naginterfaces.library.lapackeig.zunghr

naginterfaces.library.lapackeig.zunghr(ilo, ihi, a, tau)[source]

zunghr generates the complex unitary matrix which was determined by zgehrd() 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 to zgehrd(), 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 by zgebal() 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