naginterfaces.library.matop.complex_​tri_​matmul_​inplace

naginterfaces.library.matop.complex_tri_matmul_inplace(side, uplo, transa, alpha, a, b)

complex_tri_matmul_inplace performs one of the matrix-matrix operations

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

where $A$ and $B$ are complex triangular matrices, and $\alpha$ is a complex scalar.

For full information please refer to the NAG Library document for f01du

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f01/f01duf.html

Parameters

sidestr, length 1

Specifies whether $B$ is operated on from the left or the right.

$side=\text{'L'}$

$B$ is pre-multiplied from the left.

$side=\text{'R'}$

$B$ is post-multiplied from the right.

uplostr, length 1

Specifies whether $A$ and $B$ are upper or lower triangular.

$uplo=\text{'U'}$

$A$ and $B$ are upper triangular.

$uplo=\text{'L'}$

$A$ and $B$ are 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 $A^H$.

alphacomplex

The scalar $\alpha$.

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

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

bcomplex, ndarray, shape $(n,n)$, modified in place

On entry: the $n\times n$ triangular matrix $B$.

If $alpha=0$, $b$ need not be set.

On exit: $B$ is overwritten.

Raises

NagValueError

(errno $1$)

On entry, $side=⟨value⟩$.

Constraint: $side=\text{'L'}$ or $\text{'R'}$.

(errno $2$)

On entry, $uplo=⟨value⟩$.

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

(errno $3$)

On entry, $transa=⟨value⟩$.

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

(errno $4$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

Notes

complex_tri_matmul_inplace computes the matrix product $B=\alpha AB$ or $B=\alpha BA$ for two upper triangular or two lower triangular matrices. The storage method for matrices $A$ and $B$ must match (e.g., $A$ and $B$ must both be upper triangular or lower triangular matrices). When the transpose or the conjugate transpose of the input matrix $A$ is used during computation, the solution matrix $B$ is a general matrix. Otherwise, the solution matrix $B$ is a triangular matrix with the storage method identified by the input parameter $uplo$.