RDM (version 0.1.1)

sortDSMatrix: 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)

Value

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

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.

Examples

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