Class GaussJacobiWeightAndAbscissaFunction

  • All Implemented Interfaces:
    QuadratureWeightAndAbscissaFunction

    public class GaussJacobiWeightAndAbscissaFunction
    extends Object
    implements QuadratureWeightAndAbscissaFunction
    Class that generates weights and abscissas for Gauss-Jacobi quadrature. The weights $w_i$ are given by: $$ \begin{align*} w_i = \frac{2^{\alpha + \beta}(2n + \alpha + \beta)\Gamma(\alpha + n)\Gamma(\beta + n)}{n!\Gamma(n + \alpha + \beta + 1)J_i'(x_i) J_{i - 1}} \end{align*} $$ where $x_i$ is the $i^{th}$ root of the orthogonal polynomial, $J_i$ is the $i^{th}$ polynomial and $J_i'$ is the first derivative of the $i^{th}$ polynomial. The orthogonal polynomial is generated by JacobiPolynomialFunction.
    • Constructor Detail

      • GaussJacobiWeightAndAbscissaFunction

        public GaussJacobiWeightAndAbscissaFunction()
        Creates an instance. Sets $\alpha = 0$ and $\beta = 0$
      • GaussJacobiWeightAndAbscissaFunction

        public GaussJacobiWeightAndAbscissaFunction​(double alpha,
                                                    double beta)
        Creates an instance.
        Parameters:
        alpha - The value of $\alpha$ to use when generating the polynomials
        beta - The value of $\beta$ to use when generating the polynomials