(S|D)ORGTR¶

Single and double ORGTR.

Description¶

Generates an orthonormal matrix given a set of elementary reflectors and scale factors.

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

The elementary reflectors and scale factors are expected in the same form as generated by SYTRD.

When UPLO is U:

$Q = H_{N-1} \mult \dots \mult H_2 \mult H_1$

$H_i = I - \tau_i \mult v \mult \trans{v}$

The vector v has components i+1 through n of zero, component i is 1, and components 1 through i-1 are stored in the columns of A above the superdiagonal.

When UPLO is L:

$Q = H_1 \mult H_2 \mult \dots \mult H_{N-1}$

$H_i = I - \tau_i \mult v \mult \trans{v}$

The vector v has components 1 through i of zero, component i+1 is 1, and components i+2 through N are stored in the columns of A below the subdiagonal.

LAPACK Interface¶

void sorgtr(const char *UPLO, const qml_long *N, float *A, const qml_long *LDA,
    float *TAU, float *WORK, const qml_long *LWORK, qml_long *INFO);

void dorgtr(const char *UPLO, const qml_long *N, double *A, const qml_long *LDA,
    double *TAU, double *WORK, const qml_long *LWORK, qml_long *INFO);

Arguments¶

UPLO	Store upper ‘U’ or lower ‘L’ triangular part of A
N	Number of rows and columns of A
A	Elementary reflector vectors, overwritten with Q on exit
LDA	Leading dimension of A
TAU	Array of scale factors for reflectors
WORK	Work space of size at least LWORK
LWORK	Size of work space (-1 to query)
INFO	0 on success