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boost::math::detail log incomplete gamma function implemented

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This commit is contained in:
Jacob Hass
2025-12-28 14:06:20 -08:00
parent bb93d9fa46
commit d4afedc638
1 changed files with 45 additions and 0 deletions
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45
include/boost/math/special_functions/gamma.hpp
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@@ -1772,6 +1772,51 @@ BOOST_MATH_GPU_ENABLED T gamma_incomplete_imp(T a, T x, bool normalised, bool in
return gamma_incomplete_imp_final(T(a), T(x), normalised, invert, pol, p_derivative); return gamma_incomplete_imp_final(T(a), T(x), normalised, invert, pol, p_derivative);
} }
// Calculate log of incomplete gamma function
template <class T, class Policy>
T lgamma_incomplete_imp_final(T a, T x, const Policy& pol)
{
using namespace boost::math; // temporary until we're in the right namespace
BOOST_MATH_STD_USING_CORE
if (((x > 1000) && ((a < x) || (fabs(a - 50) / x < 1))) || ((x > tools::log_max_value<T>() - 10) && (x > a)))
{
//
// Take the logarithmic version of the asymtotic expansion:
//
return log(detail::incomplete_tgamma_large_x(a, x, pol)) + a * log(x) - x - lgamma(a, pol) - log(x);
}
//
// Can't do better than taking the log of Q, but...
//
// Figure out whether we need P or Q, since if we calculate Q and it's too close to unity
// we will loose precision in the result, selection logic here is extracted from gamma_incomplete_imp_final:
//
bool need_p = false;
if ((x < 0.5) && (T(-0.4) / log(x) < a))
need_p = true;
else if ((x < 1.1) && (x >= 0.5) && (x * 0.75f < a))
need_p = true;
else if ((x < a) && (x >= 1.1))
need_p = true;
if (need_p)
return log1p(-gamma_p(a, x, pol), pol);
return log(gamma_q(a, x, pol));
}
template <class T, class Policy>
T lgamma_incomplete_imp(T a, T x, const Policy& pol){
constexpr auto function = "boost::math::lgamma_p<%1%>(%1%, %1%)";
if(a <= 0)
return policies::raise_domain_error<T>(function, "Argument a to the incomplete gamma function must be greater than zero (got a=%1%).", a, pol);
if(x < 0)
return policies::raise_domain_error<T>(function, "Argument x to the incomplete gamma function must be >= 0 (got x=%1%).", x, pol);
// If input is valid proceed as normal
return lgamma_incomplete_imp_final(T(a), T(x), pol)
}
// //
// Ratios of two gamma functions: // Ratios of two gamma functions:
// //