Linear Algebra

Echelon Form

public void Echelon_Form()
{
    // Go through the first column, looking for something that is not a zero,
    // Swap it with the first row, & make it a 1.
    Fraction zero = new Fraction(0);
    
    for (int i=0; i<columns; i++) // Going up to down
    {
        // Divide each element along the column by pivot
        Fraction divisor = new Fraction(A[i][i]);
        for (int j=i; j<rows; j++)  // Left to right, divide each element in the row by pivot
            if (!(Fraction.Equals(divisor, zero)))
                A[i][j] = new Fraction(Fraction.Divide(A[i][j], divisor));

        for (int h=i+1; h<rows; h++)  // From pivot row down
        {
            divisor = Fraction.Multiply(A[h][i], new Fraction(-1));
            for (int j=i; j<columns; j++)
                A[h][j] = new Fraction(Fraction.Add(A[h][j], Fraction.Multiply(divisor, A[i][j])));
        }
    }
}