naginterfaces.library.blas.dutsrh

naginterfaces.library.blas.dutsrh(side, k1, k2, c, s, a)

dutsrh transforms a real upper triangular matrix to an upper Hessenberg matrix by applying a given sequence of plane rotations.

For full information please refer to the NAG Library document for f06qv

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/f06/f06qvf.html

Parameters

sidestr, length 1

Specifies whether $U$ is operated on from the left or the right.

$side=\text{'L'}$

$U$ is pre-multiplied from the left.

$side=\text{'R'}$

$U$ is post-multiplied from the right.

k1int

The value $k_1$.

k2int

The value $k_2$.

cfloat, array-like, shape $(k2-1)$

$c\left[\text{k}\right]$ must hold $c_{\text{k}}$, the cosine of the rotation $P_{\text{k}}$, for $\text{k}={\text{k}}_1,\dots ,{\text{k}}_2-1$.

sfloat, array-like, shape $(k2-1)$

$s\left[\text{k}\right]$ must hold $s_{\text{k}}$, the sine of the rotation $P_{\text{k}}$, for $\text{k}={\text{k}}_1,\dots ,{\text{k}}_2-1$.

afloat, array-like, shape $(n,n)$

The $n\times n$ upper triangular matrix $U$.

Returns

sfloat, ndarray, shape $(k2-1)$

$s\left[\text{k}\right]$ holds $h_{\text{k}+1,\text{k}}$, the subdiagonal element of $H$, for $\text{k}={\text{k}}_1,\dots ,{\text{k}}_2-1$.

afloat, ndarray, shape $(n,n)$

The upper triangular part of the upper Hessenberg matrix $H$.

Raises

NagValueError

(errno $1$)

On entry, error in parameter $side$.

Constraint: $side=\text{'L'}$ or $\text{'R'}$.

(errno $2$)

On entry, error in parameter $\text{n}$.

Constraint: $n\ge 0$.

Notes

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

dutsrh transforms an $n\times n$ real upper triangular matrix $U$ to an upper Hessenberg matrix $H$, by applying a given sequence of plane rotations from either the left or the right, in planes $k_1$ to $k_2$; $H$ has nonzero subdiagonal elements $h_{\text{k}+1,\text{k}}$, for $\text{k}={\text{k}}_1,\dots ,{\text{k}}_2-1$ only.

If $side=\text{'L'}$, the rotations are applied from the left:

$$H=PU\text{,}$$

where $P=P_{k_1}{P}_{k_1+1}\cdots P_{k_2-1}$.

If $side=\text{'R'}$, the rotations are applied from the right:

$$H=U{P}^T\text{,}$$

where $P=P_{k_2-1}\cdots P_{k_1+1}{P}_{k_1}$.

In either case, $P_k$ is a rotation in the $(k,k+1)$ plane.

The $2\times 2$ plane rotation part of $P_k$ has the form

$$\begin{array}{c}\left(\begin{array}{cc}{c}_k& s_k\\ -s_k& c_k\end{array}\right)\text{.}\end{array}$$