rocsolver_sgels_batched Interface Reference

rocsolver_sgels_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgels_batched Interface Reference

GELS_BATCHED solves a batch of overdetermined (or underdetermined) linear systems defined by a set of m-by-n matrices \(A_i\), and corresponding matrices \(B_i\), using the QR factorizations computed by GEQRF_BATCHED (or the LQ factorizations computed by GELQF_BATCHED). More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_sgels_batched_ (handle, trans, m, n, nrhs, A, lda, B, ldb, myInfo, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_sgels_batched_full_rank (handle, trans, m, n, nrhs, A, lda, B, ldb, myInfo, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_sgels_batched_rank_0 (handle, trans, m, n, nrhs, A, lda, B, ldb, myInfo, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_sgels_batched_rank_1 (handle, trans, m, n, nrhs, A, lda, B, ldb, myInfo, batch_count)

Detailed Description

GELS_BATCHED solves a batch of overdetermined (or underdetermined) linear systems defined by a set of m-by-n matrices \(A_i\), and corresponding matrices \(B_i\), using the QR factorizations computed by GEQRF_BATCHED (or the LQ factorizations computed by GELQF_BATCHED).

For each instance in the batch, depending on the value of trans, the problem solved by this function is either of the form

\[ \begin{array}{cl} A_i X_i = B_i & \: \text{not transposed, or}\newline A_i' X_i = B_i & \: \text{transposed if real, or conjugate transposed if complex} \end{array} \]

If m >= n (or m < n in the case of transpose/conjugate transpose), the system is overdetermined and a least-squares solution approximating X_i is found by minimizing

\[ || B_i - A_i X_i || \quad \text{(or} \: || B_i - A_i' X_i ||\text{)} \]

If m < n (or m >= n in the case of transpose/conjugate transpose), the system is underdetermined and a unique solution for X_i is chosen such that \(|| X_i ||\) is minimal.

Parameters

[in]	handle	rocblas_handle.
[in]	trans	rocblas_operation. Specifies the form of the system of equations.
[in]	m	rocblas_int. m >= 0. The number of rows of all matrices A_i in the batch.
[in]	n	rocblas_int. n >= 0. The number of columns of all matrices A_i in the batch.
[in]	nrhs	rocblas_int. nrhs >= 0. The number of columns of all matrices B_i and X_i in the batch; i.e., the columns on the right hand side.
[in,out]	A	array of pointer to type. Each pointer points to an array on the GPU of dimension lda*n. On entry, the matrices A_i. On exit, the QR (or LQ) factorizations of A_i as returned by GEQRF_BATCHED (or GELQF_BATCHED).
[in]	lda	rocblas_int. lda >= m. Specifies the leading dimension of matrices A_i.
[in,out]	B	array of pointer to type. Each pointer points to an array on the GPU of dimension ldb*nrhs. On entry, the matrices B_i. On exit, when info[i] = 0, B_i is overwritten by the solution vectors (and the residuals in the overdetermined cases) stored as columns.
[in]	ldb	rocblas_int. ldb >= max(m,n). Specifies the leading dimension of matrices B_i.
[out]	info	pointer to rocblas_int. Array of batch_count integers on the GPU. If info[i] = 0, successful exit for solution of A_i. If info[i] = j > 0, the solution of A_i could not be computed because input matrix A_i is rank deficient; the j-th diagonal element of its triangular factor is zero.
[in]	batch_count	rocblas_int. batch_count >= 0. Number of matrices in the batch.

Member Function/Subroutine Documentation