rotg: Generate Givens rotation

Functions
void	magma_crotg (magmaFloatComplex *a, magmaFloatComplex *b, float *c, magmaFloatComplex *s, magma_queue_t queue)
	Generate a Givens plane rotation. More...
void	magma_drotg (double *a, double *b, double *c, double *s, magma_queue_t queue)
	Generate a Givens plane rotation. More...
void	magma_srotg (float *a, float *b, float *c, float *s, magma_queue_t queue)
	Generate a Givens plane rotation. More...
void	magma_zrotg (magmaDoubleComplex *a, magmaDoubleComplex *b, double *c, magmaDoubleComplex *s, magma_queue_t queue)
	Generate a Givens plane rotation. More...

Detailed Description

Function Documentation

void magma_crotg	(	magmaFloatComplex *	a,
		magmaFloatComplex *	b,
		float *	c,
		magmaFloatComplex *	s,
		magma_queue_t	queue
	)

Generate a Givens plane rotation.

The rotation annihilates the second entry of the vector, such that:

(  c  s ) * ( a ) = ( r )
( -s  c )   ( b )   ( 0 )

where \( c^2 + s^2 = 1 \) and \( r = a^2 + b^2 \). Further, this computes z such that

        { (sqrt(1 - z^2), z),    if |z| < 1,
(c,s) = { (0, 1),                if |z| = 1,
        { (1/z, sqrt(1 - z^2)),  if |z| > 1.

Parameters

[in]	a	On input, entry to be modified. On output, updated to r by applying the rotation.
[in,out]	b	On input, entry to be annihilated. On output, set to z.
[in]	c	On output, cosine of rotation.
[in,out]	s	On output, sine of rotation.
[in]	queue	magma_queue_t Queue to execute in.

void magma_drotg	(	double *	a,
		double *	b,
		double *	c,
		double *	s,
		magma_queue_t	queue
	)

Generate a Givens plane rotation.

The rotation annihilates the second entry of the vector, such that:

(  c  s ) * ( a ) = ( r )
( -s  c )   ( b )   ( 0 )

where \( c^2 + s^2 = 1 \) and \( r = a^2 + b^2 \). Further, this computes z such that

        { (sqrt(1 - z^2), z),    if |z| < 1,
(c,s) = { (0, 1),                if |z| = 1,
        { (1/z, sqrt(1 - z^2)),  if |z| > 1.

Parameters

[in]	a	On input, entry to be modified. On output, updated to r by applying the rotation.
[in,out]	b	On input, entry to be annihilated. On output, set to z.
[in]	c	On output, cosine of rotation.
[in,out]	s	On output, sine of rotation.
[in]	queue	magma_queue_t Queue to execute in.

void magma_srotg	(	float *	a,
		float *	b,
		float *	c,
		float *	s,
		magma_queue_t	queue
	)

Generate a Givens plane rotation.

The rotation annihilates the second entry of the vector, such that:

(  c  s ) * ( a ) = ( r )
( -s  c )   ( b )   ( 0 )

where \( c^2 + s^2 = 1 \) and \( r = a^2 + b^2 \). Further, this computes z such that

        { (sqrt(1 - z^2), z),    if |z| < 1,
(c,s) = { (0, 1),                if |z| = 1,
        { (1/z, sqrt(1 - z^2)),  if |z| > 1.

Parameters

[in]	a	On input, entry to be modified. On output, updated to r by applying the rotation.
[in,out]	b	On input, entry to be annihilated. On output, set to z.
[in]	c	On output, cosine of rotation.
[in,out]	s	On output, sine of rotation.
[in]	queue	magma_queue_t Queue to execute in.

void magma_zrotg	(	magmaDoubleComplex *	a,
		magmaDoubleComplex *	b,
		double *	c,
		magmaDoubleComplex *	s,
		magma_queue_t	queue
	)

Generate a Givens plane rotation.

The rotation annihilates the second entry of the vector, such that:

(  c  s ) * ( a ) = ( r )
( -s  c )   ( b )   ( 0 )

where \( c^2 + s^2 = 1 \) and \( r = a^2 + b^2 \). Further, this computes z such that

        { (sqrt(1 - z^2), z),    if |z| < 1,
(c,s) = { (0, 1),                if |z| = 1,
        { (1/z, sqrt(1 - z^2)),  if |z| > 1.

Parameters

[in]	a	On input, entry to be modified. On output, updated to r by applying the rotation.
[in,out]	b	On input, entry to be annihilated. On output, set to z.
[in]	c	On output, cosine of rotation.
[in,out]	s	On output, sine of rotation.
[in]	queue	magma_queue_t Queue to execute in.