![]() |
MAGMA
1.7.0
Matrix Algebra for GPU and Multicore Architectures
|
Functions | |
magma_int_t | magma_ztsqrt_gpu (magma_int_t m, magma_int_t n, magmaDoubleComplex *A1, magmaDoubleComplex *A2, magma_int_t lda, magmaDoubleComplex *tau, magmaDoubleComplex *work, magma_int_t lwork, magmaDoubleComplex_ptr dwork, magma_int_t *info) |
ztsqrt computes a QR factorization of a rectangular matrix formed by coupling a complex N-by-N upper triangular tile A1 on top of a complex M-by-N tile A2: More... | |
magma_int_t magma_ztsqrt_gpu | ( | magma_int_t | m, |
magma_int_t | n, | ||
magmaDoubleComplex * | A1, | ||
magmaDoubleComplex * | A2, | ||
magma_int_t | lda, | ||
magmaDoubleComplex * | tau, | ||
magmaDoubleComplex * | work, | ||
magma_int_t | lwork, | ||
magmaDoubleComplex_ptr | dwork, | ||
magma_int_t * | info | ||
) |
ztsqrt computes a QR factorization of a rectangular matrix formed by coupling a complex N-by-N upper triangular tile A1 on top of a complex M-by-N tile A2:
| A1 | = Q * R | A2 |
[in] | m | INTEGER The number of columns of the tile A2. M >= 0. |
[in] | n | INTEGER The number of rows of the tile A1. The number of columns of the tiles A1 and A2. N >= 0. |
[in,out] | A1 | COMPLEX_16 array on the GPU, dimension (LDA,N) On entry, the N-by-N tile A1. On exit, the elements on and above the diagonal of the array contain the N-by-N upper trapezoidal tile R; the elements below the diagonal are not referenced. |
[in,out] | A2 | COMPLEX_16 array on the GPU, dimension (LDA,N) On entry, the M-by-N tile A2. On exit, all the elements, with the array TAU, represent the unitary tile Q as a product of elementary reflectors (see Further Details). |
[in] | lda | INTEGER The leading dimension of the tile A1 and A2. LDA >= max(1,M). |
[out] | tau | INTEGER The scalar factors of the elementary reflectors (see Further Details). |
[out] | work | COMPLEX_16 array on the CPU host, dimension (LWORK). |
[in] | lwork | INTEGER The dimension of the array WORK. TODO: LWORK >= ???. |
[out] | dwork | COMPLEX_16 array on the GPU, dimension TODO. |
[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).