naginterfaces.library.blas.zutupd¶
- naginterfaces.library.blas.zutupd(alpha, x, a)[source]¶
zutupd
performs a factorization (as a sequence of plane rotations) of a complex upper triangular matrix that has been augmented by a full row.For full information please refer to the NAG Library document for f06tq
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f06/f06tqf.html
- Parameters
- alphacomplex
The scalar .
- xcomplex, array-like, shape
The -element vector .
- acomplex, array-like, shape
The upper triangular matrix .
- Returns
- xcomplex, ndarray, shape
The referenced elements are overwritten by details of the sequence of plane rotations.
- acomplex, ndarray, shape
The upper triangular matrix .
- cfloat, ndarray, shape
The values , the cosines of the rotations , for .
- scomplex, 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.
zutupd
performs the factorizationwhere and are complex upper triangular matrices, is an -element complex vector, is a complex scalar, and is a complex unitary matrix. If has real diagonal elements, then so does .
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
with real.