rocsolver_chegvd_batched Interface Reference

rocsolver_chegvd_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_chegvd_batched Interface 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]handlerocblas_handle.
[in]ityperocblas_eform.
Specifies the form of the generalized eigenproblems.
[in]evectrocblas_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]uplorocblas_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]nrocblas_int. n >= 0.
The matrix dimensions.
[in,out]Aarray 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]ldarocblas_int. lda >= n.
Specifies the leading dimension of A_i.
[out]Barray 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]ldbrocblas_int. ldb >= n.
Specifies the leading dimension of B_i.
[out]Dpointer to real type. Array on the GPU (the size depends on the value of strideD).
On exit, the eigenvalues in increasing order.
[in]strideDrocblas_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]Epointer 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]strideErocblas_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]infopointer 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_countrocblas_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: