naginterfaces.library.lapackeig.dtzrzf

naginterfaces.library.lapackeig.dtzrzf(a)[source]

dtzrzf reduces the () real upper trapezoidal matrix to upper triangular form by means of orthogonal transformations.

For full information please refer to the NAG Library document for f08bh

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f08/f08bhf.html

Parameters
afloat, array-like, shape

The leading upper trapezoidal part of the array must contain the matrix to be factorized.

Returns
afloat, ndarray, shape

The leading upper triangular part of contains the upper triangular matrix , and elements to of the first rows of , with the array , represent the orthogonal matrix as a product of elementary reflectors (see the F08 Introduction).

taufloat, ndarray, shape

The scalar factors of the elementary reflectors.

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

The () real upper trapezoidal matrix given by

where is an upper triangular matrix and is an matrix, is factorized as

where is also an upper triangular matrix and is an orthogonal matrix.

References

Anderson, E, Bai, Z, Bischof, C, Blackford, S, Demmel, J, Dongarra, J J, Du Croz, J J, Greenbaum, A, Hammarling, S, McKenney, A and Sorensen, D, 1999, LAPACK Users’ Guide, (3rd Edition), SIAM, Philadelphia, https://www.netlib.org/lapack/lug