Added thirdparty: boost library

thirdparty/include/boost/math/special_functions/jacobi.hpp

@@ -0,0 +1,69 @@
+//  (C) Copyright Nick Thompson 2019.
+//  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_SPECIAL_JACOBI_HPP
+#define BOOST_MATH_SPECIAL_JACOBI_HPP
+
+#include <limits>
+#include <stdexcept>
+
+namespace boost { namespace math {
+
+template<typename Real>
+Real jacobi(unsigned n, Real alpha, Real beta, Real x)
+{
+    static_assert(!std::is_integral<Real>::value, "Jacobi polynomials do not work with integer arguments.");
+
+    if (n == 0) {
+        return Real(1);
+    }
+    Real y0 = 1;
+    Real y1 = (alpha+1) + (alpha+beta+2)*(x-1)/Real(2);
+
+    Real yk = y1;
+    Real k = 2;
+    Real k_max = n*(1+std::numeric_limits<Real>::epsilon());
+    while(k < k_max)
+    {
+        // Hoping for lots of common subexpression elimination by the compiler:
+        Real denom = 2*k*(k+alpha+beta)*(2*k+alpha+beta-2);
+        Real gamma1 = (2*k+alpha+beta-1)*( (2*k+alpha+beta)*(2*k+alpha+beta-2)*x + alpha*alpha -beta*beta);
+        Real gamma0 = -2*(k+alpha-1)*(k+beta-1)*(2*k+alpha+beta);
+        yk = (gamma1*y1 + gamma0*y0)/denom;
+        y0 = y1;
+        y1 = yk;
+        k += 1;
+    }
+    return yk;
+}
+
+template<typename Real>
+Real jacobi_derivative(unsigned n, Real alpha, Real beta, Real x, unsigned k)
+{
+    if (k > n) {
+        return Real(0);
+    }
+    Real scale = 1;
+    for(unsigned j = 1; j <= k; ++j) {
+        scale *= (alpha + beta + n + j)/2;
+    }
+
+    return scale*jacobi<Real>(n-k, alpha + k, beta+k, x);
+}
+
+template<typename Real>
+Real jacobi_prime(unsigned n, Real alpha, Real beta, Real x)
+{
+    return jacobi_derivative<Real>(n, alpha, beta, x, 1);
+}
+
+template<typename Real>
+Real jacobi_double_prime(unsigned n, Real alpha, Real beta, Real x)
+{
+    return jacobi_derivative<Real>(n, alpha, beta, x, 2);
+}
+
+}}
+#endif