rocsolver_ssygvd Interface Reference

rocsolver_ssygvd Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_ssygvd Interface Reference

The SYGVD 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_ssygvd_ (handle, itype, evect, uplo, n, a, lda, b, ldb, d, e, myinfo)

integer(kind(rocblas_status_success)) function	rocsolver_ssygvd_rank_0 (handle, itype, evect, uplo, n, a, lda, b, ldb, d, e, myinfo)

integer(kind(rocblas_status_success)) function	rocsolver_ssygvd_rank_1 (handle, itype, evect, uplo, n, a, lda, b, ldb, d, e, myinfo)

integer(kind(rocblas_status_success)) function	rocsolver_ssygvd_full_rank (handle, itype, evect, uplo, n, a, lda, b, ldb, d, e, myinfo)

Detailed Description

The SYGVD 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 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. The matrix dimensions.
[in,out]	A	- pointer to type. Array on the GPU of dimension lda*n. On entry, the symmetric matrix A. On exit, if evect is original, the normalized matrix Z of eigenvectors. If evect is none, then the upper or lower triangular part of the matrix A (including the diagonal) is destroyed, depending on the value of uplo.
[in]	lda	- rocblas_int. lda >= n. Specifies the leading dimension of A.
[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 B.
[out]	D	- pointer to type. Array on the GPU of dimension n. On exit, the eigenvalues in increasing order.
[out]	E	- pointer to type. Array on the GPU of dimension n. This array is used to work internally with the tridiagonal matrix T associated with the reduced eigenvalue problem. On exit, if 0 < info <= n, it contains the unconverged off-diagonal elements of T (or properly speaking, a tridiagonal matrix equivalent to T). The diagonal elements of this matrix are in D. Those that converged correspond to a subset of the eigenvalues (not necessarily ordered).
[out]	myInfo	- pointer to a rocblas_int on the GPU. If info = 0, successful exit. If info = i <= n and evect is rocblas_evect_none, i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. If info = i <= n and evect is rocblas_evect_original, the algorithm failed to compute an eigenvalue in the submatrix from [i/(n+1), i/(n+1)] to [i%(n+1), i%(n+1)]. If info = n + i, the leading minor of order i of B is not positive definite.

Member Function/Subroutine Documentation