Package de.labathome

Class CompleteEllipticIntegral

java.lang.Object

de.labathome.CompleteEllipticIntegral

public class CompleteEllipticIntegral
extends Object

Complete Elliptic Integral introduced by R. Bulirsch (1969). These routines are based on a set of three articles: * https://doi.org/10.1007/BF01397975 (Part I) * https://doi.org/10.1007/BF01436529 (Part II) * https://doi.org/10.1007/BF02165405 (Part III)

Constructor Summary

Constructors

Constructor	Description
CompleteEllipticIntegral()

Method Summary

Modifier and Type	Method	Description
static double	cel(double k_c, double p, double a, double b)	Compute the complete elliptic integral introduced in "Numerical Calculation of Elliptic Integrals and Elliptic Functions.
static double	ellipticE(double k)	Evaluate the complete elliptic integral of the second kind E(k) using cel(k_c, 1, 1, k_c^2) with k^2 + k_c^2 = 1.
static double	ellipticK(double k)	Evaluate the complete elliptic integral of the first kind K(k) using cel(k_c, 1, 1, 1) with k^2 + k_c^2 = 1.

Methods inherited from class java.lang.Object

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

Constructor Detail

CompleteEllipticIntegral

public CompleteEllipticIntegral()

Method Detail

cel

public static double cel(double k_c,
                         double p,
                         double a,
                         double b)

Compute the complete elliptic integral introduced in "Numerical Calculation of Elliptic Integrals and Elliptic Functions. III" by R. Bulirsch in "Numerische Mathematik" 13, 305-315 (1969): cel(k_c, p, a, b) = \int_0^{\pi/2} \frac{a \cos^2{\varphi} + b \sin^2{\varphi}} { \cos^2{\varphi} + p \sin^2{\varphi}} \frac{\mathrm{d}\varphi} {\sqrt{\cos^2{\varphi} + k_c^2 \sin^2{\varphi}}}

Parameters:

k_c - parameter k_c of cel(); absolute value must not be 0

p - parameter p of cel()

a - parameter a of cel()

b - parameter b of cel()

Returns:

the value of cel(k_c, p, a, b)

ellipticK

public static double ellipticK(double k)

Evaluate the complete elliptic integral of the first kind K(k) using cel(k_c, 1, 1, 1) with k^2 + k_c^2 = 1.

Parameters:

k - modulus

Returns:

complete elliptic integral of the first kind

ellipticE

public static double ellipticE(double k)

Evaluate the complete elliptic integral of the second kind E(k) using cel(k_c, 1, 1, k_c^2) with k^2 + k_c^2 = 1.

Parameters:

k - modulus

Returns:

complete elliptic integral of the first kind