Functions | |
magma_int_t | magma_dgeqlf (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) |
DGEQLF computes a QL factorization of a DOUBLE_PRECISION M-by-N matrix A: A = Q * L. | |
magma_int_t | magma_dormql (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) |
DORMQL overwrites the general real M-by-N matrix C with. | |
magma_int_t | magma_dormql2_gpu (magma_side_t side, magma_trans_t trans, magma_int_t m, magma_int_t n, magma_int_t k, magmaDouble_ptr dA, magma_int_t ldda, double *tau, magmaDouble_ptr dC, magma_int_t lddc, double *wA, magma_int_t ldwa, magma_int_t *info) |
DORMQL overwrites the general real M-by-N matrix C with. |
magma_int_t magma_dgeqlf | ( | 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 | |||
) |
DGEQLF computes a QL factorization of a DOUBLE_PRECISION M-by-N matrix A: A = Q * L.
[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, if m >= n, the lower triangle of the subarray A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L; if m <= n, the elements on and below the (n-m)-th superdiagonal contain the M-by-N lower trapezoidal matrix L; the remaining elements, 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. 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,N,2*NB^2). For optimum performance LWORK >= max(N*NB, 2*NB^2) where NB can be obtained through magma_get_dgeqlf_nb(M). 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
|
Further Details --------------- 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i).
magma_int_t magma_dormql | ( | 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 | |||
) |
DORMQL 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 real unitary matrix defined as the product of k elementary reflectors
Q = H(k) . . . H(2) H(1)
as returned by DGEQLF. Q is of order M if SIDE = MagmaLeft and of order N if SIDE = MagmaRight.
[in] | side | magma_side_t
|
[in] | trans | magma_trans_t
|
[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,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGEQLF in the last k columns 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. If SIDE = MagmaLeft, LDA >= max(1,M); if SIDE = MagmaRight, LDA >= max(1,N). |
[in] | tau | DOUBLE_PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEQLF. |
[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
|
magma_int_t magma_dormql2_gpu | ( | magma_side_t | side, | |
magma_trans_t | trans, | |||
magma_int_t | m, | |||
magma_int_t | n, | |||
magma_int_t | k, | |||
magmaDouble_ptr | dA, | |||
magma_int_t | ldda, | |||
double * | tau, | |||
magmaDouble_ptr | dC, | |||
magma_int_t | lddc, | |||
double * | wA, | |||
magma_int_t | ldwa, | |||
magma_int_t * | info | |||
) |
DORMQL 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 real unitary matrix defined as the product of k elementary reflectors
Q = H(k) . . . H(2) H(1)
as returned by DGEQLF. Q is of order M if SIDE = MagmaLeft and of order N if SIDE = MagmaRight.
[in] | side | magma_side_t
|
[in] | trans | magma_trans_t
|
[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] | dA | DOUBLE_PRECISION array, dimension (LDA,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGEQLF in the last k columns of its array argument A. The diagonal and the lower part are destroyed, the reflectors are not modified. |
[in] | ldda | INTEGER The leading dimension of the array DA. LDDA >= max(1,M) if SIDE = MagmaLeft; LDDA >= max(1,N) if SIDE = MagmaRight. |
[in] | tau | DOUBLE_PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEQLF. |
[in,out] | dC | DOUBLE_PRECISION array, dimension (LDDC,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] | lddc | INTEGER The leading dimension of the array C. LDDC >= max(1,M). |
[in] | wA | (workspace) DOUBLE_PRECISION array, dimension (LDWA,M) if SIDE = MagmaLeft (LDWA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by DSYTRD_GPU. |
[in] | ldwa | INTEGER The leading dimension of the array wA. LDWA >= max(1,M) if SIDE = MagmaLeft; LDWA >= max(1,N) if SIDE = MagmaRight. |
[out] | info | INTEGER
|