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.