naginterfaces.library.blas.zgemm

naginterfaces.library.blas.zgemm(transa, transb, m, k, alpha, a, b, beta, c=None)

zgemm performs one of the matrix-matrix operations

$$\begin{array}{c}\begin{array}{ccc}C\leftarrow \alpha AB+\beta C\text{,}& C\leftarrow \alpha A^{T}B+\beta C\text{,}& C\leftarrow \alpha A^{H}B+\beta C\text{,}\\ C\leftarrow \alpha A{B}^T+\beta C\text{,}& C\leftarrow \alpha A^T{B}^T+\beta C\text{,}& C\leftarrow \alpha A^H{B}^T+\beta C\text{,}\\ C\leftarrow \alpha A{B}^H+\beta C\text{,}& C\leftarrow \alpha A^T{B}^H+\beta C\text{or}& C\leftarrow \alpha A^H{B}^H+\beta C\text{,}\end{array}\end{array}$$

where $A$, $B$ and $C$ are complex matrices, and $\alpha$ and $\beta$ are complex scalars; $C$ is always $m\times n$.

For full information please refer to the NAG Library document for f06za

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f06/f06zaf.html

Parameters

transastr, length 1

Specifies whether the operation involves $A$, $A^T$ or $A^H$.

$transa=\text{'N'}$

The operation involves $A$.

$transa=\text{'T'}$

The operation involves $A^T$.

$transa=\text{'C'}$

The operation involves $A^H$.

transbstr, length 1

Specifies whether the operation involves $B$, $B^T$ or $B^H$.

$transb=\text{'N'}$

The operation involves $B$.

$transb=\text{'T'}$

The operation involves $B^T$.

$transb=\text{'C'}$

The operation involves $B^H$.

mint

$m$, the number of rows of the matrix $C$; the number of rows of $A$ if $transa=\text{'N'}$, or the number of columns of $A$ if $transa=\text{'T'}$ or $\text{'C'}$.

kint

$k$, the number of columns of $A$ if $transa=\text{'N'}$, or the number of rows of $A$ if $transa=\text{'T'}$ or $\text{'C'}$; the number of rows of $B$ if $transb=\text{'N'}$, or the number of columns of $B$ if $transb=\text{'T'}$ or $\text{'C'}$.

alphacomplex

The scalar $\alpha$.

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

Note: the required extent for this argument in dimension 1 is determined as follows: if $transa=\text{'N'}$: $m$; if $transa\text{in}(\text{'T'},\text{'C'})$: $k$; otherwise: $0$.

Note: the required extent for this argument in dimension 2 is determined as follows: if $transa=\text{'N'}$: $k$; if $transa\text{in}(\text{'T'},\text{'C'})$: $m$; otherwise: $0$.

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

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

Note: the required extent for this argument in dimension 1 is determined as follows: if $transb=\text{'N'}$: $k$; if $transb\text{in}(\text{'T'},\text{'C'})$: $n$; otherwise: $0$.

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

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

betacomplex

The scalar $\beta$.

cNone or complex, array-like, shape $(m,n)$, optional

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

If $beta=0.0$, $c$ need not be set.

Returns

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

The updated matrix $C$.

Raises

NagValueError

(errno $1$)

On entry, error in parameter $transa$.

Constraint: $transa=\text{'N'}$, $\text{'T'}$ or $\text{'C'}$.

(errno $2$)

On entry, error in parameter $transb$.

Constraint: $transb=\text{'N'}$, $\text{'T'}$ or $\text{'C'}$.

(errno $3$)

On entry, error in parameter $m$.

Constraint: $m\ge 0$.

(errno $4$)

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

Constraint: $n\ge 0$.

(errno $5$)

On entry, error in parameter $k$.

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.