naginterfaces.library.blas.zher2k

naginterfaces.library.blas.zher2k(uplo, trans, k, alpha, a, b, beta, c)

zher2k performs one of the Hermitian rank-$2k$ update operations

$$C\leftarrow \alpha A{B}^H+\overline{\alpha }B{A}^H+\beta C\text{or}C\leftarrow \alpha A^{H}B+\overline{\alpha }{B}^{H}A+\beta C\text{,}$$

where $A$ and $B$ are complex matrices, $C$ is an $n\times n$ complex Hermitian matrix, $\alpha$ is a complex scalar, and $\beta$ is a real scalar.

For full information please refer to the NAG Library document for f06zr

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f06/f06zrf.html

Parameters

uplostr, length 1

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

$uplo=\text{'U'}$

The upper triangular part of $C$ is stored.

$uplo=\text{'L'}$

The lower triangular part of $C$ is stored.

transstr, length 1

Specifies the operation to be performed.

$trans=\text{'N'}$

$C\leftarrow \alpha A{B}^H+\overline{\alpha }B{A}^H+\beta C$.

$trans=\text{'C'}$

$C\leftarrow \alpha A^{H}B+\overline{\alpha }{B}^{H}A+\beta C$.

kint

$k$, the number of columns of $A$ if $trans=\text{'N'}$, or the number of rows of $A$ if $trans=\text{'C'}$.

alphacomplex

The scalar $\alpha$.

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

Note: the required extent for this argument in dimension 1 is determined as follows: if $trans=\text{'N'}$: $n$; if $trans=\text{'C'}$: $k$; otherwise: $0$.

Note: the required extent for this argument in dimension 2 is determined as follows: if $trans=\text{'N'}$: $k$; if $trans=\text{'C'}$: $n$; otherwise: $0$.

The matrix $A$; $A$ is $n\times k$ if $trans=\text{'N'}$, or $k\times n$ if $trans=\text{'C'}$.

bcomplex, array-like, shape $(:,:)$

Note: the required extent for this argument in dimension 1 is determined as follows: if $trans=\text{'N'}$: $n$; if $trans=\text{'C'}$: $k$; otherwise: $0$.

Note: the required extent for this argument in dimension 2 is determined as follows: if $trans=\text{'N'}$: $k$; if $trans=\text{'C'}$: $n$; otherwise: $0$.

The matrix $B$; $B$ is $n\times k$ if $trans=\text{'N'}$, or $k\times n$ if $trans=\text{'C'}$.

betafloat

The scalar $\beta$.

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

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

Returns

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

The updated matrix $C$. 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 $trans$.

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

(errno $3$)

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

Constraint: $n\ge 0$.

(errno $4$)

On entry, error in parameter $k$.

Constraint: $k\ge 0$.

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.