naginterfaces.library.lapackeig.zunmrz

naginterfaces.library.lapackeig.zunmrz(side, trans, l, a, tau, c)

zunmrz multiplies a general complex $m\times n$ matrix $C$ by the complex unitary matrix $Z$ from an $RZ$ factorization computed by ztzrzf().

For full information please refer to the NAG Library document for f08bx

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f08/f08bxf.html

Parameters

sidestr, length 1

Indicates how $Z$ or $Z^H$ is to be applied to $C$.

$side=\text{'L'}$

$Z$ or $Z^H$ is applied to $C$ from the left.

$side=\text{'R'}$

$Z$ or $Z^H$ is applied to $C$ from the right.

transstr, length 1

Indicates whether $Z$ or $Z^H$ is to be applied to $C$.

$trans=\text{'N'}$

$Z$ is applied to $C$.

$trans=\text{'C'}$

$Z^H$ is applied to $C$.

lint

$l$, the number of columns of the matrix $A$ containing the meaningful part of the Householder reflectors.

acomplex, array-like, shape $(k,:)$

Note: the required extent for this argument in dimension 2 is determined as follows: if $side=\text{'L'}$: $m$; if $side=\text{'R'}$: $n$; otherwise: $0$.

The $\text{i}$th row of $a$ must contain the vector which defines the elementary reflector $H_{\text{i}}$, for $\text{i}=1,2,\dots ,k$, as returned by ztzrzf().

taucomplex, array-like, shape $\left(k\right)$

$tau[i-1]$ must contain the scalar factor of the elementary reflector $H_i$, as returned by ztzrzf().

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

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

Returns

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

$c$ is overwritten by $ZC$ or $Z^{H}C$ or $CZ$ or $Z^{H}C$ as specified by $side$ and $trans$.

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $side$.

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

(errno $-2$)

On entry, error in parameter $trans$.

Constraint: $trans=\text{'N'}$ or $\text{'C'}$.

(errno $-3$)

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

Constraint: $m\ge 0$.

(errno $-4$)

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

Constraint: $n\ge 0$.

(errno $-5$)

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

Constraint: $m\ge k\ge 0$.

(errno $-5$)

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

Constraint: $n\ge k\ge 0$.

(errno $-6$)

On entry, error in parameter $l$.

Constraint: $m\ge l\ge 0$.

(errno $-6$)

On entry, error in parameter $l$.

Constraint: $n\ge l\ge 0$.

Notes

zunmrz is intended to be used following a call to ztzrzf(), which performs an $RZ$ factorization of a real upper trapezoidal matrix $A$ and represents the unitary matrix $Z$ as a product of elementary reflectors.

This function may be used to form one of the matrix products

$$ZC\text{,}{Z}^{H}C\text{,}CZ\text{,}C{Z}^H\text{,}$$

overwriting the result on $C$, which may be any complex rectangular $m\times n$ matrix.

References

Anderson, E, Bai, Z, Bischof, C, Blackford, S, Demmel, J, Dongarra, J J, Du Croz, J J, Greenbaum, A, Hammarling, S, McKenney, A and Sorensen, D, 1999, LAPACK Users’ Guide, (3rd Edition), SIAM, Philadelphia, https://www.netlib.org/lapack/lug