maxvol submodule

This submodule contains routines to find good submatrices. How good matrix is depends on special extreme properties of the matrix. Two of this properties are 1-volume and 2-volume with the following formulas:

\(vol_1(A) = \left|\det(A)\right|,\, vol_2(A) = \sqrt{\max(\det(A^HA), \det(AA^H))}\)

Square 1-volume optimization

maxvol(A[, tol, max_iters, top_k_index])	Finds good square submatrix.
maxvol_qr(A[, tol, max_iters, top_k_index])	Finds good square submatrix in Q factor of QR of A.
maxvol_svd(A[, svd_tol, svd_alpha, tol, ...])	Applies SVD truncation and finds good square submatrix.

Rectangular 2-volume optimization

rect_maxvol(A[, tol, maxK, min_add_K, minK, ...])	Finds good rectangular submatrix.
rect_maxvol_qr(A[, tol, maxK, min_add_K, ...])	Finds good rectangular submatrix in Q factor of QR of A.
rect_maxvol_svd(A[, svd_tol, svd_alpha, ...])	Applies SVD truncation and finds good rectangular submatrix.