(S|D|C|Z)LARFT¶

Single, double, single complex, and double complex LARFT.

Description¶

Generates the triangular factor T of a block reflector.

The block reflector matrix H is formed as a product of elementary reflectors.

When DIRECT is ‘F’:

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

When DIRECT is ‘B’:

$H = H_k \mult H_{k-1} \mult \dots \mult H_1$

If STOREV is ‘C’, the vectors that define each elementary reflector are stored as columns of V and:

$H = I - V \mult T \mult \herm{V}$

If STOREV is ‘R’, the vectors that define each elementary reflector are stored as rows of V and:

$H = I - \herm{V} \mult T \mult V$

LAPACK Interface¶

void slarft(const char *DIRECT, const char *STOREV, const qml_long *N,
    const qml_long *K, const float *V, const qml_long *LDV, const float *TAU,
    float *T, const qml_long *LDT);

void dlarft(const char *DIRECT, const char *STOREV, const qml_long *N,
    const qml_long *K, const double *V, const qml_long *LDV, const double *TAU,
    double *T, const qml_long *LDT);

void clarft(const char *DIRECT, const char *STOREV, const qml_long *N,
    const qml_long *K, const qml_single_complex *V, const qml_long *LDV,
    const qml_single_complex *TAU, qml_single_complex *T, const qml_long *LDT);

void zlarft(const char *DIRECT, const char *STOREV, const qml_long *N,
    const qml_long *K, const qml_double_complex *V, const qml_long *LDV,
    const qml_double_complex *TAU, qml_double_complex *T, const qml_long *LDT);

Arguments¶

DIRECT	Direction to apply elementary reflectors
STOREV	Storage format of elementary reflector vectors
N	Order of the block reflector H
K	The number of elementary reflectors in the block
V	Matrix storing reflector vectors
LDV	Leading dimension of V
TAU	Vector of scale factors $\tau_i$
T	Triangular K x K matrix storing reflectors
LDT	Leading dimension of T