naginterfaces.library.lapackeig.zunghr¶
- naginterfaces.library.lapackeig.zunghr(ilo, ihi, a, tau)[source]¶
zunghr
generates the complex unitary matrix which was determined byzgehrd()
when reducing a complex general matrix to Hessenberg form.For full information please refer to the NAG Library document for f08nt
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f08/f08ntf.html
- Parameters
- iloint
These must be the same arguments and , respectively, as supplied to
zgehrd()
.- ihiint
These must be the same arguments and , respectively, as supplied to
zgehrd()
.- acomplex, array-like, shape
Details of the vectors which define the elementary reflectors, as returned by
zgehrd()
.- taucomplex, array-like, shape
Further details of the elementary reflectors, as returned by
zgehrd()
.
- Returns
- acomplex, ndarray, shape
The unitary matrix .
- Raises
- NagValueError
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
- (errno )
On entry, error in parameter .
- Notes
zunghr
is intended to be used following a call tozgehrd()
, which reduces a complex general matrix to upper Hessenberg form by a unitary similarity transformation: .zgehrd()
represents the matrix as a product of elementary reflectors. Here and are values determined byzgebal()
when balancing the matrix; if the matrix has not been balanced, and .This function may be used to generate explicitly as a square matrix. has the structure:
where occupies rows and columns to .
- References
Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore