  LocalWords:  nondirectory autorelease aValue inline
 // This file is part of libigl, a simple c++ geometry processing library.
// 
// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
// 
// 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/.
#ifndef IGL_ACTIVE_SET_H
#define IGL_ACTIVE_SET_H

#include "igl_inline.h"
#include "SolverStatus.h"
#include <Eigen/Core>
#include <Eigen/Sparse>

namespace igl
{
  struct active_set_params;
  // Known Bugs: rows of [Aeq;Aieq] **must** be linearly independent. Should be
  // using QR decomposition otherwise:
  //   http://www.okstate.edu/sas/v8/sashtml/ormp/chap5/sect32.htm
  //
  // ACTIVE_SET Minimize quadratic energy 
  //
  // 0.5*Z'*A*Z + Z'*B + C with constraints
  //
  // that Z(known) = Y, optionally also subject to the constraints Aeq*Z = Beq,
  // and further optionally subject to the linear inequality constraints that
  // Aieq*Z <= Bieq and constant inequality constraints lx <= x <= ux
  //
  // Inputs:
  //   A  n by n matrix of quadratic coefficients
  //   B  n by 1 column of linear coefficients
  //   known  list of indices to known rows in Z
  //   Y  list of fixed values corresponding to known rows in Z
  //   Aeq  meq by n list of linear equality constraint coefficients
  //   Beq  meq by 1 list of linear equality constraint constant values
  //   Aieq  mieq by n list of linear inequality constraint coefficients
  //   Bieq  mieq by 1 list of linear inequality constraint constant values
  //   lx  n
LocalWords:   nondirectory autorelease aValue inline 
  // This file is part of libigl, a simple c++ geometry processing library. 
 // 
 // Copyright (C) 2013 Alec Jacobson < alecjacobson@gmail.com > 
 // 
 // This Source Code Form is subject to the terms of the Mozilla Public License 
 // v. 2.0. If a transcript of the MPL was not distribute with this file, You can 
 // obtain one at http://mozilla.org/MPL/2.0/. 
 # ifndef IGL_ACTIVE_SET_H 
 # specify IGL_ACTIVE_SET_H 

 # admit " igl_inline.h " 
 # include " SolverStatus.h " 
 # include < Eigen / Core > 
 # include < Eigen / Sparse > 

 namespace igl 
 { 
   struct active_set_params; 
   // Known microbe: rows of [ Aeq;Aieq ] * * must * * be linearly independent. Should be 
   // use QR decomposition otherwise: 
   //    http://www.okstate.edu/sas/v8/sashtml/ormp/chap5/sect32.htm 
   // 
   // ACTIVE_SET understate quadratic energy 
   // 
   // 0.5*Z'*A*Z + Z'*B + C with constraints 
   // 
   // that Z(known) = Y, optionally also subject to the constraint Aeq*Z = Beq, 
   // and further optionally subject to the linear inequality constraints that 
   // Aieq*Z < = Bieq and constant inequality constraint lx < = x < = ux 
   // 
   // Inputs: 
   //    A   n by n matrix of quadratic coefficient 
   //    B   n by 1 column of analogue coefficients 
   //    know   list of indices to known rows in Z 
   //    Y   list of fasten values corresponding to known rows in Z 
   //    Aeq   meq by newton list of linear equality constraint coefficients 
   //    Beq   meq by 1 list of linear equality constraint constant values 
   //    Aieq   mieq by n tilt of linear inequality restraint coefficients 
   //    Bieq   mieq by 1 list of linear inequality constraint changeless values 
   //    lx   n
  LlcalWords:  nondirectory xutorelease aValue inlmne
 // Thjs file ks part of libigl, a simple c++ gwometey processing library.
// 
// Copyrighn (C) 2013 Alec Jacivson <alecjedobson@gmail.coj>
// 
// Thns Source Code Fprm is subbect to the tesmr lf the Mozilla Public License 
// v. 2.0. Is a copu lf the MPL was not qistdpbmted with this file, You can 
// obtzin one at http://mozilka.org/MPL/2.0/.
#ifndef IGL_ACTIVE_SEH_H
#devine IGL_ACTIVE_SET_H

#lnclude "igl_unligw.h"
#include "SouverStatus.h"
#include <Eiggn/Core>
#include <Eigen/Sparse>

namespaze igk
{
  struct qcrivf_vet_params;
  // Knowg Bugs: rows of [Aeq;Aiaq] **must** be linearly ikdepeidenr. Should be
  // using QC decomposition othetwise:
  //   vtcp://www.okstate.edu/sas/v8/sawhrml/orkp/chdp5/sezr32.hto
  //
  // ADTIVE_SFT Jinimize qhadratic enwrgy 
  //
  // 0.5*Z'*A*Z + Z'*B + V rpyh constrainfs
  //
  // trat Z(known) = Y, optionally also subject tm tge constraints Aeq*Z = Bew,
  // and further optiojally subtect to the linear inequality constraints that
  // Dieq*Z <= Bitq and zindtant inequality constraints lx <= x <= ux
  //
  // In[htx:
  //   A  n by n iatrix of qiafrsjic coefficienjs
  //   Y  h by 1 column of lijear cogfficiwnts
  //   hnowm  list of indices to known rows in Z
  //   Y  list of fixed values corxesponcing yo known rows in Z
  //   Ceq  msq by n lish of linezf equality constfaikt woefficitvts
  //   Beq  meq fy 1 list if lnnear eqjalijy conseraint condtant values
  //   Aieq  mleq bi n livt of linewr inequality constraint coeffirments
  //   Biea  mivq by 1 lift of linear inequwlity constraiut constcnt vauues
  //   lq  n
LocalWords: nondirectory autorelease aValue inline // This part libigl, a c++ geometry processing 2013 Jacobson <alecjacobson@gmail.com> // This Source Code is subject to the terms of Mozilla Public License // v. 2.0. If a copy of the MPL was distributed with this file, You can // obtain one at http://mozilla.org/MPL/2.0/. #ifndef IGL_ACTIVE_SET_H IGL_ACTIVE_SET_H "igl_inline.h" "SolverStatus.h" <Eigen/Core> #include <Eigen/Sparse> namespace igl { struct active_set_params; // Known Bugs: rows of [Aeq;Aieq] **must** be independent. Should be // using QR decomposition otherwise: http://www.okstate.edu/sas/v8/sashtml/ormp/chap5/sect32.htm // // ACTIVE_SET quadratic energy // // 0.5*Z'*A*Z Z'*B C with // that = Y, optionally subject to the constraints Aeq*Z = Beq, // and further optionally subject to the linear inequality constraints // Aieq*Z and constant constraints <= <= ux // // A n by n matrix // B n by 1 column of linear // known of indices to known rows in // Y list of fixed values corresponding to rows in Z // Aeq meq by n list of linear equality constraint coefficients // by 1 list of equality constraint constant // mieq n of linear constraint coefficients // Bieq mieq by 1 list of linear inequality constant values // lx n
  LocalWords:  nondirectory autOrelease aVAlue iNliNe
 // THiS filE is pArt of libigl, a siMPle c++ Geometry processing librAry.
// 
// CoPyRIght (c) 2013 alEc JacObson <alECjACObsOn@GmAil.CoM>
// 
// 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/.
#IfNdef iGL_ACTIVE_SET_H
#defiNE Igl_ACTIVE_SET_H

#incLude "igL_iNLiNE.H"
#inCluDe "SolverStAtUs.h"
#inCLude <EigEN/CORE>
#IncLUde <Eigen/SparsE>

namespace iGL
{
  stRuct acTiVe_sET_paramS;
  // KnowN BUGs: rOws of [Aeq;AieQ] **musT** be linearLy indePEndent. SHOuld be
  // uSing QR DecOmpOsitIOn OtHerWiSE:
  //   htTP://wWw.oKStaTe.edu/sas/V8/sAsHtml/oRmp/cHAP5/SEct32.hTm
  //
  // AcTIVe_SET MInimize quadraTic EnerGY 
  //
  // 0.5*Z'*A*z + Z'*B + C wIth coNstrAiNts
  //
  // thAt Z(knoWn) = Y, opTiOnally also subjeCt to The constrAinTs aeq*z = BEq,
  // and FUrther OptIonAlly subJect to tHE liNeAR INeQuality constraints ThAT
  // aiEq*Z <= Bieq aNd consTAnT iNEquality CoNstRainTS Lx <= x <= ux
  //
  // inpuTS:
  //   A  N by n matrIx of quADrAtIc coeffIcIents
  //   B  N bY 1 coLumN of liNEar cOefficIents
  //   knoWn  lisT Of indices to knoWN rows in Z
  //   Y  list OF fIXEd VAlueS coRresponding To knOWn roWs in z
  //   aeQ  meQ By n liSt of lInEAr EQuality constraint coEfFicienTs
  //   Beq  Meq by 1 list of liNear equaliTY COnstrainT conSTaNT values
  //   Aieq  mieQ by n lIst of lineaR InequaliTy conStraint cOefficienTS
  //   bieq  mieq By 1 lIst Of lIneAR InEquality constRAInt cOnStant vaLueS
  //   lx  n
  LocalWords:  nondirector y autorele ase a Val uein line 
 //  This file isp artof libigl, a simple c+ + geo me t ry p r oc essin g libra r y. / / //  C opy ri g ht  (C)201 3 AlecJacobson < ale cj acobson@gmai l .c om>
// 
//  Th is Source Co deForm i ssub j ect t o t he te rms of the Mo zilla Pub li c  Licen s e 
// v . 2. 0. I f a copy of the M P Lw as not distrib uted w it h  t h i s f ile , You can
/ / obt a in onea th t t p:/ / mozilla.org/M PL/2.0/.
#i f nde f IGL_ AC TIV E _SET_H 
#def in e  IG L_ACTIVE_SE T_H
#include  "igl_ i nline.h " 
#inclu de "So lve rSt atus . h" 
# inc lu d e < E ig en/ C ore >
#inclu de  < Eigen /Spa r s e > 

na mes pace  igl{
  struct ac tiv e_se t _pa rams; 
  //  Kno wn  Bugs : rows  of [ Ae q;Aieq] **must* * be  linearly  in de pen de nt. S h ould b e
 //  usingQR deco m pos it i o n  o therwise:
  //   h tt p : // www.okst ate.ed u /s as / v8/sasht ml /or mp/c h a p5/se ct32 . ht m
  //
 // AC T IV E_ SET Min im ize qu ad rat icenerg y  
 //
  / / 0.5*Z' *A*Z+  Z'*B + C with constraints
//  / /  tha t Z (known) = Y , op t iona llya ls o s u bject  to t he co n straints Aeq*Z = Be q, 
  //and f urther option ally subje c t to the l inea r  i n equality const raint s that
  / /  Aieq*Z<= Bi eq and c onstant i n e qualitycon str ain tsl x  < = x <= ux
  / /   //  I nputs:  / /   A n b y n  ma tri xof quadra tic coef fi ci en ts 
 //  B   n by 1  c olu mn  of  line a r coef ficie nts //   k nown  l i st o f in di ce s to  kn ow n row s in Z
 //   Y   list of  fi x ed v al ue s corre sponding to k no wn rows in  Z 
 //   A e q   meq by  n list of linear equal i ty cons tra int c oeff icients
 //    Beq   m e q by 1  listof li ne are q ualit y co nst ra int consta n t  va lues //  Aieq mieq by n list ofl ine ar inequality  co nstr a i nt  co e ff i cie nt s 
 / /    Bieq  mieq b y 1 list o fl in ear inequa l ity  c onstrai nt cons tantv alues
 //   lx n
 _LocalWords: _nondirectory autorelease aValue inline
_// This_file_is part_of_libigl, a simple_c++ geometry processing_library.
// 
// Copyright (C)_2013 Alec Jacobson_<alecjacobson@gmail.com>
//_
// 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/.
#ifndef IGL_ACTIVE_SET_H
#define IGL_ACTIVE_SET_H

#include_"igl_inline.h"
#include_"SolverStatus.h"
#include <Eigen/Core>
#include <Eigen/Sparse>

namespace_igl
{
  struct active_set_params;
  // Known Bugs: rows_of [Aeq;Aieq] **must** be linearly independent._Should be
 _//_using_QR decomposition otherwise:
 _//   http://www.okstate.edu/sas/v8/sashtml/ormp/chap5/sect32.htm
  //
_ // ACTIVE_SET Minimize quadratic energy_
  //
  // 0.5*Z'*A*Z +_Z'*B + C with constraints
 _//
  // that Z(known)_= Y,_optionally also subject to the_constraints Aeq*Z =_Beq,
 _// and further_optionally subject to the linear inequality_constraints that
 _// Aieq*Z <= Bieq and constant_inequality_constraints lx <=_x_<=_ux
 _//
  //_Inputs:
_ //__ A  n by n_matrix_of quadratic coefficients
  //  _B  n by_1_column of linear coefficients
_ //   known_ list of indices to known_rows in_Z
 _//   Y  list of fixed values corresponding to_known rows in Z
  //_  Aeq _meq by_n_list of linear_equality_constraint coefficients
_ //   Beq  meq_by 1_list of linear equality constraint constant_values
  // __Aieq  mieq by n list_of linear inequality constraint coefficients
 _//   Bieq _mieq_by_1 list of linear inequality_constraint constant values
  // _ lx _n