(S|D|C|Z)LASR¶

Single, double, single complex, and double complex LASR.

Description¶

Applies a sequence of plane rotations to a rectangular matrix.

When SIDE is L, LASR performs:

$A \assign P \mult A$

When SIDE is R, LASR performs:

$A \assign A \mult \trans{P}$

The matrix P is an orthogonal matrix formed as the product of plane rotations.

When DIRECT is F:

$P = P_{K} \mult \dots \mult P_2 \mult P_1$

When DIRECT is B:

$P = P_1 \mult P_2 \mult \dots \mult P_{K}$

Each plane rotation is formed around a pivot.

When PIVOT is T:

$P_k = \left[ \begin{matrix} c_k & & & & s_k & & & \\ & 1 & & & & & & \\ & & \ddots & & & & & \\ & & & 1 & & & & \\ -s_k & & & & c_k & & & \\ & & & & & 1 & & \\ & & & & & & \ddots & \\ & & & & & & & 1 \\ \end{matrix} \right]$

When PIVOT is B:

$P_k = \left[ \begin{matrix} 1 & & & & & & & \\ & \ddots & & & & & & \\ & & 1 & & & & & \\ & & & c_k & & & & s_k \\ & & & & 1 & & & \\ & & & & & \ddots & & \\ & & & & & & 1 & \\ & & & -s_k & & & & c_k \\ \end{matrix} \right]$

When PIVOT is V:

$P_k = \left[ \begin{matrix} 1 & & & & & & & \\ & \ddots & & & & & & \\ & & 1 & & & & & \\ & & & c_k & s_k & & & \\ & & & -s_k & c_k & & & \\ & & & & & 1 & & \\ & & & & & & \ddots & \\ & & & & & & & 1 \\ \end{matrix} \right]$

LAPACK Interface¶

void slasr(const char *SIDE, const char *PIVOT, const char *DIRECT,
    const qml_long *M,const qml_long *N, const float *C, const float *S,
    float *A, const qml_long *LDA);

void dlasr(const char *SIDE, const char *PIVOT, const char *DIRECT,
    const qml_long *M, const qml_long *N, const double *C, const double *S,
    double *A, const qml_long *LDA);

void clasr(const char *SIDE, const char *PIVOT, const char *DIRECT,
    const qml_long *M, const qml_long *N, const float *C, const float *S,
    qml_single_complex *A, const qml_long *LDA);

void zlasr(const char *SIDE, const char *PIVOT, const char *DIRECT,
    const qml_long *M, const qml_long *N, const double *C, const double *S,
    qml_double_complex *A, const qml_long *LDA);

Arguments¶

SIDE	Which side to apply plane rotations to
PIVOT	Positions of pivots
DIRECT	Direction to apply rotations
M	Number of rows of A
N	Number of columns of A
C	Array of cosine values for plane rotations
S	Array of sine values for plane rotations
A	Matrix of size M x N
LDA	Leading dimension of A