Integer, Intent (In)	::	m, n, k, lda, ldb, ldc
Complex (Kind=nag_wp), Intent (In)	::	alpha, a(lda,), b(ldb,), beta
Complex (Kind=nag_wp), Intent (Inout)	::	c(ldc,*)
Character (1), Intent (In)	::	transa, transb

C Header Interface

#include <nag.h>

void

f06zaf_ (const char *transa, const char *transb, const Integer *m, const Integer *n, const Integer *k, const Complex *alpha, const Complex a[], const Integer *lda, const Complex b[], const Integer *ldb, const Complex *beta, Complex c[], const Integer *ldc, const Charlen length_transa, const Charlen length_transb)

The routine may be called by the names f06zaf, nagf_blas_zgemm or its BLAS name zgemm.

3 Description

None.

4 References

None.

5 Arguments

1: $transa$ – Character(1) Input

On entry: specifies whether the operation involves

A

A^{T}

A^{H}

$transa ='N'$: The operation involves $A$ .
$transa ='T'$: The operation involves $A^{T}$ .
$transa ='C'$: The operation involves $A^{H}$ .

Constraint:

transa ='N'

'T'

'C'

2: $transb$ – Character(1) Input

On entry: specifies whether the operation involves

B

B^{T}

B^{H}

$transb ='N'$: The operation involves $B$ .
$transb ='T'$: The operation involves $B^{T}$ .
$transb ='C'$: The operation involves $B^{H}$ .

Constraint:

transb ='N'

'T'

'C'

3: $m$ – Integer Input

On entry:

m

, the number of rows of the matrix

C

; the number of rows of

A

transa ='N'

, or the number of columns of

A

transa ='T'

'C'

Constraint:

m \geq 0

4: $n$ – Integer Input

On entry:

n

, the number of columns of the matrix

C

; the number of columns of

B

transb ='N'

, or the number of rows of

B

transb ='T'

'C'

Constraint:

n \geq 0

5: $k$ – Integer Input

On entry:

k

, the number of columns of

A

transa ='N'

, or the number of rows of

A

transa ='T'

'C'

; the number of rows of

B

transb ='N'

, or the number of columns of

B

transb ='T'

'C'

Constraint:

k \geq 0

6: $alpha$ – Complex (Kind=nag_wp) Input

On entry: the scalar

α

7: $a (lda, *)$ – Complex (Kind=nag_wp) array Input

Note: the second dimension of the array a must be at least

\max (1, k)

transa ='N'

and at least

\max (1, m)

transa ='T'

'C'

On entry: the matrix

A

;

A

m \times k

transa ='N'

, or

k \times m

transa ='T'

'C'

8: $lda$ – Integer Input

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

Constraints:

if $transa ='N'$ , $lda \geq \max (1, m)$ ;
if $transa ='T'$ or $'C'$ , $lda \geq \max (1, k)$ .

9: $b (ldb, *)$ – Complex (Kind=nag_wp) array Input

Note: the second dimension of the array b must be at least

\max (1, n)

transb ='N'

and at least

\max (1, k)

transb ='T'

'C'

On entry: the matrix

B

;

B

k \times n

transb ='N'

, or

n \times k

transb ='T'

'C'

10: $ldb$ – Integer Input

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

Constraints:

if $transb ='N'$ , $ldb \geq \max (1, k)$ ;
if $transb ='T'$ or $'C'$ , $ldb \geq \max (1, n)$ .

11: $beta$ – Complex (Kind=nag_wp) Input

On entry: the scalar

β

12: $c (ldc, *)$ – Complex (Kind=nag_wp) array Input/Output

Note: the second dimension of the array c must be at least

\max (1, n)

On entry: the

m \times n

matrix

C

beta = 0.0

, c need not be set.

On exit: the updated matrix

C

13: $ldc$ – Integer Input

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

Constraint:

ldc \geq \max (1, m)

6 Error Indicators and Warnings

None.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

f06zaf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.