MAGMA  2.0.0
Matrix Algebra for GPU and Multicore Architectures

Functions

magma_int_t magma_cgeqp3 (magma_int_t m, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magma_int_t *jpvt, magmaFloatComplex *tau, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t *info)
 CGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS. More...
 
magma_int_t magma_cgeqp3_gpu (magma_int_t m, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, magma_int_t *jpvt, magmaFloatComplex *tau, magmaFloatComplex_ptr dwork, magma_int_t lwork, float *rwork, magma_int_t *info)
 CGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS. More...
 

Detailed Description

Function Documentation

magma_int_t magma_cgeqp3 ( magma_int_t  m,
magma_int_t  n,
magmaFloatComplex *  A,
magma_int_t  lda,
magma_int_t *  jpvt,
magmaFloatComplex *  tau,
magmaFloatComplex *  work,
magma_int_t  lwork,
float *  rwork,
magma_int_t *  info 
)

CGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.

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 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]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M).
[in,out]jpvtINTEGER 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]tauCOMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors.
[out]work(workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO=0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER 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) REAL array, dimension (2*N)
[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).

magma_int_t magma_cgeqp3_gpu ( magma_int_t  m,
magma_int_t  n,
magmaFloatComplex_ptr  dA,
magma_int_t  ldda,
magma_int_t *  jpvt,
magmaFloatComplex *  tau,
magmaFloatComplex_ptr  dwork,
magma_int_t  lwork,
float *  rwork,
magma_int_t *  info 
)

CGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.

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 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]lddaINTEGER The leading dimension of the array A. LDDA >= max(1,M).
[in,out]jpvtINTEGER 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]tauCOMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors.
[out]dwork(workspace) COMPLEX array on the GPU, dimension (MAX(1,LWORK)) On exit, if INFO=0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER 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) REAL array, dimension (2*N)
[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).