rocsolver_ssytrs_batched Interface Reference

rocsolver_ssytrs_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_ssytrs_batched Interface Reference

The SYTRS_BATCHED functions solve a batch of systems of n linear equations on n variables in its factorized forms. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_ssytrs_batched_ (handle, uplo, n, nrhs, a, lda, ipiv, stridep, b, ldb, batch_count)

Detailed Description

The SYTRS_BATCHED functions solve a batch of systems of n linear equations on n variables in its factorized forms.

For each instance \( l \) in the batch, it solves the linear system \( A_l X_l = B_l \), where the n-by-n matrix A is symmetric and maybe indefinite, using one of the following factorization, depending on the value of uplo:

\[ \begin{array}{cl} A_l X_l = B_l & \: \text{where} \\% A_l = U_l D_l U_l^T & \: \text{U is upper triangular, or}\\% A_l = L_l D_l L_l^T & \: \text{L is lower triangular } \end{array} \]

Matrix \(A_l\) is defined by its triangular factors as returned by SYTRF_BATCHED. Note matrix \( D_l \) contains 1-by-1 or 2-by-2 blocks on the main diagonal.

Parameters

[in]	handle	- rocblas_handle.
[in]	uplo	- rocblas_fill. Specifies whether the factorization of matrix \( A \) is upper or lower triangular.
[in]	n	- rocblas_int. n >= 0. The order of the system, that is, the number of columns and rows of all A_l matrices.
[in]	nrhs	- rocblas_int. nrhs >= 0. The number of right hand sides, that is, the number of columns of all the matrices B_l.
[in]	A	- Array of pointers to type. Each pointer points to an array on the GPU of dimension lda*n. The factors L_l (or U_l) and D_l of the factorization A_l returned by SYTRF_BATCHED.
[in]	lda	- rocblas_int. lda >= n. The leading dimension of matrices A_l.
[in]	ipiv	- pointer to rocblas_int. Array on the GPU (the size depends on the value of strideP). Contains the vectors ipiv_l of pivot indices returned by SYTRF_BATCHED.
[in]	strideP	- rocblas_stride. Stride from the start of one vector ipiv_l to the next one ipiv_(l+1). There is no restriction for the value of strideP. The normal use case is strideP >= n.
[in,out]	B	- Array of pointers to type. Each pointer points to an array on the GPU of dimension ldb*nrhs. On entry, the right hand side matrices B_l. On exit, the solution matrix X_l of each system in the batch.
[in]	ldb	- rocblas_int. ldb >= n. The leading dimension of matrices B_l.
[in]	batch_count	- rocblas_int. batch_count >= 0. Number of instances (systems) in the batch.

Member Function/Subroutine Documentation