rocsolver_sgels_batched Interface Reference

rocsolver_sgels_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgels_batched Interface Reference

The GELS_BATCHED functions solve a batch of overdetermined (or underdetermined) linear systems defined by a set of m -by-n matrices \(A_l\) and corresponding matrices \(B_l\), 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)

Detailed Description

The GELS_BATCHED functions solve a batch of overdetermined (or underdetermined) linear systems defined by a set of m -by-n matrices \(A_l\) and corresponding matrices \(B_l\), 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

\[ \begin{array}{cl} A_l X_l = B_l & \: \text{not transposed, or}\\% A_l^H X_l^{} = B_l^{} & \: \text{transposed if real, or conjugate transposed if complex} \end{array} \]

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

\[ || B_l - A_l X_l || \quad \text{(or} \: || B_l^{} - A_l^H X_l^{} ||\text{)} \]

If m < n (or m >= n in the case of transpose/conjugate transpose), the system is underdetermined and a unique solution for X_l is chosen such that \(|| X_l ||\) 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_l in the batch.
[in]	n	- rocblas_int. n >= 0. The number of columns of all matrices A_l in the batch.
[in]	nrhs	- rocblas_int. nrhs >= 0. The number of columns of all matrices B_l and X_l in the batch, that is, 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_l. On exit, the QR (or LQ) factorizations of A_l as returned by GEQRF_BATCHED (or GELQF_BATCHED).
[in]	lda	- rocblas_int. lda >= m. Specifies the leading dimension of matrices A_l.
[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_l. On exit, when info[l] = 0, B_l 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_l.
[out]	myInfo	- pointer to rocblas_int. Array of batch_count integers on the GPU. If info[l] = 0, successful exit for solution of A_l. If info[l] = i > 0, the solution of A_l could not be computed because input matrix A_l is rank deficient. The i-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