rocsolver_ssygvdj Interface Reference

rocsolver_ssygvdj Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_ssygvdj Interface Reference

The SYGVDJ functions compute the eigenvalues and (optionally) eigenvectors of a real generalized symmetric-definite eigenproblem. More...

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

Detailed Description

The SYGVDJ functions compute the eigenvalues and (optionally) eigenvectors of a real generalized symmetric-definite eigenproblem.

The problem solved by this function is either of the form

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

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 of eigenvectors is normalized as follows:

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

Parameters

[in]	handle	- rocblas_handle.
[in]	itype	- `rocblas_eform`. Specifies the form of the generalized eigenproblem.
[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 and B are stored. If uplo indicates lower (or upper), then the upper (or lower) parts of A and B are not used.
[in]	n	- rocblas_int. n >= 0. Number of rows and columns of matrix A.
[in,out]	A	- pointer to type. Array on the GPU of dimension lda*n. On entry, the matrix A. On exit, the normalized matrix Z of eigenvectors if they were computed and the algorithm converged. Otherwise, the contents of A are destroyed.
[in]	lda	- rocblas_int. lda >= n. Specifies the leading dimension of matrix A.
[in,out]	B	- pointer to type. Array on the GPU of dimension ldb*n. On entry, the symmetric positive definite matrix B. On exit, the triangular factor of B as returned by POTRF.
[in]	ldb	- rocblas_int. ldb >= n. Specifies the leading dimension of matrix B.
[out]	D	- pointer to type. Array on the GPU of dimension n. The eigenvalues in increasing order.
[out]	myInfo	- pointer to a rocblas_int on the GPU. If info = 0, successful exit. If info = 1, the algorithm did not converge. If info = n + i, the leading minor of order i of B is not positive definite.

Member Function/Subroutine Documentation