Divide and conquer matrix multiplication base case + how to split matrix into 4 quarters

Question

I've been trying to code the divide and conquer matrix multiplication algorithm

There's problem that when I try to divide matrix into four quarters it gives me an error ArrayOutOfIndexBound

• I'm not sure if I'm right about the base case, so can you help me out guys?

The problem that I get is at double[][] a21

    public static double[][] divideAndConquer(double[][] a , double[][] b, int dimension){

if (a.length == 1){
    double[][] result = new double[1][1];
    result[0][0]= a[0][0]*b[0][0];
    return result;
}
else {
    int m = dimension/2;
    double[][] a11 = new double[m][m];
    for(int i = 0; i < m ; i++){
        for (int j = 0 ; j< m ; j++)
            a11[i][j]= a[i][j];
    }

              double[][] a21 = new double[m][m];
            for(int i = m; i < dimension; i++){
        for (int j = 0 ; j< m ; j++)
            a21[i][j]= a[i][j];
    }
     double[][] a12 = new double[m][m];
            for(int i = 0; i < m ; i++){
        for (int j = m ; j< dimension ; j++)
            a12[i][j]= a[i][j];
    }



    double[][] a22 = new double[m][m];
            for(int i = m; i < dimension; i++){
        for (int j =  m; j < dimension; j++)
            a21[i][j]= a[i][j];
    }


    double[][] b11 = new double[m][m];
    for(int i = 0; i < m ; i++){
        for (int j = 0 ; j< m ; j++)
            b11[i][j]= b[i][j];
    }

     double[][] b12 = new double[m][m];
            for(int i = 0; i < m ; i++){
        for (int j = m ; j< dimension ; j++)
            b12[i][j]= b[i][j];
    }

      double[][] b21 = new double[m][m];
            for(int i = m; i < dimension; i++){
        for (int j = 0 ; j< m ; j++)
            b21[i][j]= b[i][j];
    }

    double[][] b22 = new double[m][m];
            for(int i = m; i < dimension; i++){
        for (int j =  m; j < dimension; j++)
            b21[i][j]= b[i][j];
    }

            double[][] x1 = divideAndConquer(a11,b11,m);
            double[][] x2 = divideAndConquer(a12,b21,m);
            double[][] x3 = divideAndConquer(a11,b12,m);
            double[][] x4 = divideAndConquer(a12,b22,m);
            double[][] x5 = divideAndConquer(a21,b11,m);
            double[][] x6 = divideAndConquer(a22,b21,m);
            double[][] x7 = divideAndConquer(a21,b12,m);
            double[][] x8 = divideAndConquer(a22,b22,m);
        ..........................etc

Answer 1

As written, your problem is that you need to subtract off the array offset; e.g.,

a12[i][j]= a[i][j];

should be

a12[i][j-dimension]= a[i][j];

Your bigger problem is that you're creating 4 new submatrices, which is going to generate tons of garbage. Once you've gotten this working, I would strongly think about ways of doing this "in-place" by manipulating array indexes.

E.g., your new api would look like

public static double[][] divideAndConquer(double[][] a , double[][] b, int aMinIndex, int aMaxIndex, int bMinIndex, bMaxIndex){

and your divide and conquer would build subsets of the min & max indices.