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
◆ rocsolver_chegvd_batched_()
integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_chegvd_batched::rocsolver_chegvd_batched_ | ( | type(c_ptr), value | handle, |
integer(kind(rocblas_eform_ax)), value | itype, | ||
integer(kind(rocblas_evect_original)), value | evect, | ||
integer(kind(rocblas_fill_upper)), value | uplo, | ||
integer(c_int), value | n, | ||
type(c_ptr) | A, | ||
integer(c_int), value | lda, | ||
type(c_ptr) | B, | ||
integer(c_int), value | ldb, | ||
type(c_ptr), value | D, | ||
integer(c_int64_t), value | strideD, | ||
type(c_ptr), value | E, | ||
integer(c_int64_t), value | strideE, | ||
integer(c_int) | myInfo, | ||
integer(c_int), value | batch_count | ||
) |
◆ rocsolver_chegvd_batched_full_rank()
integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_chegvd_batched::rocsolver_chegvd_batched_full_rank | ( | type(c_ptr) | handle, |
integer(kind(rocblas_eform_ax)) | itype, | ||
integer(kind(rocblas_evect_original)) | evect, | ||
integer(kind(rocblas_fill_upper)) | uplo, | ||
integer(c_int) | n, | ||
complex(c_float_complex), dimension(:,:,:), target | A, | ||
integer(c_int) | lda, | ||
complex(c_float_complex), dimension(:,:,:), target | B, | ||
integer(c_int) | ldb, | ||
real(c_float), dimension(:), target | D, | ||
integer(c_int64_t) | strideD, | ||
real(c_float), dimension(:), target | E, | ||
integer(c_int64_t) | strideE, | ||
integer(c_int) | myInfo, | ||
integer(c_int) | batch_count | ||
) |
◆ rocsolver_chegvd_batched_rank_0()
integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_chegvd_batched::rocsolver_chegvd_batched_rank_0 | ( | type(c_ptr) | handle, |
integer(kind(rocblas_eform_ax)) | itype, | ||
integer(kind(rocblas_evect_original)) | evect, | ||
integer(kind(rocblas_fill_upper)) | uplo, | ||
integer(c_int) | n, | ||
complex(c_float_complex), target | A, | ||
integer(c_int) | lda, | ||
complex(c_float_complex), target | B, | ||
integer(c_int) | ldb, | ||
real(c_float), target | D, | ||
integer(c_int64_t) | strideD, | ||
real(c_float), target | E, | ||
integer(c_int64_t) | strideE, | ||
integer(c_int) | myInfo, | ||
integer(c_int) | batch_count | ||
) |
◆ rocsolver_chegvd_batched_rank_1()
integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_chegvd_batched::rocsolver_chegvd_batched_rank_1 | ( | type(c_ptr) | handle, |
integer(kind(rocblas_eform_ax)) | itype, | ||
integer(kind(rocblas_evect_original)) | evect, | ||
integer(kind(rocblas_fill_upper)) | uplo, | ||
integer(c_int) | n, | ||
complex(c_float_complex), dimension(:), target | A, | ||
integer(c_int) | lda, | ||
complex(c_float_complex), dimension(:), target | B, | ||
integer(c_int) | ldb, | ||
real(c_float), dimension(:), target | D, | ||
integer(c_int64_t) | strideD, | ||
real(c_float), dimension(:), target | E, | ||
integer(c_int64_t) | strideE, | ||
integer(c_int) | myInfo, | ||
integer(c_int) | batch_count | ||
) |
The documentation for this interface was generated from the following file: