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Correct non-central-t series convergence bug. #1038

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Oct 14, 2023
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Correct non-central-t series convergence bug. #1038

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13 changes: 12 additions & 1 deletion include/boost/math/distributions/non_central_t.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -396,10 +396,12 @@ namespace boost
pois = gamma_p_derivative(T(k+1), d2, pol)
* tgamma_delta_ratio(T(k + 1), T(0.5f))
* delta / constants::root_two<T>();
BOOST_MATH_INSTRUMENT_VARIABLE(pois);
// Starting beta term:
xterm = x < y
? ibeta_derivative(T(k + 1), n / 2, x, pol)
: ibeta_derivative(n / 2, T(k + 1), y, pol);
BOOST_MATH_INSTRUMENT_VARIABLE(xterm);
T poisf(pois), xtermf(xterm);
T sum = init_val;
if((pois == 0) || (xterm == 0))
Expand All @@ -410,12 +412,16 @@ namespace boost
// direction for recursion:
//
std::uintmax_t count = 0;
T old_ratio = 1; // arbitrary "large" value
for(auto i = k; i >= 0; --i)
{
T term = xterm * pois;
sum += term;
if(((fabs(term/sum) < errtol) && (i != k)) || (term == 0))
BOOST_MATH_INSTRUMENT_VARIABLE(sum);
T ratio = fabs(term / sum);
if(((ratio < errtol) && (i != k) && (ratio < old_ratio)) || (term == 0))
break;
old_ratio = ratio;
pois *= (i + 0.5f) / d2;
xterm *= (i) / (x * (n / 2 + i));
++count;
Expand All @@ -426,6 +432,7 @@ namespace boost
"Series did not converge, closest value was %1%", sum, pol);
}
}
BOOST_MATH_INSTRUMENT_VARIABLE(sum);
for(auto i = k + 1; ; ++i)
{
poisf *= d2 / (i + 0.5f);
Expand All @@ -442,6 +449,7 @@ namespace boost
"Series did not converge, closest value was %1%", sum, pol);
}
}
BOOST_MATH_INSTRUMENT_VARIABLE(sum);
return sum;
}

Expand Down Expand Up @@ -505,9 +513,12 @@ namespace boost
// Calculate pdf:
//
T dt = n * t / (n * n + 2 * n * t * t + t * t * t * t);
BOOST_MATH_INSTRUMENT_VARIABLE(dt);
T result = non_central_beta_pdf(a, b, d2, x, y, pol);
BOOST_MATH_INSTRUMENT_VARIABLE(result);
T tol = tools::epsilon<T>() * result * 500;
result = non_central_t2_pdf(n, delta, x, y, pol, result);
BOOST_MATH_INSTRUMENT_VARIABLE(result);
if(result <= tol)
result = 0;
result *= dt;
Expand Down
9 changes: 9 additions & 0 deletions test/test_nc_t.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -320,6 +320,15 @@ void test_spots(RealType)
BOOST_CHECK(boost::math::isnan(pdf(d2, 0.5)));
BOOST_CHECK(boost::math::isnan(cdf(d2, 0.5)));
}

// Bug cases,
// https://github.com/scipy/scipy/issues/19348
//
{
distro1 d(8.0f, 8.5f);
BOOST_CHECK_CLOSE(pdf(d, -1), static_cast<RealType>(6.1747948083757028903541988987716621647020752431287e-20), 2e-5); // Can we do better on accuracy here?
}

} // template <class RealType>void test_spots(RealType)

template <class T>
Expand Down