single precision
[QR with pivoting]

Functions

magma_int_t magma_sgeqp3 (magma_int_t m, magma_int_t n, float *A, magma_int_t lda, magma_int_t *jpvt, float *tau, float *work, magma_int_t lwork, float *rwork, magma_int_t *info)
 SGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.
magma_int_t magma_sgeqp3_gpu (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t *jpvt, float *tau, magmaFloat_ptr dwork, magma_int_t lwork, float *rwork, magma_int_t *info)
 SGEQP3 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_sgeqp3 ( magma_int_t  m,
magma_int_t  n,
float *  A,
magma_int_t  lda,
magma_int_t *  jpvt,
float *  tau,
float *  work,
magma_int_t  lwork,
float *  rwork,
magma_int_t *  info 
)

SGEQP3 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 REAL 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 REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors.
[out] work (workspace) REAL 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) REAL 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 real scalar, and v is a real 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_sgeqp3_gpu ( magma_int_t  m,
magma_int_t  n,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magma_int_t *  jpvt,
float *  tau,
magmaFloat_ptr  dwork,
magma_int_t  lwork,
float *  rwork,
magma_int_t *  info 
)

SGEQP3 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 REAL 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 REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors.
[out] dwork (workspace) REAL 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) REAL 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 real scalar, and v is a real 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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