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MAGMA
2.0.0
Matrix Algebra for GPU and Multicore Architectures
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Functions | |
magma_int_t | magma_dgelqf (magma_int_t m, magma_int_t n, double *A, magma_int_t lda, double *tau, double *work, magma_int_t lwork, magma_int_t *info) |
DGELQF computes an LQ factorization of a DOUBLE PRECISION M-by-N matrix A: A = L * Q. More... | |
magma_int_t | magma_dgelqf_gpu (magma_int_t m, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, double *tau, double *work, magma_int_t lwork, magma_int_t *info) |
DGELQF computes an LQ factorization of a DOUBLE PRECISION M-by-N matrix dA: dA = L * Q. More... | |
magma_int_t | magma_dorglq (magma_int_t m, magma_int_t n, magma_int_t k, double *A, magma_int_t lda, double *tau, double *work, magma_int_t lwork, magma_int_t *info) |
Purpose:DORGLQ generates an M-by-N real matrix Q with orthonormal rows, which is defined as the first M rows of a product of K elementary reflectors of order N More... | |
magma_int_t | magma_dormlq (magma_side_t side, magma_trans_t trans, magma_int_t m, magma_int_t n, magma_int_t k, double *A, magma_int_t lda, double *tau, double *C, magma_int_t ldc, double *work, magma_int_t lwork, magma_int_t *info) |
DORMLQ overwrites the general real M-by-N matrix C with. More... | |
magma_int_t magma_dgelqf | ( | magma_int_t | m, |
magma_int_t | n, | ||
double * | A, | ||
magma_int_t | lda, | ||
double * | tau, | ||
double * | work, | ||
magma_int_t | lwork, | ||
magma_int_t * | info | ||
) |
DGELQF computes an LQ factorization of a DOUBLE PRECISION M-by-N matrix A: A = L * Q.
[in] | m | INTEGER The number of rows of the matrix A. M >= 0. |
[in] | n | INTEGER The number of columns of the matrix A. N >= 0. |
[in,out] | A | DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details). Higher performance is achieved if A is in pinned memory, e.g. allocated using magma_malloc_pinned. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,M). |
[out] | tau | DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | work | (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. |
[in] | lwork | INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued. TODO: work is currently unused. dgeqrf2 allocates its own work of (m + n)*nb. |
[out] | info | INTEGER
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The matrix Q is represented as a product of elementary reflectors
Q = H(k) . . . H(2) H(1), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), and tau in TAU(i).
magma_int_t magma_dgelqf_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaDouble_ptr | dA, | ||
magma_int_t | ldda, | ||
double * | tau, | ||
double * | work, | ||
magma_int_t | lwork, | ||
magma_int_t * | info | ||
) |
DGELQF computes an LQ factorization of a DOUBLE PRECISION M-by-N matrix dA: dA = L * Q.
[in] | m | INTEGER The number of rows of the matrix A. M >= 0. |
[in] | n | INTEGER The number of columns of the matrix A. N >= 0. |
[in,out] | dA | DOUBLE PRECISION array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix dA. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details). |
[in] | ldda | INTEGER The leading dimension of the array dA. LDDA >= max(1,M). |
[out] | tau | DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | work | (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. Higher performance is achieved if WORK is in pinned memory, e.g. allocated using magma_malloc_pinned. |
[in] | lwork | INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued. |
[out] | info | INTEGER
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The matrix Q is represented as a product of elementary reflectors
Q = H(k) . . . H(2) H(1), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), and tau in TAU(i).
magma_int_t magma_dorglq | ( | magma_int_t | m, |
magma_int_t | n, | ||
magma_int_t | k, | ||
double * | A, | ||
magma_int_t | lda, | ||
double * | tau, | ||
double * | work, | ||
magma_int_t | lwork, | ||
magma_int_t * | info | ||
) |
Q = H(k)**H . . . H(2)**H H(1)**H
as returned by DGELQF.
[in] | m | INTEGER The number of rows of the matrix Q. M >= 0. |
[in] | n | INTEGER The number of columns of the matrix Q. N >= M. |
[in] | k | INTEGER The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0. |
[in,out] | A | DOUBLE PRECISION array, dimension (LDA,N) On entry, the i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGELQF in the first k rows of its array argument A. On exit, the M-by-N matrix Q. |
[in] | lda | INTEGER The first dimension of the array A. LDA >= max(1,M). |
[in] | tau | DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGELQF. |
[out] | work | DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
[in] | lwork | INTEGER The dimension of the array WORK. LWORK >= NB*NB, where NB is the optimal blocksize. |
If LWORK = -1, a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[out] | info | INTEGER
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magma_int_t magma_dormlq | ( | magma_side_t | side, |
magma_trans_t | trans, | ||
magma_int_t | m, | ||
magma_int_t | n, | ||
magma_int_t | k, | ||
double * | A, | ||
magma_int_t | lda, | ||
double * | tau, | ||
double * | C, | ||
magma_int_t | ldc, | ||
double * | work, | ||
magma_int_t | lwork, | ||
magma_int_t * | info | ||
) |
DORMLQ overwrites the general real M-by-N matrix C with.
SIDE = MagmaLeft SIDE = MagmaRight TRANS = MagmaNoTrans: Q * C C * Q TRANS = MagmaTrans: Q**H * C C * Q**H
where Q is a realorthogonal matrix defined as the product of k elementary reflectors
Q = H(k)**H . . . H(2)**H H(1)**H
as returned by DGELQF. Q is of order M if SIDE = MagmaLeft and of order N if SIDE = MagmaRight.
[in] | side | magma_side_t
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[in] | trans | magma_trans_t
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[in] | m | INTEGER The number of rows of the matrix C. M >= 0. |
[in] | n | INTEGER The number of columns of the matrix C. N >= 0. |
[in] | k | INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = MagmaLeft, M >= K >= 0; if SIDE = MagmaRight, N >= K >= 0. |
[in] | A | DOUBLE PRECISION array, dimension (LDA,M) if SIDE = MagmaLeft, (LDA,N) if SIDE = MagmaRight. The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGELQF in the first k rows of its array argument A. A is modified by the routine but restored on exit. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,K). |
[in] | tau | DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGELQF. |
[in,out] | C | DOUBLE PRECISION array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. |
[in] | ldc | INTEGER The leading dimension of the array C. LDC >= max(1,M). |
[out] | work | (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. |
[in] | lwork | INTEGER The dimension of the array WORK. If SIDE = MagmaLeft, LWORK >= max(1,N); if SIDE = MagmaRight, LWORK >= max(1,M). For optimum performance if SIDE = MagmaLeft, LWORK >= N*NB; if SIDE = MagmaRight, LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. |
[out] | info | INTEGER
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