NAG Library Routine Document

F06ZCF (ZHEMM)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{SIDE}$ – 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:     $\mathrm{UPLO}$ – CHARACTER(1)Input

On entry: specifies whether the upper or lower triangular part of $A$ is stored.

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

The upper triangular part of $A$ is stored.

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

The lower triangular part of $A$ is stored.

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

3:     $\mathrm{M}$ – INTEGERInput

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

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

4:     $\mathrm{N}$ – INTEGERInput

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

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

5:     $\mathrm{ALPHA}$ – COMPLEX (KIND=nag_wp)Input

On entry: the scalar $\alpha$.

6:     $\mathrm{A}\left(\mathbf{LDA},*\right)$ – 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 Hermitian matrix $A$; $A$ is $m$ by $m$ if $\mathbf{SIDE}=\text{'L'}$, or $n$ by $n$ if $\mathbf{SIDE}=\text{'R'}$.

• If $\mathbf{UPLO}=\text{'U'}$, the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.
• If $\mathbf{UPLO}=\text{'L'}$, the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.

7:     $\mathrm{LDA}$ – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F06ZCF (ZHEMM) is called.

Constraints:

• if $\mathbf{SIDE}=\text{'L'}$, $\mathbf{LDA}\ge \max \left(1,\mathbf{M}\right)$;
• if $\mathbf{SIDE}=\text{'R'}$, $\mathbf{LDA}\ge \max \left(1,\mathbf{N}\right)$.

8:     $\mathrm{B}\left(\mathbf{LDB},*\right)$ – COMPLEX (KIND=nag_wp) arrayInput

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 $B$.

9:     $\mathrm{LDB}$ – INTEGERInput

On entry: the first dimension of the array B as declared in the (sub)program from which F06ZCF (ZHEMM) is called.

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

10:   $\mathrm{BETA}$ – COMPLEX (KIND=nag_wp)Input

On entry: the scalar $\beta$.

11:   $\mathrm{C}\left(\mathbf{LDC},*\right)$ – COMPLEX (KIND=nag_wp) arrayInput/Output

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

On entry: the $m$ by $n$ matrix $C$.

If $\mathbf{BETA}=0$, C need not be set.

On exit: the updated matrix $C$.

12:   $\mathrm{LDC}$ – INTEGERInput

On entry: the first dimension of the array C as declared in the (sub)program from which F06ZCF (ZHEMM) is called.

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

6  Error Indicators and Warnings

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example