(S|D|C|Z)ROTG¶

Single, double, single complex, and double complex ROTG.

Description¶

Generates a single plane rotation.

$\left[ \begin{array}{cc} \cos \theta & \sin \theta \\ - \sin \theta & \cos \theta \end{array} \right] \mult \left[ \begin{array}{c} A \\ B \end{array} \right] = \left[ \begin{array}{c} R \\ 0 \end{array} \right]$

BLAS Interface¶

void srotg(float *A, float *B, float *C, float *S);

void drotg(double *A, double *B, double *C, double *S);

void crotg(qml_single_complex *A, const qml_single_complex *B,
           float *C, qml_single_complex *S);

void zrotg(qml_double_complex *A, const qml_double_complex *B,
           double *C, qml_double_complex *S);

CBLAS Interface¶

void cblas_srotg(float *A, float *B, float *C, float *S);

void cblas_drotg(double *A, double *B, double *C, double *S);

void cblas_crotg(qml_single_complex *A, const qml_single_complex *B,
                 float *C, qml_single_complex *S);

void cblas_zrotg(qml_double_complex *A, const qml_double_complex *B,
                 double *C, qml_double_complex *S);

Arguments¶

A	First component of vector to rotate
	On output contains R
B	Second component of vector to rotate
	On output contains Z, which is:
	$\begin{array}{rcl} \fvar{S} & \textrm{if} & \abs{\fvar{A}} > \abs{\fvar{B}} \\ 1/\fvar{C} & \textrm{if} & \abs{\fvar{A}} \le \abs{\fvar{B}} \andrm C\ne 0 \andrm R\ne 0 \\1 & \textrm{if} & \abs{\fvar{A}} \le \abs{\fvar{B}} \andrm C = 0 \andrm R\ne 0 \\0 & \textrm{if} & R = 0 \\\end{array}$
C	On output contains $\cos \theta$
S	On output contains $\sin \theta$