naginterfaces.library.matop.complex_​tri_​matmul

naginterfaces.library.matop.complex_tri_matmul(uplo, transa, transb, alpha, a, b, beta, c=None)

complex_tri_matmul 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 triangular matrices, and $\alpha$ and $\beta$ are complex scalars.

For full information please refer to the NAG Library document for f01dt

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f01/f01dtf.html

Parameters

uplostr, length 1

Specifies whether $C$ is upper or lower triangular.

$uplo=\text{'U'}$

$C$ is upper triangular.

$uplo=\text{'L'}$

$C$ is lower triangular.

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 $B^H$.

alphacomplex

The scalar $\alpha$.

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

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

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

The $n\times n$ triangular matrix $B$.

betacomplex

The scalar $\beta$.

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

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

If $beta=0$, $c$ need not be set and may be None.

Returns

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

The triangular part of $C$, as specified by $uplo$, is updated.

Raises

NagValueError

(errno $1$)

On entry, $uplo=⟨value⟩$.

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

(errno $2$)

On entry, $transa=⟨value⟩$.

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

(errno $3$)

On entry, $transb=⟨value⟩$.

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

(errno $4$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

Notes

complex_tri_matmul computes the triangular matrix product $C=\alpha op\left(A\right)op\left(B\right)+\beta C$, where $op\left(A\right)$, $op\left(B\right)$, and $C$ are all upper triangular or all lower triangular matrices, and where $op\left(A\right)$ is either $A$, $A^T$, or $A^H$.