rocsolver_cheevj Interface Reference

rocsolver_cheevj Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_cheevj Interface Reference

The HEEVJ functions compute the eigenvalues and optionally the eigenvectors of a complex Hermitian matrix A. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_cheevj_ (handle, esort, evect, uplo, n, a, lda, abstol, residual, max_sweeps, n_sweeps, w, myinfo)

Detailed Description

The HEEVJ functions compute the eigenvalues and optionally the eigenvectors of a complex Hermitian matrix A.

The eigenvalues are found using the iterative Jacobi algorithm and returned in an order that depends on the value of esort. The eigenvectors are computed depending on the value of evect. The computed eigenvectors are orthonormal.

At the \(k\)-th iteration (or "sweep"), \(A\) is transformed by a product of Jacobi rotations \(V\) as

\[ A^{(k)} = V^H A^{(k-1)} V \]

such that \(off(A^{(k)}) < off(A^{(k-1)})\), where \(A^{(0)} = A\) and \(off(A^{(k)})\) is the Frobenius norm of the off-diagonal elements of \(A^{(k)}\). As \(off(A^{(k)}) \rightarrow 0\), the diagonal elements of \(A^{(k)}\) increasingly resemble the eigenvalues of \(A\).

Note: In order to carry out calculations, this method could potentially synchronize the stream contained within the rocblas_handle.

Parameters

[in]	handle	- rocblas_handle.
[in]	esort	- `rocblas_esort`. Specifies the order of the returned eigenvalues. If esort is rocblas_esort_ascending, then the eigenvalues are sorted and returned in ascending order. If esort is rocblas_esort_none, then the order of the returned eigenvalues is unspecified.
[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 part of the Hermitian matrix A is stored. If uplo indicates lower (or upper), then the upper (or lower) part of A is 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 eigenvectors of A if they were computed and the algorithm converged. Otherwise, the contents of A are unchanged.
[in]	lda	- rocblas_int. lda >= n. Specifies the leading dimension of matrix A.
[in]	abstol	- real type. The absolute tolerance. The algorithm is considered to have converged once off(A) is <= abstol. If abstol <= 0, then the tolerance will be set to machine precision.
[out]	residual	- pointer to real type on the GPU. The Frobenius norm of the off-diagonal elements of A (that is, off(A)) at the final iteration.
[in]	max_sweeps	- rocblas_int. max_sweeps > 0. Maximum number of sweeps (iterations) to be used by the algorithm.
[out]	n_sweeps	- pointer to a rocblas_int on the GPU. The actual number of sweeps (iterations) used by the algorithm.
[out]	W	- pointer to real type. Array on the GPU of dimension n. The eigenvalues of A 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.

Member Function/Subroutine Documentation