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MAGMA
2.0.2
Matrix Algebra for GPU and Multicore Architectures
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Functions | |
magma_int_t | magma_zgeqr2x2_gpu (magma_int_t m, magma_int_t n, magmaDoubleComplex_ptr dA, magma_int_t ldda, magmaDoubleComplex_ptr dtau, magmaDoubleComplex_ptr dT, magmaDoubleComplex_ptr ddA, magmaDouble_ptr dwork, magma_int_t *info) |
ZGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R. More... | |
magma_int_t | magma_zgeqr2x3_gpu (magma_int_t m, magma_int_t n, magmaDoubleComplex_ptr dA, magma_int_t ldda, magmaDoubleComplex_ptr dtau, magmaDoubleComplex_ptr dT, magmaDoubleComplex_ptr ddA, magmaDouble_ptr dwork, magma_int_t *info) |
ZGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R. More... | |
magma_int_t | magma_zgeqr2x_gpu (magma_int_t m, magma_int_t n, magmaDoubleComplex_ptr dA, magma_int_t ldda, magmaDoubleComplex_ptr dtau, magmaDoubleComplex_ptr dT, magmaDoubleComplex_ptr ddA, magmaDouble_ptr dwork, magma_int_t *info) |
ZGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R. More... | |
magma_int_t | magma_zgeqr2_gpu (magma_int_t m, magma_int_t n, magmaDoubleComplex_ptr dA, magma_int_t ldda, magmaDoubleComplex_ptr dtau, magmaDouble_ptr dwork, magma_queue_t queue, magma_int_t *info) |
ZGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R using the non-blocking Householder QR. More... | |
magma_int_t magma_zgeqr2_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaDoubleComplex_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaDoubleComplex_ptr | dtau, | ||
magmaDouble_ptr | dwork, | ||
magma_queue_t | queue, | ||
magma_int_t * | info | ||
) |
ZGEQR2 computes a QR factorization of a complex 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 | COMPLEX*16 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 | COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
dwork | (workspace) DOUBLE PRECISION array, dimension (N) | |
[in] | queue | magma_queue_t Queue to execute in. |
[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_zgeqr2x2_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaDoubleComplex_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaDoubleComplex_ptr | dtau, | ||
magmaDoubleComplex_ptr | dT, | ||
magmaDoubleComplex_ptr | ddA, | ||
magmaDouble_ptr | dwork, | ||
magma_int_t * | info | ||
) |
ZGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R.
This expert routine requires two more arguments than the standard zgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's zgeqr2 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 | COMPLEX_16 array, dimension (LDDA,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. LDDA >= max(1,M). |
[out] | dtau | COMPLEX_16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | dT | COMPLEX_16 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 | COMPLEX_16 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 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_zgeqr2x3_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaDoubleComplex_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaDoubleComplex_ptr | dtau, | ||
magmaDoubleComplex_ptr | dT, | ||
magmaDoubleComplex_ptr | ddA, | ||
magmaDouble_ptr | dwork, | ||
magma_int_t * | info | ||
) |
ZGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R.
This expert routine requires two more arguments than the standard zgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's zgeqr2 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 | COMPLEX_16 array, dimension (LDDA,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. LDDA >= max(1,M). |
[out] | dtau | COMPLEX_16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | dT | COMPLEX_16 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 | COMPLEX_16 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 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_zgeqr2x_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaDoubleComplex_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaDoubleComplex_ptr | dtau, | ||
magmaDoubleComplex_ptr | dT, | ||
magmaDoubleComplex_ptr | ddA, | ||
magmaDouble_ptr | dwork, | ||
magma_int_t * | info | ||
) |
ZGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R.
This expert routine requires two more arguments than the standard zgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's zgeqr2 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 | COMPLEX_16 array, dimension (LDDA,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. LDDA >= max(1,M). |
[out] | dtau | COMPLEX_16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). |
[out] | dT | COMPLEX_16 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 | COMPLEX_16 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) COMPLEX_16 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 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).