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Update and extend documentation #8

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2 changes: 1 addition & 1 deletion docs/src/api.md
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# API

## Exact optimal transport (Kantorovich) problem
## Exact optimal transport

```@docs
emd
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101 changes: 64 additions & 37 deletions src/lib.jl
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"""
emd(μ, ν, C; kwargs...)

Compute the optimal transport map for the Monge-Kantorovich problem with source and target
Compute the optimal transport plan for the Monge-Kantorovich problem with source and target
marginals `μ` and `ν` and cost matrix `C` of size `(length(μ), length(ν))`.

The optimal transport map `γ` is of the same size as `C` and solves
The optimal transport plan `γ` is of the same size as `C` and solves
```math
\\inf_{\\gamma \\in \\Pi(\\mu, \\nu)} \\langle \\gamma, C \\rangle.
```
Expand All @@ -20,9 +20,7 @@ julia> μ = [0.5, 0.2, 0.3];

julia> ν = [0.0, 1.0];

julia> C = [0.0 1.0;
2.0 0.0;
0.5 1.5];
julia> C = [0.0 1.0; 2.0 0.0; 0.5 1.5];

julia> emd(μ, ν, C)
3×2 Matrix{Float64}:
Expand Down Expand Up @@ -59,9 +57,7 @@ julia> μ = [0.5, 0.2, 0.3];

julia> ν = [0.0, 1.0];

julia> C = [0.0 1.0;
2.0 0.0;
0.5 1.5];
julia> C = [0.0 1.0; 2.0 0.0; 0.5 1.5];

julia> emd2(μ, ν, C)
0.95
Expand All @@ -76,11 +72,11 @@ end
"""
sinkhorn(μ, ν, C, ε; kwargs...)

Compute the optimal transport map for the entropic regularization optimal transport problem
Compute the optimal transport plan for the entropic regularization optimal transport problem
with source and target marginals `μ` and `ν`, cost matrix `C` of size
`(length(μ), length(ν))`, and entropic regularization parameter `ε`.

The optimal transport map `γ` is of the same size as `C` and solves
The optimal transport plan `γ` is of the same size as `C` and solves
```math
\\inf_{\\gamma \\in \\Pi(\\mu, \\nu)} \\langle \\gamma, C \\rangle
+ \\varepsilon \\Omega(\\gamma),
Expand All @@ -94,14 +90,12 @@ Transport package. Keyword arguments are listed in the documentation of the Pyth

# Examples

```jldoctest
```jldoctest sinkhorn
julia> μ = [0.5, 0.2, 0.3];

julia> ν = [0.0, 1.0];

julia> C = [0.0 1.0;
2.0 0.0;
0.5 1.5];
julia> C = [0.0 1.0; 2.0 0.0; 0.5 1.5];

julia> sinkhorn(μ, ν, C, 0.01)
3×2 Matrix{Float64}:
Expand All @@ -110,6 +104,18 @@ julia> sinkhorn(μ, ν, C, 0.01)
0.0 0.3
```

It is possible to provide multiple target marginals as columns of a matrix. In this case the
optimal transport costs are returned:

```jldoctest sinkhorn
julia> ν = [0.0 0.5; 1.0 0.5];

julia> round.(sinkhorn(μ, ν, C, 0.01); sigdigits=6)
2-element Vector{Float64}:
0.95
0.45
```

See also: [`sinkhorn2`](@ref)
"""
function sinkhorn(μ, ν, C, ε; kwargs...)
Expand Down Expand Up @@ -137,20 +143,29 @@ Transport package. Keyword arguments are listed in the documentation of the Pyth

# Examples

```jldoctest
```jldoctest sinkhorn2
julia> μ = [0.5, 0.2, 0.3];

julia> ν = [0.0, 1.0];

julia> C = [0.0 1.0;
2.0 0.0;
0.5 1.5];
julia> C = [0.0 1.0; 2.0 0.0; 0.5 1.5];

julia> round.(sinkhorn2(μ, ν, C, 0.01); sigdigits=6)
1-element Vector{Float64}:
0.95
```

It is possible to provide multiple target marginals as columns of a matrix.

```jldoctest sinkhorn2
julia> ν = [0.0 0.5; 1.0 0.5];

julia> round.(sinkhorn2(μ, ν, C, 0.01); sigdigits=6)
2-element Vector{Float64}:
0.95
0.45
```

See also: [`sinkhorn`](@ref)
"""
function sinkhorn2(μ, ν, C, ε; kwargs...)
Expand All @@ -160,12 +175,12 @@ end
"""
sinkhorn_unbalanced(μ, ν, C, ε, λ; kwargs...)

Compute the optimal transport map for the unbalanced entropic regularization optimal
Compute the optimal transport plan for the unbalanced entropic regularization optimal
transport problem with source and target marginals `μ` and `ν`, cost matrix `C` of size
`(length(μ), length(ν))`, entropic regularization parameter `ε`, and marginal relaxation
term `λ`.

The optimal transport map `γ` is of the same size as `C` and solves
The optimal transport plan `γ` is of the same size as `C` and solves
```math
\\inf_{\\gamma} \\langle \\gamma, C \\rangle
+ \\varepsilon \\Omega(\\gamma)
Expand All @@ -182,14 +197,12 @@ Python function.

# Examples

```jldoctest
```jldoctest sinkhorn_unbalanced
julia> μ = [0.5, 0.2, 0.3];

julia> ν = [0.0, 1.0];

julia> C = [0.0 1.0;
2.0 0.0;
0.5 1.5];
julia> C = [0.0 1.0; 2.0 0.0; 0.5 1.5];

julia> sinkhorn_unbalanced(μ, ν, C, 0.01, 1_000)
3×2 Matrix{Float64}:
Expand All @@ -198,6 +211,18 @@ julia> sinkhorn_unbalanced(μ, ν, C, 0.01, 1_000)
0.0 0.29983
```

It is possible to provide multiple target marginals as columns of a matrix. In this case the
optimal transport costs are returned:

```jldoctest sinkhorn_unbalanced
julia> ν = [0.0 0.5; 1.0 0.5];

julia> round.(sinkhorn_unbalanced(μ, ν, C, 0.01, 1_000); sigdigits=6)
2-element Vector{Float64}:
0.949709
0.449411
```

See also: [`sinkhorn_unbalanced2`](@ref)
"""
function sinkhorn_unbalanced(μ, ν, C, ε, λ; kwargs...)
Expand Down Expand Up @@ -231,20 +256,29 @@ Python function.

# Examples

```jldoctest
```jldoctest sinkhorn_unbalanced2
julia> μ = [0.5, 0.2, 0.3];

julia> ν = [0.0, 1.0];

julia> C = [0.0 1.0;
2.0 0.0;
0.5 1.5];
julia> C = [0.0 1.0; 2.0 0.0; 0.5 1.5];

julia> round.(sinkhorn_unbalanced2(μ, ν, C, 0.01, 1_000); sigdigits=6)
1-element Vector{Float64}:
0.949709
```

It is possible to provide multiple target marginals as columns of a matrix:

```jldoctest sinkhorn_unbalanced2
julia> ν = [0.0 0.5; 1.0 0.5];

julia> round.(sinkhorn_unbalanced2(μ, ν, C, 0.01, 1_000); sigdigits=6)
2-element Vector{Float64}:
0.949709
0.449411
```

See also: [`sinkhorn_unbalanced`](@ref)
"""
function sinkhorn_unbalanced2(μ, ν, C, ε, λ; kwargs...)
Expand All @@ -263,7 +297,7 @@ The Wasserstein barycenter is a histogram and solves
```math
\\inf_{a} \\sum_{i} W_{\\varepsilon,C}(a, a_i),
```
where the histograms ``a_i`` are columns of matrix `A` and ``W_{\\varepsilon,C}(a, a_i)}``
where the histograms ``a_i`` are columns of matrix `A` and ``W_{\\varepsilon,C}(a, a_i)``
is the optimal transport cost for the entropically regularized optimal transport problem
with marginals ``a`` and ``a_i``, cost matrix ``C``, and entropic regularization parameter
``\\varepsilon``. Optionally, weights of the histograms ``a_i`` can be provided with the
Expand All @@ -287,11 +321,4 @@ julia> isapprox(sum(barycenter(A, C, 0.01; method="sinkhorn_stabilized")), 1; at
true
```
"""
function barycenter(A, C, ε; kwargs...)
return pot.barycenter(
PyCall.PyReverseDims(permutedims(A)),
PyCall.PyReverseDims(permutedims(C)),
ε;
kwargs...,
)
end
barycenter(A, C, ε; kwargs...) = pot.barycenter(A, C, ε; kwargs...)
4 changes: 1 addition & 3 deletions src/smooth.jl
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Expand Up @@ -42,9 +42,7 @@ julia> μ = [0.5, 0.2, 0.3];

julia> ν = [0.0, 1.0];

julia> C = [0.0 1.0;
2.0 0.0;
0.5 1.5];
julia> C = [0.0 1.0; 2.0 0.0; 0.5 1.5];

julia> smooth_ot_dual(μ, ν, C, 0.01)
3×2 Matrix{Float64}:
Expand Down