F06YAF (DGEMM) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06YAF (DGEMM)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

 Contents

    1  Purpose
    7  Accuracy
    10  Example

1  Purpose

F06YAF (DGEMM) performs one of the matrix-matrix operations
CαAB+βC, CαATB+βC, CαABT+βC  or CαATBT+βC,  
where A, B and C are real matrices, and α and β are real scalars; C is always m by n.

2  Specification

SUBROUTINE F06YAF ( TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
INTEGER  M, N, K, LDA, LDB, LDC
REAL (KIND=nag_wp)  ALPHA, A(LDA,*), B(LDB,*), BETA, C(LDC,*)
CHARACTER(1)  TRANSA, TRANSB
The routine may be called by its BLAS name dgemm.

3  Description

None.

4  References

None.

5  Arguments

1:     TRANSA – CHARACTER(1)Input
On entry: specifies whether the operation involves A or AT.
TRANSA='N'
The operation involves A.
TRANSA='T' or 'C'
The operation involves AT.
Constraint: TRANSA='N', 'T' or 'C'.
2:     TRANSB – CHARACTER(1)Input
On entry: specifies whether the operation involves B or BT.
TRANSB='N'
The operation involves B.
TRANSB='T' or 'C'
The operation involves BT.
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: M0.
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: N0.
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: K0.
6:     ALPHA – REAL (KIND=nag_wp)Input
On entry: the scalar α.
7:     ALDA* – REAL (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 F06YAF (DGEMM) is called.
Constraints:
  • if TRANSA='N', LDA max1,M ;
  • if TRANSA='T' or 'C', LDA max1,K .
9:     BLDB* – REAL (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 F06YAF (DGEMM) is called.
Constraints:
  • if TRANSB='N', LDB max1,K ;
  • if TRANSB='T' or 'C', LDB max1,N .
11:   BETA – REAL (KIND=nag_wp)Input
On entry: the scalar β.
12:   CLDC* – REAL (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 F06YAF (DGEMM) is called.
Constraint: LDC max1,M .

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Parallelism and Performance

F06YAF (DGEMM) 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.

F06YAF (DGEMM) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2016