(S|D|C|Z)BDSQR¶

Single, double, single complex, and double complex BDSQR.

Description¶

Computes the singular values and (optionally) the right/left singular vectors from the singular value decomposition of a square bidiagonal matrix.

A general dense matrix A can be bidiagonalized to matrix B before calling BDSQR.

$A = U \mult B \mult VT$

BDSQR then computes the singular value decomposition of B as:

$B = Q \mult S \mult \herm{P}$

The result can be interpreted as the singular value decomposition of the original matrix A:

$A = (U \mult Q) \mult S \mult (\herm{P} \mult VT)$

The matrices B, U, and VT are provided as input. BDSQR computes $S$ , $U \mult Q$ , and $\herm{P} \mult VT$ .

LAPACK Interface¶

void sbdsqr(const char *UPLO, const qml_long *N, const qml_long *NCVT,
    const qml_long *NRU, const qml_long *NCC, float *D, float *E,
    float *VT, const qml_long *LDVT, float *U, const qml_long *LDU,
    float *C, const qml_long *LDC, float *RWORK, qml_long *INFO);

void dbdsqr(const char *UPLO, const qml_long *N, const qml_long *NCVT,
    const qml_long *NRU, const qml_long *NCC, double *D, double *E,
    double *VT, const qml_long *LDVT, double *U, const qml_long *LDU,
    double *C, const qml_long *LDC, double *RWORK, qml_long *INFO);

void cbdsqr(const char *UPLO, const qml_long *N, const qml_long *NCVT,
    const qml_long *NRU, const qml_long *NCC, float *D, float *E,
    qml_single_complex *VT, const qml_long *LDVT, qml_single_complex *U,
    const qml_long *LDU, qml_single_complex *C, const qml_long *LDC,
    float *RWORK, qml_long *INFO);

void zbdsqr(const char *UPLO, const qml_long *N, const qml_long *NCVT,
    const qml_long *NRU, const qml_long *NCC, double *D, double *E,
    qml_double_complex *VT, const qml_long *LDVT, qml_double_complex *U,
    const qml_long *LDU, qml_double_complex *C, const qml_long *LDC,
    double *RWORK, qml_long *INFO);

Arguments¶

UPLO	Specify whether B is upper (‘U’) or lower (‘L’) triangular
N	Order of matrix B
NCVT	Number of columns of VT
NRU	Number of rows of U
NCC	Number of columns of C
D	Vector of diagonal elements of B of length N, overwritten by sorted singular values on exit
E	Vector of off-diagonal elements of B of length N - 1, destroyed on exit
VT	Matrix of size N x NCVT, overwritten by $\herm{P} \mult VT$ on exit
LDVT	Leading dimension of VT
U	Matrix of size NRU x N, overwritten by $U\mult Q$ on exit
LDU	Leading dimension of U
C	Matrix of size N x NCC, overwritten by $\herm{Q} \mult C$ on exit
LDC	Leading dimension of C
RWORK	Work space of size 4N
INFO	0 on success, <0 for bad arguments, >0 if no convergence