Task: Gaussian elimination
C#: using System;

namespace Rosetta
{
    internal class Vector
    {
        private double[] b;
        internal readonly int rows;

        internal Vector(int rows)
        {
            this.rows = rows;
            b = new double[rows];
        }

        internal Vector(double[] initArray)
        {
            b = (double[])initArray.Clone();
            rows = b.Length;
        }

        internal Vector Clone()
        {
            Vector v = new Vector(b);
            return v;
        }

        internal double this[int row]
        {
            get { return b[row]; }
            set { b[row] = value; }
        }

        internal void SwapRows(int r1, int r2)
        {
            if (r1 == r2) return;
            double tmp = b[r1];
            b[r1] = b[r2];
            b[r2] = tmp;
        }

        internal double norm(double[] weights)
        {
            double sum = 0;
            for (int i = 0; i < rows; i++)
            {
                double d = b[i] * weights[i];
                sum +=  d*d;
            }
            return Math.Sqrt(sum);
        }

        internal void print()
        {
            for (int i = 0; i < rows; i++)
                Console.WriteLine(b[i]);
            Console.WriteLine();
        }

        public static Vector operator-(Vector lhs, Vector rhs)
        {
            Vector v = new Vector(lhs.rows);
            for (int i = 0; i < lhs.rows; i++)
                v[i] = lhs[i] - rhs[i];
            return v;
        }
    }

    class Matrix
    {
        private double[] b;
        internal readonly int rows, cols;

        internal Matrix(int rows, int cols)
        {
            this.rows = rows;
            this.cols = cols;
            b = new double[rows * cols];            
        }

        internal Matrix(int size)
        {
            this.rows = size;
            this.cols = size;
            b = new double[rows * cols];
            for (int i = 0; i < size; i++)
                this[i, i] = 1;
        }

        internal Matrix(int rows, int cols, double[] initArray)
        {
            this.rows = rows;
            this.cols = cols;
            b = (double[])initArray.Clone();
            if (b.Length != rows * cols) throw new Exception("bad init array");
        }

        internal double this[int row, int col]
        {
            get { return b[row * cols + col]; }
            set { b[row * cols + col] = value; }
        }        
        
        public static Vector operator*(Matrix lhs, Vector rhs)
        {
            if (lhs.cols != rhs.rows) throw new Exception("I can't multiply matrix by vector");
            Vector v = new Vector(lhs.rows);
            for (int i = 0; i < lhs.rows; i++)
            {
                double sum = 0;
                for (int j = 0; j < rhs.rows; j++)
                    sum += lhs[i,j]*rhs[j];
                v[i] = sum;
            }
            return v;
        }

        internal void SwapRows(int r1, int r2)
        {
            if (r1 == r2) return;
            int firstR1 = r1 * cols;
            int firstR2 = r2 * cols;
            for (int i = 0; i < cols; i++)
            {
                double tmp = b[firstR1 + i];
                b[firstR1 + i] = b[firstR2 + i];
                b[firstR2 + i] = tmp;
            }
        }

        
        internal void ElimPartial(Vector B)
        {
            for (int diag = 0; diag < rows; diag++)
            {
                int max_row = diag;
                double max_val = Math.Abs(this[diag, diag]);
                double d;
                for (int row = diag + 1; row < rows; row++)
                    if ((d = Math.Abs(this[row, diag])) > max_val)
                    {
                        max_row = row;
                        max_val = d;
                    }
                SwapRows(diag, max_row);
                B.SwapRows(diag, max_row);
                double invd = 1 / this[diag, diag];
                for (int col = diag; col < cols; col++)
                    this[diag, col] *= invd;
                B[diag] *= invd;
                for (int row = 0; row < rows; row++)
                {
                    d = this[row, diag];
                    if (row != diag)
                    {
                        for (int col = diag; col < cols; col++)
                            this[row, col] -= d * this[diag, col];
                        B[row] -= d * B[diag];
                    }
                }
            }
        }
        
        internal void print()
        {
            for (int i = 0; i < rows; i++)
            {
                for (int j = 0; j < cols; j++)
                    Console.Write(this[i,j].ToString()+"  ");
                Console.WriteLine();
            }
        }
    }
}

PHP: function swap_rows(&$a, &$b, $r1, $r2)
{
    if ($r1 == $r2) return;

    $tmp = $a[$r1];
    $a[$r1] = $a[$r2];
    $a[$r2] = $tmp;

    $tmp = $b[$r1];
    $b[$r1] = $b[$r2];
    $b[$r2] = $tmp;
}

function gauss_eliminate($A, $b, $N)
{
    for ($col = 0; $col < $N; $col++)
    {
        $j = $col;
        $max = $A[$j][$j];

        for ($i = $col + 1; $i < $N; $i++)
        {
            $tmp = abs($A[$i][$col]);
            if ($tmp > $max)
            {
                $j = $i;
                $max = $tmp;
            }
        }

        swap_rows($A, $b, $col, $j);

        for ($i = $col + 1; $i < $N; $i++)
        {
            $tmp = $A[$i][$col] / $A[$col][$col];
            for ($j = $col + 1; $j < $N; $j++)
            {
                $A[$i][$j] -= $tmp * $A[$col][$j];
            }
            $A[$i][$col] = 0;
            $b[$i] -= $tmp * $b[$col];
        }
    }
    $x = array();
    for ($col = $N - 1; $col >= 0; $col--)
    {
        $tmp = $b[$col];
        for ($j = $N - 1; $j > $col; $j--)
        {
            $tmp -= $x[$j] * $A[$col][$j];
        }
        $x[$col] = $tmp / $A[$col][$col];
    }
    return $x;
}

function test_gauss()
{
    $a = array(
        array(1.00, 0.00, 0.00,  0.00,  0.00, 0.00),
        array(1.00, 0.63, 0.39,  0.25,  0.16, 0.10),
        array(1.00, 1.26, 1.58,  1.98,  2.49, 3.13),
        array(1.00, 1.88, 3.55,  6.70, 12.62, 23.80),
        array(1.00, 2.51, 6.32, 15.88, 39.90, 100.28),
        array(1.00, 3.14, 9.87, 31.01, 97.41, 306.02)
    );
    $b = array( -0.01, 0.61, 0.91, 0.99, 0.60, 0.02 );

    $x = gauss_eliminate($a, $b, 6);

    ksort($x);
    print_r($x);
}

test_gauss();