rocsolver_chegvd_batched Interface Reference

rocsolver_chegvd_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_chegvd_batched Interface Reference

The HEGVD_BATCHED functions compute the eigenvalues and (optionally) eigenvectors of a batch of complex generalized Hermitian-definite eigenproblems. More...

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

integer(kind(rocblas_status_success)) function	rocsolver_chegvd_batched_rank_0 (handle, itype, evect, uplo, n, a, lda, b, ldb, d, strided, e, stridee, myinfo, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_chegvd_batched_rank_1 (handle, itype, evect, uplo, n, a, lda, b, ldb, d, strided, e, stridee, myinfo, batch_count)

Detailed Description

The HEGVD_BATCHED functions compute the eigenvalues and (optionally) eigenvectors of a batch of complex generalized Hermitian-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 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:

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

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]	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. The matrix dimensions.
[in,out]	A	- array of pointers to type. Each pointer points to an array on the GPU of dimension lda*n. On entry, the Hermitian matrices A_l. On exit, if evect is original, the normalized matrix Z_l of eigenvectors. If evect is none, then the upper or lower triangular part of the matrices A_l (including the diagonal) are destroyed, depending on the value of uplo.
[in]	lda	- rocblas_int. lda >= n. Specifies the leading dimension of A_l.
[out]	B	- array of pointers to type. Each pointer points to an array on the GPU of dimension ldb*n. On entry, the Hermitian 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 B_l.
[out]	D	- pointer to real type. Array on the GPU (the size depends on the value of strideD). On exit, 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]	E	- pointer to real type. Array on the GPU (the size depends on the value of strideE). This array is used to work internally with the tridiagonal matrix T_l associated with the l-th reduced eigenvalue problem. On exit, if 0 < info[l] <= n, it contains the unconverged off-diagonal elements of T_l (or properly speaking, a tridiagonal matrix equivalent to T_l). The diagonal elements of this matrix are in D_l. Those that converged correspond to a subset of the eigenvalues (not necessarily ordered).
[in]	strideE	- rocblas_stride. Stride from the start of one vector E_l to the next one E_(l+1). There is no restriction for the value of strideE. Normal usage is strideE >= n.
[out]	myInfo	- pointer to rocblas_int. Array of batch_count integers on the GPU. If info[l] = 0, successful exit of batch l. If info[l] = i <= n and evect is rocblas_evect_none, i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. If info[l] = 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[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 matrices in the batch.

Member Function/Subroutine Documentation