Barycentric projection of a transport plan

$$\bar{T}(x_i) = \frac{1}{a_i}\sum_j P_{ij} y_j$$ Peyre & Cuturi (2019), Remark 4.11, eq. (4.19).

Usage

Otbarmap(T, Y)

Arguments

T

Coupling matrix, n x m.

Y

Destination points, m x d.

Value

Named list with estimate (n x d image points), mass, displacement, method.

References

Peyre & Cuturi (2019), eq. (4.19).

Examples

Tm <- matrix(c(0.4, 0.1, 0.1, 0.4), 2)   # a 2 x 2 coupling
Y <- matrix(c(0, 1, 0, 1), 2)              # two destination points in the plane
Otbarmap(Tm, Y)
#> $estimate
#>      [,1] [,2]
#> [1,]  0.2  0.2
#> [2,]  0.8  0.8
#> 
#> $mass
#> [1] 0.5 0.5
#> 
#> $displacement
#> [1] 0.32
#> 
#> $method
#> [1] "Barycentric projection of a plan -- Peyre & Cuturi (2019) eq. (4.19)"
#>