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Ruta de la carpeta: \\game3dprogramming\materials\GameFactory\GameFactoryDemo\references\boost_1_35_0\boost\math\special_functions\detail\ibeta_inv_ab.hpp
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// (C) Copyright John Maddock 2006. // 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) // // This is not a complete header file, it is included by beta.hpp // after it has defined it's definitions. This inverts the incomplete // beta functions ibeta and ibetac on the first parameters "a" // and "b" using a generic root finding algorithm (TOMS Algorithm 748). // #ifndef BOOST_MATH_SP_DETAIL_BETA_INV_AB #define BOOST_MATH_SP_DETAIL_BETA_INV_AB #include
#include
namespace boost{ namespace math{ namespace detail{ template
struct beta_inv_ab_t { beta_inv_ab_t(T b_, T z_, T p_, bool invert_, bool swap_ab_) : b(b_), z(z_), p(p_), invert(invert_), swap_ab(swap_ab_) {} T operator()(T a) { return invert ? p - boost::math::ibetac(swap_ab ? b : a, swap_ab ? a : b, z, Policy()) : boost::math::ibeta(swap_ab ? b : a, swap_ab ? a : b, z, Policy()) - p; } private: T b, z, p; bool invert, swap_ab; }; template
T inverse_negative_binomial_cornish_fisher(T n, T sf, T sfc, T p, T q, const Policy& pol) { BOOST_MATH_STD_USING // mean: T m = n * (sfc) / sf; T t = sqrt(n * (sfc)); // standard deviation: T sigma = t / sf; // skewness T sk = (1 + sfc) / t; // kurtosis: T k = (6 - sf * (5+sfc)) / (n * (sfc)); // Get the inverse of a std normal distribution: T x = boost::math::erfc_inv(p > q ? 2 * q : 2 * p, pol) * constants::root_two
(); // Set the sign: if(p < 0.5) x = -x; T x2 = x * x; // w is correction term due to skewness T w = x + sk * (x2 - 1) / 6; // // Add on correction due to kurtosis. // if(n >= 10) w += k * x * (x2 - 3) / 24 + sk * sk * x * (2 * x2 - 5) / -36; w = m + sigma * w; if(w < tools::min_value
()) return tools::min_value
(); return w; } template
T ibeta_inv_ab_imp(const T& b, const T& z, const T& p, const T& q, bool swap_ab, const Policy& pol) { BOOST_MATH_STD_USING // for ADL of std lib math functions // // Special cases first: // BOOST_MATH_INSTRUMENT_CODE("b = " << b << " z = " << z << " p = " << p << " q = " << " swap = " << swap_ab); if(p == 0) { return swap_ab ? tools::min_value
() : tools::max_value
(); } if(q == 0) { return swap_ab ? tools::max_value
() : tools::min_value
(); } // // Function object, this is the functor whose root // we have to solve: // beta_inv_ab_t
f(b, z, (p < q) ? p : q, (p < q) ? false : true, swap_ab); // // Tolerance: full precision. // tools::eps_tolerance
tol(policies::digits
()); // // Now figure out a starting guess for what a may be, // we'll start out with a value that'll put p or q // right bang in the middle of their range, the functions // are quite sensitive so we should need too many steps // to bracket the root from there: // T guess = 0; T factor = 5; // // Convert variables to parameters of a negative binomial distribution: // T n = b; T sf = swap_ab ? z : 1-z; T sfc = swap_ab ? 1-z : z; T u = swap_ab ? p : q; T v = swap_ab ? q : p; if(u <= pow(sf, n)) { // // Result is less than 1, negative binomial approximation // is useless.... // if((p < q) != swap_ab) { guess = (std::min)(b * 2, T(1)); } else { guess = (std::min)(b / 2, T(1)); } } if(n * n * n * u * sf > 0.005) guess = 1 + inverse_negative_binomial_cornish_fisher(n, sf, sfc, u, v, pol); if(guess < 10) { // // Negative binomial approximation not accurate in this area: // if((p < q) != swap_ab) { guess = (std::min)(b * 2, T(10)); } else { guess = (std::min)(b / 2, T(10)); } } else factor = (v < sqrt(tools::epsilon
())) ? 2 : (guess < 20 ? 1.2f : 1.1f); BOOST_MATH_INSTRUMENT_CODE("guess = " << guess); // // Max iterations permitted: // boost::uintmax_t max_iter = policies::get_max_root_iterations
(); std::pair
r = bracket_and_solve_root(f, guess, factor, swap_ab ? true : false, tol, max_iter, pol); if(max_iter >= policies::get_max_root_iterations
()) policies::raise_evaluation_error
("boost::math::ibeta_invab_imp<%1%>(%1%,%1%,%1%)", "Unable to locate the root within a reasonable number of iterations, closest approximation so far was %1%", r.first, pol); return (r.first + r.second) / 2; } } // namespace detail template
typename tools::promote_args
::type ibeta_inva(RT1 b, RT2 x, RT3 p, const Policy& pol) { typedef typename tools::promote_args
::type result_type; typedef typename policies::evaluation
::type value_type; typedef typename policies::normalise< Policy, policies::promote_float
, policies::promote_double
, policies::discrete_quantile<>, policies::assert_undefined<> >::type forwarding_policy; if(p == 0) { return tools::max_value
(); } if(p == 1) { return tools::min_value
(); } return policies::checked_narrowing_cast
( detail::ibeta_inv_ab_imp( static_cast
(b), static_cast
(x), static_cast
(p), 1 - static_cast
(p), false, pol), "boost::math::ibeta_inva<%1%>(%1%,%1%,%1%)"); } template
typename tools::promote_args
::type ibetac_inva(RT1 b, RT2 x, RT3 q, const Policy& pol) { typedef typename tools::promote_args
::type result_type; typedef typename policies::evaluation
::type value_type; typedef typename policies::normalise< Policy, policies::promote_float
, policies::promote_double
, policies::discrete_quantile<>, policies::assert_undefined<> >::type forwarding_policy; if(q == 1) { return tools::max_value
(); } if(q == 0) { return tools::min_value
(); } return policies::checked_narrowing_cast
( detail::ibeta_inv_ab_imp( static_cast
(b), static_cast
(x), 1 - static_cast
(q), static_cast
(q), false, pol), "boost::math::ibetac_inva<%1%>(%1%,%1%,%1%)"); } template
typename tools::promote_args
::type ibeta_invb(RT1 a, RT2 x, RT3 p, const Policy& pol) { typedef typename tools::promote_args
::type result_type; typedef typename policies::evaluation
::type value_type; typedef typename policies::normalise< Policy, policies::promote_float
, policies::promote_double
, policies::discrete_quantile<>, policies::assert_undefined<> >::type forwarding_policy; if(p == 0) { return tools::min_value
(); } if(p == 1) { return tools::max_value
(); } return policies::checked_narrowing_cast
( detail::ibeta_inv_ab_imp( static_cast
(a), static_cast
(x), static_cast
(p), 1 - static_cast
(p), true, pol), "boost::math::ibeta_invb<%1%>(%1%,%1%,%1%)"); } template
typename tools::promote_args
::type ibetac_invb(RT1 a, RT2 x, RT3 q, const Policy& pol) { typedef typename tools::promote_args
::type result_type; typedef typename policies::evaluation
::type value_type; typedef typename policies::normalise< Policy, policies::promote_float
, policies::promote_double
, policies::discrete_quantile<>, policies::assert_undefined<> >::type forwarding_policy; if(q == 1) { return tools::min_value
(); } if(q == 0) { return tools::max_value
(); } return policies::checked_narrowing_cast
( detail::ibeta_inv_ab_imp( static_cast
(a), static_cast
(x), 1 - static_cast
(q), static_cast
(q), true, pol), "boost::math::ibetac_invb<%1%>(%1%,%1%,%1%)"); } template
inline typename tools::promote_args
::type ibeta_inva(RT1 b, RT2 x, RT3 p) { return boost::math::ibeta_inva(b, x, p, policies::policy<>()); } template
inline typename tools::promote_args
::type ibetac_inva(RT1 b, RT2 x, RT3 q) { return boost::math::ibetac_inva(b, x, q, policies::policy<>()); } template
inline typename tools::promote_args
::type ibeta_invb(RT1 a, RT2 x, RT3 p) { return boost::math::ibeta_invb(a, x, p, policies::policy<>()); } template
inline typename tools::promote_args
::type ibetac_invb(RT1 a, RT2 x, RT3 q) { return boost::math::ibetac_invb(a, x, q, policies::policy<>()); } } // namespace math } // namespace boost #endif // BOOST_MATH_SP_DETAIL_BETA_INV_AB
ibeta_inv_ab.hpp
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