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MAGMA
1.5.0
Matrix Algebra for GPU and Multicore Architectures
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Functions | |
magma_int_t | magma_dlarfb_gpu (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, const double *dV, magma_int_t ldv, const double *dT, magma_int_t ldt, double *dC, magma_int_t ldc, double *dwork, magma_int_t ldwork) |
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 (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, const double *dV, magma_int_t ldv, const double *dT, magma_int_t ldt, double *dC, magma_int_t ldc, double *dwork, magma_int_t ldwork, double *dworkvt, magma_int_t ldworkvt) |
DLARFB applies a real block reflector H or its transpose H' to a DOUBLE_PRECISION m by n matrix C, from the left. More... | |
magma_int_t magma_dlarfb_gpu | ( | 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, | ||
const double * | dV, | ||
magma_int_t | ldv, | ||
const double * | dT, | ||
magma_int_t | ldt, | ||
double * | dC, | ||
magma_int_t | ldc, | ||
double * | dwork, | ||
magma_int_t | ldwork | ||
) |
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 (LDV,K) if STOREV = MagmaColumnwise (LDV,M) if STOREV = MagmaRowwise and SIDE = MagmaLeft (LDV,N) if STOREV = MagmaRowwise and SIDE = MagmaRight The matrix V. See further details. |
[in] | ldv | INTEGER The leading dimension of the array V. If STOREV = MagmaColumnwise and SIDE = MagmaLeft, LDV >= max(1,M); if STOREV = MagmaColumnwise and SIDE = MagmaRight, LDV >= max(1,N); if STOREV = MagmaRowwise, LDV >= K. |
[in] | dT | DOUBLE_PRECISION array on the GPU, dimension (LDT,K) The triangular k by k matrix T in the representation of the block reflector. |
[in] | ldt | INTEGER The leading dimension of the array T. LDT >= K. |
[in,out] | dC | DOUBLE_PRECISION array on the GPU, dimension (LDC,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] | ldc | INTEGER The leading dimension of the array C. LDA >= 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); |
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 | ( | 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, | ||
const double * | dV, | ||
magma_int_t | ldv, | ||
const double * | dT, | ||
magma_int_t | ldt, | ||
double * | dC, | ||
magma_int_t | ldc, | ||
double * | dwork, | ||
magma_int_t | ldwork, | ||
double * | dworkvt, | ||
magma_int_t | ldworkvt | ||
) |
DLARFB applies a real block reflector H or its transpose 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 (LDV,K) if STOREV = MagmaColumnwise (LDV,M) if STOREV = MagmaRowwise and SIDE = MagmaLeft (LDV,N) if STOREV = MagmaRowwise and SIDE = MagmaRight The matrix V. See further details. |
[in] | ldv | INTEGER The leading dimension of the array V. If STOREV = MagmaColumnwise and SIDE = MagmaLeft, LDV >= max(1,M); if STOREV = MagmaColumnwise and SIDE = MagmaRight, LDV >= max(1,N); if STOREV = MagmaRowwise, LDV >= K. |
[in] | dT | DOUBLE_PRECISION array on the GPU, dimension (LDT,K) The triangular k by k matrix T in the representation of the block reflector. |
[in] | ldt | INTEGER The leading dimension of the array T. LDT >= K. |
[in,out] | dC | DOUBLE_PRECISION array on the GPU, dimension (LDC,N) On entry, the m by n matrix C. On exit, C is overwritten by H*C, or H'*C, or C*H, or C*H'. |
[in] | ldc | INTEGER The leading dimension of the array C. LDA >= 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)); |
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 )