NAG Library Routine Document

f06zcf (zhemm)

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

On entry: the scalar $\alpha$.

6:     $\mathbf{a}\left(\mathbf{lda},*\right)$ – 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 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:     $\mathbf{lda}$ – 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:     $\mathbf{b}\left(\mathbf{ldb},*\right)$ – 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:     $\mathbf{ldb}$ – 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:   $\mathbf{beta}$ – Complex (Kind=nag_wp)Input

On entry: the scalar $\beta$.

11:   $\mathbf{c}\left(\mathbf{ldc},*\right)$ – 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:   $\mathbf{ldc}$ – 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