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

using Markdown
using InteractiveUtils

# ╔═╡ 92256604-8f75-11eb-0e65-4df8abfdc276
using PlutoUI; TableOfContents(title = "Visual Perspective")

# ╔═╡ 3f57a160-9042-11eb-2981-a58c990f6dfe
begin
	using CSV, DataFrames
	using FreqTables
	using Plots; theme(:wong)
	using StatsPlots
	using Pipe
	using Statistics
	# using MixedModels
	using DisplayAs
	using Arrow
	using StatsBase # zscore
end

# ╔═╡ e385fbc8-8f75-11eb-08bf-232a909b8db2
md"""
# 0. Load Packages and Variables
"""

# ╔═╡ 2e42988c-903d-11eb-1f06-9f74eaa45252
md"""
**Levels of `Agent` variable**

- Ex1: LN - Left Normal; RN - Right Normal
- Ex2: LN/M - Left Normal/Mirror; RN/M - Right Normal/Mirror
- Ex3: LA/H - Left Arrow / Human; RA/H - Right Arrow / Human
"""

# ╔═╡ e1eb18d4-8de3-11eb-1d26-4b637d2ab921
md"""
# 1. Experiment One
"""

# ╔═╡ 8d3eca82-4a30-4880-a85e-9e062c228830
cd(@__DIR__)

# ╔═╡ 08226178-a9ff-4e6a-b77e-ffccec373e40
begin # cell begin
# 1. List csv files
csv_list = filter(x -> endswith(x, ".csv"),
	readdir("data/Experiment_1", join = true))

# 2. Convert file list to dataframe list, remove `Column44` if exists
df_list = [CSV.read(csv, DataFrame, drop = ["Column44"], stringtype = String)
	for csv in csv_list]

# 3. Concantate df list to a single df
df = reduce(vcat, df_list)

# 4. Columns rename
rename!(df,
	:Letter                    => "letter",
	:type                      => "letter_type",
	:Orientation               => "letter_rotation",
	:human                     => "agent_position",
	:face_type                 => "agent_type",
	Symbol("key_JUDGE.keys")   => "key",
	Symbol("key_JUDGE.rt")     => "rt")

# 5. Remove rows with column `rt` contain missing data
dropmissing!(df, [:letter, :letter_type, :letter_rotation,
	:agent_position, :agent_type, :key, :rt, :image])

# 6. Convert key pressed to True and False: N(normal)-up; Mirror(M)-down
check_key(letter_type, key) = letter_type == "N" ? key == "up" : key == "down"
transform!(df, [:letter_type, :key] => ByRow((x, y) -> check_key(x, y)) => :tf)

# 7. Create the column `agent`
transform!(df, [:agent_position, :agent_type] => ByRow(*) => :agent)

# 8. Create a newcolumn, rt_new: rt_new = rt - stimulus_duration
transform!(df, [:rt, :stimulus_duration] => ByRow(-) => :rt_new)

# 9. Change participant name: "1" -> "S01"
transform!(df, :participant =>
	ByRow(x -> string("S", lpad(x, 2, "0"))) => :participant)

# 10. Select columns
select!(df, [:participant, :letter, :letter_type, :letter_rotation,
	:agent_position, :agent_type, :agent, :rt, :rt_new, :tf])

end; # cell end

# ╔═╡ 239ecc47-2225-40bf-8314-41ca71e8ec7c
describe(df)

# ╔═╡ eb8e85e3-825a-4212-885c-5f8debbb542b
# ex1_original = Arrow.Table("data/Experiment_1.arrow") |> DataFrame;

# ╔═╡ f6f39e41-4de5-4fbb-9a70-fd68edd04ac5
describe(ex1_original)

# ╔═╡ 0ca08b87-9108-4dd3-a2dd-78056b917e60
filter(:rt => x -> x <= 0, ex1_original)

# ╔═╡ 10abea61-40d9-4d0c-bc5b-8c83f326111f
length(unique(ex1_original.participant))

# ╔═╡ e876a08c-8ef7-11eb-3650-31ae7ed843b7
freqtable(ex1_original, :agent, :letter_rotation)

# ╔═╡ f4a99bfb-14b5-4f82-b8e7-c60a5f8141e0
# StatsPlots.density(ex1.rt, group = ex1.agent)

# ╔═╡ d001b7e8-6e58-48c3-a031-30866dce7e5f
md"""
- Models used in the analyses
"""

# ╔═╡ 18a3cfea-d57e-40c7-b1c2-eb5f3f1681ca
fmFull = @formula(rt ~ 1 + agent * letter_rotation + (1 + agent * letter_rotation | participant) + (1 + agent * letter_rotation | letter) );

# ╔═╡ cc0958be-f517-457a-bb7d-41cbaec2b132
fmBest = @formula(rt ~ 1 + letter_rotation + (1 + letter_rotation | participant) + (1 | letter) );

# ╔═╡ 6299cd52-8ecc-11eb-1558-27598f1704f1
fm1 = @formula(rt ~ 1 + agent + (1 + agent | participant) + (1 + agent | letter) );

# ╔═╡ e4516da4-8ecd-11eb-274c-2d51c0dd2ad3
contr1 = Dict(:agent => DummyCoding(base = "__"));

# ╔═╡ afd5a40b-0228-460e-8777-b6c01844cdc1
md"""
- 0 - 180 degree
"""

# ╔═╡ c874a10e-9b82-4267-a8f5-7f319a699ace
# MixedModels.likelihoodratiotest(Ex1LFull, Ex1LBset)

# ╔═╡ b003fbe2-699d-41ea-b12d-f09a8917d03e
md"""
- 180 - 360 degree
"""

# ╔═╡ 78741f03-4327-4513-b1b1-c4749804af95
# Ex1RFull = fit(MixedModel, fm1Full, ex1[ex1.letter_rotation .>= 180, :], contrasts = contr1);

# ╔═╡ 0c0e7464-d810-498c-a25a-392d120e0a3f
# MixedModels.likelihoodratiotest(Ex1RFull, Ex1RBest)

# ╔═╡ 413471ea-6335-4d54-afe4-e9b1163e73ec
md"""
- Each Degree
"""

# ╔═╡ 075e834f-7924-4ed8-bb2f-2f5d77ad4829
# fit(MixedModel, fm1, ex1[ex1.letter_rotation .== 0, :], contrasts = contr1)

# ╔═╡ c2ea33eb-0dd6-4f91-a136-8096b2fc26ff
# fit(MixedModel, fm1, ex1[ex1.letter_rotation .== 45, :], contrasts = contr1)

# ╔═╡ 5c6ef065-7bd2-4187-b841-5f4308c59160
# fit(MixedModel, fm1, ex1[ex1.letter_rotation .== 90, :], contrasts = contr1)

# ╔═╡ fcf5583c-4f45-4063-a155-963666b6c793
# fit(MixedModel, fm1, ex1[ex1.letter_rotation .== 135, :], contrasts = contr1)

# ╔═╡ 65fa3bbf-6661-424a-a1a4-f7aebedc5024
# fit(MixedModel, fm1, ex1[ex1.letter_rotation .== 180, :], contrasts = contr1)

# ╔═╡ 79c1fa5c-8ed3-11eb-02ec-ab660761b467
md"""
# 2. Experiment Two
"""

# ╔═╡ 3858c858-907b-11eb-2189-a900a8380ecb
ex2_original = Arrow.Table("data/Experiment_2.arrow") |> DataFrame;

# ╔═╡ bb6de250-0638-4263-9dfd-d05312cbd7ef
length(unique(ex2_original.participant))

# ╔═╡ 83cb4264-8ef7-11eb-33be-69bced1d6db1
freqtable(ex2_original, :agent, :letter_rotation)

# ╔═╡ e938ec7e-6d2b-46ac-ab46-f55e17af18bf
# StatsPlots.density(ex2.rt, group = ex2.agent)

# ╔═╡ 9d8152fd-017a-41b0-b7a5-b7bda9fd995f
md"""
- Left, 1 - 180 degree
"""

# ╔═╡ 5fe9f5e7-c0e4-4d0c-91f2-f5b9bd3eb322
# Ex2LLFull = fit(MixedModel, fmFull, ex2L[ex2L.letter_rotation .<= 180, :], contrasts = contr1);

# ╔═╡ 4f225a11-8283-4028-ae6b-2cbedf2c086d
# MixedModels.likelihoodratiotest(Ex2LLFull, Ex2LLBest)

# ╔═╡ 898bdad2-f058-4555-a78f-e2eb24d5e84c
md"""
- Left, 180 - 360 degree
"""

# ╔═╡ 2e36ca45-176e-4049-bb07-3f7ee5cabf94
# Ex2LRFull = fit(MixedModel, fmFull, ex2L[ex2L.letter_rotation .>= 180, :], contrasts = contr1);

# ╔═╡ dac9a1bd-1150-4c8a-8864-20a6aa585fab
# MixedModels.likelihoodratiotest(Ex2LRFull, Ex2LRBest)

# ╔═╡ dd3b7f4f-ecba-4c48-b9f3-569b3dddd2fa
md"""
- Right, 0 - 180 degree
"""

# ╔═╡ f975a0fb-559f-4d00-8203-26cbd61989ab
# Ex2RLFull = fit(MixedModel, fmFull, ex2R[ex2R.letter_rotation .<= 180, :], contrasts = contr1);

# ╔═╡ aad4d8a1-0cc6-4dff-908f-0f8236c8bb92
# MixedModels.likelihoodratiotest(Ex2RLFull, Ex2RLBest)

# ╔═╡ 4265e70e-39ca-47ae-a27a-c1fbf12be8f4
md"""
- Right, 180 - 360 degree
"""

# ╔═╡ 6cf4f05b-09d1-4859-89e6-a18576a1dff6
# Ex2RRFull = fit(MixedModel, fmFull, ex2R[ex2R.letter_rotation .>= 180, :], contrasts = contr1);

# ╔═╡ b3a433a8-69b3-46d8-b866-f271abb2df8a
# MixedModels.likelihoodratiotest(Ex2RRFull, Ex2RRBest)

# ╔═╡ f2dfe2f1-169e-4ee8-83d2-e6e5693ab9fb
md"""
- Each Degree
"""

# ╔═╡ e61c3cee-72b4-40b6-afe3-366182bdcb94
# fit(MixedModel, fm1, ex2[ex2.letter_rotation .== 0, :], contrasts = contr1)

# ╔═╡ 2a97c1e8-8f56-11eb-3c7d-bdee7918a422
# fit(MixedModel, fm1, ex2[ex2.letter_rotation .== 45, :], contrasts = contr1)

# ╔═╡ 990c8a26-e218-44ff-b129-13b79c9a1905
# fit(MixedModel, fm1, ex2[ex2.letter_rotation .== 90, :], contrasts = contr1)

# ╔═╡ e589e872-7de9-4a55-919c-a97a7bbebbda
# fit(MixedModel, fm1, ex2[ex2.letter_rotation .== 135, :], contrasts = contr1)

# ╔═╡ 0153aec7-cb05-4e1a-8c07-7435e373a539
# fit(MixedModel, fm1, ex2[ex2.letter_rotation .== 180, :], contrasts = contr1)

# ╔═╡ 9c28e875-6b99-4419-90c6-0e83a06464be
# fit(MixedModel, fm1, ex2[ex2.letter_rotation .== 225, :], contrasts = contr1)

# ╔═╡ be05135c-8eec-11eb-3e6a-c3bd9c8a1950
md"""
# 3. Experiment Three
"""

# ╔═╡ 53c5a418-8f94-11eb-21ed-6905d9a227ae
ex3_original = Arrow.Table("data/Experiment_3.arrow") |> DataFrame;

# ╔═╡ 937e4a69-2489-40bd-bc39-3b846e03bda9
length(unique(ex3_original.participant))

# ╔═╡ 9b1b7fcc-8f58-11eb-1b2a-e1104e001cb7
freqtable(ex3_original, :agent, :letter_rotation)

# ╔═╡ 54c4d22e-4f31-4ede-92fe-c16f90abb846
# StatsPlots.density(ex3.rt, group = ex3.agent)

# ╔═╡ 5755a99d-54fa-4f1e-8191-2de60bfec84f
md"""
- Left, 0 - 180 degree
"""

# ╔═╡ 3219b380-885f-4cf4-880e-3d6ddf7e2b6f
# Ex3LLFull = fit(MixedModel, fmFull, ex3L[ex3L.letter_rotation .<= 180, :], contrasts = contr1);

# ╔═╡ ed45791b-6294-446c-ab59-9502178a90f5
# MixedModels.likelihoodratiotest(Ex3LLFull, Ex3LLBest)

# ╔═╡ f54ec6aa-6190-44dc-b0c1-0f8dc07fc823
md"""
- Left, 180 - 360 degree
"""

# ╔═╡ bc5c021b-2088-4858-8bc5-5b377397b0b6
# Ex3LRFull = fit(MixedModel, fmFull, ex3L[ex3L.letter_rotation .>= 180, :], contrasts = contr1);

# ╔═╡ e3eb942e-75d8-49ef-ad91-56fc6b84f008
# MixedModels.likelihoodratiotest(Ex3LRFull, Ex3LRBest)

# ╔═╡ 4e6ca633-7a01-4634-9075-c4085b27076f
md"""
- Right, 0 - 180 degree
"""

# ╔═╡ 343f34ac-9ab1-4558-b816-ccf9fe33bec3
# Ex3RLFull = fit(MixedModel, fmFull, ex3R[ex3R.letter_rotation .<= 180, :], contrasts = contr1);

# ╔═╡ 65a29136-a9f6-429a-8804-d276fd03acd6
# MixedModels.likelihoodratiotest(Ex3RLFull, Ex3RLBest)

# ╔═╡ 0db091f2-deb3-43fa-9c73-de45cb211250
md"""
- Right, 180 - 360 degree

"""

# ╔═╡ 568aadbe-e707-4c43-8376-f13dfc8cede1
# Ex3RRFull = fit(MixedModel, fmFull, ex3R[ex3R.letter_rotation .>= 180, :], contrasts = contr1);

# ╔═╡ 2fabd0b0-ebb7-470a-b228-1dd4c190e383
# MixedModels.likelihoodratiotest(Ex3RRFull, Ex3RRBest)

# ╔═╡ 2e5a6e6b-48c3-411a-9893-5f90e19608b9
md"""
- Each degree
"""

# ╔═╡ 5cb8db92-c9e7-4ce3-ac19-520a21b19c19
# fit(MixedModel, fm1, ex3[ex3.letter_rotation .== 0, :], contrasts = contr1)

# ╔═╡ c82e5780-df3e-44ee-88e0-068c5cba956a
# fit(MixedModel, fm1, ex3[ex3.letter_rotation .== 45, :], contrasts = contr1)

# ╔═╡ db8da0e5-d8d5-40af-b6f2-ee26bba56580
# fit(MixedModel, fm1, ex3[ex3.letter_rotation .== 90, :], contrasts = contr1)

# ╔═╡ 097f7e08-db6a-4649-945a-2a694e2d56da
# fit(MixedModel, fm1, ex3[ex3.letter_rotation .== 135, :], contrasts = contr1)

# ╔═╡ 0fd5be15-b9d6-4e67-8dda-5dfe8833ca9a
# fit(MixedModel, fm1, ex3[ex3.letter_rotation .== 180, :], contrasts = contr1)

# ╔═╡ 505c28b2-a9f5-4344-bb19-e7e33b554fac
# fit(MixedModel, fm1, ex3[ex3.letter_rotation .== 315, :], contrasts = contr1)

# ╔═╡ e8045e32-8f74-11eb-08d7-0781a63175a3
md"""
# 4. Appendixes
"""

# ╔═╡ 6110d00c-903e-11eb-2b38-99a816047bc3
md"""
**Column names and their meanings in the data**
- participant: Participant Number;
- type: Letter Type, N - Normal; M - Mirror;
- Orientation: Degree of rotation;
- human (Exp3 - face_orientation): L - Left; R -  Right; _ - No human;
- face_type: N - faced table; M - back(Ex2); _ - No human;
- Condition(Ex3): H - Human(faced_table); A - Arrow; __ - No;
- key\_JUDGE.keys (Ex3: key\_judge.keys): left - normal; right - mirror
- key\_JUDGE.rt (Ex3: key\_judge.rt): Response latency
- Number: Image Number
"""

# ╔═╡ 083f51ca-8de0-11eb-05d7-513b912438ed
## Experiments 1 and 2
rename12 = Dict(
	:Letter      => "letter",
	:type        => "letter_type",
	:Orientation => "letter_rotation",
	:human       => "agent_position",
	:face_type   => "agent_type",
	Symbol("key_JUDGE.keys")   => "key",
	Symbol("key_JUDGE.rt")     => "rt"
);

# ╔═╡ e8ca0eb0-8dd9-11eb-20a5-e1d5e04fa2e8
columns12 = vcat(collect(values(rename12)), "participant", "tf", "agent"); # [[1:4..., 6:7...]]

# ╔═╡ 9c771fc6-8f57-11eb-2408-33b89126fa4d
## Experiments 3
rename3 = Dict(
	:Letter      => "letter",
	:type        => "letter_type",
	:Orientation => "letter_rotation",
	Symbol("key_judge.keys")   => "key",
	Symbol("key_judge.rt")     => "rt",
	Symbol("face_orientation") => "agent_position",
	:Condition   => "agent_type"
);

# ╔═╡ fb0dfa1e-8f57-11eb-306d-bf0057bc7e12
columns3 = vcat(collect(values(rename3)), "participant", "tf", "agent"); # [[1,2,4,5,7,8]]

# ╔═╡ f6a47f47-c761-4f8c-b265-8374bede24a5
"""
# Experiment 1 and 3: N-up M-down
# Experiment 2:
- 1-31按键：     N-left      M-right
- 32-57 按键：   N-right     M-left
- 401-402 按键： N-right     M-left
- 403-407 按键： N-d         M-a

"""
function key_2_TF(directory, participant, letter_type, key)
	if directory == "Experiment_2"
		if participant <= 31
			if letter_type == "M"
				return key == "right" ? 1 : 0
			elseif letter_type == "N"
				return key == "left" ? 1 : 0
			end
		else
			if letter_type == "M"
				return key ∈ ["left", "a"] ? 1 : 0
			elseif letter_type == "N"
				return key ∈ ["right","d"] ? 1 : 0
			end
		end

	else
		if letter_type == "M"
			return key ∈ ["down", "right"] ? 1 : 0
		elseif letter_type == "N"
			return key ∈ ["up",    "left"] ? 1 : 0
		end
	end
end

# ╔═╡ a110c5fe-8f94-11eb-0f0f-b71e5b9353a6
function read_rename_select!(directory, rename_columns, select_columns)
	files = filter(x -> endswith(x, ".csv"), readdir(directory, join = true))
	list = [DataFrame(CSV.File(f))[1:(end-1), :] for f in files]
	for (ind, df) in enumerate(list)
		rename!(df, rename_columns)
		# Ex1 and Ex2: 401-407 calculate
		if directory == "Experiment_1" ||
			(directory == "Experiment_2" && ncol(df) > 40)
		 df.rt = df.rt - df.stimulus_duration
		end
		insertcols!(df, 1, :tf      =>
					key_2_TF.(directory, df.participant, df.letter_type, df.key));
		insertcols!(df, 1, :agent    => df.agent_position .* df.agent_type);
		# transform!(df, :letter_angle =>
		# 	ByRow(x -> x < 180 ? (x * π / 180) : (360 - x) * π / 180) =>
		# 	:letter_rotation)
		df.participant = string.(df.participant)
		list[ind] = df[:, select_columns]
	end
	df = reduce(vcat, list)
	Arrow.write(directory * ".arrow", df)
	return df
end

# ╔═╡ 0e44dbf8-9141-11eb-368c-5d76fa7db518
# cd("/Users/lzhan/Desktop/ITOM/Data"); pwd()

# ╔═╡ 783dd676-907f-11eb-213d-b5a1cb14569d
# read_rename_select!("Experiment_2", rename12, columns12);

# ╔═╡ 89265a5a-8f95-11eb-1d1d-0b9c84742e9b
function filter_data(data, correct_rate, rt_lower, rt_upper)
	participants = @pipe data |>
		groupby(_, :participant) |>
		combine(_, :tf => mean)  |>
		filter(:tf_mean => >=(correct_rate), _) |>
		select(_, :participant)
	dt = @pipe data |>
		dropmissing(_, :rt) |>
		filter(:participant => ∈(participants.participant), _) |>
		# filter(:tf => ==(1), _) |>
		filter(:rt => x -> x >= rt_lower && x <= rt_upper, _)
	return dt
end

# ╔═╡ 07386f3e-8f96-11eb-20f4-09d27ddfa926
ex1 = filter_data(ex1_original, 0.8, 0.15, 2);

# ╔═╡ ad887468-b8f3-4b2c-a079-dffca99d27b0
describe(ex1)

# ╔═╡ 5ef3d9c0-9031-11eb-3839-e7db22fbf21b
length(unique(ex1.participant))

# ╔═╡ 74745418-ea01-4a64-b0e2-fec6b7eb0202
Ex1LFull = fit(MixedModel, fmFull, ex1[ex1.letter_rotation .<= 180, :], contrasts = contr1);

# ╔═╡ 97b2a942-3763-4be5-aefc-2b2b28f2c84e
Ex1LBset = fit(MixedModel, fmBest, ex1[ex1.letter_rotation .<= 180, :], contrasts = contr1);

# ╔═╡ b2355780-cecc-41ea-998f-28263d9e4da9
Ex1LBset

# ╔═╡ 0dce03e5-441e-4637-a2bd-e4790cb4e144
Ex1RBest = fit(MixedModel, fmBest, ex1[ex1.letter_rotation .>= 180, :], contrasts = contr1);

# ╔═╡ bcbec652-e9ba-4e39-b267-feb2f3e6a9b2
Ex1RBest

# ╔═╡ d41e3e10-9109-11eb-356b-b95bea9b44a2
fit(MixedModel, fm1, ex1[ex1.letter_rotation .== 225, :], contrasts = contr1)

# ╔═╡ 2b3d9e00-8ecd-11eb-3d55-b92db51bd635
fit(MixedModel, fm1, ex1[ex1.letter_rotation .== 315, :], contrasts = contr1)

# ╔═╡ 2b93a9e8-8f96-11eb-3c59-5155ec37e662
ex2 = filter_data(ex2_original, 0.8, 0.15, 2);

# ╔═╡ 7de82660-9036-11eb-1c3f-49b8e64e495b
length(unique(ex2.participant))

# ╔═╡ ff604e88-902d-11eb-2481-751fb18eed11
ex2L = ex2[findall(∈(["LM", "LN", "__"]), ex2.agent), :];

# ╔═╡ 9991a4a4-3c7d-4be7-b168-38adc905eed9
Ex2LLBest = fit(MixedModel, fmBest, ex2L[ex2L.letter_rotation .<= 180, :], contrasts = contr1);

# ╔═╡ 9e315cd8-fecd-4067-b953-c0d67155e1a8
Ex2LLBest

# ╔═╡ 4ba14814-2db3-4d8a-a8f9-1c550cc3fabf
Ex2LRBest = fit(MixedModel, fmBest, ex2L[ex2L.letter_rotation .>= 180, :], contrasts = contr1);

# ╔═╡ ac46128e-daf5-415d-b1e7-8b7af30662a0
Ex2LRBest

# ╔═╡ 0f1791ec-902e-11eb-1927-2bdc219c0976
ex2R = ex2[findall(∈(["RM", "RN", "__"]), ex2.agent), :];

# ╔═╡ f8d05bac-2989-4a62-ae20-122a91304125
Ex2RLBest = fit(MixedModel, fmBest, ex2R[ex2R.letter_rotation .<= 180, :], contrasts = contr1);

# ╔═╡ b9a810c2-4984-484e-afa8-c174b65b15d0
Ex2RLBest

# ╔═╡ 9b3fc630-9405-41b9-9ebd-6d589ae8ae98
Ex2RRBest = fit(MixedModel, fmBest, ex2R[ex2R.letter_rotation .>= 180, :], contrasts = contr1);

# ╔═╡ 0eea1567-f2b2-4413-84cf-267b3e5668d1
 Ex2RRBest

# ╔═╡ 59690c76-910a-11eb-3785-ed75d30e3e95
fit(MixedModel, fm1, ex2[ex2.letter_rotation .== 270, :], contrasts = contr1)

# ╔═╡ 7046f3a2-910a-11eb-2705-09c2358c95e2
fit(MixedModel, fm1, ex2[ex2.letter_rotation .== 315, :], contrasts = contr1)

# ╔═╡ 3a73aeae-8f96-11eb-0a03-f147003a4128
ex3 = filter_data(ex3_original, 0.8, 0.15, 2);

# ╔═╡ 66990d2e-9031-11eb-2cc7-09cdde9af93b
length(unique(ex3.participant))

# ╔═╡ 9771d9fa-902c-11eb-3ff5-0fec27d703f1
ex3L = ex3[findall(∈(["LA", "LH", "__"]), ex3.agent), :];

# ╔═╡ 4aca37fb-83b1-40db-89d0-3ff295508633
Ex3LLBest = fit(MixedModel, fmBest, ex3L[ex3L.letter_rotation .<= 180, :], contrasts = contr1);

# ╔═╡ 7629c86a-96b9-4d40-a08b-119946f26256
Ex3LLBest

# ╔═╡ 946f6e05-6713-4a12-9cf9-b1a461010eb6
Ex3LRBest = fit(MixedModel, fmBest, ex3L[ex3L.letter_rotation .>= 180, :], contrasts = contr1);

# ╔═╡ bc1f20e5-54dc-40b2-bf68-d544346a6f00
Ex3LRBest

# ╔═╡ 85ae5cde-902c-11eb-282c-79a93395e5f0
ex3R = ex3[findall(∈(["RA", "RH", "__"]), ex3.agent), :];

# ╔═╡ 45429031-555f-4142-8b38-9518f02df73c
Ex3RLBest = fit(MixedModel, fmBest, ex3R[ex3R.letter_rotation .<= 180, :], contrasts = contr1);

# ╔═╡ 986b3160-ac7b-4438-8875-21b9e40c6ff9
Ex3RLBest

# ╔═╡ 8d54a42a-caf5-44d8-b08a-8d5dcccacb4e
Ex3RRBest = fit(MixedModel, fmBest, ex3R[ex3R.letter_rotation .>= 180, :], contrasts = contr1);

# ╔═╡ 7eb01dcc-1644-44ca-bb2e-bbc560b1f626
Ex3RRBest

# ╔═╡ 9a8325d1-1241-44e2-9eac-8fa3eb5c4cc7
fit(MixedModel, fm1, ex3[ex3.letter_rotation .== 225, :], contrasts = contr1)

# ╔═╡ ffd34186-1320-447e-9054-05d9c5827c22
fit(MixedModel, fm1, ex3[ex3.letter_rotation .== 270, :], contrasts = contr1)

# ╔═╡ 00147106-8f98-11eb-34e2-a98d0f6c046a
function summarize_4_plot(dt)
	dtm = @pipe dt |>
		groupby(_, [:letter_rotation, :agent]) |>
		combine(_, :rt => mean)
	new_rows = insertcols!(dtm[dtm.letter_rotation .== 0, 2:end], 1,
	:letter_rotation => 360)
	dtmn = vcat(dtm, new_rows)
	return dtmn
end

# ╔═╡ 10acbb8a-8fad-11eb-2d8a-913e1c002326
function polar_plot(dt; lower = 1.0, upper = 1.4)
	plot(
		(dt.letter_rotation),# / 360 * 2π,
		dt.rt_mean,
		group = dt.agent,
		ylim = (lower, upper),
		yticks = 1.0:0.1:1.5,
		xticks = 0:45:360,
		xrotation = 0,
		seriestype = :line,
		# projection = :polar,
		linewidth = 1.5,
		marker = 4)
end

# ╔═╡ 6ea41f1c-8fad-11eb-193d-dbc8b73fadc2
polar_plot(summarize_4_plot(ex1))

# ╔═╡ c798e31c-8faa-11eb-22c3-69269a304f67
plot(polar_plot(summarize_4_plot(ex2L)), polar_plot(summarize_4_plot(ex2R)), layout = 2)

# ╔═╡ d74bde4c-8fad-11eb-20d7-41b985c55506
plot(polar_plot(summarize_4_plot(ex3L)), polar_plot(summarize_4_plot(ex3R)), layout = 2)

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Arrow = "69666777-d1a9-59fb-9406-91d4454c9d45"
CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
DisplayAs = "0b91fe84-8a4c-11e9-3e1d-67c38462b6d6"
FreqTables = "da1fdf0e-e0ff-5433-a45f-9bb5ff651cb1"
Pipe = "b98c9c47-44ae-5843-9183-064241ee97a0"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"

[compat]
Arrow = "~2.2.0"
CSV = "~0.9.10"
DataFrames = "~1.2.2"
DisplayAs = "~0.1.2"
FreqTables = "~0.4.5"
Pipe = "~1.3.0"
Plots = "~1.23.2"
PlutoUI = "~0.7.17"
StatsBase = "~0.33.12"
StatsPlots = "~0.14.28"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

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[[GR]]
deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
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[[GR_jll]]
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git-tree-sha1 = "fd75fa3a2080109a2c0ec9864a6e14c60cca3866"
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[[GeometryBasics]]
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[[Gettext_jll]]
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git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
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[[Glib_jll]]
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[[Graphite2_jll]]
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git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
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[[Grisu]]
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[[HTTP]]
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[[HarfBuzz_jll]]
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git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
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[[Hyperscript]]
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[[HypertextLiteral]]
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[[IOCapture]]
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[[IniFile]]
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[[InlineStrings]]
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[[IntelOpenMP_jll]]
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git-tree-sha1 = "d979e54b71da82f3a65b62553da4fc3d18c9004c"
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version = "2018.0.3+2"

[[InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"

[[Interpolations]]
deps = ["AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
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[[InverseFunctions]]
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[[InvertedIndices]]
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[[IrrationalConstants]]
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[[IterTools]]
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[[IteratorInterfaceExtensions]]
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[[JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
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[[JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
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[[JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
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[[KernelDensity]]
deps = ["Distributions", "DocStringExtensions", "FFTW", "Interpolations", "StatsBase"]
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uuid = "5ab0869b-81aa-558d-bb23-cbf5423bbe9b"
version = "0.6.3"

[[LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.1+0"

[[LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
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[[LaTeXStrings]]
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[[Latexify]]
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git-tree-sha1 = "a8f4f279b6fa3c3c4f1adadd78a621b13a506bce"
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[[LazyArtifacts]]
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uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"

[[LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"

[[LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"

[[LibGit2]]
deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
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[[LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"

[[Libdl]]
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[[Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
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[[Libgcrypt_jll]]
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git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
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[[Libglvnd_jll]]
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git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.3.0+3"

[[Libgpg_error_jll]]
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git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
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[[Libiconv_jll]]
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git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
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[[Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
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[[Libtiff_jll]]
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git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9"
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[[Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
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[[LinearAlgebra]]
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[[LogExpFunctions]]
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[[Logging]]
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[[Lz4_jll]]
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git-tree-sha1 = "5d494bc6e85c4c9b626ee0cab05daa4085486ab1"
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[[MKL_jll]]
deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
git-tree-sha1 = "5455aef09b40e5020e1520f551fa3135040d4ed0"
uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
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[[MacroTools]]
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[[Markdown]]
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[[MbedTLS]]
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[[MbedTLS_jll]]
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[[Measures]]
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[[Missings]]
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[[Mmap]]
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[[Mocking]]
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[[MozillaCACerts_jll]]
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[[MultivariateStats]]
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[[NaNMath]]
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[[NamedArrays]]
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[[NearestNeighbors]]
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[[NetworkOptions]]
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[[Observables]]
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[[OffsetArrays]]
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[[Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
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[[OpenBLAS_jll]]
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[[OpenLibm_jll]]
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uuid = "05823500-19ac-5b8b-9628-191a04bc5112"

[[OpenSSL_jll]]
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git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
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[[OpenSpecFun_jll]]
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git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
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[[Opus_jll]]
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git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
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[[OrderedCollections]]
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[[PCRE_jll]]
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git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
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[[PDMats]]
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[[Parsers]]
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[[Pipe]]
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[[Pixman_jll]]
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git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
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[[Pkg]]
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uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

[[PlotThemes]]
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[[PlotUtils]]
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[[Plots]]
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version = "1.23.2"

[[PlutoUI]]
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uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
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[[PooledArrays]]
deps = ["DataAPI", "Future"]
git-tree-sha1 = "a193d6ad9c45ada72c14b731a318bedd3c2f00cf"
uuid = "2dfb63ee-cc39-5dd5-95bd-886bf059d720"
version = "1.3.0"

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

[[PrettyTables]]
deps = ["Crayons", "Formatting", "Markdown", "Reexport", "Tables"]
git-tree-sha1 = "d940010be611ee9d67064fe559edbb305f8cc0eb"
uuid = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d"
version = "1.2.3"

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

[[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"

[[QuadGK]]
deps = ["DataStructures", "LinearAlgebra"]
git-tree-sha1 = "78aadffb3efd2155af139781b8a8df1ef279ea39"
uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
version = "2.4.2"

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

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

[[Ratios]]
deps = ["Requires"]
git-tree-sha1 = "01d341f502250e81f6fec0afe662aa861392a3aa"
uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
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[[RecipesBase]]
git-tree-sha1 = "44a75aa7a527910ee3d1751d1f0e4148698add9e"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
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[[RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
git-tree-sha1 = "7ad0dfa8d03b7bcf8c597f59f5292801730c55b8"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
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[[Reexport]]
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uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
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[[Rmath]]
deps = ["Random", "Rmath_jll"]
git-tree-sha1 = "bf3188feca147ce108c76ad82c2792c57abe7b1f"
uuid = "79098fc4-a85e-5d69-aa6a-4863f24498fa"
version = "0.7.0"

[[Rmath_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "68db32dff12bb6127bac73c209881191bf0efbb7"
uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f"
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[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

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

[[SentinelArrays]]
deps = ["Dates", "Random"]
git-tree-sha1 = "f45b34656397a1f6e729901dc9ef679610bd12b5"
uuid = "91c51154-3ec4-41a3-a24f-3f23e20d615c"
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[[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"

[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.0.1"

[[SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[SpecialFunctions]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "f0bccf98e16759818ffc5d97ac3ebf87eb950150"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "1.8.1"

[[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 = "1958272568dc176a1d881acb797beb909c785510"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.0.0"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "eb35dcc66558b2dda84079b9a1be17557d32091a"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.12"

[[StatsFuns]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
git-tree-sha1 = "95072ef1a22b057b1e80f73c2a89ad238ae4cfff"
uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
version = "0.9.12"

[[StatsPlots]]
deps = ["Clustering", "DataStructures", "DataValues", "Distributions", "Interpolations", "KernelDensity", "LinearAlgebra", "MultivariateStats", "Observables", "Plots", "RecipesBase", "RecipesPipeline", "Reexport", "StatsBase", "TableOperations", "Tables", "Widgets"]
git-tree-sha1 = "eb007bb78d8a46ab98cd14188e3cec139a4476cf"
uuid = "f3b207a7-027a-5e70-b257-86293d7955fd"
version = "0.14.28"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "2ce41e0d042c60ecd131e9fb7154a3bfadbf50d3"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
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[[SuiteSparse]]
deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"

[[TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"

[[TableOperations]]
deps = ["SentinelArrays", "Tables", "Test"]
git-tree-sha1 = "e383c87cf2a1dc41fa30c093b2a19877c83e1bc1"
uuid = "ab02a1b2-a7df-11e8-156e-fb1833f50b87"
version = "1.2.0"

[[TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "fed34d0e71b91734bf0a7e10eb1bb05296ddbcd0"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.6.0"

[[Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

[[Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[TimeZones]]
deps = ["Dates", "Downloads", "InlineStrings", "LazyArtifacts", "Mocking", "Pkg", "Printf", "RecipesBase", "Serialization", "Unicode"]
git-tree-sha1 = "8de32288505b7db196f36d27d7236464ef50dba1"
uuid = "f269a46b-ccf7-5d73-abea-4c690281aa53"
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[[TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.6"

[[URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[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"

[[WeakRefStrings]]
deps = ["DataAPI", "InlineStrings", "Parsers"]
git-tree-sha1 = "c69f9da3ff2f4f02e811c3323c22e5dfcb584cfa"
uuid = "ea10d353-3f73-51f8-a26c-33c1cb351aa5"
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[[Widgets]]
deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
git-tree-sha1 = "80661f59d28714632132c73779f8becc19a113f2"
uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
version = "0.6.4"

[[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"

[[libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"

[[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"
"""

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text:
####
#### Robust online (co-)variance estimators.
####

abstract type MassMatrixAdaptor <: AbstractAdaptor end

initialize!(::MassMatrixAdaptor, ::Int) = nothing
finalize!(::MassMatrixAdaptor) = nothing

function adapt!(
    adaptor::MassMatrixAdaptor,
    θ::AbstractVecOrMat{<:AbstractFloat},
    α::AbstractScalarOrVec{<:AbstractFloat},
    is_update::Bool=true
)
    resize!(adaptor, θ)
    push!(adaptor, θ)
    is_update && update!(adaptor)
end

## Unit mass matrix adaptor

struct UnitMassMatrix{T<:AbstractFloat} <: MassMatrixAdaptor end

Base.show(io::IO, ::UnitMassMatrix) = print(io, "UnitMassMatrix")

UnitMassMatrix() = UnitMassMatrix{Float64}()

Base.string(::UnitMassMatrix) = "I"

Base.resize!(pc::UnitMassMatrix, θ::AbstractVecOrMat) = nothing

reset!(::UnitMassMatrix) = nothing

getM⁻¹(::UnitMassMatrix{T}) where {T} = LinearAlgebra.UniformScaling{T}(one(T))

adapt!(
    ::UnitMassMatrix,
    ::AbstractVecOrMat{<:AbstractFloat},
    ::AbstractScalarOrVec{<:AbstractFloat},
    is_update::Bool=true
) = nothing

## Diagonal mass matrix adaptor

abstract type DiagMatrixEstimator{T} <: MassMatrixAdaptor end

getM⁻¹(ve::DiagMatrixEstimator) = ve.var

Base.string(ve::DiagMatrixEstimator) = string(getM⁻¹(ve))

function update!(ve::DiagMatrixEstimator)
    ve.n >= ve.n_min && (ve.var .= get_estimation(ve))
end

# NOTE: this naive variance estimator is used only in testing
struct NaiveVar{T<:AbstractFloat, E<:AbstractVector{<:AbstractVecOrMat{T}}} <: DiagMatrixEstimator{T}
    S :: E
    NaiveVar(S::E) where {E} = new{eltype(eltype(E)), E}(S)
end

NaiveVar{T}(sz::Tuple{Int}) where {T<:AbstractFloat} = NaiveVar(Vector{Vector{T}}())
NaiveVar{T}(sz::Tuple{Int,Int}) where {T<:AbstractFloat} = NaiveVar(Vector{Matrix{T}}())

NaiveVar(sz::Union{Tuple{Int}, Tuple{Int,Int}}) = NaiveVar{Float64}(sz)

Base.push!(nv::NaiveVar, s::AbstractVecOrMat) = push!(nv.S, s)

reset!(nv::NaiveVar) = resize!(nv.S, 0)

function get_estimation(nv::NaiveVar)
    @assert length(nv.S) >= 2 "Cannot estimate variance with only one sample"
    return Statistics.var(nv.S)
end

# Ref： https://github.com/stan-dev/math/blob/develop/stan/math/prim/mat/fun/welford_var_estimator.hpp
mutable struct WelfordVar{T<:AbstractFloat, E<:AbstractVecOrMat{T}} <: DiagMatrixEstimator{T}
    n     :: Int
    n_min :: Int
    μ     :: E
    M     :: E
    δ     :: E    # cache for diff
    var   :: E    # cache for variance
    function WelfordVar(n::Int, n_min::Int, μ::E, M::E, δ::E, var::E) where {E}
        return new{eltype(E), E}(n, n_min, μ, M, δ, var)
    end
end

Base.show(io::IO, ::WelfordVar) = print(io, "WelfordVar")

function WelfordVar{T}(
    sz::Union{Tuple{Int}, Tuple{Int,Int}};
    n_min::Int=10, var=ones(T, sz)
) where {T<:AbstractFloat}
    return WelfordVar(0, n_min, zeros(T, sz), zeros(T, sz), zeros(T, sz), var)
end

WelfordVar(sz::Union{Tuple{Int}, Tuple{Int,Int}}; kwargs...) = WelfordVar{Float64}(sz; kwargs...)

function Base.resize!(wv::WelfordVar, θ::AbstractVecOrMat{T}) where {T<:AbstractFloat}
    if size(θ) != size(wv.var)
        @assert wv.n == 0 "Cannot resize a var estimator when it contains samples."
        wv.μ = zeros(T, size(θ))
        wv.M = zeros(T, size(θ))
        wv.δ = zeros(T, size(θ))
        wv.var = ones(T, size(θ))
    end
end

function reset!(wv::WelfordVar{T}) where {T<:AbstractFloat}
    wv.n = 0
    wv.μ .= zero(T)
    wv.M .= zero(T)
end

function Base.push!(wv::WelfordVar, s::AbstractVecOrMat{T}) where {T}
    wv.n += 1
    @unpack δ, μ, M, n = wv
    n = T(n)
    δ .= s - μ
    μ .= μ + δ / n
    M .= M + δ .* δ * ((n - 1) / n)    # eqv. to `M + (s - μ) .* δ`
end

# https://github.com/stan-dev/stan/blob/develop/src/stan/mcmc/var_adaptation.hpp
function get_estimation(wv::WelfordVar{T}) where {T<:AbstractFloat}
    @unpack n, M, var = wv
    @assert n >= 2 "Cannot estimate variance with only one sample"
    n, ϵ = T(n), T(1e-3)
    return n / ((n + 5) * (n - 1)) * M .+ ϵ * (5 / (n + 5))
end

## Dense mass matrix adaptor

abstract type DenseMatrixEstimator{T} <: MassMatrixAdaptor end

getM⁻¹(ce::DenseMatrixEstimator) = ce.cov

Base.string(ce::DenseMatrixEstimator) = string(LinearAlgebra.diag(getM⁻¹(ce)))

function update!(ce::DenseMatrixEstimator)
    ce.n >= ce.n_min && (ce.cov .= get_estimation(ce))
end

# NOTE: This naive covariance estimator is used only in testing.
struct NaiveCov{F<:AbstractFloat, T<:AbstractVector{<:AbstractVector{F}}} <: DenseMatrixEstimator{T}
    S :: T
    NaiveCov(S::E) where {E} = new{eltype(eltype(E)), E}(S)
end

NaiveCov{T}(sz::Tuple{Int}) where {T<:AbstractFloat} = NaiveCov(Vector{Vector{T}}())

NaiveCov(sz::Union{Tuple{Int}, Tuple{Int,Int}}; kwargs...) = NaiveCov{Float64}(sz; kwargs...)

Base.push!(nc::NaiveCov, s::AbstractVector) = push!(nc.S, s)

reset!(nc::NaiveCov{T}) where {T} = resize!(nc.S, 0)

function get_estimation(nc::NaiveCov)
    @assert length(nc.S) >= 2 "Cannot get covariance with only one sample"
    return Statistics.cov(nc.S)
end

# Ref: https://github.com/stan-dev/math/blob/develop/stan/math/prim/mat/fun/welford_covar_estimator.hpp
mutable struct WelfordCov{F<:AbstractFloat} <: DenseMatrixEstimator{F}
    n     :: Int
    n_min :: Int
    μ     :: Vector{F}
    M     :: Matrix{F}
    δ     :: Vector{F}  # cache for diff
    cov   :: Matrix{F}
end

Base.show(io::IO, ::WelfordCov) = print(io, "WelfordCov")

function WelfordCov{T}(
    sz::Tuple{Int}; n_min::Int=10, cov=LinearAlgebra.diagm(0 => ones(T, first(sz)))
) where {T<:AbstractFloat}
    d = first(sz)
    return WelfordCov(0, n_min, zeros(T, d), zeros(T, d, d), zeros(T, d), cov)
end

WelfordCov(sz::Tuple{Int}; kwargs...) = WelfordCov{Float64}(sz; kwargs...)

function Base.resize!(wc::WelfordCov, θ::AbstractVector{T}) where {T<:AbstractFloat}
    if length(θ) != size(wc.cov, 1)
        @assert wc.n == 0 "Cannot resize a var estimator when it contains samples."
        wc.μ = zeros(T, length(θ))
        wc.δ = zeros(T, length(θ))
        wc.M = zeros(T, length(θ), length(θ))
        wc.cov = LinearAlgebra.diagm(0 => ones(T, length(θ)))
    end
end

function reset!(wc::WelfordCov{T}) where {T<:AbstractFloat}
    wc.n = 0
    wc.μ .= zero(T)
    wc.M .= zero(T)
end

function Base.push!(wc::WelfordCov, s::AbstractVector{T}) where {T}
    wc.n += 1
    @unpack δ, μ, n, M = wc
    n = T(n)
    δ .= s - μ
    μ .= μ + δ / n
    M .= M + (s - μ) * δ'
end

# Ref: https://github.com/stan-dev/stan/blob/develop/src/stan/mcmc/covar_adaptation.hpp
function get_estimation(wc::WelfordCov{T}) where {T<:AbstractFloat}
    @unpack n, M, cov = wc
    @assert n >= 2 "Cannot get covariance with only one sample"
    n, ϵ = T(n), T(1e-3)
    return n / ((n + 5) * (n - 1)) * M + ϵ * (5 / (n + 5)) * LinearAlgebra.I
end

ext: jl


text:
################
# Trans-parsing  Julia AST to Math AST

const binops_renames =Dict( :(<=) => "\\le",
                            :(>=) => "\\ge",
                            :in   => "\\in",
                            :±  => "\\pm")
const binops = [Symbol.(split("+ - < > ∈ ≈ *"))..., keys(binops_renames)...]

val_or_expr(x::Expr) = x
val_or_expr(x) = Val{x}()

function MathSequence(v_vs, binop)
    dlm = to_math(binop)
    vs = to_math.(collect(v_vs))

    frags = Vector{MathExpressionFragment}()
    sizehint!(frags, 2*length(vs)-1)
    for v in vs[1:end-1]
        push!(frags,v)
        push!(frags,dlm)
    end
    push!(frags, vs[end])
    MathSequence(frags)
end

to_math(::Val{sym}) where {sym}= to_math(sym)
to_math(sym::Number) = MathSymbol(sym)
function to_math(sym::Symbol)
    if haskey(binops_renames, sym)
        return MathSymbol(binops_renames[sym])
    end

    sym_str = String(sym)
    frags = split(String(sym), "_")
    if length(frags) == 1
        MathSymbol(sym)
    else
        base = Symbol(frags[1])
        sub = Symbol(join(frags[2:end], ","))
        MathSubscript(base, sub)
    end
end

function to_math(::Val{:call}, v_binop::Union{(Val{binop} for binop in binops)...}, vs...)
    #Binary Operators: the julia paster rolls `1+2+3` into (+,(1,2,3))
    length(vs) < 2 && warn("attempting to parse for $(v_binop) with less than 2 args: $(vs)")
    MathSequence(vs, v_binop)
end

# Uniary minux
function to_math(::Val{:call}, ::Val{:-}, v)
    # HACK: say it is a function call
    MathFunctionCall(:-, MathSequence([to_math(v)]))
end

function to_math(::Val{:call}, ::Val{:^}, v_base, v_expo)
    MathSuperscript(to_math(v_base), to_math(v_expo))
end

function to_math(::Val{:call}, ::Val{:/}, v_base, v_expo)
    MathFrac(to_math(v_base), to_math(v_expo))
end

function to_math(::Val{:call}, v_func::Val{func}, v_args...) where func
    MathFunctionCall(func, MathSequence(v_args, Symbol(", ")))
end

function to_math(ast::Expr)
    to_math(Val{ast.head}(), val_or_expr.(ast.args)... )
end

# Matrixes and Vectors

to_math(::Val{:vect},vs...) = to_math_vector(vs)
function to_math_vector(col)
    math_col = MathExpressionFragment[to_math(c) for c in col]
    MathMatrix(math_col[:,:]) #A vector is a column matrix
end

to_math(::Val{:hcat},row...) = to_math_matrix(row)
function to_math_matrix(rows...)
	function math_row(row)
		row_vec = MathExpressionFragment[to_math(r) for r in row.args]
		permutedims(row_vec[:,:], (2,1))
	end
    MathMatrix(vcat(map(math_row, rows)...))
end

function to_math(::Val{:vcat},vs...)
    if typeof(vs[1])<:Expr && vs[1].head == :row
        to_math_matrix(vs...)
    else
        to_math_vector(vs)
    end
end


text:
# This file is a part of BAT.jl, licensed under the MIT License (MIT).

using BAT
using Compat.Test

using Distributions

@testset "shims" begin
    @testset "_iszero" begin
        @test BAT._iszero(zero(Float64))
        @test BAT._iszero(zeros(Float32,4,4))
        @test !BAT._iszero(ones(Float32,4,4))
        @test BAT._iszero(Distributions.ZeroVector(Float64, 4))
    end
end


text:
using Printf

function sternbrocot(f::Function=(x) -> length(x) ≥ 20)::Vector{Int}
    rst = Int[1, 1]
    i = 3
    while !f(rst)
        append!(rst, Int[rst[i-1] + rst[i-2], rst[i-2]])
        i += 1
    end
    return rst
end

println("First 15 elements of Stern-Brocot series:\n", sternbrocot(x -> length(x) ≥ 15)[1:15], "\n")

for i in (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100)
    occurr = findfirst(x -> x == i, sternbrocot(x -> i ∈ x))
    @printf("Index of first occurrence of %3i in the series: %4i\n", i, occurr)
end

print("\nAssertion: the greatest common divisor of all the two\nconsecutive members of the series up to the 1000th member, is always one: ")
sb = sternbrocot(x -> length(x) > 1000)
if all(gcd(prev, this) == 1 for (prev, this) in zip(sb[1:1000], sb[2:1000]))
    println("Confirmed.")
else
    println("Rejected.")
end

max_stars_repo_name: ethansaxenian/RosettaDecode

max_issues_repo_name: ethansaxenian/RosettaDecode

max_forks_repo_name: ethansaxenian/RosettaDecode


text:
abstract type Sense end
struct Max<:Sense end
struct Min<:Sense end

mutable struct NonDomPoints{T}
	xe::Vector{Vector{Int}}
	yn::Vector{Tuple{Int,Int}}
	λ::Tuple{Int,Int}
	nadirs::Vector{Tuple{Int,Int}}
	worst_nadir::Tuple{Int,Int}
	function NonDomPoints(t::Type{T}, xe, yn) where T<:Sense
		@assert issorted(yn, by = y-> y[1])
		λ = round(Int, yn[1][2] - yn[end][2]), round(Int, yn[end][1] - yn[1][1])
		λ = λ[1]÷gcd(λ[1], λ[2]), λ[2]÷gcd(λ[1], λ[2])
		res = new{T}([round.(Int, x) for x in xe], [round.(Int, x) for x in yn], λ, [])
		update_ln!(res)
		res
	end
end

function update_ln!(p::NonDomPoints{Max})
	p.nadirs = [(p.yn[i][1], p.yn[i+1][2]) for i = 1:length(p.yn)-1]
	if isempty(p.nadirs)
		p.worst_nadir = p.yn[1].+1
		return p
	end
	p.worst_nadir = p.nadirs[1].+1
	for n in p.nadirs
		if sum((n.+1).*p.λ) < sum(p.worst_nadir.*p.λ)
			p.worst_nadir = n.+1
		end
	end
	p
end

function update_ln!(p::NonDomPoints{Min})
	p.nadirs = [(p.yn[i+1][1], p.yn[i][2]) for i = 1:length(p.yn)-1]
	if isempty(p.nadirs)
		p.worst_nadir = p.yn[1].-1
		return p
	end
	p.worst_nadir = p.nadirs[1].-1
	for n in p.nadirs
		if sum((n.-1).*p.λ) > sum(p.worst_nadir.*p.λ)
			p.worst_nadir = n.-1
		end
	end
	p
end

nadirs(p::NonDomPoints) = p.nadirs
worst_nadir(p::NonDomPoints) = p.worst_nadir
isfathomable(z, p::NonDomPoints{Min}) = z > sum(worst_nadir(p).*p.λ)
isfathomable(z, p::NonDomPoints{Max}) = z < sum(worst_nadir(p).*p.λ)
local_nadir(p::NonDomPoints{Min}) = (p.yn[end][1], p.yn[1][2])
local_nadir(p::NonDomPoints{Max}) = (p.yn[1][1], p.yn[end][2])

function isweaklydominated(z1, z2, p::NonDomPoints{Min})
	for (v1, v2) in p.yn
		if v1 <= z1 && v2 <= z2
			return true
		end
	end
	false
end

function isweaklydominated(z1, z2, p::NonDomPoints{Max})
	for (v1, v2) in p.yn
		if v1 >= z1 && v2 >= z2
			return true
		end
	end
	false
end

Base.length(p::NonDomPoints) = length(p.yn)

function Base.push!(p::NonDomPoints{S}, x, y) where S<:Sense
	#@assert !isweaklydominated(y..., p) "y : $y \n p : $p"
	if isweaklydominated(y..., p)
		return p
	end
	ind = searchsortedfirst(p.yn, y, by = y -> first(y))
	insert!(p.xe, ind, x)
	insert!(p.yn, ind, y)
	inds_delete = find(x->dominates(S, y, x), p.yn)

	deleteat!(p.xe, inds_delete)
	deleteat!(p.yn, inds_delete)
	update_ln!(p)
end