Initial commit

2022-01-19 14:26:18 +01:00
parent 2378dec60c
commit 43889993a9
2044 changed files with 6553027 additions and 0 deletions
--- a/imagerie/boost/math/special_functions/detail/bessel_yn.hpp
+++ b/imagerie/boost/math/special_functions/detail/bessel_yn.hpp
@@ -0,0 +1,112 @@
+//  Copyright (c) 2006 Xiaogang Zhang
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_BESSEL_YN_HPP
+#define BOOST_MATH_BESSEL_YN_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/special_functions/detail/bessel_y0.hpp>
+#include <boost/math/special_functions/detail/bessel_y1.hpp>
+#include <boost/math/special_functions/detail/bessel_jy_series.hpp>
+#include <boost/math/policies/error_handling.hpp>
+
+// Bessel function of the second kind of integer order
+// Y_n(z) is the dominant solution, forward recurrence always OK (though unstable)
+
+namespace boost { namespace math { namespace detail{
+
+template <typename T, typename Policy>
+T bessel_yn(int n, T x, const Policy& pol)
+{
+    BOOST_MATH_STD_USING
+    T value, factor, current, prev;
+
+    using namespace boost::math::tools;
+
+    static const char* function = "boost::math::bessel_yn<%1%>(%1%,%1%)";
+
+    if ((x == 0) && (n == 0))
+    {
+       return -policies::raise_overflow_error<T>(function, 0, pol);
+    }
+    if (x <= 0)
+    {
+       return policies::raise_domain_error<T>(function,
+            "Got x = %1%, but x must be > 0, complex result not supported.", x, pol);
+    }
+
+    //
+    // Reflection comes first:
+    //
+    if (n < 0)
+    {
+        factor = static_cast<T>((n & 0x1) ? -1 : 1);  // Y_{-n}(z) = (-1)^n Y_n(z)
+        n = -n;
+    }
+    else
+    {
+        factor = 1;
+    }
+    if(x < policies::get_epsilon<T, Policy>())
+    {
+       T scale = 1;
+       value = bessel_yn_small_z(n, x, &scale, pol);
+       if(tools::max_value<T>() * fabs(scale) < fabs(value))
+          return boost::math::sign(scale) * boost::math::sign(value) * policies::raise_overflow_error<T>(function, 0, pol);
+       value /= scale;
+    }
+    else if(asymptotic_bessel_large_x_limit(n, x))
+    {
+       value = factor * asymptotic_bessel_y_large_x_2(static_cast<T>(abs(n)), x);
+    }
+    else if (n == 0)
+    {
+        value = bessel_y0(x, pol);
+    }
+    else if (n == 1)
+    {
+        value = factor * bessel_y1(x, pol);
+    }
+    else
+    {
+       prev = bessel_y0(x, pol);
+       current = bessel_y1(x, pol);
+       int k = 1;
+       BOOST_ASSERT(k < n);
+       policies::check_series_iterations<T>("boost::math::bessel_y_n<%1%>(%1%,%1%)", n, pol);
+       T mult = 2 * k / x;
+       value = mult * current - prev;
+       prev = current;
+       current = value;
+       ++k;
+       if((mult > 1) && (fabs(current) > 1))
+       {
+          prev /= current;
+          factor /= current;
+          value /= current;
+          current = 1;
+       }
+       while(k < n)
+       {
+           mult = 2 * k / x;
+           value = mult * current - prev;
+           prev = current;
+           current = value;
+           ++k;
+       }
+       if(fabs(tools::max_value<T>() * factor) < fabs(value))
+          return sign(value) * sign(factor) * policies::raise_overflow_error<T>(function, 0, pol);
+       value /= factor;
+    }
+    return value;
+}
+
+}}} // namespaces
+
+#endif // BOOST_MATH_BESSEL_YN_HPP
+