naginterfaces.library.blas.zsyrk

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

zsyrk performs one of the symmetric rank-$k$ update operations

$$C\leftarrow \alpha A{A}^T+\beta C\text{or}C\leftarrow \alpha A^{T}A+\beta C\text{,}$$

where $A$ is a complex matrix, $C$ is an $n\times n$ complex symmetric matrix, and $\alpha$ and $\beta$ are complex scalars.

For full information please refer to the NAG Library document for f06zu

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f06/f06zuf.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.

$trans=\text{'N'}$

$C\leftarrow \alpha A{A}^T+\beta C$.

$trans=\text{'T'}$

$C\leftarrow \alpha A^{T}A+\beta C$.

kint

$k$, the number of columns of $A$ and $B$ if $trans=\text{'N'}$, or the number of rows of $A$ and $B$ if $trans=\text{'T'}$.

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 $trans=\text{'T'}$: $k$; otherwise: $0$.

Note: the required extent for this argument in dimension 2 is determined as follows: if $trans=\text{'N'}$: $k$; if $trans=\text{'T'}$: $n$; otherwise: $0$.

The matrix $A$; $A$ is $n\times k$ if $trans=\text{'N'}$, or $k\times n$ if $trans=\text{'T'}$.

betacomplex

The scalar $\beta$.

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

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

Returns

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

The updated matrix $C$.

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 $\text{'T'}$.

(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.