NAG Library Routine Document

F06ZAF (ZGEMM)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     TRANSA – CHARACTER(1)Input

On entry: specifies whether the operation involves A, AT or AH.

TRANSA='N'

The operation involves A.

TRANSA='T'

The operation involves AT.

TRANSA='C'

The operation involves AH.

Constraint: TRANSA='N', 'T' or 'C'.

2:     TRANSB – CHARACTER(1)Input

On entry: specifies whether the operation involves B, BT or BH.

TRANSB='N'

The operation involves B.

TRANSB='T'

The operation involves BT.

TRANSB='C'

The operation involves BH.

Constraint: TRANSB='N', 'T' or 'C'.

3:     M – INTEGERInput

On entry: m, the number of rows of the matrix C; the number of rows of A if TRANSA='N', or the number of columns of A if TRANSA='T' or 'C'.

Constraint: M≥0.

4:     N – INTEGERInput

On entry: n, the number of columns of the matrix C; the number of columns of B if TRANSB='N', or the number of rows of B if TRANSB='T' or 'C'.

Constraint: N≥0.

5:     K – INTEGERInput

On entry: k, the number of columns of A if TRANSA='N', or the number of rows of A if TRANSA='T' or 'C'; the number of rows of B if TRANSB='N', or the number of columns of B if TRANSB='T' or 'C'.

Constraint: K≥0.

6:     ALPHA – COMPLEX (KIND=nag_wp)Input

On entry: the scalar α.

7:     A(LDA,*) – COMPLEX (KIND=nag_wp) arrayInput

Note: the second dimension of the array A must be at least max1,K if TRANSA='N' and at least max1,M if TRANSA='T' or 'C'.

On entry: the matrix A; A is m by k if TRANSA='N', or k by m if TRANSA='T' or 'C'.

8:     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 TRANSA='N', LDA≥ max1,M ;
• if TRANSA='T' or 'C', LDA≥ max1,K .

9:     B(LDB,*) – COMPLEX (KIND=nag_wp) arrayInput

Note: the second dimension of the array B must be at least max1,N if TRANSB='N' and at least max1,K if TRANSB='T' or 'C'.

On entry: the matrix B; B is k by n if TRANSB='N', or n by k if TRANSB='T' or 'C'.

10:   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 TRANSB='N', LDB≥ max1,K ;
• if TRANSB='T' or 'C', LDB≥ max1,N .

11:   BETA – COMPLEX (KIND=nag_wp)Input

On entry: the scalar β.

12:   C(LDC,*) – COMPLEX (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array C must be at least max1,N.

On entry: the m by n matrix C.

If BETA=0, C need not be set.

On exit: the updated matrix C.

13:   LDC – INTEGERInput

On entry: the first dimension of the array C as declared in the (sub)program from which F06ZAF (ZGEMM) is called.

Constraint: LDC≥ max1,M .

6  Error Indicators and Warnings

7  Accuracy

8  Further Comments

9  Example