Multiplying Matrices Using dgemm

Use dgemm to Multiply Matrices

This exercise demonstrates declaring variables, storing matrix values in the arrays, and calling dgemm to compute the product of the matrices. The arrays are used to store these matrices:

The one-dimensional arrays in the exercises store the matrices by placing the elements of each column in successive cells of the arrays.

* Fortran source code is found in dgemm_example.f

      PROGRAM   MAIN

      IMPLICIT NONE

      DOUBLE PRECISION ALPHA, BETA
      INTEGER          M, K, N, I, J
      PARAMETER        (M=2000, K=200, N=1000)
      DOUBLE PRECISION A(M,K), B(K,N), C(M,N)

      PRINT *, "This example computes real matrix C=alpha*A*B+beta*C"
      PRINT *, "using Intel® MKL function dgemm, where A, B, and C"
      PRINT *, "are matrices and alpha and beta are double precision "
      PRINT *, "scalars"
      PRINT *, ""

      PRINT *, "Initializing data for matrix multiplication C=A*B for "
      PRINT 10, " matrix A(",M," x",K, ") and matrix B(", K," x", N, ")"
10    FORMAT(a,I5,a,I5,a,I5,a,I5,a)
      PRINT *, ""
      ALPHA = 1.0 
      BETA = 0.0

      PRINT *, "Intializing matrix data"
      PRINT *, ""
      DO I = 1, M
        DO J = 1, K
          A(I,J) = (I-1) * K + J
        END DO
      END DO

      DO I = 1, K
        DO J = 1, N
          B(I,J) = -((I-1) * N + J)
        END DO
      END DO

      DO I = 1, M
        DO J = 1, N
          C(I,J) = 0.0
        END DO
      END DO

      PRINT *, "Computing matrix product using Intel® MKL DGEMM "
      PRINT *, "subroutine"
      CALL DGEMM('N','N',M,N,K,ALPHA,A,M,B,K,BETA,C,M)
      PRINT *, "Computations completed."
      PRINT *, ""

      PRINT *, "Top left corner of matrix A:"
      PRINT 20, ((A(I,J), J = 1,MIN(K,6)), I = 1,MIN(M,6))
      PRINT *, ""

      PRINT *, "Top left corner of matrix B:"
      PRINT 20, ((B(I,J),J = 1,MIN(N,6)), I = 1,MIN(K,6))
      PRINT *, ""

 20   FORMAT(6(F12.0,1x))

      PRINT *, "Top left corner of matrix C:"
      PRINT 30, ((C(I,J), J = 1,MIN(N,6)), I = 1,MIN(M,6))
      PRINT *, ""

 30   FORMAT(6(ES12.4,1x))

      PRINT *, "Example completed."
      STOP 

      END

This call to the dgemm routine multiplies the matrices:

CALL DGEMM('N','N',M,N,K,ALPHA,A,M,B,K,BETA,C,M)

The arguments provide options for how Intel MKL performs the operation. In this case:

'N'

Character indicating that the matrices A and B should not be transposed or conjugate transposed before multiplication.

M, N, K

Integers indicating the size of the matrices:

• A: M rows by K columns

• B: K rows by N columns

• C: M rows by N columns

ALPHA

Real value used to scale the product of matrices A and B.

A

Array used to store matrix A.

M

Leading dimension of array A, or the number of elements between successive columns (for column major storage) in memory. In the case of this exercise the leading dimension is the same as the number of rows.

B

Array used to store matrix B.

K

Leading dimension of array B, or the number of elements between successive columns (for column major storage) in memory. In the case of this exercise the leading dimension is the same as the number of rows.

BETA

Real value used to scale matrix C.

C

Array used to store matrix C.

M

Leading dimension of array C, or the number of elements between successive columns (for column major storage) in memory. In the case of this exercise the leading dimension is the same as the number of rows.

Compile and Link Your Code

Intel MKL provides many options for creating code for multiple processors and operating systems, compatible with different compilers and third-party libraries, and with different interfaces. To compile and link the exercises in this tutorial with Intel® Parallel Studio XE Composer Edition, type

• Windows* OS: ifort /Qmkl dgemm_example.f
• Linux* OS, OS X*: ifort -mkl dgemm_example.f

For other compilers, use the Intel MKL Link Line Advisor to generate a command line to compile and link the exercises in this tutorial: http://software.intel.com/en-us/articles/intel-mkl-link-line-advisor/.

After compiling and linking, execute the resulting executable file, named dgemm_example.exe on Windows* OS or a.out on Linux* OS and OS X*.