naginterfaces.library.blas.zsgesr

naginterfaces.library.blas.zsgesr(side, pivot, direct, m, k1, k2, c, s, a)

zsgesr applies to a complex rectangular matrix a sequence of plane rotations having real cosines and complex sines.

For full information please refer to the NAG Library document for f06vx

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f06/f06vxf.html

Parameters

sidestr, length 1

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

$side=\text{'L'}$

$A$ is pre-multiplied from the left.

$side=\text{'R'}$

$A$ is post-multiplied from the right.

pivotstr, length 1

Specifies the plane rotated by $P_k$.

$pivot=\text{'V'}$ (variable pivot)

$P_k$ rotates the $(k,k+1)$ plane.

$pivot=\text{'T'}$ (top pivot)

$P_k$ rotates the $(k_1,k+1)$ plane.

$pivot=\text{'B'}$ (bottom pivot)

$P_k$ rotates the $(k,k_2)$ plane.

directstr, length 1

Specifies the sequence direction.

$direct=\text{'F'}$ (forward sequence)

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

$direct=\text{'B'}$ (backward sequence)

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

mint

$m$, the number of rows of the matrix $A$.

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 $\text{k}={\text{k}}_1,\dots ,{\text{k}}_2-1$.

acomplex, array-like, shape $(m,n)$

The $m\times n$ matrix $A$.

Returns

acomplex, ndarray, shape $(m,n)$

The transformed matrix $A$.

Raises

NagValueError

(errno $1$)

On entry, error in parameter $side$.

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

(errno $2$)

On entry, error in parameter $pivot$.

Constraint: $pivot=\text{'V'}$, $\text{'T'}$ or $\text{'B'}$.

(errno $3$)

On entry, error in parameter $direct$.

Constraint: $direct=\text{'F'}$ or $\text{'B'}$.

(errno $4$)

On entry, error in parameter $m$.

Constraint: $m\ge 0$.

(errno $5$)

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.

zsgesr performs the transformation

$$A\leftarrow PA\text{or}A\leftarrow A{P}^H\text{,}$$

where $A$ is an $m\times n$ complex matrix and $P$ is a real orthogonal matrix, defined as a sequence of real plane rotations, $P_k$, applied in planes $k_1$ to $k_2$.

The $2\times 2$ plane rotation part of $P_k$ is assumed to have the form

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

with $c_k$ and $s_k$ real.