rocsolver_ssygvdj_batched Interface Reference

rocsolver_ssygvdj_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_ssygvdj_batched Interface Reference

The SYGVDJ_BATCHED functions compute the eigenvalues and (optionally) eigenvectors of a batch of real generalized symmetric-definite eigenproblems. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_ssygvdj_batched_ (handle, itype, evect, uplo, n, a, lda, b, ldb, d, strided, myinfo, batch_count)

Detailed Description

The SYGVDJ_BATCHED functions compute the eigenvalues and (optionally) eigenvectors of a batch of real generalized symmetric-definite eigenproblems.

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

\[ \begin{array}{cl} A_l X_l = \lambda B_l X_l & \: \text{1st form,}\\% A_l B_l X_l = \lambda X_l & \: \text{2nd form, or}\\% B_l A_l X_l = \lambda X_l & \: \text{3rd form,} \end{array} \]

depending on the value of itype. The eigenvalues are found using the iterative Jacobi algorithm and returned in ascending order. The eigenvectors are computed using a divide-and-conquer algorithm, depending on the value of evect.

When computed, the matrix Z_l of eigenvectors is normalized as follows:

\[ \begin{array}{cl} Z^T_l B_l Z_l=I & \: \text{if 1st or 2nd form, or}\\% Z^T_l B^{-1}_l Z_l=I & \: \text{if 3rd form.} \end{array} \]

Parameters

[in]	handle	- rocblas_handle.
[in]	itype	- `rocblas_eform`. Specifies the form of the generalized eigenproblems.
[in]	evect	- `rocblas_evect`. Specifies whether the eigenvectors are to be computed. If evect is rocblas_evect_original, then the eigenvectors are computed. rocblas_evect_tridiagonal is not supported.
[in]	uplo	- rocblas_fill. Specifies whether the upper or lower parts of the matrices A_l and B_l are stored. If uplo indicates lower (or upper), then the upper (or lower) parts of A_l and B_l are not used.
[in]	n	- rocblas_int. n >= 0. Number of rows and columns of matrix A_l.
[in,out]	A	- array of pointers to type. Each pointer points to an array on the GPU of dimension lda*n. On entry, the matrices A_l. On exit, the normalized matrices Z_l of eigenvectors if they were computed and the algorithm converged. Otherwise, the contents of A_l are destroyed.
[in]	lda	- rocblas_int. lda >= n. Specifies the leading dimension of matrices A_l.
[in,out]	B	- array of pointers to type. Each pointer points to an array on the GPU of dimension ldb*n. On entry, the symmetric positive definite matrices B_l. On exit, the triangular factor of B_l as returned by POTRF_BATCHED.
[in]	ldb	- rocblas_int. ldb >= n. Specifies the leading dimension of matrices B_l.
[out]	D	- pointer to type. Array on the GPU (the size depends on the value of strideD). The eigenvalues in increasing order.
[in]	strideD	- rocblas_stride. Stride from the start of one vector D_l to the next one D_(l+1). There is no restriction for the value of strideD. Normal usage is strideD >= n.
[out]	myInfo	- pointer to rocblas_int. Array of batch_count integers on the GPU. If info[l] = 0, successful exit. If info[l] = 1, the algorithm did not converge for matrix A_l. If info[l] = n + i, the leading minor of order i of B_l is not positive definite.
[in]	batch_count	- rocblas_int. batch_count >= 0. Number of eigenproblems in the batch.

Member Function/Subroutine Documentation