Package org.hipparchus.special.elliptic.jacobi

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
    FieldJacobiElliptic(T m)
    Simple constructor.

  • Method Summary

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