Package org.hipparchus.special.elliptic.jacobi

Class JacobiElliptic

  • public abstract class JacobiElliptic
extends Object
    Algorithm computing Jacobi elliptic functions.
    Since:
    2.0

    • Constructor Summary

      Constructors 
      Modifier Constructor Description
      protected JacobiElliptic​(double m)
      Simple constructor.

    • Method Summary

      All Methods Instance Methods Abstract Methods Concrete Methods 
      Modifier and Type Method Description
      double arccd​(double x)
      Evaluate inverse of Jacobi elliptic function cd.
      double arccn​(double x)
      Evaluate inverse of Jacobi elliptic function cn.
      double arccs​(double x)
      Evaluate inverse of Jacobi elliptic function cs.
      double arcdc​(double x)
      Evaluate inverse of Jacobi elliptic function dc.
      double arcdn​(double x)
      Evaluate inverse of Jacobi elliptic function dn.
      double arcds​(double x)
      Evaluate inverse of Jacobi elliptic function ds.
      double arcnc​(double x)
      Evaluate inverse of Jacobi elliptic function nc.
      double arcnd​(double x)
      Evaluate inverse of Jacobi elliptic function nd.
      double arcns​(double x)
      Evaluate inverse of Jacobi elliptic function ns.
      double arcsc​(double x)
      Evaluate inverse of Jacobi elliptic function sc.
      double arcsd​(double x)
      Evaluate inverse of Jacobi elliptic function sd.
      double arcsn​(double x)
      Evaluate inverse of Jacobi elliptic function sn.
      double getM()
      Get the parameter of the function.
      CopolarC valuesC​(double u)
      Evaluate the three subsidiary Jacobi elliptic functions with pole at point c in Glaisher’s Notation.
      CopolarD valuesD​(double u)
      Evaluate the three subsidiary Jacobi elliptic functions with pole at point d in Glaisher’s Notation.
      abstract CopolarN valuesN​(double u)
      Evaluate the three principal Jacobi elliptic functions with pole at point n in Glaisher’s Notation.
      CopolarS valuesS​(double u)
      Evaluate the three subsidiary Jacobi elliptic functions with pole at point s in Glaisher’s Notation.

    • Constructor Detail

      • JacobiElliptic

        protected JacobiElliptic​(double m)
        Simple constructor.
        Parameters:
        m - parameter of the function

    • Method Detail

      • getM

        public double getM()
        Get the parameter of the function.
        Returns:
        parameter of the function

      • valuesN

        public abstract CopolarN valuesN​(double u)
        Evaluate the three principal Jacobi elliptic functions with pole at point n in Glaisher’s Notation.
        Parameters:
        u - argument of the functions
        Returns:
        copolar trio containing the three principal Jacobi elliptic functions sn(u|m), cn(u|m), and dn(u|m).

      • valuesS

        public CopolarS valuesS​(double u)
        Evaluate the three subsidiary Jacobi elliptic functions with pole at point s in Glaisher’s Notation.
        Parameters:
        u - argument of the functions
        Returns:
        copolar trio containing the three subsidiary Jacobi elliptic functions cs(u|m), ds(u|m) and ns(u|m).

      • valuesC

        public CopolarC valuesC​(double u)
        Evaluate the three subsidiary Jacobi elliptic functions with pole at point c in Glaisher’s Notation.
        Parameters:
        u - argument of the functions
        Returns:
        copolar trio containing the three subsidiary Jacobi elliptic functions dc(u|m), nc(u|m), and sc(u|m).

      • valuesD

        public CopolarD valuesD​(double u)
        Evaluate the three subsidiary Jacobi elliptic functions with pole at point d in Glaisher’s Notation.
        Parameters:
        u - argument of the functions
        Returns:
        copolar trio containing the three subsidiary Jacobi elliptic functions nd(u|m), sd(u|m), and cd(u|m).

      • arcsn

        public double arcsn​(double x)
        Evaluate inverse of Jacobi elliptic function sn.
        Parameters:
        x - value of Jacobi elliptic function sn(u|m)
        Returns:
        u such that x=sn(u|m)
        Since:
        2.1

      • arccn

        public double arccn​(double x)
        Evaluate inverse of Jacobi elliptic function cn.
        Parameters:
        x - value of Jacobi elliptic function cn(u|m)
        Returns:
        u such that x=cn(u|m)
        Since:
        2.1

      • arcdn

        public double arcdn​(double x)
        Evaluate inverse of Jacobi elliptic function dn.
        Parameters:
        x - value of Jacobi elliptic function dn(u|m)
        Returns:
        u such that x=dn(u|m)
        Since:
        2.1

      • arccs

        public double arccs​(double x)
        Evaluate inverse of Jacobi elliptic function cs.
        Parameters:
        x - value of Jacobi elliptic function cs(u|m)
        Returns:
        u such that x=cs(u|m)
        Since:
        2.1

      • arcds

        public double arcds​(double x)
        Evaluate inverse of Jacobi elliptic function ds.
        Parameters:
        x - value of Jacobi elliptic function ds(u|m)
        Returns:
        u such that x=ds(u|m)
        Since:
        2.1

      • arcns

        public double arcns​(double x)
        Evaluate inverse of Jacobi elliptic function ns.
        Parameters:
        x - value of Jacobi elliptic function ns(u|m)
        Returns:
        u such that x=ns(u|m)
        Since:
        2.1

      • arcdc

        public double arcdc​(double x)
        Evaluate inverse of Jacobi elliptic function dc.
        Parameters:
        x - value of Jacobi elliptic function dc(u|m)
        Returns:
        u such that x=dc(u|m)
        Since:
        2.1

      • arcnc

        public double arcnc​(double x)
        Evaluate inverse of Jacobi elliptic function nc.
        Parameters:
        x - value of Jacobi elliptic function nc(u|m)
        Returns:
        u such that x=nc(u|m)
        Since:
        2.1

      • arcsc

        public double arcsc​(double x)
        Evaluate inverse of Jacobi elliptic function sc.
        Parameters:
        x - value of Jacobi elliptic function sc(u|m)
        Returns:
        u such that x=sc(u|m)
        Since:
        2.1

      • arcnd

        public double arcnd​(double x)
        Evaluate inverse of Jacobi elliptic function nd.
        Parameters:
        x - value of Jacobi elliptic function nd(u|m)
        Returns:
        u such that x=nd(u|m)
        Since:
        2.1

      • arcsd

        public double arcsd​(double x)
        Evaluate inverse of Jacobi elliptic function sd.
        Parameters:
        x - value of Jacobi elliptic function sd(u|m)
        Returns:
        u such that x=sd(u|m)
        Since:
        2.1

      • arccd

        public double arccd​(double x)
        Evaluate inverse of Jacobi elliptic function cd.
        Parameters:
        x - value of Jacobi elliptic function cd(u|m)
        Returns:
        u such that x=cd(u|m)
        Since:
        2.1