naginterfaces.library.blas.dutupd

naginterfaces.library.blas.dutupd(alpha, x, a)[source]

dutupd performs a factorization (as a sequence of plane rotations) of a real upper triangular matrix that has been augmented by a full row.

For full information please refer to the NAG Library document for f06qq

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f06/f06qqf.html

Parameters
alphafloat

The scalar .

xfloat, array-like, shape

The vector .

afloat, array-like, shape

The upper triangular matrix .

Returns
xfloat, ndarray, shape

The referenced elements are overwritten by the tangents of the rotations , for .

afloat, ndarray, shape

The upper triangular matrix .

cfloat, ndarray, shape

The values , the cosines of the rotations , for .

sfloat, ndarray, shape

The values , the sines of the rotations , for .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

dutupd performs the factorization

where and are real upper triangular matrices, is an -element real vector, is a real scalar, and is a real orthogonal matrix.

is formed as a sequence of plane rotations

where is a rotation in the plane, chosen to annihilate .

The plane rotation part of has the form