naginterfaces.library.blas.zhpr2

naginterfaces.library.blas.zhpr2(uplo, alpha, x, y, ap)

zhpr2 computes the rank-2 update of a complex Hermitian matrix stored in packed form.

For full information please refer to the NAG Library document for f06ss

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f06/f06ssf.html

Parameters

uplostr, length 1

Specifies whether the upper or lower triangular part of $A$ is stored.

$uplo=\text{'U'}$

The upper triangular part of $A$ is stored.

$uplo=\text{'L'}$

The lower triangular part of $A$ is stored.

alphacomplex

The scalar $\alpha$.

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

The $n$-element vector $x$.

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

The $n$-element vector $y$.

apcomplex, array-like, shape $(n\times (n+1)/2)$

The $n\times n$ Hermitian matrix $A$, packed by columns.

Returns

apcomplex, ndarray, shape $(n\times (n+1)/2)$

The updated matrix $A$. The imaginary parts of the diagonal elements are set to zero.

Raises

NagValueError

(errno $1$)

On entry, error in parameter $uplo$.

Constraint: $uplo=\text{'U'}$ or $\text{'L'}$.

(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.

zhpr2 performs the Hermitian rank-2 update operation

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

where $A$ is an $n\times n$ complex Hermitian matrix, stored in packed form, $x$ and $y$ are $n$-element complex vectors, and $\alpha$ is a complex scalar.