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MAGMA
2.0.0
Matrix Algebra for GPU and Multicore Architectures
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Functions | |
void | magma_dlarfy (magma_int_t n, double *A, magma_int_t lda, const double *V, const double *TAU, double *work) |
magma_dlarfy applies an elementary reflector, or Householder matrix, H, to a n-by-n symmetric matrix C, from both the left and the right. 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_dlarfb_gpu_q (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, magma_int_t lddv, magmaDouble_const_ptr dT, magma_int_t lddt, magmaDouble_ptr dC, magma_int_t lddc, magmaDouble_ptr dwork, magma_int_t ldwork, 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_dlarfb_gpu_gemm_q (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, magma_int_t lddv, magmaDouble_const_ptr dT, magma_int_t lddt, magmaDouble_ptr dC, magma_int_t lddc, magmaDouble_ptr dwork, magma_int_t ldwork, magmaDouble_ptr dworkvt, magma_int_t ldworkvt, 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... | |
void | magma_dlarfbx_gpu (magma_int_t m, magma_int_t k, magmaDouble_ptr V, magma_int_t ldv, magmaDouble_ptr dT, magma_int_t ldt, magmaDouble_ptr c, magmaDouble_ptr dwork) |
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.
[in] | side | magma_side_t
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[in] | trans | magma_trans_t
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[in] | direct | magma_direct_t Indicates how H is formed from a product of elementary reflectors
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[in] | storev | magma_storev_t Indicates how the vectors which define the elementary reflectors are stored:
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[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 H*C, or H^H*C, or C*H, or C*H^H. |
[in] | lddc | INTEGER The leading dimension of the array C. LDA >= 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. |
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_gpu_gemm_q | ( | 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, | ||
magma_int_t | lddv, | ||
magmaDouble_const_ptr | dT, | ||
magma_int_t | lddt, | ||
magmaDouble_ptr | dC, | ||
magma_int_t | lddc, | ||
magmaDouble_ptr | dwork, | ||
magma_int_t | ldwork, | ||
magmaDouble_ptr | dworkvt, | ||
magma_int_t | ldworkvt, | ||
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 is 0 because it is referenced. Same for upper/lower part of dT.
[in] | side | magma_side_t
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[in] | trans | magma_trans_t
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[in] | direct | magma_direct_t Indicates how H is formed from a product of elementary reflectors
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[in] | storev | magma_storev_t Indicates how the vectors which define the elementary reflectors are stored:
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[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 | 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 | 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 | DOUBLE PRECISION array on the GPU, dimension (LDDC,N) On entry, the m by n matrix C. On exit, C is overwritten by H*C, or H^H*C, or C*H, or C*H^H. |
[in] | lddc | INTEGER The leading dimension of the array C. LDDC >= max(1,M). |
dwork | (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 | (workspace) DOUBLE PRECISION array, dimension (LDWORKT,K) | |
[in] | ldworkvt | INTEGER The leading dimension of the array WORKVT. LDWORKVT >= max(1,min(M,N)); |
[in] | queue | magma_queue_t Queue to execute in. |
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_gpu_q | ( | 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, | ||
magma_int_t | lddv, | ||
magmaDouble_const_ptr | dT, | ||
magma_int_t | lddt, | ||
magmaDouble_ptr | dC, | ||
magma_int_t | lddc, | ||
magmaDouble_ptr | dwork, | ||
magma_int_t | ldwork, | ||
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.
[in] | side | magma_side_t
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[in] | trans | magma_trans_t
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[in] | direct | magma_direct_t Indicates how H is formed from a product of elementary reflectors
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[in] | storev | magma_storev_t Indicates how the vectors which define the elementary reflectors are stored:
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[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 | 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 | 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 | DOUBLE PRECISION array on the GPU, dimension (LDDC,N) On entry, the m by n matrix C. On exit, C is overwritten by H*C, or H^H*C, or C*H, or C*H^H. |
[in] | lddc | INTEGER The leading dimension of the array C. LDDC >= max(1,M). |
dwork | (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); |
[in] | queue | magma_queue_t Queue to execute in. |
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 )
void magma_dlarfbx_gpu | ( | magma_int_t | m, |
magma_int_t | k, | ||
magmaDouble_ptr | V, | ||
magma_int_t | ldv, | ||
magmaDouble_ptr | dT, | ||
magma_int_t | ldt, | ||
magmaDouble_ptr | c, | ||
magmaDouble_ptr | dwork | ||
) |
void magma_dlarfy | ( | magma_int_t | n, |
double * | A, | ||
magma_int_t | lda, | ||
const double * | V, | ||
const double * | TAU, | ||
double * | work | ||
) |
magma_dlarfy applies an elementary reflector, or Householder matrix, H, to a n-by-n symmetric matrix C, from both the left and the right.
H is represented in the form
H = I - tau * v * v'
where tau is a scalar and v is a vector.
If tau is zero, then H is taken to be the unit matrix.
[in] | n | The number of rows and columns of the matrix C. n >= 0. |
[in,out] | A | DOUBLE PRECISION array, dimension (lda, n) On entry, the Hermetian matrix A. On exit, A is overwritten by H * A * H'. |
[in] | lda | The leading dimension of the array A. lda >= max(1,n). |
[in] | V | The vector V that contains the Householder reflectors. |
[in] | TAU | The value tau. |
[out] | work | Workspace. |