NAG Library Routine Document

f06zaf  (zgemm)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

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

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

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

The operation involves $A$.

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

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

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

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

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

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

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

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

The operation involves $B$.

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

The operation involves $B^{\mathrm{T}}$.

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

The operation involves $B^{\mathrm{H}}$.

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

3:     $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of rows of the matrix $C$; the number of rows of $A$ if $\mathbf{transa}=\text{'N'}$, or the number of columns of $A$ if $\mathbf{transa}=\text{'T'}$ or $\text{'C'}$.

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

4:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of columns of the matrix $C$; the number of columns of $B$ if $\mathbf{transb}=\text{'N'}$, or the number of rows of $B$ if $\mathbf{transb}=\text{'T'}$ or $\text{'C'}$.

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

5:     $\mathbf{k}$ – IntegerInput

On entry: $k$, the number of columns of $A$ if $\mathbf{transa}=\text{'N'}$, or the number of rows of $A$ if $\mathbf{transa}=\text{'T'}$ or $\text{'C'}$; the number of rows of $B$ if $\mathbf{transb}=\text{'N'}$, or the number of columns of $B$ if $\mathbf{transb}=\text{'T'}$ or $\text{'C'}$.

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

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

On entry: the scalar $\alpha$.

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

Note: the second dimension of the array a must be at least $\max \left(1,\mathbf{k}\right)$ if $\mathbf{transa}=\text{'N'}$ and at least $\max \left(1,\mathbf{m}\right)$ if $\mathbf{transa}=\text{'T'}$ or $\text{'C'}$.

On entry: the matrix $A$; $A$ is $m$ by $k$ if $\mathbf{transa}=\text{'N'}$, or $k$ by $m$ if $\mathbf{transa}=\text{'T'}$ or $\text{'C'}$.

8:     $\mathbf{lda}$ – IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which f06zaf (zgemm) is called.

Constraints:

• if $\mathbf{transa}=\text{'N'}$, $\mathbf{lda}\ge \max \left(1,\mathbf{m}\right)$;
• if $\mathbf{transa}=\text{'T'}$ or $\text{'C'}$, $\mathbf{lda}\ge \max \left(1,\mathbf{k}\right)$.

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

Note: the second dimension of the array b must be at least $\max \left(1,\mathbf{n}\right)$ if $\mathbf{transb}=\text{'N'}$ and at least $\max \left(1,\mathbf{k}\right)$ if $\mathbf{transb}=\text{'T'}$ or $\text{'C'}$.

On entry: the matrix $B$; $B$ is $k$ by $n$ if $\mathbf{transb}=\text{'N'}$, or $n$ by $k$ if $\mathbf{transb}=\text{'T'}$ or $\text{'C'}$.

10:   $\mathbf{ldb}$ – IntegerInput

On entry: the first dimension of the array b as declared in the (sub)program from which f06zaf (zgemm) is called.

Constraints:

• if $\mathbf{transb}=\text{'N'}$, $\mathbf{ldb}\ge \max \left(1,\mathbf{k}\right)$;
• if $\mathbf{transb}=\text{'T'}$ or $\text{'C'}$, $\mathbf{ldb}\ge \max \left(1,\mathbf{n}\right)$.

11:   $\mathbf{beta}$ – Complex (Kind=nag_wp)Input

On entry: the scalar $\beta$.

12:   $\mathbf{c}\left(\mathbf{ldc},*\right)$ – 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 $C$.

13:   $\mathbf{ldc}$ – IntegerInput

On entry: the first dimension of the array c as declared in the (sub)program from which f06zaf (zgemm) 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