SHOGUN  6.0.0
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Macros Modules
JacobiEllipticFunctions.h File Reference

Go to the source code of this file.


class  CJacobiEllipticFunctions
 Class that contains methods for computing Jacobi elliptic functions related to complex analysis. These functions are inverse of the elliptic integral of first kind, i.e.

\[ u(k,m)=\int_{0}^{k}\frac{dt}{\sqrt{(1-t^{2})(1-m^{2}t^{2})}} =\int_{0}^{\varphi}\frac{d\theta}{\sqrt{(1-m^{2}sin^{2}\theta)}} \]

where \(k=sin\varphi\), \(t=sin\theta\) and parameter \(m, 0\le m \le 1\) is called modulus. Three main Jacobi elliptic functions are defined as \(sn(u,m)=k=sin\theta\), \(cn(u,m)=cos\theta=\sqrt{1-sn(u,m)^{2}}\) and \(dn(u,m)=\sqrt{1-m^{2}sn(u,m)^{2}}\). For \(k=1\), i.e. \(\varphi=\frac{\pi}{2}\), \(u(1,m)=K(m)\) is known as the complete elliptic integral of first kind. Similarly, \(u(1,m'))= K'(m')\), \(m'=\sqrt{1-m^{2}}\) is called the complementary complete elliptic integral of first kind. Jacobi functions are double periodic with quardratic periods \(K\) and \(K'\). More...


SHOGUN Machine Learning Toolbox - Documentation