MAGMA  1.5.0
Matrix Algebra for GPU and Multicore Architectures
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double-complex precision

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 *dwork, magma_int_t *info)
 ZGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R. More...
 

Detailed Description

Function Documentation

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 *  dwork,
magma_int_t *  info 
)

ZGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.

Parameters
[in]mINTEGER The number of rows of the matrix A. M >= 0.
[in]nINTEGER The number of columns of the matrix A. N >= 0.
[in,out]ACOMPLEX_16 array on the GPU, 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).
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]tauCOMPLEX_16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]work(workspace) COMPLEX_16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
Higher performance is achieved if WORK is in pinned memory, e.g. allocated using magma_malloc_pinned.
[in]lworkINTEGER The dimension of the array WORK. LWORK >= (M+N+NB)*NB, where NB can be obtained through magma_get_zgeqrf_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.
[out]dwork(workspace) COMPLEX_16 array on the GPU, dimension 2*N*NB, where NB can be obtained through magma_get_zgeqrf_nb(M). It starts with NB*NB blocks that store the triangular T matrices, followed by the NB*NB blocks of the diagonal inverses for the R matrix.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

Further Details

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).