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MAGMA
1.7.0
Matrix Algebra for GPU and Multicore Architectures
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Functions | |
magma_int_t | magma_sgeqr2x2_gpu (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dtau, magmaFloat_ptr dT, magmaFloat_ptr ddA, magmaFloat_ptr dwork, magma_int_t *info) |
SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More... | |
magma_int_t | magma_sgeqr2x3_gpu (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dtau, magmaFloat_ptr dT, magmaFloat_ptr ddA, magmaFloat_ptr dwork, magma_int_t *info) |
SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More... | |
magma_int_t | magma_sgeqr2x_gpu (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dtau, magmaFloat_ptr dT, magmaFloat_ptr ddA, magmaFloat_ptr dwork, magma_int_t *info) |
SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More... | |
magma_int_t | magma_sgeqr2_gpu (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dtau, magmaFloat_ptr dwork, magma_int_t *info) |
SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R using the non-blocking Householder QR. More... | |
magma_int_t | magma_sgeqr2_batched (magma_int_t m, magma_int_t n, float **dA_array, magma_int_t ldda, float **dtau_array, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue) |
SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More... | |
void | sgeqrf_copy_upper_batched (magma_int_t n, magma_int_t nb, float **dV_array, magma_int_t lddv, float **dR_array, magma_int_t lddr, magma_int_t batchCount, magma_queue_t queue) |
These are internal routines that might have many assumption. More... | |
magma_int_t | magma_sgeqr2x4_gpu (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dtau, magmaFloat_ptr dT, magmaFloat_ptr ddA, magmaFloat_ptr dwork, magma_queue_t queue, magma_int_t *info) |
SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More... | |
magma_int_t magma_sgeqr2_batched | ( | magma_int_t | m, |
magma_int_t | n, | ||
float ** | dA_array, | ||
magma_int_t | ldda, | ||
float ** | dtau_array, | ||
magma_int_t * | info_array, | ||
magma_int_t | batchCount, | ||
magma_queue_t | queue | ||
) |
SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R.
This version implements the right-looking QR with non-blocking.
[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 REAL 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 REAL 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 real scalar, and v is a real 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_sgeqr2_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaFloat_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaFloat_ptr | dtau, | ||
magmaFloat_ptr | dwork, | ||
magma_int_t * | info | ||
) |
SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R using the non-blocking Householder QR.
[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 | REAL 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 unitary matrix Q as a product of elementary reflectors (see Further Details). |
[in] | ldda | INTEGER The leading dimension of the array A. LDA >= max(1,M). |
[out] | dtau | REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
dwork | (workspace) DOUBLE_PRECISION array, dimension (N) | |
[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 real scalar, and v is a real 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_sgeqr2x2_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaFloat_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaFloat_ptr | dtau, | ||
magmaFloat_ptr | dT, | ||
magmaFloat_ptr | ddA, | ||
magmaFloat_ptr | dwork, | ||
magma_int_t * | info | ||
) |
SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R.
This expert routine requires two more arguments than the standard sgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's sgeqr2 routine (see below).
The first is used to output the triangular n x n factor T of the block reflector used in the factorization. The second holds the diagonal nxn blocks of A, i.e., the diagonal submatrices of R. This routine implements the left looking QR.
[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 | REAL array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the unitary matrix Q as a product of elementary reflectors (see Further Details). 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 unitary matrix Q as a product of elementary reflectors (see Further Details). |
[in] | ldda | INTEGER The leading dimension of the array A. LDA >= max(1,M). |
[out] | dtau | REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | dT | REAL array, dimension N x N. Stores the triangular N x N factor T of the block reflector used in the factorization. The lower triangular part is 0. |
[out] | ddA | REAL array, dimension N x N. Stores the elements of the upper N x N diagonal block of A. LAPACK stores this array in A. There are 0s below the diagonal. |
dwork | (workspace) DOUBLE_PRECISION array, dimension (3 N) | |
[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 real scalar, and v is a real 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_sgeqr2x3_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaFloat_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaFloat_ptr | dtau, | ||
magmaFloat_ptr | dT, | ||
magmaFloat_ptr | ddA, | ||
magmaFloat_ptr | dwork, | ||
magma_int_t * | info | ||
) |
SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R.
This expert routine requires two more arguments than the standard sgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's sgeqr2 routine (see below).
The first is used to output the triangular n x n factor T of the block reflector used in the factorization. The second holds the diagonal nxn blocks of A, i.e., the diagonal submatrices of R. This routine implements the left looking QR.
This version adds internal blocking.
[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 | REAL array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the unitary matrix Q as a product of elementary reflectors (see Further Details). 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 unitary matrix Q as a product of elementary reflectors (see Further Details). |
[in] | ldda | INTEGER The leading dimension of the array A. LDA >= max(1,M). |
[out] | dtau | REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | dT | REAL array, dimension N x N. Stores the triangular N x N factor T of the block reflector used in the factorization. The lower triangular part is 0. |
[out] | ddA | REAL array, dimension N x N. Stores the elements of the upper N x N diagonal block of A. LAPACK stores this array in A. There are 0s below the diagonal. |
dwork | (workspace) DOUBLE_PRECISION array, dimension (3 N) | |
[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 real scalar, and v is a real 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_sgeqr2x4_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaFloat_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaFloat_ptr | dtau, | ||
magmaFloat_ptr | dT, | ||
magmaFloat_ptr | ddA, | ||
magmaFloat_ptr | dwork, | ||
magma_queue_t | queue, | ||
magma_int_t * | info | ||
) |
SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R.
This expert routine requires two more arguments than the standard sgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's sgeqr2 routine (see below).
The first is used to output the triangular n x n factor T of the block reflector used in the factorization. The second holds the diagonal nxn blocks of A, i.e., the diagonal submatrices of R. This routine implements the left looking QR.
This version adds internal blocking.
[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 | REAL array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the unitary matrix Q as a product of elementary reflectors (see Further Details). 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 unitary matrix Q as a product of elementary reflectors (see Further Details). |
[in] | ldda | INTEGER The leading dimension of the array A. LDA >= max(1,M). |
[out] | dtau | REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | dT | REAL array, dimension N x N. Stores the triangular N x N factor T of the block reflector used in the factorization. The lower triangular part is 0. |
[out] | ddA | REAL array, dimension N x N. Stores the elements of the upper N x N diagonal block of A. LAPACK stores this array in A. There are 0s below the diagonal. |
dwork | (workspace) DOUBLE_PRECISION array, dimension (3 N) | |
[out] | info | INTEGER
|
[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**H
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:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).
magma_int_t magma_sgeqr2x_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaFloat_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaFloat_ptr | dtau, | ||
magmaFloat_ptr | dT, | ||
magmaFloat_ptr | ddA, | ||
magmaFloat_ptr | dwork, | ||
magma_int_t * | info | ||
) |
SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R.
This expert routine requires two more arguments than the standard sgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's sgeqr2 routine (see below).
The first is used to output the triangular n x n factor T of the block reflector used in the factorization. The second holds the diagonal nxn blocks of A, i.e., the diagonal submatrices of R.
This version implements the right-looking QR. A hard-coded requirement for N is to be <= min(M, 128). For larger N one should use a blocking QR version.
[in] | m | INTEGER The number of rows of the matrix A. M >= 0. |
[in] | n | INTEGER The number of columns of the matrix A. 0 <= N <= min(M, 128). |
[in,out] | dA | REAL array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the unitary matrix Q as a product of elementary reflectors (see Further Details). 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 unitary matrix Q as a product of elementary reflectors (see Further Details). |
[in] | ldda | INTEGER The leading dimension of the array A. LDA >= max(1,M). |
[out] | dtau | REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | dT | REAL array, dimension N x N. Stores the triangular N x N factor T of the block reflector used in the factorization. The lower triangular part is 0. |
[out] | ddA | REAL array, dimension N x N. Stores the elements of the upper N x N diagonal block of A. LAPACK stores this array in A. There are 0s below the diagonal. |
dwork | (workspace) REAL array, dimension (N) | |
[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 real scalar, and v is a real 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).
void sgeqrf_copy_upper_batched | ( | magma_int_t | n, |
magma_int_t | nb, | ||
float ** | dV_array, | ||
magma_int_t | lddv, | ||
float ** | dR_array, | ||
magma_int_t | lddr, | ||
magma_int_t | batchCount, | ||
magma_queue_t | queue | ||
) |
These are internal routines that might have many assumption.
They are used in sgeqrf_batched.cpp
Copy part of the data in dV to dR
[in] | n | INTEGER The order of the matrix . N >= 0. |
[in] | nb | INTEGER Tile size in matrix. nb <= N. |
[in] | dV_array | Array of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDA,N). |
[in] | lddv | INTEGER The leading dimension of each array V. LDDV >= max(1,N). |
[in,out] | dR_array | Array of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDR,N). |
[in] | lddr | INTEGER The leading dimension of each array R. LDDR >= max(1,N). |
[in] | batchCount | INTEGER The number of matrices to operate on. |
[in] | queue | magma_queue_t Queue to execute in. |