elfun

elfun, a MATLAB code which evaluates elliptic integrals, include Bulirsch's integrals cel(), cel1(), cel2(), cel3(), Carlson integrals rc(), rd(), rf(), rg(), rj(), and Jacobi functions cn(), dn(), sn(), by Milan Batista.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

elfun is available in a MATLAB version.

Related Data and Programs:

elfun_test

elliptic_integral, a MATLAB code which evaluates elliptic integral functions using Carlson's elliptic functions.

test_values, a MATLAB code which supplies test values of various mathematical functions.

toms577, a MATLAB code which evaluates Carlson's elliptic integral functions RC, RD, RF and RJ. This is a version of ACM TOMS algorithm 577;

Reference:

1. Milan Batista,
   Elfun18 - A collection of MATLAB functions for the computation of elliptic integrals and Jacobian elliptic functions of real arguments,
   SoftwareX,
   Volume 10, 2019,
   https://github.com/ElsevierSoftwareX/SOFTX_2018_246

Source Code:

• cel.m, evaluates Bulirsch's general complete elliptic integral.
• cel1.m, evaluates the complete Bulirsch's elliptic integral of the 1st kind.
• cel2.m, evaluates the complete Bulirsch's elliptic integral of the 2nd kind.
• cel3.m, evaluates the complete Bulirsch's elliptic integral of the 3rd kind.
• ijsn.m, inverse of Jacobi elliptic function SN.
• jacobi_cn_values.m, returns some values of the Jacobi elliptic function cn().
• jacobi_cnk.m, evaluates the Jacobi elliptic function x=cn(u,k).
• jacobi_cnk_inverse.m, computes the inverse of the Jacobi elliptic function x=cn(u,k).
• jacobi_dn_values.m, returns some values of the Jacobi elliptic function dn().
• jacobi_dnk.m, evaluates the Jacobi elliptic function x=dn(u,k).
• jacobi_dnk_inverse.m, computes the inverse of the Jacobi elliptic function x=dn(u,k).
• jacobi_sn_values.m, returns some values of the Jacobi elliptic function sn().
• jacobi_snk.m, evaluates the Jacobi elliptic function x=sn(u,k).
• jacobi_snk_inverse.m, computes the inverse of the Jacobi elliptic function x=sn(u,k).
• jcn.m, evaluates the Jacobi elliptic function cn(x,k).
• jdn.m, evaluates the Jacobi elliptic function dn(x,k).
• jsn.m, evaluates the Jacobi elliptic function sn(x,k).
• melf.m, evaluates incomplete elliptic integrals of the 1st kind.
• melk.m, evaluates complete elliptic integrals of the 1st kind.
• mijsn.m, computes the inverse of Jacobi elliptic function sn(x,m).
• pendulum_nonlinear_conserved.m, evaluates a quantity that should be conserved by the nonlinear pendulum ODE.
• pendulum_nonlinear_deriv.m, evaluates the right hand side of the nonlinear pendulum ODE.
• pendulum_nonlinear_exact.m, returns the exact solution of the nonlinear pendulum ODE;
• pendulum_nonlinear_parameters.m, returns parameters of the nonlinear pendulum ODE.
• r8_sign.m, returns the sign (+1 or -1 only) of a real value.
• rc.m, evaluates Carlson's degenerate elliptic integral of the 1st kind.
• rd.m, evaluates Carlson's degenerate elliptic integral of the 2nd kind.
• rf.m, evaluates Carlson's elliptic integral of the first kind.
• rg.m, evaluates Carlson's elliptic integral of the second kind.
• rj.m, evaluates Carlson's elliptic integral of the third kind.
• sncndn.m, evaluates the Jacobi elliptic functions sn, cn, dn.
• ufun1.m, mimics the elemental behavior of a function of 1 argument.
• ufun2.m, mimics the elemental behavior of a function of 2 arguments.
• ufun3.m, mimics the elemental behavior of a function of 3 arguments.
• ufun4.m, mimics the elemental behavior of a function of 4 arguments.
• umodpi.m, reduces |z| mod pi.