naginterfaces.library.lapackeig.zhpgst

naginterfaces.library.lapackeig.zhpgst(itype, uplo, n, ap, bp)[source]

zhpgst reduces a complex Hermitian-definite generalized eigenproblem , or to the standard form , where is a complex Hermitian matrix and has been factorized by lapacklin.zpptrf, using packed storage.

For full information please refer to the NAG Library document for f08ts

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/f08/f08tsf.html

Parameters
itypeint

Indicates how the standard form is computed.

if , ;

if , .

or

if , ;

if , .

uplostr, length 1

Indicates whether the upper or lower triangular part of is stored and how has been factorized.

The upper triangular part of is stored and .

The lower triangular part of is stored and .

nint

, the order of the matrices and .

apcomplex, array-like, shape

The upper or lower triangle of the Hermitian matrix , packed by columns.

bpcomplex, array-like, shape

The Cholesky factor of as specified by and returned by lapacklin.zpptrf.

Returns
apcomplex, ndarray, shape

The upper or lower triangle of is overwritten by the corresponding upper or lower triangle of as specified by and , using the same packed storage format as described above.

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: .

Notes

To reduce the complex Hermitian-definite generalized eigenproblem , or to the standard form using packed storage, zhpgst must be preceded by a call to lapacklin.zpptrf which computes the Cholesky factorization of ; must be positive definite.

The different problem types are specified by the argument , as indicated in the table below. The table shows how is computed by the function, and also how the eigenvectors of the original problem can be recovered from the eigenvectors of the standard form.

Problem

‘U’ ‘L’

‘U’ ‘L’

‘U’ ‘L’

References

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore