(S|D|C|Z)LARFG¶

Single, double, single complex, and double complex LARFG.

Description¶

Generates a single elementary reflector matrix.

$\herm{H} \mult \left[ \begin{matrix} \alpha \\ x \end{matrix} \right] = \left[ \begin{matrix} \beta \\ 0 \end{matrix} \right]$

$\herm{H} \mult H = I$

The reflector matrix is represented in the form:

$H = I - \tau \mult \left[ \begin{matrix} 1 \\ v \end{matrix} \right] \mult \left[ \begin{matrix} 1 & \herm{v} \end{matrix} \right]$

LAPACK Interface¶

void slarfg(const qml_long *N, float *ALPHA, float *X, const qml_long *INCX,
    float *TAU);

void dlarfg(const qml_long *N, double *ALPHA, double *X, const qml_long *INCX,
    double *TAU);

void clarfg(const qml_long *N, qml_single_complex *ALPHA, qml_single_complex *X,
    const qml_long *INCX, qml_single_complex *TAU);

void zlarfg(const qml_long *N, qml_double_complex *ALPHA, qml_double_complex *X,
    const qml_long *INCX, qml_double_complex *TAU);

Arguments¶

N	Order of the elementary reflector matrix
ALPHA	On entry $\alpha$ , on exit holds $\beta$
X	On entry the vector x, on exit the vector v
INCX	The stride between elements of x
TAU	On exit the value $\tau$