naginterfaces.library.blas.zusqr¶
- naginterfaces.library.blas.zusqr(side, k1, k2, s, a)[source]¶
zusqr
performs a or factorization (as a sequence of plane rotations) of a complex upper spiked matrix.For full information please refer to the NAG Library document for f06ts
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f06/f06tsf.html
- Parameters
- sidestr, length 1
Specifies whether is operated on from the left or the right.
is pre-multiplied from the left.
is post-multiplied from the right.
- k1int
The value .
- k2int
The value .
- scomplex, array-like, shape
The nonzero elements of the spike of : must hold if , and if , for .
- acomplex, array-like, shape
The upper triangular part of the upper spiked matrix . The imaginary parts of the diagonal elements must be zero, except for the element if , or the element if .
- Returns
- cfloat, ndarray, shape
holds , the cosine of the rotation , for .
- scomplex, ndarray, shape
holds , the sine of the rotation , for ; holds , the th diagonal element of , if , or , the th diagonal element of , if .
- acomplex, ndarray, shape
The upper triangular matrix . The imaginary parts of the diagonal elements are set to zero.
- Raises
- NagValueError
- (errno )
On entry, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: .
- Notes
No equivalent traditional C interface for this routine exists in the NAG Library.
zusqr
transforms an complex upper spiked matrix to upper triangular form by applying a complex unitary matrix from the left or the right. is assumed to have real diagonal elements except where the spike joins the diagonal; has real diagonal elements. is formed as a sequence of plane rotations in planes to .If , is assumed to have a row spike, with nonzero elements , for . The rotations are applied from the left:
where , is a rotation in the plane and with .
If , is assumed to have a column spike, with nonzero elements , for . The rotations are applied from the right:
where , is a rotation in the plane and with .
The plane rotation part of has the form
with real.