Class UpperBounds


  • public class UpperBounds
    extends Object
    Utility class to compute upper bounds for truncation algorithms.
    Author:
    Pascal Parraud
    • Method Detail

      • getDnl

        public static double getDnl​(double xx,
                                    double xpl,
                                    int n,
                                    int l)
        Get the upper bound value Dnl(Χ).
        Parameters:
        xx - value of Χ²
        xpl - value of Χ * (Χ² / 2)l
        n - index n (power of a/R)
        l - index l (power of eccentricity)
        Returns:
        the upper bound Dnl(Χ)
      • getDnl

        public static <T extends CalculusFieldElement<T>> T getDnl​(T xx,
                                                                   T xpl,
                                                                   int n,
                                                                   int l)
        Get the upper bound value Dnl(Χ).
        Type Parameters:
        T - the type of the field elements
        Parameters:
        xx - value of Χ²
        xpl - value of Χ * (Χ² / 2)l
        n - index n (power of a/R)
        l - index l (power of eccentricity)
        Returns:
        the upper bound Dnl(Χ)
      • getRnml

        public static double getRnml​(double gamma,
                                     int n,
                                     int l,
                                     int m,
                                     int eps,
                                     int irf)
        Get the upper bound value Rεn,m,l(γ).
        Parameters:
        gamma - value of γ
        n - index n
        l - index l
        m - index m
        eps - ε value (+1/-1)
        irf - retrograde factor I (+1/-1)
        Returns:
        the upper bound Rεn,m,l(γ)
      • getRnml

        public static <T extends CalculusFieldElement<T>> T getRnml​(T gamma,
                                                                    int n,
                                                                    int l,
                                                                    int m,
                                                                    int eps,
                                                                    int irf)
        Get the upper bound value Rεn,m,l(γ).
        Type Parameters:
        T - the type of the field elements
        Parameters:
        gamma - value of γ
        n - index n
        l - index l
        m - index m
        eps - ε value (+1/-1)
        irf - retrograde factor I (+1/-1)
        Returns:
        the upper bound Rεn,m,l(γ)