sortDSMatrix {RDM}

Sort a (possibly non-square) doubly stochastic matrix

Description

Sorts an arbitrary doubly stochastic N_1 \times N_2 matrix A into the matrix A^\uparrow such that the induced checkerboard copula C(A^\uparrow) is stochastically increasing.

Usage

sortDSMatrix(A)

Arguments

A

A (possibly non-square) doubly stochastic matrix or (possibly non-square) checkerboard mass density.

Details

The algorithm to sort a doubly stochastic matrix A is given in Strothmann, Dette and Siburg (2022) <arXiv:2201.03329>. Since this implementation does not depend on the appropriate scaling of the matrix A, both doubly stochastic matrices and checkerboard mass densities are admissible inputs.

Value

The sorted version A^\uparrow of the matrix A.

Examples

n <- 4
A <- diag(n)[n:1, ]
print(A)
sortDSMatrix(A)