naginterfaces.library.lapackeig.zupgtr¶
- naginterfaces.library.lapackeig.zupgtr(uplo, n, ap, tau)[source]¶
zupgtr
generates the complex unitary matrix , which was determined byzhptrd()
when reducing a Hermitian matrix to tridiagonal form.For full information please refer to the NAG Library document for f08gt
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f08/f08gtf.html
- Parameters
- uplostr, length 1
This must be the same argument as supplied to
zhptrd()
.- nint
, the order of the matrix .
- apcomplex, array-like, shape
Details of the vectors which define the elementary reflectors, as returned by
zhptrd()
.- taucomplex, array-like, shape
Further details of the elementary reflectors, as returned by
zhptrd()
.
- Returns
- qcomplex, ndarray, shape
The unitary matrix .
- Raises
- NagValueError
- (errno )
On entry, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: .
- Notes
zupgtr
is intended to be used after a call tozhptrd()
, which reduces a complex Hermitian matrix to real symmetric tridiagonal form by a unitary similarity transformation: .zhptrd()
represents the unitary matrix as a product of elementary reflectors.This function may be used to generate explicitly as a square matrix.
- References
Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore