Class FieldJacobiElliptic<T extends CalculusFieldElement<T>>

java.lang.Object
org.hipparchus.special.elliptic.jacobi.FieldJacobiElliptic<T>
Type Parameters:
T - the type of the field elements

public abstract class FieldJacobiElliptic<T extends CalculusFieldElement<T>> extends Object
Computation of Jacobi elliptic functions. The Jacobi elliptic functions are related to elliptic integrals.
Since:
2.0
  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    protected
    Simple constructor.
  • Method Summary

    Modifier and Type
    Method
    Description
    arccd(double x)
    Evaluate inverse of Jacobi elliptic function cd.
    arccd(T x)
    Evaluate inverse of Jacobi elliptic function cd.
    arccn(double x)
    Evaluate inverse of Jacobi elliptic function cn.
    arccn(T x)
    Evaluate inverse of Jacobi elliptic function cn.
    arccs(double x)
    Evaluate inverse of Jacobi elliptic function cs.
    arccs(T x)
    Evaluate inverse of Jacobi elliptic function cs.
    arcdc(double x)
    Evaluate inverse of Jacobi elliptic function dc.
    arcdc(T x)
    Evaluate inverse of Jacobi elliptic function dc.
    arcdn(double x)
    Evaluate inverse of Jacobi elliptic function dn.
    arcdn(T x)
    Evaluate inverse of Jacobi elliptic function dn.
    arcds(double x)
    Evaluate inverse of Jacobi elliptic function ds.
    arcds(T x)
    Evaluate inverse of Jacobi elliptic function ds.
    arcnc(double x)
    Evaluate inverse of Jacobi elliptic function nc.
    arcnc(T x)
    Evaluate inverse of Jacobi elliptic function nc.
    arcnd(double x)
    Evaluate inverse of Jacobi elliptic function nd.
    arcnd(T x)
    Evaluate inverse of Jacobi elliptic function nd.
    arcns(double x)
    Evaluate inverse of Jacobi elliptic function ns.
    arcns(T x)
    Evaluate inverse of Jacobi elliptic function ns.
    arcsc(double x)
    Evaluate inverse of Jacobi elliptic function sc.
    arcsc(T x)
    Evaluate inverse of Jacobi elliptic function sc.
    arcsd(double x)
    Evaluate inverse of Jacobi elliptic function sd.
    arcsd(T x)
    Evaluate inverse of Jacobi elliptic function sd.
    arcsn(double x)
    Evaluate inverse of Jacobi elliptic function sn.
    arcsn(T x)
    Evaluate inverse of Jacobi elliptic function sn.
    Get the parameter of the function.
    valuesC(double u)
    Evaluate the three subsidiary Jacobi elliptic functions with pole at point c in Glaisher’s Notation.
    Evaluate the three subsidiary Jacobi elliptic functions with pole at point c in Glaisher’s Notation.
    valuesD(double u)
    Evaluate the three subsidiary Jacobi elliptic functions with pole at point d in Glaisher’s Notation.
    Evaluate the three subsidiary Jacobi elliptic functions with pole at point d in Glaisher’s Notation.
    valuesN(double u)
    Evaluate the three principal Jacobi elliptic functions with pole at point n in Glaisher’s Notation.
    abstract FieldCopolarN<T>
    Evaluate the three principal Jacobi elliptic functions with pole at point n in Glaisher’s Notation.
    valuesS(double u)
    Evaluate the three subsidiary Jacobi elliptic functions with pole at point s in Glaisher’s Notation.
    Evaluate the three subsidiary Jacobi elliptic functions with pole at point s in Glaisher’s Notation.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
  • Constructor Details

    • FieldJacobiElliptic

      protected FieldJacobiElliptic(T m)
      Simple constructor.
      Parameters:
      m - parameter of the function
  • Method Details

    • getM

      public T getM()
      Get the parameter of the function.
      Returns:
      parameter of the function
    • valuesN

      public abstract FieldCopolarN<T> valuesN(T 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).
    • valuesN

      public FieldCopolarN<T> 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 FieldCopolarS<T> valuesS(T 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).
    • valuesS

      public FieldCopolarS<T> 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 FieldCopolarC<T> valuesC(T 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).
    • valuesC

      public FieldCopolarC<T> 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 FieldCopolarD<T> valuesD(T 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).
    • valuesD

      public FieldCopolarD<T> 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 T arcsn(T 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
    • arcsn

      public T 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 T arccn(T 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
    • arccn

      public T 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 T arcdn(T 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
    • arcdn

      public T 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 T arccs(T 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
    • arccs

      public T 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 T arcds(T 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
    • arcds

      public T 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 T arcns(T 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
    • arcns

      public T 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 T arcdc(T 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
    • arcdc

      public T 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 T arcnc(T 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
    • arcnc

      public T 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 T arcsc(T 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
    • arcsc

      public T 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 T arcnd(T 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
    • arcnd

      public T 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 T arcsd(T 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
    • arcsd

      public T 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 T arccd(T 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
    • arccd

      public T 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