naginterfaces.library.lapackeig.zhbevd¶
- naginterfaces.library.lapackeig.zhbevd(job, uplo, kd, ab)[source]¶
zhbevd
computes all the eigenvalues and, optionally, all the eigenvectors of a complex Hermitian band matrix. If the eigenvectors are requested, then it uses a divide-and-conquer algorithm to compute eigenvalues and eigenvectors. However, if only eigenvalues are required, then it uses the Pal–Walker–Kahan variant of the or algorithm.For full information please refer to the NAG Library document for f08hq
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f08/f08hqf.html
- Parameters
- jobstr, length 1
Indicates whether eigenvectors are computed.
Only eigenvalues are computed.
Eigenvalues and eigenvectors are computed.
- uplostr, length 1
Indicates whether the upper or lower triangular part of is stored.
The upper triangular part of is stored.
The lower triangular part of is stored.
- kdint
If , the number of superdiagonals, , of the matrix .
If , the number of subdiagonals, , of the matrix .
- abcomplex, array-like, shape
The upper or lower triangle of the Hermitian band matrix .
- Returns
- abcomplex, ndarray, shape
is overwritten by values generated during the reduction to tridiagonal form.
The first superdiagonal or subdiagonal and the diagonal of the tridiagonal matrix are returned in using the same storage format as described above.
- wfloat, ndarray, shape
The eigenvalues of the matrix in ascending order.
- zcomplex, ndarray, shape
If , is overwritten by the unitary matrix which contains the eigenvectors of . The th column of contains the eigenvector which corresponds to the eigenvalue .
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 )
On entry, error in parameter .
Constraint: .
- (errno )
If and , the algorithm failed to converge; elements of an intermediate tridiagonal form did not converge to zero; if and , then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and column through .
- Notes
zhbevd
computes all the eigenvalues and, optionally, all the eigenvectors of a complex Hermitian band matrix . In other words, it can compute the spectral factorization of aswhere is a real diagonal matrix whose diagonal elements are the eigenvalues , and is the (complex) unitary matrix whose columns are the eigenvectors . Thus
- 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