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

Functions

magma_int_t magma_zgelqf (magma_int_t m, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex *tau, magmaDoubleComplex *work, magma_int_t lwork, magma_int_t *info)
 ZGELQF computes an LQ factorization of a COMPLEX_16 M-by-N matrix A: A = L * Q. More...
 
magma_int_t magma_zgelqf_gpu (magma_int_t m, magma_int_t n, magmaDoubleComplex *dA, magma_int_t lda, magmaDoubleComplex *tau, magmaDoubleComplex *work, magma_int_t lwork, magma_int_t *info)
 ZGELQF computes an LQ factorization of a COMPLEX_16 M-by-N matrix dA: dA = L * Q. More...
 

Detailed Description

Function Documentation

magma_int_t magma_zgelqf ( magma_int_t  m,
magma_int_t  n,
magmaDoubleComplex *  A,
magma_int_t  lda,
magmaDoubleComplex *  tau,
magmaDoubleComplex *  work,
magma_int_t  lwork,
magma_int_t *  info 
)

ZGELQF computes an LQ factorization of a COMPLEX_16 M-by-N matrix A: A = L * Q.

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, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details).
Higher performance is achieved if A is in pinned memory, e.g. allocated using magma_malloc_pinned.
[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 >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize.
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]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value if INFO = -10 internal GPU memory allocation failed.

Further Details

The matrix Q is represented as a product of elementary reflectors

Q = H(k) . . . H(2) H(1), 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:n) is stored on exit in A(i,i+1:n), and tau in TAU(i).

magma_int_t magma_zgelqf_gpu ( magma_int_t  m,
magma_int_t  n,
magmaDoubleComplex *  dA,
magma_int_t  lda,
magmaDoubleComplex *  tau,
magmaDoubleComplex *  work,
magma_int_t  lwork,
magma_int_t *  info 
)

ZGELQF computes an LQ factorization of a COMPLEX_16 M-by-N matrix dA: dA = L * Q.

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]dACOMPLEX_16 array on the GPU, dimension (LDA,N) On entry, the M-by-N matrix dA. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details).
[in]ldaINTEGER The leading dimension of the array dA. 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 >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize.
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]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value if INFO = -10 internal GPU memory allocation failed.

Further Details

The matrix Q is represented as a product of elementary reflectors

Q = H(k) . . . H(2) H(1), 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:n) is stored on exit in A(i,i+1:n), and tau in TAU(i).