naginterfaces.library.blas.ztrsm

naginterfaces.library.blas.ztrsm(side, uplo, transa, diag, m, alpha, a, b)

ztrsm performs one of the matrix-matrix operations

$$\begin{array}{c}\begin{array}{ccc}B\leftarrow \alpha A^{-1}B\text{,}& B\leftarrow \alpha A^{-T}B\text{,}& B\leftarrow \alpha A^{-H}B\text{,}\\ B\leftarrow \alpha B{A}^{-1}\text{,}& B\leftarrow \alpha B{A}^{-T}\text{or}& B\leftarrow \alpha B{A}^{-H}\text{,}\end{array}\end{array}$$

where $A$ is a complex triangular matrix, $B$ is an $m\times n$ complex matrix, and $\alpha$ is a complex scalar. $A^{-T}$ denotes ${\left(A^T\right)}^{-1}$ or equivalently ${\left(A^{-1}\right)}^T$; $A^{-H}$ denotes ${\left(A^H\right)}^{-1}$ or equivalently ${\left(A^{-1}\right)}^H$.

No test for singularity or near-singularity of $A$ is included in this function. Such tests must be performed before calling this function.

For full information please refer to the NAG Library document for f06zj

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f06/f06zjf.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 $A$ is upper or lower triangular.

$uplo=\text{'U'}$

$A$ is upper triangular.

$uplo=\text{'L'}$

$A$ is lower triangular.

transastr, length 1

Specifies whether the operation involves $A^{-1}$, $A^{-T}$ or $A^{-H}$.

$transa=\text{'N'}$

The operation involves $A^{-1}$.

$transa=\text{'T'}$

The operation involves $A^{-T}$.

$transa=\text{'C'}$

The operation involves $A^{-H}$.

diagstr, length 1

Specifies whether $A$ has nonunit or unit diagonal elements.

$diag=\text{'N'}$

The diagonal elements are stored explicitly.

$diag=\text{'U'}$

The diagonal elements are assumed to be $1$, and are not referenced.

mint

$m$, the number of rows of the matrix $B$; the order of $A$ if $side=\text{'L'}$.

alphacomplex

The scalar $\alpha$.

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

Note: the required extent for this argument in dimension 1 is determined as follows: if $side=\text{'L'}$: $m$; if $side=\text{'R'}$: $n$; otherwise: $0$.

Note: the required extent for this argument in dimension 2 is determined as follows: if $side=\text{'L'}$: $m$; if $side=\text{'R'}$: $n$; otherwise: $0$.

The triangular matrix $A$; $A$ is $m\times m$ if $side=\text{'L'}$, or $n\times n$ if $side=\text{'R'}$.

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

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

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

Returns

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

The updated matrix $B$.

Raises

NagValueError

(errno $1$)

On entry, error in parameter $side$.

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

(errno $2$)

On entry, error in parameter $uplo$.

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

(errno $3$)

On entry, error in parameter $transa$.

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

(errno $4$)

On entry, error in parameter $diag$.

Constraint: $diag=\text{'N'}$ or $\text{'U'}$.

(errno $5$)

On entry, error in parameter $m$.

Constraint: $m\ge 0$.

(errno $6$)

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

Constraint: $n\ge 0$.

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.