MAGMA  2.3.0 Matrix Algebra for GPU and Multicore Architectures
geqp3: QR factorization with column pivoting

## 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...

magma_int_t magma_dgeqp3 (magma_int_t m, magma_int_t n, double *A, magma_int_t lda, magma_int_t *jpvt, double *tau, double *work, magma_int_t lwork, magma_int_t *info)
DGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS. More...

magma_int_t magma_dgeqp3_gpu (magma_int_t m, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, magma_int_t *jpvt, double *tau, magmaDouble_ptr dwork, magma_int_t lwork, magma_int_t *info)
DGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS. More...

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, magma_int_t *info)
SGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS. More...

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, magma_int_t *info)
SGEQP3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS. More...

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. More...

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. More...

## 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] 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 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 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] 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 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] 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 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 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] 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 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_dgeqp3 ( magma_int_t m, magma_int_t n, double * A, magma_int_t lda, magma_int_t * jpvt, double * tau, double * work, magma_int_t lwork, magma_int_t * info )

DGEQP3 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 DOUBLE PRECISION 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 orthogonal 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 DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors. [out] work (workspace) DOUBLE PRECISION 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. [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_dgeqp3_gpu ( magma_int_t m, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, magma_int_t * jpvt, double * tau, magmaDouble_ptr dwork, magma_int_t lwork, magma_int_t * info )

DGEQP3 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 DOUBLE PRECISION 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 orthogonal 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 DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors. [out] dwork (workspace) DOUBLE PRECISION 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. [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 ( 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, 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 orthogonal 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. [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, 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 orthogonal 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. [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_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).