rocsolver_chegvx_batched Interface Reference

rocsolver_chegvx_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_chegvx_batched Interface Reference

The HEGVX_BATCHED functions compute a set of the eigenvalues and optionally the corresponding eigenvectors of a batch of complex generalized Hermitian-definite eigenproblems. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_chegvx_batched_ (handle, itype, evect, erange, uplo, n, a, lda, b, ldb, vl, vu, il, iu, abstol, nev, w, stridew, z, ldz, ifail, stridef, myinfo, batch_count)

Detailed Description

The HEGVX_BATCHED functions compute a set of the eigenvalues and optionally the corresponding 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 depending on the value of evect.

When computed, the matrix \(Z_l\) of eigenvectors is normalized as follows:

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

This function computes all the eigenvalues, all the eigenvalues in the half-open interval \((vl, vu]\), or the il -th through iu -th eigenvalues, depending on the value of erange. If evect is rocblas_evect_original, the eigenvectors for these eigenvalues will be computed as well.

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]	erange	- `rocblas_erange`. Specifies the type of range or interval of the eigenvalues to be computed.
[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 matrices A_l. On exit, the contents of A_l are destroyed.
[in]	lda	- rocblas_int. lda >= n. Specifies the leading dimension of matrices 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.
[in]	vl	- real type. vl < vu. The lower bound of the search interval (vl, vu]. Ignored if range indicates to look for all the eigenvalues of A_l or the eigenvalues within a set of indices.
[in]	vu	- real type. vl < vu. The upper bound of the search interval (vl, vu]. Ignored if range indicates to look for all the eigenvalues of A_l or the eigenvalues within a set of indices.
[in]	il	- rocblas_int. il = 1 if n = 0, and 1 <= il <= iu otherwise. The index of the smallest eigenvalue to be computed. Ignored if range indicates to look for all the eigenvalues of A_l or the eigenvalues in a half-open interval.
[in]	iu	- rocblas_int. iu = 0 if n = 0, and 1 <= il <= iu otherwise. The index of the largest eigenvalue to be computed. Ignored if range indicates to look for all the eigenvalues of A_l or the eigenvalues in a half-open interval.
[in]	abstol	- real type. The absolute tolerance. An eigenvalue is considered to be located if it lies in an interval whose width is <= abstol. If abstol is negative, then machine-epsilon times the 1-norm of the tridiagonal form of A_l will be used as the tolerance. If abstol=0, then the tolerance will be set to twice the underflow threshold. This is the tolerance that could get the most accurate results.
[out]	nev	- pointer to rocblas_int. Array of batch_count integers on the GPU. The total number of eigenvalues found. If erange is rocblas_erange_all, nev[l] = n. If erange is rocblas_erange_index, nev[l] = iu - il + 1. Otherwise, 0 <= nev[l] <= n.
[out]	W	- pointer to real type. Array on the GPU (the size depends on the value of strideW). The first nev[l] elements contain the computed eigenvalues. (The remaining elements can be used as workspace for internal computations.)
[in]	strideW	- rocblas_stride. Stride from the start of one vector W_l to the next one W_(l+1). There is no restriction for the value of strideW. The normal use case is strideW >= n.
[out]	Z	- Array of pointers to type. Each pointer points to an array on the GPU of dimension ldz*nev[l]. On exit, if evect is not rocblas_evect_none and info[l] = 0, the first nev[l] columns contain the eigenvectors of A_l corresponding to the output eigenvalues. Not referenced if evect is rocblas_evect_none. Note: If erange is rocblas_range_value, then the values of nev[l] are not known in advance. The user should ensure that Z_l is large enough to hold n columns, as all n columns can be used as workspace for internal computations.
[in]	ldz	- rocblas_int. ldz >= n. Specifies the leading dimension of matrices Z_l.
[out]	ifail	- pointer to rocblas_int. Array on the GPU (the size depends on the value of strideF). If info[l] = 0, the first nev[l] elements of ifail_l are zero. If info[l] = i <= n, ifail_l contains the indices of the i eigenvectors that failed to converge. Not referenced if evect is rocblas_evect_none.
[in]	strideF	- rocblas_stride. Stride from the start of one vector ifail_l to the next one ifail_(l+1). There is no restriction for the value of strideF. The normal use case is strideF >= n.
[out]	myInfo	- pointer to rocblas_int. Array of batch_count integers on the GPU. If info[l] = 0, successful exit of batch instance l. If info[l] = i <= n, i columns of Z_l did not converge. 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.

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