ELLIPTIC_INTEGRAL
Elliptic Integrals

ELLIPTIC_INTEGRAL, a C++ 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 C++ library which supplies test values of various mathematical functions.

TOMS577, a C++ 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_integral.cpp, the source code.
• elliptic_integral.hpp, the include file.

Examples and Tests:

• elliptic_integral_test.cpp, a sample calling program.
• elliptic_integral_test.txt, the output file.

List of Routines:

• ELLIPTIC_EA evaluates the complete elliptic integral E(A).
• ELLIPTIC_EA_VALUES: values of the complete elliptic integral E(ALPHA).
• ELLIPTIC_EK evaluates the complete elliptic integral E(K).
• ELLIPTIC_EK_VALUES returns values of the complete elliptic integral E(K).
• ELLIPTIC_EM evaluates the complete elliptic integral E(M).
• ELLIPTIC_EM_VALUES returns values of the complete elliptic integral E(M).
• ELLIPTIC_FA evaluates the complete elliptic integral F(A).
• ELLIPTIC_FA_VALUES: values of the complete elliptic integral F(ALPHA).
• ELLIPTIC_FK evaluates the complete elliptic integral F(K).
• ELLIPTIC_FK_VALUES returns values of the complete elliptic integral F(K).
• ELLIPTIC_FM evaluates the complete elliptic integral F(M).
• ELLIPTIC_FM_VALUES returns values of the complete elliptic integral F(M).
• ELLIPTIC_PIA evaluates the complete elliptic integral Pi(N,A).
• ELLIPTIC_PIA_VALUES returns values of the complete elliptic integral Pi(N,A).
• ELLIPTIC_PIK evaluates the complete elliptic integral Pi(N,K).
• ELLIPTIC_PIK_VALUES returns values of the complete elliptic integral Pi(N,K).
• ELLIPTIC_PIM evaluates the complete elliptic integral Pi(N,M).
• ELLIPTIC_PIM_VALUES returns values of the complete elliptic integral Pi(N,M).
• RC computes the elementary integral RC(X,Y).
• RD computes an incomplete elliptic integral of the second kind, RD(X,Y,Z).
• RF computes an incomplete elliptic integral of the first kind, RF(X,Y,Z).
• RJ computes an incomplete elliptic integral of the third kind, RJ(X,Y,Z,P).
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the C++ source codes.