About maxvolpy¶
Module maxvolpy is designed for constructing different low-rank skeleton and cross approximations.
Right now, cross approximation techniques are not implemented yet, but all kinds of algorithms of finding good submatrices to build skeleton approximations are presented in maxvol submodule. What does good submatrix mean is noted in documentation for maxvol submodule.
Contents:
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. |