Package org.hipparchus.special.elliptic.jacobi

Class JacobiElliptic

java.lang.Object

org.hipparchus.special.elliptic.jacobi.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

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.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

JacobiElliptic

protected JacobiElliptic(double m)

Simple constructor.

Parameters:

m - parameter of the function

Method Details

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