Recursive matrix multiplication

Question

I've just written a recursive matrix multiplication and I want to know my mistakes or problems. Is there a better way doing this?

public static double[,] Multiply(double[,] a, double[,] b, int rowA,int colA,int rowB,int colB, double[,] c)
{
    double[,] result = new double[a.GetLength(0), b.GetLength(1)];

    if (c != null)
        result = c;

    result[rowA, colB] += a[rowA, colA] * b[rowB, colB];

    colA += 1;
    rowB += 1;
    if (colA >= a.GetLength(1))
    {
        colA = 0;
        rowB = 0;
        rowA += 1;
        if(rowA >= a.GetLength(0))
        {
            rowA = 0;
            colB += 1;
        }
    }

    if (colB >= b.GetLength(1))
        return result;

    return Multiply(a, b, rowA, colA, rowB, colB, result);
}

Edit: The rowA, colA variables are the indices for the element of the first matrix which is multiplied by the [rowB, colB] element of the second matrix. Then we increase colA and rowB so we can multiply the next elements of the matrices.

When the colA reaches the end of the matrix (it is obvious that rowB has also reached the end of the second matrix) we reset them to 0 and move to the next row of the first matrix. when we reach the last row of the first matrix we move to the next column of the second matrix by increasing colB by 1; We then set rowA to 0 so that the multiplication begins from the first row of the first matrix again.

Finally, if colB exceeds the end column of the second matrix we have finished multiplying and we return our result.

Edit 2:

public static double[,] Multiply(double[,] a, double[,] b, int rowA,int colA,int rowB,int colB, double[,] c)
{
    double[,] result;
    if (c != null)
        result = c;
    else
        result = new double[a.GetLength(0), b.GetLength(1)];

    result[rowA, colB] += a[rowA, colA] * b[rowB, colB];

    colA += 1;
    rowB += 1;
    if (colA >= a.GetLength(1))
    {
        colA = 0;
        rowB = 0;
        rowA += 1;
        if(rowA >= a.GetLength(0))
        {
            rowA = 0;
            colB += 1;
        }
    }

    if (colB >= b.GetLength(1))
        return result;

    return Multiply(a, b, rowA, colA, rowB, colB, result);
}

Answer 1

You're allocating a new result matrix every time, then almost always throwing it away. Only allocate one if the passed in c matrix is null.

Since you're recursion comes at the end (tail recursion), this could be changed over from recursion to a loop. If your matrix is too large, the recursion depth will be too deep and you'll run out of stack space. This won't happen with a loop.