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MAGMA
2.0.0
Matrix Algebra for GPU and Multicore Architectures
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Functions | |
magma_int_t | magma_cgegqr_gpu (magma_int_t ikind, magma_int_t m, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex_ptr dwork, magmaFloatComplex *work, magma_int_t *info) |
CGEGQR orthogonalizes the N vectors given by a complex M-by-N matrix A: More... | |
magma_int_t | magma_cgeqrf (magma_int_t m, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *work, magma_int_t lwork, magma_int_t *info) |
CGEQRF computes a QR factorization of a COMPLEX M-by-N matrix A: A = Q * R. More... | |
magma_int_t | magma_cgeqrf2_gpu (magma_int_t m, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex *tau, magma_int_t *info) |
CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R. More... | |
magma_int_t | magma_cgeqrf3_gpu (magma_int_t m, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex *tau, magmaFloatComplex_ptr dT, magma_int_t *info) |
CGEQRF3 computes a QR factorization of a complex M-by-N matrix A: A = Q * R. More... | |
magma_int_t | magma_cgeqrf_batched (magma_int_t m, magma_int_t n, magmaFloatComplex **dA_array, magma_int_t ldda, magmaFloatComplex **dtau_array, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue) |
CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R. More... | |
magma_int_t | magma_cgeqrf_expert_batched (magma_int_t m, magma_int_t n, magmaFloatComplex **dA_array, magma_int_t ldda, magmaFloatComplex **dR_array, magma_int_t lddr, magmaFloatComplex **dT_array, magma_int_t lddt, magmaFloatComplex **dtau_array, magma_int_t provide_RT, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue) |
CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R. More... | |
magma_int_t | magma_cgeqrf_gpu (magma_int_t m, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex *tau, magmaFloatComplex_ptr dT, magma_int_t *info) |
CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R. More... | |
magma_int_t | magma_cgeqrf_m (magma_int_t ngpu, magma_int_t m, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *work, magma_int_t lwork, magma_int_t *info) |
CGEQRF computes a QR factorization of a COMPLEX M-by-N matrix A: A = Q * R using multiple GPUs. More... | |
magma_int_t | magma_cgeqrf2_mgpu (magma_int_t ngpu, magma_int_t m, magma_int_t n, magmaFloatComplex_ptr dlA[], magma_int_t ldda, magmaFloatComplex *tau, magma_int_t *info) |
CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R. More... | |
magma_int_t | magma_cgeqrf_ooc (magma_int_t m, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *work, magma_int_t lwork, magma_int_t *info) |
CGEQRF_OOC computes a QR factorization of a COMPLEX M-by-N matrix A: A = Q * R. More... | |
magma_int_t | magma_cungqr (magma_int_t m, magma_int_t n, magma_int_t k, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex_ptr dT, magma_int_t nb, magma_int_t *info) |
CUNGQR generates an M-by-N COMPLEX matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M. More... | |
magma_int_t | magma_cungqr2 (magma_int_t m, magma_int_t n, magma_int_t k, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magma_int_t *info) |
CUNGQR generates an M-by-N COMPLEX matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M. More... | |
magma_int_t | magma_cungqr_gpu (magma_int_t m, magma_int_t n, magma_int_t k, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex *tau, magmaFloatComplex_ptr dT, magma_int_t nb, magma_int_t *info) |
CUNGQR generates an M-by-N COMPLEX matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M. More... | |
magma_int_t | magma_cungqr_m (magma_int_t m, magma_int_t n, magma_int_t k, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *T, magma_int_t nb, magma_int_t *info) |
CUNGQR generates an M-by-N COMPLEX matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M. More... | |
magma_int_t | magma_cunmqr (magma_side_t side, magma_trans_t trans, magma_int_t m, magma_int_t n, magma_int_t k, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *C, magma_int_t ldc, magmaFloatComplex *work, magma_int_t lwork, magma_int_t *info) |
CUNMQR overwrites the general complex M-by-N matrix C with. More... | |
magma_int_t | magma_cunmqr2_gpu (magma_side_t side, magma_trans_t trans, magma_int_t m, magma_int_t n, magma_int_t k, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex *tau, magmaFloatComplex_ptr dC, magma_int_t lddc, const magmaFloatComplex *wA, magma_int_t ldwa, magma_int_t *info) |
CUNMQR overwrites the general complex M-by-N matrix C with. More... | |
magma_int_t | magma_cunmqr_gpu (magma_side_t side, magma_trans_t trans, magma_int_t m, magma_int_t n, magma_int_t k, magmaFloatComplex_const_ptr dA, magma_int_t ldda, magmaFloatComplex const *tau, magmaFloatComplex_ptr dC, magma_int_t lddc, magmaFloatComplex *hwork, magma_int_t lwork, magmaFloatComplex_ptr dT, magma_int_t nb, magma_int_t *info) |
CUNMQR_GPU overwrites the general complex M-by-N matrix C with. More... | |
magma_int_t | magma_cunmqr_m (magma_int_t ngpu, magma_side_t side, magma_trans_t trans, magma_int_t m, magma_int_t n, magma_int_t k, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *C, magma_int_t ldc, magmaFloatComplex *work, magma_int_t lwork, magma_int_t *info) |
CUNMQR overwrites the general complex M-by-N matrix C with. More... | |
magma_int_t magma_cgegqr_gpu | ( | magma_int_t | ikind, |
magma_int_t | m, | ||
magma_int_t | n, | ||
magmaFloatComplex_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaFloatComplex_ptr | dwork, | ||
magmaFloatComplex * | work, | ||
magma_int_t * | info | ||
) |
CGEGQR orthogonalizes the N vectors given by a complex M-by-N matrix A:
A = Q * R.
On exit, if successful, the orthogonal vectors Q overwrite A and R is given in work (on the CPU memory). The routine is designed for tall-and-skinny matrices: M >> N, N <= 128.
This version uses normal equations and SVD in an iterative process that makes the computation numerically accurate.
[in] | ikind | INTEGER Several versions are implemented indiceted by the ikind value: 1: This version uses normal equations and SVD in an iterative process that makes the computation numerically accurate. 2: This version uses a standard LAPACK-based orthogonalization through MAGMA's QR panel factorization (magma_cgeqr2x3_gpu) and magma_cungqr 3: Modified Gram-Schmidt (MGS)
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[in] | m | INTEGER The number of rows of the matrix A. m >= n >= 0. |
[in] | n | INTEGER The number of columns of the matrix A. 128 >= n >= 0. |
[in,out] | dA | COMPLEX array on the GPU, dimension (ldda,n) On entry, the m-by-n matrix A. On exit, the m-by-n matrix Q with orthogonal columns. |
[in] | ldda | INTEGER The leading dimension of the array dA. LDDA >= max(1,m). To benefit from coalescent memory accesses LDDA must be divisible by 16. |
dwork | (GPU workspace) COMPLEX array, dimension: n^2 for ikind = 1 3 n^2 + min(m, n) + 2 for ikind = 2 0 (not used) for ikind = 3 n^2 for ikind = 4 | |
[out] | work | (CPU workspace) COMPLEX array, dimension 3 n^2. On exit, work(1:n^2) holds the rectangular matrix R. Preferably, for higher performance, work should be in pinned memory. |
[out] | info | INTEGER
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magma_int_t magma_cgeqrf | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
magmaFloatComplex * | tau, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
magma_int_t * | info | ||
) |
CGEQRF computes a QR factorization of a COMPLEX M-by-N matrix A: A = Q * R.
This version does not require work space on the GPU passed as input. GPU memory is allocated in the routine.
This uses 2 queues to overlap communication and computation.
[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 | COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) 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 | COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | work | (workspace) COMPLEX 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( N*NB, 2*NB*NB ), where NB can be obtained through magma_get_cgeqrf_nb( M, N ). 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(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).
magma_int_t magma_cgeqrf2_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaFloatComplex_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaFloatComplex * | tau, | ||
magma_int_t * | info | ||
) |
CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.
This version has LAPACK-complaint arguments.
Other versions (magma_cgeqrf_gpu and magma_cgeqrf3_gpu) store the intermediate T matrices.
[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 | COMPLEX array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details). |
[in] | ldda | INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16. |
[out] | tau | COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | info | INTEGER
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The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v^H
where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).
magma_int_t magma_cgeqrf2_mgpu | ( | magma_int_t | ngpu, |
magma_int_t | m, | ||
magma_int_t | n, | ||
magmaFloatComplex_ptr | dlA[], | ||
magma_int_t | ldda, | ||
magmaFloatComplex * | tau, | ||
magma_int_t * | info | ||
) |
CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.
This is a GPU interface of the routine.
[in] | ngpu | INTEGER Number of GPUs to use. ngpu > 0. |
[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] | dlA | COMPLEX array of pointers on the GPU, dimension (ngpu). On entry, the M-by-N matrix A distributed over GPUs (d_lA[d] points to the local matrix on d-th GPU). It uses 1D block column cyclic format with the block size of nb, and each local matrix is stored by column. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details). |
[in] | ldda | INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16. |
[out] | tau | COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | info | INTEGER
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The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).
magma_int_t magma_cgeqrf3_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaFloatComplex_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaFloatComplex * | tau, | ||
magmaFloatComplex_ptr | dT, | ||
magma_int_t * | info | ||
) |
CGEQRF3 computes a QR factorization of a complex M-by-N matrix A: A = Q * R.
This version stores the triangular dT matrices used in the block QR factorization so that they can be applied directly (i.e., without being recomputed) later. As a result, the application of Q is much faster. Also, the upper triangular matrices for V have 0s in them. The corresponding parts of the upper triangular R are stored separately in dT.
[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 | COMPLEX array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details). |
[in] | ldda | INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16. |
[out] | tau | COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | dT | (workspace) COMPLEX array on the GPU, dimension (2*MIN(M, N) + ceil(N/32)*32 )*NB, where NB can be obtained through magma_get_cgeqrf_nb( M, N ). It starts with a MIN(M,N)*NB block that stores the triangular T matrices, followed by a MIN(M,N)*NB block that stores the diagonal blocks of the R matrix. The rest of the array is used as workspace. |
[out] | info | INTEGER
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The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v^H
where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).
magma_int_t magma_cgeqrf_batched | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaFloatComplex ** | dA_array, | ||
magma_int_t | ldda, | ||
magmaFloatComplex ** | dtau_array, | ||
magma_int_t * | info_array, | ||
magma_int_t | batchCount, | ||
magma_queue_t | queue | ||
) |
CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.
[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_array | Array of pointers, dimension (batchCount). Each is a COMPLEX array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details). |
[in] | ldda | INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16. |
[out] | dtau_array | Array of pointers, dimension (batchCount). Each is a COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | info_array | Array of INTEGERs, dimension (batchCount), for corresponding matrices.
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[in] | batchCount | INTEGER The number of matrices to operate on. |
[in] | queue | magma_queue_t Queue to execute in. |
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).
magma_int_t magma_cgeqrf_expert_batched | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaFloatComplex ** | dA_array, | ||
magma_int_t | ldda, | ||
magmaFloatComplex ** | dR_array, | ||
magma_int_t | lddr, | ||
magmaFloatComplex ** | dT_array, | ||
magma_int_t | lddt, | ||
magmaFloatComplex ** | dtau_array, | ||
magma_int_t | provide_RT, | ||
magma_int_t * | info_array, | ||
magma_int_t | batchCount, | ||
magma_queue_t | queue | ||
) |
CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.
[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_array | Array of pointers, dimension (batchCount). Each is a COMPLEX array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details). |
[in] | ldda | INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16. |
[in,out] | dR_array | Array of pointers, dimension (batchCount). Each is a COMPLEX array on the GPU, dimension (LDDR, N/NB) dR should be of size (LDDR, N) when provide_RT > 0 and of size (LDDT, NB) otherwise. NB is the local blocking size. On exit, the elements of R are stored in dR only when provide_RT > 0. |
[in] | lddr | INTEGER The leading dimension of the array dR. LDDR >= min(M,N) when provide_RT == 1 otherwise LDDR >= min(NB, min(M,N)). NB is the local blocking size. To benefit from coalescent memory accesses LDDR must be divisible by 16. |
[in,out] | dT_array | Array of pointers, dimension (batchCount). Each is a COMPLEX array on the GPU, dimension (LDDT, N/NB) dT should be of size (LDDT, N) when provide_RT > 0 and of size (LDDT, NB) otherwise. NB is the local blocking size. On exit, the elements of T are stored in dT only when provide_RT > 0. |
[in] | lddt | INTEGER The leading dimension of the array dT. LDDT >= min(NB,min(M,N)). NB is the local blocking size. To benefit from coalescent memory accesses LDDR must be divisible by 16. |
[out] | dtau_array | Array of pointers, dimension (batchCount). Each is a COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[in] | provide_RT | INTEGER provide_RT = 0 no R and no T in output. dR and dT are used as local workspace to store the R and T of each step. provide_RT = 1 the whole R of size (min(M,N), N) and the nbxnb block of T are provided in output. provide_RT = 2 the nbxnb diag block of R and of T are provided in output. |
[out] | info_array | Array of INTEGERs, dimension (batchCount), for corresponding matrices.
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[in] | batchCount | INTEGER The number of matrices to operate on. |
[in] | queue | magma_queue_t Queue to execute in. |
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).
magma_int_t magma_cgeqrf_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaFloatComplex_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaFloatComplex * | tau, | ||
magmaFloatComplex_ptr | dT, | ||
magma_int_t * | info | ||
) |
CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.
This version stores the triangular dT matrices used in the block QR factorization so that they can be applied directly (i.e., without being recomputed) later. As a result, the application of Q is much faster. Also, the upper triangular matrices for V have 0s in them. The corresponding parts of the upper triangular R are inverted and stored separately in dT.
[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 | COMPLEX array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details). |
[in] | ldda | INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16. |
[out] | tau | COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | dT | (workspace) COMPLEX array on the GPU, dimension (2*MIN(M, N) + ceil(N/32)*32 )*NB, where NB can be obtained through magma_get_cgeqrf_nb( M, N ). It starts with a MIN(M,N)*NB block that stores the triangular T matrices, followed by a MIN(M,N)*NB block that stores inverses of the diagonal blocks of the R matrix. The rest of the array is used as workspace. |
[out] | info | INTEGER
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The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v^H
where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).
magma_int_t magma_cgeqrf_m | ( | magma_int_t | ngpu, |
magma_int_t | m, | ||
magma_int_t | n, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
magmaFloatComplex * | tau, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
magma_int_t * | info | ||
) |
CGEQRF computes a QR factorization of a COMPLEX M-by-N matrix A: A = Q * R using multiple GPUs.
This version does not require work space on the GPU passed as input. GPU memory is allocated in the routine.
[in] | ngpu | INTEGER Number of GPUs to use. ngpu > 0. |
[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 | COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) 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 | COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | work | (workspace) COMPLEX 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 >= N*NB, where NB can be obtained through magma_get_cgeqrf_nb( M, N ). 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
|
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).
magma_int_t magma_cgeqrf_ooc | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
magmaFloatComplex * | tau, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
magma_int_t * | info | ||
) |
CGEQRF_OOC computes a QR factorization of a COMPLEX M-by-N matrix A: A = Q * R.
This version does not require work space on the GPU passed as input. GPU memory is allocated in the routine. This is an out-of-core (ooc) version that is similar to magma_cgeqrf but the difference is that this version can use a GPU even if the matrix does not fit into the GPU memory at once.
[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 | COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) 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 | COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | work | (workspace) COMPLEX 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 >= N*NB, where NB can be obtained through magma_get_cgeqrf_nb( M, N ). 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
|
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).
magma_int_t magma_cungqr | ( | magma_int_t | m, |
magma_int_t | n, | ||
magma_int_t | k, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
magmaFloatComplex * | tau, | ||
magmaFloatComplex_ptr | dT, | ||
magma_int_t | nb, | ||
magma_int_t * | info | ||
) |
CUNGQR generates an M-by-N COMPLEX matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M.
Q = H(1) H(2) . . . H(k)
as returned by CGEQRF.
[in] | m | INTEGER The number of rows of the matrix Q. M >= 0. |
[in] | n | INTEGER The number of columns of the matrix Q. M >= N >= 0. |
[in] | k | INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. |
[in,out] | A | COMPLEX array A, dimension (LDDA,N). On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGEQRF_GPU in the first k columns 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 | COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQRF_GPU. |
[in] | dT | COMPLEX array on the GPU device. DT contains the T matrices used in blocking the elementary reflectors H(i), e.g., this can be the 6th argument of magma_cgeqrf_gpu. |
[in] | nb | INTEGER This is the block size used in CGEQRF_GPU, and correspondingly the size of the T matrices, used in the factorization, and stored in DT. |
[out] | info | INTEGER
|
magma_int_t magma_cungqr2 | ( | magma_int_t | m, |
magma_int_t | n, | ||
magma_int_t | k, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
magmaFloatComplex * | tau, | ||
magma_int_t * | info | ||
) |
CUNGQR generates an M-by-N COMPLEX matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M.
Q = H(1) H(2) . . . H(k)
as returned by CGEQRF.
This version recomputes the T matrices on the CPU and sends them to the GPU.
[in] | m | INTEGER The number of rows of the matrix Q. M >= 0. |
[in] | n | INTEGER The number of columns of the matrix Q. M >= N >= 0. |
[in] | k | INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. |
[in,out] | A | COMPLEX array A, dimension (LDDA,N). On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGEQRF_GPU in the first k columns 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 | COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQRF_GPU. |
[out] | info | INTEGER
|
magma_int_t magma_cungqr_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magma_int_t | k, | ||
magmaFloatComplex_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaFloatComplex * | tau, | ||
magmaFloatComplex_ptr | dT, | ||
magma_int_t | nb, | ||
magma_int_t * | info | ||
) |
CUNGQR generates an M-by-N COMPLEX matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M.
Q = H(1) H(2) . . . H(k)
as returned by CGEQRF_GPU.
[in] | m | INTEGER The number of rows of the matrix Q. M >= 0. |
[in] | n | INTEGER The number of columns of the matrix Q. M >= N >= 0. |
[in] | k | INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. |
[in,out] | dA | COMPLEX array A on the GPU, dimension (LDDA,N). On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGEQRF_GPU in the first k columns of its array argument A. On exit, the M-by-N matrix Q. |
[in] | ldda | INTEGER The first dimension of the array A. LDDA >= max(1,M). |
[in] | tau | COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQRF_GPU. |
[in] | dT | (workspace) COMPLEX work space array on the GPU, dimension (2*MIN(M, N) + ceil(N/32)*32 )*NB. This must be the 6th argument of magma_cgeqrf_gpu [ note that if N here is bigger than N in magma_cgeqrf_gpu, the workspace requirement DT in magma_cgeqrf_gpu must be as specified in this routine ]. |
[in] | nb | INTEGER This is the block size used in CGEQRF_GPU, and correspondingly the size of the T matrices, used in the factorization, and stored in DT. |
[out] | info | INTEGER
|
magma_int_t magma_cungqr_m | ( | magma_int_t | m, |
magma_int_t | n, | ||
magma_int_t | k, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
magmaFloatComplex * | tau, | ||
magmaFloatComplex * | T, | ||
magma_int_t | nb, | ||
magma_int_t * | info | ||
) |
CUNGQR generates an M-by-N COMPLEX matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M.
Q = H(1) H(2) . . . H(k)
as returned by CGEQRF.
[in] | m | INTEGER The number of rows of the matrix Q. M >= 0. |
[in] | n | INTEGER The number of columns of the matrix Q. M >= N >= 0. |
[in] | k | INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. |
[in,out] | A | COMPLEX array A, dimension (LDDA,N). On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGEQRF_GPU in the first k columns 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 | COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQRF_GPU. |
[in] | T | COMPLEX array, dimension (NB, min(M,N)). T contains the T matrices used in blocking the elementary reflectors H(i), e.g., this can be the 6th argument of magma_cgeqrf_gpu (except stored on the CPU, not the GPU). |
[in] | nb | INTEGER This is the block size used in CGEQRF_GPU, and correspondingly the size of the T matrices, used in the factorization, and stored in T. |
[out] | info | INTEGER
|
magma_int_t magma_cunmqr | ( | magma_side_t | side, |
magma_trans_t | trans, | ||
magma_int_t | m, | ||
magma_int_t | n, | ||
magma_int_t | k, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
magmaFloatComplex * | tau, | ||
magmaFloatComplex * | C, | ||
magma_int_t | ldc, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
magma_int_t * | info | ||
) |
CUNMQR overwrites the general complex M-by-N matrix C with.
SIDE = MagmaLeft SIDE = MagmaRight TRANS = MagmaNoTrans: Q * C C * Q TRANS = Magma_ConjTrans: Q**H * C C * Q**H
where Q is a complex unitary matrix defined as the product of k elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by CGEQRF. 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 | COMPLEX 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 CGEQRF in the first 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 | COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQRF. |
[in,out] | C | COMPLEX 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) COMPLEX 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_cunmqr2_gpu | ( | magma_side_t | side, |
magma_trans_t | trans, | ||
magma_int_t | m, | ||
magma_int_t | n, | ||
magma_int_t | k, | ||
magmaFloatComplex_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaFloatComplex * | tau, | ||
magmaFloatComplex_ptr | dC, | ||
magma_int_t | lddc, | ||
const magmaFloatComplex * | wA, | ||
magma_int_t | ldwa, | ||
magma_int_t * | info | ||
) |
CUNMQR overwrites the general complex M-by-N matrix C with.
SIDE = MagmaLeft SIDE = MagmaRight TRANS = MagmaNoTrans: Q * C C * Q TRANS = Magma_ConjTrans: Q**H * C C * Q**H
where Q is a complex unitary matrix defined as the product of k elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by CGEQRF. 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,out] | dA | COMPLEX array on the GPU, dimension (LDDA,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGEQRF in the first k columns of its array argument dA. The diagonal and the upper part are destroyed, the reflectors are not modified. |
[in] | ldda | INTEGER The leading dimension of the array dA. If SIDE = MagmaLeft, LDDA >= max(1,M); if SIDE = MagmaRight, LDDA >= max(1,N). |
[in] | tau | COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQRF. |
[in,out] | dC | COMPLEX array on the GPU, 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 dC. LDDC >= max(1,M). |
[in] | wA | COMPLEX array, dimension (LDWA,M) if SIDE = MagmaLeft (LDWA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by CHETRD_GPU. (A copy of the upper or lower part of dA, on the host.) |
[in] | ldwa | INTEGER The leading dimension of the array wA. If SIDE = MagmaLeft, LDWA >= max(1,M); if SIDE = MagmaRight, LDWA >= max(1,N). |
[out] | info | INTEGER
|
magma_int_t magma_cunmqr_gpu | ( | magma_side_t | side, |
magma_trans_t | trans, | ||
magma_int_t | m, | ||
magma_int_t | n, | ||
magma_int_t | k, | ||
magmaFloatComplex_const_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaFloatComplex const * | tau, | ||
magmaFloatComplex_ptr | dC, | ||
magma_int_t | lddc, | ||
magmaFloatComplex * | hwork, | ||
magma_int_t | lwork, | ||
magmaFloatComplex_ptr | dT, | ||
magma_int_t | nb, | ||
magma_int_t * | info | ||
) |
CUNMQR_GPU overwrites the general complex M-by-N matrix C with.
SIDE = MagmaLeft SIDE = MagmaRight TRANS = MagmaNoTrans: Q * C C * Q TRANS = Magma_ConjTrans: Q**H * C C * Q**H
where Q is a complex unitary matrix defined as the product of k elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by CGEQRF. 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 | COMPLEX array on the GPU, dimension (LDDA,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGEQRF in the first k columns of its array argument dA. dA is modified by the routine but restored on exit. |
[in] | ldda | INTEGER The leading dimension of the array dA. If SIDE = MagmaLeft, LDDA >= max(1,M); if SIDE = MagmaRight, LDDA >= max(1,N). |
[in] | tau | COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQRF. |
[in,out] | dC | COMPLEX array on the GPU, 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 DC. LDDC >= max(1,M). |
[out] | hwork | (workspace) COMPLEX array, dimension (MAX(1,LWORK)) Currently, cgetrs_gpu assumes that on exit, hwork contains the last block of A and C. This will change and should not be relied on! |
[in] | lwork | INTEGER The dimension of the array HWORK. LWORK >= (M-K+NB)*(N+NB) + N*NB if SIDE = MagmaLeft, and LWORK >= (N-K+NB)*(M+NB) + M*NB if SIDE = MagmaRight, where NB is the given blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the HWORK array, returns this value as the first entry of the HWORK array, and no error message related to LWORK is issued by XERBLA. |
[in,out] | dT | COMPLEX array on the GPU that is the output (the 9th argument) of magma_cgeqrf_gpu. Part used as workspace. |
[in] | nb | INTEGER This is the blocking size that was used in pre-computing DT, e.g., the blocking size used in magma_cgeqrf_gpu. |
[out] | info | INTEGER
|
magma_int_t magma_cunmqr_m | ( | magma_int_t | ngpu, |
magma_side_t | side, | ||
magma_trans_t | trans, | ||
magma_int_t | m, | ||
magma_int_t | n, | ||
magma_int_t | k, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
magmaFloatComplex * | tau, | ||
magmaFloatComplex * | C, | ||
magma_int_t | ldc, | ||
magmaFloatComplex * | work, | ||
magma_int_t | lwork, | ||
magma_int_t * | info | ||
) |
CUNMQR overwrites the general complex M-by-N matrix C with.
SIDE = MagmaLeft SIDE = MagmaRight TRANS = MagmaNoTrans: Q * C C * Q TRANS = Magma_ConjTrans: Q**H * C C * Q**H
where Q is a complex unitary matrix defined as the product of k elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by CGEQRF. Q is of order M if SIDE = MagmaLeft and of order N if SIDE = MagmaRight.
[in] | ngpu | INTEGER Number of GPUs to use. ngpu > 0. |
[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 | COMPLEX 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 CGEQRF in the first k columns of its array argument A. |
[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 | COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQRF. |
[in,out] | C | COMPLEX 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) COMPLEX 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 LWORK >= N*NB if SIDE = MagmaLeft, and LWORK >= M*NB if SIDE = MagmaRight, 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
|