### A Pluto.jl notebook ###
# v0.15.1

using Markdown
using InteractiveUtils

# ╔═╡ 7357f256-ead0-401c-9cff-1aa099b67aa0
begin
	using LinearAlgebra
	using DifferentialEquations
	using Parameters
	using LabelledArrays
	using Setfield

	using Plots
	Plots.gr(fmt=:png, lw=2)

	using PlutoUI
	PlutoUI.TableOfContents()
end

# ╔═╡ 0e455e50-bdcb-11eb-08b9-8d2d26788d14
md"""
# Fig 1.07 Collins toggle switch

For Figures 1.7, 7.13, 7.14, 7.15
"""

# ╔═╡ 796ff12c-b74d-4fcf-b228-4e3c6fed2a89
begin
	# Convenience functions
    hill(x, k) = x / (x + k)
    hill(x, k, n) = hill(x^n, k^n)
    exprel(x) = ifelse(x≈zero(x), one(x), x / expm1(x))
end

# ╔═╡ 34178e95-cff5-400e-a5a6-bdbcf8326214
# The model
	function collins!(du, u, p, t)
		@unpack a1, a2, β, γ, i1, i2 = p
		@unpack s1, s2 = u
		du.s1 = a1 * hill(1 + i2, s2, β) - s1
		du.s2 = a2 * hill(1 + i1, s1, γ) - s2
    	return du
	end

# ╔═╡ 30cdc452-ff17-4b08-939a-98c7dbc0c674
# Initial conditions
u0 = LVector(s1=0.075, s2=2.5)

# ╔═╡ 520f36c3-e164-459e-8869-99a8421774f6
# Simulation time
tend = 50.0

# ╔═╡ f47e84f9-7ff5-4c32-996a-47c600b1a71a
# Parameters
p = (a1 = 3.0, a2 = 2.5, β = 4.0, γ = 4.0, i1 = 0.0, i2 = 0.0)

# ╔═╡ 463ef6e7-73db-4b55-b97f-71e90c2f14f4
begin
	# Events and callbacks
    on_i1!(integrator) = integrator.p = @set p.i1 = 10.0
    off_i1!(integrator) = integrator.p = @set p.i1 = 0.0
    on_i2!(integrator) = integrator.p = @set p.i2 = 10.0
    off_i2!(integrator) = integrator.p = @set p.i2 = 0.0

    cbs = CallbackSet(PresetTimeCallback([10.0], on_i2!),
                  PresetTimeCallback([20.0], off_i2!),
                  PresetTimeCallback([30.0], on_i1!),
                  PresetTimeCallback([40.0], off_i1!))
end

# ╔═╡ 759580e6-0910-43a2-b81a-cdaa3bf34441
sol = solve(ODEProblem(collins!, u0, tend, p), callback=cbs)

# ╔═╡ b922fac1-e43c-45eb-a6db-0a9b18f541aa
plot(sol, legend=:right, xlabel="Time", ylabel="Concentration", title="Figure 1.7")

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
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LabelledArrays = "2ee39098-c373-598a-b85f-a56591580800"
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Parameters = "d96e819e-fc66-5662-9728-84c9c7592b0a"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"

[compat]
DifferentialEquations = "~6.17.2"
LabelledArrays = "~1.6.2"
Parameters = "~0.12.2"
Plots = "~1.18.0"
PlutoUI = "~0.7.9"
Setfield = "~0.7.0"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
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[[Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll"]
git-tree-sha1 = "2839f1c1296940218e35df0bbb220f2a79686670"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.18.0+4"

[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "9e7a1e8ca60b742e508a315c17eef5211e7fbfd7"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.1"

[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "acc685bcf777b2202a904cdcb49ad34c2fa1880c"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.14.0+4"

[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7a5780a0d9c6864184b3a2eeeb833a0c871f00ab"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "0.1.6+4"

[[libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+0"

[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"

[[x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d713c1ce4deac133e3334ee12f4adff07f81778f"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2020.7.14+2"

[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "487da2f8f2f0c8ee0e83f39d13037d6bbf0a45ab"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.0.0+3"

[[xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

# ╔═╡ Cell order:
# ╠═0e455e50-bdcb-11eb-08b9-8d2d26788d14
# ╠═7357f256-ead0-401c-9cff-1aa099b67aa0
# ╠═796ff12c-b74d-4fcf-b228-4e3c6fed2a89
# ╠═34178e95-cff5-400e-a5a6-bdbcf8326214
# ╠═463ef6e7-73db-4b55-b97f-71e90c2f14f4
# ╠═30cdc452-ff17-4b08-939a-98c7dbc0c674
# ╠═520f36c3-e164-459e-8869-99a8421774f6
# ╠═f47e84f9-7ff5-4c32-996a-47c600b1a71a
# ╠═759580e6-0910-43a2-b81a-cdaa3bf34441
# ╠═b922fac1-e43c-45eb-a6db-0a9b18f541aa
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002


### The following code defines all the policies that can be used in the simulator

### A large family of policies are priority policies (based on a priority rule
### such as order of arrival, deadline order, etc)
### The general_priority_policty implements this general case. perm is the priority permutation

function general_priority_policy(evs::Array{EVinstance},C::Number,perm::Array{<:Integer})

    p=0.0;
    i=1;

    while p<C && i<=length(evs)
        alloc = min(evs[perm[i]].chargingPower,C-p);
        p=p+alloc;
        evs[perm[i]].currentPower=alloc;
        i=i+1;
    end

    while i<=length(evs)
        evs[perm[i]].currentPower=0.0;
        i=i+1
    end

    return p;
end

### Priority based policies

### Earliest Deadline first.
function edf_policy(evs::Array{EVinstance},C::Number)

    deadlines = [ev.currentReportedDeadline for ev in evs];
    perm = sortperm(deadlines);

    return general_priority_policy(evs::Array{EVinstance},C::Number,perm::Array{<:Integer})
end

@addpolicy("edf")

### Least laxity first
function llf_policy(evs::Array{EVinstance},C::Number)

    laxities = [ev.currentReportedDeadline-ev.currentWorkload/ev.chargingPower for ev in evs];
    perm = sortperm(laxities);

    return general_priority_policy(evs::Array{EVinstance},C::Number,perm::Array{<:Integer})
end

@addpolicy("llf")

function llr_policy(evs::Array{EVinstance},C::Number)

    relative_laxities = [ev.currentReportedDeadline*ev.chargingPower/ev.currentWorkload for ev in evs];
    perm = sortperm(relative_laxities);

    return general_priority_policy(evs::Array{EVinstance},C::Number,perm::Array{<:Integer})
end

@addpolicy("llr")

### FIFO. It's a priority policy with arrival time as priority vector.
function fifo_policy(evs::Array{EVinstance},C::Number)

    perm = 1:length(evs)

    return general_priority_policy(evs::Array{EVinstance},C::Number,perm::Array{<:Integer})
end

@addpolicy("fifo")

### FIFO. It's a priority policy with reversed arrival time as priority vector.
function lifo_policy(evs::Array{EVinstance},C::Number)

    perm = length(evs):-1:1

    return general_priority_policy(evs::Array{EVinstance},C::Number,perm::Array{<:Integer})
end

@addpolicy("lifo")

### LAR: least attained ratio
function lar_policy(evs::Array{EVinstance},C::Number)

    relative_attained = [(ev.departureTime-ev.arrivalTime-ev.currentReportedDeadline)*ev.chargingPower/ev.currentWorkload for ev in evs];
    perm = sortperm(relative_attained,rev=true);

    return general_priority_policy(evs::Array{EVinstance},C::Number,perm::Array{<:Integer})
end

@addpolicy("lar")

### LAS: least attained service
function las_policy(evs::Array{EVinstance},C::Number)

    attained = [ev.requestedEnergy-ev.currentWorkload for ev in evs];
    perm = sortperm(attained);

    return general_priority_policy(evs::Array{EVinstance},C::Number,perm::Array{<:Integer})
end

@addpolicy("las")

### RATIO policy: just sort by current percentage of charge remaining
function ratio_policy(evs::Array{EVinstance},C::Number)

    ratios = [ev.currentWorkload/ev.requestedEnergy for ev in evs];
    perm = sortperm(ratios,rev=true);

    return general_priority_policy(evs::Array{EVinstance},C::Number,perm::Array{<:Integer})
end

@addpolicy("ratio")

### LRPT: Largest remaining processing tiem
function lrpt_policy(evs::Array{EVinstance},C::Number)

    remaining = [ev.currentWorkload for ev in evs];
    perm = sortperm(remaining,rev=true);

    return general_priority_policy(evs::Array{EVinstance},C::Number,perm::Array{<:Integer})
end

@addpolicy("lrpt")

### Non-priority based policies

### Processor sharing Policy
function parallel_policy(evs::Array{EVinstance},C::Number)

    totPower=sum([ev.chargingPower for ev in evs]);
    curtail = min(1,C/totPower);

    [ev.currentPower = curtail*ev.chargingPower for ev in evs]

    return curtail*totPower
end

@addpolicy("parallel")

### Proportional fairness policy
function pf_policy(evs::Array{EVinstance},C::Number)

    ##TODO Revisar comput_pf. Parece estar bien.
    workloads = [ev.currentWorkload for ev in evs];
    deadlines = [ev.currentReportedDeadline for ev in evs];
    U=compute_pf(workloads,deadlines,C)

    for i=1:length(evs)
        evs[i].currentPower = U[i]
    end

    return sum(U);
end

function compute_pf(workloads,deadlines,C)

    w=workloads./deadlines;

    U=zeros(size(w));
    perm = sortperm(w,rev=true);
    w=sort(w,rev=true);

    for i=1:length(w)

        aux = w[i:end]/sum(w[i:end])*C;
        if aux[1]>1
            U[i] = 1;
            C=C-1;
        else
            U[i:end] = aux;
            break
        end
    end
    U[perm]=U;
    return U;

end

@addpolicy("pf")

### Exact scheduling.
function exact_policy(evs::Array{EVinstance},C::Number)

    #exact scheduling o potencia maxima
    U = [min(ev.currentWorkload/ev.currentReportedDeadline,ev.chargingPower) for ev in evs];

    #curtailing si me paso de C
    if sum(U)>C
        U = C/sum(U)*U;
        #otra posibilidad es ordernar por rate y asignar hasta C
    end

    for i=1:length(evs)
        evs[i].currentPower = U[i]
    end

    return sum(U);
end

@addpolicy("exact")

### MPC peak minimizer policy. Check whether this is needed to reduce dependencies.
function peak_policy(evs::Array{EVinstance},C::Number)

    U=zeros(length(evs));

    idx = sortperm([ev.currentReportedDeadline for ev in evs]);

    sigma = [ev.currentWorkload for ev in evs][idx];
    tau = [ev.currentReportedDeadline for ev in evs][idx];
    deltat=diff([0;tau]);
    power = [ev.chargingPower for ev in evs][idx];
    n=length(evs);

    m=Model(GLPK.Optimizer)

    @variable(m,x[1:n,1:n]>=0)
    @variable(m,auxvar)

    @constraint(m,[i=1:n,j=i+1:n],x[i,j]==0)

    @constraint(m,[i=1:n,j=1:i],x[i,j]<=power[i])
    @constraint(m,[i=1:n],sum(x[i,:].*deltat)==sigma[i])
    @constraint(m,sum(x,dims=1).<=auxvar)

    @objective(m,Min,auxvar)

    solve(m)

    U[idx] = max.(getvalue(x)[:,1],0.0);

    for i=1:length(evs)
        evs[i].currentPower = U[i]
    end

    return sum(U);

end

@addpolicy("peak")

#### WEIRD POLICIES: This are only for trial purposes. Will be depurated.

#max weight policy where weight is minimum between rem. work and rem. deadline
function mw_policy(evs::Array{EVinstance},C::Number)

    remaining_w = [ev.currentWorkload for ev in evs];
    remaining_d = [ev.currentReportedDeadline for ev in evs];

    weights = min.(remaining_w,remaining_d)
    perm = sortperm(weights,rev=true);

    return general_priority_policy(evs::Array{EVinstance},C::Number,perm::Array{<:Integer})
end

@addpolicy("mw")

#this policy comes from maximizing myopically the potential amount of work one can perform, ignoring future arrivals
#it underload it behaves exactly as exact scheduling!
function weird_policy(evs::Array{EVinstance},C::Number)

    perm = sortperm([ev.currentReportedDeadline for ev in evs], rev=true)

    remaining_w = [ev.currentWorkload for ev in evs];
    remaining_d = [ev.currentReportedDeadline for ev in evs];

    return general_priority_policy(evs::Array{EVinstance},C::Number,perm::Array{<:Integer})
end

@addpolicy("weird")

### Curtailed policies (for reported deadlines)
function edfc_policy(evs::Array{EVinstance},C::Number)

    deadlines = [ev.currentReportedDeadline for ev in evs];

    positivas = findall(deadlines.>0)
    negativas = findall(deadlines.<=0)

    perm1 = sortperm(deadlines[positivas]);
    perm2 = sortperm(deadlines[negativas], rev=true);

    perm = [positivas[perm1];negativas[perm2]]

    return general_priority_policy(evs::Array{EVinstance},C::Number,perm::Array{<:Integer})

end

@addpolicy("edfc")

function llfc_policy(evs::Array{EVinstance},C::Number)

    deadlines = [ev.currentReportedDeadline for ev in evs];
    laxities = [ev.currentReportedDeadline-ev.currentWorkload/ev.chargingPower for ev in evs];

    positivas = findall(deadlines.>0)
    negativas = findall(deadlines.<=0)

    perm1 = sortperm(laxities[positivas]);
    perm2 = sortperm(laxities[negativas], rev=true);

    perm = [positivas[perm1];negativas[perm2]]

    return general_priority_policy(evs::Array{EVinstance},C::Number,perm::Array{<:Integer})

end

@addpolicy("llfc")


using JuMP, MOModelingExtensions
using Test, GLPK

@testset "Modeling extensions" begin
    @testset "Maximum" begin
        @testset "No bounds" begin
            m = Model()
            @variable(m, x <= 5)
            @variable(m, y <= 5)

            @test_throws ErrorException @constraint(m, max(x, y) <= 4)
            @test_throws ErrorException @constraint(m, maximum([x, y]) <= 4)
        end

        @testset "max" begin
            @testset "Both variables nonnegative" begin
                m = Model(with_optimizer(GLPK.Optimizer))
                @variable(m, 0 <= x <= 5)
                @variable(m, 0 <= y <= 5)
                @constraint(m, max(x, y) <= 4)
                @objective(m, Max, x + y)
                optimize!(m)

                @test value(x) ≈ 4.0
                @test value(y) ≈ 4.0
            end

            @testset "First variable nonpositive" begin
                m = Model(with_optimizer(GLPK.Optimizer))
                @variable(m, -5 <= x <= 0)
                @variable(m, 0 <= y <= 5)
                @constraint(m, max(x, y) <= 4)
                @objective(m, Max, x + y)
                optimize!(m)

                @test value(x) ≈ 0.0
                @test value(y) ≈ 4.0
            end

            @testset "Second variable nonpositive" begin
                m = Model(with_optimizer(GLPK.Optimizer))
                @variable(m, 0 <= x <= 5)
                @variable(m, -5 <= y <= 0)
                @constraint(m, max(x, y) <= 4)
                @objective(m, Max, x + y)
                optimize!(m)

                @test value(x) ≈ 4.0
                @test value(y) ≈ 0.0
            end

            @testset "Both variables mixed sign" begin
                m = Model(with_optimizer(GLPK.Optimizer))
                @variable(m, -5 <= x <= 5)
                @variable(m, -5 <= y <= 5)
                @constraint(m, max(x, y) <= 4)
                @objective(m, Max, x + y)
                optimize!(m)

                @test value(x) ≈ 4.0
                @test value(y) ≈ 4.0
            end
        end

        @testset "maximum" begin
            @testset "maximum([x, y])" begin
                m = Model(with_optimizer(GLPK.Optimizer))
                @variable(m, 0 <= x <= 5)
                @variable(m, 0 <= y <= 5)
                @constraint(m, maximum([x, y]) <= 4)
                @objective(m, Max, x + y)
                optimize!(m)

                @test value(x) ≈ 4.0
                @test value(y) ≈ 4.0
            end

            @testset "maximum([x, y, z])" begin
                m = Model(with_optimizer(GLPK.Optimizer))
                @variable(m, 0 <= x <= 5)
                @variable(m, 0 <= y <= 5)
                @variable(m, 4 <= z <= 5)
                @constraint(m, maximum([x, y, z]) <= 4)
                @objective(m, Max, x + y + z)
                optimize!(m)

                @test value(x) ≈ 4.0
                @test value(y) ≈ 4.0
                @test value(y) ≈ 4.0
            end
        end
    end

    @testset "Minimum" begin
        @testset "No bounds" begin
            m = Model()
            @variable(m, x <= 5)
            @variable(m, y <= 5)

            @test_throws ErrorException @constraint(m, min(x, y) <= 4)
            @test_throws ErrorException @constraint(m, minimum([x, y]) <= 4)
        end

        @testset "min" begin
            @testset "Both variables nonnegative" begin
                m = Model(with_optimizer(GLPK.Optimizer))
                @variable(m, 0 <= x <= 5)
                @variable(m, 0 <= y <= 5)
                @constraint(m, min(x, y) <= 4)
                @objective(m, Max, x + y)
                optimize!(m)

                if value(x) ≈ 4.0
                    @test value(x) ≈ 4.0
                    @test value(y) ≈ 5.0
                else
                    @test value(x) ≈ 5.0
                    @test value(y) ≈ 4.0
                end
            end

            @testset "First variable nonpositive" begin
                m = Model(with_optimizer(GLPK.Optimizer))
                @variable(m, -5 <= x <= 0)
                @variable(m, 0 <= y <= 5)
                @constraint(m, min(x, y) <= 4)
                @objective(m, Max, x + y)
                optimize!(m)

                @test value(x) ≈ 0.0
                @test value(y) ≈ 5.0
            end

            @testset "Second variable nonpositive" begin
                m = Model(with_optimizer(GLPK.Optimizer))
                @variable(m, 0 <= x <= 5)
                @variable(m, -5 <= y <= 0)
                @constraint(m, min(x, y) <= 4)
                @objective(m, Max, x + y)
                optimize!(m)

                @test value(x) ≈ 5.0
                @test value(y) ≈ 0.0
            end

            @testset "Both variables mixed sign" begin
                m = Model(with_optimizer(GLPK.Optimizer))
                @variable(m, -5 <= x <= 5)
                @variable(m, -5 <= y <= 5)
                @constraint(m, min(x, y) <= 4)
                @objective(m, Max, x + y)
                optimize!(m)

                if value(x) ≈ 4.0
                    @test value(x) ≈ 4.0
                    @test value(y) ≈ 5.0
                else
                    @test value(x) ≈ 5.0
                    @test value(y) ≈ 4.0
                end
            end
        end

        @testset "minimum" begin
            @testset "minimum([x, y])" begin
                m = Model(with_optimizer(GLPK.Optimizer))
                @variable(m, 0 <= x <= 5)
                @variable(m, 0 <= y <= 5)
                @constraint(m, minimum([x, y]) <= 4)
                @objective(m, Max, x + y)
                optimize!(m)

                if value(x) ≈ 4.0
                    @test value(x) ≈ 4.0
                    @test value(y) ≈ 5.0
                else
                    @test value(x) ≈ 5.0
                    @test value(y) ≈ 4.0
                end
            end

            @testset "minimum([x, y, z])" begin
                m = Model(with_optimizer(GLPK.Optimizer))
                @variable(m, 0 <= x <= 5)
                @variable(m, 0 <= y <= 5)
                @variable(m, 4 <= z <= 5)
                @constraint(m, minimum([x, y, z]) <= 4)
                @objective(m, Max, x + y + z)
                optimize!(m)

                if value(x) ≈ 4.0
                    @test value(x) ≈ 4.0
                    @test value(y) ≈ 5.0
                    @test value(z) ≈ 5.0
                elseif value(y) ≈ 4.0
                    @test value(x) ≈ 5.0
                    @test value(y) ≈ 4.0
                    @test value(z) ≈ 5.0
                else
                    @test value(x) ≈ 5.0
                    @test value(y) ≈ 5.0
                    @test value(z) ≈ 4.0
                end
            end
        end
    end

    @testset "Boolean operators" begin
        @testset "&" begin
            m = Model(with_optimizer(GLPK.Optimizer))
            @variable(m, x, Bin)
            @variable(m, y, Bin)
            @constraint(m, x & y == true)
            @objective(m, Max, x + y)
            optimize!(m)

            @test value(x) ≈ 1.0
            @test value(y) ≈ 1.0

            m = Model(with_optimizer(GLPK.Optimizer))
            @variable(m, x, Bin)
            @variable(m, y, Bin)
            @constraint(m, x & y == true)
            @constraint(m, x + y <= 1)
            @objective(m, Max, x + y)
            optimize!(m)

            @test termination_status(m) == MOI.INFEASIBLE
        end

        @testset "all([x, y])" begin
            m = Model(with_optimizer(GLPK.Optimizer))
            @variable(m, x, Bin)
            @variable(m, y, Bin)
            @constraint(m, all([x, y]) == true)
            @objective(m, Max, x + y)
            optimize!(m)

            @test value(x) ≈ 1.0
            @test value(y) ≈ 1.0

            m = Model(with_optimizer(GLPK.Optimizer))
            @variable(m, x, Bin)
            @variable(m, y, Bin)
            @constraint(m, all([x, y]) == true)
            @constraint(m, x + y <= 1)
            @objective(m, Max, x + y)
            optimize!(m)

            @test termination_status(m) == MOI.INFEASIBLE
        end

        @testset "all([x, y, z])" begin
            m = Model(with_optimizer(GLPK.Optimizer))
            @variable(m, x, Bin)
            @variable(m, y, Bin)
            @variable(m, z, Bin)
            @constraint(m, all([x, y, z]) == true)
            @objective(m, Max, x + y)
            optimize!(m)

            @test value(x) ≈ 1.0
            @test value(y) ≈ 1.0
            @test value(z) ≈ 1.0

            m = Model(with_optimizer(GLPK.Optimizer))
            @variable(m, x, Bin)
            @variable(m, y, Bin)
            @variable(m, z, Bin)
            @constraint(m, all([x, y, z]) == true)
            @constraint(m, x + y <= 1)
            @objective(m, Max, x + y + z)
            optimize!(m)

            @test termination_status(m) == MOI.INFEASIBLE
        end

        @testset "|" begin
            m = Model(with_optimizer(GLPK.Optimizer))
            @variable(m, x, Bin)
            @variable(m, y, Bin)
            @constraint(m, x | y == true)
            @objective(m, Min, x + y)
            optimize!(m)

            if value(x) ≈ 1.0
                @test value(x) ≈ 1.0
                @test value(y) ≈ 0.0
            else
                @test value(x) ≈ 0.0
                @test value(y) ≈ 1.0
            end

            m = Model(with_optimizer(GLPK.Optimizer))
            @variable(m, x, Bin)
            @variable(m, y, Bin)
            @constraint(m, x | y == true)
            @constraint(m, x + y <= 1)
            @objective(m, Max, x + y)
            optimize!(m)

            if value(x) ≈ 1.0
                @test value(x) ≈ 1.0
                @test value(y) ≈ 0.0
            else
                @test value(x) ≈ 0.0
                @test value(y) ≈ 1.0
            end
        end

        @testset "any([x, y])" begin
            m = Model(with_optimizer(GLPK.Optimizer))
            @variable(m, x, Bin)
            @variable(m, y, Bin)
            @constraint(m, any([x, y]) == true)
            @objective(m, Min, x + y)
            optimize!(m)

            if value(x) ≈ 1.0
                @test value(x) ≈ 1.0
                @test value(y) ≈ 0.0
            else
                @test value(x) ≈ 0.0
                @test value(y) ≈ 1.0
            end

            m = Model(with_optimizer(GLPK.Optimizer))
            @variable(m, x, Bin)
            @variable(m, y, Bin)
            @constraint(m, any([x, y]) == true)
            @constraint(m, x + y <= 1)
            @objective(m, Max, x + y)
            optimize!(m)

            if value(x) ≈ 1.0
                @test value(x) ≈ 1.0
                @test value(y) ≈ 0.0
            else
                @test value(x) ≈ 0.0
                @test value(y) ≈ 1.0
            end
        end

        @testset "any([x, y, z])" begin
            m = Model(with_optimizer(GLPK.Optimizer))
            @variable(m, x, Bin)
            @variable(m, y, Bin)
            @variable(m, z, Bin)
            @constraint(m, any([x, y, z]) == true)
            @objective(m, Min, x + y + z)
            optimize!(m)

            @test value(x) + value(y) + value(z) ≈ 1.0
        end

        @testset "⊻" begin
            m = Model(with_optimizer(GLPK.Optimizer))
            @variable(m, x, Bin)
            @variable(m, y, Bin)
            @constraint(m, x ⊻ y == true)
            @objective(m, Min, x + y)
            optimize!(m)

            if value(x) ≈ 1.0
                @test value(x) ≈ 1.0
                @test value(y) ≈ 0.0
            else
                @test value(x) ≈ 0.0
                @test value(y) ≈ 1.0
            end
        end
    end
end


using BenchmarkTools, SegmentIntersections

random_coordinates = 100 .* rand(500, 4);
segments = Segment{Float64}[]
for datap in eachrow(random_coordinates)
    push!(segments, Segment(datap...))
end

println("Running brute force...")
@btime find_intersections_brute(segments);

println("Running Bentley-Ottman...")
@btime find_intersections(segments);


# test the April grid camera calibration functions

using Test
using AprilTags
using FileIO
using Optim

# using ImageView

##

@testset "April grid camera calibration test" begin

##

# load the image used for calibration
imgfile = joinpath(dirname(dirname(pathof(AprilTags))), "data/CameraCalibration/taggridphoto.jpg")
img = load(imgfile);

##

# construct the cost function
IMGS = Vector{typeof(img)}()
push!(IMGS, img)

detector = AprilTagDetector()
tags = detector.(IMGS);

##

taglength = 0.0315

# assume obj([f_width, f_height, c_width, c_height])
obj = (fc_wh) -> calcCalibResidualAprilTags!(IMGS, tags,
                                            taglength=taglength,
                                            f_width =fc_wh[1],
                                            f_height=fc_wh[2],
                                            c_width =fc_wh[3],
                                            c_height=fc_wh[4]  )
#

## Run the optimization

# f_width, c_width, c_height = size(img, 1), size(img, 1)/2, size(img, 2)/2
# f_height = f_width

# nearby calibration
f_width  = 3370.4878918701756 + 5
f_height = 3352.8348099534364 + 5
c_width  = 2005.641610450976  + 5
c_height = 1494.8282013012076 + 5
# the physical size of the tag
# taglength = 0.0315

result = optimize(obj, [f_width, f_height, c_width, c_height], BFGS(), Optim.Options(iterations = 10, x_tol=1e-6, show_trace=true))

result.minimizer

## draw the result

SEL = 1

cimg_ = deepcopy(IMGS[SEL])
calcCornerProjectionsAprilTags!( cimg_, tags[SEL],
                                  taglength=0.0315,
                                  f_width=f_width,
                                  f_height=f_height,
                                  c_width=c_width,
                                  c_height=c_height,
                                  dodraw=true )
#

# imshow(cimg_)

##

freeDetector!(detector)

##

end

#


using Test
using Catlab.Graphs
using Catlab.CategoricalAlgebra
using Catlab.Present
using Catlab.Theories

using CSetAutomorphisms
using Catlab.Graphs.BasicGraphs: TheoryGraph

using Random

# Auxillary function tests
##########################

@test common([],[]) == 0
@test common([1],Int[]) == 0
@test common([1],Int[1]) == 1
@test common([1],Int[1,2]) == 1
@test common([1,2,3],Int[1,2]) == 2

# Helper functions for writing automorphism tests
#################################################

# Tests
#######

G,H = Graph(4), Graph(4);
add_edges!(G,[1,2,4,4,3],[2,4,3,3,2]);
add_edges!(H,[2,3,1,4,4],[1,1,4,3,3]);
test_iso(G,H, TheoryGraph) # 196 automorphisms

Triangle = Graph(3) # f;g = h
add_edges!(Triangle, [1,1,2], [2,3,3]) # f,h,g

Tri_, (G,H) = init_graphs(:Tri, Triangle,[2,2,2])
for i in 1:3 set_subpart!(G, Symbol("e$i"), [1,1]) end
for i in 1:3 set_subpart!(H, Symbol("e$i"), [2,2]) end
test_iso(G, H, Tri_)

Loop = Graph(1)
add_edge!(Loop, 1, 1)
Loo_, (G, H) = init_graphs(:Loo, Loop, [3])
set_subpart!(G, Symbol("e1"), [3,2,1])
set_subpart!(H, Symbol("e1"), [1,3,2])
test_iso(G, H, Loo_)

cyclel, cycler = Graph(3), Graph(3)
add_edges!(cyclel,[1,2,3],[2,3,1])
add_edges!(cycler,[3,2,1],[2,1,3])
test_iso(cyclel, cycler, TheoryGraph)

Loop2 = Graph(1)
add_edges!(Loop2, [1,1],[1,1])

Loo2_, (G,H) = init_graphs(:Loo2, Loop2, [2])
set_subpart!(G, :e1, [2,1])
set_subpart!(G, :e2, [2,1])
set_subpart!(H, :e1, [1,1])
set_subpart!(H, :e2, [2,2])
test_iso(G, H, Loo2_)

# Example from Hartke and Radcliffe exposition of Nauty.
# G is their optimal ordering. H is the original.
G, H = Graph(9), Graph(9)
add_edges!(G,[1,1,2,2,3,3,4,4,5,6,7,8],
             [7,8,5,6,6,8,5,7,9,9,9,9])
add_edges!(H,[1,1,3,3,7,7,9,9,2,4,6,8],
             [2,4,2,6,4,8,6,8,5,5,5,5])
res, tree = autos(H);
# When branching is restricted to :V as is the case in Nauty
# length should be 13 without auto pruning
# length is 10 with auto pruning tactic #1
# length is 6 with auto pruning tactic #2 too
# However, we can branch on :E too. This leads to just length 4 soln.

test_iso(G,H) # nauty doesn't seem to terminate

"""Graph corresponding to schema for finite limit sketch for categories"""
catschema = @acset Graph begin
  V = 7
  E = 17
  src = [2,2,1, 3,3,3, 4,4,5,5,4, 6,6,6, 7,7,7]
  tgt = [1,1,2, 2,2,2, 2,2,2,2,5, 1,2,3, 1,2,3]
end
random_perm = Dict([:V=>randperm(7), :E=>randperm(17)])
catschema2 = apply_automorphism(catschema, random_perm)
test_iso(catschema,catschema2, TheoryGraph)

# ACSet Tests
#############

G = @acset Labeled{String} begin
  V = 4
  E = 4
  src = [1,2,3,4]
  tgt = [2,3,4,1]
  dec = ["a","b","c","d"]
end;

H = @acset Labeled{String} begin
  V = 4
  E = 4
  src = [1,3,2,4]
  tgt = [3,2,4,1]
  dec = ["a","b","c","d"]
end;

test_iso(G, H, TheoryDecGraph) # vertices permuted

I = @acset Labeled{String} begin
V = 4
E = 4
src = [1,2,3,4]
tgt = [2,3,4,1]
dec = ["b","c","d","a"]
end;

test_iso(G, I, TheoryDecGraph) # labels permuted

N = @acset Labeled{String} begin
  V = 4
  E = 4
  src = [1,2,3,4]
  tgt = [2,3,4,1]
  dec = ["a","a","b","c"]
end;

test_iso(G,N) # label mismatch

K = @acset Labeled{String} begin
  V = 4
  E = 4
  src = [1,3,2,4]
  tgt = [2,3,4,1]
  dec = ["a","d","b","c"]
end;

test_iso(G, K) # vertex mismatch

G1 = @acset Labeled{String} begin
  V = 1
  E = 1
  src = [1]
  tgt = [1]
  dec = ["a"]
end;

H1 = @acset Labeled{String} begin
  V = 1
  E = 1
  src = [1]
  tgt = [1]
  dec = ["b"]
end;

test_iso(G1, H1) # label values different


struct LinearAnalysis
    options::Dict{Symbol, Any}
end

LinearAnalysis(; kwargs...) = LinearAnalysis(Dict{Symbol, Any}(kwargs))

add_intercept_column(x::AbstractVector{T}) where {T} = [ones(T, length(x)) x]

# TODO: add multidimensional version
function (l::LinearAnalysis)(le::Entry)
    entry = map(le) do p, n
        x, y = p
        weights = get(n, :weights, similar(x, 0))
        npoints = get(l.options, :npoints, 200)
        interval = get(l.options, :interval, length(weights) > 0 ? nothing : :confidence)
        dropcollinear = get(l.options, :dropcollinear, false)
        lin_model = GLM.lm(add_intercept_column(x), collect(y); wts=weights, dropcollinear)
        isnothing(lin_model) && return Entry[]
        x̂ = range(extrema(x)..., length=npoints)
        pred = GLM.predict(lin_model, add_intercept_column(x̂); interval)
        return if !isnothing(interval)
            ŷ, lower, upper = map(vec, pred) # GLM prediction returns matrices
            (x̂, ŷ), (; lower, upper)
        else
            ŷ = vec(pred) # GLM prediction returns matrix
            (x̂, ŷ), (;)
        end
    end
    default_plottype = isempty(entry.named) ? Lines : LinesFill
    plottype = Makie.plottype(entry.plottype, default_plottype)
    return Entry(entry; plottype)
end

"""
    linear(; interval)

Compute a linear fit of `y ~ 1 + x`. An optional named mapping `weights` determines the weights.
Use `interval` to specify what type of interval the shaded band should represent.
Valid values of interval are `:confidence` delimiting the uncertainty of the predicted
relationship, and `:prediction` delimiting estimated bounds for new data points.
"""
linear(; kwargs...) = transformation(LinearAnalysis(; kwargs...))


# Parses distribution expression and returns expression for a segment cost function
# Required for PELT and BS macros
function cost_function(data::Any, dist_expr::Expr)
    if !Meta.isexpr(dist_expr,:call)
        error("Syntax error: expected distribution as argument")
    end

    dist_type = dist_expr.args[1]

    if dist_type == :Normal
        if length(dist_expr.args) != 3
            error("Normal distribution has two parameters")
        end
        μ, σ = dist_expr.args[2:3]
        if μ == :(:?) && σ != :(:?)
            println("Changepoint distribution is Normal with changing mean and fixed variance")
            return :(NormalMeanSegment($data , $σ))
        elseif μ != :(:?) && σ == :(:?)
            println("Changepoint distribution is Normal with fixed mean and changing variance")
            #μ = eval(Main, μ)
            return :(NormalVarSegment($data, $μ))
        elseif μ == :(:?) && σ == :(:?)
            println("Changepoint distribution is Normal with changing mean and changing variance")
            return :(NormalMeanVarSegment($data))
        else
            error("Must mark at least one Normal parameter as changing with a :? symbol")
        end

    elseif dist_type == :Exponential
        println("Changepoint distribution is Exponential with changing mean")
        return :(ExponentialSegment($data))

    elseif dist_type == :Poisson
        println("Changepoint distribution is Poisson with changing mean")
        return :(PoissonSegment($data))

    elseif dist_type == :Gamma
        if length(dist_expr.args) != 3
            error("Gamma distribution has two parameters")
        end
        alpha , beta = dist_expr.args[2:3]
        if alpha == :(:?) && beta != :(:?)
            println("Changepoint distribution is Gamma with changing shape and fixed rate")
            return :(GammaShapeSegment($data, $beta))
        elseif alpha != :(:?) && beta == :(:?)
            println("Changepoint distribution is Gamma with fixed shape and changing rate")
            return :(GammaRateSegment($data, $alpha))
        else
            error("Must mark at least one Gamma parameter as changing with a :? symbol")
        end

    elseif dist_type == :Nonparametric
        K = dist_expr.args[2]
        println("Changepoint method is Nonparametric")
        return :(NonparametricSegment($data, $K))

    elseif dist_type == :OLS
        println("Changepoints in piecewise linear regressions")
        return :(OLSSegment($data))

    elseif dist_type == :CUSUM
        println("CUSUM cost function")
        sigma = dist_expr.args[2]
        return :(CUSUM($data , $sigma))

    else
        error("Distribution $(dist_type) has no implemented cost functions")
    end
end

function cost_function_CUSUM(data::Any, sigma::Any)#dist_expr::Expr)
    println("CUSUM cost function")    #sigma = dist_expr.args[2]
    return :(CUSUM($data , $sigma))
end

macro mad(data::Any)
    println("Estimate sigma by MAD")
    return   :(mad($data) )
end

"""
    @segment_cost data changepoint_model

Creates a segment cost function given data and changepoint model expression.

# Cost functions

`changepoint_model` is an expression which describes what segment cost function
should be constructed for use with PELT. For parametric segment cost functions,
this is represented by the name of a distribution (as in the Distributions package)
with some parameters replaced by ':?' to indicate that the parameters change.
The full list of available cost functions based on parametric distributions is
as follows:

* `Normal(:?, σ)`: Normal model with changing mean and fixed standard deviation `σ` (see also [`NormalMeanSegment`](@ref))
* `Normal(μ, :?)`: Normal model with fixed mean `μ` and changing standard deviation (see also [`NormalVarSegment`](@ref))
* `Normal(:?, :?)`: Normal model with changing mean and standard deviation (see also [`NormalMeanVarSegment`](@ref))
* `Exponential(:?)`: Exponential model with changing mean (see also [`ExponentialSegment`](@ref))
* `Poisson(:?)`: Poisson model with changing mean (see also [`PoissonSegment`](@ref))
* `Gamma(:?, β)`: Gamma model with fixed rate parameter `β` and changing shape parameter (see also [`GammaShapeSegment`](@ref))
* `Gamma(α, :?)`: Gamma model with fixed shape parameter `α` and changing rate parameter (see also [`GammaRateSegment`](@ref))

The following others models are also available:

* `Nonparametric(k)`: Nonparametric cost function with parameter `k` (see also [`NonparametricSegment`](@ref))
* `OLS` : Cost function for piecewise linear regressions (see also [`OLSSegment`](@ref))

# Example
```julia-repl
n = 1000
λ = 100
μ, σ = Normal(0.0, 10.0), 1.0
# Samples changepoints from Normal distribution with changing mean
sample, cps = @changepoint_sampler n λ Normal(μ, σ)
# Create cost function
seg_cost = @segment_cost sample Normal(:?, σ)
# Calculate changepoints using PELT and BS
pelt_cps, cost = PELT(seg_cost, n)
bs_cps = BS(seg_cost, n)
```
"""
macro segment_cost(data, dist)
    esc(cost_function(data, dist))
end

"""
    @PELT data changepoint_model [β₁ [β₂] ]

Runs the PELT algorithm on time series `data` using a specified `changepoint_model` and penalties.
If no penalty `β₁` provided, a default of value `log(length(data))` is used.
If two penalties `β₁` and `β₂` are provided then the CROPS algorithm is run which finds
all optimal segmentations for all penalties between `β₁` and `β₂`.

See also: [`PELT`](@ref), [`CROPS`](@ref)

# Example
```
n = 1000
λ = 100
μ, σ = Normal(0.0, 10.0), 1.0
# Samples changepoints from Normal distribution with changing mean
sample, cps = @changepoint_sampler n λ Normal(μ, σ)
# Run PELT on sample
pelt_cps, pelt_cost = @PELT sample Normal(:?, σ)
```
"""
macro PELT(data, dist, args...)
    cost_func = cost_function(data, dist)
    if length(args) == 0
        return esc(:(PELT($(cost_func), length($data))))
    elseif length(args) == 1
        return esc(:(PELT($(cost_func), length($data), pen=$(args[1]))))
    else
        return esc(:(CROPS($(cost_func), length($data), $(args[1]), $(args[2]))))
    end
end

"""
    @BS data changepoint_model [β₁]

Runs the Binary Segmentation algorithm using a specified `changepoint_model` for a given penalty `β₁`.
If no penalty specified, use penalty `log(length(data))` by default.

See also: [`BS`](@ref), [`@segment_cost`](@ref)

# Example
```
n = 1000   # Length of time series
λ = 100    # Frequency of changepoints
α, β = Uniform(0.0, 10.0), 1.0
# Samples changepoints from Gamma distribution with changing shape
sample, cps = @changepoint_sampler n λ Gamma(α, β)
# Run binary segmentation on sample
bs_cps = @BS sample Gamma(:?, β)
```
"""
macro BS(data, dist, args...)
    cost_func = cost_function(data, dist)
    if length(args) == 0
        return esc(:(BS($(cost_func), length($data))))
    else
        return esc(:(BS($(cost_func), length($data), pen=$(args[1]))))
    end
end


function isaksprime(n::Int64)
    if n < 2
        return false
    end
    for c in polycoefs(n)[2:(end-1)]
        if c%n != 0
            return false
        end
    end
    return true
end


"""
Convert a matrix A which is the output of a real FFT to a real vector, keeping
only unqiue real/imaginary entries of A
"""
function rfft2vec(A::AbstractMatrix)
    m,n = size(A)
    ireal,iimag = fftsyms(Val(m),Val(n))
    [real(A[ireal]); imag(A[iimag])]
end

"""
Convert a vector produced by rfft2vec back into a complex matrix.
"""
function vec2rfft(v::AbstractVector{<:Real})
    n = round(Int,sqrt(length(v)))
    m = n÷2+1
    nreal = (n^2)÷2 + (iseven(n) ? 2 : 1)
    ireal,iimag,inegks = fftsyms(Val(m),Val(n))
    A = fill(NaN+im*NaN,m,n)
    A[ireal] = v[1:nreal]
    A[iimag] += im*v[nreal+1:end]
    for i=1:m, j=1:n
        if isnan(A[i,j])
            A[i,j] = A[inegks[i,j]...]'
        end
    end
    A
end

"""
Convert an M×N matrix (with M=N÷2+1) which is the output a real FFT to a full
N×N one via symmetries.
"""
unfold(Tls::AbstractArray{<:Complex,3}, Ny) = mapslices(X -> unfold(X, Ny), Array(Tls), dims=(1,2))
unfold(Tl::AbstractMatrix{<:Complex}, Ny) = unfold(Array(Tl), Ny)
function unfold(Tl::Matrix{<:Complex}, Ny::Int)
    m,n = size(Tl)
    @assert m==Ny÷2+1
    m2 = iseven(Ny) ? 2m : 2m+1
    n2 = iseven(n) ?  n+2 : n+3
    Tlu = similar(Tl,Ny,n)
    Tlu[1:m,1:n] = Tl
    @inbounds for i=m+1:Ny
        Tlu[i,1] = Tl[m2-i, 1]'
        @simd for j=2:n
            Tlu[i,j] = Tl[m2-i, n2-j]'
        end
    end
    Tlu
end

"""
Arguments `m` and `n` refer to the sizes of an `m`×`n` matrix (call it `A`) that is the output of a
real FFT (thus `m=n÷2+1`)

Returns a tuple of (ireal, iimag, negks) where these are

* `ireal` — `m`×`n` mask corrsponding to unique real entries of `A`
* `iimag` — `m`×`n` mask corrsponding to unique imaginary entries of `A`
* `negks` — `m`×`n` matrix of giving the index into A where the negative k-vector
            is, s.t. `A[i,j] = A[negks[i,j]]'`
"""
@generated function fftsyms(::Val{m},::Val{n}) where {m,n}
    k = ifftshift(-n÷2:(n-1)÷2)
    ks = tuple.(k',k)[1:n÷2+1,:]
    wrapk(k) = mod(k+n÷2,n) - n÷2
    negk(k) = @. wrapk(-k)
    k_in_ks(k) = -n÷2<=k[1]<=(n-1)÷2 && (0<=k[2]<=(n-1)÷2 || k[2]==-n÷2)
    ireal = map(k->(negk(k)==k || !k_in_ks(negk(k)) || (k[1]>0 || k[2]>0)), ks)
    iimag = map(k->(negk(k)!=k && !k_in_ks(negk(k)) || (k[1]>0 || k[2]>0)), ks)
    indexof(k) = (mod(k[2],n)+1, mod(k[1],n)+1)
    inegks = indexof.(negk.(ks))
    inegks[.!k_in_ks.(negk.(ks))] .= Ref((0,0))
    ireal,iimag,inegks#,ks,negk.(ks)#,k_in_ks.(negk.(ks)),map(k->k_in_ks(negk(k)),ks)
end


using QuadGK
using SpecialFunctions
using Roots
using RCall

function Gammadist(gamma)
	return ((adap.be^adap.al)/SpecialFunctions.gamma(adap.al))*(gamma^(adap.al-1))*exp(-adap.be*gamma)
end

function pip0(gamma)
	U = 4*adap.theta_f*adap.Lf/(2.0*adap.NN)
	R = 2*adap.Lf*adap.rho/(2.0*adap.NN)
	return Gammadist(gamma)*exp(-(Gammadist(gamma)*U/(2.0*adap.NN))/(gamma/(adap.NN+0.0)+R/(2.0*adap.NN)))
end

function intpip0()

	f(gam) = pip0(gam)
	return QuadGK.quadgk(f,0,1000)[1]
end

function calcBGam(L,alpha,beta,theta)
	# not sure whats going on here, seems to overestimate or under sometimes
	u = 2*theta/(2.0*adap.NN)
	r = adap.rho/(2.0*adap.NN)

	a = -1.0*(2^(alpha+1))*exp(L*adap.NN*r*beta)*L*adap.N*((1.0/(L*adap.N*r))^(1-alpha))*u*(beta^alpha)
	b =  convert(Float64,SpecialFunctions.gamma_inc(1-alpha,L*adap.NN*r*beta,1)[2])
	#fudge = 1-gamInt.cdf(0.2,a=adap.al2,scale=1./adap.be2)
	#fudge = 1.
	fudge = 0.25

	c = exp(a*b*fudge)

	return c
end

function set_theta_f_gam()
	i(theta) = calcBGam(adap.Lf,adap.al2,adap.be2,theta)-adap.B
	# theta_f  = fsolve(lambda theta ,0.0000001)
	theta_f  = Roots.find_zero(i,0.0000001)
	adap.theta_f = theta_f
end

function calcB(L,theta)
	t = -1.0*adap.gam_neg/(adap.NN+0.)
	u = 2.0*theta/(2.0*adap.NN)
	r = adap.rho/(2.0*adap.NN)

	#return u*t/((t+r*L)^2)
	#return u*t/(2*(t+(1.-np.exp(-2*r*L))/2.)^2)

	# Nordborg models
	#####return u/(2*r*t*(1+((1.-np.exp(-2*r*L))/2.)*(1-t)/t)^2)
	#return u/(t*(1+((1-np.exp(-2.0*r*L))/2.)*(1-t)/t)^2)
	#return u/(t*(1+r*L*(1-t)/t)^2)
	#####return u/(t*(1+(np.exp(-2*r*L)/2)/t)^2)
end

# Br() needs L and theta, not working right now
function get_B_vals()
	ret = Array{Float64}(undef,30)
	for i in 20:50
		L = convert(Int64,round(1.3^i,digits=0))
		ret[i] = (Br(L),L)
	end
	return ret
end

"""
	Estimating and plotting MAP using locfit and ggplot2 in R. It assume your folder contains the posterior estimated through ABCreg
"""
function plotMap(;analysis::String,output::String)

	try
		@eval using RCall
		@eval R"""library(ggplot2);library(abc)"""

		out = filter(x -> occursin("post",x), readdir(analysis,join=true))
		out = filter(x -> !occursin(".1.",x),out)

		open(x) = Array(CSV.read(GZip.open(x),DataFrame,header=false))
		posteriors = open.(out)

		maxp = DataFrame(Array{Float64,2}(undef,size(posteriors,1),5),[:aw,:as,:a,:gamNeg,:shape])
		R"""getmap <- function(df){
				temp = as.data.frame(df)
			    d <-locfit(~temp[,1],temp);
			    map<-temp[,1][which.max(predict(d,newdata=temp))]
			}"""
		getmap(x) = rcopy(R"""matrix(apply($x,2,getmap),nrow=1)""")
		tmp = getmap.(posteriors)
		maxp = DataFrame(vcat(tmp...),[:aw,:as,:a,:gamNeg,:shape])

		al  = maxp[:,1:3]
		gam  = maxp[:,4:end]
		p = rcopy(R"""al = $al
			dal = melt(al)
			pal = ggplot(dal) + geom_density(aes(x=value,fill=variable),alpha=0.5) + scale_fill_manual(values=c('#30504f', '#e2bd9a', '#ab2710'))
			ggsave(pal,filename=paste0($output))
			""")
		return(maxp)
	catch
		println("Please install R, ggplot2 and abc in your system before execute this function")
	end
end

function set_ppos!(param::parameters)

	function f!(F,x,param=param)
		F[1] = alpha_exp_sim_tot(param,x[1],x[2])-param.al_tot
		F[2] = alpha_exp_sim_low(param,x[1],x[2])-param.al_low
	end

	ppos_l,ppos_h = nlsolve(f!,[0.0; 0.0]).zero

	param.ppos_l,param.ppos_h = ppos_l, ppos_h

end

function poisson_fixation(;observed_values::Vector{S}, λds::Vector{Float64}, λdn::Vector{Float64},λweak::Vector{Float64},λstrong::Vector{Float64}) where S <: Union{Int64,Float64}

		ds = @. λds / (λds + λdn) * observed_values
		dn = @. λdn / (λds + λdn) * observed_values
		dweak = @. λweak / (λds + λdn) * observed_values
		dstrong = @. λstrong / (λds + λdn) * observed_values

		sampled_ds     = pois_rand.(ds)
		sampled_dn     = pois_rand.(dn)
		sampled_weak   = pois_rand.(dweak)

		if all(dstrong .> 0)
			sampled_strong = pois_rand.(dstrong)
		else
			sampled_strong = .-pois_rand.(.-dstrong)
		end

		if all(sampled_weak .≈ 0)
			sampled_weak .= 0
		elseif all(sampled_strong .≈ 0)
			sampled_strong .= 0
		end

		alphas = @. [sampled_weak/sampled_dn sampled_strong/sampled_dn (sampled_weak+sampled_strong)/sampled_dn]

		out = alphas,sampled_dn, sampled_ds
		return out
end