NAG Library Routine Document

F06ZJF (ZTRSM)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     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:     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:     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:     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:     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:     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:     ALPHA – COMPLEX (KIND=nag_wp)Input

On entry: the scalar $\alpha$.

8:     A(LDA,$*$) – 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:     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:   B(LDB,$*$) – 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:   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

7  Accuracy

8  Further Comments

9  Example