ELLIPTIC_INTEGRAL
Elliptic Integrals

ELLIPTIC_INTEGRAL, a Python library which evaluates elliptic integral functions using Carlson's elliptic functions.

The complete and incomplete elliptic integrals 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).

Routines are also supplied to evaluate Jacobi's elliptic functions CN, DN and SN.

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:

TEST_VALUES, a Python library which supplies test values of various mathematical functions.

TOMS577, a Python library which evaluates Carlson's elliptic integral functions RC, RD, RF and RJ. This is a version of ACM TOMS algorithm 577;

Reference:

1. Bille Carlson,
   Computing Elliptic Integrals by Duplication,
   Numerische Mathematik,
   Volume 33, 1979, pages 1-16.
2. 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.py evaluates the complete elliptic integral E(A).
• elliptic_ea_values.py returns values of the complete elliptic integral E(A).
• elliptic_ek.py evaluates the complete elliptic integral E(K).
• elliptic_ek_values.py returns values of the complete elliptic integral E(K).
• elliptic_em.py evaluates the complete elliptic integral E(M).
• elliptic_em_values.py returns values of the complete elliptic integral E(M).
• elliptic_fa.py evaluates the complete elliptic integral F(A).
• elliptic_fa_values.py returns values of the complete elliptic integral F(A).
• elliptic_fk.py evaluates the complete elliptic integral F(K).
• elliptic_fk_values.py returns values of the complete elliptic integral F(K).
• elliptic_fm.py evaluates the complete elliptic integral F(M).
• elliptic_fm_values.py returns values of the complete elliptic integral F(M).
• elliptic_pia.py evaluates the complete elliptic integral Pi(N,A).
• elliptic_pia_values.py returns values of the complete elliptic integral Pi(N,A).
• elliptic_pik.py evaluates the complete elliptic integral Pi(N,K).
• elliptic_pik_values.py returns values of the complete elliptic integral Pi(N,K).
• elliptic_pim.py evaluates the complete elliptic integral Pi(N,M).
• elliptic_pim_values.py returns values of the complete elliptic integral Pi(N,M).
• elliptic_inc_ea.py evaluates the incomplete elliptic integral E(PHI,A).
• elliptic_inc_ea_values.py returns values of the incomplete elliptic integral E(PHI,A).
• elliptic_inc_ek.py evaluates the incomplete elliptic integral E(PHI,K).
• elliptic_inc_ek_values.py returns values of the incomplete elliptic integral E(PHI,K).
• elliptic_inc_em.py evaluates the incomplete elliptic integral E(PHI,M).
• elliptic_inc_em_values.py returns values of the incomplete elliptic integral E(PHI,M).
• elliptic_inc_fa.py evaluates the incomplete elliptic integral F(PHI,A).
• elliptic_inc_fa_values.py returns values of the incomplete elliptic integral F(PHI,A).
• elliptic_inc_fk.py evaluates the incomplete elliptic integral F(PHI,K).
• elliptic_inc_fk_values.py returns values of the incomplete elliptic integral F(PHI,K).
• elliptic_inc_fm.py evaluates the incomplete elliptic integral F(PHI,M).
• elliptic_inc_fm_values.py returns values of the incomplete elliptic integral F(PHI,M).
• elliptic_inc_pia.py evaluates the incomplete elliptic integral Pi(PHI,N,A).
• elliptic_inc_pia_values.py returns values of the incomplete elliptic integral Pi(PHI,N,A).
• elliptic_inc_pik.py evaluates the incomplete elliptic integral Pi(PHI,N,K).
• elliptic_inc_pik_values.py returns values of the incomplete elliptic integral Pi(N,K).
• elliptic_inc_pim.py evaluates the incomplete elliptic integral Pi(N,M).
• elliptic_inc_pim_values.py returns values of the incomplete elliptic integral Pi(N,M).
• jacobi_cn.py evaluates the Jacobi elliptic function CN(U,M).
• jacobi_cn_values.py returns some values of the Jacobi elliptic function CN(U,M).
• jacobi_dn.py evaluates the Jacobi elliptic function DN(U,M).
• jacobi_dn_values.py returns some values of the Jacobi elliptic function DN(U,M.
• jacobi_sn.py evaluates the Jacobi elliptic function SN(U,M).
• jacobi_sn_values.py returns some values of the Jacobi elliptic function SN((U,M.
• rc.py computes the elementary integral RC(X,Y).
• rd.py computes an incomplete elliptic integral of the second kind, RD(X,Y,Z).
• rf.py computes an incomplete elliptic integral of the first kind, RF(X,Y,Z).
• rj.py computes an incomplete elliptic integral of the third kind, RJ(X,Y,Z,P).
• sncndn.py, evaluates Jacobi elliptic functions SN(U,M), CN(U,M), DN(U,M).
• timestamp.py, prints the YMDHMS date as a timestamp.
• elliptic_integral_test.py
• elliptic_integral_test.txt

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