sinkhorn_knopp

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sinkhorn_knopp(mat, num_iter=100, rescalings=False)

Given a matrix of weights, generates a bistochastic matrix using the Sinkhorn-Knopp algorithm.

A bistochastic matrix is one where the sum of rows is always equal to one, and the sum of columns is always equal to one. That is, \(T_{ij}\) is bistochastic if \(\sum_{j} T_{ij} = \sum_{j} T_{ji} = 1\) for all \(i\).

For any matrix \(M\), there is a unique pair of diagonal matrices \(D_L\) and \(D_R\) such that \(D_L^{-1} M D_R^{-1}\) is bistochastic. The Sinkhorn-Knopp algorithm determines these matrices iteratively. This function will return the resulting bistochastic matrix and, optionally, the diagonal weights of the rescaling matrices.