(S|D|C|Z)GEQRF¶

Single, double, single complex, and double complex GEQRF.

Description¶

Computes the QR factorization of a matrix using a blocked algorithm.

$A = Q \mult R$

The upper triangular matrix R is stored in A on the diagonal and above. The matrix Q is not stored explicitly. Instead, the elements below the diagonal of A together with TAU store Q as the product of scaled elementary reflectors.

$Q = H_1 \mult H_2 \mult \dots \mult H_k$

$H_i = I - \tau_i \mult v_i \mult \herm{v_i}$

LAPACK Interface¶

void sgeqrf(const qml_long *M, const qml_long *N, float *A, const qml_long *LDA,
    float *TAU, float *WORK, const qml_long *LWORK, qml_long *INFO);

void dgeqrf(const qml_long *M, const qml_long *N, double *A, const qml_long *LDA,
    double *TAU, double *WORK, const qml_long *LWORK, qml_long *INFO);

void cgeqrf(const qml_long *M, const qml_long *N, qml_single_complex *A,
    const qml_long *LDA, qml_single_complex *TAU, qml_single_complex *WORK,
    const qml_long *LWORK, qml_long *INFO);

void zgeqrf(const qml_long *M, const qml_long *N, qml_double_complex *A,
    const qml_long *LDA, qml_double_complex *TAU, qml_double_complex *WORK,
    const qml_long *LWORK, qml_long *INFO);

Arguments¶

M	Number of rows of A
N	Number of columns of A
A	Matrix of size M x N
LDA	Leading dimension of A
TAU	On exit contains vector of scale factors for reflectors
WORK	Work space of size at least LWORK
LWORK	Size of work space, at least N but optimally a larger multiple of N (-1 to query)
INFO	0 on success