elliptic_integral

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

The complete and incomplete elliptic functions of the first, second and third kind can be evaluated, with parameters A (angle in degrees), K (sine of A) or M (the modulus, K^2).

The Jacobi elliptic functions CN(U,M), DN(U,M) and SN(U,M) can be evaluated with parameter M.

Licensing:

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

Languages:

elliptic_integral is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

elfun, a MATLAB code which evaluates elliptic integrals and Jacobi elliptic functions cn(), dn(), sn(), by Milan Batista.

elliptic_integral_test

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. Roland Bulirsch,,
   Numerical calculation of elliptic integrals and elliptic functions,,
   Numerische Mathematik,,
   Volume 7, Number 1, 1965, pages 78-90.
2. Bille Carlson,
   Computing Elliptic Integrals by Duplication,
   Numerische Mathematik,
   Volume 33, 1979, pages 1-16.
3. Bille Carlson, Elaine Notis,
   Algorithm 577, Algorithms for Incomplete Elliptic Integrals,
   ACM Transactions on Mathematical Software,
   Volume 7, Number 3, pages 398-403, September 1981.

Source Code:

• elliptic_ea.m evaluates the complete elliptic integral E(A).
• elliptic_ea_values.m returns values of the complete elliptic integral E(A).
• elliptic_ek.m evaluates the complete elliptic integral E(K).
• elliptic_ek_values.m returns values of the complete elliptic integral E(K).
• elliptic_em.m evaluates the complete elliptic integral E(M).
• elliptic_em_values.m returns values of the complete elliptic integral E(M).
• elliptic_fa.m evaluates the complete elliptic integral F(A).
• elliptic_fa_values.m returns values of the complete elliptic integral F(A).
• elliptic_fk.m evaluates the complete elliptic integral F(K).
• elliptic_fk_values.m returns values of the complete elliptic integral F(K).
• elliptic_fm.m evaluates the complete elliptic integral F(M).
• elliptic_fm_values.m returns values of the complete elliptic integral F(M).
• elliptic_inc_ea.m evaluates the incomplete elliptic integral E(PHI,A).
• elliptic_inc_ek.m evaluates the incomplete elliptic integral E(PHI,K).
• elliptic_inc_em.m evaluates the incomplete elliptic integral E(PHI,M).
• elliptic_inc_fa.m evaluates the incomplete elliptic integral F(PHI,A).
• elliptic_inc_fk.m evaluates the incomplete elliptic integral F(PHI,K).
• elliptic_inc_fm.m evaluates the incomplete elliptic integral F(PHI,M).
• elliptic_inc_pia.m evaluates the incomplete elliptic integral Pi(PHI,N,A).
• elliptic_inc_pik.m evaluates the incomplete elliptic integral Pi(PHI,N,K).
• elliptic_inc_pim.m evaluates the incomplete elliptic integral Pi(PHI,N,M).
• elliptic_pia.m evaluates the complete elliptic integral Pi(N,A).
• elliptic_pia_values.m returns values of the complete elliptic integral Pi(N,A).
• elliptic_pik.m evaluates the complete elliptic integral Pi(N,K).
• elliptic_pik_values.m returns values of the complete elliptic integral Pi(N,K).
• elliptic_pim.m evaluates the complete elliptic integral Pi(N,M).
• elliptic_pim_values.m returns values of the complete elliptic integral Pi(N,M).
• jacobi_cnm.m evaluates the Jacobi elliptic function CN(U,M).
• jacobi_cn_values.m returns some values of the Jacobi elliptic function CN(U,M).
• jacobi_dnm.m evaluates the Jacobi elliptic function DN(U,M).
• jacobi_dn_values.m returns some values of the Jacobi elliptic function DN(U,M).
• jacobi_snm.m evaluates the Jacobi elliptic function SN(U,M).
• jacobi_sn_values.m returns some values of the Jacobi elliptic function SN(U,M).
• rc.m computes the elementary integral RC(X,Y).
• rd.m computes an incomplete elliptic integral of the second kind, RD(X,Y,Z).
• rf.m computes an incomplete elliptic integral of the first kind, RF(X,Y,Z).
• rj.m computes an incomplete elliptic integral of the third kind, RJ(X,Y,Z,P).
• sncndn.m evaluates the Jacobi elliptic functions SN(U,M), CN(U,M) and DN(U,M).