naginterfaces.library.blas.zgerc

naginterfaces.library.blas.zgerc(alpha, x, y, a)

zgerc computes the rank-1 update of a complex general matrix using a conjugated vector.

For full information please refer to the NAG Library document for f06sn

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/f06/f06snf.html

Parameters

alphacomplex

The scalar $\alpha$.

xcomplex, array-like, shape $\left(m\right)$

The $m$ element vector $x$.

Intermediate elements of X are not referenced.

ycomplex, array-like, shape $\left(n\right)$

The $n$-element vector $y$.

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

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

Returns

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

The updated matrix $A$.

Raises

NagValueError

(errno $1$)

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

Constraint: $m\ge 0$.

(errno $2$)

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

Constraint: $n\ge 0$.

(errno $5$)

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

Constraint: $\text{incx}\ne 0$.

(errno $7$)

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

Constraint: $\text{incy}\ne 0$.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

zgerc performs the rank-1 update operation

$$A\leftarrow \alpha x{y}^H+A\text{,}$$

where $A$ is an $m\times n$ complex matrix, $x$ is an $m$ element complex vector, $y$ is an $n$-element complex vector, and $\alpha$ is a complex scalar.