### A Pluto.jl notebook ###
# v0.18.2

using Markdown
using InteractiveUtils

# ╔═╡ 348236ba-8a69-11ec-23a2-3d09e5fc86f2
begin
	using Downloads
	using ARFFFiles
	using ScientificTypes
	using DataFrames
	import StatsBase
	using MLJ
	using MLJDecisionTreeInterface
	using Plots
	using PlutoUI
end

# ╔═╡ d91ebf78-571b-43a6-a091-29c53ed671a3
using AbstractTrees

# ╔═╡ 5825f015-5688-4a8b-8b1b-927f5289bae4
using GraphRecipes

# ╔═╡ 0ffb6837-d03f-421c-8e1f-d5d5142c1621
html"""
<div style="
position: absolute;
width: calc(100% - 30px);
border: 50vw solid SteelBlue;
border-top: 500px solid SteelBlue;
border-bottom: none;
box-sizing: content-box;
left: calc(-50vw + 15px);
top: -500px;
height: 300px;
pointer-events: none;
"></div>

<div style="
height: 300px;
width: 100%;
background: SteelBlue;
color: #88BBD6;
padding-top: 68px;
padding-left: 5px;
">

<span style="
font-family: Vollkorn, serif;
font-weight: 700;
font-feature-settings: 'lnum', 'pnum';
"> 

<p style="
font-family: Alegreya sans;
font-size: 1.4rem;
font-weight: 300;
opacity: 1.0;
color: #CDCDCD;
">Machine Learning using Julia and its ecosystem</p>
<p style="text-align: left; font-size: 2.8rem;">
If things are not 'ready to use' (Part III)
</p>

<p style="
font-family: 'Alegreya Sans'; 
font-size: 0.7rem; 
font-weight: 300;
color: #CDCDCD;">

&copy  Dr. Roland Schätzle
</p>
"""

# ╔═╡ 26fe03ce-2744-4a83-8db6-cfa1267dfa81
PlutoUI.TableOfContents(title = "Using a Decision Tree")

# ╔═╡ 4d7fd8ec-9e6f-4d35-8620-9482225951d0
md"""
## Setting up the environment
"""

# ╔═╡ ef618961-3223-4024-b797-79fa1364e0d2
begin
	glass_file = Downloads.download(
		"http://storm.cis.fordham.edu/~gweiss/data-mining/weka-data/glass.arff")
	glass = ARFFFiles.load(DataFrame, glass_file);
end

# ╔═╡ d2863600-a745-43f3-827e-217b27d96fab
begin
	yGlass, XGlass = unpack(glass, ==(:Type), rng = 123)
	MyDecisionTree = @load DecisionTreeClassifier pkg="DecisionTree"
	dc = MyDecisionTree()
	(Xtrain, Xtest), (ytrain, ytest) = 
		partition((XGlass, yGlass), 0.7, multi = true, rng = 123)
	dc.max_depth = 3
	dc_mach = machine(dc, Xtrain, ytrain)
	fit!(dc_mach)
end

# ╔═╡ 3fa6c643-25c0-4490-8590-d0268e918421
md"""
# If things are not 'ready to use'
"""

# ╔═╡ 44f81e6d-4b4b-448b-8aa5-068c1b60e18c
md"""
The output of `print_tree()` in part II of the tutorial gives an impression of how the decision tree looks like ... but to be honest, it's a bit rudimentary: It's just ASCII-text and the nodes shwo only the attribute number, not the attribute name which is used for branching.

Wouldn't it be nice, to have a graphical depiction with more information? As there is no ready to use function for this purpose, we have to look on how this can be achieved using other means in the Julia ecosystem.
"""

# ╔═╡ 86bc822a-7616-4958-8d20-4b4efde2932e
md"""
## The building blocks
"""

# ╔═╡ e5261c62-d2f7-4fa0-ab2b-68db4bda6d24
md"""
What do we need to implement this by ourselves? Well, the following ingredients are surely the main building blocks:
1. The decision tree itself (the data structure)
2. Information about how this data structure looks like (internally)
3. A graphics package with the ability to plot trees

... and of course an idea, on how to glue these things together :-)
"""

# ╔═╡ 359b851e-2cd3-4bbd-b502-8266c46f42fb
md"""
### 1. The decision tree
"""

# ╔═╡ 965c5a42-de7c-4f2d-b914-039ae171f81f
md"""
The MLJ function `fitted_params()` delivers for each trained machine all the parameters which result from training. Of course this depends heavily on the model used. In case of a decision tree classifier one of these parameters is simply the tree itself:
"""

# ╔═╡ bcdb446c-43bf-4d3a-af37-7a895117de8c
fp = fitted_params(dc_mach)

# ╔═╡ 4d9e6b5c-4822-4c1c-a12c-15f21158e44b
typeof(fp.tree)

# ╔═╡ 6c07c132-94c7-4fb8-acbf-1e5787dac13a
md"""
### 2. Information about the data structure
"""

# ╔═╡ 8a37cdb4-0ff7-42f8-8c62-5888cc16515b
md"""
In order to get some information about the internal structure of the decision tree, we have to look at the source code of the `DecisionTree.jl` [package](https://github.com/bensadeghi/DecisionTree.jl/blob/468720922bc18bda751bf937b03cac3d26247bbd/src/DecisionTree.jl) on GitHub.

There we find the following definitions for `Leaf` and `Node`:

```Julia
struct Leaf{T}
    majority :: T
    values   :: Vector{T}
end

struct Node{S, T}
    featid  :: Int
    featval :: S
    left    :: Union{Leaf{T}, Node{S, T}}
    right   :: Union{Leaf{T}, Node{S, T}}
end
```


"""

# ╔═╡ 4379bbca-9029-4687-9349-b5c9571cd104
md"""
I.e. the tree structure is made up of `Node`s which store the number of the feature which is used for branching (`featid`) at that node and the threshold (`featval`) at which the branching took place. In addition each node has a `left` and a `right` subtree which is again a `Node` or a `Leaf` (if the bottom of the tree is reached).

The `Leaf`s know the majority class (`majority`) which will be predicted when reaching this leaf as well as a list of all target values (`values`) that have been classified into this leaf.
"""

# ╔═╡ 6dafc7d0-7fed-4012-a9f0-bf249466b6cd
md"""
### 3. A graphics package
"""

# ╔═╡ 12e68c64-bc54-4f53-8d8a-57981fbcb866
md"""
The Julia graphics package [`Plots.jl`](https://github.com/JuliaPlots/Plots.jl) by itself isn't capable of plotting trees. But there is a 'helper' package called [`GraphRecipes.jl`](https://github.com/JuliaPlots/GraphRecipes.jl) which contains several so-called plotting recipes. These are specifications which describe how different graph structures can be plotted using `Plots` (or another graphics package). Among other recipes, there is one for [trees](https://docs.juliaplots.org/stable/graphrecipes/examples/#AbstractTrees-Trees) (called `TreePlot`). 

The `GraphRecipes` serve also as an abstraction layer between a structure to be plotted and a graphics package that does the plotting.
"""

# ╔═╡ ceb43211-4f01-47b0-9d27-81d03de3fdfb
md"""
## Bringing it all together
"""

# ╔═╡ 2a93ef90-5495-422a-9550-956610e312d5
md"""
### The basic concepts
"""

# ╔═╡ 4488c8e6-feeb-4258-8d36-f5b0886b0fda
md"""
As we have the main building blocks identified now, the question remains of how we can fit these things together, to obtain the desired result. The main question is: How does the plot recipe `TreePlot` know, what our decision tree looks like in detail, so that it can be plotted by `TreePlot`? Both packages (`DecisionTree.jl` and `GraphRecipes.jl`) have been developed independently. They don't know anything about each other.

The documentation of `TreePlot` tells us, that it expects a structure of type `AbstractTree` (from the package [`AbstractTree.jl`](https://github.com/JuliaCollections/AbstractTrees.jl). But a decision tree from the `DecisionTree.jl` package doesn't conform to this type. So are we stuck now?

We would be stuck, if we were using an 'ordinary' object-oriented language. In this case we could perhaps try to define a new class which inherits from `Node` as well as from `AbstractTree`. But that works only, if the language supports multiple inheritance. If not, we could try to define a new class which inherits from `AbstractTree` and wrap somehow the `Node` and `Leaf` structures inside. All of this involves probably quite a bit of work and doesn't seem to be an elegant solution.

Fortunately we use Julia. Here we only have to (re-)define a few functions from `AbstractTree` on our decision tree, that makes it *look like* an `AbstractTree`. The `TreePlot` recipe expects only a specific *behaviour* from our decision tree (it really doesn't care about the type of this data structure): It wants the tree to have
- a function `children(t)` that, when applied to the tree `t` (or to a node of the tree), returns a list of its subtrees
- and a function `printnode(io::IO, node)` that prints a representation of the node `node` to the output stream `io`. 

That's all we need. Then the decision tree conforms to an `AbstractTree` (as far as `TreePlot` is concerned). So let's do it:
"""

# ╔═╡ 476c8e3c-b11f-4451-9256-de9a99d3689f
md"""
### A first and simple implementation
"""

# ╔═╡ 571a4abc-c9e8-47ab-99f8-e8f62e648228
md"""
As we will use some type and function definitions from the packages `DecisionTree` and `AbstractTree`, we have to declare their usage.
"""

# ╔═╡ 2951f22e-99e7-40f9-be2c-3972e8ff47c9
import DecisionTree

# ╔═╡ 89d53141-0675-40ac-8c2b-dd8d9c24b826
md"""
The implementation of `children` is a simple one-line function:
"""

# ╔═╡ e1ff9b54-583b-40c1-b6a7-87711ca47f16
AbstractTrees.children(node::DecisionTree.Node) = (node.left, node.right)

# ╔═╡ 0aa2e192-5443-44ce-a49f-0f5ee435465c
md"""
For printing we have to differentiate between nodes and leafs, because the output of a node looks different from that of a leaf. In most programming languages we would need an implementation that checks the type of the node/leaf to be printed and use an `if ... then ... else`-statement in this case.

Not so in Julia! Here we can use its multiple dispatch capability and implement two versions of `printnode`: One for `Node`s and another one for `Leaf`s. Julia chooses automatically the correct one, depending on the type of the second parameter.
"""

# ╔═╡ 1099149e-1988-40b5-913c-11966285e840
AbstractTrees.printnode(io::IO, node::DecisionTree.Node) = 
	print(io, "Feature: ", node.featid, " - Threshold: ", node.featval)

# ╔═╡ ef4ae455-784a-414a-84f5-85cccf4455da
AbstractTrees.printnode(io::IO, leaf::DecisionTree.Leaf) =
	print(io, "maj: ", leaf.majority, " - vals: ", length(leaf.values))

# ╔═╡ a77fff5a-dd21-4254-96a6-f7181625123b
md"""
Here we have chosen a very simple implementation for `printnode` as a first step. The version for `Node` prints the same information as does the built-in `print_tree()` which we've used above (the ID of the feature and the threshold). The variant for `Leaf` is even simpler: It prints the ID of the predicted class and the number of values under consideration in this leaf.
"""

# ╔═╡ b6179be1-30bc-473c-8fc9-8320192f42e4
md"""
The `AbstractTree.jl` package also has a function `print_tree` which does a text based output of a tree using the two functions we've implemented above. Let's use `AbstractTree.print_tree` to test our first implementation:
"""

# ╔═╡ a14c820c-e57b-4307-a96a-9891f3c9a0df
AbstractTrees.print_tree(fp.tree)

# ╔═╡ a4ef1944-b093-4c90-9c2e-8bfa45b29798
md"""
Looks pretty good and all values correspond to the ones in our first printout of the decision tree above. So the implementation seems to work flawlessly!
"""

# ╔═╡ 8e85e7f5-350a-4a85-8877-b2a512c8b814
md"""
And now the graphical representation using `Plots` and `GraphRecipes`: As we already have implemented the necessary functions, we can just call `plot` using a `TreePlot`. That's it!
"""

# ╔═╡ d48b106b-1921-4594-bea7-c9f2bee6cef5
plt = plot(TreePlot(fp.tree), method = :buchheim, markeralpha = 0.5, root = :left,
		nodeshape = :rect, curves = false, shorten = 0.1, fontsize = 12,
		size = (1200, 1200))

# ╔═╡ 85edb2ff-a933-47f0-89d4-676002fdb65b
md"""
### Fine tuning the output
"""

# ╔═╡ 5776968d-0f54-41e8-ba6e-5e29f16febb8
md"""
In the next step we want a tree which shows feature *names* on its nodes and the *names* of the predicted classes on its leafs (instead of the IDs used before). Unfortunately a `DecisionTree` doesn't know this information at all. I.e. we have to add that information somehow so that they can be used by the mechanisms applied in the last section.
"""

# ╔═╡ 95bb56c0-9604-40b2-962e-134348eedc98
md"""
The idea is to add this information while traversing the decision tree using `children`, so that `printnode` has access to it. That's the only place where we need this information. There is no need to change the decision tree structures in any way.

So, instead of returning the `Node` and `Leaf` structures from `DecisionTree` directly, `children` will return enriched structures with added information. These enriched structures are defined as follows:
"""

# ╔═╡ 65f2c840-369b-406a-b9d9-81f8f32990cc
struct NamedNode{S, T} 
	info :: NamedTuple
	dt_node :: Union{DecisionTree.Node{S, T}, DecisionTree.Leaf{T}}
end

# ╔═╡ fb689ff3-1906-4043-be75-d94f9e84990c
struct NamedLeaf{T}
	info :: NamedTuple
	dt_leaf :: DecisionTree.Leaf{T}
end

# ╔═╡ 632668d6-bdc3-492b-a028-ec97601329b0
md"""
The attribute `info` within these new `struct`s may contain any information we like to show on the printed tree. `dt_node` and `dt_leaf` are simply the decision tree elements we already used before.
"""

# ╔═╡ cd25e531-a82e-4dd9-b5fc-10278680ee44
md"""
In order to create these enriched structures on each call of `children`, we define a function `wrap_element` with two implementations: One to create a `NamedNode` and a second one to create a `NamedLeaf`. This is another situation where we rely on the multiple dispatch mechanism of Julia. Depending on the type of the second argument (a `Node` or a `Leaf`) the correct method will be chosen.
"""

# ╔═╡ 5adac17a-d13b-4759-a3d1-3a5364ae0746
wrap_element(infos::NamedTuple, dt_node::DecisionTree.Node) = 		
	NamedNode(infos, dt_node)

# ╔═╡ 1345a07d-1b73-4257-b15d-9b1e6fcfc19e
wrap_element(infos::NamedTuple, dt_leaf::DecisionTree.Leaf) = 			
	NamedLeaf(infos, dt_leaf)

# ╔═╡ e57d3aa8-4d2d-4595-886d-234c1d7d44db
md"""
This makes the implementation of our new `children` function quite easy: Just two calls to `makeNamedElement`, where we add the attribute names and the class names as parameters (as a `NamedTuple`; a Julia standard type which comes in handy here).
"""

# ╔═╡ f62753ae-5746-41b3-975c-75f6c2ba7e14
AbstractTrees.children(node::NamedNode) = (
	wrap_element((atr = names(XGlass), cls = levels(yGlass)), node.dt_node.left), 
	wrap_element((atr = names(XGlass), cls = levels(yGlass)), node.dt_node.right)
)

# ╔═╡ 090871c6-63ad-4c10-af20-ce3b25cd3337
md"""
The implementations of `printnode` receive now a `NamedNode` or a `NamedLeaf` and can use the information within these elements for printing:
"""

# ╔═╡ 27ea6187-2303-4ca5-8acd-b9f9600acb5d
function AbstractTrees.printnode(io::IO, node::NamedNode)
	print(io, node.info.atr[node.dt_node.featid], " → ", node.dt_node.featval)
end

# ╔═╡ 98fe2763-00e7-4f8a-9b8f-da58cf56facc
function AbstractTrees.printnode(io::IO, leaf::NamedLeaf)
	matches     = findall(leaf.dt_leaf.values .== leaf.dt_leaf.majority)
	match_count = length(matches)
	val_count   = length(leaf.dt_leaf.values)
	print(io, leaf.info.cls[leaf.dt_leaf.majority], " ($match_count/$val_count)")
end

# ╔═╡ 387185f5-50a4-4b6b-9f2e-31f38dd190b3
md"""
`matches` are the instances which have been correctly classified on this leaf (out of all instances on this leaf in `values`).
"""

# ╔═╡ b63e004a-6e6f-4591-abc0-a3e26c684fdf
md"""
Now we can create a `NamedNode` for the root of the decision tree and use it for printing. First using `print_tree` and then using `plot` with the `TreePlot` recipe to obtain the desired result.
"""

# ╔═╡ eb824384-08fd-4071-9b51-4da8e85bc2ea
nn = NamedNode((atr = names(XGlass), cls = levels(yGlass)), fp.tree)

# ╔═╡ 36dedce2-2763-4d17-ac4c-d5480538fb51
AbstractTrees.print_tree(nn)

# ╔═╡ 74a38c54-ccca-430d-b4cc-3f54dbee9a23
plt2 = plot(TreePlot(nn), method = :buchheim, root = :left, nodeshape = :rect, 
		markeralpha = 0.5, fontsize = 12, nodesize = 0.1, 
		curves = false, shorten = 0.1,
		size = (1200, 1200))

# ╔═╡ 3cc12cde-20cf-4527-a8b4-441ccaebd618
md"""
And finally a few explanations about the parameters used in the call to `plot`:
- `method`, `root` and `nodeshape` are the basic parameters, which choose the layout algorithm (`buchheim`), the orientation of the tree (`left` = from left to right) and the shape of the nodes (`rect` = rectangles).
- the remaining parameters are just for beautifying the tree:
  - a `markeralpha` of 0.5 gives the nodes a bit of transparency
  - `fontsize` sets the size of the font (a bit larger than the default)
  - a `nodesize` of 0.1 makes the nodes a bit larger than the default
  - with `curves = false` we get straight lines between the nodes
  - `shorten` avoids that the connecting lines interfere with the contents of the nodes
  - `size` sets the resolution for the plot.
"""

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deps = ["Random", "Rmath_jll"]
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[[deps.Rmath_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "68db32dff12bb6127bac73c209881191bf0efbb7"
uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f"
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[[deps.SHA]]
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[[deps.ScientificTypes]]
deps = ["CategoricalArrays", "ColorTypes", "Dates", "Distributions", "PrettyTables", "Reexport", "ScientificTypesBase", "StatisticalTraits", "Tables"]
git-tree-sha1 = "ba70c9a6e4c81cc3634e3e80bb8163ab5ef57eb8"
uuid = "321657f4-b219-11e9-178b-2701a2544e81"
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[[deps.ScientificTypesBase]]
git-tree-sha1 = "a8e18eb383b5ecf1b5e6fc237eb39255044fd92b"
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[[deps.ScikitLearnBase]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "7877e55c1523a4b336b433da39c8e8c08d2f221f"
uuid = "6e75b9c4-186b-50bd-896f-2d2496a4843e"
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[[deps.Scratch]]
deps = ["Dates"]
git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
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[[deps.Serialization]]
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[[deps.SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[deps.Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
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[[deps.SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
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[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
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[[deps.SparseArrays]]
deps = ["LinearAlgebra", "Random"]
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[[deps.SpecialFunctions]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "5ba658aeecaaf96923dce0da9e703bd1fe7666f9"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.1.4"

[[deps.StableRNGs]]
deps = ["Random", "Test"]
git-tree-sha1 = "3be7d49667040add7ee151fefaf1f8c04c8c8276"
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[[deps.StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "6976fab022fea2ffea3d945159317556e5dad87c"
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[[deps.StatisticalTraits]]
deps = ["ScientificTypesBase"]
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version = "3.0.0"

[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "c3d8ba7f3fa0625b062b82853a7d5229cb728b6b"
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[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "8977b17906b0a1cc74ab2e3a05faa16cf08a8291"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
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[[deps.StatsFuns]]
deps = ["ChainRulesCore", "HypergeometricFunctions", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
git-tree-sha1 = "25405d7016a47cf2bd6cd91e66f4de437fd54a07"
uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
version = "0.9.16"

[[deps.StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "57617b34fa34f91d536eb265df67c2d4519b8b98"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.5"

[[deps.SuiteSparse]]
deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.0"

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

[[deps.Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "OrderedCollections", "TableTraits", "Test"]
git-tree-sha1 = "5ce79ce186cc678bbb5c5681ca3379d1ddae11a1"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.7.0"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.0"

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

[[deps.TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.6"

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

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

[[deps.UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

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

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.UnicodePlots]]
deps = ["Contour", "Crayons", "Dates", "LinearAlgebra", "MarchingCubes", "NaNMath", "SparseArrays", "StaticArrays", "StatsBase", "Unitful"]
git-tree-sha1 = "1785494cb9484f9ab05bbc9d81a2d4de4341eb39"
uuid = "b8865327-cd53-5732-bb35-84acbb429228"
version = "2.9.0"

[[deps.Unitful]]
deps = ["ConstructionBase", "Dates", "LinearAlgebra", "Random"]
git-tree-sha1 = "b649200e887a487468b71821e2644382699f1b0f"
uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
version = "1.11.0"

[[deps.Unzip]]
git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.1.2"

[[deps.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"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.25.0+0"

[[deps.WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.5"

[[deps.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"

[[deps.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"

[[deps.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"

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

[[deps.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"

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

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

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

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

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

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.12+1"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.2+0"

[[deps.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"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "4.0.0+0"

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

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

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.41.0+1"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "16.2.1+1"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

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

[[deps.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:
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