Functions
magma_int_t	magma_clarfb_gemm_batched (magma_side_t side, magma_trans_t trans, magma_direct_t direct, magma_storev_t storev, magma_int_t m, magma_int_t n, magma_int_t k, magmaFloatComplex_const_ptr dV_array[], magma_int_t lddv, magmaFloatComplex_const_ptr dT_array[], magma_int_t lddt, magmaFloatComplex_ptr dC_array[], magma_int_t lddc, magmaFloatComplex_ptr dwork_array[], magma_int_t ldwork, magmaFloatComplex_ptr dworkvt_array[], magma_int_t ldworkvt, magma_int_t batchCount, magma_queue_t queue)
	CLARFB applies a complex block reflector H or its transpose H^H to a COMPLEX m by n matrix C, from the left. More...

magma_int_t	magma_dlarfb_gemm_batched (magma_side_t side, magma_trans_t trans, magma_direct_t direct, magma_storev_t storev, magma_int_t m, magma_int_t n, magma_int_t k, magmaDouble_const_ptr dV_array[], magma_int_t lddv, magmaDouble_const_ptr dT_array[], magma_int_t lddt, magmaDouble_ptr dC_array[], magma_int_t lddc, magmaDouble_ptr dwork_array[], magma_int_t ldwork, magmaDouble_ptr dworkvt_array[], magma_int_t ldworkvt, magma_int_t batchCount, magma_queue_t queue)
	DLARFB applies a real block reflector H or its transpose H^H to a DOUBLE PRECISION m by n matrix C, from the left. More...

magma_int_t	magma_slarfb_gemm_batched (magma_side_t side, magma_trans_t trans, magma_direct_t direct, magma_storev_t storev, magma_int_t m, magma_int_t n, magma_int_t k, magmaFloat_const_ptr dV_array[], magma_int_t lddv, magmaFloat_const_ptr dT_array[], magma_int_t lddt, magmaFloat_ptr dC_array[], magma_int_t lddc, magmaFloat_ptr dwork_array[], magma_int_t ldwork, magmaFloat_ptr dworkvt_array[], magma_int_t ldworkvt, magma_int_t batchCount, magma_queue_t queue)
	SLARFB applies a real block reflector H or its transpose H^H to a REAL m by n matrix C, from the left. More...

magma_int_t	magma_zlarfb_gemm_batched (magma_side_t side, magma_trans_t trans, magma_direct_t direct, magma_storev_t storev, magma_int_t m, magma_int_t n, magma_int_t k, magmaDoubleComplex_const_ptr dV_array[], magma_int_t lddv, magmaDoubleComplex_const_ptr dT_array[], magma_int_t lddt, magmaDoubleComplex_ptr dC_array[], magma_int_t lddc, magmaDoubleComplex_ptr dwork_array[], magma_int_t ldwork, magmaDoubleComplex_ptr dworkvt_array[], magma_int_t ldworkvt, magma_int_t batchCount, magma_queue_t queue)
	ZLARFB applies a complex block reflector H or its transpose H^H to a COMPLEX_16 m by n matrix C, from the left. More...

Detailed Description

Function Documentation

magma_int_t magma_clarfb_gemm_batched	(	magma_side_t	side,
		magma_trans_t	trans,
		magma_direct_t	direct,
		magma_storev_t	storev,
		magma_int_t	m,
		magma_int_t	n,
		magma_int_t	k,
		magmaFloatComplex_const_ptr	dV_array[],
		magma_int_t	lddv,
		magmaFloatComplex_const_ptr	dT_array[],
		magma_int_t	lddt,
		magmaFloatComplex_ptr	dC_array[],
		magma_int_t	lddc,
		magmaFloatComplex_ptr	dwork_array[],
		magma_int_t	ldwork,
		magmaFloatComplex_ptr	dworkvt_array[],
		magma_int_t	ldworkvt,
		magma_int_t	batchCount,
		magma_queue_t	queue
	)

CLARFB applies a complex block reflector H or its transpose H^H to a COMPLEX m by n matrix C, from the left.

Note that this function assumes that the upper part of dV_array is 0 because it is referenced. Same for upper/lower part of dT_array.

Parameters

[in]	side	magma_side_t = MagmaLeft: apply H or H^H from the Left = MagmaRight: apply H or H^H from the Right
[in]	trans	magma_trans_t = MagmaNoTrans: apply H (No transpose) = Magma_ConjTrans: apply H^H (Conjugate transpose)
[in]	direct	magma_direct_t Indicates how H is formed from a product of elementary reflectors = MagmaForward: H = H(1) H(2) . . . H(k) (Forward) = MagmaBackward: H = H(k) . . . H(2) H(1) (Backward)
[in]	storev	magma_storev_t Indicates how the vectors which define the elementary reflectors are stored: = MagmaColumnwise: Columnwise = MagmaRowwise: Rowwise
[in]	m	INTEGER The number of rows of the matrix C.
[in]	n	INTEGER The number of columns of the matrix C.
[in]	k	INTEGER The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector).
[in]	dV_array	COMPLEX array on the GPU, dimension (LDDV,K) if STOREV = MagmaColumnwise (LDDV,M) if STOREV = MagmaRowwise and SIDE = MagmaLeft (LDDV,N) if STOREV = MagmaRowwise and SIDE = MagmaRight The matrix V. See further details.
[in]	lddv	INTEGER The leading dimension of the array V. If STOREV = MagmaColumnwise and SIDE = MagmaLeft, LDDV >= max(1,M); if STOREV = MagmaColumnwise and SIDE = MagmaRight, LDDV >= max(1,N); if STOREV = MagmaRowwise, LDDV >= K.
[in]	dT_array	COMPLEX array on the GPU, dimension (LDDT,K) The triangular k by k matrix T in the representation of the block reflector.
[in]	lddt	INTEGER The leading dimension of the array T. LDDT >= K.
[in,out]	dC_array	COMPLEX array on the GPU, dimension (LDDC,N) On entry, the m by n matrix C. On exit, C is overwritten by HC, or H^HC, or CH, or CH^H.
[in]	lddc	INTEGER The leading dimension of the array C. LDDC >= max(1,M).
	dwork_array	(workspace) COMPLEX array, dimension (LDWORK,K)
[in]	ldwork	INTEGER The leading dimension of the array WORK. If SIDE = MagmaLeft, LDWORK >= max(1,N); if SIDE = MagmaRight, LDWORK >= max(1,M);
	dworkvt_array	(workspace) COMPLEX array, dimension (LDWORKT,K)
[in]	ldworkvt	INTEGER The leading dimension of the array WORKVT. LDWORKVT >= max(1,min(M,N));
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

Further Details

The shape of the matrix V and the storage of the vectors which define the H(i) is best illustrated by the following example with n = 5 and k = 3. All elements including 0's and 1's are stored, unlike LAPACK.

DIRECT = MagmaForward and         DIRECT = MagmaForward and
STOREV = MagmaColumnwise:         STOREV = MagmaRowwise:

         V = (  1  0  0 )                 V = (  1 v1 v1 v1 v1 )
             ( v1  1  0 )                     (  0  1 v2 v2 v2 )
             ( v1 v2  1 )                     (  0  0  1 v3 v3 )
             ( v1 v2 v3 )
             ( v1 v2 v3 )

DIRECT = MagmaBackward and        DIRECT = MagmaBackward and
STOREV = MagmaColumnwise:         STOREV = MagmaRowwise:

         V = ( v1 v2 v3 )                 V = ( v1 v1  1  0  0 )
             ( v1 v2 v3 )                     ( v2 v2 v2  1  0 )
             (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
             (  0  1 v3 )
             (  0  0  1 )

magma_int_t magma_dlarfb_gemm_batched	(	magma_side_t	side,
		magma_trans_t	trans,
		magma_direct_t	direct,
		magma_storev_t	storev,
		magma_int_t	m,
		magma_int_t	n,
		magma_int_t	k,
		magmaDouble_const_ptr	dV_array[],
		magma_int_t	lddv,
		magmaDouble_const_ptr	dT_array[],
		magma_int_t	lddt,
		magmaDouble_ptr	dC_array[],
		magma_int_t	lddc,
		magmaDouble_ptr	dwork_array[],
		magma_int_t	ldwork,
		magmaDouble_ptr	dworkvt_array[],
		magma_int_t	ldworkvt,
		magma_int_t	batchCount,
		magma_queue_t	queue
	)

DLARFB applies a real block reflector H or its transpose H^H to a DOUBLE PRECISION m by n matrix C, from the left.

Note that this function assumes that the upper part of dV_array is 0 because it is referenced. Same for upper/lower part of dT_array.

Parameters

[in]	side	magma_side_t = MagmaLeft: apply H or H^H from the Left = MagmaRight: apply H or H^H from the Right
[in]	trans	magma_trans_t = MagmaNoTrans: apply H (No transpose) = MagmaTrans: apply H^H (Conjugate transpose)
[in]	direct	magma_direct_t Indicates how H is formed from a product of elementary reflectors = MagmaForward: H = H(1) H(2) . . . H(k) (Forward) = MagmaBackward: H = H(k) . . . H(2) H(1) (Backward)
[in]	storev	magma_storev_t Indicates how the vectors which define the elementary reflectors are stored: = MagmaColumnwise: Columnwise = MagmaRowwise: Rowwise
[in]	m	INTEGER The number of rows of the matrix C.
[in]	n	INTEGER The number of columns of the matrix C.
[in]	k	INTEGER The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector).
[in]	dV_array	DOUBLE PRECISION array on the GPU, dimension (LDDV,K) if STOREV = MagmaColumnwise (LDDV,M) if STOREV = MagmaRowwise and SIDE = MagmaLeft (LDDV,N) if STOREV = MagmaRowwise and SIDE = MagmaRight The matrix V. See further details.
[in]	lddv	INTEGER The leading dimension of the array V. If STOREV = MagmaColumnwise and SIDE = MagmaLeft, LDDV >= max(1,M); if STOREV = MagmaColumnwise and SIDE = MagmaRight, LDDV >= max(1,N); if STOREV = MagmaRowwise, LDDV >= K.
[in]	dT_array	DOUBLE PRECISION array on the GPU, dimension (LDDT,K) The triangular k by k matrix T in the representation of the block reflector.
[in]	lddt	INTEGER The leading dimension of the array T. LDDT >= K.
[in,out]	dC_array	DOUBLE PRECISION array on the GPU, dimension (LDDC,N) On entry, the m by n matrix C. On exit, C is overwritten by HC, or H^HC, or CH, or CH^H.
[in]	lddc	INTEGER The leading dimension of the array C. LDDC >= max(1,M).
	dwork_array	(workspace) DOUBLE PRECISION array, dimension (LDWORK,K)
[in]	ldwork	INTEGER The leading dimension of the array WORK. If SIDE = MagmaLeft, LDWORK >= max(1,N); if SIDE = MagmaRight, LDWORK >= max(1,M);
	dworkvt_array	(workspace) DOUBLE PRECISION array, dimension (LDWORKT,K)
[in]	ldworkvt	INTEGER The leading dimension of the array WORKVT. LDWORKVT >= max(1,min(M,N));
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

Further Details

The shape of the matrix V and the storage of the vectors which define the H(i) is best illustrated by the following example with n = 5 and k = 3. All elements including 0's and 1's are stored, unlike LAPACK.

DIRECT = MagmaForward and         DIRECT = MagmaForward and
STOREV = MagmaColumnwise:         STOREV = MagmaRowwise:

         V = (  1  0  0 )                 V = (  1 v1 v1 v1 v1 )
             ( v1  1  0 )                     (  0  1 v2 v2 v2 )
             ( v1 v2  1 )                     (  0  0  1 v3 v3 )
             ( v1 v2 v3 )
             ( v1 v2 v3 )

DIRECT = MagmaBackward and        DIRECT = MagmaBackward and
STOREV = MagmaColumnwise:         STOREV = MagmaRowwise:

         V = ( v1 v2 v3 )                 V = ( v1 v1  1  0  0 )
             ( v1 v2 v3 )                     ( v2 v2 v2  1  0 )
             (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
             (  0  1 v3 )
             (  0  0  1 )

magma_int_t magma_slarfb_gemm_batched	(	magma_side_t	side,
		magma_trans_t	trans,
		magma_direct_t	direct,
		magma_storev_t	storev,
		magma_int_t	m,
		magma_int_t	n,
		magma_int_t	k,
		magmaFloat_const_ptr	dV_array[],
		magma_int_t	lddv,
		magmaFloat_const_ptr	dT_array[],
		magma_int_t	lddt,
		magmaFloat_ptr	dC_array[],
		magma_int_t	lddc,
		magmaFloat_ptr	dwork_array[],
		magma_int_t	ldwork,
		magmaFloat_ptr	dworkvt_array[],
		magma_int_t	ldworkvt,
		magma_int_t	batchCount,
		magma_queue_t	queue
	)

SLARFB applies a real block reflector H or its transpose H^H to a REAL m by n matrix C, from the left.

Note that this function assumes that the upper part of dV_array is 0 because it is referenced. Same for upper/lower part of dT_array.

Parameters

[in]	side	magma_side_t = MagmaLeft: apply H or H^H from the Left = MagmaRight: apply H or H^H from the Right
[in]	trans	magma_trans_t = MagmaNoTrans: apply H (No transpose) = MagmaTrans: apply H^H (Conjugate transpose)
[in]	direct	magma_direct_t Indicates how H is formed from a product of elementary reflectors = MagmaForward: H = H(1) H(2) . . . H(k) (Forward) = MagmaBackward: H = H(k) . . . H(2) H(1) (Backward)
[in]	storev	magma_storev_t Indicates how the vectors which define the elementary reflectors are stored: = MagmaColumnwise: Columnwise = MagmaRowwise: Rowwise
[in]	m	INTEGER The number of rows of the matrix C.
[in]	n	INTEGER The number of columns of the matrix C.
[in]	k	INTEGER The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector).
[in]	dV_array	REAL array on the GPU, dimension (LDDV,K) if STOREV = MagmaColumnwise (LDDV,M) if STOREV = MagmaRowwise and SIDE = MagmaLeft (LDDV,N) if STOREV = MagmaRowwise and SIDE = MagmaRight The matrix V. See further details.
[in]	lddv	INTEGER The leading dimension of the array V. If STOREV = MagmaColumnwise and SIDE = MagmaLeft, LDDV >= max(1,M); if STOREV = MagmaColumnwise and SIDE = MagmaRight, LDDV >= max(1,N); if STOREV = MagmaRowwise, LDDV >= K.
[in]	dT_array	REAL array on the GPU, dimension (LDDT,K) The triangular k by k matrix T in the representation of the block reflector.
[in]	lddt	INTEGER The leading dimension of the array T. LDDT >= K.
[in,out]	dC_array	REAL array on the GPU, dimension (LDDC,N) On entry, the m by n matrix C. On exit, C is overwritten by HC, or H^HC, or CH, or CH^H.
[in]	lddc	INTEGER The leading dimension of the array C. LDDC >= max(1,M).
	dwork_array	(workspace) REAL array, dimension (LDWORK,K)
[in]	ldwork	INTEGER The leading dimension of the array WORK. If SIDE = MagmaLeft, LDWORK >= max(1,N); if SIDE = MagmaRight, LDWORK >= max(1,M);
	dworkvt_array	(workspace) REAL array, dimension (LDWORKT,K)
[in]	ldworkvt	INTEGER The leading dimension of the array WORKVT. LDWORKVT >= max(1,min(M,N));
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

Further Details

The shape of the matrix V and the storage of the vectors which define the H(i) is best illustrated by the following example with n = 5 and k = 3. All elements including 0's and 1's are stored, unlike LAPACK.

DIRECT = MagmaForward and         DIRECT = MagmaForward and
STOREV = MagmaColumnwise:         STOREV = MagmaRowwise:

         V = (  1  0  0 )                 V = (  1 v1 v1 v1 v1 )
             ( v1  1  0 )                     (  0  1 v2 v2 v2 )
             ( v1 v2  1 )                     (  0  0  1 v3 v3 )
             ( v1 v2 v3 )
             ( v1 v2 v3 )

DIRECT = MagmaBackward and        DIRECT = MagmaBackward and
STOREV = MagmaColumnwise:         STOREV = MagmaRowwise:

         V = ( v1 v2 v3 )                 V = ( v1 v1  1  0  0 )
             ( v1 v2 v3 )                     ( v2 v2 v2  1  0 )
             (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
             (  0  1 v3 )
             (  0  0  1 )

magma_int_t magma_zlarfb_gemm_batched	(	magma_side_t	side,
		magma_trans_t	trans,
		magma_direct_t	direct,
		magma_storev_t	storev,
		magma_int_t	m,
		magma_int_t	n,
		magma_int_t	k,
		magmaDoubleComplex_const_ptr	dV_array[],
		magma_int_t	lddv,
		magmaDoubleComplex_const_ptr	dT_array[],
		magma_int_t	lddt,
		magmaDoubleComplex_ptr	dC_array[],
		magma_int_t	lddc,
		magmaDoubleComplex_ptr	dwork_array[],
		magma_int_t	ldwork,
		magmaDoubleComplex_ptr	dworkvt_array[],
		magma_int_t	ldworkvt,
		magma_int_t	batchCount,
		magma_queue_t	queue
	)

ZLARFB applies a complex block reflector H or its transpose H^H to a COMPLEX_16 m by n matrix C, from the left.

Note that this function assumes that the upper part of dV_array is 0 because it is referenced. Same for upper/lower part of dT_array.

Parameters

[in]	side	magma_side_t = MagmaLeft: apply H or H^H from the Left = MagmaRight: apply H or H^H from the Right
[in]	trans	magma_trans_t = MagmaNoTrans: apply H (No transpose) = Magma_ConjTrans: apply H^H (Conjugate transpose)
[in]	direct	magma_direct_t Indicates how H is formed from a product of elementary reflectors = MagmaForward: H = H(1) H(2) . . . H(k) (Forward) = MagmaBackward: H = H(k) . . . H(2) H(1) (Backward)
[in]	storev	magma_storev_t Indicates how the vectors which define the elementary reflectors are stored: = MagmaColumnwise: Columnwise = MagmaRowwise: Rowwise
[in]	m	INTEGER The number of rows of the matrix C.
[in]	n	INTEGER The number of columns of the matrix C.
[in]	k	INTEGER The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector).
[in]	dV_array	COMPLEX_16 array on the GPU, dimension (LDDV,K) if STOREV = MagmaColumnwise (LDDV,M) if STOREV = MagmaRowwise and SIDE = MagmaLeft (LDDV,N) if STOREV = MagmaRowwise and SIDE = MagmaRight The matrix V. See further details.
[in]	lddv	INTEGER The leading dimension of the array V. If STOREV = MagmaColumnwise and SIDE = MagmaLeft, LDDV >= max(1,M); if STOREV = MagmaColumnwise and SIDE = MagmaRight, LDDV >= max(1,N); if STOREV = MagmaRowwise, LDDV >= K.
[in]	dT_array	COMPLEX_16 array on the GPU, dimension (LDDT,K) The triangular k by k matrix T in the representation of the block reflector.
[in]	lddt	INTEGER The leading dimension of the array T. LDDT >= K.
[in,out]	dC_array	COMPLEX_16 array on the GPU, dimension (LDDC,N) On entry, the m by n matrix C. On exit, C is overwritten by HC, or H^HC, or CH, or CH^H.
[in]	lddc	INTEGER The leading dimension of the array C. LDDC >= max(1,M).
	dwork_array	(workspace) COMPLEX_16 array, dimension (LDWORK,K)
[in]	ldwork	INTEGER The leading dimension of the array WORK. If SIDE = MagmaLeft, LDWORK >= max(1,N); if SIDE = MagmaRight, LDWORK >= max(1,M);
	dworkvt_array	(workspace) COMPLEX_16 array, dimension (LDWORKT,K)
[in]	ldworkvt	INTEGER The leading dimension of the array WORKVT. LDWORKVT >= max(1,min(M,N));
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

Further Details

The shape of the matrix V and the storage of the vectors which define the H(i) is best illustrated by the following example with n = 5 and k = 3. All elements including 0's and 1's are stored, unlike LAPACK.

DIRECT = MagmaForward and         DIRECT = MagmaForward and
STOREV = MagmaColumnwise:         STOREV = MagmaRowwise:

         V = (  1  0  0 )                 V = (  1 v1 v1 v1 v1 )
             ( v1  1  0 )                     (  0  1 v2 v2 v2 )
             ( v1 v2  1 )                     (  0  0  1 v3 v3 )
             ( v1 v2 v3 )
             ( v1 v2 v3 )

DIRECT = MagmaBackward and        DIRECT = MagmaBackward and
STOREV = MagmaColumnwise:         STOREV = MagmaRowwise:

         V = ( v1 v2 v3 )                 V = ( v1 v1  1  0  0 )
             ( v1 v2 v3 )                     ( v2 v2 v2  1  0 )
             (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
             (  0  1 v3 )
             (  0  0  1 )

Functions

Detailed Description

Function Documentation

Further Details

Further Details

Further Details

Further Details