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Unexpected behavior may occur. └ @ /tmp/jl_YHjA0B/Manifest.toml:0  Installed Adapt ─ v3.6.0 Resolving... === ┌ Info: Operation failed. Updating registries and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled └  └─restricted to versions 1.9.0 by an explicit requirement — no versions left Resolving... === ┌ Warning: Operation failed. Removing Manifest and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled │  └─restricted to versions 1.9.0 by an explicit requirement — no versions left └ @ Pluto ~/.julia/packages/Pluto/6smog/src/packages/Packages.jl:494 Resolving... ===  Updating `/tmp/jl_YHjA0B/Project.toml` ⌅ [91a5bcdd] + Plots v1.38.17 [7f904dfe] + PlutoUI v0.7.60 [e88e6eb3] + Zygote v0.6.72 [37e2e46d] ~ LinearAlgebra ⇒ v1.11.0  Updating `/tmp/jl_YHjA0B/Manifest.toml` [621f4979] + AbstractFFTs v1.5.0 [6e696c72] + AbstractPlutoDingetjes v1.3.2 [79e6a3ab] + Adapt v4.0.4 [d1d4a3ce] + BitFlags v0.1.9 [fa961155] + CEnum v0.5.0 [082447d4] + ChainRules v1.71.0 [d360d2e6] + ChainRulesCore v1.25.0 [944b1d66] + CodecZlib v0.7.6 [35d6a980] + ColorSchemes v3.26.0 [3da002f7] + ColorTypes v0.11.5 [c3611d14] + ColorVectorSpace v0.10.0 [5ae59095] + Colors v0.12.11 [bbf7d656] + 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[76f85450] + LibGit2 v1.11.0 [8f399da3] + Libdl v1.11.0 [37e2e46d] + LinearAlgebra v1.11.0 [56ddb016] + Logging v1.11.0 [d6f4376e] + Markdown v1.11.0 [a63ad114] + Mmap v1.11.0 [ca575930] + NetworkOptions v1.2.0 [44cfe95a] + Pkg v1.11.0 [de0858da] + Printf v1.11.0 [3fa0cd96] + REPL v1.11.0 [9a3f8284] + Random v1.11.0 [ea8e919c] + SHA v0.7.0 [9e88b42a] + Serialization v1.11.0 [6462fe0b] + Sockets v1.11.0 [2f01184e] + SparseArrays v1.11.0 [f489334b] + StyledStrings v1.11.0 [4607b0f0] + SuiteSparse [fa267f1f] + TOML v1.0.3 [a4e569a6] + Tar v1.10.0 [8dfed614] + Test v1.11.0 [cf7118a7] + UUIDs v1.11.0 [4ec0a83e] + Unicode v1.11.0 [e66e0078] + CompilerSupportLibraries_jll v1.1.1+0 [deac9b47] + LibCURL_jll v8.6.0+0 [e37daf67] + LibGit2_jll v1.7.2+0 [29816b5a] + LibSSH2_jll v1.11.0+1 [c8ffd9c3] + MbedTLS_jll v2.28.6+0 [14a3606d] + MozillaCACerts_jll v2023.12.12 [4536629a] + OpenBLAS_jll v0.3.27+1 [05823500] + OpenLibm_jll v0.8.1+2 [efcefdf7] + PCRE2_jll v10.42.0+1 [bea87d4a] + SuiteSparse_jll v7.7.0+0 [83775a58] + Zlib_jll v1.2.13+1 [8e850b90] + libblastrampoline_jll v5.11.0+0 [8e850ede] + nghttp2_jll v1.59.0+0 [3f19e933] + p7zip_jll v17.4.0+2  Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m` Instantiating... === Precompiling... ===  Activating project at `/tmp/jl_YHjA0B`Șnbpkg_syncÚ9â Instantiating... === ┌ Warning: The active manifest file has dependencies that were resolved with a different julia version (1.9.0-beta4). Unexpected behavior may occur. └ @ /tmp/jl_YHjA0B/Manifest.toml:0  Installed Adapt ─ v3.6.0 Resolving... === ┌ Info: Operation failed. Updating registries and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled └  └─restricted to versions 1.9.0 by an explicit requirement — no versions left Resolving... === ┌ Warning: Operation failed. Removing Manifest and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled │  └─restricted to versions 1.9.0 by an explicit requirement — no versions left └ @ Pluto ~/.julia/packages/Pluto/6smog/src/packages/Packages.jl:494 Resolving... ===  Updating `/tmp/jl_YHjA0B/Project.toml` ⌅ [91a5bcdd] + Plots v1.38.17 [7f904dfe] + PlutoUI v0.7.60 [e88e6eb3] + Zygote v0.6.72 [37e2e46d] ~ LinearAlgebra ⇒ v1.11.0  Updating `/tmp/jl_YHjA0B/Manifest.toml` [621f4979] + AbstractFFTs v1.5.0 [6e696c72] + AbstractPlutoDingetjes v1.3.2 [79e6a3ab] + Adapt v4.0.4 [d1d4a3ce] + BitFlags v0.1.9 [fa961155] + CEnum v0.5.0 [082447d4] + ChainRules v1.71.0 [d360d2e6] + ChainRulesCore v1.25.0 [944b1d66] + CodecZlib v0.7.6 [35d6a980] + ColorSchemes v3.26.0 [3da002f7] + ColorTypes v0.11.5 [c3611d14] + ColorVectorSpace v0.10.0 [5ae59095] + Colors v0.12.11 [bbf7d656] + CommonSubexpressions v0.3.1 [34da2185] + Compat v4.16.0 [f0e56b4a] + ConcurrentUtilities v2.4.2 [187b0558] + ConstructionBase v1.5.8 [d38c429a] + Contour v0.6.3 [9a962f9c] + DataAPI v1.16.0 [864edb3b] + DataStructures v0.18.20 [e2d170a0] + DataValueInterfaces v1.0.0 [8bb1440f] + DelimitedFiles v1.9.1 [163ba53b] + DiffResults v1.1.0 [b552c78f] + DiffRules v1.15.1 [ffbed154] + DocStringExtensions v0.9.3 [460bff9d] + ExceptionUnwrapping v0.1.10 [c87230d0] + FFMPEG v0.4.2 [1a297f60] + FillArrays v1.13.0 [53c48c17] + FixedPointNumbers v0.8.5 [1fa38f19] + Format v1.3.7 [f6369f11] + ForwardDiff v0.10.36 [0c68f7d7] + GPUArrays v10.3.1 [46192b85] + GPUArraysCore v0.1.6 ⌅ [28b8d3ca] + GR v0.72.10 [42e2da0e] + Grisu v1.0.2 [cd3eb016] + HTTP v1.10.8 [47d2ed2b] + Hyperscript v0.0.5 [ac1192a8] + HypertextLiteral v0.9.5 [b5f81e59] + IOCapture v0.2.5 [7869d1d1] + IRTools v0.4.14 [92d709cd] + IrrationalConstants v0.2.2 [82899510] + IteratorInterfaceExtensions v1.0.0 [1019f520] + JLFzf v0.1.8 [692b3bcd] 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To see why use `status --outdated -m` Instantiating... === Precompiling... ===  Activating project at `/tmp/jl_YHjA0B`­LinearAlgebraÚ9â Instantiating... === ┌ Warning: The active manifest file has dependencies that were resolved with a different julia version (1.9.0-beta4). Unexpected behavior may occur. └ @ /tmp/jl_YHjA0B/Manifest.toml:0  Installed Adapt ─ v3.6.0 Resolving... === ┌ Info: Operation failed. Updating registries and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled └  └─restricted to versions 1.9.0 by an explicit requirement — no versions left Resolving... === ┌ Warning: Operation failed. Removing Manifest and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled │  └─restricted to versions 1.9.0 by an explicit requirement — no versions left └ @ Pluto ~/.julia/packages/Pluto/6smog/src/packages/Packages.jl:494 Resolving... ===  Updating `/tmp/jl_YHjA0B/Project.toml` ⌅ [91a5bcdd] + Plots v1.38.17 [7f904dfe] + PlutoUI v0.7.60 [e88e6eb3] + Zygote v0.6.72 [37e2e46d] ~ LinearAlgebra ⇒ v1.11.0  Updating `/tmp/jl_YHjA0B/Manifest.toml` [621f4979] + AbstractFFTs v1.5.0 [6e696c72] + AbstractPlutoDingetjes v1.3.2 [79e6a3ab] + Adapt v4.0.4 [d1d4a3ce] + BitFlags v0.1.9 [fa961155] + CEnum v0.5.0 [082447d4] + ChainRules v1.71.0 [d360d2e6] + ChainRulesCore v1.25.0 [944b1d66] + CodecZlib v0.7.6 [35d6a980] + ColorSchemes v3.26.0 [3da002f7] + ColorTypes v0.11.5 [c3611d14] + ColorVectorSpace v0.10.0 [5ae59095] + Colors v0.12.11 [bbf7d656] + 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v7.7.0+0 [83775a58] + Zlib_jll v1.2.13+1 [8e850b90] + libblastrampoline_jll v5.11.0+0 [8e850ede] + nghttp2_jll v1.59.0+0 [3f19e933] + p7zip_jll v17.4.0+2  Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m` Instantiating... === Precompiling... ===  Activating project at `/tmp/jl_YHjA0B`§PlutoUIÚ9â Instantiating... === ┌ Warning: The active manifest file has dependencies that were resolved with a different julia version (1.9.0-beta4). Unexpected behavior may occur. └ @ /tmp/jl_YHjA0B/Manifest.toml:0  Installed Adapt ─ v3.6.0 Resolving... === ┌ Info: Operation failed. Updating registries and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled └  └─restricted to versions 1.9.0 by an explicit requirement — no versions left Resolving... === ┌ Warning: Operation failed. Removing Manifest and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled │  └─restricted to versions 1.9.0 by an explicit requirement — no versions left └ @ Pluto ~/.julia/packages/Pluto/6smog/src/packages/Packages.jl:494 Resolving... ===  Updating `/tmp/jl_YHjA0B/Project.toml` ⌅ [91a5bcdd] + Plots v1.38.17 [7f904dfe] + PlutoUI v0.7.60 [e88e6eb3] + Zygote v0.6.72 [37e2e46d] ~ LinearAlgebra ⇒ v1.11.0  Updating `/tmp/jl_YHjA0B/Manifest.toml` [621f4979] + AbstractFFTs v1.5.0 [6e696c72] + AbstractPlutoDingetjes v1.3.2 [79e6a3ab] + Adapt v4.0.4 [d1d4a3ce] + BitFlags v0.1.9 [fa961155] + CEnum v0.5.0 [082447d4] + ChainRules v1.71.0 [d360d2e6] + ChainRulesCore v1.25.0 [944b1d66] + CodecZlib v0.7.6 [35d6a980] + ColorSchemes v3.26.0 [3da002f7] + ColorTypes v0.11.5 [c3611d14] + ColorVectorSpace v0.10.0 [5ae59095] + Colors v0.12.11 [bbf7d656] + 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[76f85450] + LibGit2 v1.11.0 [8f399da3] + Libdl v1.11.0 [37e2e46d] + LinearAlgebra v1.11.0 [56ddb016] + Logging v1.11.0 [d6f4376e] + Markdown v1.11.0 [a63ad114] + Mmap v1.11.0 [ca575930] + NetworkOptions v1.2.0 [44cfe95a] + Pkg v1.11.0 [de0858da] + Printf v1.11.0 [3fa0cd96] + REPL v1.11.0 [9a3f8284] + Random v1.11.0 [ea8e919c] + SHA v0.7.0 [9e88b42a] + Serialization v1.11.0 [6462fe0b] + Sockets v1.11.0 [2f01184e] + SparseArrays v1.11.0 [f489334b] + StyledStrings v1.11.0 [4607b0f0] + SuiteSparse [fa267f1f] + TOML v1.0.3 [a4e569a6] + Tar v1.10.0 [8dfed614] + Test v1.11.0 [cf7118a7] + UUIDs v1.11.0 [4ec0a83e] + Unicode v1.11.0 [e66e0078] + CompilerSupportLibraries_jll v1.1.1+0 [deac9b47] + LibCURL_jll v8.6.0+0 [e37daf67] + LibGit2_jll v1.7.2+0 [29816b5a] + LibSSH2_jll v1.11.0+1 [c8ffd9c3] + MbedTLS_jll v2.28.6+0 [14a3606d] + MozillaCACerts_jll v2023.12.12 [4536629a] + OpenBLAS_jll v0.3.27+1 [05823500] + OpenLibm_jll v0.8.1+2 [efcefdf7] + PCRE2_jll v10.42.0+1 [bea87d4a] + SuiteSparse_jll v7.7.0+0 [83775a58] + Zlib_jll v1.2.13+1 [8e850b90] + libblastrampoline_jll v5.11.0+0 [8e850ede] + nghttp2_jll v1.59.0+0 [3f19e933] + p7zip_jll v17.4.0+2  Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m` Instantiating... === Precompiling... ===  Activating project at `/tmp/jl_YHjA0B`„PlotsÚ9â Instantiating... === ┌ Warning: The active manifest file has dependencies that were resolved with a different julia version (1.9.0-beta4). Unexpected behavior may occur. └ @ /tmp/jl_YHjA0B/Manifest.toml:0  Installed Adapt ─ v3.6.0 Resolving... === ┌ Info: Operation failed. Updating registries and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled └  └─restricted to versions 1.9.0 by an explicit requirement — no versions left Resolving... === ┌ Warning: Operation failed. Removing Manifest and trying again... │  exception = │  Unsatisfiable requirements detected for package Statistics [10745b16]: │  Statistics [10745b16] log: │  ├─possible versions are: 1.11.0 - 1.11.1 or uninstalled │  └─restricted to versions 1.9.0 by an explicit requirement — no versions left └ @ Pluto ~/.julia/packages/Pluto/6smog/src/packages/Packages.jl:494 Resolving... ===  Updating `/tmp/jl_YHjA0B/Project.toml` ⌅ [91a5bcdd] + Plots v1.38.17 [7f904dfe] + PlutoUI v0.7.60 [e88e6eb3] + Zygote v0.6.72 [37e2e46d] ~ LinearAlgebra ⇒ v1.11.0  Updating `/tmp/jl_YHjA0B/Manifest.toml` [621f4979] + AbstractFFTs v1.5.0 [6e696c72] + AbstractPlutoDingetjes v1.3.2 [79e6a3ab] + Adapt v4.0.4 [d1d4a3ce] + BitFlags v0.1.9 [fa961155] + CEnum v0.5.0 [082447d4] + ChainRules v1.71.0 [d360d2e6] + ChainRulesCore v1.25.0 [944b1d66] + CodecZlib v0.7.6 [35d6a980] + ColorSchemes v3.26.0 [3da002f7] + ColorTypes v0.11.5 [c3611d14] + ColorVectorSpace v0.10.0 [5ae59095] + Colors v0.12.11 [bbf7d656] + 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To see why use `status --outdated -m` Instantiating... === Precompiling... ===  Activating project at `/tmp/jl_YHjA0B`§enabledĂ·restart_recommended_msgÀŽrestart_required_msgÀ­busy_packages¶waiting_for_permissionÂÙ,waiting_for_permission_but_probably_disabled«cell_inputsȚÙ$b4e81aef-3750-4fe7-ad59-12f67f0fc8bd„§cell_idÙ$b4e81aef-3750-4fe7-ad59-12f67f0fc8bd€codeÙifunction busemann(p, x::AbstractVector{T}) where {T} log(ℓÂČ(p .- x)) - log(1 - ℓÂČ(x) + eps(T)) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$4bd99ceb-4f4d-4e93-8f4d-843ee938d0f5„§cell_idÙ$4bd99ceb-4f4d-4e93-8f4d-843ee938d0f5€codeÙĂfunction plot_grad!(X, P, η) ∇X = Zygote.gradient(X) do X busemann(P, X) end |> first quiver!( [X[1]], [X[2]], quiver=( [-η * ∇X[1]], [-η * ∇X[2]], ), c=:gray ) endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$e5f4c5bb-c428-44ad-9742-d9100fde81b8„§cell_idÙ$e5f4c5bb-c428-44ad-9742-d9100fde81b8€code­import Zygotešmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$2d83e522-adf7-49ff-9ee3-103ad114729b„§cell_idÙ$2d83e522-adf7-49ff-9ee3-103ad114729b€codeč@bind y Slider(1:-0.01:0)šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$9f51ead7-9c85-43bf-a130-2fb83f73bf07„§cell_idÙ$9f51ead7-9c85-43bf-a130-2fb83f73bf07€code©Î· = 0.02šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$dddb092c-9f77-424d-a121-d322ac48c486„§cell_idÙ$dddb092c-9f77-424d-a121-d322ac48c486€code·â„“ÂČ(x) = sum(abs2, x)šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$831ded87-a43d-49cb-ad00-798e91278f3b„§cell_idÙ$831ded87-a43d-49cb-ad00-798e91278f3b€codeźbusemann(P, X)šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$c990f454-b742-11ed-27cc-0329720bd3ae„§cell_idÙ$c990f454-b742-11ed-27cc-0329720bd3ae€code«using Plotsšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$35fcbd85-7e9c-4472-8aeb-5827e882306c„§cell_idÙ$35fcbd85-7e9c-4472-8aeb-5827e882306c€codeŹX = [0.2, y]šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$ebf877da-fe89-44e2-a336-173c9e947365„§cell_idÙ$ebf877da-fe89-44e2-a336-173c9e947365€code­using PlutoUIšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$3d1cc33f-6f77-43a0-a443-7f9457712936„§cell_idÙ$3d1cc33f-6f77-43a0-a443-7f9457712936€codeÙYshow_point!((x, y); kwargs...) = scatter!([atan(y, x)], [sqrt(x ^ 2 + y ^ 2)]; kwargs...)šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$b0cfeeda-f0a4-4044-9021-1fa65148984a„§cell_idÙ$b0cfeeda-f0a4-4044-9021-1fa65148984a€codeÙ;∇X = Zygote.gradient(X) do X busemann(P, X) end |> firstšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$cb6999da-4eff-49b9-8925-bde8233f0864„§cell_idÙ$cb6999da-4eff-49b9-8925-bde8233f0864€codeÚ$let plot(proj = :polar) ylims!(0., 1.) ∇XΞ = atan(-∇X[2], -∇X[1]) ∇XR = √(ℓÂČ(∇X)) quiver!( [atan(X[2], X[1])], [√(ℓÂČ(X))], quiver=( [∇XΞ], # [η * ∇X[1]], [∇XR] # [η * ∇X[2]], ) ) show_point!(P, label="P") show_point!(X, label="X") endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$21af9a69-ad7f-4871-8a21-5ee9c45a1bc4„§cell_idÙ$21af9a69-ad7f-4871-8a21-5ee9c45a1bc4€codełusing LinearAlgebrašmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$8a59810b-0de9-46c8-b71d-deb33525ae27„§cell_idÙ$8a59810b-0de9-46c8-b71d-deb33525ae27€codeÚÆlet circleshape() = let Ξ = LinRange(0, 2π, 100) cos.(Ξ), sin.(Ξ) end plot(circleshape(), size=(800,800), label=nothing) scatter!([P[1]], [P[2]], label="P") #scatter!([X[1]], [X[2]], label="X") ylims!(-1, 1) xlims!(-1, 1.) for Ξ in π:-0.1:-π for r in -.2:0.08:0.95 X = [r * cos(Ξ), r * sin(Ξ)] # scatter!([X[1]],[X[2]], label=nothing) plot_grad!(X, P, η) end end title!("Gradient busemann(p, x)") plot!() endšmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_foldedÂÙ$db4fb9a0-2c40-41b0-9c17-2bdd0cb634d4„§cell_idÙ$db4fb9a0-2c40-41b0-9c17-2bdd0cb634d4€codeŹP = [1., 0.]šmetadataƒ©show_logsĂšdisabledÂźskip_as_script«code_folded«notebook_idÙ$e92d7406-8a3e-11ef-2607-7f4f71c39a44«in_temp_diršmetadata€