Functions
magma_int_t	magma_cgeqrf_batched (magma_int_t m, magma_int_t n, magmaFloatComplex dA_array, magma_int_t ldda, magmaFloatComplex dtau_array, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
	CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.

magma_int_t	magma_cgeqrf_expert_batched (magma_int_t m, magma_int_t n, magma_int_t nb, magmaFloatComplex dA_array, magma_int_t ldda, magmaFloatComplex dR_array, magma_int_t lddr, magmaFloatComplex dT_array, magma_int_t lddt, magmaFloatComplex dtau_array, magma_int_t provide_RT, magmaFloatComplex *dW_array, magma_int_t info_array, magma_int_t batchCount, magma_queue_t queue)
	CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.

magma_int_t	magma_dgeqrf_batched (magma_int_t m, magma_int_t n, double dA_array, magma_int_t ldda, double dtau_array, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
	DGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.

magma_int_t	magma_dgeqrf_expert_batched (magma_int_t m, magma_int_t n, magma_int_t nb, double dA_array, magma_int_t ldda, double dR_array, magma_int_t lddr, double dT_array, magma_int_t lddt, double dtau_array, magma_int_t provide_RT, double *dW_array, magma_int_t info_array, magma_int_t batchCount, magma_queue_t queue)
	DGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.

magma_int_t	magma_sgeqrf_batched (magma_int_t m, magma_int_t n, float dA_array, magma_int_t ldda, float dtau_array, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
	SGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.

magma_int_t	magma_sgeqrf_expert_batched (magma_int_t m, magma_int_t n, magma_int_t nb, float dA_array, magma_int_t ldda, float dR_array, magma_int_t lddr, float dT_array, magma_int_t lddt, float dtau_array, magma_int_t provide_RT, float *dW_array, magma_int_t info_array, magma_int_t batchCount, magma_queue_t queue)
	SGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.

magma_int_t	magma_zgeqrf_batched (magma_int_t m, magma_int_t n, magmaDoubleComplex dA_array, magma_int_t ldda, magmaDoubleComplex dtau_array, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
	ZGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.

magma_int_t	magma_zgeqrf_expert_batched (magma_int_t m, magma_int_t n, magma_int_t nb, magmaDoubleComplex dA_array, magma_int_t ldda, magmaDoubleComplex dR_array, magma_int_t lddr, magmaDoubleComplex dT_array, magma_int_t lddt, magmaDoubleComplex dtau_array, magma_int_t provide_RT, magmaDoubleComplex *dW_array, magma_int_t info_array, magma_int_t batchCount, magma_queue_t queue)
	ZGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.

magma_int_t	magma_cgeqrf_batched_smallsq (magma_int_t n, magmaFloatComplex dA_array, magma_int_t Ai, magma_int_t Aj, magma_int_t ldda, magmaFloatComplex dtau_array, magma_int_t taui, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
	CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.

magma_int_t	magma_dgeqrf_batched_smallsq (magma_int_t n, double dA_array, magma_int_t Ai, magma_int_t Aj, magma_int_t ldda, double dtau_array, magma_int_t taui, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
	DGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.

magma_int_t	magma_sgeqrf_batched_smallsq (magma_int_t n, float dA_array, magma_int_t Ai, magma_int_t Aj, magma_int_t ldda, float dtau_array, magma_int_t taui, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
	SGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.

magma_int_t	magma_zgeqrf_batched_smallsq (magma_int_t n, magmaDoubleComplex dA_array, magma_int_t Ai, magma_int_t Aj, magma_int_t ldda, magmaDoubleComplex dtau_array, magma_int_t taui, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
	ZGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.

Detailed Description

Function Documentation

◆ magma_cgeqrf_batched()

magma_int_t magma_cgeqrf_batched	(	magma_int_t	m,
		magma_int_t	n,
		magmaFloatComplex **	dA_array,
		magma_int_t	ldda,
		magmaFloatComplex **	dtau_array,
		magma_int_t *	info_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.

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_array	Array of pointers, dimension (batchCount). Each is a COMPLEX array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16.
[out]	dtau_array	Array of pointers, dimension (batchCount). Each is a COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	info_array	Array of INTEGERs, dimension (batchCount), for corresponding matrices. = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

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_cgeqrf_expert_batched()

magma_int_t magma_cgeqrf_expert_batched	(	magma_int_t	m,
		magma_int_t	n,
		magma_int_t	nb,
		magmaFloatComplex **	dA_array,
		magma_int_t	ldda,
		magmaFloatComplex **	dR_array,
		magma_int_t	lddr,
		magmaFloatComplex **	dT_array,
		magma_int_t	lddt,
		magmaFloatComplex **	dtau_array,
		magma_int_t	provide_RT,
		magmaFloatComplex **	dW_array,
		magma_int_t *	info_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.

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]	nb	INTEGER The blocking size.
[in,out]	dA_array	Array of pointers, dimension (batchCount). Each is a COMPLEX array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16.
[in,out]	dR_array	Array of pointers, dimension (batchCount). Each is a COMPLEX array on the GPU, dimension (LDDR, N/NB) dR should be of size (LDDR, N) when provide_RT > 0 and of size (LDDT, NB) otherwise. NB is the local blocking size. On exit, the elements of R are stored in dR only when provide_RT > 0.
[in]	lddr	INTEGER The leading dimension of the array dR. LDDR >= min(M,N) when provide_RT == 1 otherwise LDDR >= min(NB, min(M,N)). NB is the local blocking size. To benefit from coalescent memory accesses LDDR must be divisible by 16.
[in,out]	dT_array	Array of pointers, dimension (batchCount). Each is a COMPLEX array on the GPU, dimension (LDDT, N/NB) dT should be of size (LDDT, N) when provide_RT > 0 and of size (LDDT, NB) otherwise. NB is the local blocking size. On exit, the elements of T are stored in dT only when provide_RT > 0.
[in]	lddt	INTEGER The leading dimension of the array dT. LDDT >= min(NB,min(M,N)). NB is the local blocking size. To benefit from coalescent memory accesses LDDR must be divisible by 16.
[out]	dtau_array	Array of pointers, dimension (batchCount). Each is a COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[in]	provide_RT	INTEGER provide_RT = 0 no R and no T in output. dR and dT are used as local workspace to store the R and T of each step. provide_RT = 1 the whole R of size (min(M,N), N) and the nbxnb block of T are provided in output. provide_RT = 2 the nbxnb diag block of R and of T are provided in output.
[out]	dW_array	Array of pointers, dimension (2*batchCount). Each is a COMPLEX array on the GPU, dimension (LDDW, N), where LDDW >= NB. Used as a workspace.
[out]	info_array	Array of INTEGERs, dimension (batchCount), for corresponding matrices. = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

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_dgeqrf_batched()

magma_int_t magma_dgeqrf_batched	(	magma_int_t	m,
		magma_int_t	n,
		double **	dA_array,
		magma_int_t	ldda,
		double **	dtau_array,
		magma_int_t *	info_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

DGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.

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_array	Array of pointers, dimension (batchCount). Each is a DOUBLE PRECISION array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16.
[out]	dtau_array	Array of pointers, dimension (batchCount). Each is a DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	info_array	Array of INTEGERs, dimension (batchCount), for corresponding matrices. = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

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_dgeqrf_expert_batched()

magma_int_t magma_dgeqrf_expert_batched	(	magma_int_t	m,
		magma_int_t	n,
		magma_int_t	nb,
		double **	dA_array,
		magma_int_t	ldda,
		double **	dR_array,
		magma_int_t	lddr,
		double **	dT_array,
		magma_int_t	lddt,
		double **	dtau_array,
		magma_int_t	provide_RT,
		double **	dW_array,
		magma_int_t *	info_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

DGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.

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]	nb	INTEGER The blocking size.
[in,out]	dA_array	Array of pointers, dimension (batchCount). Each is a DOUBLE PRECISION array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16.
[in,out]	dR_array	Array of pointers, dimension (batchCount). Each is a DOUBLE PRECISION array on the GPU, dimension (LDDR, N/NB) dR should be of size (LDDR, N) when provide_RT > 0 and of size (LDDT, NB) otherwise. NB is the local blocking size. On exit, the elements of R are stored in dR only when provide_RT > 0.
[in]	lddr	INTEGER The leading dimension of the array dR. LDDR >= min(M,N) when provide_RT == 1 otherwise LDDR >= min(NB, min(M,N)). NB is the local blocking size. To benefit from coalescent memory accesses LDDR must be divisible by 16.
[in,out]	dT_array	Array of pointers, dimension (batchCount). Each is a DOUBLE PRECISION array on the GPU, dimension (LDDT, N/NB) dT should be of size (LDDT, N) when provide_RT > 0 and of size (LDDT, NB) otherwise. NB is the local blocking size. On exit, the elements of T are stored in dT only when provide_RT > 0.
[in]	lddt	INTEGER The leading dimension of the array dT. LDDT >= min(NB,min(M,N)). NB is the local blocking size. To benefit from coalescent memory accesses LDDR must be divisible by 16.
[out]	dtau_array	Array of pointers, dimension (batchCount). Each is a DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[in]	provide_RT	INTEGER provide_RT = 0 no R and no T in output. dR and dT are used as local workspace to store the R and T of each step. provide_RT = 1 the whole R of size (min(M,N), N) and the nbxnb block of T are provided in output. provide_RT = 2 the nbxnb diag block of R and of T are provided in output.
[out]	dW_array	Array of pointers, dimension (2*batchCount). Each is a DOUBLE PRECISION array on the GPU, dimension (LDDW, N), where LDDW >= NB. Used as a workspace.
[out]	info_array	Array of INTEGERs, dimension (batchCount), for corresponding matrices. = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

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_sgeqrf_batched()

magma_int_t magma_sgeqrf_batched	(	magma_int_t	m,
		magma_int_t	n,
		float **	dA_array,
		magma_int_t	ldda,
		float **	dtau_array,
		magma_int_t *	info_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

SGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.

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_array	Array of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16.
[out]	dtau_array	Array of pointers, dimension (batchCount). Each is a REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	info_array	Array of INTEGERs, dimension (batchCount), for corresponding matrices. = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

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_sgeqrf_expert_batched()

magma_int_t magma_sgeqrf_expert_batched	(	magma_int_t	m,
		magma_int_t	n,
		magma_int_t	nb,
		float **	dA_array,
		magma_int_t	ldda,
		float **	dR_array,
		magma_int_t	lddr,
		float **	dT_array,
		magma_int_t	lddt,
		float **	dtau_array,
		magma_int_t	provide_RT,
		float **	dW_array,
		magma_int_t *	info_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

SGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.

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]	nb	INTEGER The blocking size.
[in,out]	dA_array	Array of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16.
[in,out]	dR_array	Array of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDR, N/NB) dR should be of size (LDDR, N) when provide_RT > 0 and of size (LDDT, NB) otherwise. NB is the local blocking size. On exit, the elements of R are stored in dR only when provide_RT > 0.
[in]	lddr	INTEGER The leading dimension of the array dR. LDDR >= min(M,N) when provide_RT == 1 otherwise LDDR >= min(NB, min(M,N)). NB is the local blocking size. To benefit from coalescent memory accesses LDDR must be divisible by 16.
[in,out]	dT_array	Array of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDT, N/NB) dT should be of size (LDDT, N) when provide_RT > 0 and of size (LDDT, NB) otherwise. NB is the local blocking size. On exit, the elements of T are stored in dT only when provide_RT > 0.
[in]	lddt	INTEGER The leading dimension of the array dT. LDDT >= min(NB,min(M,N)). NB is the local blocking size. To benefit from coalescent memory accesses LDDR must be divisible by 16.
[out]	dtau_array	Array of pointers, dimension (batchCount). Each is a REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[in]	provide_RT	INTEGER provide_RT = 0 no R and no T in output. dR and dT are used as local workspace to store the R and T of each step. provide_RT = 1 the whole R of size (min(M,N), N) and the nbxnb block of T are provided in output. provide_RT = 2 the nbxnb diag block of R and of T are provided in output.
[out]	dW_array	Array of pointers, dimension (2*batchCount). Each is a REAL array on the GPU, dimension (LDDW, N), where LDDW >= NB. Used as a workspace.
[out]	info_array	Array of INTEGERs, dimension (batchCount), for corresponding matrices. = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

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_zgeqrf_batched()

magma_int_t magma_zgeqrf_batched	(	magma_int_t	m,
		magma_int_t	n,
		magmaDoubleComplex **	dA_array,
		magma_int_t	ldda,
		magmaDoubleComplex **	dtau_array,
		magma_int_t *	info_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

ZGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.

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_array	Array of pointers, dimension (batchCount). Each is a COMPLEX_16 array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16.
[out]	dtau_array	Array of pointers, dimension (batchCount). Each is a COMPLEX_16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	info_array	Array of INTEGERs, dimension (batchCount), for corresponding matrices. = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

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_zgeqrf_expert_batched()

magma_int_t magma_zgeqrf_expert_batched	(	magma_int_t	m,
		magma_int_t	n,
		magma_int_t	nb,
		magmaDoubleComplex **	dA_array,
		magma_int_t	ldda,
		magmaDoubleComplex **	dR_array,
		magma_int_t	lddr,
		magmaDoubleComplex **	dT_array,
		magma_int_t	lddt,
		magmaDoubleComplex **	dtau_array,
		magma_int_t	provide_RT,
		magmaDoubleComplex **	dW_array,
		magma_int_t *	info_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

ZGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.

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]	nb	INTEGER The blocking size.
[in,out]	dA_array	Array of pointers, dimension (batchCount). Each is a COMPLEX_16 array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16.
[in,out]	dR_array	Array of pointers, dimension (batchCount). Each is a COMPLEX_16 array on the GPU, dimension (LDDR, N/NB) dR should be of size (LDDR, N) when provide_RT > 0 and of size (LDDT, NB) otherwise. NB is the local blocking size. On exit, the elements of R are stored in dR only when provide_RT > 0.
[in]	lddr	INTEGER The leading dimension of the array dR. LDDR >= min(M,N) when provide_RT == 1 otherwise LDDR >= min(NB, min(M,N)). NB is the local blocking size. To benefit from coalescent memory accesses LDDR must be divisible by 16.
[in,out]	dT_array	Array of pointers, dimension (batchCount). Each is a COMPLEX_16 array on the GPU, dimension (LDDT, N/NB) dT should be of size (LDDT, N) when provide_RT > 0 and of size (LDDT, NB) otherwise. NB is the local blocking size. On exit, the elements of T are stored in dT only when provide_RT > 0.
[in]	lddt	INTEGER The leading dimension of the array dT. LDDT >= min(NB,min(M,N)). NB is the local blocking size. To benefit from coalescent memory accesses LDDR must be divisible by 16.
[out]	dtau_array	Array of pointers, dimension (batchCount). Each is a COMPLEX_16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[in]	provide_RT	INTEGER provide_RT = 0 no R and no T in output. dR and dT are used as local workspace to store the R and T of each step. provide_RT = 1 the whole R of size (min(M,N), N) and the nbxnb block of T are provided in output. provide_RT = 2 the nbxnb diag block of R and of T are provided in output.
[out]	dW_array	Array of pointers, dimension (2*batchCount). Each is a COMPLEX_16 array on the GPU, dimension (LDDW, N), where LDDW >= NB. Used as a workspace.
[out]	info_array	Array of INTEGERs, dimension (batchCount), for corresponding matrices. = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

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_cgeqrf_batched_smallsq()

magma_int_t magma_cgeqrf_batched_smallsq	(	magma_int_t	n,
		magmaFloatComplex **	dA_array,
		magma_int_t	Ai,
		magma_int_t	Aj,
		magma_int_t	ldda,
		magmaFloatComplex **	dtau_array,
		magma_int_t	taui,
		magma_int_t *	info_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.

This is a batched version of the routine, and works only for small square matrices of size up to 32.

Parameters

[in]	n	INTEGER The size of the matrix A. N >= 0.
[in,out]	dA_array	Array of pointers, dimension (batchCount). Each is a COMPLEX array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16.
[out]	dtau_array	Array of pointers, dimension (batchCount). Each is a COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	info_array	Array of INTEGERs, dimension (batchCount), for corresponding matrices. = 0: successful exit
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

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_dgeqrf_batched_smallsq()

magma_int_t magma_dgeqrf_batched_smallsq	(	magma_int_t	n,
		double **	dA_array,
		magma_int_t	Ai,
		magma_int_t	Aj,
		magma_int_t	ldda,
		double **	dtau_array,
		magma_int_t	taui,
		magma_int_t *	info_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

DGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.

This is a batched version of the routine, and works only for small square matrices of size up to 32.

Parameters

[in]	n	INTEGER The size of the matrix A. N >= 0.
[in,out]	dA_array	Array of pointers, dimension (batchCount). Each is a DOUBLE PRECISION array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16.
[out]	dtau_array	Array of pointers, dimension (batchCount). Each is a DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	info_array	Array of INTEGERs, dimension (batchCount), for corresponding matrices. = 0: successful exit
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

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_sgeqrf_batched_smallsq()

magma_int_t magma_sgeqrf_batched_smallsq	(	magma_int_t	n,
		float **	dA_array,
		magma_int_t	Ai,
		magma_int_t	Aj,
		magma_int_t	ldda,
		float **	dtau_array,
		magma_int_t	taui,
		magma_int_t *	info_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

SGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.

This is a batched version of the routine, and works only for small square matrices of size up to 32.

Parameters

[in]	n	INTEGER The size of the matrix A. N >= 0.
[in,out]	dA_array	Array of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16.
[out]	dtau_array	Array of pointers, dimension (batchCount). Each is a REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	info_array	Array of INTEGERs, dimension (batchCount), for corresponding matrices. = 0: successful exit
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

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_zgeqrf_batched_smallsq()

magma_int_t magma_zgeqrf_batched_smallsq	(	magma_int_t	n,
		magmaDoubleComplex **	dA_array,
		magma_int_t	Ai,
		magma_int_t	Aj,
		magma_int_t	ldda,
		magmaDoubleComplex **	dtau_array,
		magma_int_t	taui,
		magma_int_t *	info_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

ZGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.

This is a batched version of the routine, and works only for small square matrices of size up to 32.

Parameters

[in]	n	INTEGER The size of the matrix A. N >= 0.
[in,out]	dA_array	Array of pointers, dimension (batchCount). Each is a COMPLEX_16 array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16.
[out]	dtau_array	Array of pointers, dimension (batchCount). Each is a COMPLEX_16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	info_array	Array of INTEGERs, dimension (batchCount), for corresponding matrices. = 0: successful exit
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

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_cgeqrf_batched()

Further Details

◆ magma_cgeqrf_expert_batched()

Further Details

◆ magma_dgeqrf_batched()

Further Details

◆ magma_dgeqrf_expert_batched()

Further Details

◆ magma_sgeqrf_batched()

Further Details

◆ magma_sgeqrf_expert_batched()

Further Details

◆ magma_zgeqrf_batched()

Further Details

◆ magma_zgeqrf_expert_batched()

Further Details

◆ magma_cgeqrf_batched_smallsq()

Further Details

◆ magma_dgeqrf_batched_smallsq()

Further Details

◆ magma_sgeqrf_batched_smallsq()

Further Details

◆ magma_zgeqrf_batched_smallsq()

Further Details