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tratamento-de-dados.jl
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tratamento-de-dados.jl
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### A Pluto.jl notebook ###
# v0.15.1
using Markdown
using InteractiveUtils
# ╔═╡ 969784ea-f9d3-11eb-151f-f104cfb3a15a
using Plots, DataFrames, CSV, PlutoUI, Random, Colors, StatsPlots, Statistics, LinearAlgebra
# ╔═╡ a190fcdc-6e51-459b-9345-b35c08d2ab2c
function pairplot(df, columns, target)
eltypes = eltype.(eachcol(df[!,columns]))
m = length(columns)
p = plot(layout=grid(m, m), size=(m * 250, m * 250), leg=false)
function escala(v)
eltype(v) <: Number || return 0
n = floor(Int, log10(maximum(abs.(v))))
return n > 2 ? div(n, 3) * 3 : (n < -1 ? n + 1 : 0)
end
function super_str(x)
x == "." && return " ̇"
["⁰", "¹", "²", "³", "⁴", "⁵", "⁶", "⁷", "⁸", "⁹"][Meta.parse(x) + 1]
end
super(x) = super_str.(string(x))
function numencoder(v)
eltype(v) <: Number && return v
U = unique(v)
indexin(v, U)
end
escalas = [escala(df[!,columns[i]]) for i = 1:m]
tgt = df[!,target]
tgtU = sort(unique(tgt))
colors = Colors.distinguishable_colors(length(tgtU), RGB(0,0,1))
for i = 1:m
ci = columns[i]
vi = numencoder(df[!,ci])
for (k,u) in enumerate(tgtU)
I = findall(tgt .== u)
histogram!(p[i,i], vi[I], bins=10, opacity=0.6, c=colors[k])
end
if eltypes[i] <: Number
v = round.(range(extrema(vi)..., length=4), sigdigits=2)
xticks!(p[i,i], v, string.(v * 10.0^(-escalas[i])))
else
U = unique(df[!,ci])
xticks!(p[i,i], 1:length(U), U)
end
for j = 1:m
j == i && continue
cj = columns[j]
vj = numencoder(df[!,cj])
scatter!(p[i,j], vj, vi, c=colors, opacity=0.6, xticks=[], yticks=[])
if j == 1 || (j == 2 && i == 1)
if eltypes[i] <: Number
v = round.(range(extrema(vi)..., length=4), sigdigits=2)
yticks!(p[i,j], v, string.(v * 10.0^(-escalas[i])))
else
U = unique(df[!,columns[i]])
yticks!(p[i,j], 1:length(U), U)
end
end
end
lbl = string(ci)
if escalas[i] != 0
lbl *= " (× 10$(super(escalas[i])))"
end
ylabel!(p[i,1], lbl)
end
for j = 1:m
lbl = string(columns[j])
if escalas[j] != 0
lbl *= " (× 10$(super(escalas[j])))"
end
xlabel!(p[m,j], lbl)
vj = numencoder(df[!,columns[j]])
if eltypes[j] <: Number
v = round.(range(extrema(vj)..., length=4), sigdigits=2)
xticks!(p[m,j], v, string.(v * 10.0^(-escalas[j])))
else
U = unique(df[!,columns[j]])
xticks!(p[m,j], 1:length(U), U)
end
end
p
end
# ╔═╡ 308aa0f4-1767-4c52-a0e8-6606d2fc34cf
function normaliza(v)
m, M = extrema(v)
return (v .- m) / (M - m)
end
# ╔═╡ 38aaf8be-afe2-4c2b-8de4-58f8deb2085b
let
Random.seed!(0)
n = 300
idade = randn(n)
idade = (idade .- minimum(idade)) / (maximum(idade) - minimum(idade))
idade = 18 .+ idade * (60 - 18)
idade = round.(Int, idade)
salario = round.(idade .* (1.5 .+ randn(n) * 0.5) .- 5 + 0.2 * exp.(randn(n) * 2.5) + 60 * rand(n) + (rand(n) .> 0.8) .* 40) * 100
data = DataFrame(
idade = [rand() < 0.05 ? missing : idade[i] for i = 1:n],
salario = salario,
estado_civil = rand(["solteiro", "casado", "separado"], n)
)
idade = normaliza(idade)
salario = normaliza(salario)
concedido = Int.(
0.2 * idade +
0.3 * salario +
0.2 * (salario .> 0.7) +
0.1 * randn(n) .> 0.3
)
data[!,:concedido] = concedido
data |> CSV.write("trat-dados.csv")
nothing
end
# ╔═╡ 9e59183e-3719-4b7b-8b16-ce0b8ddb17c0
md"""
## Análise dos dados
"""
# ╔═╡ dd2a9aec-2122-46fd-82b6-4789a28ea517
data = CSV.read("trat-dados.csv", DataFrame)
# ╔═╡ be62806b-eee2-4779-85a6-f53a7e097ad0
describe(data)
# ╔═╡ d5a3bc6e-b681-4422-8230-af5d32e5faab
begin
missing_set = union([findall(ismissing.(col)) for col in eachcol(data)]...)
data[missing_set,:]
end
# ╔═╡ 067c1cc4-f1d9-4f60-b7d0-a371be1be67f
md"""
### Distribuição dos dados
"""
# ╔═╡ 30c911a5-0631-4ad4-a22a-c6398c3f3e93
let
plot(leg=false)
df = dropmissing(data)
U = sort(unique(df[!,:estado_civil]))
v = indexin(df[!,:estado_civil], U)
df[!,:estado_civil] = [x for x in v]
p11 = boxplot(df.concedido, df.idade, opacity=0.8, leg=false)
xticks!([0, 1])
title!("Idade")
p21 = violin(df.concedido, df.idade, leg=false)
xticks!([0, 1])
p31 = dotplot(df.concedido, df.idade, opacity=0.5, ms=3, leg=false)
xticks!([0, 1])
p41 = groupedhist(df.idade, group=df.concedido, opacity=0.5)
p12 = boxplot(df.concedido, df.salario, opacity=0.8, leg=false)
xticks!([0, 1])
title!("Salário")
p22 = violin(df.concedido, df.salario, leg=false)
xticks!([0, 1])
p32 = dotplot(df.concedido, df.salario, opacity=0.5, leg=false)
xticks!([0, 1])
p42 = groupedhist(df.salario, group=df.concedido, opacity=0.5)
p13 = boxplot(df.concedido, df.estado_civil, opacity=0.8, leg=false)
xticks!([0, 1])
yticks!(1:length(U), U)
title!("Estado Civil")
p23 = violin(df.concedido, df.estado_civil, leg=false)
xticks!([0, 1])
yticks!(1:length(U), U)
p33 = dotplot(df.concedido, df.estado_civil, opacity=0.5, leg=false)
xticks!([0, 1])
yticks!(1:length(U), U)
p43 = plot()
p43 = groupedhist(df.estado_civil, group=df.concedido, opacity=0.5)
xticks!(1:length(U), U)
plot(p11, p12, p13,
p21, p22, p23,
p31, p32, p33,
p41, p42, p43,
size=(3 * 250, 4 * 250),
# layout=@layout([a b c; d e f; g h i; j _ _]))
layout=grid(4,3))
xlabel!("Concedido")
end
# ╔═╡ 25700116-bc9f-4af1-a348-f49dcbd90825
md"""
### Pairplot - Relacionamentos em pares
"""
# ╔═╡ c3a853c1-f9e2-4caa-adbe-26577aab1924
pairplot(dropmissing(data), names(data)[1:end-1], :concedido)
# ╔═╡ 18dea9d2-7b1f-4045-b05d-436455f3af60
md"""
### Correlação
"""
# ╔═╡ db4141b4-fac8-4d94-b1a2-bcb6e8634e54
let
df = dropmissing(data)
U = unique(df[!,:estado_civil])
v = indexin(df[!,:estado_civil], U)
df[!,:estado_civil] = v
C = [cor(c1, c2) for c1 in eachcol(df), c2 in eachcol(df)]
heatmap(C, zlim=(-1,1), c=:heat)
C = round.(C, digits=2)
annotate!([(i,j,string(C[i,j])) for i = 1:size(C,1), j = 1:size(C,2)][:])
end
# ╔═╡ 5c03e336-0aa8-4903-97d3-25aca07809fa
md"""
# Tratamento de dados
"""
# ╔═╡ 317f7e8c-7122-4750-86ee-952c9b644aa0
md"""
## Variáveis faltantes
- Remover?
- Substituir
- Por 0 ou um valor padrão
"""
# ╔═╡ 1e0cd30a-db12-4db9-a210-f910d0e3104b
let
df = copy(data)
I = findall(ismissing.(data.idade))
df[I,:idade] .= 0
pairplot(dropmissing(df), names(df)[1:end-1], :concedido)
end
# ╔═╡ f7cdf801-0e01-465f-98ed-5d54d393d5d0
md"""
- Substituir pela média
"""
# ╔═╡ 72e069ea-b2cb-42df-9034-98415cd4e5a9
let
df = copy(data)
I = findall(ismissing.(data.idade))
df[I,:idade] .= round(Int, mean(skipmissing(data.idade)))
pairplot(dropmissing(df), names(df)[1:end-1], :concedido)
end
# ╔═╡ 3d431465-262f-410f-98da-072f8d35c443
md"""
- Subsituir por uma amostra
"""
# ╔═╡ 8ed34201-2435-47c4-84f0-00184efb073b
let
df = copy(data)
v = dropmissing(data).idade
I = findall(ismissing.(data.idade))
df[I,:idade] .= rand(v, length(I))
pairplot(dropmissing(df), names(df)[1:end-1], :concedido)
end
# ╔═╡ e32b705d-8630-4357-a384-2c743836b702
md"""
- Uma regressão em função de outra variável
"""
# ╔═╡ b1612568-53fa-451f-af21-68fadc96acc1
md"""
## Variáveis categóricas
"""
# ╔═╡ 561f95d1-93b7-43a4-99d5-dadaf5139c5b
data[!,[:estado_civil]]
# ╔═╡ 7f766d08-256e-4a42-8bb7-65a3557f37ea
md"""
**Label encoder ou Ordinal encoder**
- Cada valor é trocado por um número.
"""
# ╔═╡ 50c7a031-98b9-4013-ae31-dde63bf45baf
let
df = copy(data)
U = unique(df.estado_civil)
df[!,:estado_civil] = indexin(df.estado_civil, U)
df
end
# ╔═╡ 5a244cc7-91b3-4bd6-8607-3bb75a7d00c0
md"""
**One-hot encoding**
Supondo que existem $k$ diferentes valores, criamos $k$ colunas.
Cada coluna tem $1$ para o valor original correspondente e $0$ para os outros.
"""
# ╔═╡ f33a4dc5-23d4-459a-a1e2-c5098dee0739
let
df = copy(data[!,[1,2,4]])
U = unique(data.estado_civil)
for u in U
df[!,"estado_civil_$u"] = Int.(data.estado_civil .== u)
end
delete!(df, 2)
df
end
# ╔═╡ 4cba0f65-7225-410c-9734-909ec455c2dd
md"""
## Normalização
- Vamos rodar o KNN
"""
# ╔═╡ b9df86c3-53b5-437d-9d2b-b8049b770ced
let
n_viz = 1
df = dropmissing(data)
X = Matrix(df[!,[1,2]])
y = df.concedido
n = size(X, 1)
xg = range(extrema(X[:,1])..., length=150)
yg = range(extrema(X[:,2])..., length=150)
zg = [begin
D = [norm([xi; yi] - X[i,:]) for i = 1:n]
I = sortperm(D)
round(Int, sum(y[I[1:n_viz]]) / n_viz)
end for xi in xg, yi in yg]
contourf(xg, yg, zg', c=cgrad([:lightblue,:pink]), leg=false)
I = findall(y .== 0)
scatter!(X[I,1], X[I,2], m=(:lightblue,stroke(1,:blue),3,:circle), leg=false)
I = findall(y .== 1)
scatter!(X[I,1], X[I,2], m=(:pink,stroke(1,:red),3,:square))
end
# ╔═╡ 9b9e3858-8837-42ca-8f1b-98469a4c4bd4
md"""
- A distância vertical é muita maior que a horizontal.
- Normalização: $\tilde{x}_i = \dfrac{x_i - \mu}{\sigma}$, onde $\mu$ é a média do vetor $x$ e $\sigma$ é o desvio padrão.
- A normalização deixa o vetor $x$ com média 0 e desvio padrão 1.
- Padronização: $\tilde{x}_i = \dfrac{x_i - x_{\min}}{x_{\max} - x_{\min}}$, onde $x_{\min}$ e $x_{\max}$ são o mínimo e o máximo do vetor, respectivamente.
- A padronização deixa o vetor $x$ com valores entre $0$ e $1$.
"""
# ╔═╡ d25072a5-e161-45d5-9ea2-2a9fbe8958cc
let
n_viz = 1
df = dropmissing(data)
df.idade = normaliza(df.idade)
df.salario = normaliza(df.salario)
X = Matrix(df[!,[1,2]])
y = df.concedido
n = size(X, 1)
xg = range(extrema(X[:,1])..., length=150)
yg = range(extrema(X[:,2])..., length=150)
zg = [begin
D = [norm([xi; yi] - X[i,:]) for i = 1:n]
I = sortperm(D)
round(Int, sum(y[I[1:n_viz]]) / n_viz)
end for xi in xg, yi in yg]
contourf(xg, yg, zg', c=cgrad([:lightblue,:pink]), leg=false)
I = findall(y .== 0)
scatter!(X[I,1], X[I,2], m=(:lightblue,stroke(1,:blue),3,:circle), leg=false)
I = findall(y .== 1)
scatter!(X[I,1], X[I,2], m=(:pink,stroke(1,:red),3,:square))
end
# ╔═╡ c4d83260-04a8-4f38-b0d3-7f5eb3856e5f
md"""
## Conjunto desbalanceado
"""
# ╔═╡ f11362c7-5974-45d8-8e85-b16c586bc0a8
histogram(data.concedido, title="Concedido")
# ╔═╡ 5f31ae59-3b46-4951-ba93-ca3e44874ee0
md"""
- Cuidado com conjuntos desbalanceados.
- Preditor de classe majoritária.
- Remover dados para ficarem iguais (?).
- Repetir dados para ficarem iguais.
"""
# ╔═╡ 7d97ba98-9d7c-42c0-8278-2cd0b9fcec2b
let
df = copy(data)
y = df.concedido
n0 = sum(y .== 0)
n1 = sum(y .== 1)
I = findall(y .== 1)
append!(df, df[rand(I, n0 - n1),:])
histogram(df.concedido, title="Concedido")
end
# ╔═╡ 89bf3149-d7a8-4ca5-8964-73167f058187
let
df = copy(data)
y = df.concedido
n0 = sum(y .== 0)
n1 = sum(y .== 1)
I = findall(y .== 1)
append!(df, df[rand(I, n0 - n1),:])
pairplot(dropmissing(df), names(df)[1:end-1], :concedido)
end
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
[compat]
CSV = "~0.8.5"
Colors = "~0.12.8"
DataFrames = "~1.2.2"
Plots = "~1.20.0"
PlutoUI = "~0.7.9"
StatsPlots = "~0.14.26"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised
[[AbstractFFTs]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.0.1"
[[Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.3.1"
[[ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
[[Arpack]]
deps = ["Arpack_jll", "Libdl", "LinearAlgebra"]
git-tree-sha1 = "2ff92b71ba1747c5fdd541f8fc87736d82f40ec9"
uuid = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
version = "0.4.0"
[[Arpack_jll]]
deps = ["Libdl", "OpenBLAS_jll", "Pkg"]
git-tree-sha1 = "e214a9b9bd1b4e1b4f15b22c0994862b66af7ff7"
uuid = "68821587-b530-5797-8361-c406ea357684"
version = "3.5.0+3"
[[Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
[[AxisAlgorithms]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
git-tree-sha1 = "a4d07a1c313392a77042855df46c5f534076fab9"
uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
version = "1.0.0"
[[Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
[[Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c3598e525718abcc440f69cc6d5f60dda0a1b61e"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.6+5"
[[CSV]]
deps = ["Dates", "Mmap", "Parsers", "PooledArrays", "SentinelArrays", "Tables", "Unicode"]
git-tree-sha1 = "b83aa3f513be680454437a0eee21001607e5d983"
uuid = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
version = "0.8.5"
[[Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "e2f47f6d8337369411569fd45ae5753ca10394c6"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.0+6"
[[ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "bdc0937269321858ab2a4f288486cb258b9a0af7"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.3.0"
[[Clustering]]
deps = ["Distances", "LinearAlgebra", "NearestNeighbors", "Printf", "SparseArrays", "Statistics", "StatsBase"]
git-tree-sha1 = "75479b7df4167267d75294d14b58244695beb2ac"
uuid = "aaaa29a8-35af-508c-8bc3-b662a17a0fe5"
version = "0.14.2"
[[ColorSchemes]]
deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random"]
git-tree-sha1 = "9995eb3977fbf67b86d0a0a0508e83017ded03f2"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.14.0"
[[ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.0"
[[Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.8"
[[Compat]]
deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
git-tree-sha1 = "344f143fa0ec67e47917848795ab19c6a455f32c"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "3.32.0"
[[CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
[[Contour]]
deps = ["StaticArrays"]
git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.5.7"
[[Crayons]]
git-tree-sha1 = "3f71217b538d7aaee0b69ab47d9b7724ca8afa0d"
uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
version = "4.0.4"
[[DataAPI]]
git-tree-sha1 = "ee400abb2298bd13bfc3df1c412ed228061a2385"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.7.0"
[[DataFrames]]
deps = ["Compat", "DataAPI", "Future", "InvertedIndices", "IteratorInterfaceExtensions", "LinearAlgebra", "Markdown", "Missings", "PooledArrays", "PrettyTables", "Printf", "REPL", "Reexport", "SortingAlgorithms", "Statistics", "TableTraits", "Tables", "Unicode"]
git-tree-sha1 = "d785f42445b63fc86caa08bb9a9351008be9b765"
uuid = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
version = "1.2.2"
[[DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "7d9d316f04214f7efdbb6398d545446e246eff02"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.10"
[[DataValueInterfaces]]
git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
version = "1.0.0"
[[DataValues]]
deps = ["DataValueInterfaces", "Dates"]
git-tree-sha1 = "d88a19299eba280a6d062e135a43f00323ae70bf"
uuid = "e7dc6d0d-1eca-5fa6-8ad6-5aecde8b7ea5"
version = "0.4.13"
[[Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
[[DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
[[Distances]]
deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
git-tree-sha1 = "abe4ad222b26af3337262b8afb28fab8d215e9f8"
uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
version = "0.10.3"
[[Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
[[Distributions]]
deps = ["FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns"]
git-tree-sha1 = "3889f646423ce91dd1055a76317e9a1d3a23fff1"
uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
version = "0.25.11"
[[DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "a32185f5428d3986f47c2ab78b1f216d5e6cc96f"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.8.5"
[[Downloads]]
deps = ["ArgTools", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
[[EarCut_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "92d8f9f208637e8d2d28c664051a00569c01493d"
uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
version = "2.1.5+1"
[[Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b3bfd02e98aedfa5cf885665493c5598c350cd2f"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.2.10+0"
[[FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.1"
[[FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "LibVPX_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "3cc57ad0a213808473eafef4845a74766242e05f"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.3.1+4"
[[FFTW]]
deps = ["AbstractFFTs", "FFTW_jll", "LinearAlgebra", "MKL_jll", "Preferences", "Reexport"]
git-tree-sha1 = "f985af3b9f4e278b1d24434cbb546d6092fca661"
uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
version = "1.4.3"
[[FFTW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3676abafff7e4ff07bbd2c42b3d8201f31653dcc"
uuid = "f5851436-0d7a-5f13-b9de-f02708fd171a"
version = "3.3.9+8"
[[FillArrays]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "Statistics"]
git-tree-sha1 = "8c8eac2af06ce35973c3eadb4ab3243076a408e7"
uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
version = "0.12.1"
[[FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"
[[Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "35895cf184ceaab11fd778b4590144034a167a2f"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.1+14"
[[Formatting]]
deps = ["Printf"]
git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
version = "0.4.2"
[[FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "cbd58c9deb1d304f5a245a0b7eb841a2560cfec6"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
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[[FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
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version = "1.0.10+0"
[[Future]]
deps = ["Random"]
uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
[[GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
git-tree-sha1 = "dba1e8614e98949abfa60480b13653813d8f0157"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.5+0"
[[GR]]
deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
git-tree-sha1 = "182da592436e287758ded5be6e32c406de3a2e47"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
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[[GR_jll]]
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git-tree-sha1 = "d59e8320c2747553788e4fc42231489cc602fa50"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
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[[GeometryBasics]]
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git-tree-sha1 = "58bcdf5ebc057b085e58d95c138725628dd7453c"
uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
version = "0.4.1"
[[Gettext_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
version = "0.21.0+0"
[[Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "7bf67e9a481712b3dbe9cb3dac852dc4b1162e02"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.68.3+0"
[[Grisu]]
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uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"
[[HTTP]]
deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
git-tree-sha1 = "44e3b40da000eab4ccb1aecdc4801c040026aeb5"
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[[IniFile]]
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[[IntelOpenMP_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d979e54b71da82f3a65b62553da4fc3d18c9004c"
uuid = "1d5cc7b8-4909-519e-a0f8-d0f5ad9712d0"
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"]
git-tree-sha1 = "61aa005707ea2cebf47c8d780da8dc9bc4e0c512"
uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
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[[InvertedIndices]]
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uuid = "41ab1584-1d38-5bbf-9106-f11c6c58b48f"
version = "1.0.0"
[[IterTools]]
git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
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[[IteratorInterfaceExtensions]]
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uuid = "82899510-4779-5014-852e-03e436cf321d"
version = "1.0.0"
[[JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.3.0"
[[JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "8076680b162ada2a031f707ac7b4953e30667a37"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.2"
[[JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.0+0"
[[KernelDensity]]
deps = ["Distributions", "DocStringExtensions", "FFTW", "Interpolations", "StatsBase"]
git-tree-sha1 = "591e8dc09ad18386189610acafb970032c519707"
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"
version = "2.10.1+0"
[[LaTeXStrings]]
git-tree-sha1 = "c7f1c695e06c01b95a67f0cd1d34994f3e7db104"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.2.1"
[[Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"]
git-tree-sha1 = "a4b12a1bd2ebade87891ab7e36fdbce582301a92"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.15.6"
[[LazyArtifacts]]
deps = ["Artifacts", "Pkg"]
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"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
[[LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
[[LibVPX_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "12ee7e23fa4d18361e7c2cde8f8337d4c3101bc7"
uuid = "dd192d2f-8180-539f-9fb4-cc70b1dcf69a"
version = "1.10.0+0"
[[Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
[[Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "761a393aeccd6aa92ec3515e428c26bf99575b3b"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.2+0"
[[Libgcrypt_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
version = "1.8.7+0"
[[Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.3.0+3"
[[Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.42.0+0"
[[Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.16.1+1"
[[Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.35.0+0"
[[Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.3.0+0"
[[Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.36.0+0"
[[LinearAlgebra]]
deps = ["Libdl"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
[[LogExpFunctions]]
deps = ["DocStringExtensions", "LinearAlgebra"]
git-tree-sha1 = "7bd5f6565d80b6bf753738d2bc40a5dfea072070"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.2.5"
[[Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
[[MKL_jll]]
deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
git-tree-sha1 = "c253236b0ed414624b083e6b72bfe891fbd2c7af"
uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
version = "2021.1.1+1"
[[MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "0fb723cd8c45858c22169b2e42269e53271a6df7"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.7"
[[Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
[[MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.0.3"
[[MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
[[Measures]]
git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.1"
[[Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "4ea90bd5d3985ae1f9a908bd4500ae88921c5ce7"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.0.0"
[[Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"
[[MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
[[MultivariateStats]]
deps = ["Arpack", "LinearAlgebra", "SparseArrays", "Statistics", "StatsBase"]
git-tree-sha1 = "8d958ff1854b166003238fe191ec34b9d592860a"
uuid = "6f286f6a-111f-5878-ab1e-185364afe411"
version = "0.8.0"
[[NaNMath]]
git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "0.3.5"
[[NearestNeighbors]]
deps = ["Distances", "StaticArrays"]
git-tree-sha1 = "16baacfdc8758bc374882566c9187e785e85c2f0"
uuid = "b8a86587-4115-5ab1-83bc-aa920d37bbce"
version = "0.4.9"
[[NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
[[Observables]]
git-tree-sha1 = "fe29afdef3d0c4a8286128d4e45cc50621b1e43d"
uuid = "510215fc-4207-5dde-b226-833fc4488ee2"
version = "0.4.0"
[[OffsetArrays]]
deps = ["Adapt"]
git-tree-sha1 = "c0f4a4836e5f3e0763243b8324200af6d0e0f90c"
uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.10.5"
[[Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.5+0"
[[OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
[[OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]