NAG FL Interface
f06zaf (zgemm)

1 Purpose

f06zaf performs one of the matrix-matrix operations
CαAB+βC, CαATB+βC, CαAHB+βC, CαABT+βC, CαATBT+βC, CαAHBT+βC, CαABH+βC, CαATBH+βC  or CαAHBH+βC,  
where A, B and C are complex matrices, and α and β are complex scalars; C is always m by n.

2 Specification

Fortran Interface
Subroutine f06zaf ( transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
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, 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 Integer Input
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: m0.
4: n Integer Input
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: n0.
5: k Integer Input
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: k0.
6: alpha Complex (Kind=nag_wp) Input
On entry: the scalar α.
7: alda* Complex (Kind=nag_wp) array Input
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 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 max1,m ;
  • if transa='T' or 'C', lda max1,k .
9: bldb* Complex (Kind=nag_wp) array Input
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 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 max1,k ;
  • if transb='T' or 'C', ldb max1,n .
11: beta Complex (Kind=nag_wp) Input
On entry: the scalar β.
12: cldc* Complex (Kind=nag_wp) array Input/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 Integer Input
On entry: the first dimension of the array c as declared in the (sub)program from which f06zaf is called.
Constraint: ldc max1,m .

6 Error Indicators and Warnings

None.

7 Accuracy

Not applicable.

8 Parallelism and Performance

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.

9 Further Comments

None.

10 Example

None.