naginterfaces.library.lapackeig.dorghr

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

dorghr generates the real orthogonal matrix which was determined by dgehrd() when reducing a real general matrix to Hessenberg form.

For full information please refer to the NAG Library document for f08nf

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/f08/f08nff.html

Parameters
iloint

These must be the same arguments and , respectively, as supplied to dgehrd().

ihiint

These must be the same arguments and , respectively, as supplied to dgehrd().

afloat, array-like, shape

Details of the vectors which define the elementary reflectors, as returned by dgehrd().

taufloat, array-like, shape

Further details of the elementary reflectors, as returned by dgehrd().

Returns
afloat, ndarray, shape

The orthogonal matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

(errno )

On entry, error in parameter .

Notes

dorghr is intended to be used following a call to dgehrd(), which reduces a real general matrix to upper Hessenberg form by an orthogonal similarity transformation: . dgehrd() represents the matrix as a product of elementary reflectors. Here and are values determined by dgebal() 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