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:
-
Bille Carlson,
Computing Elliptic Integrals by Duplication,
Numerische Mathematik,
Volume 33, 1979, pages 1-16.
-
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:
Examples and Tests:
List of Routines:
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R8_MAX returns the maximum of two R8's.
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ELLIPTIC_EA evaluates the complete elliptic integral E(A).
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ELLIPTIC_EA_VALUES returns values of the complete elliptic integral E(A).
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ELLIPTIC_EK evaluates the complete elliptic integral E(K).
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ELLIPTIC_EK_VALUES returns values of the complete elliptic integral E(K).
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ELLIPTIC_EM evaluates the complete elliptic integral E(M).
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ELLIPTIC_EM_VALUES returns values of the complete elliptic integral E(M).
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ELLIPTIC_FA evaluates the complete elliptic integral F(A).
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ELLIPTIC_FA_VALUES returns values of the complete elliptic integral F(A).
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ELLIPTIC_FK evaluates the complete elliptic integral F(K).
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ELLIPTIC_FK_VALUES returns values of the complete elliptic integral F(K).
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ELLIPTIC_FM evaluates the complete elliptic integral F(M).
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ELLIPTIC_FM_VALUES returns values of the complete elliptic integral F(M).
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ELLIPTIC_INC_EA evaluates the incomplete elliptic integral E(PHI,A).
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ELLIPTIC_INC_EA_VALUES: values of the incomplete elliptic integral E(PHI,A).
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ELLIPTIC_INC_EK evaluates the incomplete elliptic integral E(PHI,K).
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ELLIPTIC_INC_EK_VALUES: values of the incomplete elliptic integral E(PHI,K).
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ELLIPTIC_INC_EM evaluates the incomplete elliptic integral E(PHI,M).
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ELLIPTIC_INC_EM_VALUES: values of the incomplete elliptic integral E(PHI,M).
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ELLIPTIC_INC_FA evaluates the incomplete elliptic integral F(PHI,A).
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ELLIPTIC_INC_FA_VALUES: values of the incomplete elliptic integral F(PHI,A).
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ELLIPTIC_INC_FK evaluates the incomplete elliptic integral F(PHI,K).
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ELLIPTIC_INC_FK_VALUES: values of the incomplete elliptic integral F(PHI,K).
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ELLIPTIC_INC_FM evaluates the incomplete elliptic integral F(PHI,M).
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ELLIPTIC_INC_FM_VALUES: values of the incomplete elliptic integral F(PHI,M).
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ELLIPTIC_INC_PIA evaluates the incomplete elliptic integral Pi(PHI,N,A).
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ELLIPTIC_INC_PIA_VALUES: values of incomplete elliptic integral Pi(PHI,N,A).
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ELLIPTIC_INC_PIK evaluates the incomplete elliptic integral Pi(PHI,N,K).
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ELLIPTIC_INC_PIK_VALUES: values of incomplete elliptic integral Pi(PHI,N,K).
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ELLIPTIC_INC_PIM evaluates the incomplete elliptic integral Pi(PHI,N,M).
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ELLIPTIC_INC_PIM_VALUES: values of incomplete elliptic integral Pi(PHI,N,M).
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ELLIPTIC_PIA evaluates the complete elliptic integral Pi(N,A).
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ELLIPTIC_PIA_VALUES returns values of the complete elliptic integral Pi(A).
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ELLIPTIC_PIK evaluates the complete elliptic integral Pi(N,K).
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ELLIPTIC_PIK_VALUES returns values of the complete elliptic integral Pi(K).
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ELLIPTIC_PIM evaluates the complete elliptic integral Pi(N,M).
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ELLIPTIC_PIM_VALUES returns values of the complete elliptic integral Pi(M).
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RC computes the elementary integral RC(X,Y).
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RD computes an incomplete elliptic integral of the second kind, RD(X,Y,Z).
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RF computes an incomplete elliptic integral of the first kind, RF(X,Y,Z).
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RJ computes an incomplete elliptic integral of the third kind, RJ(X,Y,Z,P).
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TIMESTAMP prints the current YMDHMS date as a time stamp.
You can go up one level to
the C source codes.
Last revised on 25 June 2018.