text:
### A Pluto.jl notebook ###
# v0.17.2

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ 813ea500-a2ec-11eb-29cb-89ed915aa25a

begin
	#try
		using PlutoUI
		using Plots
		using Plots.PlotMeasures
		using LaTeXStrings
		using Markdown
		using Images
		#using LinearAlgebra
		#using SparseArrays
		#using SpecialFunctions
		#using StatsBase
		#using Random
		#using Distributions
		md"""
		### Packages

		All needed Packages available :) """

	#=
	catch
		using Pkg;
		Pkg.activate(mktempdir())
		Pkg.add("PlutoUI")
		Pkg.add("Plots")
		Pkg.add("LaTeXStrings")
		Pkg.add("Markdown")
		Pkg.add("Images")
		#Pkg.add("LinearAlgebra")
		#Pkg.add("SparseArrays")
		#Pkg.add("SpecialFunctions")
		#Pkg.add("StatsBase")
		#Pkg.add("Distributions")
		using PlutoUI, Plots, LaTeXStrings, Markdown, Images, Plots.PlotMeasures
		#using LinearAlgebra
		#using SparseArrays
		#using StatsBase
		#using Random
		md"""
		### Packages

		Some Package sources not added, this will take approx. 3 minutes"""
	end
	=#
end

# ╔═╡ b9f3e82b-0792-4c42-a7c4-04b11ac9a44e
md"""
# Antigen tests
Experience why the **percentage of infected people** is important to **correctly interprete your personal test result.**
Note: The properties of a test - **sensitivity and specificity** - are independent of the population size or number of infected people!

> **Sensitivity** describes how good a test recognizes an infected person, so the percentage of the test to be positive if the person has the virus

> **Specificity** is the quantity that tells us how well healthy people (not infected) are recognized as such, so the probability that the test is negative for a healthy person
"""

# ╔═╡ 325c3295-20b3-4f67-84d0-277e9b01ecd3
md""" The **population size** of your city is $(@bind pop_size Slider(10000:10000:1000000, default = 300000, show_value = true)) among whom $(@bind test_ratio_percentage Scrubbable(1:100, default = 5))% **got tested** (think of an example where this number could be important).

The **percentage of infected people** is estimated to be $(@bind inf_rate_percent Scrubbable(0:1:100, default = 5))%

"""

# ╔═╡ 31c61c6d-1a97-451f-b07c-864eca18bff2
md"""
The **sensitvity** of an antigen test 💉 is ``P(B\mid V) = `` $(@bind sensi_percent Scrubbable(1:1:100, default = 95))%

and the **specificity** of the test is ``P(\neg B\mid \neg V) = `` $(@bind spec_percent Scrubbable(1:100, default = 90))%

"""

# ╔═╡ d5e23d38-5a43-470d-846e-a05d8a56a726
begin
	inf_rate = inf_rate_percent / 100
	spec = spec_percent/100
	sensi = sensi_percent/100
	test_ratio = test_ratio_percentage/100

	tested_people = pop_size * test_ratio

	infected = pop_size * inf_rate

	P_positive_test = sensi*inf_rate + (1-spec)*(1-inf_rate)
	P_V_B = sensi * inf_rate/ P_positive_test

	P_neg_V_neg_B = spec * (1-inf_rate)/(1-P_positive_test)

	P_V_neg_B = (1-sensi)*inf_rate/(1-P_positive_test)
	md"""Program"""
end

# ╔═╡ 8b39a33a-d7bd-45f2-91e9-173688ea1ec5
function sr(variable, dig = 2)
	# string and round - converts a variable into a string with the predifined precission - to be extended to scientific and other formats
	if dig == 0
		return string(round(Int, variable))
	else
		return string(round(variable, digits = dig))
	end
end

# ╔═╡ 1b7fd8d9-daa2-4808-939a-44548569fcc5
begin
	plot([0,1,1,0,0], [0,0,1,1,0],
		line=(1,1,:path),
		fill = (1,:white),
		aspect_ratio=:equal,
		grid = :none,
		label=latexstring("\\textrm{ Tested persons: } " * sr(tested_people,0)),
		xlabel = latexstring(""),
		ylabel = latexstring(""),
		linewidth = 3,
		#aspect ratio for printing font sizes etc.
		size = (600,400),
		xlim = [0,1],
		legendfontsize = 10,
		leg = :outerright,
	tickfontsize = 15,
	bottom_margin =5mm,
	left_margin = 5mm,

	foreground_color = :black,
	foreground_color_yticks = :transparent,
	titlefontsize = 20,
	#foreground_color_grid = :black,
	#foreground_color_xticks = :black,
	background_color = :transparent,
	#foreground_color_axis = :black,
	#foreground_color_text = :black,
	#foreground_color_border = :black,
	fontfamily="Computer Modern"

		)

	plot!([0,inf_rate,inf_rate,0,0], [0,0,1,1,0],
		line=(1,0,:path),
		fill = (1,:green),
		fillalpha = 0.1,
		label=latexstring("\\textrm{Infected}: "* sr(tested_people*(inf_rate),0)),
		)
	plot!([inf_rate, inf_rate], [0,1],
		label = :none)

	plot!([1,inf_rate,inf_rate,1,1], [0,0,(1-spec),(1-spec),0],
		fill = (1,:red),
		fillalpha = 0.1,
		label=latexstring("\\textrm{False positive}: "* sr(tested_people*(1-inf_rate)*(1-spec),0)),

		)
	plot!([0,inf_rate,inf_rate,0,0], [0,0,(1-sensi),(1-sensi),0],
		fill = (1,:yellow),
		fillalpha = 0.4,
		label=latexstring("\\textrm{False negative}: "* sr(tested_people*(inf_rate)*(1-sensi),0)),
	)

end

# ╔═╡ b70ab060-2117-4c24-adac-27982e5065f3
md"""
The probability to have the virus if the test is positive or negative is
-  ``P(V\mid B) = `` $(sr(P_V_B,5))
-  ``P(V\mid \neg B) = `` $(sr(P_V_neg_B,5))

The probability for a positive test is:
-  ``P(B) = `` $(sr(P_positive_test))
"""

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0"
LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"

[compat]
Images = "~0.25.0"
LaTeXStrings = "~1.3.0"
Plots = "~1.24.0"
PlutoUI = "~0.7.20"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
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[[Gettext_jll]]
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[[Glib_jll]]
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[[Graphics]]
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[[Graphite2_jll]]
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[[Graphs]]
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[[Grisu]]
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[[HTTP]]
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[[HarfBuzz_jll]]
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[[Hyperscript]]
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[[HypertextLiteral]]
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[[IOCapture]]
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[[IfElse]]
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[[ImageCore]]
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[[ImageDistances]]
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[[ImageFiltering]]
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[[ImageIO]]
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[[ImageMagick]]
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[[ImageMagick_jll]]
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git-tree-sha1 = "ea2b6fd947cdfc43c6b8c15cff982533ec1f72cd"
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[[ImageMetadata]]
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[[ImageMorphology]]
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[[ImageQualityIndexes]]
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[[ImageSegmentation]]
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[[ImageShow]]
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[[ImageTransformations]]
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[[Images]]
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[[Imath_jll]]
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git-tree-sha1 = "87f7662e03a649cffa2e05bf19c303e168732d3e"
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[[IndirectArrays]]
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[[Inflate]]
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[[IniFile]]
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[[IntegralArrays]]
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[[IntelOpenMP_jll]]
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git-tree-sha1 = "d979e54b71da82f3a65b62553da4fc3d18c9004c"
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[[InteractiveUtils]]
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[[Interpolations]]
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[[IntervalSets]]
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[[InverseFunctions]]
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[[IrrationalConstants]]
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[[IteratorInterfaceExtensions]]
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[[JLD2]]
deps = ["DataStructures", "FileIO", "MacroTools", "Mmap", "Pkg", "Printf", "Reexport", "TranscodingStreams", "UUIDs"]
git-tree-sha1 = "46b7834ec8165c541b0b5d1c8ba63ec940723ffb"
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[[JLLWrappers]]
deps = ["Preferences"]
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[[JSON]]
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[[JpegTurbo_jll]]
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[[LAME_jll]]
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git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
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[[LZO_jll]]
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[[LaTeXStrings]]
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[[Latexify]]
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[[LazyArtifacts]]
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[[LibCURL]]
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[[LibCURL_jll]]
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uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"

[[LibGit2]]
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[[LibSSH2_jll]]
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uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"

[[Libdl]]
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[[Libffi_jll]]
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[[Libgcrypt_jll]]
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[[Libglvnd_jll]]
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[[Libgpg_error_jll]]
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[[Libiconv_jll]]
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git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
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[[Libmount_jll]]
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[[Libtiff_jll]]
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[[Libuuid_jll]]
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[[LinearAlgebra]]
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[[LogExpFunctions]]
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[[Logging]]
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[[MKL_jll]]
deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
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[[MacroTools]]
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[[MappedArrays]]
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[[Markdown]]
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[[MbedTLS]]
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git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
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[[MbedTLS_jll]]
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uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"

[[Measures]]
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[[MetaGraphs]]
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[[Missings]]
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[[Mmap]]
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[[MosaicViews]]
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uuid = "e94cdb99-869f-56ef-bcf0-1ae2bcbe0389"
version = "0.3.3"

[[MozillaCACerts_jll]]
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[[NaNMath]]
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[[NearestNeighbors]]
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uuid = "b8a86587-4115-5ab1-83bc-aa920d37bbce"
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[[Netpbm]]
deps = ["FileIO", "ImageCore"]
git-tree-sha1 = "18efc06f6ec36a8b801b23f076e3c6ac7c3bf153"
uuid = "f09324ee-3d7c-5217-9330-fc30815ba969"
version = "1.0.2"

[[NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"

[[OffsetArrays]]
deps = ["Adapt"]
git-tree-sha1 = "043017e0bdeff61cfbb7afeb558ab29536bbb5ed"
uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.10.8"

[[Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.5+0"

[[OpenEXR]]
deps = ["Colors", "FileIO", "OpenEXR_jll"]
git-tree-sha1 = "327f53360fdb54df7ecd01e96ef1983536d1e633"
uuid = "52e1d378-f018-4a11-a4be-720524705ac7"
version = "0.3.2"

[[OpenEXR_jll]]
deps = ["Artifacts", "Imath_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "923319661e9a22712f24596ce81c54fc0366f304"
uuid = "18a262bb-aa17-5467-a713-aee519bc75cb"
version = "3.1.1+0"

[[OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"

[[OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.10+0"

[[OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.5+0"

[[Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.3.2+0"

[[OrderedCollections]]
git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.1"

[[PCRE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
version = "8.44.0+0"

[[PNGFiles]]
deps = ["Base64", "CEnum", "ImageCore", "IndirectArrays", "OffsetArrays", "libpng_jll"]
git-tree-sha1 = "6d105d40e30b635cfed9d52ec29cf456e27d38f8"
uuid = "f57f5aa1-a3ce-4bc8-8ab9-96f992907883"
version = "0.3.12"

[[PaddedViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "646eed6f6a5d8df6708f15ea7e02a7a2c4fe4800"
uuid = "5432bcbf-9aad-5242-b902-cca2824c8663"
version = "0.5.10"

[[Parameters]]
deps = ["OrderedCollections", "UnPack"]
git-tree-sha1 = "34c0e9ad262e5f7fc75b10a9952ca7692cfc5fbe"
uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
version = "0.12.3"

[[Parsers]]
deps = ["Dates"]
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uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.1.2"

[[Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.40.1+0"

[[Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

[[PkgVersion]]
deps = ["Pkg"]
git-tree-sha1 = "a7a7e1a88853564e551e4eba8650f8c38df79b37"
uuid = "eebad327-c553-4316-9ea0-9fa01ccd7688"
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[[PlotThemes]]
deps = ["PlotUtils", "Requires", "Statistics"]
git-tree-sha1 = "a3a964ce9dc7898193536002a6dd892b1b5a6f1d"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "2.0.1"

[[PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "b084324b4af5a438cd63619fd006614b3b20b87b"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.0.15"

[[Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun"]
git-tree-sha1 = "02a083caba3f73e42decb810b2e0740783022978"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.24.0"

[[PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "Dates", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "Markdown", "Random", "Reexport", "UUIDs"]
git-tree-sha1 = "1e0cb51e0ccef0afc01aab41dc51a3e7f781e8cb"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.20"

[[Preferences]]
deps = ["TOML"]
git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.2.2"

[[Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[ProgressMeter]]
deps = ["Distributed", "Printf"]
git-tree-sha1 = "afadeba63d90ff223a6a48d2009434ecee2ec9e8"
uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
version = "1.7.1"

[[Qt5Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
git-tree-sha1 = "ad368663a5e20dbb8d6dc2fddeefe4dae0781ae8"
uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
version = "5.15.3+0"

[[REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[Random]]
deps = ["Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[RangeArrays]]
git-tree-sha1 = "b9039e93773ddcfc828f12aadf7115b4b4d225f5"
uuid = "b3c3ace0-ae52-54e7-9d0b-2c1406fd6b9d"
version = "0.3.2"

[[Ratios]]
deps = ["Requires"]
git-tree-sha1 = "01d341f502250e81f6fec0afe662aa861392a3aa"
uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
version = "0.4.2"

[[RecipesBase]]
git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.2.1"

[[RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
git-tree-sha1 = "7ad0dfa8d03b7bcf8c597f59f5292801730c55b8"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
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[[Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[RegionTrees]]
deps = ["IterTools", "LinearAlgebra", "StaticArrays"]
git-tree-sha1 = "4618ed0da7a251c7f92e869ae1a19c74a7d2a7f9"
uuid = "dee08c22-ab7f-5625-9660-a9af2021b33f"
version = "0.3.2"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.1.3"

[[Rotations]]
deps = ["LinearAlgebra", "Random", "StaticArrays", "Statistics"]
git-tree-sha1 = "6a23472b6b097d66da87785b61137142ac104f94"
uuid = "6038ab10-8711-5258-84ad-4b1120ba62dc"
version = "1.0.4"

[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[Scratch]]
deps = ["Dates"]
git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.0"

[[Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"

[[SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
version = "0.9.4"

[[SimpleWeightedGraphs]]
deps = ["Graphs", "LinearAlgebra", "Markdown", "SparseArrays", "Test"]
git-tree-sha1 = "a6f404cc44d3d3b28c793ec0eb59af709d827e4e"
uuid = "47aef6b3-ad0c-573a-a1e2-d07658019622"
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[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
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[[SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[SpecialFunctions]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "e08890d19787ec25029113e88c34ec20cac1c91e"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.0.0"

[[StackViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "46e589465204cd0c08b4bd97385e4fa79a0c770c"
uuid = "cae243ae-269e-4f55-b966-ac2d0dc13c15"
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[[Static]]
deps = ["IfElse"]
git-tree-sha1 = "e7bc80dc93f50857a5d1e3c8121495852f407e6a"
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
version = "0.4.0"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "3c76dde64d03699e074ac02eb2e8ba8254d428da"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
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[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[StatsAPI]]
git-tree-sha1 = "0f2aa8e32d511f758a2ce49208181f7733a0936a"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
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[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "2bb0cb32026a66037360606510fca5984ccc6b75"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
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[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "2ce41e0d042c60ecd131e9fb7154a3bfadbf50d3"
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[[TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"

[[TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
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[[Tables]]
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[[Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

[[TensorCore]]
deps = ["LinearAlgebra"]
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[[Test]]
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uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[TiffImages]]
deps = ["ColorTypes", "DataStructures", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "OffsetArrays", "PkgVersion", "ProgressMeter", "UUIDs"]
git-tree-sha1 = "c342ae2abf4902d65a0b0bf59b28506a6e17078a"
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[[TiledIteration]]
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[[TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
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[[URIs]]
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[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[UnPack]]
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uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
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[[Unicode]]
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[[UnicodeFun]]
deps = ["REPL"]
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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"]
git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
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[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.5"

[[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"

[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[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 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[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:
# ╟─b9f3e82b-0792-4c42-a7c4-04b11ac9a44e
# ╟─325c3295-20b3-4f67-84d0-277e9b01ecd3
# ╟─31c61c6d-1a97-451f-b07c-864eca18bff2
# ╟─1b7fd8d9-daa2-4808-939a-44548569fcc5
# ╟─b70ab060-2117-4c24-adac-27982e5065f3
# ╟─813ea500-a2ec-11eb-29cb-89ed915aa25a
# ╟─d5e23d38-5a43-470d-846e-a05d8a56a726
# ╟─8b39a33a-d7bd-45f2-91e9-173688ea1ec5
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002

max_stars_repo_name: moserjo/bayes-imoox

max_issues_repo_name: moserjo/bayes-imoox

max_forks_repo_name: moserjo/bayes-imoox


text:
using ReinforcementLearningEnvironmentDiscrete, ReinforcementLearning

env = DiscreteMaze(ngoals = 5)
rlsetup = RLSetup(SmallBackups(na = 4, ns = env.mdp.observationspace.n, γ = .99),
                  env, ConstantNumberSteps(200),
                  callbacks = [Visualize()])
@info("Before learning.")
run!(rlsetup)
rlsetup.callbacks = []
rlsetup.stoppingcriterion = ConstantNumberSteps(10^6)
learn!(rlsetup)
@info("After learning.")
rlsetup.callbacks = [Visualize()]
rlsetup.stoppingcriterion = ConstantNumberSteps(100)
run!(rlsetup)

ext: jl


text:
module Mangal

using HTTP
using JSON
using GeoInterface
using EcologicalNetworks
using Dates

const web_root = "https://mangal.io/"
const api_root = web_root * "api/v2/"

# Login
include(joinpath(".", "login.jl"))

# Types
include(joinpath(".", "types.jl"))
export MangalDataset
export MangalNetwork
export MangalReferenceTaxon
export MangalNode
export MangalInteraction
export MangalReference
export MangalAttribute
export MangalUser

# Endpoints
const _MANGAL_ENDPOINTS = Dict(
    MangalReferenceTaxon => "taxonomy",
    MangalNode => "node",
    MangalInteraction => "interaction",
    MangalNetwork => "network",
    MangalDataset => "dataset",
    MangalReference => "reference",
    MangalAttribute => "attribute",
    MangalUser => "user",
)

#trait = "trait",

# The cache!
global _MANGAL_CACHES = Dict(
    MangalNode => Dict{Int64,MangalNode}(),
    MangalReferenceTaxon => Dict{Int64,MangalReferenceTaxon}(),
    MangalNetwork => Dict{Int64,MangalNetwork}(),
    MangalAttribute => Dict{Int64,MangalAttribute}(),
)

# Response formatters
include("response_format.jl")

# Basic functions
include(joinpath(".", "basics.jl"))

# Generate code to write most of the API -- including count method
include(joinpath(".", "generators.jl"))
export nodes, node
export backbones, backbone
export datasets, dataset
export networks, network
export references, reference
export interactions, interaction
export attributes, attribute
export users, user

# Datasets
include(joinpath(".", "dataset.jl"))

# Networks
include(joinpath(".", "network.jl"))

# Taxonomy backbone(s)
include(joinpath(".", "backbone.jl"))

# Network nodes
include(joinpath(".", "node.jl"))

# Interactions
include(joinpath(".", "interaction.jl"))

# References
include(joinpath(".", "reference.jl"))

# Counts
include(joinpath(".", "count.jl"))

# Show
include(joinpath(".", "show.jl"))

# EcologicalNetworks wrapper
using EcologicalNetworks: EcologicalNetworks
include(joinpath(".", "ecologicalnetworks.jl"))
export taxonize

end # module


text:
include("je_mmle_struct.jl")
include("je_mmle_optimize.jl")
include("je_mmle_optimize_2pl_1d_super_fast.jl")

function joint_estimate_mmle!(
    items::Vector{<:AbstractItem},
    examinees::Vector{<:AbstractExaminee},
    responses::Vector{<:AbstractResponse};
    dist::Distributions.DiscreteUnivariateDistribution = Distributions.DiscreteNonParametric([0.0,1.0], [0.5, 0.5]),
    metric::Vector{Float64} = [0.0, 1.0],
    max_iter::Int64 = 10,
    max_time::Int64 = 100,
    x_tol_rel::Float64 = 0.0001,
    f_tol_rel::Float64 = 0.000001,
    int_opt_max_time::Float64 = 100.0,
    int_opt_x_tol_rel::Float64 = 0.00001,
    int_opt_f_tol_rel::Float64 = 0.0000001,
    verbosity::Int64 = 2,
    rescale_latent::Bool = true,
    super_fast_2pl_1d = false,
    kwargs...
    )
    I = size(items, 1)
    N = size(examinees, 1)

    #set priors
    set_prior!(examinees, dist);

    #from now we work only on these, the algorithm is dependent on the type of latents and parameters.
    response_matrix = get_response_matrix(responses, size(items,1), size(examinees,1));
    parameters = map( i -> copy(get_parameters(i)), items)
    latents = map( e -> copy(get_latents(e)), examinees)

    #extract items per examinee and examinees per item indices
    n_index = Vector{Vector{Int64}}(undef, I)
    i_index = Array{Array{Int64,1},1}(undef, N)
    for n = 1 : N
        i_index[n] = findall(.!ismissing.(response_matrix[:, n]))
        if n <= I
            n_index[n] = findall(.!ismissing.(response_matrix[n, :]))
        end
    end

    responses_per_item = [Vector{Float64}(response_matrix[i, n_index[i]]) for i = 1 : I]
    responses_per_examinee = [Vector{Float64}(response_matrix[i_index[n], n]) for n = 1 : N]

    je_mmle_model = JointEstimationMMLEModel(
        parameters,
        latents,
        responses_per_item,
        responses_per_examinee,
        n_index,
        i_index,
        copy(dist),
        metric,
        rescale_latent,
        [Float64(max_iter), Float64(max_time), x_tol_rel, f_tol_rel, Float64(verbosity)],
        [int_opt_max_time, int_opt_x_tol_rel, int_opt_f_tol_rel]
    )

    if !super_fast_2pl_1d
        parameters, latents, dist = optimize(je_mmle_model)
    else
        parameters, latents, dist = optimize_2pl_1d_super_fast(je_mmle_model)
    end

    for n in 1 : N
        l = copy(latents[n])
        l.prior = dist
        l.posterior = Distributions.DiscreteNonParametric(dist.support, l.posterior.p)
        l.val = l.posterior.p'*l.posterior.support
        examinees[n] = Examinee(examinees[n].idx, examinees[n].id, l)
        if n<=I
            p = copy(parameters[n])
            items[n] = Item(items[n].idx, items[n].id, p)
        end
    end
    return nothing
end
#too slow!
# function joint_estimate_mmle!(
#     items::Vector{<:AbstractItem},
#     examinees::Vector{<:AbstractExaminee},
#     responses::Vector{<:AbstractResponse};
#     dist::Distributions.DiscreteUnivariateDistribution = Distributions.DiscreteNonParametric([0.0,1.0], [0.5, 0.5]),
#     metric::Vector{Float64} = [0.0, 1.0],
#     max_time::Int64 = 100,
#     max_iter::Int64 = 10,
#     x_tol_rel::Float64 = 0.001,
#     f_tol_rel::Float64 = 0.00001,
#     kwargs...
#     )
#     #start points and probs
#     probs = Distributions.pdf(Distributions.Normal(metric[1], metric[2]), collect(-6.0:0.3:6.0))
#     probs = probs / sum(probs)
#     dist = Distributions.DiscreteNonParametric(collect(-6.0:0.3:6.0), probs)

#     #set priors
#     set_prior!(examinees, dist);

#     #update posteriors
#     update_posterior!(examinees, items, responses; already_sorted = false);

#     #gr()
#     # starting values
#     before_time = time()
#     stop = false
#     old_likelihood = 0.0
#     old_pars = get_parameters_vals(items)
#     start_time = time()
#     response_matrix = get_response_matrix(responses, size(items,1), size(examinees,1));

#     #extract items per examinee and examinees per item indices
#     n_index = Vector{Vector{Int64}}(undef, size(items, 1))
#     i_index = Array{Array{Int64,1},1}(undef, size(examinees, 1))
#     for n = 1: size(examinees,1)
#         i_index[n] = findall(.!ismissing.(response_matrix[:, n]))
#         if n <= size(items, 1)
#             n_index[n] = findall(.!ismissing.(response_matrix[n, :]))
#         end
#     end #15ms
#     iter = 1
#     while !stop
#         #calibrate items
#         #calibrate_item_mmle!(items, examinees, responses);
#         Distributed.@sync Distributed.@distributed for i in 1 : size(items, 1)
#             calibrate_item_mmle!(items[i], examinees, responses);
#         end
#         #calibrate_item_mmle!(items, examinees, response_matrix);
#         #rescale dist
#         rescale!(
#             dist,
#             examinees;
#             metric = [0.0, 1.0]
#         )
#         #println("dist")
#         #display(plot(dist.support, dist.p))
#         #update examinees' support
#         map( e -> e.latent.prior = dist, examinees)

#         #update posteriors
#         #update_posterior!(examinees, items, response_matrix; already_sorted = false);
#         Distributed.@sync Distributed.@distributed for n in 1 : size(examinees, 1)
#             update_posterior!(examinees[n], items, responses);
#         end
#         if any([
#             check_iter(iter; max_iter = max_iter),
#             check_time(start_time; max_time = max_time),
#             check_f_tol_rel!(
#                 examinees,
#                 old_likelihood;
#                 f_tol_rel = f_tol_rel
#                 ),
#             check_x_tol_rel!(
#                 items,
#                 old_pars;
#                 x_tol_rel = x_tol_rel
#             )]
#             )
#             stop = true
#         end
#         iter += 1

#     end
#     map( e -> e.latent.posterior = Distributions.DiscreteNonParametric(dist.support, e.latent.posterior.p), examinees);
#     map( e -> e.latent.val = e.latent.posterior.p' * e.latent.posterior.support, examinees);

#     return nothing
# end


text:
using HTTP
using Gumbo
using AbstractTrees

print("in file okay")
url="https://stackoverflow.com/questions/37360340/how-to-pass-dict-as-the-argument-to-method-julia"

response = HTTP.get(url)
#print("successfully got url")
#print(response)
#print(response.body)
res=String(response.body)
fields = split(res, "<a")
#for field in fields
#	println(field)
#	end
"""
println(fields[1])

println("")
println("")
println(length(fields))
"""

# let's try this as a regex
#regex = r"^<a [a-z][A-Z][0-9]/=*</a"
#testregex=r"<a\s+(?:[^>]*?\s+)?href=([\"'])(.*?)\1"
#m = match(testregex, res)
#print(m)

doc = parsehtml(res)
print(doc)
println("")
print(typeof(doc))

#this is what we need. now we need to get the href inside of the a element!
for elem in PostOrderDFS(doc.root)
	if typeof(elem) == Gumbo.HTMLElement{:a}
		#we now get the href element
		link = get(elem.attributes, "href", 0)
		println(link)
		end
	end

# okay, we're going to use Gumbo to parse the html document and not regexes. let's try that

# let's test the argparse things

using ArgParse

# okay, let's set up some thingsfor our setting

#s = ArgParseSettings()

#now we add ourtable of arguments

#@add_arg_table s begin
#	"--opt1"
#		help = "an option with an argument"
#	"--opt2"
#		help="blqeh"
#		arg_type=Int
#		default = 0

#	"--flag1"
#		help="flag"
#		action=:store_true
#		"arg1"
#			help="a positional argument"
#			required=true

# so for our actual thing we would do something like

#t = ArgParseSettings()

#we can also improve our arg parse settings as follows with proper program descriptions and such which is really cool!

t = ArgParseSettings(	prog="Julia Web Crawler",
						description="A webcrawler written in Julia",
						commands_are_required=false,
						version="0.0.1"
						add_version=true,
						show_help=true)
@add_arg_table t begin
	"urls"
		help="either a url to start at or a set of urls to start visiting"
		required=true
	"--breadth-first", "-b"
		help="a flag of whether the crawler should search  breadth first or depth first"
		action=:store_true
end

# we then do actual arg parsing
parsed_args = parse_args(ARGS, t)

max_stars_repo_name: Bmillidgework/Misc-Maths

max_issues_repo_name: Bmillidgework/Misc-Maths

max_forks_repo_name: Bmillidgework/Misc-Maths


text:
for (name, c) in usual_constraints
    @testset "Constraint: $name" begin
        for i in 1:100000
            al = args_length(c)
            x = rand(1:10, isnothing(al) ? 5 : al)

            pl = params_length(c)
            y_aux = rand(1:10, isnothing(pl) ? 5 : pl)
            y = length(y_aux) == 1 ? first(y_aux) : y_aux

            ds = 10

            c_concept = pl == 0 ? concept(c, x) : concept(c, x; param = y)
            c_error_f = pl == 0 ? error_f(c, x; dom_size = ds) : error_f(c, x; param = y, dom_size = ds)

            @test c_concept ? (c_error_f == 0.0) : (c_error_f > 0.0)
        end
        symmetries(c)
    end
end


text:
function solve_baseline_tvf(ap, mp)

    ################################
    ################################
    # required data inputs
    ################################
    ################################

    ### ACTUAL ECONOMY TIME PATHS
    # μ_baseline: actual migration shares ((J+1)Rx(J+1)RxT)
    # xbilat_baseline: actual bilateral expenditures (JNxNxT)
    # wages_baseline: change in wages (JxNxT)
    # λ_baseline: actual expenditure shares (JNxNxT)
    # labor_baseline: change in labor for mobile regions ((J+1)xRxT)
    # L0: actual initial labor for mobile regions ((J+1)Rx1)

    ### INITIAL VALUES AND PARAMETERS
    # VARjn00: structures value added (JxN)
    # VALjn00: labor value added (JxN)
    # λ00: initial expenditure shares (JNxN)
    # xbilat00: initial bilateral expenditures (JNxN)
    # Sn00: trade imbalances not explained by global portfolio (Nx1)
    # α: final consumption shares (JxN)
    # io: share of each region in global portfolio (Nx1)
    # Ψ: share of structures in structure-labor aggregate (JxN)
    # G: share of materials in gross output (JNxN)
    # γ: share of value added in gross output (JxN)
    # θinv: inverse of trade elasticity (Jx1)

    ################################
    ################################
    # load data
    ################################
    ################################

    actual_economy = matread("data/Baseline_2000_2007_economy_actual_data.mat")
    Base_year = matread("data/Base_year.mat")
    extract(Base_year)

    # actual_economy variables + L0_initial
    μ_baseline = [actual_economy["series_mu"][:,:,t] for t = 1:mp.T-1]
    xbilat_baseline = [actual_economy["series_xbilat"][:,:,t] for t = 1:mp.T]
    wages_baseline = [actual_economy["series_wageshat"][:,:,t] for t = 1:mp.T]
    λ_baseline = [actual_economy["Din_baseline"][:,:,t] for t = 1:mp.T]
    labor_baseline = [actual_economy["series_Ljn0hat"][:,:,t] for t = 1:mp.T]
    L0 = actual_economy["L0_initial"]

    labor0_usa = [labor_baseline[t][2:mp.J+1,:] for t = 1:mp.T]
    labor0 = [ones(mp.J, mp.N) for t = 1:mp.T]
    for t = 1:mp.T
        labor0[t][:,1:mp.R] = labor0_usa[t]
    end

    μ = μ_baseline
    μ00 = μ[1]

    # using the mobility flows to construct the evolution of labor allocations in the baseline economy
    L00 = reshape(L0, mp.J+1, mp.R)
    L00_aux0 = reshape(L00, (mp.J+1)*mp.R, 1)
    L00_aux1 = repeat(L00_aux0, 1, (mp.J+1)*mp.R)
    L00_aux1 = μ00.*L00_aux1
    L1 = sum(L00_aux1, dims = 1)'
    L1 = reshape(L1, mp.J+1, mp.R)

    # compute full labor path
    Ldyn = similar(labor_baseline)
    Ldyn[2] = L1
    Ldyn[1] = reshape(L0, mp.J+1, mp.R)

    for t = 2:(mp.T-1)
        aux = μ[t] .* repeat(reshape(Ldyn[t], (mp.J+1) * mp.R, 1), 1, (mp.J+1) * mp.R)
        aux = sum(aux, dims = 1)'
        Ldyn[t+1] = reshape(aux, (mp.J+1), mp.R)
    end

    Ltemp = [Ldyn[t][2:mp.J+1,:] for t = 1:mp.T]

    # set initial conditions
    VALjn0 = VALjn00 # labor value added
    VARjn0 = VARjn00 # structures value added
    Sn = Sn00 #trade imbalances not explained by global portfolio (they are zero by construction)
    Sn_prime = zeros(size(Sn)) # trade balance [exogenous] 2nd term on RHS of eq (14)
    λ = Din00 # bilateral trade shares
    xbilat = xbilat00 # bilateral trade flows
    real_wages = [ones(mp.J, mp.N) for i = 1:mp.T]
    Zs = [ones(mp.J, mp.N) for i = 1:mp.T] # fundamental productivity
    κ_hat = ones(mp.J * mp.N, mp.N) # relative changes in trade costs [exogenous]

    io = Base_year["io"] # region shares
    α = alphas # sector shares in final demand
    γ = gamma # share of value added in output
    Ψ = B # share of structures in structure-labor aggregate

    G = Base_year["G"]' # share of materials (TRANSPOSE SO WE PULL COLUMNS NOT ROWS)
    G_vec = [G[:,n:n+mp.J-1] for n = 1:mp.J:size(G,2)] # vector form for quicker algebra

    θinv = T # inverse of theta
    θinv_stack = similar(λ[:,1]) # stack θinv JxJ submatrices for easier multiplication later
    for j in 1:mp.J
        index = 1+(j-1)*mp.N:mp.N*j
        θinv_stack[index,:] = ones(mp.N)*θinv[j]
    end
    θinv_stack = repeat(θinv_stack, 1, mp.N)

    # storage vectors
    wages_out = [ones(mp.J, mp.N) for i = 1:mp.T]
    λ_out = [similar(λ) for i = 1:mp.T]
    xbilat_out = [similar(VARjn0) for i = 1:mp.T]

    wages_out[1] = ones(mp.J, mp.N)
    λ_out[1] = Din00
    xbilat_out[1] = xbilat_baseline[1]
    labor_out = [ones(mp.J, mp.N) for i = 1:mp.T]
    ωs = [wages_baseline[t+1].*labor0[t+1].^Ψ for t in 1:mp.T-1]
    ################################
    # PART 2: given labor supply, solve for temporary
    # equilibrium (static production problem)
    ################################

    # initial phat guess
    phat = ones(mp.J, mp.N)

    # Solve static subproblem at time t
    for t = 1:(mp.T-1)

        println("Baseline economy: solving year $(t) of $(mp.T) with time-varying fundamentals.")

        Z_hat = Zs[t] # relative changes in technology/productivity

        labor = ones(mp.J, mp.N) # [exogenous] change in employment in other countries
        labor[:,1:mp.R] = Ltemp[t+1] ./ Ltemp[t]

        # lambdas
        λ_1 = λ_baseline[t+1]
        λ_0 = λ_baseline[t]
        # set initial guess to be baseline economy value
        ω0 = wages_baseline[t+1].*labor0[t+1].^Ψ
        ω = ωs[t]
        ω, wages, Phat, rental_rate, phat, VARjn_prime, VALjn_prime, X_prime, λ_prime, xbilat_prime =
            solve_temp_equilibrium(
            ω, ω0, phat, labor, VARjn0, VALjn0, λ, λ_0, λ_1, Sn_prime,
            κ_hat, Z_hat, α, io, θinv, θinv_stack, Ψ, G, G_vec, γ,
            mp, ap
        )

        ωs[t] = ω
        λ = λ_prime
        VARjn0 = VARjn_prime
        VALjn0 = VALjn_prime

        wages_out[t+1] = wages
        λ_out[t+1] = λ_prime
        xbilat_out[t+1] = xbilat_prime
        labor_out[t+1] = labor

    end

    save("data/base_tvf.jld",
    "wages", wages_out,
    "λs", λ_out,
    "xbilats", xbilat_out,
    "labor", labor_out
    )

end

function solve_baseline_cf(ap, mp)

    ################################
    ################################
    # required data inputs
    ################################
    ################################

    ### TIME VARYING FUNDAMENTAL BASELINE ECONOMY TIME PATHS
    # μ_baseline: time varying fundamental baseline economy migration shares ((J+1)Rx(J+1)RxT)
    # L0_initial: actual initial labor for mobile regions in first year of TVF baseline economy ((J+1)Rx1)

    ### INITIAL VALUES AND PARAMETERS
    # VARjn00: structures value added (JxN)
    # VALjn00: labor value added (JxN)
    # λ00: initial expenditure shares (JNxN)
    # xbilat00: initial bilateral expenditures (JNxN)
    # Sn00: trade imbalances not explained by global portfolio (Nx1)
    # α: final consumption shares (JxN)
    # io: share of each region in global portfolio (Nx1)
    # Ψ: share of structures in structure-labor aggregate (JxN)
    # G: share of materials in gross output (JNxN)
    # γ: share of value added in gross output (JxN)
    # θinv: inverse of trade elasticity (Jx1)
    # μ: initial migration shares for first constant fundamental period (last tvf period) ((J+1)Rx(J+1)R)

    ### INITIAL GUESSES
    # H: initial guesses of udots ((J+1)xRxT)
    # ωs: initial guesses of factor prices (JxNxT)

    ################################
    ################################
    # compute initial conditions
    # based on tvf baseline results
    ################################
    ################################

    mu = matread("data/mu.mat")
    base_year = matread("data/Baseline_2000_2007_economy_actual.mat")
    extract(base_year)

    μs = mu["series_mu_adj"]
    μ0 =μs[:,:,end]
    μ = μs[:,:,1]
    labor = [similar(base_year["L0_initial"]) for n = 1:size(mu["series_mu_adj"],3)+1]
    labor[1] = base_year["L0_initial"]
    labor[2] = μ' * labor[1]

    for t = 2:size(μs,3)
        labor[t+1] = μs[:,:,t]' * labor[t]
    end

    L0 = labor[end]

    ################################
    ################################
    # initialize variables
    ################################
    ################################

    initial_H = matread("data/Baseline_2007.mat")
    H = [reshape(initial_H["Hvectnoshock"][:,t], mp.J + 1, mp.R) for t = 1:mp.T]
    # H = load("data/base_cf_climate2.jld")["H"]

    # # # initial guess for trajectory of changes in utility udot = exp(Vt+1 - V)^1/ν
    # H = [ones((mp.J + 1), mp.R) for i = 1:mp.T]
    # #

    # # initial factor price guesses
    #ωs = load("data/base_cf.jld")["ωs"]
    ωs = [ones(mp.J, mp.N) for i = 1:mp.T]

    real_wages = [ones(mp.J, mp.N) for i = 1:mp.T]
    phats = [ones(mp.J, mp.N) for i = 1:mp.T] # initial factor price guesses
    wages = [ones(mp.J, mp.N) for i = 1:mp.T]
    Phats = [Array{Float64}(undef, mp.N) for i = 1:mp.T]
    xbilats = [ones(mp.J*mp.N, mp.N) for i = 1:mp.T]
    labor = [ones(mp.J, mp.N) for i = 1:mp.T]
    λs = similar(xbilats)
    Zs = [ones(mp.J, mp.N) for i = 1:mp.T] # fundamental productivity
    κ_hat = ones(mp.J * mp.N, mp.N) # relative changes in trade costs [exogenous]

    VALjn0 = VALjn00 # labor value added
    VARjn0 = VARjn00 # structures value added

    Sn = Sn00 # trade balance
    Sn_prime = zeros(size(Sn)) # trade balance [exogenous] 2nd term on RHS of eq (14)

    λ = Din00 # bilateral trade shares
    xbilat = xbilat00 # bilateral trade flows
    xbilats[1] = xbilat00 # bilateral trade flows
    io = base_year["io"] # region shares
    α = alphas # sector shares in final demand
    γ = gamma # share of value added in output

    G = base_year["G"]' # share of materials (TRANSPOSE SO WE PULL COLUMNS NOT ROWS)
    G_vec = [G[:,n:n+mp.J-1] for n = 1:mp.J:size(G,2)] # vector form for quicker algebra

    Ψ = B # share of structures in structure-labor aggregate

    θinv = T # inverse of theta
    θinv_stack = similar(λ[:,1]) # stack θinv JxJ submatrices for easier multiplication later
    for j in 1:mp.J
        index = 1+(j-1)*mp.N:mp.N*j
        θinv_stack[index,:] = ones(mp.N)*θinv[j]
    end
    θinv_stack = repeat(θinv_stack, 1, mp.N)

    iter = 1
    howard_iter = 1

    ################################
    ################################
    # outer loop
    ################################
    ################################

    while (iter <= ap.maxit) & (ap.Hmax > ap.tol_out)

        # reassign initial values
        VALjn0 = VALjn00 # labor value added
        VARjn0 = VARjn00 # structures value added
        λ = Din00 # bilateral trade shares

        println("Computing labor path.")
        ################################
        # PART 1: solve for migration
        # flows μdot and labor supply L
        ################################

        ################################
        # STEP 1: Create auxiliary udot matrix (need to make sure this works identically to matlab)
        # NJxNJ, the udot trajectory in equation (16)

        Haux = reshape.(H, 1, (mp.J + 1) * mp.R)
        Haux = repeat.(Haux, (mp.J + 1) * mp.R, 1)

        ################################
        # STEP 2: Determine the trajectory of migration shares using the initial migration share
        # (at t=-1) and the guess for the udot trajectory in Step 1

        # eq (16) numerator
        num = μ0 .* (Haux[2] .^ mp.beta)

        # eq (16) denominator
        den = sum(num', dims = 1)'
        den = repeat(den, 1, mp.R * (mp.J + 1))

        # time 0 migration share
        μ00 = num ./ den

        # initialize vector of migration shares
        μ = similar(H)
        μ[1] = μ00

        # given udot and mu(t), compute mu(t+1) using eqn(16) on p.755
        for t = 1:(mp.T-2)
            num = μ[t] .* (Haux[t+2] .^ mp.beta)
            den = sum(num', dims = 1)'
            den = repeat(den, 1, mp.R * (mp.J + 1))
            μ[t+1] = num ./ den
        end

        μ[mp.T] = μ[mp.T - 1]

        ################################
        # STEP 3: Use the trajectory of migration shares mu and the initial labor allocation L0
        # to compute the path of labor supply / allocations, given by eqn (18) on p.755

        # compute labor allocation at time t = 1
        L00 = reshape(L0, (mp.J + 1), mp.R)
        L00 = μ[1] .* repeat(reshape(L00, (mp.J + 1) * mp.R, 1), 1, (mp.J + 1) * mp.R)
        L1 = sum(L00, dims = 1)'
        L1 = reshape(L1, (mp.J + 1), mp.R)

        # compute full labor path
        Ldyn = similar(H)
        Ldyn[2] = L1
        Ldyn[1] = reshape(L0, (mp.J + 1), mp.R)

        for t = 2:(mp.T-1)
            aux = μ[t] .* repeat(reshape(Ldyn[t], (mp.J + 1) * mp.R, 1), 1, (mp.J + 1) * mp.R)
            aux = sum(aux, dims = 1)'
            Ldyn[t+1] = reshape(aux, (mp.J + 1), mp.R)
        end

        # labor in the final period is zero
        Ldyn[mp.T] .= 0

        ################################
        # PART 2: given labor supply, solve for temporary
        # equilibrium (static production problem)
        ################################

        if iter < ap.howard_start || howard_iter > ap.howard_its
            println("Solving static subproblems.")
            # Solve the static subproblem: path of temporary equilibria
            ωs, wages, phats, Phats, real_wages, xbilats, λs, labor = solve_static_subproblem(
                VARjn0, VALjn0, Zs, Ldyn, λ, μ, Haux, Sn_prime,
                κ_hat, α, io, θinv, θinv_stack, Ψ, G, G_vec, γ,
                mp, ap, ωs, phats
            )
            howard_iter = 1
        else
            howard_iter += 1
            println("Howard iteration $(howard_iter-1).")
        end

        println("Updating utility change guess.")

        ################################
        # PART 3: update guess of udot
        ################################

        # From real wages, compute Y
        real_wages_aux = [[1; (real_wages[t][:,1:mp.R]).^(1/mp.ν)] for t in 1:mp.T]
        real_wages_aux = repeat.(reshape.(real_wages_aux, mp.R*(mp.J+1), 1), 1, mp.R*(mp.J+1)) # 1st term on rhs of eq (17)

        real_wages_nu = [μ[t] .* real_wages_aux[t+1] for t in 1:mp.T-1] # 2nd term on rhs of eq (17)
        pushfirst!(real_wages_nu, zeros(size(real_wages_nu[1])))

        num = [real_wages_nu[t] .* Haux[t+1].^mp.beta for t in 1:mp.T-1] # RHS of eq (17) before summation
        push!(num, zeros(size(num[1])))

        H_new = [sum(num[t]', dims = 1)' for t = 1:mp.T] # new path of y's

        H_new[mp.T] .= 1.
        H[mp.T] .= 1
        H_old = reshape.(H, (mp.J+1)*mp.R, 1)

        # CDP error criterion
        if howard_iter == 1
            last_error = ap.Hmax
            ap.Hmax = maximum([maximum(abs.(H_new[t] - H_old[t])) for t in 2:mp.T])
            # ap.Hmax = maximum([maximum(abs.(Y[t] - Y_old[t])./Y_old[t]) for t in 2:mp.T])
            println("Outer loop iteration $iter error: $(ap.Hmax), previous iteration error: $(last_error).")
            iter += 1
        end

        H = [0.5 * reshape(H_new[t], (mp.J+1), mp.R) + 0.5 * H[t] for t in 1:mp.T]

        # Tighten up tolerance once close, switch back to solving
        if ap.Hmax < ap.tol_out .* 2.0
            if ap.tol_in < 1e-7
                println("Decreasing tolerance.")
            end
            ap.tol_in = max(ap.tol_in ./ 10, 1e-7)
            howard_iter = ap.howard_its + 1
        end

        save("data/base_cf_TEMP_$(ap.tol_out)_$(ap.tol_in).jld", "H", H, "ωs", ωs)

    end

    save("data/base_cf.jld", "H", H, "real_wages", real_wages, "ωs", ωs, "wages", wages, "Phats", Phats, "phats", phats, "xbilats", xbilats, "μs", μ, "λs", λs, "labor", labor)

end

function combine_baseline(mp_tvf, mp_cf)

    ################################
    ################################
    # required data inputs
    ################################
    ################################

    ### TIME VARYING FUNDAMENTAL BASELINE ECONOMY TIME PATHS
    # xbilats: tvf bilateral expenditures (JNxNxT)
    # wages: tvf baseline wages (JxNxT)
    # λs: tvf baseline expenditure shares (JNxNxT)
    # labor: tvf baseline change in labor for mobile regions (JxRxT)

    tvf_data = load("data/base_tvf.jld")

    ### CONSTANT FUNDAMENTAL BASELINE ECONOMY TIME PATHS
    # μs: cf baseline economy migration shares ((J+1)Rx(J+1)RxT)
    # xbilats: cf baseline bilateral expenditures (JNxNxT)
    # wages: cf baseline wages (JxNxT)
    # λs: cf baseline expenditure shares (JNxNxT)
    # labor: cf baseline change in labor for mobile regions (JxRxT)

    cf_data = load("data/base_cf.jld")

    ### DATA
    # μ: actual economy migration shares ((J+1)Rx(J+1)RxT)
    # labor0:

    μ_actual = matread("data/mu.mat")["series_mu_adj"]
    μ_actual = [μ_actual[:,:,t] for t = 1:mp_tvf.T-1]
    L0 = matread("data/Baseline_2000_2007_economy_actual_data.mat")["L0_initial"]

    ################################
    ################################
    # compute required baseline
    # economy paths
    ################################
    ################################

    # baseline migration shares
    μ_baseline = [similar(μ_actual[1]) for t = 1:(mp_cf.T + mp_tvf.T)]
    for t in 1:(mp_cf.T + mp_tvf.T)-1

        if t < mp_tvf.T
            μ_baseline[t] = μ_actual[t]
        else
            μ_baseline[t] = cf_data["μs"][t - mp_tvf.T + 1]
        end

    end

    # baseline bilateral expenditures
    xbilat_baseline = [tvf_data["xbilats"]; cf_data["xbilats"][2:end]]

    # baseline change in expenditure shares
    λ_baseline = [tvf_data["λs"]; cf_data["λs"][2:end]]

    # baseline change in labor allocation
    labor_baseline = [tvf_data["labor"]; cf_data["labor"][2:end]]

    # baseline change in wages
    wages_baseline = [tvf_data["wages"]; cf_data["wages"][2:end]]

    save("data/baseline_economy.jld",
    "μ_baseline", μ_baseline,
    "xbilat_baseline", xbilat_baseline,
    "λ_baseline", λ_baseline,
    "labor_baseline", labor_baseline,
    "wages_baseline", wages_baseline,
    "L0", L0
    )

end

max_stars_repo_name: rafserqui/class-repo

max_issues_repo_name: rafserqui/class-repo

max_forks_repo_name: rafserqui/class-repo


text:
using CSV, DataFrames
using ScikitLearn
using Random, Statistics
using JLD2

# Import the necessary modules and libraries from ScikitLearn
@sk_import ensemble:RandomForestClassifier

# Import our training function which trains a random forest
include("rf.jl")

# Load the data for training and validation
train = CSV.read("data/listings_clean_train.csv", header=false)
val = CSV.read("data/listings_clean_val.csv", header=false)

# Load the parameters dataframe
@load "params.jld2" params

# Get the experiment ID from the arguments that were passed to julia

# Set a random seed - always a good idea when using functions you didn't write
Random.seed!(1776)

# Actually run the experiment


text:
# Direct unimodal bearing range only calculation

# ground truth
wX1 = [1;0;0] # [x,y,th]
wL1 = [-1;3]
wL2 = [3;3]
wL3 = [3;0]

# cartesian measurements
DX1 = wL1-wX1[1:2]
DX2 = wL2-wX1[1:2]
DX3 = wL3-wX1[1:2]

# find location
# wTb = [R(th) tr; 0 0 1]
# Use linear relationship: bDX = bTw*wL
bDX = ones(3,3)
bDX[1:2,1] = DX1
bDX[1:2,2] = DX2
bDX[1:2,3] = DX3

wL = ones(3,3)
wL[1:2,1] = wL1
wL[1:2,2] = wL2
wL[1:2,3] = wL3

bTw = (wL'\bDX')' # use transpose for pivoted Cholesky inverse
wTb = inv(bTw)

# answers
wThetab = atan(wTb[1,2], wTb[1,1])
wTransb = wTb[1:2,3]

# Brute force least squares: (A'A)\(A')*y
# https://en.wikipedia.org/wiki/Linear_least_squares_(mathematics)

wL4 = [0;-3]
DX4 = wL4-wX1[1:2]

bDX = ones(3,4)
bDX[1:2,1] = DX1
bDX[1:2,2] = DX2
bDX[1:2,3] = DX3
bDX[1:2,4] = DX4

wL = ones(3,4)
wL[1:2,1] = wL1
wL[1:2,2] = wL2
wL[1:2,3] = wL3
wL[1:2,4] = wL4

# bDX*bDX' = bDX*wL'*bTw'
bTw = ((bDX*wL')\(bDX*bDX'))'


text:
module TunnelIonization

function newton(f, x)
    return x
end
# Write your package code here.

end


text:
function simMats(newfmat, fmat)
    tol = 1e-8
    evA = eig(full(newfmat))
    evB = eig(full(fmat))
    aNz = find(abs(evA) > tol)
    bNz = find(abs(evB) > tol)
    diffLen = length(aNz) - length(bNz)

    if diffLen < 0
        res = norm(sort(real(evB(bNz))) - (sort(real([evA(aNz);zeros(-diffLen,1)]))))
    elseif diffLen == 0
        res = norm(sort(real(evB(bNz))) - (sort(real(evA(aNz)))));
    elseif diffLen > 0
        res = norm(sort(real([evB(bNz);zeros(diffLen,1)]))-sort(real(evA(aNz))))
    end

    return res
end


text:
if VERSION < v"0.7"
    Cvoid = Void
end

function jamsd_set_modeltype(m::JAMSDMathProgModel)
    discrete = any((m.vartypes .== :Int) + (m.vartypes .== :Bin) .> 0)
    if discrete
        if m.model_type == qcp
            m.model_type = miqcp
        elseif m.model_type == nlp
             m.model_type = minlp
        end
    end
    jamsd_set_modeltype(m.jamsd_ctx, m.model_type)
    res = ccall((:ctx_setobjsense, libjamsd), Cint, (Ptr{context}, Cint), m.jamsd_ctx, sense_to_jamsd[m.sense])
    res != 0 && error("return code $res from JAMSD")
end

function jamsd_set_modeltype(ctx::Ptr{context}, model_type)
    res = ccall((:ctx_setmodeltype, libjamsd), Cint, (Ptr{context}, Cint), ctx, model_type)
    res != 0 && error("return code $res from JAMSD")
end

# TODO(xhub) reimplement writemodel using CONVERTD
function jamsd_solve(ctx::Ptr{context}, ctx_dest::Ptr{context}, solver_name::String, emp::Ptr{empinfo}=Ptr{empinfo}(C_NULL))

    CONFIG[:solver_log] && hack_solver_log()

    if emp != C_NULL
        res = ccall((:empinfo_transform, libjamsd), Cint, (Ptr{empinfo}, Ptr{context}), emp, ctx_dest)
        res != 0 && error("return code $res from JAMSD")

        if CONFIG[:export_gms]
#            ccall((:ctx_writemodel, libjamsd), Cint, (Ptr{context}, Cstring), ctx_dest, "validation.gms")
            ccall((:ctx_setsolverstr, libjamsd), Cint, (Ptr{context}, Cstring), ctx_dest, "CONVERTD")
            ccall((:ctx_callsolver, libjamsd), Cint, (Ptr{context},), ctx_dest)
        end

        ccall((:ctx_setsolverstr, libjamsd), Cint, (Ptr{JAMSDWriter.context}, Cstring), ctx_dest, solver_name)

        res = ccall((:empinfo_solve, libjamsd), Cint, (Ptr{empinfo},), emp)
        return res
    else
        res = ccall((:model_compress, libjamsd), Cint, (Ptr{context}, Ptr{context}, Ptr{empinfo}, Ptr{Cvoid}), ctx, ctx_dest, emp, C_NULL)
        res != 0 && error("return code $res from JAMSD")
        res = ccall((:ctx_exportmodel, libjamsd), Cint, (Ptr{context}, Ptr{context}), ctx, ctx_dest)
        res != 0 && error("return code $res from JAMSD")

        if CONFIG[:export_gms]
#            ccall((:ctx_writemodel, libjamsd), Cint, (Ptr{context}, Cstring), ctx_dest, "validation.gms")
            ccall((:ctx_setsolverstr, libjamsd), Cint, (Ptr{context}, Cstring), ctx_dest, "CONVERTD")
            ccall((:ctx_callsolver, libjamsd), Cint, (Ptr{context},), ctx_dest)
        end

        # switch back to the default solver
        ccall((:ctx_setsolverstr, libjamsd), Cint, (Ptr{JAMSDWriter.context}, Cstring), ctx_dest, solver_name)

        return ccall((:ctx_callsolver, libjamsd), Cint, (Ptr{context},), ctx_dest)
    end
end

function jamsd_setup_gams()
    ctx = ccall((:ctx_alloc, libjamsd), Ptr{context}, (Cuint,), 0)

    gamscntr_template_file = joinpath(solverdata_dir, "gamscntr.dat")

    if !isfile(gamscntr_template_file)
        jamsd_init_gams_solverdata()
    end
    if !isfile(gamscntr_template_file)
        error("Could not create template GAMS control file! Make sure that GAMS is properly installed and available via the system path")
    end

    gamscntr_template = read(gamscntr_template_file, String)

    gams_dir = mktempdir(pwd())
    cur_dir = gams_dir

    open(joinpath(gams_dir, "gamscntr.dat"), "w") do gamscntr_file
        println(gamscntr_file, replace(gamscntr_template, r"@@SUB@@" => cur_dir))
    end

    # we need an empty Matrixfile
    touch(joinpath(cur_dir, "gamsmatr.dat"))

    res = ccall((:gams_set_gamscntr, libjamsd), Cint, (Ptr{context}, Cstring), ctx, joinpath(cur_dir, "gamscntr.dat"))
    res != 0 && error("return code $res from JAMSD")

    # hm bad hack
    gamsdir = split(gamscntr_template, term_str)[29]

    CONFIG[:debug] && println("DEBUG: gamsdir is ``$gamsdir''")

    res = ccall((:gams_set_gamsdir, libjamsd), Cint, (Ptr{context}, Cstring), ctx, gamsdir)
    res != 0 && error("return code $res from JAMSD")

    ENV["PATH"] *= ":" * gamsdir

    # This is needed to prevent the listing of the Process directory
    ENV["DEBUG_PGAMS"] = '0'

    return (ctx, gams_dir)
end

function jamsd_init_gams_solverdata()
    if !isdir(solverdata_dir)
        error("No directory named $solverdata_dir. ")
    end

    gamscntr = joinpath(solverdata_dir, "gamscntr.dat")
    if isfile(gamscntr)
        return
    end

    gms_file = joinpath(solverdata_dir, "dummy.gms")

    mktempdir(solverdata_dir) do substr
        # use run(`gams $gms_file scrdir=$substr lo=0 curdir=$substr`) ?
        run(`gams $gms_file scrdir=$substr lo=0`)

        open(gamscntr, "w") do out_gamscntr
            input = read(joinpath(substr, "gamscntr.dat"), String)
            input = replace(input, pwd() => "@@SUB@@")
            println(out_gamscntr, replace(input, substr => "@@SUB@@"))
        end
    end
end


text:
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
#
# Description
# ==============================================================================
#
#   Compute the satellite lighting condition considering the Earth eclipse.
#
# References
# ==============================================================================
#
# [1] Longo, C. R. O., Rickman, S. L (1995). Method for the Calculation of
#     Spacecraft Umbra and Penumbra Shadow Terminator Points. NASA Technical
#     Paper 3547.
#
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #

export lighting_condition

"""
    lighting_condition(r_i::AbstractVector, s_i::AbstractVector)

Compute the lighting condition at the position `r_i` [m] considering the Sun
position vector `s_i` [m]. The possible return values are:

- `:sunlight`: The point is under direct sunlight.
- `:penumbra`: The point is in penumbra region.
- `:umbra`: The point is in umbra region.

!!! note
    The vectors `r_i` and `s_i` must be represented in the same reference frame.
"""
function lighting_condition(r_i::AbstractVector, s_i::AbstractVector)
    # Distance from the Earth to the Sun.
    norm_s_i = norm(s_i)

    # Projection of the satellite position vector on the Sun direction [1].
    rs_i = (r_i ⋅ s_i) * s_i / (norm_s_i * norm_s_i)

    # Check if the satellite is under sunlight, umbra or penumbra.

    if (rs_i ⋅ s_i / norm_s_i) < 0
        # Distance of the umbral cone and the spacecraft [1].
        Δ_i = r_i - rs_i
        norm_Δ_i = norm(Δ_i)

        # Penumbra section [1].
        xp = R0 * norm_s_i / (Rs + R0)
        αp = asin(R0 / xp)

        # Location of the penumbral cone terminator at the projected spacecraft
        # location [1].
        kp_i = (xp + norm(rs_i)) * tan(αp)

        if norm_Δ_i > kp_i
            return :sunlight
        else
            # Umbra section [1].
            xu = R0 * norm_s_i / (Rs - R0)
            αu = asin(R0 / xu)

            # Location of the umbral cone terminator at the projected spacecraft
            # location [1].
            ep_i = (xu - norm(rs_i)) * tan(αu)

            if norm_Δ_i < ep_i
                return :umbra
            else
                return :penumbra
            end
        end
    else
        return :sunlight
    end
end


text:
# Autogenerated wrapper script for FGlT_jll for x86_64-w64-mingw32
export libfglt

using CompilerSupportLibraries_jll
using cilkrts_jll
JLLWrappers.@generate_wrapper_header("FGlT")
JLLWrappers.@declare_library_product(libfglt, "libfglt-0.dll")
function __init__()
    JLLWrappers.@generate_init_header(CompilerSupportLibraries_jll, cilkrts_jll)
    JLLWrappers.@init_library_product(
        libfglt,
        "bin\\libfglt-0.dll",
        RTLD_LAZY | RTLD_DEEPBIND,
    )

    JLLWrappers.@generate_init_footer()
end  # __init__()


text:
# ============================================================
# Structs of Particle
# ============================================================

"""
    Particle(M, X, V, E, IDX, FLAG = zeros(eltype(IDX), axes(IDX, 1)), T = zero(M))

Struct of arrays for particle simulation

@vars: m, x, v, e, idx, flag, tc

"""
mutable struct Particle{T1,T2,T3,T4,T5} <: AbstractParticle

    m::T1
    x::T2
    v::T3
    e::T1
    idx::T4
    ref::T4
    flag::T5
    tc::T1

    function Particle(
        M,
        X,
        V,
        E,
        IDX,
        REF = zeros(eltype(IDX), axes(IDX, 1)),
        FLAG = zeros(eltype(IDX), axes(IDX, 1)),
        T = zero(M),
    )
        m = deepcopy(M)
        x = deepcopy(X)
        v = deepcopy(V)
        e = deepcopy(E)
        idx = deepcopy(IDX)
        ref = deepcopy(REF)
        flag = deepcopy(FLAG)
        tc = deepcopy(T)

        new{typeof(m),typeof(x),typeof(v),typeof(idx),typeof(flag)}(
            m,
            x,
            v,
            e,
            idx,
            ref,
            flag,
            tc,
        )
    end

end

"""
    Particle1D(M::AbstractFloat, X::Real, V::AbstractArray, IDX::Integer, T::Real)

1D particle

@vars: m, x, v, e, idx, tc

"""
mutable struct Particle1D{T1,T2,T3} <: AbstractParticle1D

    m::T1
    x::T1
    v::T2
    e::T1
    idx::T3
    flag::T3
    tc::T1

    function Particle1D(M, X, V, E, IDX::Integer, FLAG = zero(IDX), T = zero(M))
        m = deepcopy(M)
        x = deepcopy(X)
        v = deepcopy(V)
        e = deepcopy(E)
        idx = deepcopy(IDX)
        flag = deepcopy(FLAG)
        tc = deepcopy(T)

        new{typeof(m),typeof(v),typeof(idx)}(m, x, v, e, idx, flag, tc)
    end

end

"""
    Particle2D(M::AbstractFloat, X::Real, V::AbstractArray, IDX::Integer, T::Real)

2D particle

@vars: m, x, v, idx, tb

"""
mutable struct Particle2D{T1,T2,T3} <: AbstractParticle2D

    m::T1
    x::T1
    y::T1
    v::T2
    e::T1
    idx::T3
    idy::T3
    flag::T3
    tc::T1

    function Particle2D(
        M::AbstractFloat,
        X::Real,
        Y::Real,
        V::AbstractArray,
        E,
        IDX::Integer,
        IDY::Integer,
        FLAG = zero(IDX),
        T = zero(M)::Real,
    )
        m = deepcopy(M)
        x = deepcopy(X)
        y = deepcopy(Y)
        v = deepcopy(V)
        e = deepcopy(E)
        idx = deepcopy(IDX)
        idy = deepcopy(IDY)
        flag = deepcopy(FLAG)
        tc = deepcopy(T)

        new{typeof(m),typeof(v),typeof(idx)}(m, x, y, v, e, idx, idy, flag, tc)
    end

end

"""
    ControlVolume1D(X::Real, DX::Real, W::AbstractArray, PRIM::AbstractArray)

1D control volume in correspondence with particle simulation

@vars: x, dx, w, prim, sw, wg, τ, np, vrmax, remainder

"""
mutable struct ControlVolumeParticle1D{F,A,I<:Integer} <: AbstractControlVolume1D

    x::F
    dx::F

    w::A
    prim::A
    sw::A

    wf::A
    wp::A
    τ::F

    np::I
    ip::I
    vrmax::F
    remainder::F

    function ControlVolumeParticle1D(
        X::Real,
        DX::Real,
        W::AbstractArray,
        PRIM::AbstractArray,
        TAU = 0.0::Real,
        NP = 0::Integer,
        IP = 0::Integer,
        VR = 3.0 * sqrt(PRIM[end])::Real,
        RE = 0::Integer,
    )
        x = deepcopy(X)
        dx = deepcopy(DX)

        w = deepcopy(W)
        prim = deepcopy(PRIM)
        sw = zeros(eltype(w), axes(w))

        wf = deepcopy(W)
        wp = zero(W)
        τ = deepcopy(TAU)

        np = deepcopy(NP)
        ip = deepcopy(IP)
        vrmax = deepcopy(VR)
        remainder = deepcopy(RE)

        new{typeof(x),typeof(w),typeof(np)}(
            x,
            dx,
            w,
            prim,
            sw,
            wf,
            wp,
            τ,
            np,
            ip,
            vrmax,
            remainder,
        )
    end

end

"""
    ControlVolume2D(X::Real, DX::Real, Y::Real, DY::Real, W::AbstractArray, PRIM::AbstractArray)

2D control volume in correspondence with particle simulation

@vars: x, y, dx, dy, w, prim, sw, wg, τ, np, vrmax, remainder

"""
mutable struct ControlVolumeParticle2D{F,A,B,I} <: AbstractControlVolume2D

    x::F
    y::F
    dx::F
    dy::F

    w::A
    prim::A
    sw::B

    wf::A
    wp::A
    τ::F

    np::I
    ip::I
    vrmax::F
    remainder::F

    function ControlVolumeParticle2D(
        X::Real,
        DX::Real,
        Y::Real,
        DY::Real,
        W::AbstractArray,
        PRIM::AbstractArray,
        TAU = 0.0::Real,
        NP = 0::Integer,
        IP = 0::Integer,
        VR = 3.0 * sqrt(PRIM[end])::Real,
        RE = 0::Integer,
    )

        x = deepcopy(X)
        dx = deepcopy(DX)
        y = deepcopy(Y)
        dy = deepcopy(DY)

        w = deepcopy(W)
        prim = deepcopy(PRIM)
        sw = zeros(eltype(W), (axes(W)..., Base.OneTo(2)))

        wf = deepcopy(W)
        wp = zero(W)
        τ = deepcopy(TAU)

        np = deepcopy(NP)
        ip = deepcopy(IP)
        vrmax = deepcopy(VR)
        remainder = deepcopy(RE)

        new{typeof(x),typeof(w),typeof(sw),typeof(np)}(
            x,
            dx,
            y,
            dy,
            w,
            prim,
            sw,
            wf,
            wp,
            τ,
            np,
            ip,
            vrmax,
            remainder,
        )

    end

end