(S|D|C|Z)GESDD¶

Single, double, single complex, and double complex GESDD.

Description¶

Computes the singular value decomposition (SVD) of a general matrix, and optionally the right/left singular vectors.

The matrix A is decomposed:

$A = U \mult \Sigma \mult \herm{V}$

The matrix $\Sigma$ is an MxN matrix that is zero except on the diagonal. U is an MxM unitary matrix, and V is an NxN unitary matrix. The diagonal elements of $\Sigma$ are the singular values, ordered from largest to smallest in magnitude.

Uses the divide-and-conquer algorithm.

LAPACK Interface¶

void sgesdd(const char *JOBZ, const qml_long *M, const qml_long *N, float *A,
    const qml_long *LDA, float *S, float *U, const qml_long *LDU,
    float *VT, const qml_long *LDVT, float *WORK, const qml_long *LWORK,
    qml_long *IWORK, qml_long *INFO);

void dgesdd(const char *JOBZ, const qml_long *M, const qml_long *N, double *A,
    const qml_long *LDA, double *S, double *U, const qml_long *LDU,
    double *VT, const qml_long *LDVT, double *WORK, const qml_long *LWORK,
    qml_long *IWORK, qml_long *INFO);

void cgesdd(const char *JOBZ, const qml_long *M, const qml_long *N,
    qml_single_complex *A, const qml_long *LDA, float *S,
    qml_single_complex *U, const qml_long *LDU, qml_single_complex *VT,
    const qml_long *LDVT, qml_single_complex *WORK, const qml_long *LWORK,
    float *RWORK, qml_long *IWORK, qml_long *INFO);

void zgesdd(const char *JOBZ, const qml_long *M, const qml_long *N,
    qml_double_complex *A, const qml_long *LDA, double *S,
    qml_double_complex *U, const qml_long *LDU, qml_double_complex *VT,
    const qml_long *LDVT, qml_double_complex *WORK, const qml_long *LWORK,
    double *RWORK, qml_long *IWORK, qml_long *INFO);

Arguments¶

JOBU	What to compute for U and VT, ‘A’ (all), ‘S’ (singular vectors), ‘O’ (overwrite A), ‘N’ (none)
M	Number of rows of A
N	Number of columns of A
A	Matrix of size M x N, overwritten on exit
LDA	Leading dimension of A
S	Array of size min(M, N), singular values in decreasing order
U	Matrix containing left singular vectors as columns
LDU	Leading dimension of U
VT	Matrix containing right singular vectors as rows
LDVT	Leading dimension of VT
WORK	Workspace of size at least LWORK
LWORK	Size of workspace (-1 to query)
IWORK	Integer workspace of size 8*min(M, N)
INFO	0 on success, <0 for bad arguments, >0 if no convergence