NAG FL Interface
f06yaf (dgemm)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

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

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

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

The operation involves $A$.

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

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

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

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

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

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

The operation involves $B$.

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

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

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

3: $\mathbf{m}$ – Integer Input

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: $\mathbf{n}$ – Integer Input

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: $\mathbf{k}$ – Integer Input

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

On entry: the scalar $\alpha$.

7: $\mathbf{a}\left(\mathbf{lda},*\right)$ – Real (Kind=nag_wp) array Input

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: $\mathbf{lda}$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f06yaf 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: $\mathbf{b}\left(\mathbf{ldb},*\right)$ – Real (Kind=nag_wp) array Input

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: $\mathbf{ldb}$ – Integer Input

On entry: the first dimension of the array b as declared in the (sub)program from which f06yaf 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: $\mathbf{beta}$ – Real (Kind=nag_wp) Input

On entry: the scalar $\beta$.

12: $\mathbf{c}\left(\mathbf{ldc},*\right)$ – Real (Kind=nag_wp) array Input/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: $\mathbf{ldc}$ – Integer Input

On entry: the first dimension of the array c as declared in the (sub)program from which f06yaf 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