Þ ¥bonds€¬cell_resultsƒÙ$84ad50e6-f233-11ec-052c-097e5edd711aŠ¦queuedÂ¤logs§runningÂ¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÙÃKhl
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The function `isless` exists, but no method is defined for this combination of argument types.

[0mClosest candidates are:
[0m  isless([91m::Missing[39m, ::Any)
[0m[90m   @[39m [90mBase[39m [90m[4mmissing.jl:87[24m[39m
[0m  isless(::Any, [91m::Missing[39m)
[0m[90m   @[39m [90mBase[39m [90m[4mmissing.jl:88[24m[39m
[0m  isless([91m::Base.UUID[39m, [91m::Base.UUID[39m)
[0m[90m   @[39m [90mBase[39m [90m[4muuid.jl:106[24m[39m
[0m  ...
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            Installed           MathOptInterface â”€â”€â”€ v1.4.0                     [32m[1m[22m[39m
                                                                                
[0m[1mResolving...[22m
[90m===[39m
[36m[1mâ”Œ [22m[39m[36m[1mInfo: [22m[39mOperation failed. Updating registries and trying again...
[36m[1mâ”‚ [22m[39m  exception =
[36m[1mâ”‚ [22m[39m   Unsatisfiable requirements detected for package StaticArrays [90137ffa]:
[36m[1mâ”‚ [22m[39m    StaticArrays [90137ffa] log:
[36m[1mâ”‚ [22m[39m    â”œâ”€possible versions are: 0.8.0 - 1.9.7 or uninstalled
[36m[1mâ”‚ [22m[39m    â”œâ”€restricted to versions 1.4.7 by an explicit requirement, leaving only versions: 1.4.7
[36m[1mâ”” [22m[39m    â””â”€restricted by julia compatibility requirements to versions: [0.12.0 - 0.12.6, 1.5.0 - 1.9.7] or uninstalled â€” no versions left

[0m[1mResolving...[22m
[90m===[39m
[33m[1mâ”Œ [22m[39m[33m[1mWarning: [22m[39mOperation failed. Removing Manifest and trying again...
[33m[1mâ”‚ [22m[39m  exception =
[33m[1mâ”‚ [22m[39m   Unsatisfiable requirements detected for package StaticArrays [90137ffa]:
[33m[1mâ”‚ [22m[39m    StaticArrays [90137ffa] log:
[33m[1mâ”‚ [22m[39m    â”œâ”€possible versions are: 0.8.0 - 1.9.7 or uninstalled
[33m[1mâ”‚ [22m[39m    â”œâ”€restricted to versions 1.4.7 by an explicit requirement, leaving only versions: 1.4.7
[33m[1mâ”‚ [22m[39m    â””â”€restricted by julia compatibility requirements to versions: [0.12.0 - 0.12.6, 1.5.0 - 1.9.7] or uninstalled â€” no versions left
[33m[1mâ”” [22m[39m[90m@ Pluto ~/.julia/packages/Pluto/6smog/src/packages/Packages.jl:494[39m

[0m[1mResolving...[22m
[90m===[39m
[32m[1m    Updating[22m[39m `/tmp/jl_v7AI8l/Project.toml`
[33mâŒ…[39m [90m[60bf3e95] [39m[92m+ GLPK v1.0.1[39m
[33mâŒ…[39m [90m[4076af6c] [39m[92m+ JuMP v1.1.1[39m
[32m[1m    Updating[22m[39m `/tmp/jl_v7AI8l/Manifest.toml`
  [90m[6e4b80f9] [39m[92m+ BenchmarkTools v1.5.0[39m
  [90m[49dc2e85] [39m[92m+ Calculus v0.5.1[39m
  [90m[523fee87] [39m[92m+ CodecBzip2 v0.8.4[39m
  [90m[944b1d66] [39m[92m+ CodecZlib v0.7.6[39m
  [90m[bbf7d656] [39m[92m+ CommonSubexpressions v0.3.1[39m
  [90m[34da2185] [39m[92m+ Compat v4.16.0[39m
  [90m[864edb3b] [39m[92m+ DataStructures v0.18.20[39m
  [90m[163ba53b] [39m[92m+ DiffResults v1.1.0[39m
  [90m[b552c78f] [39m[92m+ DiffRules v1.15.1[39m
  [90m[ffbed154] [39m[92m+ DocStringExtensions v0.9.3[39m
  [90m[f6369f11] [39m[92m+ ForwardDiff v0.10.36[39m
[33mâŒ…[39m [90m[60bf3e95] [39m[92m+ GLPK v1.0.1[39m
  [90m[92d709cd] [39m[92m+ IrrationalConstants v0.2.2[39m
  [90m[692b3bcd] [39m[92m+ JLLWrappers v1.6.1[39m
  [90m[682c06a0] [39m[92m+ JSON v0.21.4[39m
[33mâŒ…[39m [90m[4076af6c] [39m[92m+ JuMP v1.1.1[39m
  [90m[2ab3a3ac] [39m[92m+ LogExpFunctions v0.3.28[39m
  [90m[1914dd2f] [39m[92m+ MacroTools v0.5.13[39m
  [90m[b8f27783] [39m[92m+ MathOptInterface v1.31.2[39m
  [90m[d8a4904e] [39m[92m+ MutableArithmetics v1.5.1[39m
  [90m[77ba4419] [39m[92m+ NaNMath v1.0.2[39m
  [90m[bac558e1] [39m[92m+ OrderedCollections v1.6.3[39m
  [90m[69de0a69] [39m[92m+ Parsers v2.8.1[39m
  [90m[aea7be01] [39m[92m+ PrecompileTools v1.2.1[39m
  [90m[21216c6a] [39m[92m+ Preferences v1.4.3[39m
  [90m[276daf66] [39m[92m+ SpecialFunctions v2.4.0[39m
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  [90m[ca575930] [39m[92m+ NetworkOptions v1.2.0[39m
  [90m[44cfe95a] [39m[92m+ Pkg v1.11.0[39m
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  [90m[9abbd945] [39m[92m+ Profile v1.11.0[39m
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  [90m[ea8e919c] [39m[92m+ SHA v0.7.0[39m
  [90m[9e88b42a] [39m[92m+ Serialization v1.11.0[39m
  [90m[2f01184e] [39m[92m+ SparseArrays v1.11.0[39m
  [90m[fa267f1f] [39m[92m+ TOML v1.0.3[39m
  [90m[a4e569a6] [39m[92m+ Tar v1.10.0[39m
  [90m[8dfed614] [39m[92m+ Test v1.11.0[39m
  [90m[cf7118a7] [39m[92m+ UUIDs v1.11.0[39m
  [90m[4ec0a83e] [39m[92m+ Unicode v1.11.0[39m
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  [90m[deac9b47] [39m[92m+ LibCURL_jll v8.6.0+0[39m
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  [90m[29816b5a] [39m[92m+ LibSSH2_jll v1.11.0+1[39m
  [90m[c8ffd9c3] [39m[92m+ MbedTLS_jll v2.28.6+0[39m
  [90m[14a3606d] [39m[92m+ MozillaCACerts_jll v2023.12.12[39m
  [90m[4536629a] [39m[92m+ OpenBLAS_jll v0.3.27+1[39m
  [90m[05823500] [39m[92m+ OpenLibm_jll v0.8.1+2[39m
  [90m[bea87d4a] [39m[92m+ SuiteSparse_jll v7.7.0+0[39m
  [90m[83775a58] [39m[92m+ Zlib_jll v1.2.13+1[39m
  [90m[8e850b90] [39m[92m+ libblastrampoline_jll v5.11.0+0[39m
  [90m[8e850ede] [39m[92m+ nghttp2_jll v1.59.0+0[39m
  [90m[3f19e933] [39m[92m+ p7zip_jll v17.4.0+2[39m
[36m[1m        Info[22m[39m Packages marked with [33mâŒ…[39m have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

[0m[1mInstantiating...[22m
[90m===[39m

[0m[1mPrecompiling...[22m
[90m===[39m
[32m[1m  Activating[22m[39m project at `/tmp/jl_v7AI8l`
[92m[1mPrecompiling[22m[39m project...
   1313.6 ms[32m  âœ“ [39m[90mCalculus[39m
   9777.0 ms[32m  âœ“ [39mGLPK
  13898.2 ms[32m  âœ“ [39mJuMP
  3 dependencies successfully precompiled in 15 seconds. 64 already precompiled.¤JuMPÚ
[0m[1mInstantiating...[22m
[90m===[39m
[33m[1mâ”Œ [22m[39m[33m[1mWarning: [22m[39mThe active manifest file has dependencies that were resolved with a different julia version (1.7.3). Unexpected behavior may occur.
[33m[1mâ”” [22m[39m[90m@ /tmp/jl_v7AI8l/Manifest.toml:0[39m
[32m[1m   Installed[22m[39m JuMP â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.1.1
            Installed           ForwardDiff â”€â”€â”€â”€â”€â”€â”€â”€ v0.10.30                  [32m[1m[22m[39m
            Installed           LogExpFunctions â”€â”€â”€â”€ v0.3.15                   [32m[1m[22m[39m
            Installed           DiffRules â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.11.0                   [32m[1m[22m[39m
            Installed           StaticArrays â”€â”€â”€â”€â”€â”€â”€ v1.4.7                    [32m[1m[22m[39m
            Installed           SpecialFunctions â”€â”€â”€ v2.1.6                    [32m[1m[22m[39m
            Installed           MutableArithmetics â”€ v1.0.4                    [32m[1m[22m[39m
            Installed           ChainRulesCore â”€â”€â”€â”€â”€ v1.15.0                   [32m[1m[22m[39m
            Installed           ChangesOfVariables â”€ v0.1.3                    [32m[1m[22m[39m
            Installed           GLPK â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.0.1                    [32m[1m[22m[39m
            Installed           MathOptInterface â”€â”€â”€ v1.4.0                     [32m[1m[22m[39m
                                                                                
[0m[1mResolving...[22m
[90m===[39m
[36m[1mâ”Œ [22m[39m[36m[1mInfo: [22m[39mOperation failed. Updating registries and trying again...
[36m[1mâ”‚ [22m[39m  exception =
[36m[1mâ”‚ [22m[39m   Unsatisfiable requirements detected for package StaticArrays [90137ffa]:
[36m[1mâ”‚ [22m[39m    StaticArrays [90137ffa] log:
[36m[1mâ”‚ [22m[39m    â”œâ”€possible versions are: 0.8.0 - 1.9.7 or uninstalled
[36m[1mâ”‚ [22m[39m    â”œâ”€restricted to versions 1.4.7 by an explicit requirement, leaving only versions: 1.4.7
[36m[1mâ”” [22m[39m    â””â”€restricted by julia compatibility requirements to versions: [0.12.0 - 0.12.6, 1.5.0 - 1.9.7] or uninstalled â€” no versions left

[0m[1mResolving...[22m
[90m===[39m
[33m[1mâ”Œ [22m[39m[33m[1mWarning: [22m[39mOperation failed. Removing Manifest and trying again...
[33m[1mâ”‚ [22m[39m  exception =
[33m[1mâ”‚ [22m[39m   Unsatisfiable requirements detected for package StaticArrays [90137ffa]:
[33m[1mâ”‚ [22m[39m    StaticArrays [90137ffa] log:
[33m[1mâ”‚ [22m[39m    â”œâ”€possible versions are: 0.8.0 - 1.9.7 or uninstalled
[33m[1mâ”‚ [22m[39m    â”œâ”€restricted to versions 1.4.7 by an explicit requirement, leaving only versions: 1.4.7
[33m[1mâ”‚ [22m[39m    â””â”€restricted by julia compatibility requirements to versions: [0.12.0 - 0.12.6, 1.5.0 - 1.9.7] or uninstalled â€” no versions left
[33m[1mâ”” [22m[39m[90m@ Pluto ~/.julia/packages/Pluto/6smog/src/packages/Packages.jl:494[39m

[0m[1mResolving...[22m
[90m===[39m
[32m[1m    Updating[22m[39m `/tmp/jl_v7AI8l/Project.toml`
[33mâŒ…[39m [90m[60bf3e95] [39m[92m+ GLPK v1.0.1[39m
[33mâŒ…[39m [90m[4076af6c] [39m[92m+ JuMP v1.1.1[39m
[32m[1m    Updating[22m[39m `/tmp/jl_v7AI8l/Manifest.toml`
  [90m[6e4b80f9] [39m[92m+ BenchmarkTools v1.5.0[39m
  [90m[49dc2e85] [39m[92m+ Calculus v0.5.1[39m
  [90m[523fee87] [39m[92m+ CodecBzip2 v0.8.4[39m
  [90m[944b1d66] [39m[92m+ CodecZlib v0.7.6[39m
  [90m[bbf7d656] [39m[92m+ CommonSubexpressions v0.3.1[39m
  [90m[34da2185] [39m[92m+ Compat v4.16.0[39m
  [90m[864edb3b] [39m[92m+ DataStructures v0.18.20[39m
  [90m[163ba53b] [39m[92m+ DiffResults v1.1.0[39m
  [90m[b552c78f] [39m[92m+ DiffRules v1.15.1[39m
  [90m[ffbed154] [39m[92m+ DocStringExtensions v0.9.3[39m
  [90m[f6369f11] [39m[92m+ ForwardDiff v0.10.36[39m
[33mâŒ…[39m [90m[60bf3e95] [39m[92m+ GLPK v1.0.1[39m
  [90m[92d709cd] [39m[92m+ IrrationalConstants v0.2.2[39m
  [90m[692b3bcd] [39m[92m+ JLLWrappers v1.6.1[39m
  [90m[682c06a0] [39m[92m+ JSON v0.21.4[39m
[33mâŒ…[39m [90m[4076af6c] [39m[92m+ JuMP v1.1.1[39m
  [90m[2ab3a3ac] [39m[92m+ LogExpFunctions v0.3.28[39m
  [90m[1914dd2f] [39m[92m+ MacroTools v0.5.13[39m
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  [90m[aea7be01] [39m[92m+ PrecompileTools v1.2.1[39m
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  [90m[6e34b625] [39m[92m+ Bzip2_jll v1.0.8+1[39m
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  [90m[b77e0a4c] [39m[92m+ InteractiveUtils v1.11.0[39m
  [90m[b27032c2] [39m[92m+ LibCURL v0.6.4[39m
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  [90m[44cfe95a] [39m[92m+ Pkg v1.11.0[39m
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  [90m[c8ffd9c3] [39m[92m+ MbedTLS_jll v2.28.6+0[39m
  [90m[14a3606d] [39m[92m+ MozillaCACerts_jll v2023.12.12[39m
  [90m[4536629a] [39m[92m+ OpenBLAS_jll v0.3.27+1[39m
  [90m[05823500] [39m[92m+ OpenLibm_jll v0.8.1+2[39m
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  [90m[83775a58] [39m[92m+ Zlib_jll v1.2.13+1[39m
  [90m[8e850b90] [39m[92m+ libblastrampoline_jll v5.11.0+0[39m
  [90m[8e850ede] [39m[92m+ nghttp2_jll v1.59.0+0[39m
  [90m[3f19e933] [39m[92m+ p7zip_jll v17.4.0+2[39m
[36m[1m        Info[22m[39m Packages marked with [33mâŒ…[39m have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

[0m[1mInstantiating...[22m
[90m===[39m

[0m[1mPrecompiling...[22m
[90m===[39m
[32m[1m  Activating[22m[39m project at `/tmp/jl_v7AI8l`
[92m[1mPrecompiling[22m[39m project...
   1313.6 ms[32m  âœ“ [39m[90mCalculus[39m
   9777.0 ms[32m  âœ“ [39mGLPK
  13898.2 ms[32m  âœ“ [39mJuMP
  3 dependencies successfully precompiled in 15 seconds. 64 already precompiled.§enabledÃ·restart_recommended_msgÀ´restart_required_msgÀ­busy_packages¶waiting_for_permissionÂÙ,waiting_for_permission_but_probably_disabledÂ«cell_inputsƒÙ$84ad50e6-f233-11ec-052c-097e5edd711a„§cell_idÙ$84ad50e6-f233-11ec-052c-097e5edd711a¤code°using JuMP, GLPK¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$2af8710a-30a7-4abe-b1ec-f55628e06e54„§cell_idÙ$2af8710a-30a7-4abe-b1ec-f55628e06e54¤codeÚUfunction emd_dual_c_transform(a, b, C)
	Nx = length(a); Ny = length(b)

	# Create the JuMP model
	model = Model(GLPK.Optimizer)
	
	@variable(model, f[1:Nx] >= 0)

	# Create the objective which is the cost
	@objective(model, Max, sum(
		a[i] * f[i] for i in 1:Nx
	) + sum(
		b[j] * minimum(C[i,j] - f[i] for i in 1:Nx) for j in 1:Ny
	))


end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$9ecb68db-05eb-459e-b0e5-99ff7e0c13ec„§cell_idÙ$9ecb68db-05eb-459e-b0e5-99ff7e0c13ec¤codeÙOlet
	a = [.9, .1]
	b = a
	C = [.2 .1; 2. 3.]
	emd_dual_c_transform(a, b, C)
end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂ«notebook_idÙ$5a357266-8a3a-11ef-2685-b32a7fa9e767«in_temp_dirÂ¨metadata€