[OpenMP] Solution 8 : Matrix-Matrix Multiplication

This material is part of the course Practical Introduction to Parallel Programming and meant for educational purposes only.

Task

Write a parallel implementation of the matrix-matrix multiplication

\begin{equation*} \mathbf{A}\in\mathbb{R}^{N\times M},\, \mathbf{B}\in\mathbb{R}^{M\times O}\,: \quad \mathbf{C}=\mathbf{A}\cdot \mathbf{B}\in\mathbb{R}^{N\times O} \end{equation*}

where each entry of matrix \(\mathbf{C}\) is computed from

\begin{equation*} c_{ik}=\sum_{j=1}^M a_{ij}\cdot b_{jk}. \end{equation*}

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Question 1: Matrix-Matrix Multiplication

#include <stdio.h>
#include <stdlib.h>

#ifdef _OPENMP
#include <omp.h>
#else
#define omp_get_num_threads() 1
#define omp_get_max_threads() 1
#define omp_get_thread_num()  0
#endif

int main ( int argc, char** argv )
{
    const int    N = 500;
    const int    M = 500;
    const int    O = 500;

    double       A[N][M];
    double       B[M][O];
    double       C[N][O];

    double t0 = omp_get_wtime();

#pragma omp parallel shared(A,B,C)
    {

        /* Initialize the matrices. */
#pragma omp for collapse(2) nowait
        for ( int i = 0; i < N; i++ )
            for ( int j = 0; j < M; j++ )
            {
                A[i][j] = i+j;
            }

#pragma omp for collapse(2)
        for ( int i = 0; i < M; i++ )
            for ( int j = 0; j < O; j++ )
            {
                B[i][j] = i+j;
            }

        /* Parallel matrix-matrix multiplication. */
#pragma omp for collapse(2)
        for ( int i = 0; i < N; i++ )
            for ( int k = 0; k < O; k++ )
            {
                double c = 0.0;

#pragma omp simd reduction(+:c)
                for ( int j = 0; j < M; j++ )
                {
                    c += A[i][j] * B[j][k];
                }

                C[i][k] = c;
            }
    }

    double t1 = omp_get_wtime();

    if (N<10 && O<10)
    {
        printf("Matrix-matrix product (in %g seconds):\n", t1-t0);
        for (int i=0; i<N; i++)
        {
            for (int k=0; k<O; k++)
                printf("%f ", C[i][k]);
            printf("\n");
        }
    }
    else
        printf("Matrix-matrix product (in %g seconds):\nSet N<10 and O<10 to produce output\n", t1-t0);

    return 0;
}

Question 2: OpenMP environment variables

Specify the OpenMP environment variables that should be used for running your program (export OMP_NUM_THREADS=1 ...). Use semicolons to separate multiple variables

Question 3: Command Line Argument

Specify the command line arguments that should be passed to your program when it is run. Arguments must be given in quotes and separated by commas. Leave this filed empty if you do not want to specify command line arguments.

Example: "1","int","arg=2" is interpreted as three arguments 1, int, and arg=2.

Author(s)	Erik-Jan Lingen, Matthias Möller
Deadline	No deadline
Submission limit	No limitation

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