naginterfaces.library.blas.dutr1

naginterfaces.library.blas.dutr1(alpha, x, y, a)[source]

dutr1 performs a factorization (as a sequence of plane rotations) of a real upper triangular matrix that has been modified by a rank-1 update.

For full information please refer to the NAG Library document for f06qp

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f06/f06qpf.html

Parameters
alphafloat

The scalar .

xfloat, array-like, shape

The -element vector .

yfloat, array-like, shape

The -element vector .

afloat, array-like, shape

The upper triangular matrix .

Returns
xfloat, ndarray, shape

The referenced elements are overwritten by details of the sequence of plane rotations.

afloat, ndarray, shape

The upper triangular matrix .

cfloat, ndarray, shape

The cosines of the rotations , for .

sfloat, ndarray, shape

The sines of the rotations , for .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(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.

dutr1 performs a factorization of an upper triangular matrix which has been modified by a rank-1 update:

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

is formed as the product of two sequences of plane rotations:

where

is a rotation in the plane, chosen to annihilate : thus , where and is the last column of the unit matrix;

is a rotation in the plane, chosen to annihilate the element of , and thus restore it to upper triangular form.

The plane rotation part of or has the form

The tangents of the rotations are returned in the array ; the cosines and sines of these rotations can be recovered by calling dcsg(). The cosines and sines of the rotations are returned directly in the arrays and .