boost/math
2
0
Fork 0
mirror of https://github.com/boostorg/math.git synced 2026-01-27 07:02:08 +00:00
Code Issues Projects Releases Wiki Activity

[Ellint Pi] Add some more special case handling, plus tests.

Browse Source
This commit is contained in:
jzmaddock
2014-12-26 17:21:10 +00:00
parent 18dd27295d
commit 47c2f9254c
3 changed files with 65 additions and 19 deletions
Download Patch File Download Diff File Expand all files Collapse all files

25
include/boost/math/special_functions/ellint_3.hpp
View File

@@ -24,6 +24,7 @@
#include <boost/math/special_functions/ellint_1.hpp>
#include <boost/math/special_functions/ellint_2.hpp>
#include <boost/math/special_functions/log1p.hpp>
#include <boost/math/special_functions/atanh.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/math/policies/error_handling.hpp>
#include <boost/math/tools/workaround.hpp>
@@ -55,6 +56,7 @@ T ellint_pi_imp(T v, T phi, T k, T vc, const Policy& pol)
}
T sphi = sin(fabs(phi));
T result = 0;
if(v > 1 / (sphi * sphi))
{
@@ -69,6 +71,15 @@ T ellint_pi_imp(T v, T phi, T k, T vc, const Policy& pol)
// A&S 17.7.18 & 19
return (k == 0) ? phi : ellint_f_imp(phi, k, pol);
}
if(v == 1)
{
// http://functions.wolfram.com/08.06.03.0008.01
T m = k * k;
result = sqrt(1 - m * sphi * sphi) * tan(phi) - ellint_e_imp(phi, k, pol);
result /= 1 - m;
result += ellint_f_imp(phi, k, pol);
return result;
}
if(phi == constants::half_pi<T>())
{
// Have to filter this case out before the next
@@ -80,7 +91,6 @@ T ellint_pi_imp(T v, T phi, T k, T vc, const Policy& pol)
//
return ellint_pi_imp(v, k, vc, pol);
}
T result = 0;
if((phi > constants::half_pi<T>()) || (phi < 0))
{
// Carlson's algorithm works only for |phi| <= pi/2,
@@ -109,6 +119,10 @@ T ellint_pi_imp(T v, T phi, T k, T vc, const Policy& pol)
T rphi = boost::math::tools::fmod_workaround(T(fabs(phi)), T(constants::half_pi<T>()));
T m = boost::math::round((fabs(phi) - rphi) / constants::half_pi<T>());
int sign = 1;
if((m != 0) && (k >= 1))
{
return policies::raise_domain_error<T>(function, "Got k=1 and phi=%1% but the result is complex in that domain", phi, pol);
}
if(boost::math::tools::fmod_workaround(m, T(2)) > 0.5)
{
m += 1;
@@ -193,6 +207,13 @@ T ellint_pi_imp(T v, T phi, T k, T vc, const Policy& pol)
return (boost::math::log1p(arg, pol) - boost::math::log1p(-arg, pol)) / (2 * vcr);
}
}
if(k == 1)
{
// See http://functions.wolfram.com/08.06.03.0013.01
result = sqrt(v) * atanh(sqrt(v) * sin(phi)) - log(1 / cos(phi) + tan(phi));
result /= v - 1;
return result;
}
#if 0 // disabled but retained for future reference: see below.
if(v > 1)
{
@@ -231,7 +252,7 @@ T ellint_pi_imp(T v, T phi, T k, T vc, const Policy& pol)
// normalised above.
//
BOOST_ASSERT(fabs(phi) < constants::half_pi<T>());
BOOST_ASSERT(phi > 0);
BOOST_ASSERT(phi >= 0);
T x, y, z, p, t;
T cosp = cos(phi);
x = cosp * cosp;