[Boost-commit] svn:boost r42999 - in sandbox/math_toolkit: boost/math/distributions libs/math/test

From: john_at_[hidden]
Date: 2008-01-28 13:29:38

Author: johnmaddock
Date: 2008-01-28 13:29:37 EST (Mon, 28 Jan 2008)
New Revision: 42999
URL: http://svn.boost.org/trac/boost/changeset/42999

Log:
Added initial commit of non-central beta distribution: CDF and quantile work OK, but nothing else!
Added:
   sandbox/math_toolkit/boost/math/distributions/non_central_beta.hpp   (contents, props changed)
   sandbox/math_toolkit/libs/math/test/ncbeta.ipp   (contents, props changed)
   sandbox/math_toolkit/libs/math/test/ncbeta_big.ipp   (contents, props changed)
   sandbox/math_toolkit/libs/math/test/test_nc_beta.cpp   (contents, props changed)

Added: sandbox/math_toolkit/boost/math/distributions/non_central_beta.hpp
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/boost/math/distributions/non_central_beta.hpp	2008-01-28 13:29:37 EST (Mon, 28 Jan 2008)
@@ -0,0 +1,684 @@
+// boost\math\distributions\non_central_beta.hpp
+
+// Copyright John Maddock 2008.
+
+// 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_NON_CENTRAL_BETA_HPP
+#define BOOST_MATH_SPECIAL_NON_CENTRAL_BETA_HPP
+
+#include <boost/math/distributions/fwd.hpp>
+#include <boost/math/special_functions/beta.hpp> // for incomplete gamma. gamma_q
+#include <boost/math/distributions/complement.hpp> // complements
+#include <boost/math/distributions/beta.hpp> // central distribution
+#include <boost/math/distributions/normal.hpp> // central distribution
+#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks
+#include <boost/math/special_functions/fpclassify.hpp> // isnan.
+#include <boost/math/tools/roots.hpp> // for root finding.
+#include <boost/math/tools/minima.hpp> // function minimization for mode
+
+namespace boost
+{
+   namespace math
+   {
+
+      template <class RealType, class Policy>
+      class non_central_beta_distribution;
+
+      namespace detail{
+
+         template <class T, class Policy>
+         T non_central_beta_p(T a, T b, T lam, T x, const Policy& pol, T init_val = 0)
+         {
+            BOOST_MATH_STD_USING
+               using namespace boost::math;
+            //
+            // Variables come first:
+            //
+            boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
+            T errtol = ldexp(1.0, -boost::math::policies::digits<T, Policy>());
+            T l2 = lam / 2;
+            //
+            // k is the starting point for iteration, and is the
+            // maximum of the poisson weighting term:
+            //
+            int k = itrunc(l2);
+            // Starting Poisson weight:
+            T pois = gamma_p_derivative(k+1, l2, pol);
+            // Starting beta term:
+            T beta = ibeta(a + k, b, x, pol);
+            // recurance term:
+            T xterm = ibeta_derivative(a + k, b, x, pol) * (1 - x) / (a + b + k - 1);
+            T poisf(pois), betaf(beta), xtermf(xterm);
+            T sum = init_val;
+
+            //
+            // Backwards recursion first, this is the stable
+            // direction for recursion:
+            //
+            T last_term = 0;
+            for(int i = k; i >= 0; --i)
+            {
+               T term = beta * pois;
+               sum += term;
+               if((fabs(term/sum) < errtol) && (last_term > term))
+               {
+                  break;
+               }
+               pois *= i / l2;
+               beta += xterm;
+               xterm *= (a + i - 1) / (x * (a + b + i - 2));
+               last_term = term;
+            }
+            for(int i = k + 1; i - k < max_iter; ++i)
+            {
+               poisf *= l2 / i;
+               xtermf *= (x * (a + b + i - 2)) / (a + i - 1);
+               betaf -= xtermf;
+
+               T term = poisf * betaf;
+               sum += term;
+               if(fabs(term/sum) < errtol)
+               {
+                  break;
+               }
+            }
+            return sum;
+         }
+
+         template <class T, class Policy>
+         T non_central_beta_q(T a, T b, T lam, T x, const Policy& pol, T init_val = 0)
+         {
+            BOOST_MATH_STD_USING
+               using namespace boost::math;
+            //
+            // Variables come first:
+            //
+            boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
+            T errtol = ldexp(1.0, -boost::math::policies::digits<T, Policy>());
+            T l2 = lam / 2;
+            //
+            // k is the starting point for iteration, and is the
+            // maximum of the poisson weighting term:
+            //
+            int k = itrunc(l2);
+            // Starting Poisson weight:
+            T pois = gamma_p_derivative(k+1, l2, pol);
+            // Starting beta term:
+            T beta = ibetac(a + k, b, x, pol);
+            // recurance term:
+            T xterm = ibeta_derivative(a + k, b, x, pol) * (1 - x) / (a + b + k - 1);
+            T poisf(pois), betaf(beta), xtermf(xterm);
+            T sum = init_val;
+
+            //
+            // Backwards recursion first, this is the unstable
+            // direction for recursion:
+            //
+            for(int i = k; i >= 0; --i)
+            {
+               T term = beta * pois;
+               sum += term;
+               if(fabs(term/sum) < errtol)
+               {
+                  break;
+               }
+               pois *= i / l2;
+               beta -= xterm;
+               xterm *= (a + i - 1) / (x * (a + b + i - 2));
+            }
+            T last_term = 0;
+            for(int i = k + 1; i - k < max_iter; ++i)
+            {
+               poisf *= l2 / i;
+               xtermf *= (x * (a + b + i - 2)) / (a + i - 1);
+               betaf += xtermf;
+
+               T term = poisf * betaf;
+               sum += term;
+               if((fabs(term/sum) < errtol) && (last_term > term))
+               {
+                  break;
+               }
+               last_term = term;
+            }
+            return sum;
+         }
+
+         template <class RealType, class Policy>
+         inline RealType non_central_beta_cdf(RealType x, RealType a, RealType b, RealType l, bool invert, const Policy&)
+         {
+            typedef typename policies::evaluation<RealType, Policy>::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float<false>, 
+               policies::promote_double<false>, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+
+            BOOST_MATH_STD_USING
+
+            if(x == 0)
+               return invert ? 1 : 0;
+            if(x == 1)
+               return invert ? 0 : 1;
+            value_type result;
+            value_type c = a + b + l / 2;
+            value_type cross = 1 - (b / c) * (1 + l / (2 * c * c));
+            if(l == 0)
+               result = cdf(boost::math::beta_distribution<RealType, Policy>(a, b), x);
+            else if(x > cross)
+            {
+               // Complement is the smaller of the two:
+               result = detail::non_central_beta_q(
+                  static_cast<value_type>(a), 
+                  static_cast<value_type>(b), 
+                  static_cast<value_type>(l), 
+                  static_cast<value_type>(x), 
+                  forwarding_policy(), 
+                  static_cast<value_type>(invert ? 0 : -1));
+               invert = !invert;
+            }
+            else
+            {
+               result = detail::non_central_beta_p(
+                  static_cast<value_type>(a), 
+                  static_cast<value_type>(b), 
+                  static_cast<value_type>(l), 
+                  static_cast<value_type>(x), 
+                  forwarding_policy(),
+                  static_cast<value_type>(invert ? -1 : 0));
+            }
+            if(invert)
+               result = -result;
+            return policies::checked_narrowing_cast<RealType, forwarding_policy>(
+               result, 
+               "boost::math::non_central_beta_cdf<%1%>(%1%, %1%, %1%)");
+         }
+
+         template <class T, class Policy>
+         struct nc_beta_quantile_functor
+         {
+            nc_beta_quantile_functor(const non_central_beta_distribution<T,Policy>& d, T t, bool c)
+               : dist(d), target(t), comp(c) {}
+
+            T operator()(const T& x)
+            {
+               return comp ?
+                  target - cdf(complement(dist, x))
+                  : cdf(dist, x) - target;
+            }
+
+         private:
+            non_central_beta_distribution<T,Policy> dist;
+            T target;
+            bool comp;
+         };
+
+         template <class F, class T, class Tol, class Policy>
+         std::pair<T, T> bracket_and_solve_root_01(F f, const T& guess, T factor, bool rising, Tol tol, boost::uintmax_t& max_iter, const Policy& pol)
+         {
+            BOOST_MATH_STD_USING
+               static const char* function = "boost::math::tools::bracket_and_solve_root_01<%1%>";
+            //
+            // Set up inital brackets:
+            //
+            T a = guess;
+            T b = a;
+            T fa = f(a);
+            T fb = fa;
+            //
+            // Set up invocation count:
+            //
+            boost::uintmax_t count = max_iter - 1;
+
+            if((fa < 0) == (guess < 0 ? !rising : rising))
+            {
+               //
+               // Zero is to the right of b, so walk upwards
+               // until we find it:
+               //
+               while((boost::math::sign)(fb) == (boost::math::sign)(fa))
+               {
+                  if(count == 0)
+                     policies::raise_evaluation_error(function, "Unable to bracket root, last nearest value was %1%", b, pol);
+                  //
+                  // Heuristic: every 20 iterations we double the growth factor in case the
+                  // initial guess was *really* bad !
+                  //
+                  if((max_iter - count) % 20 == 0)
+                     factor *= 2;
+                  //
+                  // Now go ahead and move are guess by "factor":
+                  //
+                  a = b;
+                  fa = fb;
+                  b = 1 - ((1 - b) / factor);
+                  fb = f(b);
+                  --count;
+                  BOOST_MATH_INSTRUMENT_CODE("a = " << a << " b = " << b << " fa = " << fa << " fb = " << fb << " count = " << count);
+               }
+            }
+            else
+            {
+               //
+               // Zero is to the left of a, so walk downwards
+               // until we find it:
+               //
+               while((boost::math::sign)(fb) == (boost::math::sign)(fa))
+               {
+                  if(fabs(a) < tools::min_value<T>())
+                  {
+                     // Escape route just in case the answer is zero!
+                     max_iter -= count;
+                     max_iter += 1;
+                     return a > 0 ? std::make_pair(T(0), T(a)) : std::make_pair(T(a), T(0)); 
+                  }
+                  if(count == 0)
+                     policies::raise_evaluation_error(function, "Unable to bracket root, last nearest value was %1%", a, pol);
+                  //
+                  // Heuristic: every 20 iterations we double the growth factor in case the
+                  // initial guess was *really* bad !
+                  //
+                  if((max_iter - count) % 20 == 0)
+                     factor *= 2;
+                  //
+                  // Now go ahead and move are guess by "factor":
+                  //
+                  b = a;
+                  fb = fa;
+                  a /= factor;
+                  fa = f(a);
+                  --count;
+                  BOOST_MATH_INSTRUMENT_CODE("a = " << a << " b = " << b << " fa = " << fa << " fb = " << fb << " count = " << count);
+               }
+            }
+            max_iter -= count;
+            max_iter += 1;
+            std::pair<T, T> r = toms748_solve(
+               f, 
+               (a < 0 ? b : a), 
+               (a < 0 ? a : b), 
+               (a < 0 ? fb : fa), 
+               (a < 0 ? fa : fb), 
+               tol, 
+               count, 
+               pol);
+            max_iter += count;
+            BOOST_MATH_INSTRUMENT_CODE("max_iter = " << max_iter << " count = " << count);
+            return r;
+         }
+
+         template <class RealType, class Policy>
+         RealType nc_beta_quantile(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& p, bool comp)
+         {
+            static const char* function = "quantile(non_central_beta_distribution<%1%>, %1%)";
+            typedef typename policies::evaluation<RealType, Policy>::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float<false>, 
+               policies::promote_double<false>, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+
+            value_type a = dist.alpha();
+            value_type b = dist.beta();
+            value_type l = dist.non_centrality();
+            value_type r;
+            if(!beta_detail::check_alpha(
+               function,
+               a, &r, Policy())
+               ||
+            !beta_detail::check_beta(
+               function,
+               a, &r, Policy())
+               ||            
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy())
+               ||
+            !detail::check_probability(
+               function,
+               static_cast<value_type>(p),
+               &r,
+               Policy()))
+                  return (RealType)r;
+            //
+            // Special cases first:
+            //
+            if(p == 0)
+               return comp
+               ? 1
+               : 0;
+            if(p == 1)
+               return !comp
+               ? 1
+               : 0;
+
+            value_type c = a + b + l / 2;
+            value_type mean = 1 - (b / c) * (1 + l / (2 * c * c));
+            /*
+            //
+            // Calculate a normal approximation to the quantile, 
+            // uses mean and variance approximations from:
+            // Algorithm AS 310: 
+            // Computing the Non-Central Beta Distribution Function
+            // R. Chattamvelli; R. Shanmugam
+            // Applied Statistics, Vol. 46, No. 1. (1997), pp. 146-156.
+            //
+            // Unfortunately, when this is wrong it tends to be *very*
+            // wrong, so it's disabled for now, even though it often
+            // gets the initial guess quite close.  Probably we could
+            // do much better by factoring in the skewness if only
+            // we could calculate it....
+            //
+            value_type delta = l / 2;
+            value_type delta2 = delta * delta;
+            value_type delta3 = delta * delta2;
+            value_type delta4 = delta2 * delta2;
+            value_type G = c * (c + 1) + delta;
+            value_type alpha = a + b;
+            value_type alpha2 = alpha * alpha;
+            value_type eta = (2 * alpha + 1) * (2 * alpha + 1) + 1;
+            value_type H = 3 * alpha2 + 5 * alpha + 2;
+            value_type F = alpha2 * (alpha + 1) + H * delta 
+               + (2 * alpha + 4) * delta2 + delta3;
+            value_type P = (3 * alpha + 1) * (9 * alpha + 17)
+               + 2 * alpha * (3 * alpha + 2) * (3 * alpha + 4) + 15;
+            value_type Q = 54 * alpha2 + 162 * alpha + 130;
+            value_type R = 6 * (6 * alpha + 11);
+            value_type D = delta 
+               * (H * H + 2 * P * delta + Q * delta2 + R * delta3 + 9 * delta4);
+            value_type variance = (b / G)
+               * (1 + delta * (l * l + 3 * l + eta) / (G * G))
+               - (b * b / F) * (1 + D / (F * F));
+            value_type sd = sqrt(variance);
+
+            value_type guess = comp 
+               ? quantile(complement(normal_distribution<RealType, Policy>(static_cast<RealType>(mean), static_cast<RealType>(sd)), p))
+               : quantile(normal_distribution<RealType, Policy>(static_cast<RealType>(mean), static_cast<RealType>(sd)), p);
+
+            if(guess >= 1)
+               guess = mean;
+            if(guess <= tools::min_value<value_type>())
+               guess = mean;
+            */
+            value_type guess = mean;
+            detail::nc_beta_quantile_functor<value_type, Policy>
+               f(non_central_beta_distribution<value_type, Policy>(a, b, l), p, comp);
+            tools::eps_tolerance<value_type> tol(policies::digits<RealType, Policy>());
+            boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
+
+            std::pair<value_type, value_type> ir 
+               = bracket_and_solve_root_01(
+                  f, guess, value_type(2.5), true, tol, 
+                  max_iter, Policy());
+            value_type result = ir.first + (ir.second - ir.first) / 2;
+
+            if(max_iter == policies::get_max_root_iterations<Policy>())
+            {
+               policies::raise_evaluation_error<value_type>(function, "Unable to locate solution in a reasonable time:"
+                  " either there is no answer to quantile of the non central beta distribution"
+                  " or the answer is infinite.  Current best guess is %1%", result, Policy());
+            }
+            return policies::checked_narrowing_cast<RealType, forwarding_policy>(
+               result, 
+               function);
+         }
+
+         template <class RealType, class Policy>
+         RealType nc_beta_pdf(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& x)
+         {
+            BOOST_MATH_STD_USING
+            static const char* function = "pdf(non_central_beta_distribution<%1%>, %1%)";
+            typedef typename policies::evaluation<RealType, Policy>::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float<false>, 
+               policies::promote_double<false>, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+
+            value_type a = dist.alpha();
+            value_type b = dist.beta();
+            value_type l = dist.non_centrality();
+            value_type r;
+            if(!beta_detail::check_alpha(
+               function,
+               a, &r, Policy())
+               ||
+            !beta_detail::check_beta(
+               function,
+               a, &r, Policy())
+               ||            
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy())
+               ||
+            !detail::check_probability(
+               function,
+               static_cast<value_type>(p),
+               &r,
+               Policy()))
+                  return (RealType)r;
+
+         BOOST_MATH_STD_USING
+         if(l == 0)
+            return pdf(boost::math::beta_distribution<RealType, forwarding_policy>(dist.degrees_of_freedom()), x);
+
+         }
+
+      }
+
+      template <class RealType = double, class Policy = policies::policy<> >
+      class non_central_beta_distribution
+      {
+      public:
+         typedef RealType value_type;
+         typedef Policy policy_type;
+
+         non_central_beta_distribution(RealType a_, RealType b_, RealType lambda) : a(a_), b(b_), ncp(lambda)
+         { 
+            const char* function = "boost::math::non_central_beta_distribution<%1%>::non_central_beta_distribution(%1%,%1%)";
+            RealType r;
+            beta_detail::check_alpha(
+               function,
+               a, &r, Policy());
+            beta_detail::check_beta(
+               function,
+               a, &r, Policy());
+            detail::check_non_centrality(
+               function,
+               lambda,
+               &r,
+               Policy());
+         } // non_central_beta_distribution constructor.
+
+         RealType alpha() const
+         { // Private data getter function.
+            return a;
+         }
+         RealType beta() const
+         { // Private data getter function.
+            return b;
+         }
+         RealType non_centrality() const
+         { // Private data getter function.
+            return ncp;
+         }
+      private:
+         // Data member, initialized by constructor.
+         RealType a;   // alpha.
+         RealType b;   // beta.
+         RealType ncp; // non-centrality parameter
+      }; // template <class RealType, class Policy> class non_central_beta_distribution
+
+      typedef non_central_beta_distribution<double> non_central_beta; // Reserved name of type double.
+
+      // Non-member functions to give properties of the distribution.
+
+      template <class RealType, class Policy>
+      inline const std::pair<RealType, RealType> range(const non_central_beta_distribution<RealType, Policy>& /* dist */)
+      { // Range of permissible values for random variable k.
+         using boost::math::tools::max_value;
+         return std::pair<RealType, RealType>(0, 1);
+      }
+
+      template <class RealType, class Policy>
+      inline const std::pair<RealType, RealType> support(const non_central_beta_distribution<RealType, Policy>& /* dist */)
+      { // Range of supported values for random variable k.
+         // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
+         using boost::math::tools::max_value;
+         return std::pair<RealType, RealType>(0, 1);
+      }
+
+      template <class RealType, class Policy>
+      inline RealType mean(const non_central_beta_distribution<RealType, Policy>& dist)
+      { 
+         // TODO
+         return 0;
+      } // mean
+
+      template <class RealType, class Policy>
+      inline RealType mode(const non_central_beta_distribution<RealType, Policy>& dist)
+      { // mode.
+         // TODO
+         return 0;
+      }
+
+      template <class RealType, class Policy>
+      inline RealType variance(const non_central_beta_distribution<RealType, Policy>& dist)
+      { // variance.
+         const char* function = "boost::math::non_central_beta_distribution<%1%>::variance()";
+         // TODO
+         return 0;
+      }
+
+      // RealType standard_deviation(const non_central_beta_distribution<RealType, Policy>& dist)
+      // standard_deviation provided by derived accessors.
+
+      template <class RealType, class Policy>
+      inline RealType skewness(const non_central_beta_distribution<RealType, Policy>& dist)
+      { // skewness = sqrt(l).
+         const char* function = "boost::math::non_central_beta_distribution<%1%>::skewness()";
+         // TODO
+         return 0;
+      }
+
+      template <class RealType, class Policy>
+      inline RealType kurtosis_excess(const non_central_beta_distribution<RealType, Policy>& dist)
+      { 
+         const char* function = "boost::math::non_central_beta_distribution<%1%>::kurtosis_excess()";
+         // TODO
+         return 0;
+      } // kurtosis_excess
+
+      template <class RealType, class Policy>
+      inline RealType kurtosis(const non_central_beta_distribution<RealType, Policy>& dist)
+      {
+         return kurtosis_excess(dist) + 3;
+      }
+
+      template <class RealType, class Policy>
+      inline RealType pdf(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& x)
+      { // Probability Density/Mass Function.
+         return detail::nc_beta_pdf(dist, x);
+      } // pdf
+
+      template <class RealType, class Policy>
+      RealType cdf(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& x)
+      { 
+         const char* function = "boost::math::non_central_beta_distribution<%1%>::cdf(%1%)";
+            RealType a = dist.alpha();
+            RealType b = dist.beta();
+            RealType l = dist.non_centrality();
+            RealType r;
+            if(!beta_detail::check_alpha(
+               function,
+               a, &r, Policy())
+               ||
+            !beta_detail::check_beta(
+               function,
+               a, &r, Policy())
+               ||            
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy())
+               ||
+            !beta_detail::check_x(
+               function,
+               x,
+               &r,
+               Policy()))
+                  return (RealType)r;
+
+         return detail::non_central_beta_cdf(x, a, b, l, false, Policy());
+      } // cdf
+
+      template <class RealType, class Policy>
+      RealType cdf(const complemented2_type<non_central_beta_distribution<RealType, Policy>, RealType>& c)
+      { // Complemented Cumulative Distribution Function
+         const char* function = "boost::math::non_central_beta_distribution<%1%>::cdf(%1%)";
+         non_central_beta_distribution<RealType, Policy> const& dist = c.dist;
+            RealType a = dist.alpha();
+            RealType b = dist.beta();
+            RealType l = dist.non_centrality();
+            RealType x = c.param;
+            RealType r;
+            if(!beta_detail::check_alpha(
+               function,
+               a, &r, Policy())
+               ||
+            !beta_detail::check_beta(
+               function,
+               a, &r, Policy())
+               ||            
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy())
+               ||
+            !beta_detail::check_x(
+               function,
+               x,
+               &r,
+               Policy()))
+                  return (RealType)r;
+
+         return detail::non_central_beta_cdf(x, a, b, l, true, Policy());
+      } // ccdf
+
+      template <class RealType, class Policy>
+      inline RealType quantile(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& p)
+      { // Quantile (or Percent Point) function.
+         return detail::nc_beta_quantile(dist, p, false);
+      } // quantile
+
+      template <class RealType, class Policy>
+      inline RealType quantile(const complemented2_type<non_central_beta_distribution<RealType, Policy>, RealType>& c)
+      { // Quantile (or Percent Point) function.
+         return detail::nc_beta_quantile(c.dist, c.param, true);
+      } // quantile complement.
+
+   } // namespace math
+} // namespace boost
+
+// This include must be at the end, *after* the accessors
+// for this distribution have been defined, in order to
+// keep compilers that support two-phase lookup happy.
+#include <boost/math/distributions/detail/derived_accessors.hpp>
+
+#endif // BOOST_MATH_SPECIAL_NON_CENTRAL_BETA_HPP
+
+
+

Added: sandbox/math_toolkit/libs/math/test/ncbeta.ipp
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/test/ncbeta.ipp	2008-01-28 13:29:37 EST (Mon, 28 Jan 2008)
@@ -0,0 +1,3005 @@
+#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
+   static const boost::array<boost::array<T, 6>, 3000> ncbeta = {{
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454305052757263183593750000000000000000e-1), SC_(5.940588760375976562500000000000000000000e1), SC_(9.976066350936889648437500000000000000000e-1), SC_(2.759834870217354705236013708534509068967e-1), SC_(7.240165129782645294763986291465490931033e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454305052757263183593750000000000000000e-1), SC_(1.451677856445312500000000000000000000000e2), SC_(9.990068674087524414062500000000000000000e-1), SC_(2.757975665000284929998400439182434398680e-1), SC_(7.242024334999715070001599560817565601320e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454305052757263183593750000000000000000e-1), SC_(1.929777069091796875000000000000000000000e2), SC_(9.992512464523315429687500000000000000000e-1), SC_(2.757802819095769722518059796277858159202e-1), SC_(7.242197180904230277481940203722141840798e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(3.635762631893157958984375000000000000000e-1), SC_(6.038262176513671875000000000000000000000e1), SC_(9.961022734642028808593750000000000000000e-1), SC_(4.949484084085013882284839924844591052030e-1), SC_(5.050515915914986117715160075155408947970e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(3.635762631893157958984375000000000000000e-1), SC_(1.481294555664062500000000000000000000000e2), SC_(9.983823299407958984375000000000000000000e-1), SC_(4.946201811284367289305268285202655846240e-1), SC_(5.053798188715632710694731714797344153760e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(3.635762631893157958984375000000000000000e-1), SC_(1.935389862060546875000000000000000000000e2), SC_(9.987584948539733886718750000000000000000e-1), SC_(4.945965085725495633413346642780624277086e-1), SC_(5.054034914274504366586653357219375722914e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(7.271525263786315917968750000000000000000e-1), SC_(6.163340759277343750000000000000000000000e1), SC_(9.943350553512573242187500000000000000000e-1), SC_(7.067242511174509034733895807356551147428e-1), SC_(2.932757488825490965266104192643448852572e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(7.271525263786315917968750000000000000000e-1), SC_(1.486264953613281250000000000000000000000e2), SC_(9.975933432579040527343750000000000000000e-1), SC_(7.063204046711177968479175758665909815947e-1), SC_(2.936795953288822031520824241334090184053e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(7.271525263786315917968750000000000000000e-1), SC_(1.937735595703125000000000000000000000000e2), SC_(9.981468915939331054687500000000000000000e-1), SC_(7.062805762166387906359787891104213355210e-1), SC_(2.937194237833612093640212108895786644790e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.090728759765625000000000000000000000000), SC_(7.225879669189453125000000000000000000000e1), SC_(9.942231774330139160156250000000000000000e-1), SC_(8.372920335940658618578320877705617571936e-1), SC_(1.627079664059341381421679122294382428064e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.090728759765625000000000000000000000000), SC_(1.515480346679687500000000000000000000000e2), SC_(9.971802234649658203125000000000000000000e-1), SC_(8.370187919390128563087545041366727719913e-1), SC_(1.629812080609871436912454958633272280087e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.090728759765625000000000000000000000000), SC_(1.941185607910156250000000000000000000000e2), SC_(9.977884292602539062500000000000000000000e-1), SC_(8.369846256186989556701034949935290540605e-1), SC_(1.630153743813010443298965050064709459395e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.308874487876892089843750000000000000000), SC_(9.566968083381652832031250000000000000000e-1), SC_(5.778348073363304138183593750000000000000e-2), SC_(1.409704128923593153631527182055535438009e-2), SC_(9.859029587107640684636847281794446456199e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.308874487876892089843750000000000000000), SC_(7.844540405273437500000000000000000000000e1), SC_(9.681322425603866577148437500000000000000e-2), SC_(2.569096227285625192995992565780836758662e-17), SC_(9.999999999999999743090377271437480700401e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.308874487876892089843750000000000000000), SC_(1.584414672851562500000000000000000000000e2), SC_(9.838468581438064575195312500000000000000e-2), SC_(7.148747906745571900269746100091585733876e-33), SC_(9.999999999999999999999999999999928512521e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.308874487876892089843750000000000000000), SC_(1.962219390869140625000000000000000000000e2), SC_(9.868995845317840576171875000000000000000e-2), SC_(3.133324157161160812982715199693443151905e-40), SC_(9.999999999999999999999999999999999999997e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.439761996269226074218750000000000000000), SC_(7.142335891723632812500000000000000000000), SC_(1.895702630281448364257812500000000000000e-1), SC_(8.246187378326890920818812693938620222737e-3), SC_(9.917538126216731090791811873060613797773e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.439761996269226074218750000000000000000), SC_(7.974770355224609375000000000000000000000e1), SC_(2.414003908634185791015625000000000000000e-1), SC_(2.743306172427076308949349814705500897953e-14), SC_(9.999999999999725669382757292369105065019e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.439761996269226074218750000000000000000), SC_(1.595857238769531250000000000000000000000e2), SC_(2.455961406230926513671875000000000000000e-1), SC_(3.615587311674064774434229582160414432976e-27), SC_(9.999999999999999999999999963844126883259e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.439761996269226074218750000000000000000), SC_(1.985762634277343750000000000000000000000e2), SC_(2.464439719915390014648437500000000000000e-1), SC_(1.769432346388276500700335757818980807043e-33), SC_(9.999999999999999999999999999999982305677e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.452850818634033203125000000000000000000), SC_(1.950807952880859375000000000000000000000e1), SC_(4.391348361968994140625000000000000000000e-1), SC_(2.673764091042295518866919574008896029552e-3), SC_(9.973262359089577044811330804259911039704e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.452850818634033203125000000000000000000), SC_(8.435225677490234375000000000000000000000e1), SC_(4.835526645183563232421875000000000000000e-1), SC_(4.197372846541376004107385263233562496292e-10), SC_(9.999999995802627153458623995892614736766e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.452850818634033203125000000000000000000), SC_(1.596211700439453125000000000000000000000e2), SC_(4.911155700683593750000000000000000000000e-1), SC_(3.695059050069457866849050715946269539742e-18), SC_(9.999999999999999963049409499305421331509e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.452850818634033203125000000000000000000), SC_(1.992922668457031250000000000000000000000e2), SC_(4.928494989871978759765625000000000000000e-1), SC_(2.004823756718951621438737650562766380258e-22), SC_(9.999999999999999999997995176243281048379e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454305052757263183593750000000000000000), SC_(2.197235107421875000000000000000000000000e1), SC_(6.670339703559875488281250000000000000000e-1), SC_(2.938827902133597908162529714537893342335e-2), SC_(9.706117209786640209183747028546210665767e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454305052757263183593750000000000000000), SC_(8.441753387451171875000000000000000000000e1), SC_(7.253233790397644042968750000000000000000e-1), SC_(1.828399814138725196172294345445724389776e-5), SC_(9.999817160018586127480382770565455427561e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454305052757263183593750000000000000000), SC_(1.600560913085937500000000000000000000000e2), SC_(7.366956472396850585937500000000000000000e-1), SC_(1.838909377742473059089666873575275698077e-9), SC_(9.999999981610906222575269409103331264247e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454450488090515136718750000000000000000), SC_(2.249290275573730468750000000000000000000e1), SC_(8.023343086242675781250000000000000000000e-1), SC_(1.444816643582166349744437266238358383054e-1), SC_(8.555183356417833650255562733761641616946e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454450488090515136718750000000000000000), SC_(9.495173645019531250000000000000000000000e1), SC_(8.735338449478149414062500000000000000000e-1), SC_(5.297391880242822813440890445530785806678e-3), SC_(9.947026081197571771865591095544692141933e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454450488090515136718750000000000000000), SC_(1.629447326660156250000000000000000000000e2), SC_(8.843094706535339355468750000000000000000e-1), SC_(2.109987510023566218907025733718046851867e-4), SC_(9.997890012489976433781092974266281953148e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.455759406089782714843750000000000000000), SC_(2.539736366271972656250000000000000000000e1), SC_(8.928544521331787109375000000000000000000e-1), SC_(3.547407387217092519571701060719919695556e-1), SC_(6.452592612782907480428298939280080304444e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.455759406089782714843750000000000000000), SC_(9.707512664794921875000000000000000000000e1), SC_(9.614732861518859863281250000000000000000e-1), SC_(2.611091095508861765371680541840956899457e-1), SC_(7.388908904491138234628319458159043100543e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.455759406089782714843750000000000000000), SC_(1.670017089843750000000000000000000000000e2), SC_(9.731349945068359375000000000000000000000e-1), SC_(1.940330038798788046724413303549101135332e-1), SC_(8.059669961201211953275586696450898864668e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.468848109245300292968750000000000000000), SC_(2.709540176391601562500000000000000000000e1), SC_(9.054616093635559082031250000000000000000e-1), SC_(3.905836257290503311421287149477297051216e-1), SC_(6.094163742709496688578712850522702948784e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.468848109245300292968750000000000000000), SC_(1.007325439453125000000000000000000000000e2), SC_(9.709756374359130859375000000000000000000e-1), SC_(3.753844614900924354145268955128904198463e-1), SC_(6.246155385099075645854731044871095801537e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.468848109245300292968750000000000000000), SC_(1.698258666992187500000000000000000000000e2), SC_(9.821102619171142578125000000000000000000e-1), SC_(3.648451596781998922228271535859833907049e-1), SC_(6.351548403218001077771728464140166092951e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.599735617637634277343750000000000000000), SC_(2.837726783752441406250000000000000000000e1), SC_(9.027946591377258300781250000000000000000e-1), SC_(3.994481344166706347071818471461165810451e-1), SC_(6.005518655833293652928181528538834189549e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.599735617637634277343750000000000000000), SC_(1.093762969970703125000000000000000000000e2), SC_(9.718407988548278808593750000000000000000e-1), SC_(3.954357512869085630066564425659524044339e-1), SC_(6.045642487130914369933435574340475955661e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.599735617637634277343750000000000000000), SC_(1.756861267089843750000000000000000000000e2), SC_(9.822134971618652343750000000000000000000e-1), SC_(3.951860745186655290524861501883898882522e-1), SC_(6.048139254813344709475138498116101117478e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.745166182518005371093750000000000000000), SC_(3.152261734008789062500000000000000000000e1), SC_(9.039335846900939941406250000000000000000e-1), SC_(4.034567451009304048585061955097242530617e-1), SC_(5.965432548990695951414938044902757469383e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.745166182518005371093750000000000000000), SC_(1.094441146850585937500000000000000000000e2), SC_(9.693817496299743652343750000000000000000e-1), SC_(3.999349356267901779097748250899115060062e-1), SC_(6.000650643732098220902251749100884939938e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.745166182518005371093750000000000000000), SC_(1.811583862304687500000000000000000000000e2), SC_(9.812008142471313476562500000000000000000e-1), SC_(3.996591569909480845917200256671608991653e-1), SC_(6.003408430090519154082799743328391008347e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.890596508979797363281250000000000000000), SC_(3.423733520507812500000000000000000000000e1), SC_(9.039308428764343261718750000000000000000e-1), SC_(4.075414522865678416055270738540772311928e-1), SC_(5.924585477134321583944729261459227688072e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.890596508979797363281250000000000000000), SC_(1.264718551635742187500000000000000000000e2), SC_(9.712282419204711914062500000000000000000e-1), SC_(4.042366483257852646737355474134075723046e-1), SC_(5.957633516742147353262644525865924276954e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.890596508979797363281250000000000000000), SC_(1.826751708984375000000000000000000000000e2), SC_(9.798489809036254882812500000000000000000e-1), SC_(4.040529458975031201558234570112972505675e-1), SC_(5.959470541024968798441765429887027494325e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(2.181457519531250000000000000000000000000), SC_(3.477303314208984375000000000000000000000e1), SC_(8.932165503501892089843750000000000000000e-1), SC_(4.196040744142951370235014827671730626531e-1), SC_(5.803959255857048629764985172328269373469e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(2.181457519531250000000000000000000000000), SC_(1.279526672363281250000000000000000000000e2), SC_(9.676080346107482910156250000000000000000e-1), SC_(4.160241471932662346234005638447945943191e-1), SC_(5.839758528067337653765994361552054056809e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(2.181457519531250000000000000000000000000), SC_(1.831471099853515625000000000000000000000e2), SC_(9.770854115486145019531250000000000000000e-1), SC_(4.158245920573030252337620932502862854216e-1), SC_(5.841754079426969747662379067497137145784e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(2.908610105514526367187500000000000000000), SC_(3.767639541625976562500000000000000000000e1), SC_(8.820433020591735839843750000000000000000e-1), SC_(4.895484702256356762390308845835055338300e-1), SC_(5.104515297743643237609691154164944661700e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(2.908610105514526367187500000000000000000), SC_(1.310955810546875000000000000000000000000e2), SC_(9.616703391075134277343750000000000000000e-1), SC_(4.852896389054532990013477094741957837547e-1), SC_(5.147103610945467009986522905258042162453e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(2.908610105514526367187500000000000000000), SC_(1.867986450195312500000000000000000000000e2), SC_(9.726884961128234863281250000000000000000e-1), SC_(4.850256268066020087353144387623113929601e-1), SC_(5.149743731933979912646855612376886070399e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(4.362915039062500000000000000000000000000), SC_(4.238486480712890625000000000000000000000e1), SC_(8.614798784255981445312500000000000000000e-1), SC_(5.884548078925982877372322454535815427048e-1), SC_(4.115451921074017122627677545464184572952e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(4.362915039062500000000000000000000000000), SC_(1.311481323242187500000000000000000000000e2), SC_(9.484174847602844238281250000000000000000e-1), SC_(5.829003968003181859827925473746335160193e-1), SC_(4.170996031996818140172074526253664839807e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(4.362915039062500000000000000000000000000), SC_(1.914333953857421875000000000000000000000e2), SC_(9.638592004776000976562500000000000000000e-1), SC_(5.824357183371835930850248019898267857302e-1), SC_(4.175642816628164069149751980101732142698e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(5.817220211029052734375000000000000000000), SC_(4.420680999755859375000000000000000000000e1), SC_(8.437643647193908691406250000000000000000e-1), SC_(6.877689126985590678729196980659326128520e-1), SC_(3.122310873014409321270803019340673871480e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(5.817220211029052734375000000000000000000), SC_(1.357470245361328125000000000000000000000e2), SC_(9.397355914115905761718750000000000000000e-1), SC_(6.802657470523751397057188962080634416444e-1), SC_(3.197342529476248602942811037919365583556e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(5.817220211029052734375000000000000000000), SC_(1.915013732910156250000000000000000000000e2), SC_(9.561730027198791503906250000000000000000e-1), SC_(6.796471288397932298915701548036010615867e-1), SC_(3.203528711602067701084298451963989384133e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(7.271525382995605468750000000000000000000), SC_(5.569964599609375000000000000000000000000e1), SC_(8.647022843360900878906250000000000000000e-1), SC_(8.223643224171615413929725001008431837543e-1), SC_(1.776356775828384586070274998991568162457e-1) }, 
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+      { SC_(1.992940368652343750000000000000000000000e2), SC_(4.982350921630859375000000000000000000000e1), SC_(1.992922668457031250000000000000000000000e2), SC_(9.523417949676513671875000000000000000000e-1), SC_(9.999999999889979505525517028101296712932e-1), SC_(1.100204944744829718987032870678465639103e-11) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(9.964701843261718750000000000000000000000e1), SC_(2.197235107421875000000000000000000000000e1), SC_(9.196114540100097656250000000000000000000e-1), SC_(9.999999999999999999999999999999995422172e-1), SC_(4.577828221881416191038550064767058633427e-34) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(9.964701843261718750000000000000000000000e1), SC_(8.441753387451171875000000000000000000000e1), SC_(9.269505739212036132812500000000000000000e-1), SC_(9.999999999999999999999999999999957188140e-1), SC_(4.281185977015024842072588006442910551722e-33) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(9.964701843261718750000000000000000000000e1), SC_(1.600560913085937500000000000000000000000e2), SC_(9.342278242111206054687500000000000000000e-1), SC_(9.999999999999999999999999999999739814039e-1), SC_(2.601859605211694321039444322773589680759e-32) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.494705200195312500000000000000000000000e2), SC_(2.249290275573730468750000000000000000000e1), SC_(9.169561266899108886718750000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(5.078757476486174488603832341669296014670e-65) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.494705200195312500000000000000000000000e2), SC_(9.495173645019531250000000000000000000000e1), SC_(9.245328307151794433593750000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(1.198062735689324460517282204391468064919e-62) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.494705200195312500000000000000000000000e2), SC_(1.629447326660156250000000000000000000000e2), SC_(9.304865002632141113281250000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(3.677801238984289092488356673198126103843e-61) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.793646240234375000000000000000000000000e2), SC_(2.539736366271972656250000000000000000000e1), SC_(5.416477844119071960449218750000000000000e-2), SC_(2.776631429595303821632471226009891519974e-150), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.793646240234375000000000000000000000000e2), SC_(9.707512664794921875000000000000000000000e1), SC_(5.800236016511917114257812500000000000000e-2), SC_(1.673138510860741999246331189907275755619e-158), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.793646240234375000000000000000000000000e2), SC_(1.670017089843750000000000000000000000000e2), SC_(6.117471680045127868652343750000000000000e-2), SC_(1.733627098870606652495088750987846784929e-167), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.973011016845703125000000000000000000000e2), SC_(2.709540176391601562500000000000000000000e1), SC_(1.297266632318496704101562500000000000000e-1), SC_(5.741110529966056682991578876376585720368e-76), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.973011016845703125000000000000000000000e2), SC_(1.007325439453125000000000000000000000000e2), SC_(1.396152824163436889648437500000000000000e-1), SC_(3.986465235013712024800527853926355261130e-82), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.973011016845703125000000000000000000000e2), SC_(1.698258666992187500000000000000000000000e2), SC_(1.475233435630798339843750000000000000000e-1), SC_(1.282914368961631556841107109769260537362e-88), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.990947418212890625000000000000000000000e2), SC_(2.837726783752441406250000000000000000000e1), SC_(2.586981952190399169921875000000000000000e-1), SC_(4.010760397811481592922659318296102139019e-28), SC_(9.999999999999999999999999995989239602189e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.990947418212890625000000000000000000000e2), SC_(1.093762969970703125000000000000000000000e2), SC_(2.802273929119110107421875000000000000000e-1), SC_(1.147074575458494625462413729160840794201e-31), SC_(9.999999999999999999999999999998852925425e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.990947418212890625000000000000000000000e2), SC_(1.756861267089843750000000000000000000000e2), SC_(2.951916158199310302734375000000000000000e-1), SC_(6.282739472900915270969727140602284966268e-35), SC_(9.999999999999999999999999999999999371726e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.992940368652343750000000000000000000000e2), SC_(3.152261734008789062500000000000000000000e1), SC_(3.892313838005065917968750000000000000000e-1), SC_(8.422189336248947153310041870225953476746e-8), SC_(9.999999157781066375105284668995812977405e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.992940368652343750000000000000000000000e2), SC_(1.094441146850585937500000000000000000000e2), SC_(4.201809167861938476562500000000000000000e-1), SC_(7.335131328288806712967036533340727031750e-9), SC_(9.999999926648686717111932870329634666593e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.992940368652343750000000000000000000000e2), SC_(1.811583862304687500000000000000000000000e2), SC_(4.443231821060180664062500000000000000000e-1), SC_(5.757614661494570228703696034256476014791e-10), SC_(9.999999994242385338505429771296303965744e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.993139648437500000000000000000000000000e2), SC_(3.423733520507812500000000000000000000000e1), SC_(4.684656560420989990234375000000000000000e-1), SC_(1.863939702782951433032535061847093568441e-2), SC_(9.813606029721704856696746493815290643156e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.993139648437500000000000000000000000000e2), SC_(1.264718551635742187500000000000000000000e2), SC_(5.114796757698059082031250000000000000000e-1), SC_(1.007244470524194476339420696922870052955e-2), SC_(9.899275552947580552366057930307712994705e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.993139648437500000000000000000000000000e2), SC_(1.826751708984375000000000000000000000000e2), SC_(5.337331295013427734375000000000000000000e-1), SC_(6.609032623936183443870278460254492940285e-3), SC_(9.933909673760638165561297215397455070597e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.994933471679687500000000000000000000000e2), SC_(3.477303314208984375000000000000000000000e1), SC_(5.153949856758117675781250000000000000000e-1), SC_(4.166545062867227029185104625407936519793e-1), SC_(5.833454937132772970814895374592063480207e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.994933471679687500000000000000000000000e2), SC_(1.279526672363281250000000000000000000000e2), SC_(5.630922913551330566406250000000000000000e-1), SC_(4.047264294803420310786201811806954855032e-1), SC_(5.952735705196579689213798188193045144968e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(1.994933471679687500000000000000000000000e2), SC_(1.831471099853515625000000000000000000000e2), SC_(5.870853066444396972656250000000000000000e-1), SC_(3.975777639882731166639751073427487388782e-1), SC_(6.024222360117268833360248926572512611218e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.012869720458984375000000000000000000000e2), SC_(3.767639541625976562500000000000000000000e1), SC_(5.195102095603942871093750000000000000000e-1), SC_(4.908453058041561326770248108124915148841e-1), SC_(5.091546941958438673229751891875084851159e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.012869720458984375000000000000000000000e2), SC_(1.310955810546875000000000000000000000000e2), SC_(5.674747824668884277343750000000000000000e-1), SC_(4.880013355565148373403579651471311501476e-1), SC_(5.119986644434851626596420348528688498524e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.012869720458984375000000000000000000000e2), SC_(1.867986450195312500000000000000000000000e2), SC_(5.917719602584838867187500000000000000000e-1), SC_(4.865115622386450054840671465169266303070e-1), SC_(5.134884377613549945159328534830733696930e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.192234497070312500000000000000000000000e2), SC_(4.238486480712890625000000000000000000000e1), SC_(5.013815760612487792968750000000000000000e-1), SC_(4.996393916841857205329558758114994140214e-1), SC_(5.003606083158142794670441241885005859786e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.192234497070312500000000000000000000000e2), SC_(1.311481323242187500000000000000000000000e2), SC_(5.470179319381713867187500000000000000000e-1), SC_(4.979590605173924270136788227743081964877e-1), SC_(5.020409394826075729863211772256918035123e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.192234497070312500000000000000000000000e2), SC_(1.914333953857421875000000000000000000000e2), SC_(5.735351443290710449218750000000000000000e-1), SC_(4.970700616975729647306042134273064266101e-1), SC_(5.029299383024270352693957865726935733899e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.391528472900390625000000000000000000000e2), SC_(4.420680999755859375000000000000000000000e1), SC_(4.807215332984924316406250000000000000000e-1), SC_(5.010267204369194276151409692506608230527e-1), SC_(4.989732795630805723848590307493391769473e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.391528472900390625000000000000000000000e2), SC_(1.357470245361328125000000000000000000000e2), SC_(5.275872349739074707031250000000000000000e-1), SC_(4.992607985019704978634733819705020939039e-1), SC_(5.007392014980295021365266180294979060961e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.391528472900390625000000000000000000000e2), SC_(1.915013732910156250000000000000000000000e2), SC_(5.522084236145019531250000000000000000000e-1), SC_(4.984164375342037717494529682030173040345e-1), SC_(5.015835624657962282505470317969826959655e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.590822448730468750000000000000000000000e2), SC_(5.569964599609375000000000000000000000000e1), SC_(4.676264822483062744140625000000000000000e-1), SC_(5.095053228212935201635041010229151710497e-1), SC_(4.904946771787064798364958989770848289503e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.590822448730468750000000000000000000000e2), SC_(1.362719116210937500000000000000000000000e2), SC_(5.082982182502746582031250000000000000000e-1), SC_(5.074424524427759223559954784280518560541e-1), SC_(4.925575475572240776440045215719481439459e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.590822448730468750000000000000000000000e2), SC_(1.918984832763671875000000000000000000000e2), SC_(5.329382419586181640625000000000000000000e-1), SC_(5.063337766350549554224443528311951973485e-1), SC_(4.936662233649450445775556471688048026515e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.989410400390625000000000000000000000000e2), SC_(5.940588760375976562500000000000000000000e1), SC_(4.393039345741271972656250000000000000000e-1), SC_(6.000880582476749937027945569110420971437e-1), SC_(3.999119417523250062972054430889579028563e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.989410400390625000000000000000000000000e2), SC_(1.451677856445312500000000000000000000000e2), SC_(4.813641905784606933593750000000000000000e-1), SC_(5.915511925062548988647870025827413811056e-1), SC_(4.084488074937451011352129974172586188944e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(2.989410400390625000000000000000000000000e2), SC_(1.929777069091796875000000000000000000000e2), SC_(5.021858811378479003906250000000000000000e-1), SC_(5.880647936741149501087277723487364132878e-1), SC_(4.119352063258850498912722276512635867122e-1) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(3.985880737304687500000000000000000000000e2), SC_(6.038262176513671875000000000000000000000e1), SC_(4.230284094810485839843750000000000000000e-1), SC_(9.977851090407225359839297939595457214636e-1), SC_(2.214890959277464016070206040454278536350e-3) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(3.985880737304687500000000000000000000000e2), SC_(1.481294555664062500000000000000000000000e2), SC_(4.606534242630004882812500000000000000000e-1), SC_(9.957282424377606356346329644628312528585e-1), SC_(4.271757562239364365367035537168747141534e-3) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(3.985880737304687500000000000000000000000e2), SC_(1.935389862060546875000000000000000000000e2), SC_(4.782629907131195068359375000000000000000e-1), SC_(9.945960851426927928055493135079582151791e-1), SC_(5.403914857307207194450686492041784820904e-3) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(5.978820800781250000000000000000000000000e2), SC_(6.163340759277343750000000000000000000000e1), SC_(3.982345759868621826171875000000000000000e-1), SC_(9.999999999983652719310843670759144107488e-1), SC_(1.634728068915632924085589251240883044304e-12) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(5.978820800781250000000000000000000000000e2), SC_(1.486264953613281250000000000000000000000e2), SC_(4.282388091087341308593750000000000000000e-1), SC_(9.999999999441405803165315291403807033859e-1), SC_(5.585941968346847085961929661413163659822e-11) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(5.978820800781250000000000000000000000000e2), SC_(1.937735595703125000000000000000000000000e2), SC_(4.426617622375488281250000000000000000000e-1), SC_(9.999999997983110564053295602949830922408e-1), SC_(2.016889435946704397050169077592286063336e-10) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(7.971761474609375000000000000000000000000e2), SC_(7.225879669189453125000000000000000000000e1), SC_(4.061267971992492675781250000000000000000e-1), SC_(9.999999999999999999999999999997290246639e-1), SC_(2.709753361367076002320691695420448945649e-31) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(7.971761474609375000000000000000000000000e2), SC_(1.515480346679687500000000000000000000000e2), SC_(4.280660748481750488281250000000000000000e-1), SC_(9.999999999999999999999999991303421392948e-1), SC_(8.696578607051932204338673773133285372742e-28) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(7.971761474609375000000000000000000000000e2), SC_(1.941185607910156250000000000000000000000e2), SC_(4.391900300979614257812500000000000000000e-1), SC_(9.999999999999999999999999789782532523897e-1), SC_(2.102174674761034080045110832943420015762e-26) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(9.964702148437500000000000000000000000000e2), SC_(9.566968083381652832031250000000000000000e-1), SC_(4.446664154529571533203125000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(6.723822936759331715719218974775798182259e-93) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(9.964702148437500000000000000000000000000e2), SC_(7.844540405273437500000000000000000000000e1), SC_(4.620748460292816162109375000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(2.547617018541288535048352060726128288630e-80) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(9.964702148437500000000000000000000000000e2), SC_(1.584414672851562500000000000000000000000e2), SC_(4.789382815361022949218750000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(2.016791451093890693491633506946470794739e-72) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(9.964702148437500000000000000000000000000e2), SC_(1.962219390869140625000000000000000000000e2), SC_(4.865405857563018798828125000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(1.362436549196397892011134548818387099631e-69) }
+   }};
+#undef SC_
+

Added: sandbox/math_toolkit/libs/math/test/ncbeta_big.ipp
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/test/ncbeta_big.ipp	2008-01-28 13:29:37 EST (Mon, 28 Jan 2008)
@@ -0,0 +1,77 @@
+#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
+   static const boost::array<boost::array<T, 6>, 72> ncbeta_big = {{
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.090561676025390625000000000000000000000e2), SC_(2.322846374511718750000000000000000000000e2), SC_(6.248598918318748474121093750000000000000e-2), SC_(5.822794103663371475941613559141512048716e-200), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.299617919921875000000000000000000000000e2), SC_(2.906821289062500000000000000000000000000e2), SC_(1.553418934345245361328125000000000000000e-1), SC_(2.376427035888773394585864365564861664654e-112), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.320523529052734375000000000000000000000e2), SC_(9.757655029296875000000000000000000000000e2), SC_(3.780863285064697265625000000000000000000e-1), SC_(9.534309971409020993977308030456117404144e-89), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.322846374511718750000000000000000000000e2), SC_(1.879048828125000000000000000000000000000e3), SC_(6.258654594421386718750000000000000000000e-1), SC_(8.273529404980685686135545983154559305766e-53), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.323078765869140625000000000000000000000e2), SC_(2.308069091796875000000000000000000000000e3), SC_(7.707736492156982421875000000000000000000e-1), SC_(6.642746074306700324296888792472255191709e-16), SC_(9.999999999999993357253925693299675703111e-1) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.325169372558593750000000000000000000000e2), SC_(8.064482421875000000000000000000000000000e3), SC_(9.388024210929870605468750000000000000000e-1), SC_(3.784012698595881643945309133853831952949e-3), SC_(9.962159873014041183560546908661461680471e-1) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.346074829101562500000000000000000000000e2), SC_(1.567437500000000000000000000000000000000e4), SC_(9.707729816436767578125000000000000000000e-1), SC_(2.935931059732195123761306546780042425559e-1), SC_(7.064068940267804876238693453219957574441e-1) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.555131072998046875000000000000000000000e2), SC_(2.000542187500000000000000000000000000000e4), SC_(9.756411910057067871093750000000000000000e-1), SC_(4.916958930557002818402814932631962599797e-1), SC_(5.083041069442997181597185067368037400203e-1) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.787415771484375000000000000000000000000e2), SC_(5.348914843750000000000000000000000000000e4), SC_(9.897736907005310058593750000000000000000e-1), SC_(4.926920140457373120750763227119217556742e-1), SC_(5.073079859542626879249236772880782443258e-1) }, 
+      { SC_(2.906821289062500000000000000000000000000e2), SC_(2.906821250915527343750000000000000000000e1), SC_(1.567437500000000000000000000000000000000e4), SC_(9.982179403305053710937500000000000000000e-1), SC_(9.994919920744164088096546647236384815783e-1), SC_(5.080079255835911903453352763615184216904e-4) }, 
+      { SC_(2.906821289062500000000000000000000000000e2), SC_(7.267053222656250000000000000000000000000e1), SC_(2.000542187500000000000000000000000000000e4), SC_(9.976629614830017089843750000000000000000e-1), SC_(9.999999999999983875164826739274160375349e-1), SC_(1.612483517326072583962465078546376039408e-15) }, 
+      { SC_(2.906821289062500000000000000000000000000e2), SC_(1.453410644531250000000000000000000000000e2), SC_(5.348914843750000000000000000000000000000e4), SC_(9.986631274223327636718750000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(3.010804490077860063798231369313535930122e-42) }, 
+      { SC_(2.906821289062500000000000000000000000000e2), SC_(3.778867492675781250000000000000000000000e2), SC_(2.322846374511718750000000000000000000000e2), SC_(5.188288092613220214843750000000000000000e-1), SC_(5.089321557957671134199777152425169214951e-1), SC_(4.910678442042328865800222847574830785049e-1) }, 
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+      { SC_(2.000542187500000000000000000000000000000e4), SC_(4.001084375000000000000000000000000000000e4), SC_(8.064482421875000000000000000000000000000e3), SC_(4.320940375328063964843750000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(2.312959578619525129783342844601108813625e-171) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(5.348915039062500000000000000000000000000e3), SC_(2.322846374511718750000000000000000000000e2), SC_(9.546350240707397460937500000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(2.237637941712600702639280257134814673880e-479) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(1.337228710937500000000000000000000000000e4), SC_(2.906821289062500000000000000000000000000e2), SC_(9.334779381752014160156250000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(7.697670330139327953085651655652971629062e-2801) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(2.674457421875000000000000000000000000000e4), SC_(9.757655029296875000000000000000000000000e2), SC_(9.171703457832336425781250000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(4.351032154164457022358781300987678516698e-8686) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(4.814023046875000000000000000000000000000e4), SC_(2.308069091796875000000000000000000000000e3), SC_(5.316342040896415710449218750000000000000e-2), SC_(7.149393115066689998913230513163359568986e-39230), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(5.295425781250000000000000000000000000000e4), SC_(8.064482421875000000000000000000000000000e3), SC_(1.301675438880920410156250000000000000000e-1), SC_(8.209475494274670414553430270177931678225e-19833), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(5.343566015625000000000000000000000000000e4), SC_(1.567437500000000000000000000000000000000e4), SC_(2.671890854835510253906250000000000000000e-1), SC_(9.106575025886434917832830930013038223616e-7308), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(5.348914843750000000000000000000000000000e4), SC_(2.000542187500000000000000000000000000000e4), SC_(4.070649147033691406250000000000000000000e-1), SC_(8.116577402645222335506750742438163224103e-1745), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(5.349450000000000000000000000000000000000e4), SC_(5.348914843750000000000000000000000000000e4), SC_(5.399778485298156738281250000000000000000e-1), SC_(4.303272623463637069485056374998013097226e-372), SC_(1.000000000000000000000000000000000000000) }
+   }};
+#undef SC_
+

Added: sandbox/math_toolkit/libs/math/test/test_nc_beta.cpp
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/test/test_nc_beta.cpp	2008-01-28 13:29:37 EST (Mon, 28 Jan 2008)
@@ -0,0 +1,368 @@
+// test_nc_beta.cpp
+
+// Copyright John Maddock 2008.
+
+// 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)
+
+#ifdef _MSC_VER
+#pragma warning (disable:4127 4512)
+#endif
+
+#if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT)
+#  define TEST_FLOAT
+#  define TEST_DOUBLE
+#  define TEST_LDOUBLE
+#  define TEST_REAL_CONCEPT
+#endif
+
+#include <boost/math/concepts/real_concept.hpp> // for real_concept
+#include <boost/math/distributions/non_central_beta.hpp> // for chi_squared_distribution
+#include <boost/test/included/test_exec_monitor.hpp> // for test_main
+#include <boost/test/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE
+
+#include "functor.hpp"
+#include "handle_test_result.hpp"
+
+#include <iostream>
+using std::cout;
+using std::endl;
+#include <limits>
+using std::numeric_limits;
+
+#define BOOST_CHECK_CLOSE_EX(a, b, prec, i) \
+   {\
+      unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
+      BOOST_CHECK_CLOSE(a, b, prec); \
+      if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
+      {\
+         std::cerr << "Failure was at row " << i << std::endl;\
+         std::cerr << std::setprecision(35); \
+         std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
+         std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
+      }\
+   }
+
+#define BOOST_CHECK_EX(a, i) \
+   {\
+      unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
+      BOOST_CHECK(a); \
+      if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
+      {\
+         std::cerr << "Failure was at row " << i << std::endl;\
+         std::cerr << std::setprecision(35); \
+         std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
+         std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
+      }\
+   }
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   const char* largest_type;
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
+   {
+      largest_type = "(long\\s+)?double|real_concept";
+   }
+   else
+   {
+      largest_type = "long double|real_concept";
+   }
+#else
+   largest_type = "(long\\s+)?double|real_concept";
+#endif
+
+   //
+   // Catch all cases come last:
+   //
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      largest_type,                     // test type(s)
+      "[^|]*medium[^|]*",               // test data group
+      "[^|]*", 700, 500);               // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      largest_type,                     // test type(s)
+      "[^|]*large[^|]*",                // test data group
+      "[^|]*", 9000, 2000);             // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+template <class RealType>
+RealType naive_pdf(RealType v, RealType lam, RealType x)
+{
+   // TODO!
+   return 0;
+}
+
+template <class RealType>
+void test_spot(
+     RealType a,     // alpha
+     RealType b,     // beta
+     RealType ncp,   // non-centrality param
+     RealType cs,    // Chi Square statistic
+     RealType P,     // CDF
+     RealType Q,     // Complement of CDF
+     RealType tol)   // Test tolerance
+{
+   boost::math::non_central_beta_distribution<RealType> dist(a, b, ncp);
+   BOOST_CHECK_CLOSE(
+      cdf(dist, cs), P, tol);
+   try{/*
+      BOOST_CHECK_CLOSE(
+         pdf(dist, cs), naive_pdf(dist.degrees_of_freedom(), ncp, cs), tol * 50);*/
+   }
+   catch(const std::overflow_error&)
+   {}
+   if((P < 0.99) && (Q < 0.99))
+   {
+      //
+      // We can only check this if P is not too close to 1,
+      // so that we can guarentee Q is reasonably free of error:
+      //
+      BOOST_CHECK_CLOSE(
+         cdf(complement(dist, cs)), Q, tol);
+      BOOST_CHECK_CLOSE(
+            quantile(dist, P), cs, tol * 10);
+      BOOST_CHECK_CLOSE(
+            quantile(complement(dist, Q)), cs, tol * 10);
+   }
+}
+
+template <class RealType> // Any floating-point type RealType.
+void test_spots(RealType)
+{
+   RealType tolerance = (std::max)(
+      boost::math::tools::epsilon<RealType>(),
+      (RealType)boost::math::tools::epsilon<double>() * 5) * 100;
+   //
+   // At float precision we need to up the tolerance, since 
+   // the input values are rounded off to inexact quantities
+   // the results get thrown off by a noticeable amount.
+   //
+   if(boost::math::tools::digits<RealType>() < 50)
+      tolerance *= 50;
+   if(boost::is_floating_point<RealType>::value != 1)
+      tolerance *= 20; // real_concept special functions are less accurate
+
+   cout << "Tolerance = " << tolerance << "%." << endl;
+
+} // template <class RealType>void test_spots(RealType)
+
+template <class T>
+T nc_beta_cdf(T a, T b, T nc, T x)
+{
+   return cdf(boost::math::non_central_beta_distribution<T>(a, b, nc), x);
+}
+
+template <class T>
+T nc_beta_ccdf(T a, T b, T nc, T x)
+{
+   return cdf(complement(boost::math::non_central_beta_distribution<T>(a, b, nc), x));
+}
+
+template <typename T>
+void do_test_nc_chi_squared(T& data, const char* type_name, const char* test)
+{
+   typedef typename T::value_type row_type;
+   typedef typename row_type::value_type value_type;
+
+   std::cout << "Testing: " << test << std::endl;
+
+   value_type (*fp1)(value_type, value_type, value_type, value_type) = nc_beta_cdf;
+   boost::math::tools::test_result<value_type> result;
+
+   result = boost::math::tools::test(
+      data,
+      bind_func(fp1, 0, 1, 2, 3),
+      extract_result(4));
+   handle_test_result(result, data[result.worst()], result.worst(),
+      type_name, "CDF", test);
+
+   fp1 = nc_beta_ccdf;
+   result = boost::math::tools::test(
+      data,
+      bind_func(fp1, 0, 1, 2, 3),
+      extract_result(5));
+   handle_test_result(result, data[result.worst()], result.worst(),
+      type_name, "CCDF", test);
+
+   std::cout << std::endl;
+
+}
+
+template <typename T>
+void quantile_sanity_check(T& data, const char* type_name, const char* test)
+{
+   typedef typename T::value_type row_type;
+   typedef typename row_type::value_type value_type;
+
+   //
+   // Tests with type real_concept take rather too long to run, so
+   // for now we'll disable them:
+   //
+   if(!boost::is_floating_point<value_type>::value)
+      return;
+
+   std::cout << "Testing: " << type_name << " quantile sanity check, with tests " << test << std::endl;
+
+   //
+   // These sanity checks test for a round trip accuracy of one half
+   // of the bits in T, unless T is type float, in which case we check
+   // for just one decimal digit.  The problem here is the sensitivity
+   // of the functions, not their accuracy.  This test data was generated
+   // for the forward functions, which means that when it is used as
+   // the input to the inverses then it is necessarily inexact.  This rounding
+   // of the input is what makes the data unsuitable for use as an accuracy check,
+   // and also demonstrates that you can't in general round-trip these functions.
+   // It is however a useful sanity check.
+   //
+   value_type precision = static_cast<value_type>(ldexp(1.0, 1-boost::math::policies::digits<value_type, boost::math::policies::policy<> >()/2)) * 100;
+   if(boost::math::policies::digits<value_type, boost::math::policies::policy<> >() < 50)
+      precision = 1;   // 1% or two decimal digits, all we can hope for when the input is truncated to float
+
+   for(unsigned i = 0; i < data.size(); ++i)
+   {
+      if(data[i][4] == 0)
+      {
+         BOOST_CHECK(0 == quantile(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1], data[i][2]), data[i][4]));
+      }
+      else if(data[i][4] < 0.9999f)
+      {
+         value_type p = quantile(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1], data[i][2]), data[i][4]);
+         value_type pt = data[i][3];
+         BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
+      }
+      if(data[i][5] == 0)
+      {
+         BOOST_CHECK(1 == quantile(complement(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1], data[i][2]), data[i][5])));
+      }
+      else if(data[i][5] < 0.9999f)
+      {
+         value_type p = quantile(complement(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1], data[i][2]), data[i][5]));
+         value_type pt = data[i][3];
+         BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
+      }
+      /*
+      if(boost::math::tools::digits<value_type>() > 50)
+      {
+         //
+         // Sanity check mode, note this may well overflow
+         // since we don't know how to compute PDF's (and hence the mode) 
+         // for large values of the parameters, in addition accuracy of
+         // the mode is at *best* the square root of the accuracy of the PDF:
+         //
+         try
+         {
+            value_type m = mode(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1]));
+            value_type p = pdf(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1]), m);
+            BOOST_CHECK_EX(pdf(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1]), m * (1 + sqrt(precision) * 10)) <= p, i);
+            BOOST_CHECK_EX(pdf(boost::math::non_central_beta_distribution<value_type>(data[i][0], data[i][1]), m * (1 - sqrt(precision)) * 10) <= p, i);
+         }
+         catch(const std::overflow_error&)
+         {
+         }
+         //
+         // Sanity check degrees-of-freedom finder, don't bother at float
+         // precision though as there's not enough data in the probability
+         // values to get back to the correct degrees of freedom or 
+         // non-cenrality parameter:
+         //
+         try{
+            if((data[i][3] < 0.99) && (data[i][3] != 0))
+            {
+               BOOST_CHECK_CLOSE_EX(
+                  boost::math::non_central_beta_distribution<value_type>::find_degrees_of_freedom(data[i][1], data[i][2], data[i][3]),
+                  data[i][0], precision, i);
+               BOOST_CHECK_CLOSE_EX(
+                  boost::math::non_central_beta_distribution<value_type>::find_non_centrality(data[i][0], data[i][2], data[i][3]),
+                  data[i][1], precision, i);
+            }
+            if((data[i][4] < 0.99) && (data[i][4] != 0))
+            {
+               BOOST_CHECK_CLOSE_EX(
+                  boost::math::non_central_beta_distribution<value_type>::find_degrees_of_freedom(boost::math::complement(data[i][1], data[i][2], data[i][4])),
+                  data[i][0], precision, i);
+               BOOST_CHECK_CLOSE_EX(
+                  boost::math::non_central_beta_distribution<value_type>::find_non_centrality(boost::math::complement(data[i][0], data[i][2], data[i][4])),
+                  data[i][1], precision, i);
+            }
+         }
+         catch(const std::exception& e)
+         {
+            BOOST_ERROR(e.what());
+         }
+      }
+      */
+   }
+}
+
+template <typename T>
+void test_accuracy(T, const char* type_name)
+{
+#include "ncbeta.ipp"
+    do_test_nc_chi_squared(ncbeta, type_name, "Non Central Beta, medium parameters");
+    quantile_sanity_check(ncbeta, type_name, "Non Central Beta, medium parameters");
+
+#include "ncbeta_big.ipp"
+    do_test_nc_chi_squared(ncbeta_big, type_name, "Non Central Beta, large parameters");
+    // quantile_sanity_check(ncbeta_big, type_name, "Non Central Beta, large parameters");
+}
+
+int test_main(int, char* [])
+{
+   BOOST_MATH_CONTROL_FP;
+   // Basic sanity-check spot values.
+   expected_results();
+   // (Parameter value, arbitrarily zero, only communicates the floating point type).
+#ifdef TEST_FLOAT
+   test_spots(0.0F); // Test float.
+#endif
+#ifdef TEST_DOUBLE
+   test_spots(0.0); // Test double.
+#endif
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+#ifdef TEST_LDOUBLE
+   test_spots(0.0L); // Test long double.
+#endif
+#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
+#ifdef TEST_REAL_CONCEPT
+   test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
+#endif
+#endif
+#endif
+
+#ifdef TEST_FLOAT
+   test_accuracy(0.0F, "float"); // Test float.
+#endif
+#ifdef TEST_DOUBLE
+   test_accuracy(0.0, "double"); // Test double.
+#endif
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+#ifdef TEST_LDOUBLE
+   test_accuracy(0.0L, "long double"); // Test long double.
+#endif
+#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
+#ifdef TEST_REAL_CONCEPT
+   test_accuracy(boost::math::concepts::real_concept(0.), "real_concept"); // Test real concept.
+#endif
+#endif
+#endif
+   return 0;
+} // int test_main(int, char* [])
+