Add mm_unbalanced function (#22)

* Add mm_unbalanced function

* Update api.md

* Update src/lib.jl

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>

* Update src/lib.jl

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>

* Update src/lib.jl

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>

* Update src/lib.jl

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>

* Update src/lib.jl

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>

* Update src/lib.jl

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>

* Update src/lib.jl

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>

* Add doctest in mm_unbalanced function

---------

Co-authored-by: David Widmann <devmotion@users.noreply.github.com>

Author: pnavaro

Project.toml

@@ -1,7 +1,7 @@
 name = "PythonOT"
 uuid = "3c485715-4278-42b2-9b5f-8f00e43c12ef"
 authors = ["David Widmann"]
-version = "0.1.5"
+version = "0.1.6"
 
 [deps]
 PyCall = "438e738f-606a-5dbb-bf0a-cddfbfd45ab0"

docs/src/api.md

@@ -35,4 +35,5 @@ PythonOT.Smooth.smooth_ot_dual
 sinkhorn_unbalanced
 sinkhorn_unbalanced2
 barycenter_unbalanced
+mm_unbalanced
 ```

src/PythonOT.jl

@@ -12,7 +12,8 @@ export emd,
     barycenter_unbalanced,
     sinkhorn_unbalanced,
     sinkhorn_unbalanced2,
-    empirical_sinkhorn_divergence
+    empirical_sinkhorn_divergence,
+    mm_unbalanced
 
 const pot = PyCall.PyNULL()
 

src/lib.jl

@@ -312,11 +312,11 @@ julia> ν = [0.0, 1.0];
 
 julia> C = [0.0 1.0; 2.0 0.0; 0.5 1.5];
 
-julia> sinkhorn_unbalanced(μ, ν, C, 0.01, 1_000)
+julia> round.(sinkhorn_unbalanced(μ, ν, C, 0.01, 1_000); sigdigits=4)
 3×2 Matrix{Float64}:
- 0.0  0.499964
- 0.0  0.200188
- 0.0  0.29983
+ 0.0  0.5
+ 0.0  0.2002
+ 0.0  0.2998
 ```
 
 It is possible to provide multiple target marginals as columns of a matrix. In this case the
@@ -325,10 +325,10 @@ 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)
+julia> round.(sinkhorn_unbalanced(μ, ν, C, 0.01, 1_000); sigdigits=4)
 2-element Vector{Float64}:
- 0.949709
- 0.449411
+ 0.9497
+ 0.4494
 ```
 
 See also: [`sinkhorn_unbalanced2`](@ref)
@@ -371,20 +371,19 @@ julia> ν = [0.0, 1.0];
 
 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
+julia> round.(sinkhorn_unbalanced2(μ, ν, C, 0.01, 1_000); sigdigits=4)
+0.9497
 ```
 
 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)
+julia> round.(sinkhorn_unbalanced2(μ, ν, C, 0.01, 1_000); sigdigits=4)
 2-element Vector{Float64}:
- 0.949709
- 0.449411
+ 0.9497
+ 0.4494
 ```
 
 See also: [`sinkhorn_unbalanced`](@ref)
@@ -516,3 +515,54 @@ Python function.
 function entropic_gromov_wasserstein(μ, ν, Cμ, Cν, ε, loss="square_loss"; kwargs...)
     return pot.gromov.entropic_gromov_wasserstein(Cμ, Cν, μ, ν, loss, ε; kwargs...)
 end
+
+"""
+    mm_unbalanced(a, b, M, reg_m; reg=0, c=a*b', kwargs...)
+
+Solve the unbalanced optimal transport problem and return the OT plan.
+The function solves the following optimization problem:
+
+```math
+W = \\min_{\\gamma \\geq 0} \\langle \\gamma, M \\rangle_F +
+    \\mathrm{reg_{m1}} \\cdot \\operatorname{div}(\\gamma \\mathbf{1}, a) +
+    \\mathrm{reg_{m2}} \\cdot \\operatorname{div}(\\gamma^\\mathsf{T} \\mathbf{1}, b) +
+    \\mathrm{reg} \\cdot \\operatorname{div}(\\gamma, c)
+```
+
+where
+
+- `M` is the metric cost matrix,
+- `a` and `b` are source and target unbalanced distributions,
+- `c` is a reference distribution for the regularization,
+- `reg_m` is the marginal relaxation term (if it is a scalar or an indexable object of length 1, then the same term is applied to both marginal relaxations), and
+- `reg` is a regularization term.
+
+This function is a wrapper of the function
+[`mm_unbalanced`](https://pythonot.github.io/gen_modules/ot.unbalanced.html#ot.unbalanced.mm_unbalanced) in the
+Python Optimal Transport package. Keyword arguments are listed in the documentation of the
+Python function.
+
+# Examples
+
+```jldoctest
+julia> a=[.5, .5];
+
+julia> b=[.5, .5];
+
+julia> M=[1. 36.; 9. 4.];
+
+julia> round.(mm_unbalanced(a, b, M, 5, div="kl"), digits=2)
+2×2 Matrix{Float64}:
+ 0.45  0.0
+ 0.0   0.34
+
+julia> round.(mm_unbalanced(a, b, M, 5, div="l2"), digits=2)
+2×2 Matrix{Float64}:
+ 0.4  0.0
+ 0.0  0.1
+```
+
+"""
+function mm_unbalanced(a, b, M, reg_m; kwargs...)
+    return pot.unbalanced.mm_unbalanced(a, b, M, reg_m; kwargs...)
+end