MAGMA  2.3.0
Matrix Algebra for GPU and Multicore Architectures
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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. More...
 
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. More...
 
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. More...
 
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. More...
 

Detailed Description

Function Documentation

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]nINTEGER The order of the elementary reflector.
[in,out]dalphaCOMPLEX* 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]dxCOMPLEX 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]incxINTEGER The increment between elements of X. INCX > 0.
[out]dtauCOMPLEX* on the GPU. Pointer to the value tau.
[in]queuemagma_queue_t Queue to execute in.
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]nINTEGER The order of the elementary reflector.
[in,out]dalphaDOUBLE 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]dxDOUBLE 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]incxINTEGER The increment between elements of X. INCX > 0.
[out]dtauDOUBLE PRECISION* on the GPU. Pointer to the value tau.
[in]queuemagma_queue_t Queue to execute in.
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]nINTEGER The order of the elementary reflector.
[in,out]dalphaREAL* 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]dxREAL 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]incxINTEGER The increment between elements of X. INCX > 0.
[out]dtauREAL* on the GPU. Pointer to the value tau.
[in]queuemagma_queue_t Queue to execute in.
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]nINTEGER The order of the elementary reflector.
[in,out]dalphaCOMPLEX_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]dxCOMPLEX_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]incxINTEGER The increment between elements of X. INCX > 0.
[out]dtauCOMPLEX_16* on the GPU. Pointer to the value tau.
[in]queuemagma_queue_t Queue to execute in.