MAGMA  1.7.0
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_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...
 

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_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 |

Parameters
[in]mINTEGER The number of columns of the tile A2. M >= 0.
[in]nINTEGER The number of rows of the tile A1. The number of columns of the tiles A1 and A2. N >= 0.
[in,out]A1COMPLEX_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]A2COMPLEX_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]ldaINTEGER The leading dimension of the tile A1 and A2. LDA >= max(1,M).
[out]tauINTEGER The scalar factors of the elementary reflectors (see Further Details).
[out]workCOMPLEX_16 array on the CPU host, dimension (LWORK).
[in]lworkINTEGER The dimension of the array WORK. TODO: LWORK >= ???.
[out]dworkCOMPLEX_16 array on the GPU, dimension TODO.
[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).