naginterfaces.library.lapackeig.zhpev¶
- naginterfaces.library.lapackeig.zhpev(jobz, uplo, n, ap)[source]¶
zhpev
computes all the eigenvalues and, optionally, all the eigenvectors of a complex Hermitian matrix in packed storage.For full information please refer to the NAG Library document for f08gn
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f08/f08gnf.html
- Parameters
- jobzstr, length 1
Indicates whether eigenvectors are computed.
Only eigenvalues are computed.
Eigenvalues and eigenvectors are computed.
- uplostr, length 1
If , the upper triangular part of is stored.
If , the lower triangular part of is stored.
- nint
, the order of the matrix .
- apcomplex, array-like, shape
The upper or lower triangle of the Hermitian matrix , packed by columns.
- Returns
- apcomplex, ndarray, shape
is overwritten by the values generated during the reduction to tridiagonal form. The elements of the diagonal and the off-diagonal of the tridiagonal matrix overwrite the corresponding elements of .
- wfloat, ndarray, shape
The eigenvalues in ascending order.
- zcomplex, ndarray, shape
If , contains the orthonormal eigenvectors of the matrix , with the th column of holding the eigenvector associated with .
If , is not referenced.
- Raises
- NagValueError
- (errno )
On entry, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
The algorithm failed to converge; off-diagonal elements of an intermediate tridiagonal form did not converge to zero.
- Notes
The Hermitian matrix is first reduced to real tridiagonal form, using unitary similarity transformations, and then the algorithm is applied to the tridiagonal matrix to compute the eigenvalues and (optionally) the eigenvectors.
- References
Anderson, E, Bai, Z, Bischof, C, Blackford, S, Demmel, J, Dongarra, J J, Du Croz, J J, Greenbaum, A, Hammarling, S, McKenney, A and Sorensen, D, 1999, LAPACK Users’ Guide, (3rd Edition), SIAM, Philadelphia, https://www.netlib.org/lapack/lug
Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore