Class AbstractRuleFactory

    • Constructor Detail

      • AbstractRuleFactory

        public AbstractRuleFactory()
        Empty constructor.

        This constructor is not strictly necessary, but it prevents spurious javadoc warnings with JDK 18 and later.

        Since:
        3.0
    • Method Detail

      • getRule

        public Pair<double[],​double[]> getRule​(int numberOfPoints)
                                              throws MathIllegalArgumentException
        Gets a copy of the quadrature rule with the given number of integration points. The number of points is arbitrarily limited to 1000. It prevents resources exhaustion. In practice the number of points is often much lower.
        Specified by:
        getRule in interface RuleFactory
        Parameters:
        numberOfPoints - Number of integration points.
        Returns:
        a copy of the integration rule.
        Throws:
        MathIllegalArgumentException - if numberOfPoints < 1.
      • computeRule

        protected abstract Pair<double[],​double[]> computeRule​(int numberOfPoints)
                                                              throws MathIllegalArgumentException
        Computes the rule for the given order.
        Parameters:
        numberOfPoints - Order of the rule to be computed.
        Returns:
        the computed rule.
        Throws:
        MathIllegalArgumentException - if the elements of the pair do not have the same length.
      • findRoots

        protected double[] findRoots​(int n,
                                     UnivariateFunction ratioEvaluator)
        Computes roots of the associated orthogonal polynomials.

        The roots are found using the Aberth method. The guess points for initializing search for degree n are fixed for degrees 1 and 2 and are selected from n-1 roots of rule n-1 (the two extreme roots are used, plus the n-1 intermediate points between all roots).

        Parameters:
        n - number of roots to search for
        ratioEvaluator - function evaluating the ratio Pₙ(x)/Pₙ'(x)
        Returns:
        sorted array of roots
      • enforceSymmetry

        protected void enforceSymmetry​(double[] roots)
        Enforce symmetry of roots.
        Parameters:
        roots - roots to process in place