(S|D|C|Z)GELSD¶

Single, double, single complex, and double complex GELSD.

Description¶

Finds the minimum norm solution to a linear least-squares problem:

$\min || b - A \mult x ||_2$

The matrix A is allowed to be rank deficient.

This routine works by computing the SVD of A. Any singular values less than RCOND times the largest singular value are assumed to be zero. Passing RCOND<0 means machine precision will be used for the cutoff.

The matrix B encodes multiple right-hand sides and produces multiple solution vectors encoded in the matrix X. Each column of B and column of X can be considered a single solution to

$A \mult x = b$

LAPACK Interface¶

void sgelsd(const qml_long *M, const qml_long *N, const qml_long *NRHS, float *A,
    const qml_long *LDA, float *B, const qml_long *LDB, float *S,
    const float *RCOND, qml_long *RANK, float *WORK, const qml_long *LWORK,
    qml_long *IWORK, qml_long *INFO);

void dgelsd(const qml_long *M, const qml_long *N, const qml_long *NRHS, double *A,
    const qml_long *LDA, double *B, const qml_long *LDB, double *S,
    const double *RCOND, qml_long *RANK, double *WORK,
    const qml_long *LWORK, qml_long *IWORK, qml_long *INFO);

void cgelsd(const qml_long *M, const qml_long *N, const qml_long *NRHS,
    qml_single_complex *A, const qml_long *LDA, qml_single_complex *B,
    const qml_long *LDB, float *S, const float *RCOND, qml_long *RANK,
    qml_single_complex *WORK, const qml_long *LWORK, float *RWORK,
    qml_long *IWORK, qml_long *INFO);

void zgelsd(const qml_long *M, const qml_long *N, const qml_long *NRHS,
    qml_double_complex *A, const qml_long *LDA, qml_double_complex *B,
    const qml_long *LDB, double *S, const double *RCOND, qml_long *RANK,
    qml_double_complex *WORK, const qml_long *LWORK, double *RWORK,
    qml_long *IWORK, qml_long *INFO);

Arguments¶

M	Number of rows of A
N	Number of columns of A
NRHS	Number of right hand sides, number of columns of B and X
A	Matrix of size M x N, overwritten on exit
LDA	Leading dimension of A
B	Matrix of right hand side vectors, overwritten with X on exit
LDB	Leading dimension of B
S	On exit contains singular values in decreasing order, length min(M, N)
RCOND	Determines which singular values to consider zero
RANK	On exit contains effective rank of A
WORK	Work space of size at least LWORK
LWORK	Size of work space (-1 to query WORK and IWORK)
RWORK	Work space (query size required with LWORK=-1)
IWORK	Integer work space (query size required with LWORK=-1)
INFO	0 on success, <0 for illegal arguments, >0 if SVD failed