svd.h File Reference

Singular value decomposition WITH the singular vectors, and the Moore-Penrose pseudo-inverse built from it. More...

#include <cstddef>
#include <vector>
#include "line/util/eig.h"
#include "line/util/error.h"
#include "line/util/matrix.h"

Include dependency graph for svd.h:

Go to the source code of this file.

Classes
struct	line::SvdFactors
	A = U diag(s) Vt, with U (m x m), s of length min(m,n) and Vt (n x n). More...

Namespaces
namespace	line

Functions
SvdFactors	line::svd_full (const Matrix< double > &A)
	Full SVD of a real matrix, singular values in descending order.
Matrix< double >	line::pinv (const Matrix< double > &A)
	Moore-Penrose pseudo-inverse, A^+ = V diag(1/s_i) U^T over the singular values above max(m,n) eps sigma_1, which is MATLAB's default pinv tolerance.

Detailed Description

Singular value decomposition WITH the singular vectors, and the Moore-Penrose pseudo-inverse built from it.

util/eig.h already exposes the singular VALUES (dgesvd with jobu = jobvt = 'N'), which is all the rank and conditioning tests need. This header adds the factors themselves, for the one place in the port that needs them: the pinv fallback of ldqbd_R, taken when a level's local block is singular.

DOUBLE ONLY, for the same reason eig.h is: singular values of a rational matrix are algebraic, not rational, so there is no exact instantiation to offer, and LAPACK has no multiprecision path. Callers templated on T must convert and state the precision loss at the call site. Configured without LAPACK the entry points throw UnsupportedError naming the dependency rather than substituting anything.

The Fortran symbol dgesvd_ is declared by eig.h under the same LAPACK guard and is reused from there, so there is exactly one declaration of it in the tree.

Definition in file svd.h.