rocsolver_sgels_strided_batched Interface Reference

rocsolver_sgels_strided_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgels_strided_batched Interface Reference

GELS_STRIDED_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_STRIDED_BATCHED (or the LQ factorizations computed by GELQF_STRIDED_BATCHED). More...

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

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

integer(kind(rocblas_status_success)) function	rocsolver_sgels_strided_batched_rank_0 (handle, trans, m, n, nrhs, A, lda, strideA, B, ldb, strideB, myInfo, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_sgels_strided_batched_rank_1 (handle, trans, m, n, nrhs, A, lda, strideA, B, ldb, strideB, myInfo, batch_count)

Detailed Description

GELS_STRIDED_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_STRIDED_BATCHED (or the LQ factorizations computed by GELQF_STRIDED_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	pointer to type. Array on the GPU (the size depends on the value of strideA). On entry, the matrices A_i. On exit, the QR (or LQ) factorizations of A_i as returned by GEQRF_STRIDED_BATCHED (or GELQF_STRIDED_BATCHED).
[in]	lda	rocblas_int. lda >= m. Specifies the leading dimension of matrices A_i.
[in]	strideA	rocblas_stride. Stride from the start of one matrix A_i to the next one A_(i+1). There is no restriction for the value of strideA. Normal use case is strideA >= lda*n
[in,out]	B	pointer to type. Array on the GPU (the size depends on the value of strideB). On entry, the matrices B_i. On exit, when info = 0, each 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.
[in]	strideB	rocblas_stride. Stride from the start of one matrix B_i to the next one B_(i+1). There is no restriction for the value of strideB. Normal use case is strideB >= ldb*nrhs
[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