NAG Library Routine Document

F06ZAF (ZGEMM)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     $\mathrm{TRANSA}$ – 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:     $\mathrm{TRANSB}$ – 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:     $\mathrm{M}$ – 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:     $\mathrm{N}$ – 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:     $\mathrm{K}$ – 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:     $\mathrm{ALPHA}$ – COMPLEX (KIND=nag_wp)Input

On entry: the scalar $\alpha$.

7:     $\mathrm{A}\left(\mathbf{LDA},*\right)$ – COMPLEX (KIND=nag_wp) arrayInput

Note: the second dimension of the array A must be at least $\max \left(1,\mathbf{K}\right)$ 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:     $\mathrm{LDA}$ – 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:     $\mathrm{B}\left(\mathbf{LDB},*\right)$ – COMPLEX (KIND=nag_wp) arrayInput

Note: the second dimension of the array B must be at least $\max \left(1,\mathbf{N}\right)$ 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:   $\mathrm{LDB}$ – 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:   $\mathrm{BETA}$ – COMPLEX (KIND=nag_wp)Input

On entry: the scalar $\beta$.

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

13:   $\mathrm{LDC}$ – 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