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]);
}
}
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]);
}
}