Functions
magma_int_t	magma_clahru (magma_int_t n, magma_int_t ihi, magma_int_t k, magma_int_t nb, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex_ptr dY, magma_int_t lddy, magmaFloatComplex_ptr dV, magma_int_t lddv, magmaFloatComplex_ptr dT, magmaFloatComplex_ptr dwork, magma_queue_t queue)
	CLAHRU is an auxiliary MAGMA routine that is used in CGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

magma_int_t	magma_clahru_m (magma_int_t n, magma_int_t ihi, magma_int_t k, magma_int_t nb, magmaFloatComplex A, magma_int_t lda, struct cgehrd_data data)
	CLAHRU is an auxiliary MAGMA routine that is used in CGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

magma_int_t	magma_dlahru (magma_int_t n, magma_int_t ihi, magma_int_t k, magma_int_t nb, double *A, magma_int_t lda, magmaDouble_ptr dA, magma_int_t ldda, magmaDouble_ptr dY, magma_int_t lddy, magmaDouble_ptr dV, magma_int_t lddv, magmaDouble_ptr dT, magmaDouble_ptr dwork, magma_queue_t queue)
	DLAHRU is an auxiliary MAGMA routine that is used in DGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

magma_int_t	magma_dlahru_m (magma_int_t n, magma_int_t ihi, magma_int_t k, magma_int_t nb, double A, magma_int_t lda, struct dgehrd_data data)
	DLAHRU is an auxiliary MAGMA routine that is used in DGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

magma_int_t	magma_slahru (magma_int_t n, magma_int_t ihi, magma_int_t k, magma_int_t nb, float *A, magma_int_t lda, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dY, magma_int_t lddy, magmaFloat_ptr dV, magma_int_t lddv, magmaFloat_ptr dT, magmaFloat_ptr dwork, magma_queue_t queue)
	SLAHRU is an auxiliary MAGMA routine that is used in SGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

magma_int_t	magma_slahru_m (magma_int_t n, magma_int_t ihi, magma_int_t k, magma_int_t nb, float A, magma_int_t lda, struct sgehrd_data data)
	SLAHRU is an auxiliary MAGMA routine that is used in SGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

magma_int_t	magma_zlahru (magma_int_t n, magma_int_t ihi, magma_int_t k, magma_int_t nb, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex_ptr dA, magma_int_t ldda, magmaDoubleComplex_ptr dY, magma_int_t lddy, magmaDoubleComplex_ptr dV, magma_int_t lddv, magmaDoubleComplex_ptr dT, magmaDoubleComplex_ptr dwork, magma_queue_t queue)
	ZLAHRU is an auxiliary MAGMA routine that is used in ZGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

magma_int_t	magma_zlahru_m (magma_int_t n, magma_int_t ihi, magma_int_t k, magma_int_t nb, magmaDoubleComplex A, magma_int_t lda, struct zgehrd_data data)
	ZLAHRU is an auxiliary MAGMA routine that is used in ZGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

Detailed Description

Function Documentation

◆ magma_clahru()

magma_int_t magma_clahru	(	magma_int_t	n,
		magma_int_t	ihi,
		magma_int_t	k,
		magma_int_t	nb,
		magmaFloatComplex *	A,
		magma_int_t	lda,
		magmaFloatComplex_ptr	dA,
		magma_int_t	ldda,
		magmaFloatComplex_ptr	dY,
		magma_int_t	lddy,
		magmaFloatComplex_ptr	dV,
		magma_int_t	lddv,
		magmaFloatComplex_ptr	dT,
		magmaFloatComplex_ptr	dwork,
		magma_queue_t	queue )

CLAHRU is an auxiliary MAGMA routine that is used in CGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

See further details below.

Parameters

[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	ihi	INTEGER Last row to update. Same as IHI in cgehrd.
[in]	k	INTEGER Number of rows of the matrix Am (see details below)
[in]	nb	INTEGER Block size
[out]	A	COMPLEX array, dimension (LDA,N-K) On entry, the N-by-(N-K) general matrix to be updated. The computation is done on the GPU. After Am is updated on the GPU only Am(1:NB) is transferred to the CPU - to update the corresponding Am matrix. See Further Details below.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in,out]	dA	COMPLEX array on the GPU, dimension (LDDA,N-K). On entry, the N-by-(N-K) general matrix to be updated. On exit, the 1st K rows (matrix Am) of A are updated by applying an orthogonal transformation from the right Am = Am (I-V T V'), and sub-matrix Ag is updated by Ag = (I - V T V') Ag (I - V T V(NB+1:)' ) where Q = I - V T V' represent the orthogonal matrix (as a product of elementary reflectors V) used to reduce the current panel of A to upper Hessenberg form. After Am is updated Am(:,1:NB) is sent to the CPU. See Further Details below.
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,N).
[in,out]	dY	(workspace) COMPLEX array on the GPU, dimension (LDDY, NB). On entry the (N-K)-by-NB Y = A V. It is used internally as workspace, so its value is changed on exit.
[in]	lddy	INTEGER The leading dimension of the array dY. LDDY >= max(1,N).
[in,out]	dV	(workspace) COMPLEX array on the GPU, dimension (LDDV, NB). On entry the (N-K)-by-NB matrix V of elementary reflectors used to reduce the current panel of A to upper Hessenberg form. The rest K-by-NB part is used as workspace. V is unchanged on exit.
[in]	lddv	INTEGER The leading dimension of the array dV. LDDV >= max(1,N).
[in]	dT	COMPLEX array on the GPU, dimension (NB, NB). On entry the NB-by-NB upper trinagular matrix defining the orthogonal Hessenberg reduction transformation matrix for the current panel. The lower triangular part are 0s.
	dwork	(workspace) COMPLEX array on the GPU, dimension N*NB.
[in]	queue	magma_queue_t Queue to execute in.

Further Details

This implementation follows the algorithm and notations described in:

S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg form through hybrid GPU-based computing," University of Tennessee Computer Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219), May 24, 2009.

The difference is that here Am is computed on the GPU. M is renamed Am, G is renamed Ag.

◆ magma_clahru_m()

magma_int_t magma_clahru_m	(	magma_int_t	n,
		magma_int_t	ihi,
		magma_int_t	k,
		magma_int_t	nb,
		magmaFloatComplex *	A,
		magma_int_t	lda,
		struct cgehrd_data *	data )

CLAHRU is an auxiliary MAGMA routine that is used in CGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

See further details below.

Parameters

[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	ihi	INTEGER Last row to update. Same as IHI in cgehrd.
[in]	k	INTEGER Number of rows of the matrix Am (see details below)
[in]	nb	INTEGER Block size
[out]	A	COMPLEX array, dimension (LDA,N-K) On entry, the N-by-(N-K) general matrix to be updated. The computation is done on the GPU. After Am is updated on the GPU only Am(1:NB) is transferred to the CPU - to update the corresponding Am matrix. See Further Details below.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in,out]	data	Structure with pointers to dA, dT, dV, dW, dY which are distributed across multiple GPUs.

Further Details

This implementation follows the algorithm and notations described in:

S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg form through hybrid GPU-based computing," University of Tennessee Computer Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219), May 24, 2009.

The difference is that here Am is computed on the GPU. M is renamed Am, G is renamed Ag.

◆ magma_dlahru()

magma_int_t magma_dlahru	(	magma_int_t	n,
		magma_int_t	ihi,
		magma_int_t	k,
		magma_int_t	nb,
		double *	A,
		magma_int_t	lda,
		magmaDouble_ptr	dA,
		magma_int_t	ldda,
		magmaDouble_ptr	dY,
		magma_int_t	lddy,
		magmaDouble_ptr	dV,
		magma_int_t	lddv,
		magmaDouble_ptr	dT,
		magmaDouble_ptr	dwork,
		magma_queue_t	queue )

DLAHRU is an auxiliary MAGMA routine that is used in DGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

See further details below.

Parameters

[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	ihi	INTEGER Last row to update. Same as IHI in dgehrd.
[in]	k	INTEGER Number of rows of the matrix Am (see details below)
[in]	nb	INTEGER Block size
[out]	A	DOUBLE PRECISION array, dimension (LDA,N-K) On entry, the N-by-(N-K) general matrix to be updated. The computation is done on the GPU. After Am is updated on the GPU only Am(1:NB) is transferred to the CPU - to update the corresponding Am matrix. See Further Details below.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in,out]	dA	DOUBLE PRECISION array on the GPU, dimension (LDDA,N-K). On entry, the N-by-(N-K) general matrix to be updated. On exit, the 1st K rows (matrix Am) of A are updated by applying an orthogonal transformation from the right Am = Am (I-V T V'), and sub-matrix Ag is updated by Ag = (I - V T V') Ag (I - V T V(NB+1:)' ) where Q = I - V T V' represent the orthogonal matrix (as a product of elementary reflectors V) used to reduce the current panel of A to upper Hessenberg form. After Am is updated Am(:,1:NB) is sent to the CPU. See Further Details below.
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,N).
[in,out]	dY	(workspace) DOUBLE PRECISION array on the GPU, dimension (LDDY, NB). On entry the (N-K)-by-NB Y = A V. It is used internally as workspace, so its value is changed on exit.
[in]	lddy	INTEGER The leading dimension of the array dY. LDDY >= max(1,N).
[in,out]	dV	(workspace) DOUBLE PRECISION array on the GPU, dimension (LDDV, NB). On entry the (N-K)-by-NB matrix V of elementary reflectors used to reduce the current panel of A to upper Hessenberg form. The rest K-by-NB part is used as workspace. V is unchanged on exit.
[in]	lddv	INTEGER The leading dimension of the array dV. LDDV >= max(1,N).
[in]	dT	DOUBLE PRECISION array on the GPU, dimension (NB, NB). On entry the NB-by-NB upper trinagular matrix defining the orthogonal Hessenberg reduction transformation matrix for the current panel. The lower triangular part are 0s.
	dwork	(workspace) DOUBLE PRECISION array on the GPU, dimension N*NB.
[in]	queue	magma_queue_t Queue to execute in.

Further Details

This implementation follows the algorithm and notations described in:

S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg form through hybrid GPU-based computing," University of Tennessee Computer Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219), May 24, 2009.

The difference is that here Am is computed on the GPU. M is renamed Am, G is renamed Ag.

◆ magma_dlahru_m()

magma_int_t magma_dlahru_m	(	magma_int_t	n,
		magma_int_t	ihi,
		magma_int_t	k,
		magma_int_t	nb,
		double *	A,
		magma_int_t	lda,
		struct dgehrd_data *	data )

DLAHRU is an auxiliary MAGMA routine that is used in DGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

See further details below.

Parameters

[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	ihi	INTEGER Last row to update. Same as IHI in dgehrd.
[in]	k	INTEGER Number of rows of the matrix Am (see details below)
[in]	nb	INTEGER Block size
[out]	A	DOUBLE PRECISION array, dimension (LDA,N-K) On entry, the N-by-(N-K) general matrix to be updated. The computation is done on the GPU. After Am is updated on the GPU only Am(1:NB) is transferred to the CPU - to update the corresponding Am matrix. See Further Details below.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in,out]	data	Structure with pointers to dA, dT, dV, dW, dY which are distributed across multiple GPUs.

Further Details

This implementation follows the algorithm and notations described in:

S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg form through hybrid GPU-based computing," University of Tennessee Computer Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219), May 24, 2009.

The difference is that here Am is computed on the GPU. M is renamed Am, G is renamed Ag.

◆ magma_slahru()

magma_int_t magma_slahru	(	magma_int_t	n,
		magma_int_t	ihi,
		magma_int_t	k,
		magma_int_t	nb,
		float *	A,
		magma_int_t	lda,
		magmaFloat_ptr	dA,
		magma_int_t	ldda,
		magmaFloat_ptr	dY,
		magma_int_t	lddy,
		magmaFloat_ptr	dV,
		magma_int_t	lddv,
		magmaFloat_ptr	dT,
		magmaFloat_ptr	dwork,
		magma_queue_t	queue )

SLAHRU is an auxiliary MAGMA routine that is used in SGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

See further details below.

Parameters

[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	ihi	INTEGER Last row to update. Same as IHI in sgehrd.
[in]	k	INTEGER Number of rows of the matrix Am (see details below)
[in]	nb	INTEGER Block size
[out]	A	REAL array, dimension (LDA,N-K) On entry, the N-by-(N-K) general matrix to be updated. The computation is done on the GPU. After Am is updated on the GPU only Am(1:NB) is transferred to the CPU - to update the corresponding Am matrix. See Further Details below.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in,out]	dA	REAL array on the GPU, dimension (LDDA,N-K). On entry, the N-by-(N-K) general matrix to be updated. On exit, the 1st K rows (matrix Am) of A are updated by applying an orthogonal transformation from the right Am = Am (I-V T V'), and sub-matrix Ag is updated by Ag = (I - V T V') Ag (I - V T V(NB+1:)' ) where Q = I - V T V' represent the orthogonal matrix (as a product of elementary reflectors V) used to reduce the current panel of A to upper Hessenberg form. After Am is updated Am(:,1:NB) is sent to the CPU. See Further Details below.
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,N).
[in,out]	dY	(workspace) REAL array on the GPU, dimension (LDDY, NB). On entry the (N-K)-by-NB Y = A V. It is used internally as workspace, so its value is changed on exit.
[in]	lddy	INTEGER The leading dimension of the array dY. LDDY >= max(1,N).
[in,out]	dV	(workspace) REAL array on the GPU, dimension (LDDV, NB). On entry the (N-K)-by-NB matrix V of elementary reflectors used to reduce the current panel of A to upper Hessenberg form. The rest K-by-NB part is used as workspace. V is unchanged on exit.
[in]	lddv	INTEGER The leading dimension of the array dV. LDDV >= max(1,N).
[in]	dT	REAL array on the GPU, dimension (NB, NB). On entry the NB-by-NB upper trinagular matrix defining the orthogonal Hessenberg reduction transformation matrix for the current panel. The lower triangular part are 0s.
	dwork	(workspace) REAL array on the GPU, dimension N*NB.
[in]	queue	magma_queue_t Queue to execute in.

Further Details

This implementation follows the algorithm and notations described in:

S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg form through hybrid GPU-based computing," University of Tennessee Computer Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219), May 24, 2009.

The difference is that here Am is computed on the GPU. M is renamed Am, G is renamed Ag.

◆ magma_slahru_m()

magma_int_t magma_slahru_m	(	magma_int_t	n,
		magma_int_t	ihi,
		magma_int_t	k,
		magma_int_t	nb,
		float *	A,
		magma_int_t	lda,
		struct sgehrd_data *	data )

SLAHRU is an auxiliary MAGMA routine that is used in SGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

See further details below.

Parameters

[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	ihi	INTEGER Last row to update. Same as IHI in sgehrd.
[in]	k	INTEGER Number of rows of the matrix Am (see details below)
[in]	nb	INTEGER Block size
[out]	A	REAL array, dimension (LDA,N-K) On entry, the N-by-(N-K) general matrix to be updated. The computation is done on the GPU. After Am is updated on the GPU only Am(1:NB) is transferred to the CPU - to update the corresponding Am matrix. See Further Details below.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in,out]	data	Structure with pointers to dA, dT, dV, dW, dY which are distributed across multiple GPUs.

Further Details

This implementation follows the algorithm and notations described in:

S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg form through hybrid GPU-based computing," University of Tennessee Computer Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219), May 24, 2009.

The difference is that here Am is computed on the GPU. M is renamed Am, G is renamed Ag.

◆ magma_zlahru()

magma_int_t magma_zlahru	(	magma_int_t	n,
		magma_int_t	ihi,
		magma_int_t	k,
		magma_int_t	nb,
		magmaDoubleComplex *	A,
		magma_int_t	lda,
		magmaDoubleComplex_ptr	dA,
		magma_int_t	ldda,
		magmaDoubleComplex_ptr	dY,
		magma_int_t	lddy,
		magmaDoubleComplex_ptr	dV,
		magma_int_t	lddv,
		magmaDoubleComplex_ptr	dT,
		magmaDoubleComplex_ptr	dwork,
		magma_queue_t	queue )

ZLAHRU is an auxiliary MAGMA routine that is used in ZGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

See further details below.

Parameters

[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	ihi	INTEGER Last row to update. Same as IHI in zgehrd.
[in]	k	INTEGER Number of rows of the matrix Am (see details below)
[in]	nb	INTEGER Block size
[out]	A	COMPLEX_16 array, dimension (LDA,N-K) On entry, the N-by-(N-K) general matrix to be updated. The computation is done on the GPU. After Am is updated on the GPU only Am(1:NB) is transferred to the CPU - to update the corresponding Am matrix. See Further Details below.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in,out]	dA	COMPLEX_16 array on the GPU, dimension (LDDA,N-K). On entry, the N-by-(N-K) general matrix to be updated. On exit, the 1st K rows (matrix Am) of A are updated by applying an orthogonal transformation from the right Am = Am (I-V T V'), and sub-matrix Ag is updated by Ag = (I - V T V') Ag (I - V T V(NB+1:)' ) where Q = I - V T V' represent the orthogonal matrix (as a product of elementary reflectors V) used to reduce the current panel of A to upper Hessenberg form. After Am is updated Am(:,1:NB) is sent to the CPU. See Further Details below.
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,N).
[in,out]	dY	(workspace) COMPLEX_16 array on the GPU, dimension (LDDY, NB). On entry the (N-K)-by-NB Y = A V. It is used internally as workspace, so its value is changed on exit.
[in]	lddy	INTEGER The leading dimension of the array dY. LDDY >= max(1,N).
[in,out]	dV	(workspace) COMPLEX_16 array on the GPU, dimension (LDDV, NB). On entry the (N-K)-by-NB matrix V of elementary reflectors used to reduce the current panel of A to upper Hessenberg form. The rest K-by-NB part is used as workspace. V is unchanged on exit.
[in]	lddv	INTEGER The leading dimension of the array dV. LDDV >= max(1,N).
[in]	dT	COMPLEX_16 array on the GPU, dimension (NB, NB). On entry the NB-by-NB upper trinagular matrix defining the orthogonal Hessenberg reduction transformation matrix for the current panel. The lower triangular part are 0s.
	dwork	(workspace) COMPLEX_16 array on the GPU, dimension N*NB.
[in]	queue	magma_queue_t Queue to execute in.

Further Details

This implementation follows the algorithm and notations described in:

S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg form through hybrid GPU-based computing," University of Tennessee Computer Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219), May 24, 2009.

The difference is that here Am is computed on the GPU. M is renamed Am, G is renamed Ag.

◆ magma_zlahru_m()

magma_int_t magma_zlahru_m	(	magma_int_t	n,
		magma_int_t	ihi,
		magma_int_t	k,
		magma_int_t	nb,
		magmaDoubleComplex *	A,
		magma_int_t	lda,
		struct zgehrd_data *	data )

ZLAHRU is an auxiliary MAGMA routine that is used in ZGEHRD to update the trailing sub-matrices after the reductions of the corresponding panels.

See further details below.

Parameters

[in]	n	INTEGER The order of the matrix A. N >= 0.
[in]	ihi	INTEGER Last row to update. Same as IHI in zgehrd.
[in]	k	INTEGER Number of rows of the matrix Am (see details below)
[in]	nb	INTEGER Block size
[out]	A	COMPLEX_16 array, dimension (LDA,N-K) On entry, the N-by-(N-K) general matrix to be updated. The computation is done on the GPU. After Am is updated on the GPU only Am(1:NB) is transferred to the CPU - to update the corresponding Am matrix. See Further Details below.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in,out]	data	Structure with pointers to dA, dT, dV, dW, dY which are distributed across multiple GPUs.

Further Details

This implementation follows the algorithm and notations described in:

S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg form through hybrid GPU-based computing," University of Tennessee Computer Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219), May 24, 2009.

The difference is that here Am is computed on the GPU. M is renamed Am, G is renamed Ag.

Functions

Detailed Description

Function Documentation

◆ magma_clahru()

Further Details

◆ magma_clahru_m()

Further Details

◆ magma_dlahru()

Further Details

◆ magma_dlahru_m()

Further Details

◆ magma_slahru()

Further Details

◆ magma_slahru_m()

Further Details

◆ magma_zlahru()

Further Details

◆ magma_zlahru_m()

Further Details