MAGMA  2.3.0 Matrix Algebra for GPU and Multicore Architectures
geqr2: QR panel factorization

## Functions

magma_int_t magma_cgeqr2_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)
CGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R. More...

magma_int_t magma_dgeqr2_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)
DGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More...

magma_int_t magma_sgeqr2_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)
SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More...

magma_int_t magma_zgeqr2_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)
ZGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R. More...

## Function Documentation

 magma_int_t magma_cgeqr2_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 )

CGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R.

This version implements the right-looking QR with non-blocking.

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_int_t magma_dgeqr2_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 )

DGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R.

This version implements the right-looking QR with non-blocking.

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_int_t magma_sgeqr2_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 )

SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R.

This version implements the right-looking QR with non-blocking.

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_int_t magma_zgeqr2_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 )

ZGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R.

This version implements the right-looking QR with non-blocking.

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).