larfg: Generate Householder reflector

Functions
void	magmablas_clarfg (magma_int_t n, magmaFloatComplex_ptr dalpha, magmaFloatComplex_ptr dx, magma_int_t incx, magmaFloatComplex_ptr dtau, magma_queue_t queue)
	CLARFG generates a complex elementary reflector (Householder matrix) H of order n, such that.
void	magmablas_dlarfg (magma_int_t n, magmaDouble_ptr dalpha, magmaDouble_ptr dx, magma_int_t incx, magmaDouble_ptr dtau, magma_queue_t queue)
	DLARFG generates a real elementary reflector (Householder matrix) H of order n, such that.
void	magmablas_slarfg (magma_int_t n, magmaFloat_ptr dalpha, magmaFloat_ptr dx, magma_int_t incx, magmaFloat_ptr dtau, magma_queue_t queue)
	SLARFG generates a real elementary reflector (Householder matrix) H of order n, such that.
void	magmablas_zlarfg (magma_int_t n, magmaDoubleComplex_ptr dalpha, magmaDoubleComplex_ptr dx, magma_int_t incx, magmaDoubleComplex_ptr dtau, magma_queue_t queue)
	ZLARFG generates a complex elementary reflector (Householder matrix) H of order n, such that.

Detailed Description

Function Documentation

magmablas_clarfg()

void magmablas_clarfg	(	magma_int_t	n,
		magmaFloatComplex_ptr	dalpha,
		magmaFloatComplex_ptr	dx,
		magma_int_t	incx,
		magmaFloatComplex_ptr	dtau,
		magma_queue_t	queue )

CLARFG generates a complex elementary reflector (Householder matrix) H of order n, such that.

 H * ( alpha ) = ( beta ),   H**H * H = I.
     (   x   )   (   0  )

where alpha and beta are scalars, with beta real and |beta| = norm([alpha, x]), and x is an (n-1)-element complex vector. H is represented in the form

 H = I - tau * ( 1 ) * ( 1 v**H ),
               ( v )

where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not Hermitian.

If the elements of x are all zero and dalpha is real, then tau = 0 and H is taken to be the unit matrix.

Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1.

Parameters

[in]	n	INTEGER The order of the elementary reflector.
[in,out]	dalpha	COMPLEX* on the GPU. On entry, pointer to the value alpha, i.e., the first entry of the vector. On exit, it is overwritten with the value beta.
[in,out]	dx	COMPLEX array, dimension (1+(N-2)*abs(INCX)), on the GPU On entry, the (n-1)-element vector x. On exit, it is overwritten with the vector v.
[in]	incx	INTEGER The increment between elements of X. INCX > 0.
[out]	dtau	COMPLEX* on the GPU. Pointer to the value tau.
[in]	queue	magma_queue_t Queue to execute in.

magmablas_dlarfg()

void magmablas_dlarfg	(	magma_int_t	n,
		magmaDouble_ptr	dalpha,
		magmaDouble_ptr	dx,
		magma_int_t	incx,
		magmaDouble_ptr	dtau,
		magma_queue_t	queue )

DLARFG generates a real elementary reflector (Householder matrix) H of order n, such that.

 H * ( alpha ) = ( beta ),   H**H * H = I.
     (   x   )   (   0  )

where alpha and beta are scalars, with beta real and |beta| = norm([alpha, x]), and x is an (n-1)-element real vector. H is represented in the form

 H = I - tau * ( 1 ) * ( 1 v**H ),
               ( v )

where tau is a real scalar and v is a real (n-1)-element vector. Note that H is not symmetric.

If the elements of x are all zero and dalpha is real, then tau = 0 and H is taken to be the unit matrix.

Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1.

Parameters

[in]	n	INTEGER The order of the elementary reflector.
[in,out]	dalpha	DOUBLE PRECISION* on the GPU. On entry, pointer to the value alpha, i.e., the first entry of the vector. On exit, it is overwritten with the value beta.
[in,out]	dx	DOUBLE PRECISION array, dimension (1+(N-2)*abs(INCX)), on the GPU On entry, the (n-1)-element vector x. On exit, it is overwritten with the vector v.
[in]	incx	INTEGER The increment between elements of X. INCX > 0.
[out]	dtau	DOUBLE PRECISION* on the GPU. Pointer to the value tau.
[in]	queue	magma_queue_t Queue to execute in.

magmablas_slarfg()

void magmablas_slarfg	(	magma_int_t	n,
		magmaFloat_ptr	dalpha,
		magmaFloat_ptr	dx,
		magma_int_t	incx,
		magmaFloat_ptr	dtau,
		magma_queue_t	queue )

SLARFG generates a real elementary reflector (Householder matrix) H of order n, such that.

 H * ( alpha ) = ( beta ),   H**H * H = I.
     (   x   )   (   0  )

where alpha and beta are scalars, with beta real and |beta| = norm([alpha, x]), and x is an (n-1)-element real vector. H is represented in the form

 H = I - tau * ( 1 ) * ( 1 v**H ),
               ( v )

where tau is a real scalar and v is a real (n-1)-element vector. Note that H is not symmetric.

If the elements of x are all zero and dalpha is real, then tau = 0 and H is taken to be the unit matrix.

Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1.

Parameters

[in]	n	INTEGER The order of the elementary reflector.
[in,out]	dalpha	REAL* on the GPU. On entry, pointer to the value alpha, i.e., the first entry of the vector. On exit, it is overwritten with the value beta.
[in,out]	dx	REAL array, dimension (1+(N-2)*abs(INCX)), on the GPU On entry, the (n-1)-element vector x. On exit, it is overwritten with the vector v.
[in]	incx	INTEGER The increment between elements of X. INCX > 0.
[out]	dtau	REAL* on the GPU. Pointer to the value tau.
[in]	queue	magma_queue_t Queue to execute in.

magmablas_zlarfg()

void magmablas_zlarfg	(	magma_int_t	n,
		magmaDoubleComplex_ptr	dalpha,
		magmaDoubleComplex_ptr	dx,
		magma_int_t	incx,
		magmaDoubleComplex_ptr	dtau,
		magma_queue_t	queue )

ZLARFG generates a complex elementary reflector (Householder matrix) H of order n, such that.

 H * ( alpha ) = ( beta ),   H**H * H = I.
     (   x   )   (   0  )

where alpha and beta are scalars, with beta real and |beta| = norm([alpha, x]), and x is an (n-1)-element complex vector. H is represented in the form

 H = I - tau * ( 1 ) * ( 1 v**H ),
               ( v )

where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not Hermitian.

If the elements of x are all zero and dalpha is real, then tau = 0 and H is taken to be the unit matrix.

Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1.

Parameters

[in]	n	INTEGER The order of the elementary reflector.
[in,out]	dalpha	COMPLEX_16* on the GPU. On entry, pointer to the value alpha, i.e., the first entry of the vector. On exit, it is overwritten with the value beta.
[in,out]	dx	COMPLEX_16 array, dimension (1+(N-2)*abs(INCX)), on the GPU On entry, the (n-1)-element vector x. On exit, it is overwritten with the vector v.
[in]	incx	INTEGER The increment between elements of X. INCX > 0.
[out]	dtau	COMPLEX_16* on the GPU. Pointer to the value tau.
[in]	queue	magma_queue_t Queue to execute in.