rotg: Generate Givens plane rotation

Functions
template<typename TA , typename TB >
void	blas::rotg (TA *a, TB *b, blas::real_type< TA, TB > *c, blas::real_type< TA, TB > *s)
	Construct plane rotation that eliminates b, such that:
template<typename TA , typename TB >
void	blas::rotg (std::complex< TA > *a, std::complex< TB > *b, blas::real_type< TA, TB > *c, blas::complex_type< TA, TB > *s)
	Construct plane rotation that eliminates b, such that:
void	blas::rotg (float *a, float *b, float *c, float *s)
void	blas::rotg (double *a, double *b, double *c, double *s)
void	blas::rotg (std::complex< float > *a, std::complex< float > *b, float *c, std::complex< float > *s)
void	blas::rotg (std::complex< double > *a, std::complex< double > *b, double *c, std::complex< double > *s)

Detailed Description

Function Documentation

rotg() [1/2]

template<typename TA , typename TB >

void blas::rotg	(	std::complex< TA > *	a,
		std::complex< TB > *	b,
		blas::real_type< TA, TB > *	c,
		blas::complex_type< TA, TB > *	s
	)

Construct plane rotation that eliminates b, such that:

\[ \begin{bmatrix} r \\ 0 \end{bmatrix} = \begin{bmatrix} c & s \\ -conjg(s) & c \end{bmatrix} \begin{bmatrix} a \\ b \end{bmatrix}. \]

See also

rot to apply the rotation.

Generic implementation for arbitrary data types.

Parameters

[in,out]	a	On entry, scalar a. On exit, set to r.
[in,out]	b	On entry, scalar b. On exit, set to s, 1/c, or 0.
[out]	c	Cosine of rotation; real.
[out]	s	Sine of rotation; complex.

Further details

Anderson E (2017) Algorithm 978: Safe scaling in the level 1 BLAS. ACM Trans Math Softw 44:. https://doi.org/10.1145/3061665

rotg() [2/2]

template<typename TA , typename TB >

void blas::rotg	(	TA *	a,
		TB *	b,
		blas::real_type< TA, TB > *	c,
		blas::real_type< TA, TB > *	s
	)

Construct plane rotation that eliminates b, such that:

\[ \begin{bmatrix} r \\ 0 \end{bmatrix} = \begin{bmatrix} c & s \\ -s & c \end{bmatrix} \begin{bmatrix} a \\ b \end{bmatrix}. \]

See also

rot to apply the rotation.

Generic implementation for arbitrary data types.

Parameters

[in,out]	a	On entry, scalar a. On exit, set to r.
[in,out]	b	On entry, scalar b. On exit, set to s, 1/c, or 0.
[out]	c	Cosine of rotation; real.
[out]	s	Sine of rotation; real.

Further details

Anderson E (2017) Algorithm 978: Safe scaling in the level 1 BLAS. ACM Trans Math Softw 44:. https://doi.org/10.1145/3061665