MathNet.Numerics.LinearAlgebra.Double.DenseMatrix.QR C# (CSharp) Method

        public override QR<double> QR(QRMethod method = QRMethod.Thin)
        {
            return DenseQR.Create(this, method);
        }

        /// <summary>
        /// Linear regression simulation for homework Q5-Q6 of the 
        ///  2nd week of the CS1156x "Learning From Data" at eDX
        /// </summary>
        static void RunQ5Q6Simulation()
        {
            const int EXPERIMENT_COUNT = 1000, N = 100;
              Random rnd = new Random();

              double avgEin = 0, avgEout = 0;
              for (int i = 1; i <= EXPERIMENT_COUNT; i++)
              {
            //pick a random line y = a1 * x + b1
            double x1 = rnd.NextDouble(), y1 = rnd.NextDouble(), x2 = rnd.NextDouble(), y2 = rnd.NextDouble();
            double a = (y1 - y2) / (x1 - x2), b = y1 - a * x1;
            Func<double, double, int> f = (x, y) => a * x + b >= y ? 1 : -1;

            //generate training set of N random points
            var X = new DenseMatrix(N, 3);
            var Y = new DenseVector(N);
            for (int j = 0; j < N; j++)
            {
              X[j, 0] = 1;
              X[j, 1] = rnd.NextDouble() * 2 - 1;
              X[j, 2] = rnd.NextDouble() * 2 - 1;

              Y[j] = f(X[j, 1], X[j, 2]);
            }

            var W = X.QR().Solve(DenseMatrix.Identity(X.RowCount)).Multiply(Y);

            Func<double, double, int> h = (x, y) => W[0] + W[1] * x + W[2] * y >= 0 ? 1 : -1;

            //find Ein
            int count = 0;
            for (int j = 0; j < N; j++) if (h(X[j, 1], X[j, 2]) != Y[j]) count++;
            avgEin += (count + 0.0) / N;

            //find p: f != g
            const int P_SAMPLE_COUNT = 1000;
            count = 0;
            for (int j = 1; j <= P_SAMPLE_COUNT; j++)
            {
              double xx = rnd.NextDouble() * 2 - 1;
              double yy = rnd. NextDouble() * 2 - 1;
              if (f(xx, yy) != h(xx, yy)) count++;
            }

            avgEout += (count + 0.0) / P_SAMPLE_COUNT;
              }

              Console.Out.WriteLine("HW2 Q5:");
              Console.Out.WriteLine("\tEin = {0}", avgEin / EXPERIMENT_COUNT);
              Console.Out.WriteLine("HW2 Q6:");
              Console.Out.WriteLine("\tEout = {0}", avgEout / EXPERIMENT_COUNT);
        }