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: AP = QR using Level 3 BLAS.

magma_int_t	magma_cgeqp3_expert_gpu_work (magma_int_t m, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, magma_int_t jpvt, magmaFloatComplex tau, void host_work, magma_int_t lwork_host, void device_work, magma_int_t lwork_device, magma_int_t *info, magma_queue_t queue)
	CGEQP3 computes a QR factorization with column pivoting of a matrix A: AP = QR using Level 3 BLAS.

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: AP = QR using Level 3 BLAS.

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: AP = QR using Level 3 BLAS.

magma_int_t	magma_dgeqp3_expert_gpu_work (magma_int_t m, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, magma_int_t jpvt, double tau, void host_work, magma_int_t lwork_host, void device_work, magma_int_t lwork_device, magma_int_t *info, magma_queue_t queue)
	DGEQP3 computes a QR factorization with column pivoting of a matrix A: AP = QR using Level 3 BLAS.

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: AP = QR using Level 3 BLAS.

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: AP = QR using Level 3 BLAS.

magma_int_t	magma_sgeqp3_expert_gpu_work (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t jpvt, float tau, void host_work, magma_int_t lwork_host, void device_work, magma_int_t lwork_device, magma_int_t *info, magma_queue_t queue)
	SGEQP3 computes a QR factorization with column pivoting of a matrix A: AP = QR 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, magma_int_t *info)
	SGEQP3 computes a QR factorization with column pivoting of a matrix A: AP = QR using Level 3 BLAS.

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: AP = QR using Level 3 BLAS.

magma_int_t	magma_zgeqp3_expert_gpu_work (magma_int_t m, magma_int_t n, magmaDoubleComplex_ptr dA, magma_int_t ldda, magma_int_t jpvt, magmaDoubleComplex tau, void host_work, magma_int_t lwork_host, void device_work, magma_int_t lwork_device, magma_int_t *info, magma_queue_t queue)
	ZGEQP3 computes a QR factorization with column pivoting of a matrix A: AP = QR 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: AP = QR using Level 3 BLAS.

Detailed Description

Function Documentation

◆ magma_cgeqp3()

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 AP (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 AP 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 + 2N; 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_cgeqp3_expert_gpu_work()

magma_int_t magma_cgeqp3_expert_gpu_work	(	magma_int_t	m,
		magma_int_t	n,
		magmaFloatComplex_ptr	dA,
		magma_int_t	ldda,
		magma_int_t *	jpvt,
		magmaFloatComplex *	tau,
		void *	host_work,
		magma_int_t *	lwork_host,
		void *	device_work,
		magma_int_t *	lwork_device,
		magma_int_t *	info,
		magma_queue_t	queue )

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 AP (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 AP was the the K-th column of A.
[out]	tau	COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors.
[in,out]	host_work	Workspace, allocated on host (CPU) memory. For faster CPU-GPU communication, user can allocate it as pinned memory using magma_malloc_pinned()
[in,out]	lwork_host	INTEGER pointer The size of the workspace (host_work) in bytes lwork_host[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_host. The workspace itself is not referenced, and no computation is performed.

lwork[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_host.

Parameters

[in,out]	device_work	Workspace, allocated on device (GPU) memory.
[in,out]	lwork_device	INTEGER pointer The size of the workspace (device_work) in bytes lwork_device[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_device. The workspace itself is not referenced, and no computation is performed. lwork_device[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_device.
[out]	info	INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.
[in]	queue	magma_queue_t created/destroyed by the user

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_cgeqp3_gpu()

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 AP (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 AP 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 + 2N; 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) For releases after 2.8.0, this argument is not used, but kept for backward compatibility. It can be passed as a null pointer.
[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_dgeqp3()

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 AP (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 AP 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 + 2N; 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_dgeqp3_expert_gpu_work()

magma_int_t magma_dgeqp3_expert_gpu_work	(	magma_int_t	m,
		magma_int_t	n,
		magmaDouble_ptr	dA,
		magma_int_t	ldda,
		magma_int_t *	jpvt,
		double *	tau,
		void *	host_work,
		magma_int_t *	lwork_host,
		void *	device_work,
		magma_int_t *	lwork_device,
		magma_int_t *	info,
		magma_queue_t	queue )

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 AP (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 AP was the the K-th column of A.
[out]	tau	DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors.
[in,out]	host_work	Workspace, allocated on host (CPU) memory. For faster CPU-GPU communication, user can allocate it as pinned memory using magma_malloc_pinned()
[in,out]	lwork_host	INTEGER pointer The size of the workspace (host_work) in bytes lwork_host[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_host. The workspace itself is not referenced, and no computation is performed.

lwork[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_host.

Parameters

[in,out]	device_work	Workspace, allocated on device (GPU) memory.
[in,out]	lwork_device	INTEGER pointer The size of the workspace (device_work) in bytes lwork_device[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_device. The workspace itself is not referenced, and no computation is performed. lwork_device[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_device.
[out]	info	INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.
[in]	queue	magma_queue_t created/destroyed by the user

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_dgeqp3_gpu()

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 AP (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 AP 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 + 2N; 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_sgeqp3()

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 AP (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 AP 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 + 2N; 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_sgeqp3_expert_gpu_work()

magma_int_t magma_sgeqp3_expert_gpu_work	(	magma_int_t	m,
		magma_int_t	n,
		magmaFloat_ptr	dA,
		magma_int_t	ldda,
		magma_int_t *	jpvt,
		float *	tau,
		void *	host_work,
		magma_int_t *	lwork_host,
		void *	device_work,
		magma_int_t *	lwork_device,
		magma_int_t *	info,
		magma_queue_t	queue )

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 AP (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 AP was the the K-th column of A.
[out]	tau	REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors.
[in,out]	host_work	Workspace, allocated on host (CPU) memory. For faster CPU-GPU communication, user can allocate it as pinned memory using magma_malloc_pinned()
[in,out]	lwork_host	INTEGER pointer The size of the workspace (host_work) in bytes lwork_host[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_host. The workspace itself is not referenced, and no computation is performed.

lwork[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_host.

Parameters

[in,out]	device_work	Workspace, allocated on device (GPU) memory.
[in,out]	lwork_device	INTEGER pointer The size of the workspace (device_work) in bytes lwork_device[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_device. The workspace itself is not referenced, and no computation is performed. lwork_device[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_device.
[out]	info	INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.
[in]	queue	magma_queue_t created/destroyed by the user

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_sgeqp3_gpu()

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 AP (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 AP 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 + 2N; 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_zgeqp3()

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 AP (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 AP 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 + 2N; 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_zgeqp3_expert_gpu_work()

magma_int_t magma_zgeqp3_expert_gpu_work	(	magma_int_t	m,
		magma_int_t	n,
		magmaDoubleComplex_ptr	dA,
		magma_int_t	ldda,
		magma_int_t *	jpvt,
		magmaDoubleComplex *	tau,
		void *	host_work,
		magma_int_t *	lwork_host,
		void *	device_work,
		magma_int_t *	lwork_device,
		magma_int_t *	info,
		magma_queue_t	queue )

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 AP (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 AP was the the K-th column of A.
[out]	tau	COMPLEX_16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors.
[in,out]	host_work	Workspace, allocated on host (CPU) memory. For faster CPU-GPU communication, user can allocate it as pinned memory using magma_malloc_pinned()
[in,out]	lwork_host	INTEGER pointer The size of the workspace (host_work) in bytes lwork_host[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_host. The workspace itself is not referenced, and no computation is performed.

lwork[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_host.

Parameters

[in,out]	device_work	Workspace, allocated on device (GPU) memory.
[in,out]	lwork_device	INTEGER pointer The size of the workspace (device_work) in bytes lwork_device[0] < 0: a workspace query is assumed, the routine calculates the required amount of workspace and returns it in lwork_device. The workspace itself is not referenced, and no computation is performed. lwork_device[0] >= 0: the routine assumes that the user has provided a workspace with the size in lwork_device.
[out]	info	INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.
[in]	queue	magma_queue_t created/destroyed by the user

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_zgeqp3_gpu()

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 AP (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 AP 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 + 2N; 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) For releases after 2.8.0, this argument is not used, but kept for backward compatibility. It can be passed as a null pointer.
[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).

Functions

Detailed Description

Function Documentation

◆ magma_cgeqp3()

Further Details

◆ magma_cgeqp3_expert_gpu_work()

Further Details

◆ magma_cgeqp3_gpu()

Further Details

◆ magma_dgeqp3()

Further Details

◆ magma_dgeqp3_expert_gpu_work()

Further Details

◆ magma_dgeqp3_gpu()

Further Details

◆ magma_sgeqp3()

Further Details

◆ magma_sgeqp3_expert_gpu_work()

Further Details

◆ magma_sgeqp3_gpu()

Further Details

◆ magma_zgeqp3()

Further Details

◆ magma_zgeqp3_expert_gpu_work()

Further Details

◆ magma_zgeqp3_gpu()

Further Details