Esempio n. 1
0
      public GaussianQuadrature(int n, GaussianOrthogonalPolynomial orthPoly)
      {
         x_ = new Vector(n);
         w_ = new Vector(n);

        // set-up matrix to compute the roots and the weights
        Vector e = new Vector(n-1);

        int i;
        for (i=1; i < n; ++i) 
        {
            x_[i] = orthPoly.alpha(i);
            e[i-1] = Math.Sqrt(orthPoly.beta(i));
        }
        x_[0] = orthPoly.alpha(0);

        TqrEigenDecomposition tqr = new TqrEigenDecomposition( x_, e,
                               TqrEigenDecomposition.EigenVectorCalculation.OnlyFirstRowEigenVector,
                               TqrEigenDecomposition.ShiftStrategy.Overrelaxation);

        x_ = tqr.eigenvalues();
        Matrix ev = tqr.eigenvectors();

        double mu_0 = orthPoly.mu_0();
        for (i=0; i<n; ++i) {
            w_[i] = mu_0*ev[0,i]*ev[0,i] / orthPoly.w(x_[i]);
        }
      }
Esempio n. 2
0
        public GaussianQuadrature(int n, GaussianOrthogonalPolynomial orthPoly)
        {
            x_ = new Vector(n);
            w_ = new Vector(n);

            // set-up matrix to compute the roots and the weights
            Vector e = new Vector(n - 1);

            int i;

            for (i = 1; i < n; ++i)
            {
                x_[i]    = orthPoly.alpha(i);
                e[i - 1] = Math.Sqrt(orthPoly.beta(i));
            }
            x_[0] = orthPoly.alpha(0);

            TqrEigenDecomposition tqr = new TqrEigenDecomposition(x_, e,
                                                                  TqrEigenDecomposition.EigenVectorCalculation.OnlyFirstRowEigenVector,
                                                                  TqrEigenDecomposition.ShiftStrategy.Overrelaxation);

            x_ = tqr.eigenvalues();
            Matrix ev = tqr.eigenvectors();

            double mu_0 = orthPoly.mu_0();

            for (i = 0; i < n; ++i)
            {
                w_[i] = mu_0 * ev[0, i] * ev[0, i] / orthPoly.w(x_[i]);
            }
        }