double-complex precision

Functions

magma_int_t magma_zgeqp3 (magma_int_t m, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magma_int_t *jpvt, magmaDoubleComplex *tau, magmaDoubleComplex *work, magma_int_t lwork, double *rwork, magma_int_t *info)
 ZGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.
magma_int_t magma_zgeqp3_gpu (magma_int_t m, magma_int_t n, magmaDoubleComplex_ptr dA, magma_int_t ldda, magma_int_t *jpvt, magmaDoubleComplex *tau, magmaDoubleComplex_ptr dwork, magma_int_t lwork, double *rwork, magma_int_t *info)
 ZGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.

Function Documentation

magma_int_t magma_zgeqp3 ( magma_int_t  m,
magma_int_t  n,
magmaDoubleComplex *  A,
magma_int_t  lda,
magma_int_t *  jpvt,
magmaDoubleComplex *  tau,
magmaDoubleComplex *  work,
magma_int_t  lwork,
double *  rwork,
magma_int_t *  info 
)

ZGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.

Parameters:
[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] A COMPLEX_16 array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the upper triangle of the array contains the min(M,N)-by-N upper trapezoidal matrix R; the elements below the diagonal, together with the array TAU, represent the unitary matrix Q as a product of min(M,N) elementary reflectors.
[in] lda INTEGER The leading dimension of the array A. LDA >= max(1,M).
[in,out] jpvt INTEGER array, dimension (N) On entry, if JPVT(J).ne.0, the J-th column of A is permuted to the front of A*P (a leading column); if JPVT(J)=0, the J-th column of A is a free column. On exit, if JPVT(J)=K, then the J-th column of A*P was the the K-th column of A.
[out] tau COMPLEX_16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors.
[out] work (workspace) COMPLEX_16 array, dimension (MAX(1,LWORK)) On exit, if INFO=0, WORK[0] returns the optimal LWORK.
[in] lwork INTEGER The dimension of the array WORK. For [sd]geqp3, LWORK >= (N+1)*NB + 2*N; for [cz]geqp3, LWORK >= (N+1)*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 by XERBLA.
rwork (workspace, for [cz]geqp3 only) DOUBLE PRECISION array, dimension (2*N)
[out] info INTEGER

  • = 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).

magma_int_t magma_zgeqp3_gpu ( magma_int_t  m,
magma_int_t  n,
magmaDoubleComplex_ptr  dA,
magma_int_t  ldda,
magma_int_t *  jpvt,
magmaDoubleComplex *  tau,
magmaDoubleComplex_ptr  dwork,
magma_int_t  lwork,
double *  rwork,
magma_int_t *  info 
)

ZGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.

Parameters:
[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 on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the upper triangle of the array contains the min(M,N)-by-N upper trapezoidal matrix R; the elements below the diagonal, together with the array TAU, represent the unitary matrix Q as a product of min(M,N) elementary reflectors.
[in] ldda INTEGER The leading dimension of the array A. LDDA >= max(1,M).
[in,out] jpvt INTEGER array, dimension (N) On entry, if JPVT(J).ne.0, the J-th column of A is permuted to the front of A*P (a leading column); if JPVT(J)=0, the J-th column of A is a free column. On exit, if JPVT(J)=K, then the J-th column of A*P was the the K-th column of A.
[out] tau COMPLEX_16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors.
[out] dwork (workspace) COMPLEX_16 array on the GPU, dimension (MAX(1,LWORK)) On exit, if INFO=0, WORK[0] returns the optimal LWORK.
[in] lwork INTEGER The dimension of the array WORK. For [sd]geqp3, LWORK >= (N+1)*NB + 2*N; for [cz]geqp3, LWORK >= (N+1)*NB, where NB is the optimal blocksize.
Note: unlike the CPU interface of this routine, the GPU interface does not support a workspace query.
rwork (workspace, for [cz]geqp3 only) DOUBLE PRECISION array, dimension (2*N)
[out] info INTEGER

  • = 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).


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