NAG Library Routine Document

f06zjf (ztrsm)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{side}$ – Character(1)Input

On entry: specifies whether $B$ is operated on from the left or the right.

$\mathbf{side}=\text{'L'}$

$B$ is pre-multiplied from the left.

$\mathbf{side}=\text{'R'}$

$B$ is post-multiplied from the right.

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

2:     $\mathbf{uplo}$ – Character(1)Input

On entry: specifies whether $A$ is upper or lower triangular.

$\mathbf{uplo}=\text{'U'}$

$A$ is upper triangular.

$\mathbf{uplo}=\text{'L'}$

$A$ is lower triangular.

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

3:     $\mathbf{transa}$ – Character(1)Input

On entry: specifies whether the operation involves $A^{-1}$, $A^{-\mathrm{T}}$ or $A^{-\mathrm{H}}$.

$\mathbf{transa}=\text{'N'}$

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

$\mathbf{transa}=\text{'T'}$

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

$\mathbf{transa}=\text{'C'}$

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

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

4:     $\mathbf{diag}$ – Character(1)Input

On entry: specifies whether $A$ has nonunit or unit diagonal elements.

$\mathbf{diag}=\text{'N'}$

The diagonal elements are stored explicitly.

$\mathbf{diag}=\text{'U'}$

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

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

5:     $\mathbf{m}$ – IntegerInput

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

Constraint: $\mathbf{m}\ge 0$.

6:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of columns of the matrix $B$; the order of $A$ if $\mathbf{side}=\text{'R'}$.

Constraint: $\mathbf{n}\ge 0$.

7:     $\mathbf{alpha}$ – Complex (Kind=nag_wp)Input

On entry: the scalar $\alpha$.

8:     $\mathbf{a}\left(\mathbf{lda},*\right)$ – Complex (Kind=nag_wp) arrayInput

Note: the second dimension of the array a must be at least $\max \left(1,\mathbf{m}\right)$ if $\mathbf{side}=\text{'L'}$ and at least $\max \left(1,\mathbf{n}\right)$ if $\mathbf{side}=\text{'R'}$.

On entry: the triangular matrix $A$; $A$ is $m$ by $m$ if $\mathbf{side}=\text{'L'}$, or $n$ by $n$ if $\mathbf{side}=\text{'R'}$.

• If $\mathbf{uplo}=\text{'U'}$, $A$ is upper triangular and the elements of the array below the diagonal are not referenced.
• If $\mathbf{uplo}=\text{'L'}$, $A$ is lower triangular and the elements of the array above the diagonal are not referenced.
• If $\mathbf{diag}=\text{'U'}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced.

9:     $\mathbf{lda}$ – IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which f06zjf (ztrsm) is called.

Constraints:

• if $\mathbf{side}=\text{'L'}$, $\mathbf{lda}\ge \max \left(1,\mathbf{m}\right)$;
• if $\mathbf{side}=\text{'R'}$, $\mathbf{lda}\ge \max \left(1,\mathbf{n}\right)$.

10:   $\mathbf{b}\left(\mathbf{ldb},*\right)$ – Complex (Kind=nag_wp) arrayInput/Output

Note: the second dimension of the array b must be at least $\max \left(1,\mathbf{n}\right)$.

On entry: the $m$ by $n$ matrix $B$.

If $\mathbf{alpha}=0$, b need not be set.

On exit: the updated matrix $B$.

11:   $\mathbf{ldb}$ – IntegerInput

On entry: the first dimension of the array b as declared in the (sub)program from which f06zjf (ztrsm) is called.

Constraint: $\mathbf{ldb}\ge \max \left(1,\mathbf{m}\right)$.

6

Error Indicators and Warnings

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Accuracy

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Parallelism and Performance

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Further Comments

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Example