Alternate row and column normalisation until the row sums deviate from 1
by less than tol (Sinkhorn 1964); converges for matrices with total
support (every nonzero entry on a positive diagonal).
Usage
SinkhornWeights(W, tol = 1e-12, maxit = 10000L)
Arguments
- W
Non-negative square matrix.
- tol
Tolerance.
- maxit
Maximum sweeps.
Value
List with W, iterations, deviation.
References
Sinkhorn, R. (1964). A relationship between arbitrary positive
matrices and doubly stochastic matrices. The Annals of Mathematical
Statistics 35, 876-879.
Examples
SinkhornWeights(rbind(c(0, 1, 1), c(1, 0, 1), c(1, 1, 0)))$W
#> [,1] [,2] [,3]
#> [1,] 0.0 0.5 0.5
#> [2,] 0.5 0.0 0.5
#> [3,] 0.5 0.5 0.0
