x)) == nrows && !anyDuplicated(row.names)) { } else row.names <- .set_row_names(nrows) } if (!is.null(names(x))) names(x) <- NULL value <- list(x) if (!optional) names(value) <- nm attr(value, "row.names") <- row.names class(value) <- "data.frame" value } ## @type x : numeric|character format.numeric_version <- function (x, ...) { x <- unclass(x) y <- rep.int(NA_character_, length(x)) names(y) <- names(x) ind <- vapply(x, length, 1L) > 0L y[ind] <- unlist(lapply(x[ind], paste, collapse = ".")) y } namespaceImportClasses <- function (self, ns, vars, from = NULL) { for (i in seq_along(vars)) vars[[i]] <- methods:::classMetaName(vars[[i]]) namespaceImportFrom(self, asNamespace(ns), vars, from = from) } namespaceImportMethods <- function (self, ns, vars, from = NULL) { allVars <- character() generics <- character() packages <- character() allFuns <- methods:::.getGenerics(ns) allPackages <- attr(allFuns, "package") pkg <- methods:::getPackageName(ns) if (!all(vars %in% allFuns)) { message(gettextf("No methods found in \"%s\" for requests: %s", pkg, paste(vars[is.na(match(vars, allFuns))], collapse = ", ")), domain = NA) vars <- vars[vars %in% allFuns] } tPrefix <- methods:::.TableMetaPrefix() allMethodTables <- methods:::.getGenerics(ns, tPrefix) if (any(is.na(match(vars, allFuns)))) stop(gettextf("requested methods not found in environment/package %s: %s", sQuote(pkg), paste(vars[is.na(match(vars, allFuns))], collapse = ", ")), call. = FALSE, domain = NA) for (i in seq_along(allFuns)) { g <- allFuns[[i]] p <- allPackages[[i]] if (exists(g, envir = self, inherits = FALSE) || g %in% vars) { tbl <- methods:::.TableMetaName(g, p) if (is.null(.mergeImportMethods(self, ns, tbl))) { allVars <- c(allVars, tbl) generics <- c(generics, g) packages <- c(packages, p) } } if (g %in% vars && !exists(g, envir = self, inherits = FALSE)) { if (exists(g, envir = ns) && methods:::is(get(g, envir = ns), "genericFunction")) { allVars <- c(allVars, g) generics <- c(generics, g) packages <- c(packages, p) } else { fun <- methods::getFunction(g, mustFind = FALSE, where = self) if (is.primitive(fun) || methods::is(fun, "genericFunction")) { } else warning(gettextf("No generic function found corresponding to requested imported methods for \"%s\" from package \"%s\" (malformed exports?)", g, pkg), domain = NA) } } } namespaceImportFrom(self, asNamespace(ns), allVars, generics, packages, from = from) } ## @type value : complex|character "row.names<-.data.frame" <- function (x, value) { if (!is.data.frame(x)) x <- as.data.frame(x) n <- .row_names_info(x, 2L) if (is.null(value)) { attr(x, "row.names") <- .set_row_names(n) return(x) } if (is.object(value) || !is.integer(value)) value <- as.character(value) if (n == 0L) { if (!is.null(attr(x, "row.names")) && length(value) > 0L) stop("invalid 'row.names' length") } else if (length(value) != n) stop("invalid 'row.names' length") if (anyDuplicated(value)) { nonuniq <- sort(unique(value[duplicated(value)])) warning(ngettext(length(nonuniq), sprintf("non-unique value when setting 'row.names': %s", sQuote(nonuniq[1L])), sprintf("non-unique values when setting 'row.names': %s", paste(sQuote(nonuniq), collapse = ", "))), domain = NA, call. = FALSE) stop("duplicate 'row.names' are not allowed") } if (anyNA(value)) stop("missing values in 'row.names' are not allowed") attr(x, "row.names") <- value x } ## @type x : numeric|character unique.numeric_version <- function (x, incomparables = FALSE, ...) x[!duplicated(x, incomparables, ...)] ## @type stringsAsFactors : logical|character as.data.frame.character <- function (x, ..., stringsAsFactors = default.stringsAsFactors()) { nm <- deparse(substitute(x), width.cutoff = 500L) if (stringsAsFactors) x <- factor(x) if (!"nm" %in% names(list(...))) as.data.frame.vector(x, ..., nm = nm) else as.data.frame.vector(x, ...) } ## @type x : numeric|character as.list.numeric_version <- function (x, ...) { nms <- names(x) names(x) <- NULL y <- lapply(seq_along(x), function(i) x[i]) names(y) <- nms y } conditionCall.condition <- function (c) c$call print.NativeRoutineList <- function (x, ...) { m <- data.frame(numParameters = sapply(x, function(x) x$numParameters), row.names = sapply(x, function(x) x$name)) print(m, ...) invisible(x) } Summary.numeric_version <- function (..., na.rm) { ok <- switch(.Generic, max = , min = , range = TRUE, FALSE) if (!ok) stop(gettextf("%s not defined for \"numeric_version\" objects", .Generic), domain = NA) x <- do.call("c", lapply(list(...), as.numeric_version)) v <- .encode_numeric_version(x) if (!na.rm && length(pos <- which(is.na(v)))) { y <- x[pos[1L]] if (as.character(.Generic) == "range") c(y, y) else y } else switch(.Generic, max = x[which.max(v)], min = x[which.min(v)], range = x[c(which.min(v), which.max(v))]) } testPlatformEquivalence <- function (built, run) { built <- gsub("([^-]*)-([^-]*)-(.*)", "\\1-\\3", built) run <- gsub("([^-]*)-([^-]*)-(.*)", "\\1-\\3", run) if (length(grep("^universal-darwin", built)) && nzchar(.Platform$r_arch)) built <- sub("^universal", R.version$arch, built) length(agrep(built, run)) > 0 } ## @type fromLast : logical anyDuplicated.data.frame <- function (x, incomparables = FALSE, fromLast = FALSE, ...) { if (!identical(incomparables, FALSE)) .NotYetUsed("incomparables != FALSE") anyDuplicated(do.call("paste", c(x, sep = "\r")), fromLast = fromLast) } ## @type row.names : character as.data.frame.data.frame <- function (x, row.names = NULL, ...) { cl <- oldClass(x) i <- match("data.frame", cl) if (i > 1L) class(x) <- cl[-(1L:(i - 1L))] if (!is.null(row.names)) { nr <- .row_names_info(x, 2L) if (length(row.names) == nr) attr(x, "row.names") <- row.names else stop(sprintf(ngettext(nr, "invalid 'row.names', length %d for a data frame with %d row", "invalid 'row.names', length %d for a data frame with %d rows"), length(row.names), nr), domain = NA) } x } default.stringsAsFactors <- function () { val <- getOption("stringsAsFactors") if (is.null(val)) val <- TRUE if (!is.logical(val) || is.na(val) || length(val) != 1L) stop("options(\"stringsAsFactors\") not set to TRUE or FALSE") val } ## @type dll : character ## @type addNames : raw|logical|character getDLLRegisteredRoutines <- function (dll, addNames = TRUE) UseMethod("getDLLRegisteredRoutines") ## @type row.names : character ## @type optional : logical as.data.frame.model.matrix <- function (x, row.names = NULL, optional = FALSE, ...) { d <- dim(x) nrows <- d[1L] dn <- dimnames(x) row.names <- dn[[1L]] value <- list(x) if (!is.null(row.names)) { row.names <- as.character(row.names) if (length(row.names) != nrows) stop(sprintf(ngettext(length(row.names), "supplied %d row name for %d rows", "supplied %d row names for %d rows"), length(row.names), nrows), domain = NA) } else row.names <- .set_row_names(nrows) if (!optional) names(value) <- deparse(substitute(x))[[1L]] attr(value, "row.names") <- row.names class(value) <- "data.frame" value } conditionMessage.condition <- function (c) c$message ## @type x : numeric|character duplicated.numeric_version <- function (x, incomparables = FALSE, ...) { x <- .encode_numeric_version(x) NextMethod("duplicated") } invokeRestartInteractively <- function (r) { if (!interactive()) stop("not an interactive session") if (!isRestart(r)) { res <- findRestart(r) if (is.null(res)) stop(gettextf("no 'restart' '%s' found", as.character(r)), domain = NA) r <- res } if (is.null(r$interactive)) { pars <- names(restartFormals(r)) args <- NULL if (length(pars)) { cat("Enter values for restart arguments:\n\n") for (p in pars) { if (p == "...") { prompt <- "... (a list): " args <- c(args, eval(parse(prompt = prompt))) } else { prompt <- paste0(p, ": ") args <- c(args, list(eval(parse(prompt = prompt)))) } } } } else args <- r$interactive() .Internal(.invokeRestart(r, args)) } print.DLLRegisteredRoutines <- function (x, ...) { n <- vapply(x, length, 1L) x <- x[n > 0] n <- max(n) d <- list() sapply(names(x), function(id) { d[[id]] <<- rep.int("", n) names <- vapply(x[[id]], function(x) x$name, "") if (length(names)) d[[id]][seq_along(names)] <<- names d[[paste(id, "numParameters")]] <<- rep.int("", n) names <- sapply(x[[id]], function(x) x$numParameters) if (length(names)) d[[paste(id, "numParameters")]][seq_along(names)] <<- names }) print(as.data.frame(d), ...) invisible(x) } ## @type x : numeric|character as.character.numeric_version <- function (x, ...) as.character(format(x)) ## @type x : numeric|character as.data.frame.numeric_version <- function (x, row.names = NULL, optional = FALSE, ..., nm = paste(deparse(substitute(x), width.cutoff = 500L), collapse = " ")) { force(nm) nrows <- length(x) if (is.null(row.names)) { if (nrows == 0L) row.names <- character() else if (length(row.names <- names(x)) == nrows && !anyDuplicated(row.names)) { } else row.names <- .set_row_names(nrows) } if (!is.null(names(x))) names(x) <- NULL value <- list(x) if (!optional) names(value) <- nm attr(value, "row.names") <- row.names class(value) <- "data.frame" value } suppressPackageStartupMessages <- function (expr) withCallingHandlers(expr, packageStartupMessage = function(c) invokeRestart("muffleMessage")) ## @type addNames : raw|logical|character ## @type dll : character getDLLRegisteredRoutines.DLLInfo <- function (dll, addNames = TRUE) { if (!inherits(dll, "DLLInfo")) stop(gettextf("must specify DLL via a %s object. See getLoadedDLLs()", dQuote("DLLInfo")), domain = NA) info <- dll[["info"]] els <- .Internal(getRegisteredRoutines(info)) if (addNames) { els <- lapply(els, function(x) { if (length(x)) names(x) <- vapply(x, function(z) z$name, "") x }) } class(els) <- "DLLRegisteredRoutines" els } ## @type dll : character ## @type addNames : raw|logical|character getDLLRegisteredRoutines.character <- function (dll, addNames = TRUE) { dlls <- getLoadedDLLs() w <- vapply(dlls, function(x) x[["name"]] == dll || x[["path"]] == dll, NA) if (!any(w)) stop(gettextf("No DLL currently loaded with name or path %s", sQuote(dll)), domain = NA) dll <- which.max(w) if (sum(w) > 1L) warning(gettextf("multiple DLLs match '%s'. Using '%s'", dll, dll[["path"]]), domain = NA) getDLLRegisteredRoutines(dlls[[dll]], addNames) }
lemma replace_1: assumes "j < n" "a \<in> s" and p: "\<forall>x\<in>s - {a}. x j = p" and "x \<in> s" shows "a \<le> x"
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin, Anne Baanen ! This file was ported from Lean 3 source module order.hom.order ! leanprover-community/mathlib commit ba2245edf0c8bb155f1569fd9b9492a9b384cde6 ! Please do not edit these lines, except to modify the commit id ! if you have ported upstream changes. -/ import Mathlib.Logic.Function.Iterate import Mathlib.Order.GaloisConnection import Mathlib.Order.Hom.Basic /-! # Lattice structure on order homomorphisms This file defines the lattice structure on order homomorphisms, which are bundled monotone functions. ## Main definitions * `OrderHom.CompleteLattice`: if `β` is a complete lattice, so is `α →o β` ## Tags monotone map, bundled morphism -/ namespace OrderHom variable {α β : Type _} section Preorder variable [Preorder α] instance [SemilatticeSup β] : Sup (α →o β) where sup f g := ⟨fun a => f a ⊔ g a, f.mono.sup g.mono⟩ --Porting note: this is the lemma that could have been generated by `@[simps]` on the --above instance but with a nicer name @[simp] lemma coe_sup [SemilatticeSup β] (f g : α →o β) : ((f ⊔ g : α →o β) : α → β) = (f : α → β) ⊔ g := rfl instance [SemilatticeSup β] : SemilatticeSup (α →o β) := { (_ : PartialOrder (α →o β)) with sup := Sup.sup le_sup_left := fun _ _ _ => le_sup_left le_sup_right := fun _ _ _ => le_sup_right sup_le := fun _ _ _ h₀ h₁ x => sup_le (h₀ x) (h₁ x) } instance [SemilatticeInf β] : Inf (α →o β) where inf f g := ⟨fun a => f a ⊓ g a, f.mono.inf g.mono⟩ --Porting note: this is the lemma that could have been generated by `@[simps]` on the --above instance but with a nicer name @[simp] lemma coe_inf [SemilatticeInf β] (f g : α →o β) : ((f ⊓ g : α →o β) : α → β) = (f : α → β) ⊓ g := rfl instance [SemilatticeInf β] : SemilatticeInf (α →o β) := { (_ : PartialOrder (α →o β)), (dualIso α β).symm.toGaloisInsertion.liftSemilatticeInf with inf := (· ⊓ ·) } instance lattice [Lattice β] : Lattice (α →o β) := { (_ : SemilatticeSup (α →o β)), (_ : SemilatticeInf (α →o β)) with } @[simps] instance [Preorder β] [OrderBot β] : Bot (α →o β) where bot := const α ⊥ instance orderBot [Preorder β] [OrderBot β] : OrderBot (α →o β) where bot := ⊥ bot_le _ _ := bot_le @[simps] instance [Preorder β] [OrderTop β] : Top (α →o β) where top := const α ⊤ instance orderTop [Preorder β] [OrderTop β] : OrderTop (α →o β) where top := ⊤ le_top _ _ := le_top instance [CompleteLattice β] : InfSet (α →o β) where infₛ s := ⟨fun x => ⨅ f ∈ s, (f : _) x, fun _ _ h => infᵢ₂_mono fun f _ => f.mono h⟩ @[simp] theorem infₛ_apply [CompleteLattice β] (s : Set (α →o β)) (x : α) : infₛ s x = ⨅ f ∈ s, (f : _) x := rfl #align order_hom.Inf_apply OrderHom.infₛ_apply theorem infᵢ_apply {ι : Sort _} [CompleteLattice β] (f : ι → α →o β) (x : α) : (⨅ i, f i) x = ⨅ i, f i x := (infₛ_apply _ _).trans infᵢ_range #align order_hom.infi_apply OrderHom.infᵢ_apply @[simp, norm_cast] theorem coe_infᵢ {ι : Sort _} [CompleteLattice β] (f : ι → α →o β) : ((⨅ i, f i : α →o β) : α → β) = ⨅ i, (f i : α → β) := by funext x; simp [infᵢ_apply] #align order_hom.coe_infi OrderHom.coe_infᵢ instance [CompleteLattice β] : SupSet (α →o β) where supₛ s := ⟨fun x => ⨆ f ∈ s, (f : _) x, fun _ _ h => supᵢ₂_mono fun f _ => f.mono h⟩ @[simp] theorem supₛ_apply [CompleteLattice β] (s : Set (α →o β)) (x : α) : supₛ s x = ⨆ f ∈ s, (f : _) x := rfl #align order_hom.Sup_apply OrderHom.supₛ_apply theorem supᵢ_apply {ι : Sort _} [CompleteLattice β] (f : ι → α →o β) (x : α) : (⨆ i, f i) x = ⨆ i, f i x := (supₛ_apply _ _).trans supᵢ_range #align order_hom.supr_apply OrderHom.supᵢ_apply @[simp, norm_cast] theorem coe_supᵢ {ι : Sort _} [CompleteLattice β] (f : ι → α →o β) : ((⨆ i, f i : α →o β) : α → β) = ⨆ i, (f i : α → β) := by funext x; simp [supᵢ_apply] #align order_hom.coe_supr OrderHom.coe_supᵢ instance [CompleteLattice β] : CompleteLattice (α →o β) := { (_ : Lattice (α →o β)), OrderHom.orderTop, OrderHom.orderBot with -- supₛ := SupSet.supₛ -- Porting note: removed, unecessary? -- Porting note: Added `by apply`, was `fun s f hf x => le_supᵢ_of_le f (le_supᵢ _ hf)` le_supₛ := fun s f hf x => le_supᵢ_of_le f (by apply le_supᵢ _ hf) supₛ_le := fun s f hf x => supᵢ₂_le fun g hg => hf g hg x --inf := infₛ -- Porting note: removed, unecessary? le_infₛ := fun s f hf x => le_infᵢ₂ fun g hg => hf g hg x infₛ_le := fun s f hf x => infᵢ_le_of_le f (infᵢ_le _ hf) } theorem iterate_sup_le_sup_iff {α : Type _} [SemilatticeSup α] (f : α →o α) : (∀ n₁ n₂ a₁ a₂, (f^[n₁ + n₂]) (a₁ ⊔ a₂) ≤ (f^[n₁]) a₁ ⊔ (f^[n₂]) a₂) ↔ ∀ a₁ a₂, f (a₁ ⊔ a₂) ≤ f a₁ ⊔ a₂ := by constructor <;> intro h · exact h 1 0 · intro n₁ n₂ a₁ a₂ have h' : ∀ n a₁ a₂, (f^[n]) (a₁ ⊔ a₂) ≤ (f^[n]) a₁ ⊔ a₂ := by intro n induction' n with n ih <;> intro a₁ a₂ · rfl · calc (f^[n + 1]) (a₁ ⊔ a₂) = (f^[n]) (f (a₁ ⊔ a₂)) := Function.iterate_succ_apply f n _ _ ≤ (f^[n]) (f a₁ ⊔ a₂) := f.mono.iterate n (h a₁ a₂) _ ≤ (f^[n]) (f a₁) ⊔ a₂ := ih _ _ _ = (f^[n + 1]) a₁ ⊔ a₂ := by rw [← Function.iterate_succ_apply] calc (f^[n₁ + n₂]) (a₁ ⊔ a₂) = (f^[n₁]) ((f^[n₂]) (a₁ ⊔ a₂)) := Function.iterate_add_apply f n₁ n₂ _ _ = (f^[n₁]) ((f^[n₂]) (a₂ ⊔ a₁)) := by rw [sup_comm] _ ≤ (f^[n₁]) ((f^[n₂]) a₂ ⊔ a₁) := f.mono.iterate n₁ (h' n₂ _ _) _ = (f^[n₁]) (a₁ ⊔ (f^[n₂]) a₂) := by rw [sup_comm] _ ≤ (f^[n₁]) a₁ ⊔ (f^[n₂]) a₂ := h' n₁ a₁ _ #align order_hom.iterate_sup_le_sup_iff OrderHom.iterate_sup_le_sup_iff end Preorder end OrderHom
proposition homotopic_paths_rinv: assumes "path p" "path_image p \<subseteq> s" shows "homotopic_paths s (p +++ reversepath p) (linepath (pathstart p) (pathstart p))"
[STATEMENT] lemma crel_vs_fun_app: "\<lbrakk>Transfer.Rel (crel_vs R0) x x\<^sub>T; Transfer.Rel (crel_vs (R0 ===>\<^sub>T R1)) f f\<^sub>T\<rbrakk> \<Longrightarrow> Transfer.Rel (crel_vs R1) (App f x) (f\<^sub>T . x\<^sub>T)" [PROOF STATE] proof (prove) goal (1 subgoal): 1. \<lbrakk>Rel (crel_vs R0) x x\<^sub>T; Rel (crel_vs (R0 ===>\<^sub>T R1)) f f\<^sub>T\<rbrakk> \<Longrightarrow> Rel (crel_vs R1) (App f x) (f\<^sub>T . x\<^sub>T) [PROOF STEP] unfolding Rel_def [PROOF STATE] proof (prove) goal (1 subgoal): 1. \<lbrakk>crel_vs R0 x x\<^sub>T; crel_vs (R0 ===>\<^sub>T R1) f f\<^sub>T\<rbrakk> \<Longrightarrow> crel_vs R1 (App f x) (f\<^sub>T . x\<^sub>T) [PROOF STEP] using fun_app_lifted_transfer[THEN rel_funD, THEN rel_funD] [PROOF STATE] proof (prove) using this: \<lbrakk>crel_vs (?R0.2 ===>\<^sub>T ?R1.2) ?x1 ?y1; crel_vs ?R0.2 ?x ?y\<rbrakk> \<Longrightarrow> crel_vs ?R1.2 (App ?x1 ?x) (?y1 . ?y) goal (1 subgoal): 1. \<lbrakk>crel_vs R0 x x\<^sub>T; crel_vs (R0 ===>\<^sub>T R1) f f\<^sub>T\<rbrakk> \<Longrightarrow> crel_vs R1 (App f x) (f\<^sub>T . x\<^sub>T) [PROOF STEP] .
-- Andreas, 2012-01-17 -- {-# OPTIONS -v tc.proj.like:50 #-} -- {-# OPTIONS -v tc.conv.atom:50 #-} module Issue553c where postulate A : Set a : A data Bool : Set where true false : Bool data WrapBool (C : Set) : Set where wrap : Bool -> WrapBool C -- a projection-like function (must not be constructor-headed!) -- the dummy C is to make Agda accept f as projection like f : {C : Set} -> WrapBool C -> A f (wrap true) = a f (wrap false) = a data _≡_ {A : Set}(a : A) : A -> Set where refl : a ≡ a -- it is important that f does not reduce, in order to enter compareAtom test : (b : Bool) -> f {C = A} (wrap b) ≡ f (wrap b) test b = refl -- An internal error has occurred. Please report this as a bug. -- Location of the error: src/full/Agda/TypeChecking/Conversion.hs:335 -- the problem is fixed now, since f is no longer projection-like -- because of deep matching
module maybe where open import level open import eq open import bool ---------------------------------------------------------------------- -- datatypes ---------------------------------------------------------------------- data maybe {ℓ}(A : Set ℓ) : Set ℓ where just : A → maybe A nothing : maybe A ---------------------------------------------------------------------- -- operations ---------------------------------------------------------------------- _≫=maybe_ : ∀ {ℓ}{A B : Set ℓ} → maybe A → (A → maybe B) → maybe B nothing ≫=maybe f = nothing (just x) ≫=maybe f = f x return-maybe : ∀ {ℓ}{A : Set ℓ} → A → maybe A return-maybe a = just a down-≡ : ∀{ℓ}{A : Set ℓ}{a a' : A} → just a ≡ just a' → a ≡ a' down-≡ refl = refl isJust : ∀{ℓ}{A : Set ℓ} → maybe A → 𝔹 isJust nothing = ff isJust (just _) = tt maybe-extract : ∀{ℓ}{A : Set ℓ} → (x : maybe A) → isJust x ≡ tt → A maybe-extract (just x) p = x maybe-extract nothing () maybe-map : ∀{ℓ}{A B : Set ℓ} → (A → B) → maybe A → maybe B maybe-map f (just x) = just (f x) maybe-map f nothing = nothing
(* Title: HOL/Auth/flash_data_cub_lemma_on_inv__97.thy Author: Yongjian Li and Kaiqiang Duan, State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences Copyright 2016 State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences *) header{*The flash_data_cub Protocol Case Study*} theory flash_data_cub_lemma_on_inv__97 imports flash_data_cub_base begin section{*All lemmas on causal relation between inv__97 and some rule r*} lemma n_PI_Remote_GetVsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_PI_Remote_Get src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_PI_Remote_Get src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_PI_Remote_GetXVsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_PI_Remote_GetX src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_PI_Remote_GetX src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_NakVsinv__97: assumes a1: "(\<exists> dst. dst\<le>N\<and>r=n_NI_Nak dst)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain dst where a1:"dst\<le>N\<and>r=n_NI_Nak dst" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(dst=p__Inv4)\<or>(dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(dst=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(dst~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_Get_Nak__part__0Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Nak__part__0 src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Nak__part__0 src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_Get_Nak__part__1Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Nak__part__1 src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Nak__part__1 src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_Get_Nak__part__2Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Nak__part__2 src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Nak__part__2 src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_Get_Get__part__0Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Get__part__0 src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Get__part__0 src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_Get_Get__part__1Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Get__part__1 src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Get__part__1 src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P3 s" apply (cut_tac a1 a2 b1, simp, rule_tac x="(neg (andForm (eqn (IVar (Field (Field (Ident ''Sta'') ''ShWbMsg'') ''Cmd'')) (Const SHWB_ShWb)) (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Pending'')) (Const false))))" in exI, auto) done then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_Get_Put_HeadVsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Put_Head N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Put_Head N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_Get_PutVsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Put src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Put src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_Get_Put_DirtyVsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Put_Dirty src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Put_Dirty src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Remote_Get_NakVsinv__97: assumes a1: "(\<exists> src dst. src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_Get_Nak src dst)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src dst where a1:"src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_Get_Nak src dst" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4\<and>dst~=p__Inv4)\<or>(src~=p__Inv4\<and>dst=p__Inv4)\<or>(src~=p__Inv4\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4\<and>dst~=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4\<and>dst=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4\<and>dst~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Remote_Get_PutVsinv__97: assumes a1: "(\<exists> src dst. src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_Get_Put src dst)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src dst where a1:"src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_Get_Put src dst" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4\<and>dst~=p__Inv4)\<or>(src~=p__Inv4\<and>dst=p__Inv4)\<or>(src~=p__Inv4\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4\<and>dst~=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4\<and>dst=p__Inv4)" have "?P3 s" apply (cut_tac a1 a2 b1, simp, rule_tac x="(neg (andForm (eqn (IVar (Field (Para (Field (Ident ''Sta'') ''UniMsg'') p__Inv4) ''Cmd'')) (Const UNI_Get)) (eqn (IVar (Field (Para (Field (Ident ''Sta'') ''Proc'') p__Inv4) ''CacheState'')) (Const CACHE_E))))" in exI, auto) done then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4\<and>dst~=p__Inv4)" have "?P3 s" apply (cut_tac a1 a2 b1, simp, rule_tac x="(neg (andForm (andForm (andForm (eqn (IVar (Field (Para (Field (Ident ''Sta'') ''UniMsg'') p__Inv4) ''Cmd'')) (Const UNI_Get)) (eqn (IVar (Field (Para (Field (Ident ''Sta'') ''UniMsg'') p__Inv4) ''HomeProc'')) (Const false))) (eqn (IVar (Field (Para (Field (Ident ''Sta'') ''UniMsg'') src) ''Cmd'')) (Const UNI_Get))) (eqn (IVar (Field (Para (Field (Ident ''Sta'') ''UniMsg'') src) ''HomeProc'')) (Const false))))" in exI, auto) done then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_Nak__part__0Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__0 src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__0 src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_Nak__part__1Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__1 src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__1 src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_Nak__part__2Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__2 src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__2 src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_GetX__part__0Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_GetX__part__0 src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_GetX__part__0 src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_GetX__part__1Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_GetX__part__1 src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_GetX__part__1 src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_1Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_1 N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_1 N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_2Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_2 N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_2 N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_3Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_3 N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_3 N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_4Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_4 N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_4 N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_5Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_5 N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_5 N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_6Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_6 N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_6 N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_7__part__0Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_7__part__0 N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_7__part__0 N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_7__part__1Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_7__part__1 N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_7__part__1 N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_7_NODE_Get__part__0Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_7_NODE_Get__part__0 N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_7_NODE_Get__part__0 N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_7_NODE_Get__part__1Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_7_NODE_Get__part__1 N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_7_NODE_Get__part__1 N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_8_HomeVsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_8_Home N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_8_Home N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_8_Home_NODE_GetVsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_8_Home_NODE_Get N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_8_Home_NODE_Get N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_8Vsinv__97: assumes a1: "(\<exists> src pp. src\<le>N\<and>pp\<le>N\<and>src~=pp\<and>r=n_NI_Local_GetX_PutX_8 N src pp)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src pp where a1:"src\<le>N\<and>pp\<le>N\<and>src~=pp\<and>r=n_NI_Local_GetX_PutX_8 N src pp" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4\<and>pp~=p__Inv4)\<or>(src~=p__Inv4\<and>pp=p__Inv4)\<or>(src~=p__Inv4\<and>pp~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4\<and>pp~=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4\<and>pp=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4\<and>pp~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_8_NODE_GetVsinv__97: assumes a1: "(\<exists> src pp. src\<le>N\<and>pp\<le>N\<and>src~=pp\<and>r=n_NI_Local_GetX_PutX_8_NODE_Get N src pp)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src pp where a1:"src\<le>N\<and>pp\<le>N\<and>src~=pp\<and>r=n_NI_Local_GetX_PutX_8_NODE_Get N src pp" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4\<and>pp~=p__Inv4)\<or>(src~=p__Inv4\<and>pp=p__Inv4)\<or>(src~=p__Inv4\<and>pp~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4\<and>pp~=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4\<and>pp=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4\<and>pp~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_9__part__0Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_9__part__0 N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_9__part__0 N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_9__part__1Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_9__part__1 N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_9__part__1 N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_10_HomeVsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_10_Home N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_10_Home N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_10Vsinv__97: assumes a1: "(\<exists> src pp. src\<le>N\<and>pp\<le>N\<and>src~=pp\<and>r=n_NI_Local_GetX_PutX_10 N src pp)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src pp where a1:"src\<le>N\<and>pp\<le>N\<and>src~=pp\<and>r=n_NI_Local_GetX_PutX_10 N src pp" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4\<and>pp~=p__Inv4)\<or>(src~=p__Inv4\<and>pp=p__Inv4)\<or>(src~=p__Inv4\<and>pp~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4\<and>pp~=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4\<and>pp=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4\<and>pp~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Local_GetX_PutX_11Vsinv__97: assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_11 N src)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_11 N src" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4)\<or>(src~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Remote_GetX_NakVsinv__97: assumes a1: "(\<exists> src dst. src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_GetX_Nak src dst)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src dst where a1:"src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_GetX_Nak src dst" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4\<and>dst~=p__Inv4)\<or>(src~=p__Inv4\<and>dst=p__Inv4)\<or>(src~=p__Inv4\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4\<and>dst~=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4\<and>dst=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4\<and>dst~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Remote_GetX_PutXVsinv__97: assumes a1: "(\<exists> src dst. src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_GetX_PutX src dst)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain src dst where a1:"src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_GetX_PutX src dst" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(src=p__Inv4\<and>dst~=p__Inv4)\<or>(src~=p__Inv4\<and>dst=p__Inv4)\<or>(src~=p__Inv4\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(src=p__Inv4\<and>dst~=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4\<and>dst=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(src~=p__Inv4\<and>dst~=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Remote_PutVsinv__97: assumes a1: "(\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_Put dst)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain dst where a1:"dst\<le>N\<and>r=n_NI_Remote_Put dst" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(dst=p__Inv4)\<or>(dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(dst=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(dst~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_Remote_PutXVsinv__97: assumes a1: "(\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_PutX dst)" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a1 obtain dst where a1:"dst\<le>N\<and>r=n_NI_Remote_PutX dst" apply fastforce done from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "(dst=p__Inv4)\<or>(dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done moreover { assume b1: "(dst=p__Inv4)" have "?P1 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } moreover { assume b1: "(dst~=p__Inv4)" have "?P2 s" proof(cut_tac a1 a2 b1, auto) qed then have "invHoldForRule s f r (invariants N)" by auto } ultimately show "invHoldForRule s f r (invariants N)" by satx qed lemma n_NI_FAckVsinv__97: assumes a1: "(r=n_NI_FAck )" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "?P1 s" proof(cut_tac a1 a2 , auto) qed then show "invHoldForRule s f r (invariants N)" by auto qed lemma n_NI_ShWbVsinv__97: assumes a1: "(r=n_NI_ShWb N )" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s") proof - from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__97 p__Inv4" apply fastforce done have "?P1 s" proof(cut_tac a1 a2 , auto) qed then show "invHoldForRule s f r (invariants N)" by auto qed lemma n_NI_Remote_GetX_PutX_HomeVsinv__97: assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_GetX_PutX_Home dst" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_PI_Local_GetX_PutX__part__0Vsinv__97: assumes a1: "r=n_PI_Local_GetX_PutX__part__0 " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_WbVsinv__97: assumes a1: "r=n_NI_Wb " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_StoreVsinv__97: assumes a1: "\<exists> src data. src\<le>N\<and>data\<le>N\<and>r=n_Store src data" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_InvAck_3Vsinv__97: assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_3 N src" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_InvAck_1Vsinv__97: assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_1 N src" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_PI_Local_GetX_GetX__part__1Vsinv__97: assumes a1: "r=n_PI_Local_GetX_GetX__part__1 " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_PI_Local_GetX_GetX__part__0Vsinv__97: assumes a1: "r=n_PI_Local_GetX_GetX__part__0 " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_PI_Remote_ReplaceVsinv__97: assumes a1: "\<exists> src. src\<le>N\<and>r=n_PI_Remote_Replace src" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_Store_HomeVsinv__97: assumes a1: "\<exists> data. data\<le>N\<and>r=n_Store_Home data" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_PI_Local_ReplaceVsinv__97: assumes a1: "r=n_PI_Local_Replace " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_InvAck_existsVsinv__97: assumes a1: "\<exists> src pp. src\<le>N\<and>pp\<le>N\<and>src~=pp\<and>r=n_NI_InvAck_exists src pp" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_PI_Remote_PutXVsinv__97: assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_PI_Remote_PutX dst" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_Remote_Get_Put_HomeVsinv__97: assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_Get_Put_Home dst" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_InvVsinv__97: assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Inv dst" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_PI_Local_PutXVsinv__97: assumes a1: "r=n_PI_Local_PutX " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_PI_Local_Get_PutVsinv__97: assumes a1: "r=n_PI_Local_Get_Put " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_PI_Local_GetX_PutX_HeadVld__part__0Vsinv__97: assumes a1: "r=n_PI_Local_GetX_PutX_HeadVld__part__0 N " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_ReplaceVsinv__97: assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Replace src" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_Remote_GetX_Nak_HomeVsinv__97: assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_GetX_Nak_Home dst" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_Local_PutXAcksDoneVsinv__97: assumes a1: "r=n_NI_Local_PutXAcksDone " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_PI_Local_GetX_PutX__part__1Vsinv__97: assumes a1: "r=n_PI_Local_GetX_PutX__part__1 " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_Remote_Get_Nak_HomeVsinv__97: assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_Get_Nak_Home dst" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_InvAck_exists_HomeVsinv__97: assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_exists_Home src" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_Replace_HomeVsinv__97: assumes a1: "r=n_NI_Replace_Home " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_Local_PutVsinv__97: assumes a1: "r=n_NI_Local_Put " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_Nak_ClearVsinv__97: assumes a1: "r=n_NI_Nak_Clear " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_PI_Local_Get_GetVsinv__97: assumes a1: "r=n_PI_Local_Get_Get " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_Nak_HomeVsinv__97: assumes a1: "r=n_NI_Nak_Home " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_NI_InvAck_2Vsinv__97: assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_2 N src" and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done lemma n_PI_Local_GetX_PutX_HeadVld__part__1Vsinv__97: assumes a1: "r=n_PI_Local_GetX_PutX_HeadVld__part__1 N " and a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__97 p__Inv4)" shows "invHoldForRule s f r (invariants N)" apply (rule noEffectOnRule, cut_tac a1 a2, auto) done end
Require Import Coq.Bool.Bool. Require Import Coq.Arith.Arith. Require Import Coq.Arith.EqNat. Require Import Coq.omega.Omega. Require Import Coq.Lists.List. Import ListNotations. Require Import Maps. Definition state := total_map nat. Definition empty_state : state := t_empty 0. Inductive aexp : Type := | ANum : nat -> aexp | AId : id -> aexp | APlus : aexp -> aexp -> aexp | AMinus : aexp -> aexp -> aexp | AMult : aexp -> aexp -> aexp. Definition X : id := Id 0. Definition Y : id := Id 1. Definition Z : id := Id 2. Inductive bexp : Type := | BTrue : bexp | BFalse : bexp | BEq : aexp -> aexp -> bexp | BLe : aexp -> aexp -> bexp | BNot : bexp -> bexp | BAnd : bexp -> bexp -> bexp. Fixpoint aeval (st : state) (a : aexp) : nat := match a with | ANum n => n | AId x => st x | APlus a1 a2 => (aeval st a1) + (aeval st a2) | AMinus a1 a2 => (aeval st a1) - (aeval st a2) | AMult a1 a2 => (aeval st a1) * (aeval st a2) end. Fixpoint beval (st : state) (b : bexp) : bool := match b with | BTrue => true | BFalse => false | BEq a1 a2 => beq_nat (aeval st a1) (aeval st a2) | BLe a1 a2 => leb (aeval st a1) (aeval st a2) | BNot b1 => negb (beval st b1) | BAnd b1 b2 => andb (beval st b1) (beval st b2) end. Inductive com : Type := | CSkip : com | CAss : id -> aexp -> com | CSeq : com -> com -> com | CIf : bexp -> com -> com -> com | CWhile : bexp -> com -> com. Notation "'SKIP'" := CSkip. Notation "x '::=' a" := (CAss x a) (at level 60). Notation "c1 ;; c2" := (CSeq c1 c2) (at level 80, right associativity). Notation "'WHILE' b 'DO' c 'END'" := (CWhile b c) (at level 80, right associativity). Notation "'IFB' c1 'THEN' c2 'ELSE' c3 'FI'" := (CIf c1 c2 c3) (at level 80, right associativity). (* Examples *) Definition fact_in_coq : com := Z ::= AId X;; Y ::= ANum 1;; WHILE BNot (BEq (AId Z) (ANum 0)) DO Y ::= AMult (AId Y) (AId Z);; Z ::= AMinus (AId Z) (ANum 1) END. Definition plus2 : com := X ::= (APlus (AId X) (ANum 2)). Definition XtimesYinZ : com := Z ::= (AMult (AId X) (AId Y)). Definition subtract_slowly_body : com := Z ::= AMinus (AId Z) (ANum 1) ;; X ::= AMinus (AId X) (ANum 1). Definition subtract_slowly : com := WHILE BNot (BEq (AId X) (ANum 0)) DO subtract_slowly_body END. Definition subtract_3_from_5_slowly : com := X ::= ANum 3 ;; Z ::= ANum 5 ;; subtract_slowly. Definition infinite_loop : com := WHILE BTrue DO SKIP END. (* ----------------------------------------------------------------- *) (** *** Operational Semantics *) (* ---------------- (E_Skip) SKIP / st \\ st aeval st a1 = n -------------------------------- (E_Ass) x := a1 / st \\ (t_update st x n) c1 / st \\ st' c2 / st' \\ st'' ------------------- (E_Seq) c1;;c2 / st \\ st'' beval st b1 = true c1 / st \\ st' ------------------------------------- (E_IfTrue) IF b1 THEN c1 ELSE c2 FI / st \\ st' beval st b1 = false c2 / st \\ st' ------------------------------------- (E_IfFalse) IF b1 THEN c1 ELSE c2 FI / st \\ st' beval st b = false ------------------------------ (E_WhileEnd) WHILE b DO c END / st \\ st beval st b = true c / st \\ st' WHILE b DO c END / st' \\ st'' --------------------------------- (E_WhileLoop) WHILE b DO c END / st \\ st'' *) Reserved Notation "c1 '/' st '\\' st'" (at level 40, st at level 39). Inductive ceval : com -> state -> state -> Prop := | E_Skip : forall st, SKIP / st \\ st | E_Ass : forall st a1 n x, aeval st a1 = n -> (x ::= a1) / st \\ (t_update st x n) | E_Seq : forall c1 c2 st st' st'', c1 / st \\ st' -> c2 / st' \\ st'' -> (c1 ;; c2) / st \\ st'' | E_IfTrue : forall st st' b c1 c2, beval st b = true -> c1 / st \\ st' -> (IFB b THEN c1 ELSE c2 FI) / st \\ st' | E_IfFalse : forall st st' b c1 c2, beval st b = false -> c2 / st \\ st' -> (IFB b THEN c1 ELSE c2 FI) / st \\ st' | E_WhileEnd : forall b st c, beval st b = false -> (WHILE b DO c END) / st \\ st | E_WhileLoop : forall st st' st'' b c, beval st b = true -> c / st \\ st' -> (WHILE b DO c END) / st' \\ st'' -> (WHILE b DO c END) / st \\ st'' where "c1 '/' st '\\' st'" := (ceval c1 st st'). Example ceval_example1: (X ::= ANum 2;; IFB BLe (AId X) (ANum 1) THEN Y ::= ANum 3 ELSE Z ::= ANum 4 FI) / empty_state \\ (t_update (t_update empty_state X 2) Z 4). Proof. apply E_Seq with (t_update empty_state X 2). apply E_Ass. reflexivity. apply E_IfFalse. reflexivity. apply E_Ass. reflexivity. Qed. Example ceval_example2: (X ::= ANum 0;; Y ::= ANum 1;; Z ::= ANum 2) / empty_state \\ (t_update (t_update (t_update empty_state X 0) Y 1) Z 2). Proof. (* FILL IN HERE *) Admitted. Theorem ceval_deterministic: forall c st st1 st2, c / st \\ st1 -> c / st \\ st2 -> st1 = st2. Proof. intros c st st1 st2 E1 E2. generalize dependent st2. induction E1; intros st2 E2; inversion E2; subst. - (* E_Skip *) reflexivity. - (* E_Ass *) reflexivity. - (* E_Seq *) assert (st' = st'0) as EQ1. { (* Proof of assertion *) apply IHE1_1; assumption. } subst st'0. apply IHE1_2. assumption. - (* E_IfTrue, b1 evaluates to true *) apply IHE1. assumption. - (* E_IfTrue, b1 evaluates to false (contradiction) *) rewrite H in H5. inversion H5. - (* E_IfFalse, b1 evaluates to true (contradiction) *) rewrite H in H5. inversion H5. - (* E_IfFalse, b1 evaluates to false *) apply IHE1. assumption. - (* E_WhileEnd, b1 evaluates to false *) reflexivity. - (* E_WhileEnd, b1 evaluates to true (contradiction) *) rewrite H in H2. inversion H2. - (* E_WhileLoop, b1 evaluates to false (contradiction) *) rewrite H in H4. inversion H4. - (* E_WhileLoop, b1 evaluates to true *) assert (st' = st'0) as EQ1. { (* Proof of assertion *) apply IHE1_1; assumption. } subst st'0. apply IHE1_2. assumption. Qed. Theorem plus2_spec : forall st n st', st X = n -> plus2 / st \\ st' -> st' X = n + 2. Proof. intros st n st' HX Heval. inversion Heval. subst. clear Heval. simpl. apply t_update_eq. Qed. Theorem loop_never_stops : forall st st', ~(infinite_loop / st \\ st'). Proof. intros st st' contra. unfold infinite_loop in contra. remember (WHILE BTrue DO SKIP END) as loopdef eqn:Heqloopdef. (* FILL IN HERE *) Admitted. Fixpoint no_whiles (c : com) : bool := match c with | SKIP => true | _ ::= _ => true | c1 ;; c2 => andb (no_whiles c1) (no_whiles c2) | IFB _ THEN ct ELSE cf FI => andb (no_whiles ct) (no_whiles cf) | WHILE _ DO _ END => false end.
The sound quality of the NS @-@ 10 has polarised opinions , characterised as " love them or hate them " . Many professionals find it indispensable , even though they may not particularly enjoy listening to it ; others refuse to give it space in their studio but will happily admit that it is an effective professional tool . The reliance on the NS @-@ 10 by top independent producers became a viral phenomenon ; thousands of studios equipped themselves with NS @-@ 10s to attract big named producers , making the speakers an industry standard .
<center><h1><strong>taudata Analytics</strong></h1></center> <center><h2><strong><font color="blue">PDE 01: Pendahuluan Fungsi dan Turunannya</font></strong></h2></center> <center></center> <b><center>(C) Taufik Sutanto</center> <center><h3><font color="blue">https://taudataid.github.io/pde01/</font></h3></center> <center></center> * Maksud pemetaan satu dan hanya satu, 1-1, & pada * Di kalkuluas fungsi biasanya fungsi real, di machine learning domain bisa berupa angka (numerik) atau bukan angka kategorik. image source: Yuliani Wibowo - https://slideplayer.info/slide/12403959/ ```python def fungsi(x): return 2*x+1 fungsi(5) ``` <center><h2><strong><font color="blue">Berbagai macam fungsi</font></strong></h2></center> ```python import numpy as np np.cos, dsb ``` <center><h2><strong><font color="blue">Limit Paradox</font></strong></h2></center> limit-paradox.png <center><h2><strong><font color="blue">Limit</font></strong></h2></center> ```python from sympy import * x = symbols('x') expr = sin(3 * x)/x; print("Expression : {}".format(expr)) # Use sympy.limit() method limit_expr = limit(expr, x, 0) print("Limit of the expression tends to 0 : {}".format(limit_expr)) ``` <center><h2><strong><font color="blue">Limit dan Kontinu </font></strong></h2></center> - Animasi dari swf ```python from sympy import Symbol, S from sympy.calculus.util import continuous_domain x = Symbol("x") f = sin(x)/x continuous_domain(f, x, S.Reals) Union(Interval.open(-oo, 0), Interval.open(0, oo)) ``` <center><h2><strong><font color="blue">Limit dan Turunan</font></strong></h2></center> ```python from sympy import * x, y, z = symbols('x y z') diff(cos(x), x) ``` <center><h2><strong><font color="blue">Makna turunan dan optimasi</font></strong></h2></center> <center><h2><strong><font color="blue">Solusi akar dan nilai optimal</font></strong></h2></center> - refer ke link di taudata ```python # optimasi di Python from scipy.optimize import minimize from numpy.random import rand # objective function def objective(x): return x[0]**2.0 + x[1]**2.0 # Plot Fungsinya # define range for input r_min, r_max = -5.0, 5.0 ``` ```python # define the starting point as a random sample from the domain pt = r_min + rand(2) * (r_max - r_min) # perform the l-bfgs-b algorithm search result = minimize(objective, pt, method='L-BFGS-B') # summarize the result print('Status : %s' % result['message']) print('Total Evaluations: %d' % result['nfev']) # evaluate solution solution = result['x'] evaluation = objective(solution) print('Solution: f(%s) = %.5f' % (solution, evaluation)) ``` <center><h2><strong><font color="blue">PDB dan PDP</font></strong></h2></center> <center><h2><strong><font color="blue">Sifat dasar turunan</font></strong></h2></center> - chainrule, dsb <center><h2><strong><font color="blue"> ... </font></strong></h2></center> # <center><font color="blue"> Akhir Modul PDE 01, Next: " _Pemodelan dan Persamaan Differensial_ "</font></center> <hr />
import Partition import Data.String main : IO () main = do argv <- getArgs n <- pure $ index' 1 argv >>= parsePositive ls <- pure $ naiveAllParN <$> n printLn ls printLn $ length <$> ls
fir_filter_sim/dspba_library_package.vhd fir_filter_sim/dspba_library.vhd fir_filter_sim/auk_dspip_math_pkg_hpfir.vhd fir_filter_sim/auk_dspip_lib_pkg_hpfir.vhd fir_filter_sim/auk_dspip_avalon_streaming_controller_hpfir.vhd fir_filter_sim/auk_dspip_avalon_streaming_sink_hpfir.vhd fir_filter_sim/auk_dspip_avalon_streaming_source_hpfir.vhd fir_filter_sim/auk_dspip_roundsat_hpfir.vhd fir_filter_sim/altera_avalon_sc_fifo.v fir_filter_sim/fir_filter_rtl_core.vhd fir_filter_sim/fir_filter_ast.vhd fir_filter_sim/fir_filter.vhd fir_filter_sim/fir_filter_nativelink.tcl fir_filter_sim/fir_filter_msim.tcl fir_filter_sim/fir_filter_tb.vhd fir_filter_sim/fir_filter_mlab.m fir_filter_sim/fir_filter_model.m fir_filter_sim/fir_filter_coef_int.txt fir_filter_sim/fir_filter_input.txt fir_filter_sim/fir_filter_param.txt
[STATEMENT] lemma Proc_CFG_sourcelabel_less_num_nodes: "prog \<turnstile> Label l -et\<rightarrow>\<^sub>p n' \<Longrightarrow> l < #:prog" [PROOF STATE] proof (prove) goal (1 subgoal): 1. prog \<turnstile> Label l -et\<rightarrow>\<^sub>p n' \<Longrightarrow> l < #:prog [PROOF STEP] proof(induct prog "Label l" et n' arbitrary:l rule:Proc_CFG.induct) [PROOF STATE] proof (state) goal (17 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>c\<^sub>1 et n' c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> Label l -et\<rightarrow>\<^sub>p n'; l < #:c\<^sub>1; n' \<noteq> Exit\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 5. \<And>c\<^sub>1 et c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> Label l -et\<rightarrow>\<^sub>p Exit; l < #:c\<^sub>1; Label l \<noteq> Entry\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 6. \<And>c\<^sub>2 n et n' c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 = Label l\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 7. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 9. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 10. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 A total of 17 subgoals... [PROOF STEP] case (Proc_CFG_SeqFirst c\<^sub>1 et n' c\<^sub>2 l) [PROOF STATE] proof (state) this: c\<^sub>1 \<turnstile> Label l -et\<rightarrow>\<^sub>p n' l < #:c\<^sub>1 n' \<noteq> Exit goal (17 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>c\<^sub>1 et n' c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> Label l -et\<rightarrow>\<^sub>p n'; l < #:c\<^sub>1; n' \<noteq> Exit\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 5. \<And>c\<^sub>1 et c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> Label l -et\<rightarrow>\<^sub>p Exit; l < #:c\<^sub>1; Label l \<noteq> Entry\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 6. \<And>c\<^sub>2 n et n' c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 = Label l\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 7. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 9. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 10. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 A total of 17 subgoals... [PROOF STEP] thus ?case [PROOF STATE] proof (prove) using this: c\<^sub>1 \<turnstile> Label l -et\<rightarrow>\<^sub>p n' l < #:c\<^sub>1 n' \<noteq> Exit goal (1 subgoal): 1. l < #:c\<^sub>1;; c\<^sub>2 [PROOF STEP] by simp [PROOF STATE] proof (state) this: l < #:c\<^sub>1;; c\<^sub>2 goal (16 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>c\<^sub>1 et c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> Label l -et\<rightarrow>\<^sub>p Exit; l < #:c\<^sub>1; Label l \<noteq> Entry\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 5. \<And>c\<^sub>2 n et n' c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 = Label l\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 6. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 9. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 10. \<And>b c'. 0 < #:while (b) c' A total of 16 subgoals... [PROOF STEP] next [PROOF STATE] proof (state) goal (16 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>c\<^sub>1 et c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> Label l -et\<rightarrow>\<^sub>p Exit; l < #:c\<^sub>1; Label l \<noteq> Entry\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 5. \<And>c\<^sub>2 n et n' c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 = Label l\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 6. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 9. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 10. \<And>b c'. 0 < #:while (b) c' A total of 16 subgoals... [PROOF STEP] case (Proc_CFG_SeqConnect c\<^sub>1 et c\<^sub>2 l) [PROOF STATE] proof (state) this: c\<^sub>1 \<turnstile> Label l -et\<rightarrow>\<^sub>p Exit l < #:c\<^sub>1 Label l \<noteq> Entry goal (16 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>c\<^sub>1 et c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> Label l -et\<rightarrow>\<^sub>p Exit; l < #:c\<^sub>1; Label l \<noteq> Entry\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 5. \<And>c\<^sub>2 n et n' c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 = Label l\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 6. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 9. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 10. \<And>b c'. 0 < #:while (b) c' A total of 16 subgoals... [PROOF STEP] thus ?case [PROOF STATE] proof (prove) using this: c\<^sub>1 \<turnstile> Label l -et\<rightarrow>\<^sub>p Exit l < #:c\<^sub>1 Label l \<noteq> Entry goal (1 subgoal): 1. l < #:c\<^sub>1;; c\<^sub>2 [PROOF STEP] by simp [PROOF STATE] proof (state) this: l < #:c\<^sub>1;; c\<^sub>2 goal (15 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>c\<^sub>2 n et n' c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 = Label l\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 9. \<And>b c'. 0 < #:while (b) c' 10. \<And>b c'. 0 < #:while (b) c' A total of 15 subgoals... [PROOF STEP] next [PROOF STATE] proof (state) goal (15 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>c\<^sub>2 n et n' c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 = Label l\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 9. \<And>b c'. 0 < #:while (b) c' 10. \<And>b c'. 0 < #:while (b) c' A total of 15 subgoals... [PROOF STEP] case (Proc_CFG_SeqSecond c\<^sub>2 n et n' c\<^sub>1 l) [PROOF STATE] proof (state) this: c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n' n = Label ?l \<Longrightarrow> ?l < #:c\<^sub>2 n \<noteq> Entry n \<oplus> #:c\<^sub>1 = Label l goal (15 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>c\<^sub>2 n et n' c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 = Label l\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 9. \<And>b c'. 0 < #:while (b) c' 10. \<And>b c'. 0 < #:while (b) c' A total of 15 subgoals... [PROOF STEP] note n = \<open>n \<oplus> #:c\<^sub>1 = Label l\<close> [PROOF STATE] proof (state) this: n \<oplus> #:c\<^sub>1 = Label l goal (15 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>c\<^sub>2 n et n' c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 = Label l\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 9. \<And>b c'. 0 < #:while (b) c' 10. \<And>b c'. 0 < #:while (b) c' A total of 15 subgoals... [PROOF STEP] note IH = \<open>\<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2\<close> [PROOF STATE] proof (state) this: n = Label ?l \<Longrightarrow> ?l < #:c\<^sub>2 goal (15 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>c\<^sub>2 n et n' c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 = Label l\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 9. \<And>b c'. 0 < #:while (b) c' 10. \<And>b c'. 0 < #:while (b) c' A total of 15 subgoals... [PROOF STEP] from n [PROOF STATE] proof (chain) picking this: n \<oplus> #:c\<^sub>1 = Label l [PROOF STEP] obtain l' where l':"n = Label l'" [PROOF STATE] proof (prove) using this: n \<oplus> #:c\<^sub>1 = Label l goal (1 subgoal): 1. (\<And>l'. n = Label l' \<Longrightarrow> thesis) \<Longrightarrow> thesis [PROOF STEP] by(cases n) auto [PROOF STATE] proof (state) this: n = Label l' goal (15 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>c\<^sub>2 n et n' c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 = Label l\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 9. \<And>b c'. 0 < #:while (b) c' 10. \<And>b c'. 0 < #:while (b) c' A total of 15 subgoals... [PROOF STEP] from IH[OF this] [PROOF STATE] proof (chain) picking this: l' < #:c\<^sub>2 [PROOF STEP] have "l' < #:c\<^sub>2" [PROOF STATE] proof (prove) using this: l' < #:c\<^sub>2 goal (1 subgoal): 1. l' < #:c\<^sub>2 [PROOF STEP] . [PROOF STATE] proof (state) this: l' < #:c\<^sub>2 goal (15 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>c\<^sub>2 n et n' c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 = Label l\<rbrakk> \<Longrightarrow> l < #:c\<^sub>1;; c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 9. \<And>b c'. 0 < #:while (b) c' 10. \<And>b c'. 0 < #:while (b) c' A total of 15 subgoals... [PROOF STEP] with n l' [PROOF STATE] proof (chain) picking this: n \<oplus> #:c\<^sub>1 = Label l n = Label l' l' < #:c\<^sub>2 [PROOF STEP] show ?case [PROOF STATE] proof (prove) using this: n \<oplus> #:c\<^sub>1 = Label l n = Label l' l' < #:c\<^sub>2 goal (1 subgoal): 1. l < #:c\<^sub>1;; c\<^sub>2 [PROOF STEP] by simp [PROOF STATE] proof (state) this: l < #:c\<^sub>1;; c\<^sub>2 goal (14 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>b c'. 0 < #:while (b) c' 9. \<And>b c'. 0 < #:while (b) c' 10. \<And>b c'. 1 < #:while (b) c' A total of 14 subgoals... [PROOF STEP] next [PROOF STATE] proof (state) goal (14 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>b c'. 0 < #:while (b) c' 9. \<And>b c'. 0 < #:while (b) c' 10. \<And>b c'. 1 < #:while (b) c' A total of 14 subgoals... [PROOF STEP] case (Proc_CFG_CondThen c\<^sub>1 n et n' b c\<^sub>2 l) [PROOF STATE] proof (state) this: c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n' n = Label ?l \<Longrightarrow> ?l < #:c\<^sub>1 n \<noteq> Entry n \<oplus> 1 = Label l goal (14 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>b c'. 0 < #:while (b) c' 9. \<And>b c'. 0 < #:while (b) c' 10. \<And>b c'. 1 < #:while (b) c' A total of 14 subgoals... [PROOF STEP] note n = \<open>n \<oplus> 1 = Label l\<close> [PROOF STATE] proof (state) this: n \<oplus> 1 = Label l goal (14 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>b c'. 0 < #:while (b) c' 9. \<And>b c'. 0 < #:while (b) c' 10. \<And>b c'. 1 < #:while (b) c' A total of 14 subgoals... [PROOF STEP] note IH = \<open>\<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1\<close> [PROOF STATE] proof (state) this: n = Label ?l \<Longrightarrow> ?l < #:c\<^sub>1 goal (14 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>b c'. 0 < #:while (b) c' 9. \<And>b c'. 0 < #:while (b) c' 10. \<And>b c'. 1 < #:while (b) c' A total of 14 subgoals... [PROOF STEP] from n [PROOF STATE] proof (chain) picking this: n \<oplus> 1 = Label l [PROOF STEP] obtain l' where l':"n = Label l'" [PROOF STATE] proof (prove) using this: n \<oplus> 1 = Label l goal (1 subgoal): 1. (\<And>l'. n = Label l' \<Longrightarrow> thesis) \<Longrightarrow> thesis [PROOF STEP] by(cases n) auto [PROOF STATE] proof (state) this: n = Label l' goal (14 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>b c'. 0 < #:while (b) c' 9. \<And>b c'. 0 < #:while (b) c' 10. \<And>b c'. 1 < #:while (b) c' A total of 14 subgoals... [PROOF STEP] from IH[OF this] [PROOF STATE] proof (chain) picking this: l' < #:c\<^sub>1 [PROOF STEP] have "l' < #:c\<^sub>1" [PROOF STATE] proof (prove) using this: l' < #:c\<^sub>1 goal (1 subgoal): 1. l' < #:c\<^sub>1 [PROOF STEP] . [PROOF STATE] proof (state) this: l' < #:c\<^sub>1 goal (14 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>c\<^sub>1 n et n' b c\<^sub>2 l. \<lbrakk>c\<^sub>1 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>1; n \<noteq> Entry; n \<oplus> 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 8. \<And>b c'. 0 < #:while (b) c' 9. \<And>b c'. 0 < #:while (b) c' 10. \<And>b c'. 1 < #:while (b) c' A total of 14 subgoals... [PROOF STEP] with n l' [PROOF STATE] proof (chain) picking this: n \<oplus> 1 = Label l n = Label l' l' < #:c\<^sub>1 [PROOF STEP] show ?case [PROOF STATE] proof (prove) using this: n \<oplus> 1 = Label l n = Label l' l' < #:c\<^sub>1 goal (1 subgoal): 1. l < #:if (b) c\<^sub>1 else c\<^sub>2 [PROOF STEP] by simp [PROOF STATE] proof (state) this: l < #:if (b) c\<^sub>1 else c\<^sub>2 goal (13 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 0 < #:while (b) c' 9. \<And>b c'. 1 < #:while (b) c' 10. \<And>c' n et n' b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n' \<noteq> Exit; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' A total of 13 subgoals... [PROOF STEP] next [PROOF STATE] proof (state) goal (13 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 0 < #:while (b) c' 9. \<And>b c'. 1 < #:while (b) c' 10. \<And>c' n et n' b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n' \<noteq> Exit; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' A total of 13 subgoals... [PROOF STEP] case (Proc_CFG_CondElse c\<^sub>2 n et n' b c\<^sub>1 l) [PROOF STATE] proof (state) this: c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n' n = Label ?l \<Longrightarrow> ?l < #:c\<^sub>2 n \<noteq> Entry n \<oplus> #:c\<^sub>1 + 1 = Label l goal (13 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 0 < #:while (b) c' 9. \<And>b c'. 1 < #:while (b) c' 10. \<And>c' n et n' b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n' \<noteq> Exit; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' A total of 13 subgoals... [PROOF STEP] note n = \<open>n \<oplus> (#:c\<^sub>1 + 1) = Label l\<close> [PROOF STATE] proof (state) this: n \<oplus> #:c\<^sub>1 + 1 = Label l goal (13 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 0 < #:while (b) c' 9. \<And>b c'. 1 < #:while (b) c' 10. \<And>c' n et n' b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n' \<noteq> Exit; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' A total of 13 subgoals... [PROOF STEP] note IH = \<open>\<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2\<close> [PROOF STATE] proof (state) this: n = Label ?l \<Longrightarrow> ?l < #:c\<^sub>2 goal (13 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 0 < #:while (b) c' 9. \<And>b c'. 1 < #:while (b) c' 10. \<And>c' n et n' b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n' \<noteq> Exit; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' A total of 13 subgoals... [PROOF STEP] from n [PROOF STATE] proof (chain) picking this: n \<oplus> #:c\<^sub>1 + 1 = Label l [PROOF STEP] obtain l' where l':"n = Label l'" [PROOF STATE] proof (prove) using this: n \<oplus> #:c\<^sub>1 + 1 = Label l goal (1 subgoal): 1. (\<And>l'. n = Label l' \<Longrightarrow> thesis) \<Longrightarrow> thesis [PROOF STEP] by(cases n) auto [PROOF STATE] proof (state) this: n = Label l' goal (13 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 0 < #:while (b) c' 9. \<And>b c'. 1 < #:while (b) c' 10. \<And>c' n et n' b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n' \<noteq> Exit; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' A total of 13 subgoals... [PROOF STEP] from IH[OF this] [PROOF STATE] proof (chain) picking this: l' < #:c\<^sub>2 [PROOF STEP] have "l' < #:c\<^sub>2" [PROOF STATE] proof (prove) using this: l' < #:c\<^sub>2 goal (1 subgoal): 1. l' < #:c\<^sub>2 [PROOF STEP] . [PROOF STATE] proof (state) this: l' < #:c\<^sub>2 goal (13 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>c\<^sub>2 n et n' b c\<^sub>1 l. \<lbrakk>c\<^sub>2 \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c\<^sub>2; n \<noteq> Entry; n \<oplus> #:c\<^sub>1 + 1 = Label l\<rbrakk> \<Longrightarrow> l < #:if (b) c\<^sub>1 else c\<^sub>2 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 0 < #:while (b) c' 9. \<And>b c'. 1 < #:while (b) c' 10. \<And>c' n et n' b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n' \<noteq> Exit; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' A total of 13 subgoals... [PROOF STEP] with n l' [PROOF STATE] proof (chain) picking this: n \<oplus> #:c\<^sub>1 + 1 = Label l n = Label l' l' < #:c\<^sub>2 [PROOF STEP] show ?case [PROOF STATE] proof (prove) using this: n \<oplus> #:c\<^sub>1 + 1 = Label l n = Label l' l' < #:c\<^sub>2 goal (1 subgoal): 1. l < #:if (b) c\<^sub>1 else c\<^sub>2 [PROOF STEP] by simp [PROOF STATE] proof (state) this: l < #:if (b) c\<^sub>1 else c\<^sub>2 goal (12 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>c' n et n' b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n' \<noteq> Exit; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' 10. \<And>c' n et b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' A total of 12 subgoals... [PROOF STEP] next [PROOF STATE] proof (state) goal (12 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>c' n et n' b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n' \<noteq> Exit; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' 10. \<And>c' n et b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' A total of 12 subgoals... [PROOF STEP] case (Proc_CFG_WhileBody c' n et n' b l) [PROOF STATE] proof (state) this: c' \<turnstile> n -et\<rightarrow>\<^sub>p n' n = Label ?l \<Longrightarrow> ?l < #:c' n \<noteq> Entry n' \<noteq> Exit n \<oplus> 2 = Label l goal (12 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>c' n et n' b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n' \<noteq> Exit; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' 10. \<And>c' n et b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' A total of 12 subgoals... [PROOF STEP] note n = \<open>n \<oplus> 2 = Label l\<close> [PROOF STATE] proof (state) this: n \<oplus> 2 = Label l goal (12 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>c' n et n' b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n' \<noteq> Exit; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' 10. \<And>c' n et b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' A total of 12 subgoals... [PROOF STEP] note IH = \<open>\<And>l. n = Label l \<Longrightarrow> l < #:c'\<close> [PROOF STATE] proof (state) this: n = Label ?l \<Longrightarrow> ?l < #:c' goal (12 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>c' n et n' b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n' \<noteq> Exit; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' 10. \<And>c' n et b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' A total of 12 subgoals... [PROOF STEP] from n [PROOF STATE] proof (chain) picking this: n \<oplus> 2 = Label l [PROOF STEP] obtain l' where l':"n = Label l'" [PROOF STATE] proof (prove) using this: n \<oplus> 2 = Label l goal (1 subgoal): 1. (\<And>l'. n = Label l' \<Longrightarrow> thesis) \<Longrightarrow> thesis [PROOF STEP] by(cases n) auto [PROOF STATE] proof (state) this: n = Label l' goal (12 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>c' n et n' b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n' \<noteq> Exit; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' 10. \<And>c' n et b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' A total of 12 subgoals... [PROOF STEP] from IH[OF this] [PROOF STATE] proof (chain) picking this: l' < #:c' [PROOF STEP] have "l' < #:c'" [PROOF STATE] proof (prove) using this: l' < #:c' goal (1 subgoal): 1. l' < #:c' [PROOF STEP] . [PROOF STATE] proof (state) this: l' < #:c' goal (12 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>c' n et n' b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p n'; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n' \<noteq> Exit; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' 10. \<And>c' n et b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' A total of 12 subgoals... [PROOF STEP] with n l' [PROOF STATE] proof (chain) picking this: n \<oplus> 2 = Label l n = Label l' l' < #:c' [PROOF STEP] show ?case [PROOF STATE] proof (prove) using this: n \<oplus> 2 = Label l n = Label l' l' < #:c' goal (1 subgoal): 1. l < #:while (b) c' [PROOF STEP] by simp [PROOF STATE] proof (state) this: l < #:while (b) c' goal (11 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>c' n et b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' 10. \<And>p es rets. 0 < #:Call p es rets A total of 11 subgoals... [PROOF STEP] next [PROOF STATE] proof (state) goal (11 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>c' n et b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' 10. \<And>p es rets. 0 < #:Call p es rets A total of 11 subgoals... [PROOF STEP] case (Proc_CFG_WhileBodyExit c' n et b l) [PROOF STATE] proof (state) this: c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit n = Label ?l \<Longrightarrow> ?l < #:c' n \<noteq> Entry n \<oplus> 2 = Label l goal (11 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>c' n et b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' 10. \<And>p es rets. 0 < #:Call p es rets A total of 11 subgoals... [PROOF STEP] note n = \<open>n \<oplus> 2 = Label l\<close> [PROOF STATE] proof (state) this: n \<oplus> 2 = Label l goal (11 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>c' n et b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' 10. \<And>p es rets. 0 < #:Call p es rets A total of 11 subgoals... [PROOF STEP] note IH = \<open>\<And>l. n = Label l \<Longrightarrow> l < #:c'\<close> [PROOF STATE] proof (state) this: n = Label ?l \<Longrightarrow> ?l < #:c' goal (11 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>c' n et b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' 10. \<And>p es rets. 0 < #:Call p es rets A total of 11 subgoals... [PROOF STEP] from n [PROOF STATE] proof (chain) picking this: n \<oplus> 2 = Label l [PROOF STEP] obtain l' where l':"n = Label l'" [PROOF STATE] proof (prove) using this: n \<oplus> 2 = Label l goal (1 subgoal): 1. (\<And>l'. n = Label l' \<Longrightarrow> thesis) \<Longrightarrow> thesis [PROOF STEP] by(cases n) auto [PROOF STATE] proof (state) this: n = Label l' goal (11 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>c' n et b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' 10. \<And>p es rets. 0 < #:Call p es rets A total of 11 subgoals... [PROOF STEP] from IH[OF this] [PROOF STATE] proof (chain) picking this: l' < #:c' [PROOF STEP] have "l' < #:c'" [PROOF STATE] proof (prove) using this: l' < #:c' goal (1 subgoal): 1. l' < #:c' [PROOF STEP] . [PROOF STATE] proof (state) this: l' < #:c' goal (11 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>c' n et b l. \<lbrakk>c' \<turnstile> n -et\<rightarrow>\<^sub>p Exit; \<And>l. n = Label l \<Longrightarrow> l < #:c'; n \<noteq> Entry; n \<oplus> 2 = Label l\<rbrakk> \<Longrightarrow> l < #:while (b) c' 10. \<And>p es rets. 0 < #:Call p es rets A total of 11 subgoals... [PROOF STEP] with n l' [PROOF STATE] proof (chain) picking this: n \<oplus> 2 = Label l n = Label l' l' < #:c' [PROOF STEP] show ?case [PROOF STATE] proof (prove) using this: n \<oplus> 2 = Label l n = Label l' l' < #:c' goal (1 subgoal): 1. l < #:while (b) c' [PROOF STEP] by simp [PROOF STATE] proof (state) this: l < #:while (b) c' goal (10 subgoals): 1. 0 < #:Skip 2. \<And>V e. 0 < #:V:=e 3. \<And>V e. 1 < #:V:=e 4. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 5. \<And>b c\<^sub>1 c\<^sub>2. 0 < #:if (b) c\<^sub>1 else c\<^sub>2 6. \<And>b c'. 0 < #:while (b) c' 7. \<And>b c'. 0 < #:while (b) c' 8. \<And>b c'. 1 < #:while (b) c' 9. \<And>p es rets. 0 < #:Call p es rets 10. \<And>p es rets. 1 < #:Call p es rets [PROOF STEP] qed (auto simp:num_inner_nodes_gr_0)
import .lib .integers .floats .maps .errors namespace ast open integers maps errors floats /- * Syntactic elements -/ /- Identifiers (names of local variables, of global symbols and functions, etc) are represented by the type [positive] of positive integers. -/ def ident := pos_num instance pos_num_eq : decidable_eq pos_num := by tactic.mk_dec_eq_instance instance ident_eq : decidable_eq ident := by tactic.mk_dec_eq_instance /- The intermediate languages are weakly typed, using the following types: -/ inductive typ : Type | Tint /- 32-bit integers or pointers -/ | Tfloat /- 64-bit double-precision floats -/ | Tlong /- 64-bit integers -/ | Tsingle /- 32-bit single-precision floats -/ | Tany32 /- any 32-bit value -/ | Tany64 /- any 64-bit value, i.e. any value -/ def typ.Tptr : typ := if archi.ptr64 then typ.Tlong else typ.Tint open typ instance typ_eq : decidable_eq typ := by tactic.mk_dec_eq_instance def typesize : typ → ℤ | Tint := 4 | Tfloat := 8 | Tlong := 8 | Tsingle := 4 | Tany32 := 4 | Tany64 := 8 lemma typesize_pos (ty) : typesize ty > 0 := by cases ty; exact dec_trivial lemma typesize_Tptr : typesize Tptr = if archi.ptr64 then 8 else 4 := by delta Tptr; cases archi.ptr64; refl /- All values of size 32 bits are also of type [Tany32]. All values are of type [Tany64]. This corresponds to the following subtyping relation over types. -/ def subtype : typ → typ → bool | Tint Tint := tt | Tlong Tlong := tt | Tfloat Tfloat := tt | Tsingle Tsingle := tt | Tint Tany32 := tt | Tsingle Tany32 := tt | Tany32 Tany32 := tt | _ Tany64 := tt | _ _ := ff def subtype_list : list typ → list typ → bool | [] [] := tt | (ty1::tys1) (ty2::tys2) := subtype ty1 ty2 && subtype_list tys1 tys2 | _ _ := ff /- Additionally, function definitions and function calls are annotated by function signatures indicating: - the number and types of arguments; - the type of the returned value, if any; - additional information on which calling convention to use. These signatures are used in particular to determine appropriate calling conventions for the function. -/ structure calling_convention : Type := mkcallconv :: (cc_vararg : bool) /- variable-arity function -/ (cc_unproto : bool) /- old-style unprototyped function -/ (cc_structret : bool) /- function returning a struct -/ instance calling_convention_eq : decidable_eq calling_convention := by tactic.mk_dec_eq_instance def cc_default : calling_convention := { cc_vararg := false, cc_unproto := false, cc_structret := false } structure signature : Type := (sig_args : list typ) (sig_res : option typ) (sig_cc : calling_convention) def proj_sig_res (s : signature) : typ := s.sig_res.get_or_else Tint instance signature_eq : decidable_eq signature := by tactic.mk_dec_eq_instance def signature_main : signature := { sig_args := [], sig_res := some Tint, sig_cc := cc_default } /- Memory accesses (load and store instructions) are annotated by a ``memory chunk'' indicating the type, size and signedness of the chunk of memory being accessed. -/ inductive memory_chunk : Type | Mint8signed /- 8-bit signed integer -/ | Mint8unsigned /- 8-bit unsigned integer -/ | Mint16signed /- 16-bit signed integer -/ | Mint16unsigned /- 16-bit unsigned integer -/ | Mint32 /- 32-bit integer, or pointer -/ | Mint64 /- 64-bit integer -/ | Mfloat32 /- 32-bit single-precision float -/ | Mfloat64 /- 64-bit double-precision float -/ | Many32 /- any value that fits in 32 bits -/ | Many64 /- any value -/ open memory_chunk instance chunk_eq : decidable_eq memory_chunk := by tactic.mk_dec_eq_instance def Mptr : memory_chunk := if archi.ptr64 then Mint64 else Mint32. /- The type (integer/pointer or float) of a chunk. -/ def memory_chunk.type : memory_chunk → typ | Mint8signed := Tint | Mint8unsigned := Tint | Mint16signed := Tint | Mint16unsigned := Tint | Mint32 := Tint | Mint64 := Tlong | Mfloat32 := Tsingle | Mfloat64 := Tfloat | Many32 := Tany32 | Many64 := Tany64 lemma memory_chunk.Mptr.type : Mptr.type = Tptr := by delta Mptr Tptr; cases archi.ptr64; refl def chunk_of_type : typ → memory_chunk | Tint := Mint32 | Tfloat := Mfloat64 | Tlong := Mint64 | Tsingle := Mfloat32 | Tany32 := Many32 | Tany64 := Many64 lemma chunk_of_Tptr : chunk_of_type Tptr = Mptr := by delta Mptr Tptr; cases archi.ptr64; refl /- * Properties of memory chunks -/ /- Memory reads and writes are performed by quantities called memory chunks, encoding the type, size and signedness of the chunk being addressed. The following functions extract the size information from a chunk. -/ def memory_chunk.size : memory_chunk → ℕ | Mint8signed := 1 | Mint8unsigned := 1 | Mint16signed := 2 | Mint16unsigned := 2 | Mint32 := 4 | Mint64 := 8 | Mfloat32 := 4 | Mfloat64 := 8 | Many32 := 4 | Many64 := 8 lemma memory_chunk.size_pos (chunk) : memory_chunk.size chunk > 0 := by cases chunk; exact dec_trivial lemma memory_chunk.Mptr.size_eq : Mptr.size = if archi.ptr64 then 8 else 4 := by delta Mptr; cases archi.ptr64; refl /- Memory reads and writes must respect alignment constraints: the byte offset of the location being addressed should be an exact multiple of the natural alignment for the chunk being addressed. This natural alignment is defined by the following [align_chunk] function. Some target architectures (e.g. PowerPC and x86) have no alignment constraints, which we could reflect by taking [align_chunk chunk = 1]. However, other architectures have stronger alignment requirements. The following definition is appropriate for PowerPC, ARM and x86. -/ def memory_chunk.align : memory_chunk → ℕ | Mint8signed := 1 | Mint8unsigned := 1 | Mint16signed := 2 | Mint16unsigned := 2 | Mint32 := 4 | Mint64 := 8 | Mfloat32 := 4 | Mfloat64 := 4 | Many32 := 4 | Many64 := 4 lemma memory_chunk.align_pos (chunk) : memory_chunk.align chunk > 0 := by cases chunk; exact dec_trivial lemma memory_chunk.Mptr.align : Mptr.align = if archi.ptr64 then 8 else 4 := by delta Mptr; cases archi.ptr64; refl lemma align_size_chunk_dvd (chunk : memory_chunk) : chunk.align ∣ chunk.size := sorry' lemma align_le_dvd (chunk1 chunk2 : memory_chunk) (h : chunk1.align ≤ chunk2.align) : chunk1.align ∣ chunk2.align := sorry' /- Initialization data for global variables. -/ inductive init_data : Type | int8 : int32 → init_data | int16 : int32 → init_data | int32 : int32 → init_data | int64 : int64 → init_data | float32 : float32 → init_data | float64 : float → init_data | space : ℕ → init_data | addrof : ident → ptrofs → init_data /- address of symbol + offset -/ namespace init_data def size : init_data → ℕ | (int8 _) := 1 | (int16 _) := 2 | (int32 _) := 4 | (int64 _) := 8 | (float32 _) := 4 | (float64 _) := 8 | (addrof _ _) := if archi.ptr64 then 8 else 4 | (space n) := n def align : init_data → ℕ | (int8 _) := 1 | (int16 _) := 2 | (int32 _) := 4 | (int64 _) := 8 | (float32 _) := 4 | (float64 _) := 4 | (addrof _ _) := if archi.ptr64 then 8 else 4 | (space _) := 1 def list_size : list init_data → ℕ | [] := 0 | (i :: il') := i.size + list_size il' lemma size_pos (i : init_data) : i.size ≥ 0 := sorry' lemma list_size_pos (il) : list_size il ≥ 0 := sorry' def list_aligned : ℕ → list init_data → Prop | p [] := true | p (i1 :: il) := i1.align ∣ p ∧ list_aligned (p + i1.size) il end init_data /- Information attached to global variables. -/ structure globvar (V : Type) : Type := (info : V) /- language-dependent info, e.g. a type -/ (init : list init_data) /- initialization data -/ (readonly : bool) /- read-only variable? (const) -/ (volatile : bool) /- volatile variable? -/ /- Whole programs consist of: - a collection of global definitions (name and description); - a set of public names (the names that are visible outside this compilation unit); - the name of the ``main'' function that serves as entry point in the program. A global definition is either a global function or a global variable. The type of function descriptions and that of additional information for variables vary among the various intermediate languages and are taken as parameters to the [program] type. The other parts of whole programs are common to all languages. -/ inductive globdef (F V : Type) : Type | Gfun {} (f : F) : globdef | Gvar {} (v : globvar V) : globdef export globdef structure program (F V : Type) : Type := (defs : list (ident × globdef F V)) (public : list ident) (main : ident) def program.defs_names {F V : Type} (p : program F V) : list ident := p.defs.map prod.fst /- The "definition map" of a program maps names of globals to their definitions. If several definitions have the same name, the one appearing last in [p.defs] wins. -/ section defmap variables {F V : Type} variable p : program F V def prog_defmap : PTree (globdef F V) := PTree.of_list p.defs lemma in_prog_defmap {id : ident} {g} : (prog_defmap p ^! id) = some g → (id, g) ∈ p.defs := sorry' lemma prog_defmap_dom {id : ident} : id ∈ p.defs_names → ∃ g, (prog_defmap p^!id) = some g := sorry' lemma prog_defmap_unique (defs1 id g defs2) : p.defs = defs1 ++ (id, g) :: defs2 → id ∉ defs2.map prod.fst → (prog_defmap p^!id) = some g := sorry' lemma prog_defmap_nodup {id : ident} {g} : p.defs_names.nodup → (id, g) ∈ p.defs → (prog_defmap p ^! id) = some g := sorry' end defmap /- * Generic transformations over programs -/ /- We now define a general iterator over programs that applies a given code transformation function to all function descriptions and leaves the other parts of the program unchanged. -/ section transf_program parameters {A B V : Type} (transf : A → B) def transform_program_globdef : ident × globdef A V → ident × globdef B V | (id, Gfun f) := (id, Gfun (transf f)) | (id, Gvar v) := (id, Gvar v) def transform_program : program A V → program B V | ⟨defs, pub, main⟩ := ⟨defs.map transform_program_globdef, pub, main⟩ end transf_program /- The following is a more general presentation of [transform_program]: - Global variable information can be transformed, in addition to function definitions. - The transformation functions can fail and return an error message. - The transformation for function definitions receives a global context (derived from the compilation unit being transformed) as additiona argument. - The transformation functions receive the name of the global as additional argument. -/ section transf_program_gen parameters {A B V W : Type} parameter transf_fun : ident → A → res B. parameter transf_var : ident → V → res W. def transf_globvar (i : ident) : globvar V → res (globvar W) | ⟨info, init, ro, vo⟩ := do info' ← transf_var i info, OK ⟨info', init, ro, vo⟩ def transf_globdefs : list (ident × globdef A V) → res (list (ident × globdef B W)) | [] := OK [] | ((id, Gfun f) :: l') := match transf_fun id f with | error msg := error (MSG "In function " :: CTX id :: MSG ": " :: msg) | OK tf := do tl' ← transf_globdefs l', OK ((id, Gfun tf) :: tl') end | ((id, Gvar v) :: l') := match transf_globvar id v with | error msg := error (MSG "In variable " :: CTX id :: MSG ": " :: msg) | OK tv := do tl' ← transf_globdefs l', OK ((id, Gvar tv) :: tl') end def transform_partial_program2 : program A V → res (program B W) | ⟨defs, pub, main⟩ := do gl' ← transf_globdefs defs, OK ⟨gl', pub, main⟩ end transf_program_gen /- The following is a special case of [transform_partial_program2], where only function definitions are transformed, but not variable definitions. -/ def transform_partial_program {A B V} (transf_fun : A → res B) : program A V → res (program B V) := transform_partial_program2 (λ i, transf_fun) (λ i, OK) lemma transform_program_partial_program {A B V} (transf_fun : A → B) (p : program A V) : transform_partial_program (λ f, OK (transf_fun f)) p = OK (transform_program transf_fun p) := sorry' /- * External functions -/ /- For most languages, the functions composing the program are either internal functions, defined within the language, or external functions, defined outside. External functions include system calls but also compiler built-in functions. We define a type for external functions and associated operations. -/ inductive external_function : Type | EF_external (name : string) (sg : signature) /- A system call or library function. Produces an event in the trace. -/ | EF_builtin (name : string) (sg : signature) /- A compiler built-in function. Behaves like an external, but can be inlined by the compiler. -/ | EF_runtime (name : string) (sg : signature) /- A function from the run-time library. Behaves like an external, but must not be redefined. -/ | EF_vload (chunk : memory_chunk) /- A volatile read operation. If the adress given as first argument points within a volatile global variable, generate an event and return the value found in this event. Otherwise, produce no event and behave like a regular memory load. -/ | EF_vstore (chunk : memory_chunk) /- A volatile store operation. If the adress given as first argument points within a volatile global variable, generate an event. Otherwise, produce no event and behave like a regular memory store. -/ | EF_malloc /- Dynamic memory allocation. Takes the requested size in bytes as argument; returns a pointer to a fresh block of the given size. Produces no observable event. -/ | EF_free /- Dynamic memory deallocation. Takes a pointer to a block allocated by an [EF_malloc] external call and frees the corresponding block. Produces no observable event. -/ | EF_memcpy (sz al : ℕ) /- Block copy, of [sz] bytes, between addresses that are [al]-aligned. -/ | EF_annot (text : string) (targs : list typ) /- A programmer-supplied annotation. Takes zero, one or several arguments, produces an event carrying the text and the values of these arguments, and returns no value. -/ | EF_annot_val (text : string) (targ : typ) /- Another form of annotation that takes one argument, produces an event carrying the text and the value of this argument, and returns the value of the argument. -/ | EF_inline_asm (text : string) (sg : signature) (clobbers : list string) /- Inline [asm] statements. Semantically, treated like an annotation with no parameters ([EF_annot text nil]). To be used with caution, as it can invalidate the semantic preservation theorem. Generated only if [-finline-asm] is given. -/ | EF_debug (kind : pos_num) (text : ident) (targs : list typ) /- Transport debugging information from the front-end to the generated assembly. Takes zero, one or several arguments like [EF_annot]. Unlike [EF_annot], produces no observable event. -/ export external_function /- The type signature of an external function. -/ def ef_sig : external_function → signature | (EF_external name sg) := sg | (EF_builtin name sg) := sg | (EF_runtime name sg) := sg | (EF_vload chunk) := ⟨[Tptr], some chunk.type, cc_default⟩ | (EF_vstore chunk) := ⟨[Tptr, chunk.type], none, cc_default⟩ | (EF_malloc) := ⟨[Tptr], some Tptr, cc_default⟩ | (EF_free) := ⟨[Tptr], none, cc_default⟩ | (EF_memcpy sz al) := ⟨[Tptr, Tptr], none, cc_default⟩ | (EF_annot text targs) := ⟨targs, none, cc_default⟩ | (EF_annot_val text targ) := ⟨[Tptr], some targ, cc_default⟩ | (EF_inline_asm text sg clob) := sg | (EF_debug kind text targs) := ⟨targs, none, cc_default⟩ /- Whether an external function should be inlined by the compiler. -/ def ef_inline : external_function → bool | (EF_external name sg) := ff | (EF_builtin name sg) := tt | (EF_runtime name sg) := ff | (EF_vload chunk) := tt | (EF_vstore chunk) := tt | (EF_malloc) := ff | (EF_free) := ff | (EF_memcpy sz al) := tt | (EF_annot text targs) := tt | (EF_annot_val text targ) := tt | (EF_inline_asm text sg clob) := tt | (EF_debug kind text targs) := tt /- Whether an external function must reload its arguments. -/ def ef_reloads : external_function → bool | (EF_annot text targs) := ff | (EF_debug kind text targs) := ff | _ := tt /- Equality between external functions. Used in module [Allocation]. -/ instance external_function_eq : decidable_eq external_function := by tactic.mk_dec_eq_instance /- Function definitions are the union of internal and external functions. -/ inductive fundef (F : Type) : Type | Internal {} : F → fundef | External {} : external_function → fundef open fundef section transf_fundef parameters {A B : Type} (transf : A → B) def transf_fundef : fundef A → fundef B | (Internal f) := Internal (transf f) | (External ef) := External ef end transf_fundef section transf_partial_fundef parameters {A B : Type} (transf_partial : A → res B) def transf_partial_fundef : fundef A → res (fundef B) | (Internal f) := do f' ← transf_partial f, OK (Internal f') | (External ef) := OK (External ef) end transf_partial_fundef /- * Register pairs -/ /- In some intermediate languages (LTL, Mach), 64-bit integers can be split into two 32-bit halves and held in a pair of registers. Syntactically, this is captured by the type [rpair] below. -/ inductive rpair (A : Type) : Type | One (r : A) : rpair | Twolong (rhi rlo : A) : rpair open rpair def typ_rpair {A} (typ_of : A → typ) : rpair A → typ | (One r) := typ_of r | (Twolong rhi rlo) := Tlong def map_rpair {A B} (f : A → B) : rpair A → rpair B | (One r) := One (f r) | (Twolong rhi rlo) := Twolong (f rhi) (f rlo) def regs_of_rpair {A} : rpair A → list A | (One r) := [r] | (Twolong rhi rlo) := [rhi, rlo] def regs_of_rpairs {A} : list (rpair A) → list A | [] := [] | (p :: l) := regs_of_rpair p ++ regs_of_rpairs l lemma in_regs_of_rpair {A} (x : A) (p) (hm : x ∈ regs_of_rpair p) (l : list (rpair A)) (hp : p ∈ l) : x ∈ regs_of_rpairs l := sorry' lemma in_regs_of_rpairs_inv {A} (x : A) (l : list (rpair A)) (hm : x ∈ regs_of_rpairs l) : ∃ p, p ∈ l ∧ x ∈ regs_of_rpair p := sorry' def forall_rpair {A} (P : A → Prop) : rpair A → Prop | (One r) := P r | (Twolong rhi rlo) := P rhi ∧ P rlo /- * Arguments and results to builtin functions -/ inductive builtin_arg (A : Type) : Type | BA {} (x : A) : builtin_arg | BA_int {} (n : int32) : builtin_arg | BA_long {} (n : int64) : builtin_arg | BA_float {} (f : float) : builtin_arg | BA_single {} (f : float32) : builtin_arg | BA_loadstack {} (chunk : memory_chunk) (ofs : ptrofs) : builtin_arg | BA_addrstack {} (ofs : ptrofs) : builtin_arg | BA_loadglobal {} (chunk : memory_chunk) (id : ident) (ofs : ptrofs) : builtin_arg | BA_addrglobal {} (id : ident) (ofs : ptrofs) : builtin_arg | BA_splitlong {} (hi lo : builtin_arg) : builtin_arg export builtin_arg inductive builtin_res (A : Type) : Type | BR {} (x : A) : builtin_res | BR_none {} : builtin_res | BR_splitlong {} (hi lo : builtin_res) : builtin_res open builtin_res def globals_of_builtin_arg {A : Type} : builtin_arg A → list ident | (BA_loadglobal chunk id ofs) := [id] | (BA_addrglobal id ofs) := [id] | (BA_splitlong hi lo) := globals_of_builtin_arg hi ++ globals_of_builtin_arg lo | _ := [] def globals_of_builtin_args {A} (al : list (builtin_arg A)) : list ident := al.foldr (λ a l, globals_of_builtin_arg a ++ l) [] def params_of_builtin_arg {A} : builtin_arg A → list A | (BA x) := [x] | (BA_splitlong hi lo) := params_of_builtin_arg hi ++ params_of_builtin_arg lo | _ := [] def params_of_builtin_args {A} (al : list (builtin_arg A)) : list A := al.foldr (λ a l, params_of_builtin_arg a ++ l) [] def params_of_builtin_res {A} : builtin_res A → list A | (BR x) := [x] | BR_none := [] | (BR_splitlong hi lo) := params_of_builtin_res hi ++ params_of_builtin_res lo def map_builtin_arg {A B} (f : A → B) : builtin_arg A → builtin_arg B | (BA x) := BA (f x) | (BA_int n) := BA_int n | (BA_long n) := BA_long n | (BA_float n) := BA_float n | (BA_single n) := BA_single n | (BA_loadstack chunk ofs) := BA_loadstack chunk ofs | (BA_addrstack ofs) := BA_addrstack ofs | (BA_loadglobal chunk id ofs) := BA_loadglobal chunk id ofs | (BA_addrglobal id ofs) := BA_addrglobal id ofs | (BA_splitlong hi lo) := BA_splitlong (map_builtin_arg hi) (map_builtin_arg lo) def map_builtin_res {A B} (f : A → B) : builtin_res A → builtin_res B | (BR x) := BR (f x) | BR_none := BR_none | (BR_splitlong hi lo) := BR_splitlong (map_builtin_res hi) (map_builtin_res lo) /- Which kinds of builtin arguments are supported by which external function. -/ inductive builtin_arg_constraint : Type | OK_default | OK_const | OK_addrstack | OK_addrglobal | OK_addrany | OK_all open builtin_arg_constraint def builtin_arg_ok {A} : builtin_arg A → builtin_arg_constraint → bool | (BA _) _ := tt | (BA_splitlong (BA _) (BA _)) _ := tt | (BA_int _) OK_const := tt | (BA_long _) OK_const := tt | (BA_float _) OK_const := tt | (BA_single _) OK_const := tt | (BA_addrstack _) OK_addrstack := tt | (BA_addrstack _) OK_addrany := tt | (BA_addrglobal _ _) OK_addrglobal := tt | (BA_addrglobal _ _) OK_addrany := tt | _ OK_all := tt | _ _ := ff end ast
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Categories.Morphism where open import Cubical.Foundations.Prelude open import Cubical.Data.Sigma open import Cubical.Categories.Category private variable ℓ ℓ' : Level module _ {C : Precategory ℓ ℓ'} where open Precategory C private variable x y z w : ob isMonic : (Hom[ x , y ]) → Type (ℓ-max ℓ ℓ') isMonic {x} {y} f = ∀ {z : ob} {a a' : Hom[ z , x ]} → (f ∘ a ≡ f ∘ a') → (a ≡ a') isEpic : (Hom[ x , y ]) → Type (ℓ-max ℓ ℓ') isEpic {x} {y} g = ∀ {z : ob} {b b' : Hom[ y , z ]} → (b ∘ g ≡ b' ∘ g) → (b ≡ b') -- A morphism is split monic if it has a *retraction* isSplitMon : (Hom[ x , y ]) → Type ℓ' isSplitMon {x} {y} f = ∃[ r ∈ Hom[ y , x ] ] r ∘ f ≡ id x -- A morphism is split epic if it has a *section* isSplitEpi : (Hom[ x , y ]) → Type ℓ' isSplitEpi {x} {y} g = ∃[ s ∈ Hom[ y , x ] ] g ∘ s ≡ id y record areInv (f : Hom[ x , y ]) (g : Hom[ y , x ]) : Type ℓ' where field sec : g ⋆ f ≡ id y ret : f ⋆ g ≡ id x open areInv symAreInv : ∀ {f : Hom[ x , y ]} {g : Hom[ y , x ]} → areInv f g → areInv g f symAreInv record { sec = sec ; ret = ret } = record { sec = ret ; ret = sec } -- equational reasoning with inverses invMoveR : ∀ {f : Hom[ x , y ]} {g : Hom[ y , x ]} {h : Hom[ z , x ]} {k : Hom[ z , y ]} → areInv f g → h ⋆ f ≡ k → h ≡ k ⋆ g invMoveR {f = f} {g} {h} {k} ai p = h ≡⟨ sym (⋆IdR _) ⟩ (h ⋆ id _) ≡⟨ cong (h ⋆_) (sym (ai .ret)) ⟩ (h ⋆ (f ⋆ g)) ≡⟨ sym (⋆Assoc _ _ _) ⟩ ((h ⋆ f) ⋆ g) ≡⟨ cong (_⋆ g) p ⟩ k ⋆ g ∎ invMoveL : ∀ {f : Hom[ x , y ]} {g : Hom[ y , x ]} {h : Hom[ y , z ]} {k : Hom[ x , z ]} → areInv f g → f ⋆ h ≡ k → h ≡ g ⋆ k invMoveL {f = f} {g} {h} {k} ai p = h ≡⟨ sym (⋆IdL _) ⟩ id _ ⋆ h ≡⟨ cong (_⋆ h) (sym (ai .sec)) ⟩ (g ⋆ f) ⋆ h ≡⟨ ⋆Assoc _ _ _ ⟩ g ⋆ (f ⋆ h) ≡⟨ cong (g ⋆_) p ⟩ (g ⋆ k) ∎ record isIso (f : Hom[ x , y ]) : Type ℓ' where field inv : Hom[ y , x ] sec : inv ⋆ f ≡ id y ret : f ⋆ inv ≡ id x open isIso isIso→areInv : ∀ {f : Hom[ x , y ]} → (isI : isIso f) → areInv f (isI .inv) isIso→areInv record { inv = inv ; sec = sec ; ret = ret } = record { sec = sec ; ret = ret } open CatIso -- isIso agrees with CatIso isIso→CatIso : ∀ {f : C [ x , y ]} → isIso f → CatIso {C = C} x y isIso→CatIso {f = f} record { inv = f⁻¹ ; sec = sec ; ret = ret } = catiso f f⁻¹ sec ret CatIso→isIso : (cIso : CatIso {C = C} x y) → isIso (cIso .mor) CatIso→isIso (catiso mor inv sec ret) = record { inv = inv ; sec = sec ; ret = ret } CatIso→areInv : (cIso : CatIso {C = C} x y) → areInv (cIso .mor) (cIso .inv) CatIso→areInv cIso = isIso→areInv (CatIso→isIso cIso) -- reverse of an iso is also an iso symCatIso : ∀ {x y} → CatIso {C = C} x y → CatIso {C = C} y x symCatIso (catiso mor inv sec ret) = catiso inv mor ret sec
Formal statement is: lemma setdist_neq_0_sing_2: "\<lbrakk>setdist S {x} = a; a \<noteq> 0\<rbrakk> \<Longrightarrow> S \<noteq> {} \<and> x \<notin> closure S" Informal statement is: If the distance between a set $S$ and a point $x$ is nonzero, then $S$ is nonempty and $x$ is not in the closure of $S$.
> We also have support for forums. Should Xubuntu have forums on the site? > There has been some interest in it before. Do kubuntu or edubuntu have separate forums?
Load LFindLoad. From lfind Require Import LFind. From QuickChick Require Import QuickChick. From adtind Require Import goal33. Derive Show for natural. Derive Arbitrary for natural. Instance Dec_Eq_natural : Dec_Eq natural. Proof. dec_eq. Qed. Lemma conj20synthconj3_hyp: forall (lv0 : natural) (lv1 : natural) (lv2 : natural), (@eq natural (plus lv0 lv1) (mult lv1 (Succ lv2))) -> (@eq natural (Succ (plus lv0 (plus lv1 lv2))) (plus (mult lv1 (plus lv2 (Succ Zero))) (plus lv2 (Succ Zero)))). Admitted. QuickChick conj20synthconj3_hyp.
(* Author: Tobias Nipkow *) section \<open>Function \textit{isin} for Tree2\<close> theory Isin2 imports Tree2 Cmp Set_Specs begin fun isin :: "('a::linorder*'b) tree \<Rightarrow> 'a \<Rightarrow> bool" where "isin Leaf x = False" | "isin (Node l (a,_) r) x = (case cmp x a of LT \<Rightarrow> isin l x | EQ \<Rightarrow> True | GT \<Rightarrow> isin r x)" lemma isin_set_inorder: "sorted(inorder t) \<Longrightarrow> isin t x = (x \<in> set(inorder t))" by (induction t rule: tree2_induct) (auto simp: isin_simps) lemma isin_set_tree: "bst t \<Longrightarrow> isin t x \<longleftrightarrow> x \<in> set_tree t" by(induction t rule: tree2_induct) auto end
Load LFindLoad. From lfind Require Import LFind. From QuickChick Require Import QuickChick. From adtind Require Import goal33. Derive Show for natural. Derive Arbitrary for natural. Instance Dec_Eq_natural : Dec_Eq natural. Proof. dec_eq. Qed. Lemma conj26eqsynthconj1 : forall (lv0 : natural), (@eq natural (lv0) (plus Zero (plus Zero lv0))). Admitted. QuickChick conj26eqsynthconj1.
(** ********************************************************** Ralph Matthes 2019, change to [z_iso] as base notion in 2021 *) (** ********************************************************** Contents : - build monoidal category for the endofunctors ************************************************************) Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. (* Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.UnitorsAndAssociatorsForEndofunctors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.HorizontalComposition. *) Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.Bicategories.MonoidalCategories.MonoidalFromBicategory. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Local Open Scope cat. Section Endofunctors_as_monoidal_category. Context (C : category). (* (** The category of endofunctors on [C] *) Local Notation "'EndC'":= ([C, C]) . Local Lemma is_nat_trans_left_unitor_data: is_nat_trans (I_pretensor (functorial_composition _ _ _) (functor_identity C)) (functor_identity [C, C]) (@λ_functors C C). Proof. intros F F' m. apply nat_trans_eq_alt. intro c. cbn. rewrite (functor_id F). do 2 rewrite id_left. apply id_right. Qed. Definition left_unitor_of_endofunctors: left_unitor (functorial_composition _ _ _) (functor_identity C). Proof. use make_nat_z_iso. + use make_nat_trans. * intro F. apply λ_functors. * apply is_nat_trans_left_unitor_data. + red. intro F. cbn. use nat_trafo_z_iso_if_pointwise_z_iso. intro c. use tpair. * exact (identity (pr1 F c)). * abstract ( apply Isos.is_inverse_in_precat_identity ). Defined. Local Lemma is_nat_trans_right_unitor_data: is_nat_trans (I_posttensor (functorial_composition _ _ _) (functor_identity C)) (functor_identity [C, C]) (@ρ_functors C C). Proof. intros F F' m. apply nat_trans_eq_alt. intro c. cbn. rewrite id_left. rewrite id_right. apply id_right. Qed. Definition right_unitor_of_endofunctors: right_unitor (functorial_composition _ _ _) (functor_identity C). Proof. use make_nat_z_iso. + use make_nat_trans. * intro F. apply ρ_functors. * apply is_nat_trans_right_unitor_data. + red. intro F. cbn. use nat_trafo_z_iso_if_pointwise_z_iso. intro c. use tpair. * exact (identity (pr1 F c)). * abstract ( apply Isos.is_inverse_in_precat_identity ). Defined. Definition associator_of_endofunctors: associator (functorial_composition _ _ _) := associativity_as_nat_z_iso C C C C. Lemma triangle_eq_of_endofunctors: triangle_eq (functorial_composition _ _ _) (functor_identity C) left_unitor_of_endofunctors right_unitor_of_endofunctors associator_of_endofunctors. Proof. intros F G. apply nat_trans_eq_alt. intro c. cbn. rewrite functor_id. do 3 rewrite id_right. apply functor_id. Qed. Lemma pentagon_eq_of_endofunctors: pentagon_eq (functorial_composition _ _ _) associator_of_endofunctors. Proof. intros F G H I. apply nat_trans_eq_alt. intro c. cbn. do 4 rewrite id_right. do 3 rewrite functor_id. rewrite id_right. apply pathsinv0, functor_id. Qed. Definition monoidal_cat_of_endofunctors: monoidal_cat. Proof. use make_monoidal_cat. - exact EndC. - apply functorial_composition. - apply functor_identity. - exact left_unitor_of_endofunctors. - exact right_unitor_of_endofunctors. - exact associator_of_endofunctors. - exact triangle_eq_of_endofunctors. - exact pentagon_eq_of_endofunctors. Defined. *) Definition monoidal_cat_of_endofunctors: monoidal_cat := monoidal_cat_from_bicat_and_ob(C:=bicat_of_cats) C. (** we need this high-level view in order to be able to instantiate [montrafotargetbicat_moncat] in [ActionBasedStrongFunctorsMonoidal] *) End Endofunctors_as_monoidal_category.
[STATEMENT] lemma objI_trg: assumes "arr a" and "trg a = a" shows "obj a" [PROOF STATE] proof (prove) goal (1 subgoal): 1. obj a [PROOF STEP] using assms obj_def' [PROOF STATE] proof (prove) using this: arr a trg a = a obj ?a = (arr ?a \<and> trg ?a = ?a) goal (1 subgoal): 1. obj a [PROOF STEP] by simp
{-# LANGUAGE BangPatterns, DeriveDataTypeable, DeriveGeneric #-} -- | -- Module : Statistics.Distribution.Normal -- Copyright : (c) 2009 Bryan O'Sullivan -- License : BSD3 -- -- Maintainer : [email protected] -- Stability : experimental -- Portability : portable -- -- The normal distribution. This is a continuous probability -- distribution that describes data that cluster around a mean. module Statistics.Distribution.Normal ( NormalDistribution -- * Constructors , normalDistr , normalFromSample , standard ) where import Data.Aeson (FromJSON, ToJSON) import Control.Applicative ((<$>), (<*>)) import Data.Binary (Binary) import Data.Binary (put, get) import Data.Data (Data, Typeable) import GHC.Generics (Generic) import Numeric.MathFunctions.Constants (m_sqrt_2, m_sqrt_2_pi) import Numeric.SpecFunctions (erfc, invErfc) import qualified Statistics.Distribution as D import qualified Statistics.Sample as S import qualified System.Random.MWC.Distributions as MWC -- | The normal distribution. data NormalDistribution = ND { mean :: {-# UNPACK #-} !Double , stdDev :: {-# UNPACK #-} !Double , ndPdfDenom :: {-# UNPACK #-} !Double , ndCdfDenom :: {-# UNPACK #-} !Double } deriving (Eq, Read, Show, Typeable, Data, Generic) instance FromJSON NormalDistribution instance ToJSON NormalDistribution instance Binary NormalDistribution where put (ND w x y z) = put w >> put x >> put y >> put z get = ND <$> get <*> get <*> get <*> get instance D.Distribution NormalDistribution where cumulative = cumulative complCumulative = complCumulative instance D.ContDistr NormalDistribution where logDensity = logDensity quantile = quantile instance D.MaybeMean NormalDistribution where maybeMean = Just . D.mean instance D.Mean NormalDistribution where mean = mean instance D.MaybeVariance NormalDistribution where maybeStdDev = Just . D.stdDev maybeVariance = Just . D.variance instance D.Variance NormalDistribution where stdDev = stdDev instance D.Entropy NormalDistribution where entropy d = 0.5 * log (2 * pi * exp 1 * D.variance d) instance D.MaybeEntropy NormalDistribution where maybeEntropy = Just . D.entropy instance D.ContGen NormalDistribution where genContVar d = MWC.normal (mean d) (stdDev d) -- | Standard normal distribution with mean equal to 0 and variance equal to 1 standard :: NormalDistribution standard = ND { mean = 0.0 , stdDev = 1.0 , ndPdfDenom = log m_sqrt_2_pi , ndCdfDenom = m_sqrt_2 } -- | Create normal distribution from parameters. -- -- IMPORTANT: prior to 0.10 release second parameter was variance not -- standard deviation. normalDistr :: Double -- ^ Mean of distribution -> Double -- ^ Standard deviation of distribution -> NormalDistribution normalDistr m sd | sd > 0 = ND { mean = m , stdDev = sd , ndPdfDenom = log $ m_sqrt_2_pi * sd , ndCdfDenom = m_sqrt_2 * sd } | otherwise = error $ "Statistics.Distribution.Normal.normalDistr: standard deviation must be positive. Got " ++ show sd -- | Create distribution using parameters estimated from -- sample. Variance is estimated using maximum likelihood method -- (biased estimation). normalFromSample :: S.Sample -> NormalDistribution normalFromSample xs = normalDistr m (sqrt v) where (m,v) = S.meanVariance xs logDensity :: NormalDistribution -> Double -> Double logDensity d x = (-xm * xm / (2 * sd * sd)) - ndPdfDenom d where xm = x - mean d sd = stdDev d cumulative :: NormalDistribution -> Double -> Double cumulative d x = erfc ((mean d - x) / ndCdfDenom d) / 2 complCumulative :: NormalDistribution -> Double -> Double complCumulative d x = erfc ((x - mean d) / ndCdfDenom d) / 2 quantile :: NormalDistribution -> Double -> Double quantile d p | p == 0 = -inf | p == 1 = inf | p == 0.5 = mean d | p > 0 && p < 1 = x * ndCdfDenom d + mean d | otherwise = error $ "Statistics.Distribution.Normal.quantile: p must be in [0,1] range. Got: "++show p where x = - invErfc (2 * p) inf = 1/0
In December 2009 , Anderson was working on a new script tentatively titled The Master , about a " charismatic intellectual " who starts a new religion in the 1950s . An associate of Anderson stated that the idea for the film had been in Anderson 's head for about twelve years . Though the film makes no reference to the movement , it has " long been widely assumed to be based on Scientology . " The Master was released on September 14 , 2012 by The Weinstein Company in the United States and Canada to critical acclaim . The film received three nominations at the 85th Academy Awards : Joaquin Phoenix for Best Leading Actor , Philip Seymour Hoffman for Best Supporting Actor and Amy Adams for Best Supporting Actress .
open import Agda.Primitive variable @0 ℓ : Level A : Set ℓ levelOf : A → Level levelOf {a} _ = a
function [newVar newMean state] = hlp_adaptExpWinMovVar(varargin) % estimate exponential window moving variance (and mean). The % moving variance is calculated in place based on new data values and % previous data. g = arg_define(varargin, ... arg_norep({'values'},[],[],'data values. can be scalar, vector or matrix'), ... arg_nogui({'instate','State'},[],[],'state'), ... arg_sub({'adaptOpts'},{},@hlp_scaleLimits,'Adaptation options'), ... arg({'reset'},false,[],'Reset adaptation state') ... ); state = g.instate; if g.reset || ~isfield(g,'instate') || isempty(state) % initialize state state.lastVar = 1; state.lastMean = 0; state.numRunsSoFar = 0; end % adapt limits using exponential window moving average [state.lastVar state.lastMean] = hlp_expWinMovVar(g.values,state.lastVar, state.lastMean, ... state.numRunsSoFar,rmfield(g.adaptOpts,'arg_direct')); state.numRunsSoFar = state.numRunsSoFar + 1; newVar = state.lastVar; newMean = state.lastMean;
#!/usr/bin/env Rscript # From https://github.com/berkeley-dsep-infra/datahub/issues/814 # https://github.com/berkeley-dsep-infra/datahub/issues/897 source("/tmp/class-libs.R") class_name = "IA C188" class_libs = c( "rdd", "0.57", "stargazer", "5.2.2", "lm.beta", "1.5-1", "multcomp", "1.4-8", "lfe", "2.8-2" ) class_libs_install_version(class_name, class_libs)
Address(Monticello Dam,38.513433,122.104453) holds back Putah Creek to form Lake Berryessa. It is in the gap between Blue Ridge/Rocky Ridge to the north and Pleasants Ridge to the south leading to Mount Vaca. While most dams have a spillway to the side to manage high waters, Monticello Dam features the lessconventional Morning Glory Spillway morning glory spillway, which is basically a concrete funnel surrounded on all sides by water. Putah Creek is recommenced from the waters discharged from the dam. The http://www.sidwater.org/ Solano Irrigation District operates the dam with permission of the http://www.usbr.gov/ United States Bureau of Reclamation. Solano Irrigation District provides water to many farmers in Solano County. When the dam was built, the town of Monticello had to be razed. Allegedly, two large bulldozers linked together by a chain were used to flatten the remains. When the lake is low, the foundations of the town are visible. Engineering estimates state that if the dam was completely vaporized (i.e., no rubble at all remained) it would flood Davis with about 3 meters of water. However the dam would never actually disappear without leaving any rubble behind. It would probably be an event like the wiki:Wikipedia:St. Francis Dam disaster. Users/StevenDaubert notes that plenty of rubble remained in the St Francis Dam disaster... The Winters Express newspaper is known as the Gateway to the Monticello Dam and uses the dam in their masthead. For news about Lake Berryessa, including current lake level information, check out the http://www.lakeberryessanews.com/ Lake Berryessa enews Pictures
\subsection{Surfaces}
Formal statement is: lemma connected_component_nonoverlap: "connected_component_set S a \<inter> connected_component_set S b = {} \<longleftrightarrow> a \<notin> S \<or> b \<notin> S \<or> connected_component_set S a \<noteq> connected_component_set S b" Informal statement is: The connected components of a set $S$ are pairwise disjoint if and only if they are distinct.
(* Title: RTS/Common/Semantics.thy *) (* Author: Susannah Mansky, UIUC 2020 *) section "Semantics model" theory Semantics imports Main begin text "General model for small-step semantics:" locale Semantics = fixes small :: "'prog \<Rightarrow> 'state \<Rightarrow> 'state set" and endset :: "'state set" assumes endset_final: "\<sigma> \<in> endset \<Longrightarrow> \<forall>P. small P \<sigma> = {}" context Semantics begin subsection "Extending @{term small} to multiple steps" primrec small_nstep :: "'prog \<Rightarrow> 'state \<Rightarrow> nat \<Rightarrow> 'state set" where small_nstep_base: "small_nstep P \<sigma> 0 = {\<sigma>}" | small_nstep_Rec: "small_nstep P \<sigma> (Suc n) = { \<sigma>2. \<exists>\<sigma>1. \<sigma>1 \<in> small_nstep P \<sigma> n \<and> \<sigma>2 \<in> small P \<sigma>1 }" lemma small_nstep_Rec2: "small_nstep P \<sigma> (Suc n) = { \<sigma>2. \<exists>\<sigma>1. \<sigma>1 \<in> small P \<sigma> \<and> \<sigma>2 \<in> small_nstep P \<sigma>1 n }" proof(induct n arbitrary: \<sigma>) case (Suc n) have right: "\<And>\<sigma>'. \<sigma>' \<in> small_nstep P \<sigma> (Suc(Suc n)) \<Longrightarrow> \<exists>\<sigma>1. \<sigma>1 \<in> small P \<sigma> \<and> \<sigma>' \<in> small_nstep P \<sigma>1 (Suc n)" proof - fix \<sigma>' assume "\<sigma>' \<in> small_nstep P \<sigma> (Suc(Suc n))" then obtain \<sigma>1 where Sucnstep: "\<sigma>1 \<in> small_nstep P \<sigma> (Suc n)" "\<sigma>' \<in> small P \<sigma>1" by fastforce obtain \<sigma>12 where nstep: "\<sigma>12 \<in> small P \<sigma> \<and> \<sigma>1 \<in> small_nstep P \<sigma>12 n" using Suc Sucnstep(1) by fastforce then show "\<exists>\<sigma>1. \<sigma>1 \<in> small P \<sigma> \<and> \<sigma>' \<in> small_nstep P \<sigma>1 (Suc n)" using Sucnstep by fastforce qed have left: "\<And>\<sigma>' . \<exists>\<sigma>1. \<sigma>1 \<in> small P \<sigma> \<and> \<sigma>' \<in> small_nstep P \<sigma>1 (Suc n) \<Longrightarrow> \<sigma>' \<in> small_nstep P \<sigma> (Suc(Suc n))" proof - fix \<sigma>' assume "\<exists>\<sigma>1. \<sigma>1 \<in> small P \<sigma> \<and> \<sigma>' \<in> small_nstep P \<sigma>1 (Suc n)" then obtain \<sigma>1 where Sucnstep: "\<sigma>1 \<in> small P \<sigma>" "\<sigma>' \<in> small_nstep P \<sigma>1 (Suc n)" by fastforce obtain \<sigma>12 where nstep: "\<sigma>12 \<in> small_nstep P \<sigma>1 n \<and> \<sigma>' \<in> small P \<sigma>12" using Sucnstep(2) by auto then show "\<sigma>' \<in> small_nstep P \<sigma> (Suc(Suc n))" using Suc Sucnstep by fastforce qed show ?case using right left by fast qed(simp) lemma small_nstep_SucD: assumes "\<sigma>' \<in> small_nstep P \<sigma> (Suc n)" shows "\<exists>\<sigma>1. \<sigma>1 \<in> small P \<sigma> \<and> \<sigma>' \<in> small_nstep P \<sigma>1 n" using small_nstep_Rec2 case_prodD assms by fastforce lemma small_nstep_Suc_nend: "\<sigma>' \<in> small_nstep P \<sigma> (Suc n1) \<Longrightarrow> \<sigma> \<notin> endset" using endset_final small_nstep_SucD by fastforce subsection "Extending @{term small} to a big-step semantics" definition big :: "'prog \<Rightarrow> 'state \<Rightarrow> 'state set" where "big P \<sigma> \<equiv> { \<sigma>'. \<exists>n. \<sigma>' \<in> small_nstep P \<sigma> n \<and> \<sigma>' \<in> endset }" lemma bigI: "\<lbrakk> \<sigma>' \<in> small_nstep P \<sigma> n; \<sigma>' \<in> endset \<rbrakk> \<Longrightarrow> \<sigma>' \<in> big P \<sigma>" by (fastforce simp add: big_def) lemma bigD: "\<lbrakk> \<sigma>' \<in> big P \<sigma> \<rbrakk> \<Longrightarrow> \<exists>n. \<sigma>' \<in> small_nstep P \<sigma> n \<and> \<sigma>' \<in> endset" by (simp add: big_def) lemma big_def2: "\<sigma>' \<in> big P \<sigma> \<longleftrightarrow> (\<exists>n. \<sigma>' \<in> small_nstep P \<sigma> n \<and> \<sigma>' \<in> endset)" proof(rule iffI) assume "\<sigma>' \<in> big P \<sigma>" then show "\<exists>n. \<sigma>' \<in> small_nstep P \<sigma> n \<and> \<sigma>' \<in> endset" using bigD big_def by auto next assume "\<exists>n. \<sigma>' \<in> small_nstep P \<sigma> n \<and> \<sigma>' \<in> endset" then show "\<sigma>' \<in> big P \<sigma>" using big_def big_def by auto qed lemma big_stepD: assumes big: "\<sigma>' \<in> big P \<sigma>" and nend: "\<sigma> \<notin> endset" shows "\<exists>\<sigma>1. \<sigma>1 \<in> small P \<sigma> \<and> \<sigma>' \<in> big P \<sigma>1" proof - obtain n where n: "\<sigma>' \<in> small_nstep P \<sigma> n" "\<sigma>' \<in> endset" using big_def2 big by auto then show ?thesis using small_nstep_SucD nend big_def2 by(cases n, simp) blast qed (***) lemma small_nstep_det_last_eq: assumes det: "\<forall>\<sigma>. small P \<sigma> = {} \<or> (\<exists>\<sigma>'. small P \<sigma> = {\<sigma>'})" shows "\<lbrakk> \<sigma>' \<in> big P \<sigma>; \<sigma>' \<in> small_nstep P \<sigma> n; \<sigma>' \<in> small_nstep P \<sigma> n' \<rbrakk> \<Longrightarrow> n = n'" proof(induct n arbitrary: n' \<sigma> \<sigma>') case 0 have "\<sigma>' = \<sigma>" using "0.prems"(2) small_nstep_base by blast then have endset: "\<sigma> \<in> endset" using "0.prems"(1) bigD by blast show ?case proof(cases n') case Suc then show ?thesis using "0.prems"(3) small_nstep_SucD endset_final[OF endset] by blast qed(simp) next case (Suc n1) then have endset: "\<sigma>' \<in> endset" using Suc.prems(1) bigD by blast have nend: "\<sigma> \<notin> endset" using small_nstep_Suc_nend[OF Suc.prems(2)] by simp then have neq: "\<sigma>' \<noteq> \<sigma>" using endset by auto obtain \<sigma>1 where \<sigma>1: "\<sigma>1 \<in> small P \<sigma>" "\<sigma>' \<in> small_nstep P \<sigma>1 n1" using small_nstep_SucD[OF Suc.prems(2)] by clarsimp then have big: "\<sigma>' \<in> big P \<sigma>1" using endset by(auto simp: big_def) show ?case proof(cases n') case 0 then show ?thesis using neq Suc.prems(3) using small_nstep_base by blast next case Suc': (Suc n1') then obtain \<sigma>1' where \<sigma>1': "\<sigma>1' \<in> small P \<sigma>" "\<sigma>' \<in> small_nstep P \<sigma>1' n1'" using small_nstep_SucD[where \<sigma>=\<sigma> and \<sigma>'=\<sigma>' and n=n1'] Suc.prems(3) by blast then have "\<sigma>1=\<sigma>1'" using \<sigma>1(1) det by auto then show ?thesis using Suc.hyps(1)[OF big \<sigma>1(2)] \<sigma>1'(2) Suc' by blast qed qed end \<comment> \<open> Semantics \<close> end
lemma cauchy_def: "Cauchy S \<longleftrightarrow> (\<forall>e>0. \<exists>N. \<forall>m n. m \<ge> N \<and> n \<ge> N \<longrightarrow> dist (S m) (S n) < e)"
import tactic open tactic /-! This file contains three tactic-programming exercises of increasing difficulty. They were (hastily) written to follow the metaprogramming tutorial at Lean for the Curious Mathematician 2020. If you're looking for more (better) exercises, we strongly recommend the exercises by Blanchette et al for the course Logical Verification at the Vrije Universiteit Amsterdam, and the corresponding chapter of the course notes: https://github.com/blanchette/logical_verification_2020/blob/master/lean/love07_metaprogramming_exercise_sheet.lean https://github.com/blanchette/logical_verification_2020/raw/master/hitchhikers_guide.pdf ## Exercise 1 Write a `contradiction` tactic. The tactic should look through the hypotheses in the local context trying to find two that contradict each other, i.e. proving `P` and `¬ P` for some proposition `P`. It should use this contradiction to close the goal. Bonus: handle `P → false` as well as `¬ P`. This exercise is to practice manipulating the hypotheses and goal. Note: this exists as `tactic.interactive.contradiction`. -/ meta def tactic.interactive.contr : tactic unit := sorry -- it only costs a factor of two to check all pairs, let's start with that -- mmap reduces to the case of having one expr and checking for a contradiction -- to start, can we just trace the pair h, p for all p in the context example (P Q R : Prop) (hp : P) (hq : Q) (hr : ¬ R) (hnq : ¬ Q) : false := by contr example (P Q R : Prop) (hnq : ¬ Q) (hp : P) (hq : Q) (hr : ¬ R) : 0 = 1 := by contr example (P Q R : Prop) (hp : P) (hq : Q) (hr : ¬ R) (hnq : Q → false) : false := by contr /-! ## Exercise 2 Write a tactic that proves a given `nat`-valued declaration is nonnegative. The tactic should take the name of a declaration whose return type is `ℕ` (presumably with some arguments), e.g. `nat.add : ℕ → ℕ → ℕ` or `list.length : Π α : Type, list α → ℕ`. It should add a new declaration to the environment which proves all applications of this function are nonnegative, e.g. `nat.add_nonneg : ∀ m n : ℕ, 0 ≤ nat.add m n`. Bonus: create reasonable names for these declarations, and/or take an optional argument for the new name. This tactic is not useful by itself, but it's a good way to practice querying and modifying an environment and working under binders. It is not a tactic to be used during a proof, but rather as a command. Hints: * For looking at declarations in the environment, you will need the `declaration` type, as well as the tactics `get_decl` and `add_decl`. * You will have to manipulate an expression under binders. The tactics `mk_local_pis` and `pis`, or their lambda equivalents, will be helpful here. * `mk_mapp` is a variant of `mk_app` that lets you provide implicit arguments. -/ meta def add_nonneg_proof (n : name) : tactic unit := sorry run_cmd add_nonneg_proof `nat.add run_cmd add_nonneg_proof `list.length #check nat.add_nonneg #check list.length_nonneg /-! ## Exercise 3 (challenge!) The mathlib tactic `cancel_denoms` is intended to get rid of division by numerals in expressions where this makes sense. For example, -/ example (q : ℚ) (h : q / 3 > 0) : q > 0 := begin cancel_denoms at h, exact h end /-! But it is not complete. In particular, it doesn't like nested division or other operators in denominators. These all fail: -/ example (q : ℚ) (h : q / (3 / 4) > 0) : false := begin cancel_denoms at h, end example (p q : ℚ) (h : q / 2 / 3 < q) : false := begin cancel_denoms at h, end example (p q : ℚ) (h : q / 2 < 3 / (4*q)) : false := begin cancel_denoms at h, end -- this one succeeds but doesn't do what it should example (p q : ℚ) (h : q / (2*3) < q) : false := begin cancel_denoms at h, end /-! Look at the code in `src/tactic/cancel_denoms.lean` and try to fix it. See if you can solve any or all of these failing test cases. If you succeed, a pull request to mathlib is strongly encouraged! -/
Motherhood, mayhem, and mirth: Playing catch-up. Christmas morning, our little Tinkerbell and Sleeping Beauty. The girls just being silly. One of my many resolutions for the year is to change my attitude. As I typed those words, I heard my Mom’s voice say them. My parents will be so happy that I’ve finally decided to do this because as a teen it’s the one phrase I’m sure I heard everyday. So there it is. I’m changing my attitude. See? In the vein of being positive with a good attitude, I thought I’d share some pictures of the girls. Nothing like a little shot of cute kids to remind you to have a good attitude. No matter what the situation, I attempt to find something good about it. Whenever I lose it with the kids, I have to remind myself: I am thankful we have them! to see my horse THeo.He's so cute! Just yesterday I got an email from my sister in law sharing the website www.acomplaintfreeworld.org She said that The premise is to monitor how much you complain each day, in turn spreading more positive energy to yourself and to the world. I haven't checked it out yet, but I will. It sounds like something I need too! Hugs to you Kathy! I hope your world is starting to smooth out. BTW met someone at a party Saturday night who went to PC with you. She knows Claudine very well too. Her initials are ML (hint: French Basque). She's a doll.
module Inductive.Examples.Product where open import Inductive open import Tuple open import Data.Fin open import Data.Product hiding (_×_; <_,_>) open import Data.List open import Data.Vec _×_ : Set → Set → Set A × B = Inductive (((A ∷ (B ∷ [])) , []) ∷ []) <_,_> : {A B : Set} → A → B → A × B < a , b > = construct zero (a ∷ (b ∷ [])) [] fst : {A B : Set} → A × B → A fst = rec ((λ a b → a) ∷ []) snd : {A B : Set} → A × B → B snd = rec ((λ a b → b) ∷ [])
""" DATAQ 4108 Device Level code author: Valentyn Stadnytskyi Date: November 2017- April 2019 fully python3 compatible. The main purpose of this module is to provide useful interface between DI-4108 and a server system level code that does all numbercrynching. This modules only job is to attend DI-4108 and insure that all data is collected and stored in a circular buffer. The communication in this module is done via XLI module developed by Valentyn Stadnytskyi. This module is based on python sockets. """#!/usr/bin/env python3 """ Simple IOC based on caproto library. It has """ from caproto.server import pvproperty, PVGroup, ioc_arg_parser, run import caproto from textwrap import dedent from pdb import pm from numpy import random, array, zeros, ndarray, nan, isnan from time import time, sleep, ctime if __name__ == '__main__': from icarus_nmr.device_server import Server from icarus_nmr.device_daq import DI4108_DL device = DI4108_DL() device.pr_buffer_size = (6400,10) from icarus_nmr.mock_driver import Driver driver = Driver() device.bind_driver(driver) device.init() ioc_options, run_options = ioc_arg_parser( default_prefix='device_dl:', desc=dedent(Server.__doc__)) ioc = Server(**ioc_options) device.pr_pracket_size = 128 ioc.device = device run(ioc.pvdb, **run_options)
-- -- copyright (c) 2017 Simon Beaumont -- ||| This module defines an AST for the Dirac notation of linear algebra. module Language.Dirac.AST import public Data.Complex -- for complex amplitides import Data.Fin -- finite domain import Data.Vect -- for finite lists import Data.Matrix -- for matrices (in one intepretation) ||| The types in Dirac notation - the attempt here is to keep these as ||| abstract as possible and then provide concrete implmentations. data Typ = ||| A real valued expression (R) Real | ||| A complex valued expression (C) Amplitude | ||| The primary type of state Ket Nat | ||| Adjoint dual of a Ket Bra Nat | ||| Unitary operator Operator Nat | ||| Self adjoint operator Measure Nat | ||| A typed functional language Function Typ Typ ||| Transform AST type to a concrete Idris type interpTyp : Typ -> Type interpTyp Real = Double interpTyp Amplitude = Complex Double interpTyp (Ket n) = Vect n (Complex Double) interpTyp (Bra n) = Vect n (Complex Double) interpTyp (Operator n) = Matrix n n (Complex Double) interpTyp (Measure n) = Matrix n n (Complex Double) interpTyp (Function a t) = interpTyp a -> interpTyp t -- Context of language evaluation - taken from well typed interpreter -- example in Idris documentation using (G : Vect n Typ) ||| Variables are deBruijn indexed data HasType : (i : Fin n) -> Vect n Typ -> Typ -> Type where Stop : HasType FZ (t :: G) t Pop : HasType k G t -> HasType (FS k) (u :: G) t ||| Type indexed expressions data Expr : Vect n Typ -> Typ -> Type where ||| Variable constructor Var : HasType i G t -> Expr G t ||| Real value RVal : (x : Double) -> Expr G Real ||| Complex value CVal : (z : (Complex Double)) -> Expr G Amplitude ||| Arbitrary binary op -- TODO might need more sophisitcated ops Op : (interpTyp a -> interpTyp b -> interpTyp c) -> Expr G a -> Expr G b -> Expr G c ||| Lambda Lam : Expr (a :: G) t -> Expr G (Function a t) ||| Function application App : Expr G (Function a t) -> Expr G a -> Expr G t ||| Get a value from the enviroment of in scope expressions data Env : Vect n Typ -> Type where Nil : Env Nil (::) : interpTyp a -> Env G -> Env (a :: G) lookup : HasType i G t -> Env G -> interpTyp t lookup Stop (x :: xs) = x lookup (Pop k) (x :: xs) = lookup k xs ||| An interpreter takes an expression in an environment ||| into an Idris value interp : Env G -> Expr G t -> interpTyp t interp env (Var i) = lookup i env interp env (RVal x) = x interp env (CVal z) = z interp env (Lam sc) = \x => interp (x :: env) sc interp env (App f s) = interp env f (interp env s) interp env (Op op x y) = op (interp env x) (interp env y) -- Examples ||| Add two complex amplitudes add : Expr G (Function Amplitude (Function Amplitude Amplitude)) add = Lam (Lam (Op (+) (Var Stop) (Var (Pop Stop)))) -- ||| Add two Kets (Qubits) sum : Expr G (Function (Ket 2) (Function (Ket 2) (Ket 2))) sum = Lam (Lam (Op (Data.Vect.zipWith (+)) (Var Stop) (Var (Pop Stop)))) -- Local Variables: -- idris-load-packages: ("base" "contrib") -- End:
[STATEMENT] lemma ring_chain: "R \<in> C \<Longrightarrow> ring R" [PROOF STATE] proof (prove) goal (1 subgoal): 1. R \<in> C \<Longrightarrow> ring R [PROOF STEP] using field.is_ring[OF field_chain] [PROOF STATE] proof (prove) using this: ?R \<in> C \<Longrightarrow> ring ?R goal (1 subgoal): 1. R \<in> C \<Longrightarrow> ring R [PROOF STEP] by blast
Load LFindLoad. From lfind Require Import LFind. From QuickChick Require Import QuickChick. From adtind Require Import goal33. Derive Show for natural. Derive Arbitrary for natural. Instance Dec_Eq_natural : Dec_Eq natural. Proof. dec_eq. Qed. Lemma conj22eqsynthconj3 : forall (lv0 : natural) (lv1 : natural), (@eq natural (plus lv0 lv1) (plus lv1 (plus lv0 Zero))). Admitted. QuickChick conj22eqsynthconj3.
/- Copyright (c) 2020 Yury G. Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Yury G. Kudryashov -/ import Mathlib.PrePort import Mathlib.Lean3Lib.init.default import Mathlib.linear_algebra.affine_space.affine_map import Mathlib.algebra.invertible import Mathlib.PostPort universes u_1 u_2 u_3 u_4 u_5 l u_6 u_7 u_8 u_9 u_10 namespace Mathlib /-! # Affine equivalences In this file we define `affine_equiv k P₁ P₂` (notation: `P₁ ≃ᵃ[k] P₂`) to be the type of affine equivalences between `P₁` and `P₂, i.e., equivalences such that both forward and inverse maps are affine maps. We define the following equivalences: * `affine_equiv.refl k P`: the identity map as an `affine_equiv`; * `e.symm`: the inverse map of an `affine_equiv` as an `affine_equiv`; * `e.trans e'`: composition of two `affine_equiv`s; note that the order follows `mathlib`'s `category_theory` convention (apply `e`, then `e'`), not the convention used in function composition and compositions of bundled morphisms. ## Tags affine space, affine equivalence -/ /-- An affine equivalence is an equivalence between affine spaces such that both forward and inverse maps are affine. We define it using an `equiv` for the map and a `linear_equiv` for the linear part in order to allow affine equivalences with good definitional equalities. -/ structure affine_equiv (k : Type u_1) (P₁ : Type u_2) (P₂ : Type u_3) {V₁ : Type u_4} {V₂ : Type u_5} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] extends P₁ ≃ P₂ where linear : linear_equiv k V₁ V₂ map_vadd' : ∀ (p : P₁) (v : V₁), coe_fn _to_equiv (v +ᵥ p) = coe_fn linear v +ᵥ coe_fn _to_equiv p protected instance affine_equiv.has_coe_to_fun (k : Type u_1) {V1 : Type u_2} (P1 : Type u_3) {V2 : Type u_4} (P2 : Type u_5) [ring k] [add_comm_group V1] [module k V1] [add_torsor V1 P1] [add_comm_group V2] [module k V2] [add_torsor V2 P2] : has_coe_to_fun (affine_equiv k P1 P2) := has_coe_to_fun.mk (fun (e : affine_equiv k P1 P2) => P1 → P2) fun (e : affine_equiv k P1 P2) => equiv.to_fun (affine_equiv.to_equiv e) namespace linear_equiv /-- Interpret a linear equivalence between modules as an affine equivalence. -/ def to_affine_equiv {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_comm_group V₂] [semimodule k V₂] (e : linear_equiv k V₁ V₂) : affine_equiv k V₁ V₂ := affine_equiv.mk (to_equiv e) e sorry @[simp] theorem coe_to_affine_equiv {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_comm_group V₂] [semimodule k V₂] (e : linear_equiv k V₁ V₂) : ⇑(to_affine_equiv e) = ⇑e := rfl end linear_equiv namespace affine_equiv /-- Identity map as an `affine_equiv`. -/ def refl (k : Type u_1) {V₁ : Type u_2} (P₁ : Type u_6) [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] : affine_equiv k P₁ P₁ := mk (equiv.refl P₁) (linear_equiv.refl k V₁) sorry @[simp] theorem coe_refl (k : Type u_1) {V₁ : Type u_2} (P₁ : Type u_6) [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] : ⇑(refl k P₁) = id := rfl theorem refl_apply (k : Type u_1) {V₁ : Type u_2} (P₁ : Type u_6) [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (x : P₁) : coe_fn (refl k P₁) x = x := rfl @[simp] theorem to_equiv_refl (k : Type u_1) {V₁ : Type u_2} (P₁ : Type u_6) [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] : to_equiv (refl k P₁) = equiv.refl P₁ := rfl @[simp] theorem linear_refl (k : Type u_1) {V₁ : Type u_2} (P₁ : Type u_6) [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] : linear (refl k P₁) = linear_equiv.refl k V₁ := rfl @[simp] theorem map_vadd {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) (p : P₁) (v : V₁) : coe_fn e (v +ᵥ p) = coe_fn (linear e) v +ᵥ coe_fn e p := map_vadd' e p v @[simp] theorem coe_to_equiv {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : ⇑(to_equiv e) = ⇑e := rfl /-- Reinterpret an `affine_equiv` as an `affine_map`. -/ def to_affine_map {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : affine_map k P₁ P₂ := affine_map.mk (⇑e) (↑(linear e)) (map_vadd' e) @[simp] theorem coe_to_affine_map {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : ⇑(to_affine_map e) = ⇑e := rfl @[simp] theorem to_affine_map_mk {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (f : P₁ ≃ P₂) (f' : linear_equiv k V₁ V₂) (h : ∀ (p : P₁) (v : V₁), coe_fn f (v +ᵥ p) = coe_fn f' v +ᵥ coe_fn f p) : to_affine_map (mk f f' h) = affine_map.mk (⇑f) (↑f') h := rfl @[simp] theorem linear_to_affine_map {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : affine_map.linear (to_affine_map e) = ↑(linear e) := rfl theorem injective_to_affine_map {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] : function.injective to_affine_map := sorry @[simp] theorem to_affine_map_inj {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] {e : affine_equiv k P₁ P₂} {e' : affine_equiv k P₁ P₂} : to_affine_map e = to_affine_map e' ↔ e = e' := function.injective.eq_iff injective_to_affine_map theorem ext {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] {e : affine_equiv k P₁ P₂} {e' : affine_equiv k P₁ P₂} (h : ∀ (x : P₁), coe_fn e x = coe_fn e' x) : e = e' := injective_to_affine_map (affine_map.ext h) theorem injective_coe_fn {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] : function.injective fun (e : affine_equiv k P₁ P₂) (x : P₁) => coe_fn e x := sorry @[simp] theorem coe_fn_inj {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] {e : affine_equiv k P₁ P₂} {e' : affine_equiv k P₁ P₂} : ⇑e = ⇑e' ↔ e = e' := function.injective.eq_iff injective_coe_fn theorem injective_to_equiv {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] : function.injective to_equiv := fun (e e' : affine_equiv k P₁ P₂) (H : to_equiv e = to_equiv e') => ext (iff.mp equiv.ext_iff H) @[simp] theorem to_equiv_inj {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] {e : affine_equiv k P₁ P₂} {e' : affine_equiv k P₁ P₂} : to_equiv e = to_equiv e' ↔ e = e' := function.injective.eq_iff injective_to_equiv /-- Construct an affine equivalence by verifying the relation between the map and its linear part at one base point. Namely, this function takes an equivalence `e : P₁ ≃ P₂`, a linear equivalece `e' : V₁ ≃ₗ[k] V₂`, and a point `p` such that for any other point `p'` we have `e p' = e' (p' -ᵥ p) +ᵥ e p`. -/ def mk' {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : P₁ ≃ P₂) (e' : linear_equiv k V₁ V₂) (p : P₁) (h : ∀ (p' : P₁), coe_fn e p' = coe_fn e' (p' -ᵥ p) +ᵥ coe_fn e p) : affine_equiv k P₁ P₂ := mk e e' sorry @[simp] theorem coe_mk' {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : P₁ ≃ P₂) (e' : linear_equiv k V₁ V₂) (p : P₁) (h : ∀ (p' : P₁), coe_fn e p' = coe_fn e' (p' -ᵥ p) +ᵥ coe_fn e p) : ⇑(mk' e e' p h) = ⇑e := rfl @[simp] theorem to_equiv_mk' {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : P₁ ≃ P₂) (e' : linear_equiv k V₁ V₂) (p : P₁) (h : ∀ (p' : P₁), coe_fn e p' = coe_fn e' (p' -ᵥ p) +ᵥ coe_fn e p) : to_equiv (mk' e e' p h) = e := rfl @[simp] theorem linear_mk' {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : P₁ ≃ P₂) (e' : linear_equiv k V₁ V₂) (p : P₁) (h : ∀ (p' : P₁), coe_fn e p' = coe_fn e' (p' -ᵥ p) +ᵥ coe_fn e p) : linear (mk' e e' p h) = e' := rfl /-- Inverse of an affine equivalence as an affine equivalence. -/ def symm {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : affine_equiv k P₂ P₁ := mk (equiv.symm (to_equiv e)) (linear_equiv.symm (linear e)) sorry @[simp] theorem symm_to_equiv {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : equiv.symm (to_equiv e) = to_equiv (symm e) := rfl @[simp] theorem symm_linear {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : linear_equiv.symm (linear e) = linear (symm e) := rfl protected theorem bijective {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : function.bijective ⇑e := equiv.bijective (to_equiv e) protected theorem surjective {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : function.surjective ⇑e := equiv.surjective (to_equiv e) protected theorem injective {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : function.injective ⇑e := equiv.injective (to_equiv e) @[simp] theorem range_eq {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : set.range ⇑e = set.univ := function.surjective.range_eq (affine_equiv.surjective e) @[simp] theorem apply_symm_apply {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) (p : P₂) : coe_fn e (coe_fn (symm e) p) = p := equiv.apply_symm_apply (to_equiv e) p @[simp] theorem symm_apply_apply {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) (p : P₁) : coe_fn (symm e) (coe_fn e p) = p := equiv.symm_apply_apply (to_equiv e) p theorem apply_eq_iff_eq_symm_apply {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) {p₁ : P₁} {p₂ : P₂} : coe_fn e p₁ = p₂ ↔ p₁ = coe_fn (symm e) p₂ := equiv.apply_eq_iff_eq_symm_apply (to_equiv e) @[simp] theorem apply_eq_iff_eq {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) {p₁ : P₁} {p₂ : P₁} : coe_fn e p₁ = coe_fn e p₂ ↔ p₁ = p₂ := equiv.apply_eq_iff_eq (to_equiv e) @[simp] theorem symm_refl {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] : symm (refl k P₁) = refl k P₁ := rfl /-- Composition of two `affine_equiv`alences, applied left to right. -/ def trans {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {V₃ : Type u_4} {P₁ : Type u_6} {P₂ : Type u_7} {P₃ : Type u_8} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] [add_comm_group V₃] [semimodule k V₃] [add_torsor V₃ P₃] (e : affine_equiv k P₁ P₂) (e' : affine_equiv k P₂ P₃) : affine_equiv k P₁ P₃ := mk (equiv.trans (to_equiv e) (to_equiv e')) (linear_equiv.trans (linear e) (linear e')) sorry @[simp] theorem coe_trans {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {V₃ : Type u_4} {P₁ : Type u_6} {P₂ : Type u_7} {P₃ : Type u_8} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] [add_comm_group V₃] [semimodule k V₃] [add_torsor V₃ P₃] (e : affine_equiv k P₁ P₂) (e' : affine_equiv k P₂ P₃) : ⇑(trans e e') = ⇑e' ∘ ⇑e := rfl theorem trans_apply {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {V₃ : Type u_4} {P₁ : Type u_6} {P₂ : Type u_7} {P₃ : Type u_8} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] [add_comm_group V₃] [semimodule k V₃] [add_torsor V₃ P₃] (e : affine_equiv k P₁ P₂) (e' : affine_equiv k P₂ P₃) (p : P₁) : coe_fn (trans e e') p = coe_fn e' (coe_fn e p) := rfl theorem trans_assoc {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {V₃ : Type u_4} {V₄ : Type u_5} {P₁ : Type u_6} {P₂ : Type u_7} {P₃ : Type u_8} {P₄ : Type u_9} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] [add_comm_group V₃] [semimodule k V₃] [add_torsor V₃ P₃] [add_comm_group V₄] [semimodule k V₄] [add_torsor V₄ P₄] (e₁ : affine_equiv k P₁ P₂) (e₂ : affine_equiv k P₂ P₃) (e₃ : affine_equiv k P₃ P₄) : trans (trans e₁ e₂) e₃ = trans e₁ (trans e₂ e₃) := ext fun (_x : P₁) => rfl @[simp] theorem trans_refl {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : trans e (refl k P₂) = e := ext fun (_x : P₁) => rfl @[simp] theorem refl_trans {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : trans (refl k P₁) e = e := ext fun (_x : P₁) => rfl @[simp] theorem trans_symm {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : trans e (symm e) = refl k P₁ := ext (symm_apply_apply e) @[simp] theorem symm_trans {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) : trans (symm e) e = refl k P₂ := ext (apply_symm_apply e) @[simp] theorem apply_line_map {k : Type u_1} {V₁ : Type u_2} {V₂ : Type u_3} {P₁ : Type u_6} {P₂ : Type u_7} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [add_comm_group V₂] [semimodule k V₂] [add_torsor V₂ P₂] (e : affine_equiv k P₁ P₂) (a : P₁) (b : P₁) (c : k) : coe_fn e (coe_fn (affine_map.line_map a b) c) = coe_fn (affine_map.line_map (coe_fn e a) (coe_fn e b)) c := affine_map.apply_line_map (to_affine_map e) a b c protected instance group {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] : group (affine_equiv k P₁ P₁) := group.mk (fun (e e' : affine_equiv k P₁ P₁) => trans e' e) sorry (refl k P₁) trans_refl refl_trans symm (div_inv_monoid.div._default (fun (e e' : affine_equiv k P₁ P₁) => trans e' e) sorry (refl k P₁) trans_refl refl_trans symm) trans_symm theorem one_def {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] : 1 = refl k P₁ := rfl @[simp] theorem coe_one {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] : ⇑1 = id := rfl theorem mul_def {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (e : affine_equiv k P₁ P₁) (e' : affine_equiv k P₁ P₁) : e * e' = trans e' e := rfl @[simp] theorem coe_mul {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (e : affine_equiv k P₁ P₁) (e' : affine_equiv k P₁ P₁) : ⇑(e * e') = ⇑e ∘ ⇑e' := rfl theorem inv_def {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (e : affine_equiv k P₁ P₁) : e⁻¹ = symm e := rfl /-- The map `v ↦ v +ᵥ b` as an affine equivalence between a module `V` and an affine space `P` with tangent space `V`. -/ def vadd_const (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (b : P₁) : affine_equiv k V₁ P₁ := mk (equiv.vadd_const b) (linear_equiv.refl k V₁) sorry @[simp] theorem linear_vadd_const (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (b : P₁) : linear (vadd_const k b) = linear_equiv.refl k V₁ := rfl @[simp] theorem vadd_const_apply (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (b : P₁) (v : V₁) : coe_fn (vadd_const k b) v = v +ᵥ b := rfl @[simp] theorem vadd_const_symm_apply (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (b : P₁) (p : P₁) : coe_fn (symm (vadd_const k b)) p = p -ᵥ b := rfl /-- `p' ↦ p -ᵥ p'` as an equivalence. -/ def const_vsub (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (p : P₁) : affine_equiv k P₁ V₁ := mk (equiv.const_vsub p) (linear_equiv.neg k) sorry @[simp] theorem coe_const_vsub (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (p : P₁) : ⇑(const_vsub k p) = has_vsub.vsub p := rfl @[simp] theorem coe_const_vsub_symm (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (p : P₁) : ⇑(symm (const_vsub k p)) = fun (v : V₁) => -v +ᵥ p := rfl /-- The map `p ↦ v +ᵥ p` as an affine automorphism of an affine space. -/ def const_vadd (k : Type u_1) {V₁ : Type u_2} (P₁ : Type u_6) [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (v : V₁) : affine_equiv k P₁ P₁ := mk (equiv.const_vadd P₁ v) (linear_equiv.refl k V₁) sorry @[simp] theorem linear_const_vadd (k : Type u_1) {V₁ : Type u_2} (P₁ : Type u_6) [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (v : V₁) : linear (const_vadd k P₁ v) = linear_equiv.refl k V₁ := rfl @[simp] theorem const_vadd_apply (k : Type u_1) {V₁ : Type u_2} (P₁ : Type u_6) [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (v : V₁) (p : P₁) : coe_fn (const_vadd k P₁ v) p = v +ᵥ p := rfl @[simp] theorem const_vadd_symm_apply (k : Type u_1) {V₁ : Type u_2} (P₁ : Type u_6) [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (v : V₁) (p : P₁) : coe_fn (symm (const_vadd k P₁ v)) p = -v +ᵥ p := rfl /-- Point reflection in `x` as a permutation. -/ def point_reflection (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (x : P₁) : affine_equiv k P₁ P₁ := trans (const_vsub k x) (vadd_const k x) theorem point_reflection_apply (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (x : P₁) (y : P₁) : coe_fn (point_reflection k x) y = x -ᵥ y +ᵥ x := rfl @[simp] theorem point_reflection_symm (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (x : P₁) : symm (point_reflection k x) = point_reflection k x := injective_to_equiv (equiv.point_reflection_symm x) @[simp] theorem to_equiv_point_reflection (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (x : P₁) : to_equiv (point_reflection k x) = equiv.point_reflection x := rfl @[simp] theorem point_reflection_self (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (x : P₁) : coe_fn (point_reflection k x) x = x := vsub_vadd x x theorem point_reflection_involutive (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (x : P₁) : function.involutive ⇑(point_reflection k x) := equiv.point_reflection_involutive x /-- `x` is the only fixed point of `point_reflection x`. This lemma requires `x + x = y + y ↔ x = y`. There is no typeclass to use here, so we add it as an explicit argument. -/ theorem point_reflection_fixed_iff_of_injective_bit0 (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] {x : P₁} {y : P₁} (h : function.injective bit0) : coe_fn (point_reflection k x) y = y ↔ y = x := equiv.point_reflection_fixed_iff_of_injective_bit0 h theorem injective_point_reflection_left_of_injective_bit0 (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (h : function.injective bit0) (y : P₁) : function.injective fun (x : P₁) => coe_fn (point_reflection k x) y := equiv.injective_point_reflection_left_of_injective_bit0 h y theorem injective_point_reflection_left_of_module (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [invertible (bit0 1)] (y : P₁) : function.injective fun (x : P₁) => coe_fn (point_reflection k x) y := sorry theorem point_reflection_fixed_iff_of_module (k : Type u_1) {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] [invertible (bit0 1)] {x : P₁} {y : P₁} : coe_fn (point_reflection k x) y = y ↔ y = x := iff.trans (function.injective.eq_iff' (injective_point_reflection_left_of_module k y) (point_reflection_self k y)) eq_comm end affine_equiv namespace affine_map theorem line_map_vadd {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (v : V₁) (v' : V₁) (p : P₁) (c : k) : coe_fn (line_map v v') c +ᵥ p = coe_fn (line_map (v +ᵥ p) (v' +ᵥ p)) c := affine_equiv.apply_line_map (affine_equiv.vadd_const k p) v v' c theorem line_map_vsub {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (p₁ : P₁) (p₂ : P₁) (p₃ : P₁) (c : k) : coe_fn (line_map p₁ p₂) c -ᵥ p₃ = coe_fn (line_map (p₁ -ᵥ p₃) (p₂ -ᵥ p₃)) c := affine_equiv.apply_line_map (affine_equiv.symm (affine_equiv.vadd_const k p₃)) p₁ p₂ c theorem vsub_line_map {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (p₁ : P₁) (p₂ : P₁) (p₃ : P₁) (c : k) : p₁ -ᵥ coe_fn (line_map p₂ p₃) c = coe_fn (line_map (p₁ -ᵥ p₂) (p₁ -ᵥ p₃)) c := affine_equiv.apply_line_map (affine_equiv.const_vsub k p₁) p₂ p₃ c theorem vadd_line_map {k : Type u_1} {V₁ : Type u_2} {P₁ : Type u_6} [ring k] [add_comm_group V₁] [semimodule k V₁] [add_torsor V₁ P₁] (v : V₁) (p₁ : P₁) (p₂ : P₁) (c : k) : v +ᵥ coe_fn (line_map p₁ p₂) c = coe_fn (line_map (v +ᵥ p₁) (v +ᵥ p₂)) c := affine_equiv.apply_line_map (affine_equiv.const_vadd k P₁ v) p₁ p₂ c theorem homothety_neg_one_apply {V₁ : Type u_2} {P₁ : Type u_6} [add_comm_group V₁] [add_torsor V₁ P₁] {R' : Type u_10} [comm_ring R'] [semimodule R' V₁] (c : P₁) (p : P₁) : coe_fn (homothety c (-1)) p = coe_fn (affine_equiv.point_reflection R' c) p := sorry
```python import numpy as np import matplotlib.pyplot as plt import scipy from sklearn.model_selection import ParameterGrid from sklearn.manifold import Isomap import time from tqdm import tqdm import librosa from librosa import cqt from librosa.core import amplitude_to_db from librosa.display import specshow import os import glob ``` ```python data_dir = '/Users/sripathisridhar/Desktop/SOL' ``` ```python file_paths= sorted(glob.glob(os.path.join(data_dir, '**', '*.wav'))) file_names= [] for file_path in file_paths: file_names.append(os.path.basename(file_path)) ``` ```python hop_size= 512 q= 24 ``` ```python import h5py with h5py.File("SOL.h5", "r") as f: features_dict = {key:f[key][()] for key in f.keys()} ``` ```python grid = { 'Q': [24], 'k': [3], 'comp': ['log'], 'instr': ['all'], 'dyn': ['all'] } settings = list(ParameterGrid(grid)) for setting in settings: if setting["instr"] == 'all': setting['instr'] = '' if setting['dyn'] == 'all': setting['dyn'] = '' ``` ```python batch_str = [] CQT_OCTAVES = 7 features_keys = list(features_dict.keys()) for setting in settings: q = setting['Q'] # Batch process and store in a folder batch_str = [setting['instr'], setting['dyn']] batch_features = [] for feature_key in features_keys: # Get features that match setting if all(x in feature_key for x in batch_str): batch_features.append(features_dict[feature_key]) batch_features = np.stack(batch_features, axis=1) # Isomap parameters hop_size = 512 compression = 'log' features = amplitude_to_db(batch_features) n_neighbors = setting['k'] n_dimensions = 3 n_octaves = 3 # Prune feature matrix bin_low = np.where((np.std(features, axis=1) / np.std(features)) > 0.1)[0][0] + q bin_high = bin_low + n_octaves*q X = features[bin_low:bin_high, :] # Z-score Standardization- improves contrast in correlation matrix mus = np.mean(X, axis=1) sigmas = np.std(X, axis=1) X_std = (X - mus[:, np.newaxis]) / (1e-6 + sigmas[:, np.newaxis]) # 1e-6 to avoid runtime division by zero # Pearson correlation matrix rho_std = np.dot(X_std, X_std.T) / X_std.shape[1] # Isomap embedding isomap = Isomap(n_components= n_dimensions, n_neighbors= n_neighbors) coords = isomap.fit_transform(rho_std) # Get note value freqs= librosa.cqt_frequencies(q*CQT_OCTAVES, fmin=librosa.note_to_hz('C1'), bins_per_octave=q) #librosa CQT default fmin is C1 chroma_list= librosa.core.hz_to_note(freqs[bin_low:bin_high]) notes = [] reps = q//12 for chroma in chroma_list: for i in range(reps): notes.append(chroma) ``` ```python curr_fig= plt.figure(figsize=(5.5, 2.75)) ax= curr_fig.add_subplot(121) ax.axis('off') import colorcet as cc subsampled_color_ids = np.floor(np.linspace(0, 256, q, endpoint=False)).astype('int') color_list= [cc.cyclic_mygbm_30_95_c78[i] for i in subsampled_color_ids] # Plot embedding with color for i in range(coords.shape[0]): plt.scatter(coords[i, 0], coords[i, 1], color= color_list[i%q], s=30.0) plt.plot(coords[:, 0], coords[:, 1], color='black', linewidth=0.2) # Plot Pearson correlation matrix rho_frequencies = freqs[bin_low:bin_high] freq_ticklabels = ['A2', 'A3', 'A4'] freq_ticks = librosa.core.note_to_hz(freq_ticklabels) tick_bins = [] tick_labels= [] for i,freq_tick in enumerate(freq_ticks): tick_bin = np.argmin(np.abs(rho_frequencies-freq_tick)) tick_bins.append(tick_bin) tick_labels.append(freq_ticklabels[i]) plt.figure(figsize=(2.5,2.5)) plt.imshow(np.abs(rho_std), cmap='magma_r') plt.xticks(tick_bins) plt.gca().set_xticklabels(freq_ticklabels) # plt.xlabel('Log-frequency (octaves)') plt.yticks(tick_bins) plt.gca().set_yticklabels(freq_ticklabels) # plt.ylabel('Log-frequency (octaves)') plt.gca().invert_yaxis() plt.clim(0, 1) ``` ### Circle projection ```python import circle_fit import importlib importlib.reload(circle_fit) from circle_fit import circle_fit A = np.transpose(coords[:,:-1]) x, r, circle_residual = circle_fit(A, verbose=True) ``` ```python import matplotlib matplotlib.rc('font', family='serif') fig, axes = plt.subplots() plt.scatter(A[0,:],A[1,:]) plt.plot(x[0],x[1],'rx') circle = plt.Circle(x, radius=r, fill=False, linestyle='-.') axes.set_aspect(1) axes.add_artist(circle) # axes.set_ylim([-5,6]) # axes.set_xlim([-2,8]) plt.title('Circle fit: TinySOL all instr', pad=10.0) plt.show() print(np.sqrt(circle_residual)/72) ``` ```python r ``` 6.355528108736576 ```python def d_squared(a, b): # Takes two n-D tuples and returns euclidean distance between them # Cast to array for computation # Cast first to tuple in case a or b are Sympy Point objects p_a = np.array(tuple(a), dtype='float') p_b = np.array(tuple(b), dtype='float') return np.sum(np.square(p_a - p_b)) ``` ```python import sympy from sympy.geometry import Circle, Point, Line center = Point(x, evaluate=False) c = Circle(center, r, evaluate=False) l = Line(Point(coords[0,:-1]), center, evaluate=False) points = [tuple(p) for p in l.points] xy_prime = [] # TODO: Optimize to a more pythonic manner for x,y in coords[:,:2]: intersections = c.intersection(Line(Point(x,y), center, evaluate=False)) if d_squared((x,y),intersections[0]) < d_squared((x,y), intersections[1]): xy_prime.append([float(p) for p in intersections[0]]) else: xy_prime.append([float(p) for p in intersections[1]]) ``` ```python fig, axes = plt.subplots() plt.scatter(np.array(xy_prime)[:,0],np.array(xy_prime)[:,1], s=10, label='projected points') plt.scatter(A[0,:],A[1,:], s=0.5, label='isomap embedding points (2D)') plt.plot(center[0],center[1],'rx') circle = plt.Circle([float(p) for p in center], radius=r, fill=False, linestyle='--', label='estimated circle fit') axes.set_aspect(1) axes.add_artist(circle) plt.title('Projected points on circle', pad=10.0) plt.legend(bbox_to_anchor=(1,1)) plt.show() ``` ### Line projection ```python z = np.arange(len(coords[:,2])) z_fit = scipy.stats.linregress(z, coords[:,2]) print(z_fit.stderr) ``` 0.0052234352623828605 ```python plt.figure() plt.title('Line fit: TinySOL all instr') plt.scatter(np.arange(len(coords[:,2])), coords[:,2]) plt.plot(z_fit.intercept + z_fit.slope*z, 'b') ``` ```python # New line coordinates z_prime = [i * z_fit.slope + z_fit.intercept for i,_ in enumerate(coords[:,2])] ``` ```python coords_prime = np.append(np.array(xy_prime), np.expand_dims(np.array(z_prime), axis=1), axis=1) coords_length = coords_prime.shape[0] ``` ### Distance matrices ```python # Projected helix self-distance matrix D_proj = np.zeros((coords_length, coords_length)) for i in range(coords_length): for j in range(i,coords_length): D_proj[i][j] = d_squared(coords_prime[i,:], coords_prime[j,:]) ``` ```python # Isomap embedding self-distance matrix D_isomap = np.zeros((coords_length, coords_length)) # Projected points same no. as isomap for i in range(coords_length): for j in range(i, coords_length): D_isomap[i][j] = d_squared(coords[i,:], coords[j,:]) ``` ```python # Geodesic self-distance matrix D_geodesic = isomap.dist_matrix_ # Convert to upper triangular sparse matrix for i in range(coords_length): for j in range(i): D_geodesic[i,j] = 0 ``` ```python ## Centering matrix def centered(A, Q=24, J=3): # Returns centered distance matrix ''' Inputs ----- A - squared distance matrix Q - quality factor, 24 by default J - number of octaves, 3 by default Returns ----- tau - MDS style diagonalized matrix of A ''' coords_length = A.shape[0] H = np.zeros((coords_length, coords_length)) const = 1/(Q*J) for i in range(coords_length): for j in range(coords_length): if j==i: H[i,j] = 1 - const else: H[i,j] = -const return -0.5 * np.matmul(np.matmul(H, A), H) ``` ```python def frobenius_distance(A, B): # Given two nxn matrices, return their 'Frobenius distance' return np.sqrt(np.sum(np.square(A - B))) ``` ```python loss_isomap = frobenius_distance(centered(D_geodesic), centered(D_isomap))/coords_length loss_total = frobenius_distance(centered(D_geodesic), centered(D_proj))/coords_length loss_proj = frobenius_distance(centered(D_isomap), centered(D_proj))/coords_length ``` ```python print(f"Isomap loss= {loss_isomap}") print(f"Projection loss= {loss_proj}") print(f"Total loss= {loss_total}") ``` Isomap loss= 20.242536163460947 Projection loss= 2.3225511781614396 Total loss= 20.914716613612924 ```python (loss_total) - (loss_isomap + loss_proj) < 0 ``` True
To Walter Jackson Bate , the use of spondees in lines 31 – 34 creates a feeling of slow flight , and " in the final stanza . . . the distinctive use of scattered spondees , together with initial inversion , lend [ s ] an approximate phonetic suggestion of the peculiar spring and bounce of the bird in its flight . "
function [gmu, gsigmavar, factors] = gpPosteriorGradMeanCovar(model, X); % GPPOSTERIORGRADMEANCOVAR Gadient of the mean and variances of the posterior at points given by X. % FORMAT % DESC computes the gradient of the mean and covariances of the % posterior distribution of a Gaussian process with respect to the % input locations. % ARG model : the model for which gradients are to be computed. % ARG X : the input locations where gradients are to be computed. % RETURN gmu : the gradient of the posterior mean with respect to % the input locations. % RETURN gCovar : the gradients of the posterior covariance with % respect to the input locations. By raw, we mean that the gradient % has not yet been multiplied by any output scale in that direction % (as is done for gpPosteriorGradMeanCovar). The gradients are % stored in a cell array of dimension MODEL.q x MODEL.d. % % DESC computes the gradient of the mean and covariances of the % posterior distribution of a Gaussian process with respect to the % input locations. Returns a compact representation for the % covariances which separates the factors associated with the % different dimensions from the covariance gradients. % ARG model : the model for which gradients are to be computed. % ARG X : the input locations where gradients are to be computed. % RETURN gmu : the gradient of the posterior mean with respect to % the input locations. % RETURN grCovar : the 'raw' gradient of the posterior covariance with % respect to the input locations. By raw, we mean that the gradient % has not yet been multiplied by any output scale in that direction % (as is done for gpPosteriorGradMeanCovar). The gradients are % stored in a cell array of length MODEL.q. % RETURN factors : the factors for multiplying the 'raw' gradients % of the covariances by. % % SEEALSO : gpCreate, gpPosteriorMeanVar % % COPYRIGHT : Neil D. Lawrence, 2005, 2006, 2009 % GP if ~isfield(model, 'alpha') model = gpComputeAlpha(model); end switch model.approx case 'ftc' gX = kernGradX(model.kern, X, model.X); kX_star = kernCompute(model.kern, X, model.X)'; case {'dtc', 'dtcvar', 'fitc', 'pitc'} gX = kernGradX(model.kern, X, model.X_u); kX_star = kernCompute(model.kern, X, model.X_u)'; otherwise error('Unrecognised approximation type'); end K = kernGradX(model.kern, X); if ~model.isMissingData for i = 1:model.q switch model.approx case 'ftc' KinvgK = model.invK_uu*squeeze(gX(:, i, :)); case {'dtc', 'dtcvar', 'fitc', 'pitc'} KinvgK = (model.invK_uu - (1/model.beta)*model.Ainv)*squeeze(gX(:, i, :)); otherwise error('Unrecognised approximation type'); end kXTKinvgK = kX_star'*KinvgK; gCovar{i} = squeeze(K(:, i, :))-kXTKinvgK - diag(diag(kXTKinvgK)); gmu{i} = squeeze(gX(:, i, :))'*model.alpha.*repmat(model.scale, ... size(X, 1), 1); end % Deal with scaling. if nargout < 3 for i = 1:model.q for j = 1:model.d gsigmavar{i, j} = gCovar{i}*model.scale(j)*model.scale(j); end end else factors = model.scale.*model.scale; gsigmavar = gCovar; end else error('Not yet implemented for models trained on missing data.'); end
module tree-test where open import tree open import nat open import bool open import bool-to-string open import list test-tree = node 2 ( (leaf 3) :: (node 4 ( (leaf 5) :: (leaf 7) :: [] )) :: (leaf 6) :: (leaf 7) :: []) perfect3 = perfect-binary-tree 3 tt perfect3-string = 𝕋-to-string 𝔹-to-string perfect3
If $f$ and $g$ are asymptotically equivalent and $f$ tends to $c$, then $g$ tends to $c$.
// This file is auto-generated, don't edit it. Thanks. #ifndef ALIBABACLOUD_CDT20210813_H_ #define ALIBABACLOUD_CDT20210813_H_ #include <alibabacloud/open_api.hpp> #include <boost/throw_exception.hpp> #include <darabonba/core.hpp> #include <darabonba/util.hpp> #include <iostream> #include <map> using namespace std; namespace Alibabacloud_CDT20210813 { class GetCdtServiceStatusRequest : public Darabonba::Model { public: shared_ptr<long> ownerId{}; GetCdtServiceStatusRequest() {} explicit GetCdtServiceStatusRequest(const std::map<string, boost::any> &config) : Darabonba::Model(config) { fromMap(config); }; void validate() override {} map<string, boost::any> toMap() override { map<string, boost::any> res; if (ownerId) { res["OwnerId"] = boost::any(*ownerId); } return res; } void fromMap(map<string, boost::any> m) override { if (m.find("OwnerId") != m.end() && !m["OwnerId"].empty()) { ownerId = make_shared<long>(boost::any_cast<long>(m["OwnerId"])); } } virtual ~GetCdtServiceStatusRequest() = default; }; class GetCdtServiceStatusResponseBody : public Darabonba::Model { public: shared_ptr<string> requestId{}; shared_ptr<bool> enabled{}; GetCdtServiceStatusResponseBody() {} explicit GetCdtServiceStatusResponseBody(const std::map<string, boost::any> &config) : Darabonba::Model(config) { fromMap(config); }; void validate() override {} map<string, boost::any> toMap() override { map<string, boost::any> res; if (requestId) { res["RequestId"] = boost::any(*requestId); } if (enabled) { res["Enabled"] = boost::any(*enabled); } return res; } void fromMap(map<string, boost::any> m) override { if (m.find("RequestId") != m.end() && !m["RequestId"].empty()) { requestId = make_shared<string>(boost::any_cast<string>(m["RequestId"])); } if (m.find("Enabled") != m.end() && !m["Enabled"].empty()) { enabled = make_shared<bool>(boost::any_cast<bool>(m["Enabled"])); } } virtual ~GetCdtServiceStatusResponseBody() = default; }; class GetCdtServiceStatusResponse : public Darabonba::Model { public: shared_ptr<map<string, string>> headers{}; shared_ptr<GetCdtServiceStatusResponseBody> body{}; GetCdtServiceStatusResponse() {} explicit GetCdtServiceStatusResponse(const std::map<string, boost::any> &config) : Darabonba::Model(config) { fromMap(config); }; void validate() override { if (!headers) { BOOST_THROW_EXCEPTION(boost::enable_error_info(std::runtime_error("headers is required."))); } if (!body) { BOOST_THROW_EXCEPTION(boost::enable_error_info(std::runtime_error("body is required."))); } } map<string, boost::any> toMap() override { map<string, boost::any> res; if (headers) { res["headers"] = boost::any(*headers); } if (body) { res["body"] = body ? boost::any(body->toMap()) : boost::any(map<string,boost::any>({})); } return res; } void fromMap(map<string, boost::any> m) override { if (m.find("headers") != m.end() && !m["headers"].empty()) { map<string, string> map1 = boost::any_cast<map<string, string>>(m["headers"]); map<string, string> toMap1; for (auto item:map1) { toMap1[item.first] = item.second; } headers = make_shared<map<string, string>>(toMap1); } if (m.find("body") != m.end() && !m["body"].empty()) { if (typeid(map<string, boost::any>) == m["body"].type()) { GetCdtServiceStatusResponseBody model1; model1.fromMap(boost::any_cast<map<string, boost::any>>(m["body"])); body = make_shared<GetCdtServiceStatusResponseBody>(model1); } } } virtual ~GetCdtServiceStatusResponse() = default; }; class OpenCdtServiceRequest : public Darabonba::Model { public: shared_ptr<long> ownerId{}; OpenCdtServiceRequest() {} explicit OpenCdtServiceRequest(const std::map<string, boost::any> &config) : Darabonba::Model(config) { fromMap(config); }; void validate() override {} map<string, boost::any> toMap() override { map<string, boost::any> res; if (ownerId) { res["OwnerId"] = boost::any(*ownerId); } return res; } void fromMap(map<string, boost::any> m) override { if (m.find("OwnerId") != m.end() && !m["OwnerId"].empty()) { ownerId = make_shared<long>(boost::any_cast<long>(m["OwnerId"])); } } virtual ~OpenCdtServiceRequest() = default; }; class OpenCdtServiceResponseBody : public Darabonba::Model { public: shared_ptr<string> requestId{}; shared_ptr<string> orderId{}; OpenCdtServiceResponseBody() {} explicit OpenCdtServiceResponseBody(const std::map<string, boost::any> &config) : Darabonba::Model(config) { fromMap(config); }; void validate() override {} map<string, boost::any> toMap() override { map<string, boost::any> res; if (requestId) { res["RequestId"] = boost::any(*requestId); } if (orderId) { res["OrderId"] = boost::any(*orderId); } return res; } void fromMap(map<string, boost::any> m) override { if (m.find("RequestId") != m.end() && !m["RequestId"].empty()) { requestId = make_shared<string>(boost::any_cast<string>(m["RequestId"])); } if (m.find("OrderId") != m.end() && !m["OrderId"].empty()) { orderId = make_shared<string>(boost::any_cast<string>(m["OrderId"])); } } virtual ~OpenCdtServiceResponseBody() = default; }; class OpenCdtServiceResponse : public Darabonba::Model { public: shared_ptr<map<string, string>> headers{}; shared_ptr<OpenCdtServiceResponseBody> body{}; OpenCdtServiceResponse() {} explicit OpenCdtServiceResponse(const std::map<string, boost::any> &config) : Darabonba::Model(config) { fromMap(config); }; void validate() override { if (!headers) { BOOST_THROW_EXCEPTION(boost::enable_error_info(std::runtime_error("headers is required."))); } if (!body) { BOOST_THROW_EXCEPTION(boost::enable_error_info(std::runtime_error("body is required."))); } } map<string, boost::any> toMap() override { map<string, boost::any> res; if (headers) { res["headers"] = boost::any(*headers); } if (body) { res["body"] = body ? boost::any(body->toMap()) : boost::any(map<string,boost::any>({})); } return res; } void fromMap(map<string, boost::any> m) override { if (m.find("headers") != m.end() && !m["headers"].empty()) { map<string, string> map1 = boost::any_cast<map<string, string>>(m["headers"]); map<string, string> toMap1; for (auto item:map1) { toMap1[item.first] = item.second; } headers = make_shared<map<string, string>>(toMap1); } if (m.find("body") != m.end() && !m["body"].empty()) { if (typeid(map<string, boost::any>) == m["body"].type()) { OpenCdtServiceResponseBody model1; model1.fromMap(boost::any_cast<map<string, boost::any>>(m["body"])); body = make_shared<OpenCdtServiceResponseBody>(model1); } } } virtual ~OpenCdtServiceResponse() = default; }; class GetCdtCbServiceStatusRequest : public Darabonba::Model { public: shared_ptr<long> ownerId{}; GetCdtCbServiceStatusRequest() {} explicit GetCdtCbServiceStatusRequest(const std::map<string, boost::any> &config) : Darabonba::Model(config) { fromMap(config); }; void validate() override {} map<string, boost::any> toMap() override { map<string, boost::any> res; if (ownerId) { res["OwnerId"] = boost::any(*ownerId); } return res; } void fromMap(map<string, boost::any> m) override { if (m.find("OwnerId") != m.end() && !m["OwnerId"].empty()) { ownerId = make_shared<long>(boost::any_cast<long>(m["OwnerId"])); } } virtual ~GetCdtCbServiceStatusRequest() = default; }; class GetCdtCbServiceStatusResponseBody : public Darabonba::Model { public: shared_ptr<string> requestId{}; shared_ptr<bool> enabled{}; GetCdtCbServiceStatusResponseBody() {} explicit GetCdtCbServiceStatusResponseBody(const std::map<string, boost::any> &config) : Darabonba::Model(config) { fromMap(config); }; void validate() override {} map<string, boost::any> toMap() override { map<string, boost::any> res; if (requestId) { res["RequestId"] = boost::any(*requestId); } if (enabled) { res["Enabled"] = boost::any(*enabled); } return res; } void fromMap(map<string, boost::any> m) override { if (m.find("RequestId") != m.end() && !m["RequestId"].empty()) { requestId = make_shared<string>(boost::any_cast<string>(m["RequestId"])); } if (m.find("Enabled") != m.end() && !m["Enabled"].empty()) { enabled = make_shared<bool>(boost::any_cast<bool>(m["Enabled"])); } } virtual ~GetCdtCbServiceStatusResponseBody() = default; }; class GetCdtCbServiceStatusResponse : public Darabonba::Model { public: shared_ptr<map<string, string>> headers{}; shared_ptr<GetCdtCbServiceStatusResponseBody> body{}; GetCdtCbServiceStatusResponse() {} explicit GetCdtCbServiceStatusResponse(const std::map<string, boost::any> &config) : Darabonba::Model(config) { fromMap(config); }; void validate() override { if (!headers) { BOOST_THROW_EXCEPTION(boost::enable_error_info(std::runtime_error("headers is required."))); } if (!body) { BOOST_THROW_EXCEPTION(boost::enable_error_info(std::runtime_error("body is required."))); } } map<string, boost::any> toMap() override { map<string, boost::any> res; if (headers) { res["headers"] = boost::any(*headers); } if (body) { res["body"] = body ? boost::any(body->toMap()) : boost::any(map<string,boost::any>({})); } return res; } void fromMap(map<string, boost::any> m) override { if (m.find("headers") != m.end() && !m["headers"].empty()) { map<string, string> map1 = boost::any_cast<map<string, string>>(m["headers"]); map<string, string> toMap1; for (auto item:map1) { toMap1[item.first] = item.second; } headers = make_shared<map<string, string>>(toMap1); } if (m.find("body") != m.end() && !m["body"].empty()) { if (typeid(map<string, boost::any>) == m["body"].type()) { GetCdtCbServiceStatusResponseBody model1; model1.fromMap(boost::any_cast<map<string, boost::any>>(m["body"])); body = make_shared<GetCdtCbServiceStatusResponseBody>(model1); } } } virtual ~GetCdtCbServiceStatusResponse() = default; }; class OpenCdtCbServiceRequest : public Darabonba::Model { public: shared_ptr<long> ownerId{}; OpenCdtCbServiceRequest() {} explicit OpenCdtCbServiceRequest(const std::map<string, boost::any> &config) : Darabonba::Model(config) { fromMap(config); }; void validate() override {} map<string, boost::any> toMap() override { map<string, boost::any> res; if (ownerId) { res["OwnerId"] = boost::any(*ownerId); } return res; } void fromMap(map<string, boost::any> m) override { if (m.find("OwnerId") != m.end() && !m["OwnerId"].empty()) { ownerId = make_shared<long>(boost::any_cast<long>(m["OwnerId"])); } } virtual ~OpenCdtCbServiceRequest() = default; }; class OpenCdtCbServiceResponseBody : public Darabonba::Model { public: shared_ptr<string> requestId{}; shared_ptr<string> orderId{}; OpenCdtCbServiceResponseBody() {} explicit OpenCdtCbServiceResponseBody(const std::map<string, boost::any> &config) : Darabonba::Model(config) { fromMap(config); }; void validate() override {} map<string, boost::any> toMap() override { map<string, boost::any> res; if (requestId) { res["RequestId"] = boost::any(*requestId); } if (orderId) { res["OrderId"] = boost::any(*orderId); } return res; } void fromMap(map<string, boost::any> m) override { if (m.find("RequestId") != m.end() && !m["RequestId"].empty()) { requestId = make_shared<string>(boost::any_cast<string>(m["RequestId"])); } if (m.find("OrderId") != m.end() && !m["OrderId"].empty()) { orderId = make_shared<string>(boost::any_cast<string>(m["OrderId"])); } } virtual ~OpenCdtCbServiceResponseBody() = default; }; class OpenCdtCbServiceResponse : public Darabonba::Model { public: shared_ptr<map<string, string>> headers{}; shared_ptr<OpenCdtCbServiceResponseBody> body{}; OpenCdtCbServiceResponse() {} explicit OpenCdtCbServiceResponse(const std::map<string, boost::any> &config) : Darabonba::Model(config) { fromMap(config); }; void validate() override { if (!headers) { BOOST_THROW_EXCEPTION(boost::enable_error_info(std::runtime_error("headers is required."))); } if (!body) { BOOST_THROW_EXCEPTION(boost::enable_error_info(std::runtime_error("body is required."))); } } map<string, boost::any> toMap() override { map<string, boost::any> res; if (headers) { res["headers"] = boost::any(*headers); } if (body) { res["body"] = body ? boost::any(body->toMap()) : boost::any(map<string,boost::any>({})); } return res; } void fromMap(map<string, boost::any> m) override { if (m.find("headers") != m.end() && !m["headers"].empty()) { map<string, string> map1 = boost::any_cast<map<string, string>>(m["headers"]); map<string, string> toMap1; for (auto item:map1) { toMap1[item.first] = item.second; } headers = make_shared<map<string, string>>(toMap1); } if (m.find("body") != m.end() && !m["body"].empty()) { if (typeid(map<string, boost::any>) == m["body"].type()) { OpenCdtCbServiceResponseBody model1; model1.fromMap(boost::any_cast<map<string, boost::any>>(m["body"])); body = make_shared<OpenCdtCbServiceResponseBody>(model1); } } } virtual ~OpenCdtCbServiceResponse() = default; }; class Client : Alibabacloud_OpenApi::Client { public: explicit Client(const shared_ptr<Alibabacloud_OpenApi::Config>& config); string getEndpoint(shared_ptr<string> productId, shared_ptr<string> regionId, shared_ptr<string> endpointRule, shared_ptr<string> network, shared_ptr<string> suffix, shared_ptr<map<string, string>> endpointMap, shared_ptr<string> endpoint); GetCdtServiceStatusResponse getCdtServiceStatusWithOptions(shared_ptr<GetCdtServiceStatusRequest> request, shared_ptr<Darabonba_Util::RuntimeOptions> runtime); GetCdtServiceStatusResponse getCdtServiceStatus(shared_ptr<GetCdtServiceStatusRequest> request); OpenCdtServiceResponse openCdtServiceWithOptions(shared_ptr<OpenCdtServiceRequest> request, shared_ptr<Darabonba_Util::RuntimeOptions> runtime); OpenCdtServiceResponse openCdtService(shared_ptr<OpenCdtServiceRequest> request); GetCdtCbServiceStatusResponse getCdtCbServiceStatusWithOptions(shared_ptr<GetCdtCbServiceStatusRequest> request, shared_ptr<Darabonba_Util::RuntimeOptions> runtime); GetCdtCbServiceStatusResponse getCdtCbServiceStatus(shared_ptr<GetCdtCbServiceStatusRequest> request); OpenCdtCbServiceResponse openCdtCbServiceWithOptions(shared_ptr<OpenCdtCbServiceRequest> request, shared_ptr<Darabonba_Util::RuntimeOptions> runtime); OpenCdtCbServiceResponse openCdtCbService(shared_ptr<OpenCdtCbServiceRequest> request); virtual ~Client() = default; }; } // namespace Alibabacloud_CDT20210813 #endif
They can be divided into two separate clusters : one to the west of the River Medway and the other on Blue Bell Hill to the east , with the distance between the two clusters measuring at between 8 and 10 km . The western group includes Coldrum Long Barrow , Addington Long Barrow , and the Chestnuts Long Barrow . The eastern group consists of Kit 's Coty House , Little Kit 's Coty House , the Coffin Stone , and several other stones which might have once been parts of chambered tombs . It is not known if they were all built at the same time , or whether they were constructed in succession , while similarly it is not known if they each served the same function or whether there was a hierarchy in their usage .