rocsolver_chegvd_batched Interface Reference

rocsolver_chegvd_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_chegvd_batched Interface Reference

HEGVD_BATCHED computes 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_full_rank (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

HEGVD_BATCHED computes 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

\[ \begin{array}{cl} A_i X_i = \lambda B_i X_i & \: \text{1st form,}\newline A_i B_i X_i = \lambda X_i & \: \text{2nd form, or}\newline B_i A_i X_i = \lambda X_i & \: \text{3rd form,} \end{array} \]

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 \(Z_i\) of eigenvectors is normalized as follows:

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

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_i and B_i are stored. If uplo indicates lower (or upper), then the upper (or lower) parts of A_i and B_i 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_i. On exit, if evect is original, the normalized matrix Z_i of eigenvectors. If evect is none, then the upper or lower triangular part of the matrices A_i (including the diagonal) are destroyed, depending on the value of uplo.
[in]	lda	rocblas_int. lda >= n. Specifies the leading dimension of A_i.
[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_i. On exit, the triangular factor of B_i as returned by POTRF_BATCHED.
[in]	ldb	rocblas_int. ldb >= n. Specifies the leading dimension of B_i.
[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_i to the next one D_(i+1). There is no restriction for the value of strideD. Normal use 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_i associated with the ith reduced eigenvalue problem. On exit, if 0 < info[i] <= n, it contains the unconverged off-diagonal elements of T_i (or properly speaking, a tridiagonal matrix equivalent to T_i). The diagonal elements of this matrix are in D_i; 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_i to the next one E_(i+1). There is no restriction for the value of strideE. Normal use is strideE >= n.
[out]	info	pointer to rocblas_int. Array of batch_count integers on the GPU. If info[i] = 0, successful exit of batch i. If info[i] = j <= n and evect is rocblas_evect_none, j off-diagonal elements of an intermediate tridiagonal form did not converge to zero. If info[i] = j <= n and evect is rocblas_evect_original, the algorithm failed to compute an eigenvalue in the submatrix from [j/(n+1), j/(n+1)] to [j%(n+1), j%(n+1)]. If info[i] = n + j, the leading minor of order j of B_i is not positive definite.
[in]	batch_count	rocblas_int. batch_count >= 0. Number of matrices in the batch.

Member Function/Subroutine Documentation