notebook_juliacon2022.jl

### A Pluto.jl notebook ###
# v0.19.9

using Markdown
using InteractiveUtils

# ╔═╡ eb67a960-b8a9-4dee-b51d-8202934cab2c
begin
    using AlgebraOfGraphics
    using BenchmarkTools
    using CairoMakie
    using DataFrames
    using JuMP
    using ProgressLogging
    using Random
    using SparseVariables
end

# ╔═╡ 907fdf86-ec90-11ec-1e2e-97884202e0e6
html"""<button onclick=present()>Present</button"""

# ╔═╡ 3a58880b-d505-4149-bb09-e2658147adc8
md"# SparseVariables.jl
###  Efficient sparse modelling with JuMP
Lars Hellemo & Truls Flatberg, SINTEF
"

# ╔═╡ b9886259-16e7-4704-9560-05011abe3227
md"# About Us
* [SINTEF](https://www.sintef.no/en/) is one of Europe’s largest independent research organisations (~2200 employees).
* Department of [Sustainable Energy](https://www.sintef.no/en/industry/topics/sustainable-energy/) Technology, optimization group
* MILP optimization (mostly modelling) for different sectors:
  - Supply chain optimization
  - Energy systems
  - Health care
  - Sustainability
* Historically used proprietary modelling languages (Mosel, AMPL, OPL, GAMS)
* Moving to more open source alternatives, more and more JuMP/Julia
* Several other exciting project using Julia ongoing
"

# ╔═╡ 1ee0b191-292c-4c6d-9e4f-7304fd7d57a6
md"# Motivation
* We love Julia and JuMP for all the usual reasons
  - fast
  - expressive
  - elegant
  - **fun**
  - **hackable**
* Commercial modeling languages are very efficient for:
  - **sparse structures**
  - **large models**
* JuMP performance and usability snags 
* Workarounds are verbose and lacking functionality
* Can we improve the situation?
"

# ╔═╡ 5ed6f654-e73f-4bb7-a2fe-ce22cf2fc1d4
md" 
# An Illustrating Example
We will illustrate some modelling approches using a simple supply chain problem. Consider a company that produces a large selection of different products and sells these to geographically dispersed customers. The company has several factories that can produce each product and they need a decision support system that helps them in deciding which factory should service each customer order. 

Let $P$ denote the set of products, $F$ the factories, $C$ the customers and $T$ the set of time periods. We are given the customer demand, $D_{c,p,t}$, for some combinations of customers, products and periods and want to find how this demand should be assigned to one or more factories in a cost optimal way. Introducing non-negative decision variables $x_{f,p,c,t}$, this corresponds to 

$\sum_{f} x_{f,p,c,t} = D_{c,p,t}.$

In addition to fulfilling demand there are constraints on the feasible solutions. Each factory has an upper limit on total production per period

$\sum_{c,p} x_{f,p,c,t} \le U_{f,t}.$

For some of combinations of factory and customer there can be an upper limit $V_{f,c}$ on the transport capacity per time period

$\sum_{p} x_{f,p,c,t} \le V_{f,c}.$

Finally, not all factories can produce every product. Let $W_{f,p}$ be a parameter with value 1 if the factory $f$ can produce product $p$ and 0 otherwise. Then we have that

$W_{f,p} = 0 \implies x_{f,p,c,t} = 0.$
"

# ╔═╡ d415dbdc-c7c4-400d-8546-23bfa0222bad
md"## Standard (Naïve) Approach
* Don't worry about the extra variables and constraints, presolve will take care of it
"

# ╔═╡ fa24bb0d-7050-4a1c-bbd0-f44ce4f3527b
function model_standard(F, C, P, T, D, U, V, W)
    m = Model()
    @variable(m, x[F, C, P, T] ≥ 0)

    for f in F, c in C, p in P, t in T
        @constraint(m, sum(x[f, c, p, t] for f in F) == get(D, (c, p, t), 0.0))
    end

    for f in F, t in T
        @constraint(m, sum(x[f, c, p, t] for c in C, p in P) ≤ U[f, t])
    end

    for (f, c) in keys(V), t in T
        @constraint(m, sum(x[f, c, p, t] for p in P) ≤ V[f, c])
    end

    for f in F, c in C, p in P, t in T
        if W[f, p] == 0
            @constraint(m, x[f, c, p, t] == 0)
        end
    end

    return m
end

# ╔═╡ f3612117-732c-41c6-a85a-7b38dae49ab8
md"## Using Base Dict
* Widely used workaround
* Create anonymous variables and put in Dict
* Verbose
* Subsetting is awkward
"

# ╔═╡ 935153cb-f77b-443f-941d-52674502e7b7
function model_dict(F, C, P, T, D, U, V, W)
    m = Model()

    # Variable creation
    x = Dict()
    for (c, p, t) in keys(D), f in F
        if W[f, p] == 1
            x[f, c, p, t] = @variable(m, lower_bound = 0)
        end
    end

    # Constraint setup
    indices = [(f, c, p, t) for (c, p, t) in keys(D), f in F if W[f, p] == 1]

    # Customer demand
    for (c̄, p̄, t̄) in keys(D)
        @constraint(
            m,
            sum(
                x[f, c, p, t] for (f, c, p, t) in
                filter(i -> i[2] == c̄ && i[3] == p̄ && i[4] == t̄, indices)
            ) == D[c̄, p̄, t̄]
        )
    end

    # Production capacity
    for (f̄, t̄) in keys(U)
        @constraint(
            m,
            sum(
                x[f, c, p, t] for
                (f, c, p, t) in filter(i -> i[1] == f̄ && i[4] == t̄, indices)
            ) ≤ U[f̄, t̄]
        )
    end

    # Transport capacity
    for (f̄, c̄) in keys(V), t̄ in T
        @constraint(
            m,
            sum(
                x[f, c, p, t] for (f, c, p, t) in
                filter(i -> i[1] == f̄ && i[2] == c̄ && i[4] == t̄, indices)
            ) ≤ V[f̄, c̄]
        )
    end

    return m
end

# ╔═╡ f7da2625-887d-46fe-b159-4fa6d89d61e5
md"## Index using Tuples
* Alternative workaround
* Bundle indices into tuples
* Also reasonably efficient
* Subsetting is awkward
"

# ╔═╡ 0fa9dc20-0cef-41b0-ac03-98031e18db7d
function model_index(F, C, P, T, D, U, V, W)
    m = Model()

    # Variable creation
    indices = [(f, c, p, t) for (c, p, t) in keys(D), f in F if W[f, p] == 1]
    @variable(m, x[indices] ≥ 0)

    # Constraint setup

    # Customer demand
    for (c̄, p̄, t̄) in keys(D)
        @constraint(
            m,
            sum(
                x[(f, c, p, t)] for (f, c, p, t) in
                filter(i -> i[2] == c̄ && i[3] == p̄ && i[4] == t̄, indices)
            ) == D[c̄, p̄, t̄]
        )
    end

    # Production capacity
    for (f̄, t̄) in keys(U)
        @constraint(
            m,
            sum(
                x[(f, c, p, t)] for
                (f, c, p, t) in filter(i -> i[1] == f̄ && i[4] == t̄, indices)
            ) ≤ U[f̄, t̄]
        )
    end

    # Transport capacity
    for (f̄, c̄) in keys(V), t in T
        @constraint(
            m,
            sum(
                x[(f, c, p, t)] for (f, c, p, t) in
                filter(i -> i[1] == f̄ && i[2] == c̄ && i[4] == t, indices)
            ) ≤ V[f̄, c̄]
        )
    end

    return m
end

# ╔═╡ f6bf3148-b32a-48e9-bfa7-c4a16d72fceb
md"## Incremental constraint building
* Build LHS incrementally
* Harder to write
* Harder to read
* Best performance
* Sacrificing convenience
"

# ╔═╡ a14714b1-8993-47af-ad61-1a715c7f58c9
function model_incremental(F, C, P, T, D, U, V, W)
    m = Model()

    # Variable creation
    x = Dict()
    for (c, p, t) in keys(D), f in F
        if W[f, p] == 1
            x[f, c, p, t] = @variable(m, lower_bound = 0)
        end
    end

    # Constraint setup
    pcap = Dict((f, t) => AffExpr() for (f, t) in keys(U))
    cdem = Dict((c, p, t) => AffExpr() for (c, p, t) in keys(D))
    tcap = Dict((f, c, t) => AffExpr() for (f, c) in keys(V), t in T)

    for (f, c, p, t) in keys(x)
        var = x[f, c, p, t]
        if (c, p, t) in keys(D)
            JuMP.add_to_expression!(cdem[c, p, t], var)
        end
        if (f, t) in keys(U)
            JuMP.add_to_expression!(pcap[f, t], var)
        end
        if (f, c) in keys(V)
            JuMP.add_to_expression!(tcap[f, c, t], var)
        end
    end

    # Customer demand
    for (c, p, t) in keys(D)
        @constraint(m, cdem[c, p, t] == D[c, p, t])
    end

    # Production capacity
    for (f, t) in keys(U)
        @constraint(m, pcap[f, t] ≤ U[f, t])
    end

    # Transport capacity
    for (f, c) in keys(V), t in T
        @constraint(m, tcap[f, c, t] ≤ V[f, c])
    end

    return m
end

# ╔═╡ c2ace375-5854-48f6-a6af-68b7d91fc788
md"
## Using SparseVariables.jl
* Dictionaries.jl under the hood
* Expressive
* Convenient
  - Easy to construct sparse variables
  - Incremental building of variables possible
  - Slicing
"

# ╔═╡ ee5ef191-abbe-400b-a172-315873325903
function model_sparse(F, C, P, T, D, U, V, W)
    m = Model()

    # Variable creation
    @sparsevariable(m, x[factory, customer, product, period])

    for f in F, (c, p, t) in keys(D)
        if W[f, p] == 1
            insertvar!(x, f, c, p, t)
        end
    end

    # Constraint creation

    # Customer demand
    for (c, p, t) in keys(D)
        @constraint(m, sum(x[:, c, p, t]) == D[c, p, t])
    end

    # Production capacity
    for (f, t) in keys(U)
        @constraint(m, sum(x[f, :, :, t]) ≤ U[f, t])
    end

    # Transport capacity
    for (f, c) in keys(V), t in T
        @constraint(m, sum(x[f, c, :, t]) ≤ V[f, c])
    end

    return m
end

# ╔═╡ a25b747b-705a-4cf6-abaa-11d2f1f76272
md"# Increasing problem size
* Increase number of customers (NC)
"

# ╔═╡ 3f883297-9ded-4619-9a92-e6e0ad1e87f7
md"# Varying Sparsity
* Increase probability DP that there is demand from a customer $c$ for product $p$ in time period $t$
"

# ╔═╡ ea9e775e-e25a-46af-b2b4-a29366831b12
md"# Check [SparseVariables.jl](https://github.com/hellemo/SparseVariables.jl) out
* Hope it can be useful
* Experiment with functionality
* Play with performance
* Feedback and PRs are welcome!
* Steal and improve our ideas 😄
"

# ╔═╡ 0a181426-a19f-4c94-a2e3-32d0d48d03d0
md"## "

# ╔═╡ 9d8b6754-1c49-4f4f-b1ad-f5d8eac427c1

# ╔═╡ 4376b3c0-d008-49f3-8b28-d22f6a30324c
md"
# 
# 
"

# ╔═╡ d69fd813-4316-49d5-87d3-dcf50f2c34f0
function create_test(
    nf,
    nc,
    np,
    nt;
    demandprob = 0.05,
    prodprob = 0.2,
    flowprob = 0.8,
    seed = 42,
)
    Random.seed!(seed)
    F = collect(1:nf)
    C = collect(1:nc)
    P = collect(1:np)
    T = collect(1:nt)
    shuffled = shuffle([(c, p, t) for c in C, p in P, t in T])
    D = Dict(
        (c, p, t) => rand() for
        #c in C, p in P, t in T if rand() < demandprob
        (c, p, t) in
        sort(first(shuffled, Int(ceil(demandprob * length(shuffled)))))
    )

    U = Dict((f, t) => rand() * 100 for f in F, t in T)
    V = Dict((f, c) => rand() * 20 for f in F, c in C if rand() < flowprob)
    W = Dict((f, p) => (rand() < prodprob ? 1 : 0) for f in F, p in P)
    return F, C, P, T, D, U, V, W
end

# ╔═╡ c352a486-bbbb-474d-839c-5c867d8a9911
nf, nc, np, nt = 5, 20, 10, 100;

# ╔═╡ d6c417f9-9c9d-4943-876d-a75ceda39336
F, C, P, T, D, U, V, W = create_test(nf, nc, np, nt);

# ╔═╡ 2e583e3b-0ee3-4d98-8dcc-be81d0f4d273
@btime model_standard(F, C, P, T, D, U, V, W)

# ╔═╡ bd1fb6e7-9f51-467a-87e8-b7a9942ce208
@btime model_dict(F, C, P, T, D, U, V, W)

# ╔═╡ e8a917cc-6c9c-438d-ba90-374e0617a3ac
@btime model_index(F, C, P, T, D, U, V, W)

# ╔═╡ b0f05a19-c01c-43dc-82ff-0b3197083b5f
@btime model_incremental(F, C, P, T, D, U, V, W)

# ╔═╡ 1004b0ce-cc9e-4edc-b585-f51a6164e64a
@btime model_sparse(F, C, P, T, D, U, V, W)

# ╔═╡ 7d205438-8e93-4528-8337-543f02aa84b3
REPS = 5

# ╔═╡ 04570ea7-885c-4d0e-be88-eb2a5f77da90
begin
    res = DataFrame(Method = Symbol[], NC = Int[], Time = Float64[])
    @progress for nc in 5:10:100
        for method in [
            model_standard,
            model_dict,
            model_index,
            model_incremental,
            model_sparse,
        ]
            t = minimum((
                @elapsed method(create_test(nf, nc, np, nt; seed = r)...)
                for r in 1:REPS
            ))
            push!(res, (Symbol(method), nc, t))
        end
    end
end

# ╔═╡ cc097148-23b1-4584-a150-c7f22376b65c
begin
    sparsity = DataFrame(Method = Symbol[], DP = Float64[], Time = Float64[])
    @progress for dp in 0.05:0.05:1.0
        for method in [
            model_standard,
            model_dict,
            model_index,
            model_incremental,
            model_sparse,
        ]
            ts = []
            for r in 1:REPS
                GC.gc()
                push!(
                    ts,
                    @elapsed method(
                        create_test(
                            5,
                            40,
                            10,
                            50;
                            demandprob = dp,
                            seed = r,
                        )...,
                    )
                )
            end
            t = minimum(ts)
            push!(sparsity, (Symbol(method), dp, t))
        end
    end
end

# ╔═╡ b0aa0499-e920-4014-b0b2-ce8ea3da7c95
function plot(df, x = :NC, y = :Time)
    CairoMakie.activate!(type = "svg")
    return draw(
        data(df) *
        mapping(x, y => "Time (s)", color = :Method, marker = :Method) *
        (visual(Lines) + visual(Scatter)),
    )
end

# ╔═╡ 4b073bba-940f-4d6f-8ba6-af7355b41e09
plot(res)

# ╔═╡ 66eaf973-3c58-4b6a-8ec3-53bf7fa7a20c
plot(sparsity, :DP, :Time)

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git-tree-sha1 = "68db32dff12bb6127bac73c209881191bf0efbb7"
uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f"
version = "0.3.0+0"

[[deps.SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
version = "0.7.0"

[[deps.SIMD]]
git-tree-sha1 = "7dbc15af7ed5f751a82bf3ed37757adf76c32402"
uuid = "fdea26ae-647d-5447-a871-4b548cad5224"
version = "3.4.1"

[[deps.ScanByte]]
deps = ["Libdl", "SIMD"]
git-tree-sha1 = "2436b15f376005e8790e318329560dcc67188e84"
uuid = "7b38b023-a4d7-4c5e-8d43-3f3097f304eb"
version = "0.3.3"

[[deps.Scratch]]
deps = ["Dates"]
git-tree-sha1 = "f94f779c94e58bf9ea243e77a37e16d9de9126bd"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.1"

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

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

[[deps.ShiftedArrays]]
git-tree-sha1 = "22395afdcf37d6709a5a0766cc4a5ca52cb85ea0"
uuid = "1277b4bf-5013-50f5-be3d-901d8477a67a"
version = "1.0.0"

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

[[deps.SignedDistanceFields]]
deps = ["Random", "Statistics", "Test"]
git-tree-sha1 = "d263a08ec505853a5ff1c1ebde2070419e3f28e9"
uuid = "73760f76-fbc4-59ce-8f25-708e95d2df96"
version = "0.4.0"

[[deps.Sixel]]
deps = ["Dates", "FileIO", "ImageCore", "IndirectArrays", "OffsetArrays", "REPL", "libsixel_jll"]
git-tree-sha1 = "8fb59825be681d451c246a795117f317ecbcaa28"
uuid = "45858cf5-a6b0-47a3-bbea-62219f50df47"
version = "0.1.2"

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

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

[[deps.SparseVariables]]
deps = ["Dictionaries", "JuMP", "Requires", "Tables"]
git-tree-sha1 = "f5139f3b785e16b4a1c8cd1431ddf893f60d11e0"
uuid = "2749762c-80ed-4b14-8f33-f0736679b02b"
version = "0.6.1"

[[deps.SpecialFunctions]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "d75bda01f8c31ebb72df80a46c88b25d1c79c56d"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.1.7"

[[deps.StackViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "46e589465204cd0c08b4bd97385e4fa79a0c770c"
uuid = "cae243ae-269e-4f55-b966-ac2d0dc13c15"
version = "0.1.1"

[[deps.Static]]
deps = ["IfElse"]
git-tree-sha1 = "46638763d3a25ad7818a15d441e0c3446a10742d"
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
version = "0.7.5"

[[deps.StaticArrays]]
deps = ["LinearAlgebra", "Random", "StaticArraysCore", "Statistics"]
git-tree-sha1 = "e972716025466461a3dc1588d9168334b71aafff"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.5.1"

[[deps.StaticArraysCore]]
git-tree-sha1 = "66fe9eb253f910fe8cf161953880cfdaef01cdf0"
uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
version = "1.0.1"

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

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "2c11d7290036fe7aac9038ff312d3b3a2a5bf89e"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.4.0"

[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "472d044a1c8df2b062b23f222573ad6837a615ba"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.19"

[[deps.StatsFuns]]
deps = ["ChainRulesCore", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
git-tree-sha1 = "5950925ff997ed6fb3e985dcce8eb1ba42a0bbe7"
uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
version = "0.9.18"

[[deps.StatsModels]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Printf", "REPL", "ShiftedArrays", "SparseArrays", "StatsBase", "StatsFuns", "Tables"]
git-tree-sha1 = "4352d5badd1bc8bf0a8c825e886fa1eda4f0f967"
uuid = "3eaba693-59b7-5ba5-a881-562e759f1c8d"
version = "0.6.30"

[[deps.StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "ec47fb6069c57f1cee2f67541bf8f23415146de7"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.11"

[[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.TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

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

[[deps.TiffImages]]
deps = ["ColorTypes", "DataStructures", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "Mmap", "OffsetArrays", "PkgVersion", "ProgressMeter", "UUIDs"]
git-tree-sha1 = "fcf41697256f2b759de9380a7e8196d6516f0310"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
version = "0.6.0"

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

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

[[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.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 = "58443b63fb7e465a8a7210828c91c08b92132dff"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.14+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_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_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_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+3"

[[deps.isoband_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51b5eeb3f98367157a7a12a1fb0aa5328946c03c"
uuid = "9a68df92-36a6-505f-a73e-abb412b6bfb4"
version = "0.2.3+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+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 = "5.1.1+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.libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "78736dab31ae7a53540a6b752efc61f77b304c5b"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.8.6+1"

[[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 = "1.47.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[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"
"""

# ╔═╡ Cell order:
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# ╠═7d205438-8e93-4528-8337-543f02aa84b3
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# ╟─00000000-0000-0000-0000-000000000002