(C|Z)UNGTR¶

Single complex and double complex UNGTR.

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 HETRD.

When UPLO is U:

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

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

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:

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

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

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 cungtr(const char *UPLO, 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 zungtr(const char *UPLO, 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¶

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