Functions
template<typename TX , typename TY >
void	blas::rot (int64_t n, TX x, int64_t incx, TY y, int64_t incy, blas::real_type< TX, TY > c, blas::scalar_type< TX, TY > s)
	Apply plane rotation:

void	blas::rot (int64_t n, float x, int64_t incx, float y, int64_t incy, float c, float s)

void	blas::rot (int64_t n, double x, int64_t incx, double y, int64_t incy, double c, double s)

void	blas::rot (int64_t n, std::complex< float > x, int64_t incx, std::complex< float > y, int64_t incy, float c, float s)
	real cosine, real sine Applies a real Givens rotation (e.g., in real tridiagonal eig) to a complex matrix (e.g., complex eigenvectors).

void	blas::rot (int64_t n, std::complex< double > x, int64_t incx, std::complex< double > y, int64_t incy, double c, double s)
	real cosine, real sine Applies a real Givens rotation (e.g., in real tridiagonal eig) to a complex matrix (e.g., complex eigenvectors).

void	blas::rot (int64_t n, std::complex< float > x, int64_t incx, std::complex< float > y, int64_t incy, float c, std::complex< float > s)
	real cosine, complex sine Applies a complex Givens rotation to a complex matrix (e.g., in complex GMRES).

void	blas::rot (int64_t n, std::complex< double > x, int64_t incx, std::complex< double > y, int64_t incy, double c, std::complex< double > s)
	real cosine, complex sine Applies a complex Givens rotation to a complex matrix (e.g., in complex GMRES).

Detailed Description

Function Documentation

◆ rot() [1/5]

void blas::rot	(	int64_t	n,
		std::complex< double > *	x,
		int64_t	incx,
		std::complex< double > *	y,
		int64_t	incy,
		double	c,
		double	s
	)

real cosine, real sine Applies a real Givens rotation (e.g., in real tridiagonal eig) to a complex matrix (e.g., complex eigenvectors).

real cosine, real sine

◆ rot() [2/5]

void blas::rot	(	int64_t	n,
		std::complex< double > *	x,
		int64_t	incx,
		std::complex< double > *	y,
		int64_t	incy,
		double	c,
		std::complex< double >	s
	)

real cosine, complex sine Applies a complex Givens rotation to a complex matrix (e.g., in complex GMRES).

real cosine, complex sine

◆ rot() [3/5]

void blas::rot	(	int64_t	n,
		std::complex< float > *	x,
		int64_t	incx,
		std::complex< float > *	y,
		int64_t	incy,
		float	c,
		float	s
	)

real cosine, real sine Applies a real Givens rotation (e.g., in real tridiagonal eig) to a complex matrix (e.g., complex eigenvectors).

real cosine, real sine This variant, with real sine, is used in the SVD or EVD where a real Givens rotation, that eliminates entries in the real bi- or tridiagonal matrix, is applied to complex singular or eigen vectors.

◆ rot() [4/5]

void blas::rot	(	int64_t	n,
		std::complex< float > *	x,
		int64_t	incx,
		std::complex< float > *	y,
		int64_t	incy,
		float	c,
		std::complex< float >	s
	)

real cosine, complex sine Applies a complex Givens rotation to a complex matrix (e.g., in complex GMRES).

real cosine, complex sine This variant, with complex sine, is used to eliminate entries in a complex matrix.

◆ rot() [5/5]

template<typename TX , typename TY >

void blas::rot	(	int64_t	n,
		TX *	x,
		int64_t	incx,
		TY *	y,
		int64_t	incy,
		blas::real_type< TX, TY >	c,
		blas::scalar_type< TX, TY >	s
	)

Apply plane rotation:

\[ \begin{bmatrix} x^T \\ y^T \end{bmatrix} = \begin{bmatrix} c & s \\ -s & c \end{bmatrix} \begin{bmatrix} x^T \\ y^T \end{bmatrix}. \]

See also: rotg to generate the rotation.

Generic implementation for arbitrary data types.

Parameters

[in]	n	Number of elements in x and y. n >= 0.
[in,out]	x	The n-element vector x, in an array of length (n-1)*abs(incx) + 1.
[in]	incx	Stride between elements of x. incx must not be zero. If incx < 0, uses elements of x in reverse order: x(n-1), ..., x(0).
[in,out]	y	The n-element vector y, in an array of length (n-1)*abs(incy) + 1.
[in]	incy	Stride between elements of y. incy must not be zero. If incy < 0, uses elements of y in reverse order: y(n-1), ..., y(0).
[in]	c	Cosine of rotation; real.
[in]	s	Sine of rotation; complex.