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| ### A Pluto.jl notebook ### | |
| # v0.15.0 | |
| using Markdown | |
| using InteractiveUtils | |
| # ╔═╡ 1344246e-87ab-11eb-0d86-d523bcdf699a | |
| begin | |
| using DiffEqFlux | |
| using Flux | |
| using Zygote | |
| using SparseArrays | |
| using LinearAlgebra | |
| end | |
| # ╔═╡ 07cd8bcd-803f-4ea2-acc1-70d2d58d2be0 | |
| md"# Standard example" | |
| # ╔═╡ 7b738e20-2712-4349-93b7-f9b5c1ba5265 | |
| md"Take a small neural network, `NN`," | |
| # ╔═╡ 7955b232-0cc7-491d-8f3e-900f9030dcab | |
| NN = FastChain(FastDense(2, 16, tanh), FastDense(16, 2, x->x^2)) # a NN | |
| # ╔═╡ ad58b8aa-e8f1-4a64-b146-11a2393bab80 | |
| md"Assign some parameters `p` and an input vector randomly," | |
| # ╔═╡ c041026b-9043-4851-9b81-d4b75c117f80 | |
| p, u = Float64.(initial_params(NN)), rand(2) | |
| # ╔═╡ e9a8b319-39c7-493f-aa74-edd29122047a | |
| md"And we can easily get its derivatives with Zygote" | |
| # ╔═╡ b481e279-fb5f-474a-aca5-45b1792e19b4 | |
| Zygote.jacobian(NN, u, p) | |
| # ╔═╡ bece2b73-699a-4492-962a-006d1ab89e17 | |
| md""" | |
| # With extra *prescribed* input variables | |
| Now let's make this a bit more complicated. | |
| Let's assume that we want a 3-element input `vars = [x, y, z]`, and 1-element output. | |
| But for the input, we will keep `y` and `z` constant. | |
| So we make `NN2` with a 3-element input and 1-element output: | |
| """ | |
| # ╔═╡ 8b67da12-d1bc-4c3c-88af-cd0dec448abd | |
| NN2 = FastChain(FastDense(3, 16, tanh), FastDense(16, 1, x->x^2)) | |
| # ╔═╡ 6150b3c7-7b7b-425b-a5d1-bb62eee8c835 | |
| md""" | |
| So we write a function `f` with single argument `x` by "wrapping" `NN2([x, y, z])`: | |
| """ | |
| # ╔═╡ 1cab1c36-494d-4b69-9aef-9ccb5c026e4e | |
| begin | |
| y = 15.9 | |
| z = 22.3 | |
| f(x, p) = NN2([x, y, z], p)[1] # note I extract the first element here | |
| end | |
| # ╔═╡ 84450eb1-28da-4aaa-b876-f0f59b7d3936 | |
| md""" | |
| And we can get its derivatives with `jacobian`: | |
| """ | |
| # ╔═╡ 2d858321-61f2-4390-ae7b-8ae43ba5f866 | |
| begin | |
| x = 0.24 | |
| Zygote.jacobian(f, x, p) | |
| end | |
| # ╔═╡ 92ab5dec-2764-4a19-a997-39a1f37f96e7 | |
| md""" | |
| # Multiple inputs from different locations | |
| Now let's assume that we have values of `x` at many different locations, so we want to use the same function `f`, but with many different `x` values, provided as a vector `X`. | |
| And then we will want to compute its Jacobian with respect to `X`. | |
| """ | |
| # ╔═╡ 652bb26e-a53c-48eb-9721-39cf29987345 | |
| F(X, p) = [f(x, p) for x in X] # almost like a broadcast, F(X) = f.(X) | |
| # ╔═╡ d144ed58-0012-43ac-b2d7-193dd393388a | |
| md""" | |
| We can get the derivatives with the same approach: | |
| """ | |
| # ╔═╡ ff34fe18-be1f-4a51-9e7e-83a783e9cb21 | |
| begin | |
| X = rand(1000) | |
| Zygote.jacobian(F, X, p) | |
| end | |
| # ╔═╡ 251d673c-f6ff-42ee-bcdb-8d12dd5ef362 | |
| md""" | |
| Notice that now the jacobian with respect to `x1vec` is a diagonal. | |
| This is simply the consequence of the structure here. | |
| Indeed, `NN2funvec` is "local" in `x1vec`, i.e., its $i$th output only depends on the $i$th entry of `x1vec`. | |
| Maybe we can exploit that. | |
| Let's define some functions to test different approaches. | |
| """ | |
| # ╔═╡ 06bcda0d-cee8-4f2b-81a6-8a3850dec56c | |
| begin | |
| A(X, p) = Zygote.jacobian(F, X, p)[1] | |
| B(X, p) = spdiagm([Zygote.jacobian(f, x, p)[1][1] for x in X]) | |
| end | |
| # ╔═╡ 9bc37149-6f74-4e5d-af97-9d2bbe303549 | |
| A(X, p) # ~10s | |
| # ╔═╡ ac95ea06-4adf-4b12-b8a4-a999421c1677 | |
| B(X, p) # ~0.15s | |
| # ╔═╡ 57f0795a-d3d6-4534-b98c-45451d84168b | |
| A(X, p) == Matrix(B(X, p)) #Check that they are the same | |
| # ╔═╡ 6774973f-1369-4d2e-a7a4-80f6700186e7 | |
| md""" | |
| So it seems getting the jacobian of `F` through `B` is much faster. | |
| That's because we did not let Zygote try all the combinations of off diagonal indices that we already know would give `0`. | |
| Instead, we dug up the underlying "scalar" function `f`, applied Zygote's derivatives element by element and constructed the diagonal Jacobian "by hand". | |
| The **question is, is that the best way to go about this?** | |
| Should I have constructed `F` differently? | |
| Can I use this under the hood with some solver of DiffEqFlux and SciML in general? | |
| """ | |
| # ╔═╡ 00000000-0000-0000-0000-000000000001 | |
| PLUTO_PROJECT_TOML_CONTENTS = """ | |
| [deps] | |
| DiffEqFlux = "aae7a2af-3d4f-5e19-a356-7da93b79d9d0" | |
| Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c" | |
| LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" | |
| SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" | |
| Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f" | |
| [compat] | |
| DiffEqFlux = "^1.34.1" | |
| Flux = "^0.11.6" | |
| Zygote = "^0.6.4" | |
| """ | |
| # ╔═╡ 00000000-0000-0000-0000-000000000002 | |
| PLUTO_MANIFEST_TOML_CONTENTS = """ | |
| # This file is machine-generated - editing it directly is not advised | |
| [[AbstractAlgebra]] | |
| deps = ["InteractiveUtils", "LinearAlgebra", "Markdown", "Random", "RandomExtensions", "SparseArrays", "Test"] | |
| git-tree-sha1 = "0633f6981ad1f6fc01c26daef94a5241c6632e86" | |
| uuid = "c3fe647b-3220-5bb0-a1ea-a7954cac585d" | |
| version = "0.13.6" | |
| [[AbstractFFTs]] | |
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| git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0" | |
| uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c" | |
| version = "1.0.1" | |
| [[AbstractTrees]] | |
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| uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c" | |
| version = "0.3.4" | |
| [[Adapt]] | |
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| git-tree-sha1 = "ffcfa2d345aaee0ef3d8346a073d5dd03c983ebe" | |
| uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" | |
| version = "3.2.0" | |
| [[ArgTools]] | |
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| [[ArnoldiMethod]] | |
| deps = ["LinearAlgebra", "Random", "StaticArrays"] | |
| git-tree-sha1 = "f87e559f87a45bece9c9ed97458d3afe98b1ebb9" | |
| uuid = "ec485272-7323-5ecc-a04f-4719b315124d" | |
| version = "0.1.0" | |
| [[ArrayInterface]] | |
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| [[Artifacts]] | |
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| [[AxisAlgorithms]] | |
| deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"] | |
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| version = "1.0.0" | |
| [[BFloat16s]] | |
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| [[Base64]] | |
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| [[CEnum]] | |
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| uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82" | |
| version = "0.4.1" | |
| [[CUDA]] | |
| deps = ["AbstractFFTs", "Adapt", "BFloat16s", "CEnum", "CompilerSupportLibraries_jll", "DataStructures", "ExprTools", "GPUArrays", "GPUCompiler", "LLVM", "LazyArtifacts", "Libdl", "LinearAlgebra", "Logging", "MacroTools", "Memoize", "NNlib", "Printf", "Random", "Reexport", "Requires", "SparseArrays", "Statistics", "TimerOutputs"] | |
| git-tree-sha1 = "870e029382294443a6578190e992bf4cbfd34e22" | |
| uuid = "052768ef-5323-5732-b1bb-66c8b64840ba" | |
| version = "2.6.2" | |
| [[ChainRules]] | |
| deps = ["ChainRulesCore", "Compat", "LinearAlgebra", "Random", "Reexport", "Requires", "Statistics"] | |
| git-tree-sha1 = "e01f521443e3700f40ad3c7c1c6aa3a6940aaea1" | |
| uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2" | |
| version = "0.7.54" | |
| [[ChainRulesCore]] | |
| deps = ["Compat", "LinearAlgebra", "SparseArrays"] | |
| git-tree-sha1 = "de4f08843c332d355852721adb1592bce7924da3" | |
| uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" | |
| version = "0.9.29" | |
| [[CodecZlib]] | |
| deps = ["TranscodingStreams", "Zlib_jll"] | |
| git-tree-sha1 = "ded953804d019afa9a3f98981d99b33e3db7b6da" | |
| uuid = "944b1d66-785c-5afd-91f1-9de20f533193" | |
| version = "0.7.0" | |
| [[ColorTypes]] | |
| deps = ["FixedPointNumbers", "Random"] | |
| git-tree-sha1 = "32a2b8af383f11cbb65803883837a149d10dfe8a" | |
| uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f" | |
| version = "0.10.12" | |
| [[Colors]] | |
| deps = ["ColorTypes", "FixedPointNumbers", "InteractiveUtils", "Reexport"] | |
| git-tree-sha1 = "ac5f2213e56ed8a34a3dd2f681f4df1166b34929" | |
| uuid = "5ae59095-9a9b-59fe-a467-6f913c188581" | |
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| [[Combinatorics]] | |
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| [[CommonSolve]] | |
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| [[CommonSubexpressions]] | |
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| [[Compat]] | |
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| [[CompilerSupportLibraries_jll]] | |
| deps = ["Artifacts", "Libdl"] | |
| uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae" | |
| [[ConsoleProgressMonitor]] | |
| deps = ["Logging", "ProgressMeter"] | |
| git-tree-sha1 = "3ab7b2136722890b9af903859afcf457fa3059e8" | |
| uuid = "88cd18e8-d9cc-4ea6-8889-5259c0d15c8b" | |
| version = "0.1.2" | |
| [[ConstructionBase]] | |
| deps = ["LinearAlgebra"] | |
| git-tree-sha1 = "48920211c95a6da1914a06c44ec94be70e84ffff" | |
| uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9" | |
| version = "1.1.0" | |
| [[DataAPI]] | |
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| uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a" | |
| version = "1.6.0" | |
| [[DataInterpolations]] | |
| deps = ["ChainRulesCore", "LinearAlgebra", "Optim", "RecipesBase", "RecursiveArrayTools", "Reexport"] | |
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| uuid = "82cc6244-b520-54b8-b5a6-8a565e85f1d0" | |
| version = "3.3.1" | |
| [[DataStructures]] | |
| deps = ["Compat", "InteractiveUtils", "OrderedCollections"] | |
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| [[DataValueInterfaces]] | |
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| [[Dates]] | |
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| deps = ["Mmap"] | |
| uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab" | |
| [[DiffEqBase]] | |
| deps = ["ArrayInterface", "ChainRulesCore", "DataStructures", "DocStringExtensions", "FunctionWrappers", "IterativeSolvers", "LabelledArrays", "LinearAlgebra", "Logging", "MuladdMacro", "NonlinearSolve", "Parameters", "Printf", "RecursiveArrayTools", "RecursiveFactorization", "Reexport", "Requires", "SciMLBase", "SparseArrays", "StaticArrays", "Statistics", "SuiteSparse", "ZygoteRules"] | |
| git-tree-sha1 = "c2ff625248a0967adff1dc1f79c6a41e2531f081" | |
| uuid = "2b5f629d-d688-5b77-993f-72d75c75574e" | |
| version = "6.57.8" | |
| [[DiffEqCallbacks]] | |
| deps = ["DataStructures", "DiffEqBase", "ForwardDiff", "LinearAlgebra", "NLsolve", "OrdinaryDiffEq", "RecipesBase", "RecursiveArrayTools", "StaticArrays"] | |
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| [[DiffEqFlux]] | |
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| version = "1.34.1" | |
| [[DiffEqJump]] | |
| deps = ["ArrayInterface", "Compat", "DataStructures", "DiffEqBase", "FunctionWrappers", "LinearAlgebra", "PoissonRandom", "Random", "RandomNumbers", "RecursiveArrayTools", "StaticArrays", "TreeViews", "UnPack"] | |
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| [[DiffEqNoiseProcess]] | |
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| version = "0.24.15" | |
| [[DistributionsAD]] | |
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| uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" | |
| [[PoissonRandom]] | |
| deps = ["Random", "Statistics", "Test"] | |
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| [[ProgressLogging]] | |
| deps = ["Logging", "SHA", "UUIDs"] | |
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| [[QuadGK]] | |
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| [[REPL]] | |
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| [[Random]] | |
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| [[Random123]] | |
| deps = ["Libdl", "Random", "RandomNumbers"] | |
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| [[Ratios]] | |
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| [[Reexport]] | |
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| [[ResettableStacks]] | |
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| [[SHA]] | |
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| [[SLEEFPirates]] | |
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| [[SafeTestsets]] | |
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| [[SciMLBase]] | |
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| git-tree-sha1 = "a7d54d6a99568b7fb0a1ff996786a39be499080c" | |
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| [[Scratch]] | |
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| [[Serialization]] | |
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| [[SimpleTraits]] | |
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| [[Sobol]] | |
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| uuid = "ed01d8cd-4d21-5b2a-85b4-cc3bdc58bad4" | |
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| [[Sockets]] | |
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| [[SortingAlgorithms]] | |
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| uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c" | |
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| [[SparseDiffTools]] | |
| deps = ["Adapt", "ArrayInterface", "Compat", "DataStructures", "FiniteDiff", "ForwardDiff", "LightGraphs", "LinearAlgebra", "Requires", "SparseArrays", "VertexSafeGraphs"] | |
| git-tree-sha1 = "d05bc362e3fa1b0e2361594a706fc63ffbd140f3" | |
| uuid = "47a9eef4-7e08-11e9-0b38-333d64bd3804" | |
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| [[SpecialFunctions]] | |
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| uuid = "276daf66-3868-5448-9aa4-cd146d93841b" | |
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| [[StableRNGs]] | |
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| [[Static]] | |
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| version = "0.2.4" | |
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| git-tree-sha1 = "9da72ed50e94dbff92036da395275ed114e04d49" | |
| uuid = "90137ffa-7385-5640-81b9-e52037218182" | |
| version = "1.0.1" | |
| [[Statistics]] | |
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| [[StatsBase]] | |
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| git-tree-sha1 = "a83fa3021ac4c5a918582ec4721bc0cf70b495a9" | |
| uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91" | |
| version = "0.33.4" | |
| [[StatsFuns]] | |
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| uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c" | |
| version = "0.9.6" | |
| [[StochasticDiffEq]] | |
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| git-tree-sha1 = "2541e979831e7753dfbfa91ae682ae3539ebf61f" | |
| uuid = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0" | |
| version = "6.33.0" | |
| [[SuiteSparse]] | |
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| uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9" | |
| [[SymbolicUtils]] | |
| deps = ["AbstractAlgebra", "AbstractTrees", "Combinatorics", "ConstructionBase", "DataStructures", "IfElse", "LabelledArrays", "NaNMath", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "TimerOutputs"] | |
| git-tree-sha1 = "7176e06fb4ad726e828c72642000a2076808ea58" | |
| uuid = "d1185830-fcd6-423d-90d6-eec64667417b" | |
| version = "0.9.1" | |
| [[Symbolics]] | |
| deps = ["AbstractAlgebra", "DiffRules", "Distributions", "DocStringExtensions", "IfElse", "Latexify", "Libdl", "LinearAlgebra", "MacroTools", "NaNMath", "RecipesBase", "Reexport", "RuntimeGeneratedFunctions", "SciMLBase", "Setfield", "SparseArrays", "SpecialFunctions", "SymbolicUtils", "TreeViews"] | |
| git-tree-sha1 = "0a8f3d870e735e9b68077316c6cd732266cb10aa" | |
| uuid = "0c5d862f-8b57-4792-8d23-62f2024744c7" | |
| version = "0.1.9" | |
| [[TOML]] | |
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| uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76" | |
| [[TableTraits]] | |
| deps = ["IteratorInterfaceExtensions"] | |
| git-tree-sha1 = "b1ad568ba658d8cbb3b892ed5380a6f3e781a81e" | |
| uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c" | |
| version = "1.0.0" | |
| [[Tables]] | |
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| uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c" | |
| version = "1.4.0" | |
| [[Tar]] | |
| deps = ["ArgTools", "SHA"] | |
| uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e" | |
| [[TerminalLoggers]] | |
| deps = ["LeftChildRightSiblingTrees", "Logging", "Markdown", "Printf", "ProgressLogging", "UUIDs"] | |
| git-tree-sha1 = "e185a19bb9172f0cf5bc71233fab92a46f7ae154" | |
| uuid = "5d786b92-1e48-4d6f-9151-6b4477ca9bed" | |
| version = "0.1.3" | |
| [[Test]] | |
| deps = ["InteractiveUtils", "Logging", "Random", "Serialization"] | |
| uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40" | |
| [[ThreadingUtilities]] | |
| deps = ["VectorizationBase"] | |
| git-tree-sha1 = "e3032c97b183e6e2baf4d2cc4fe60c4292a4a707" | |
| uuid = "8290d209-cae3-49c0-8002-c8c24d57dab5" | |
| version = "0.2.5" | |
| [[TimerOutputs]] | |
| deps = ["Printf"] | |
| git-tree-sha1 = "32cdbe6cd2d214c25a0b88f985c9e0092877c236" | |
| uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f" | |
| version = "0.5.8" | |
| [[Tracker]] | |
| deps = ["Adapt", "DiffRules", "ForwardDiff", "LinearAlgebra", "MacroTools", "NNlib", "NaNMath", "Printf", "Random", "Requires", "SpecialFunctions", "Statistics"] | |
| git-tree-sha1 = "bf4adf36062afc921f251af4db58f06235504eff" | |
| uuid = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c" | |
| version = "0.2.16" | |
| [[TranscodingStreams]] | |
| deps = ["Random", "Test"] | |
| git-tree-sha1 = "7c53c35547de1c5b9d46a4797cf6d8253807108c" | |
| uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa" | |
| version = "0.9.5" | |
| [[Trapz]] | |
| git-tree-sha1 = "aff96deaaa38e3b52a5af1dd3da376d49bf6ec9a" | |
| uuid = "592b5752-818d-11e9-1e9a-2b8ca4a44cd1" | |
| version = "2.0.2" | |
| [[TreeViews]] | |
| deps = ["Test"] | |
| git-tree-sha1 = "8d0d7a3fe2f30d6a7f833a5f19f7c7a5b396eae6" | |
| uuid = "a2a6695c-b41b-5b7d-aed9-dbfdeacea5d7" | |
| version = "0.3.0" | |
| [[UUIDs]] | |
| deps = ["Random", "SHA"] | |
| uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" | |
| [[UnPack]] | |
| git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b" | |
| uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed" | |
| version = "1.0.2" | |
| [[Unicode]] | |
| uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" | |
| [[Unitful]] | |
| deps = ["ConstructionBase", "LinearAlgebra", "Random"] | |
| git-tree-sha1 = "fdfbea79b5b9a305bf226eb4730321f603281290" | |
| uuid = "1986cc42-f94f-5a68-af5c-568840ba703d" | |
| version = "1.6.0" | |
| [[VectorizationBase]] | |
| deps = ["ArrayInterface", "Hwloc", "IfElse", "Libdl", "LinearAlgebra"] | |
| git-tree-sha1 = "486842a62c4a1bc23f7c8457d64e683a00d6d0e9" | |
| uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f" | |
| version = "0.18.14" | |
| [[VertexSafeGraphs]] | |
| deps = ["LightGraphs"] | |
| git-tree-sha1 = "b9b450c99a3ca1cc1c6836f560d8d887bcbe356e" | |
| uuid = "19fa3120-7c27-5ec5-8db8-b0b0aa330d6f" | |
| version = "0.1.2" | |
| [[WoodburyMatrices]] | |
| deps = ["LinearAlgebra", "SparseArrays"] | |
| git-tree-sha1 = "59e2ad8fd1591ea019a5259bd012d7aee15f995c" | |
| uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6" | |
| version = "0.5.3" | |
| [[ZipFile]] | |
| deps = ["Libdl", "Printf", "Zlib_jll"] | |
| git-tree-sha1 = "c3a5637e27e914a7a445b8d0ad063d701931e9f7" | |
| uuid = "a5390f91-8eb1-5f08-bee0-b1d1ffed6cea" | |
| version = "0.9.3" | |
| [[Zlib_jll]] | |
| deps = ["Libdl"] | |
| uuid = "83775a58-1f1d-513f-b197-d71354ab007a" | |
| [[Zygote]] | |
| deps = ["AbstractFFTs", "ChainRules", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"] | |
| git-tree-sha1 = "47dd50e831959f8785f8a9854783a2eebac8e1bd" | |
| uuid = "e88e6eb3-aa80-5325-afca-941959d7151f" | |
| version = "0.6.4" | |
| [[ZygoteRules]] | |
| deps = ["MacroTools"] | |
| git-tree-sha1 = "9e7a1e8ca60b742e508a315c17eef5211e7fbfd7" | |
| uuid = "700de1a5-db45-46bc-99cf-38207098b444" | |
| version = "0.2.1" | |
| [[nghttp2_jll]] | |
| deps = ["Artifacts", "Libdl"] | |
| uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" | |
| [[p7zip_jll]] | |
| deps = ["Artifacts", "Libdl"] | |
| uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" | |
| """ | |
| # ╔═╡ Cell order: | |
| # ╠═1344246e-87ab-11eb-0d86-d523bcdf699a | |
| # ╟─07cd8bcd-803f-4ea2-acc1-70d2d58d2be0 | |
| # ╟─7b738e20-2712-4349-93b7-f9b5c1ba5265 | |
| # ╠═7955b232-0cc7-491d-8f3e-900f9030dcab | |
| # ╟─ad58b8aa-e8f1-4a64-b146-11a2393bab80 | |
| # ╠═c041026b-9043-4851-9b81-d4b75c117f80 | |
| # ╟─e9a8b319-39c7-493f-aa74-edd29122047a | |
| # ╠═b481e279-fb5f-474a-aca5-45b1792e19b4 | |
| # ╟─bece2b73-699a-4492-962a-006d1ab89e17 | |
| # ╠═8b67da12-d1bc-4c3c-88af-cd0dec448abd | |
| # ╟─6150b3c7-7b7b-425b-a5d1-bb62eee8c835 | |
| # ╠═1cab1c36-494d-4b69-9aef-9ccb5c026e4e | |
| # ╟─84450eb1-28da-4aaa-b876-f0f59b7d3936 | |
| # ╠═2d858321-61f2-4390-ae7b-8ae43ba5f866 | |
| # ╟─92ab5dec-2764-4a19-a997-39a1f37f96e7 | |
| # ╠═652bb26e-a53c-48eb-9721-39cf29987345 | |
| # ╟─d144ed58-0012-43ac-b2d7-193dd393388a | |
| # ╠═ff34fe18-be1f-4a51-9e7e-83a783e9cb21 | |
| # ╟─251d673c-f6ff-42ee-bcdb-8d12dd5ef362 | |
| # ╠═06bcda0d-cee8-4f2b-81a6-8a3850dec56c | |
| # ╠═9bc37149-6f74-4e5d-af97-9d2bbe303549 | |
| # ╠═ac95ea06-4adf-4b12-b8a4-a999421c1677 | |
| # ╠═57f0795a-d3d6-4534-b98c-45451d84168b | |
| # ╟─6774973f-1369-4d2e-a7a4-80f6700186e7 | |
| # ╟─00000000-0000-0000-0000-000000000001 | |
| # ╟─00000000-0000-0000-0000-000000000002 |
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