[Boost-commit] svn:boost r42820 - in sandbox/math_toolkit: boost/math/distributions boost/math/distributions/detail libs/math/test

From: john_at_[hidden]
Date: 2008-01-16 14:02:46

Author: johnmaddock
Date: 2008-01-16 14:02:45 EST (Wed, 16 Jan 2008)
New Revision: 42820
URL: http://svn.boost.org/trac/boost/changeset/42820

Log:
Commit of more or less complete non-central chi-square distribution: docs still to come.
Text files modified: 
   sandbox/math_toolkit/boost/math/distributions/detail/common_error_handling.hpp |    20                                         
   sandbox/math_toolkit/boost/math/distributions/non_central_chi_squared.hpp      |   348 +                                       
   sandbox/math_toolkit/libs/math/test/Jamfile.v2                                 |    24                                         
   sandbox/math_toolkit/libs/math/test/nccs.ipp                                   |  8858 +++++++++++++-------------------------- 
   sandbox/math_toolkit/libs/math/test/test_nc_chi_squared.cpp                    |   207                                         
   5 files changed, 3577 insertions(+), 5880 deletions(-)

Modified: sandbox/math_toolkit/boost/math/distributions/detail/common_error_handling.hpp
==============================================================================
--- sandbox/math_toolkit/boost/math/distributions/detail/common_error_handling.hpp	(original)
+++ sandbox/math_toolkit/boost/math/distributions/detail/common_error_handling.hpp	2008-01-16 14:02:45 EST (Wed, 16 Jan 2008)
@@ -97,6 +97,26 @@
 }
 
 template <class RealType, class Policy>
+inline bool check_positive_x(
+      const char* function,
+      RealType x,
+      RealType* result,
+      const Policy& pol)
+{
+   if(!(boost::math::isfinite)(x) || (x < 0))
+   {
+      *result = policies::raise_domain_error<RealType>(
+         function,
+         "Random variate x is %1%, but must be finite and >= 0!", x, pol);
+      return false;
+   }
+   return true;
+   // Note that this test catches both infinity and NaN.
+   // Some special cases permit x to be infinite, so these must be tested 1st,
+   // leaving this test to catch any NaNs.  see Normal and cauchy for example.
+}
+
+template <class RealType, class Policy>
 inline bool check_non_centrality(
       const char* function,
       RealType ncp,

Modified: sandbox/math_toolkit/boost/math/distributions/non_central_chi_squared.hpp
==============================================================================
--- sandbox/math_toolkit/boost/math/distributions/non_central_chi_squared.hpp	(original)
+++ sandbox/math_toolkit/boost/math/distributions/non_central_chi_squared.hpp	2008-01-16 14:02:45 EST (Wed, 16 Jan 2008)
@@ -19,6 +19,7 @@
 #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
 {
@@ -394,6 +395,231 @@
                function);
          }
 
+         template <class RealType, class Policy>
+         RealType nccs_pdf(const non_central_chi_squared_distribution<RealType, Policy>& dist, const RealType& x)
+         {
+            static const char* function = "pdf(non_central_chi_squared_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 k = dist.degrees_of_freedom();
+            value_type l = dist.non_centrality();
+            value_type r;
+            if(!detail::check_df(
+               function,
+               k, &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy())
+               ||
+            !detail::check_positive_x(
+               function,
+               (value_type)x,
+               &r,
+               Policy()))
+                  return (RealType)r;
+
+         if(l == 0)
+            return pdf(boost::math::chi_squared_distribution<RealType, forwarding_policy>(dist.degrees_of_freedom()), x);
+
+         r = log(x / l) * (k / 4 - 0.5f) - (x + l) / 2;
+         if(r >= tools::log_max_value<RealType>())
+            return policies::raise_overflow_error<RealType>(function, 0, forwarding_policy());
+         if(r <= -tools::log_max_value<RealType>())
+            return policies::raise_underflow_error<RealType>(function, 0, forwarding_policy());
+
+         r = exp(r);
+         r = 0.5f * r
+            * boost::math::cyl_bessel_i(k/2 - 1, sqrt(l * x), forwarding_policy());
+            return policies::checked_narrowing_cast<RealType, forwarding_policy>(
+               r, 
+               function);
+         }
+
+         template <class RealType, class Policy>
+         struct pdf_minimizer
+         {
+            pdf_minimizer(const non_central_chi_squared_distribution<RealType, Policy>& d)
+               : dist(d) {}
+
+            RealType operator()(const RealType& x)
+            {
+               return -pdf(dist, x);
+            }
+         private:
+            non_central_chi_squared_distribution<RealType, Policy> dist;
+         };
+
+         template <class RealType, class Policy>
+         RealType nccs_mode(const non_central_chi_squared_distribution<RealType, Policy>& dist)
+         {
+            static const char* function = "mode(non_central_chi_squared_distribution<%1%> const&)";
+
+            RealType k = dist.degrees_of_freedom();
+            RealType l = dist.non_centrality();
+            RealType r;
+            if(!detail::check_df(
+               function,
+               k, &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy()))
+                  return (RealType)r;
+            //
+            // Need to begin by bracketing the maxima of the PDF:
+            //
+            RealType maxval;
+            RealType upper_bound = l + k;
+            RealType lower_bound;
+            RealType v = pdf(dist, l + k);
+            do
+            {
+               maxval = v;
+               upper_bound *= 2;
+               v = pdf(dist, upper_bound);
+            }while(maxval < v);
+
+            lower_bound = upper_bound;
+            do
+            {
+               maxval = v;
+               lower_bound /= 2;
+               v = pdf(dist, lower_bound);
+            }while(maxval < v);
+
+            boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
+
+            return tools::brent_find_minima(
+                     pdf_minimizer<RealType, Policy>(dist), 
+                     lower_bound, 
+                     upper_bound, 
+                     policies::digits<RealType, Policy>(), 
+                     max_iter).first;
+         }
+
+         template <class RealType, class Policy>
+         struct degrees_of_freedom_finder
+         {
+            degrees_of_freedom_finder(
+               RealType lam_, RealType x_, RealType p_, bool c)
+               : lam(lam_), x(x_), p(p_), comp(c) {}
+
+            RealType operator()(const RealType& v)
+            {
+               non_central_chi_squared_distribution<RealType, Policy> d(v, lam);
+               return comp ?
+                  p - cdf(complement(d, x))
+                  : cdf(d, x) - p;
+            }
+         private:
+            RealType lam;
+            RealType x;
+            RealType p;
+            bool comp;
+         };
+
+         template <class RealType, class Policy>
+         inline RealType find_degrees_of_freedom(
+            RealType lam, RealType x, RealType p, RealType q, const Policy& pol)
+         {
+            const char* function = "non_central_chi_squared<%1%>::find_degrees_of_freedom";
+            if((p == 0) || (q == 0))
+            {
+               //
+               // Can't a thing if one of p and q is zero:
+               //
+               return policies::raise_evaluation_error<RealType>(function, 
+                  "Can't find degrees of freedom when the probability is 0 or 1, only possible answer is %1%", 
+                  RealType(std::numeric_limits<RealType>::quiet_NaN()), Policy());
+            }
+            degrees_of_freedom_finder<RealType, Policy> f(lam, x, p < q ? p : q, p < q ? false : true);
+            tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>());
+            boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
+            //
+            // Pick an initial guess that we know will give us a probability
+            // right around 0.5.
+            //
+            RealType guess = x - lam;
+            if(guess < 1)
+               guess = 1;
+            std::pair<RealType, RealType> ir = tools::bracket_and_solve_root(
+               f, guess, RealType(2), false, tol, max_iter, pol);
+            RealType result = ir.first + (ir.second - ir.first) / 2;
+            if(max_iter == policies::get_max_root_iterations<Policy>())
+            {
+               policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:"
+                  " or there is no answer to problem.  Current best guess is %1%", result, Policy());
+            }
+            return result;
+         }
+
+         template <class RealType, class Policy>
+         struct non_centrality_finder
+         {
+            non_centrality_finder(
+               RealType v_, RealType x_, RealType p_, bool c)
+               : v(v_), x(x_), p(p_), comp(c) {}
+
+            RealType operator()(const RealType& lam)
+            {
+               non_central_chi_squared_distribution<RealType, Policy> d(v, lam);
+               return comp ?
+                  p - cdf(complement(d, x))
+                  : cdf(d, x) - p;
+            }
+         private:
+            RealType v;
+            RealType x;
+            RealType p;
+            bool comp;
+         };
+
+         template <class RealType, class Policy>
+         inline RealType find_non_centrality(
+            RealType v, RealType x, RealType p, RealType q, const Policy& pol)
+         {
+            const char* function = "non_central_chi_squared<%1%>::find_non_centrality";
+            if((p == 0) || (q == 0))
+            {
+               //
+               // Can't do a thing if one of p and q is zero:
+               //
+               return policies::raise_evaluation_error<RealType>(function, 
+                  "Can't find degrees of freedom when the probability is 0 or 1, only possible answer is %1%", 
+                  RealType(std::numeric_limits<RealType>::quiet_NaN()), Policy());
+            }
+            non_centrality_finder<RealType, Policy> f(v, x, p < q ? p : q, p < q ? false : true);
+            tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>());
+            boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
+            //
+            // Pick an initial guess that we know will give us a probability
+            // right around 0.5.
+            //
+            RealType guess = x - v;
+            if(guess < 1)
+               guess = 1;
+            std::pair<RealType, RealType> ir = tools::bracket_and_solve_root(
+               f, guess, RealType(2), false, tol, max_iter, pol);
+            RealType result = ir.first + (ir.second - ir.first) / 2;
+            if(max_iter == policies::get_max_root_iterations<Policy>())
+            {
+               policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:"
+                  " or there is no answer to problem.  Current best guess is %1%", result, Policy());
+            }
+            return result;
+         }
+
       }
 
       template <class RealType = double, class Policy = policies::policy<> >
@@ -425,6 +651,88 @@
          { // Private data getter function.
             return ncp;
          }
+         static RealType find_degrees_of_freedom(RealType lam, RealType x, RealType p)
+         {
+            const char* function = "non_central_chi_squared<%1%>::find_degrees_of_freedom";
+            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 result = detail::find_degrees_of_freedom(
+               static_cast<value_type>(lam), 
+               static_cast<value_type>(x), 
+               static_cast<value_type>(p), 
+               static_cast<value_type>(1-p), 
+               forwarding_policy());
+            return policies::checked_narrowing_cast<RealType, forwarding_policy>(
+               result, 
+               function);
+         }
+         template <class A, class B, class C>
+         static RealType find_degrees_of_freedom(const complemented3_type<A,B,C>& c)
+         {
+            const char* function = "non_central_chi_squared<%1%>::find_degrees_of_freedom";
+            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 result = detail::find_degrees_of_freedom(
+               static_cast<value_type>(c.dist), 
+               static_cast<value_type>(c.param1), 
+               static_cast<value_type>(1-c.param2), 
+               static_cast<value_type>(c.param2), 
+               forwarding_policy());
+            return policies::checked_narrowing_cast<RealType, forwarding_policy>(
+               result, 
+               function);
+         }
+         static RealType find_non_centrality(RealType v, RealType x, RealType p)
+         {
+            const char* function = "non_central_chi_squared<%1%>::find_non_centrality";
+            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 result = detail::find_non_centrality(
+               static_cast<value_type>(v), 
+               static_cast<value_type>(x), 
+               static_cast<value_type>(p), 
+               static_cast<value_type>(1-p), 
+               forwarding_policy());
+            return policies::checked_narrowing_cast<RealType, forwarding_policy>(
+               result, 
+               function);
+         }
+         template <class A, class B, class C>
+         static RealType find_non_centrality(const complemented3_type<A,B,C>& c)
+         {
+            const char* function = "non_central_chi_squared<%1%>::find_non_centrality";
+            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 result = detail::find_non_centrality(
+               static_cast<value_type>(c.dist), 
+               static_cast<value_type>(c.param1), 
+               static_cast<value_type>(1-c.param2), 
+               static_cast<value_type>(c.param2), 
+               forwarding_policy());
+            return policies::checked_narrowing_cast<RealType, forwarding_policy>(
+               result, 
+               function);
+         }
       private:
          // Data member, initialized by constructor.
          RealType df; // degrees of freedom.
@@ -473,8 +781,7 @@
       template <class RealType, class Policy>
       inline RealType mode(const non_central_chi_squared_distribution<RealType, Policy>& dist)
       { // mode.
-         // TODO!
-         return 0;
+         return detail::nccs_mode(dist);
       }
 
       template <class RealType, class Policy>
@@ -548,30 +855,9 @@
       }
 
       template <class RealType, class Policy>
-      RealType pdf(const non_central_chi_squared_distribution<RealType, Policy>& dist, const RealType& x)
+      inline RealType pdf(const non_central_chi_squared_distribution<RealType, Policy>& dist, const RealType& x)
       { // Probability Density/Mass Function.
-         const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::pdf(%1%)";
-         RealType k = dist.degrees_of_freedom();
-         RealType l = dist.non_centrality();
-         RealType r;
-         if(!detail::check_df(
-            function,
-            k, &r, Policy())
-            ||
-         !detail::check_non_centrality(
-            function,
-            l,
-            &r,
-            Policy()))
-               return r;
-
-         if(l == 0)
-            return pdf(boost::math::chi_squared_distribution<RealType, Policy>(k), x);
-
-         r = -(x + l) / 2 + log(x / l) * (k / 4 - 0.5f);
-
-         return 0.5f * exp(r)
-            * boost::math::cyl_bessel_i(k/2 - 1, sqrt(l * x), Policy());
+         return detail::nccs_pdf(dist, x);
       } // pdf
 
       template <class RealType, class Policy>
@@ -589,6 +875,12 @@
             function,
             l,
             &r,
+            Policy())
+            ||
+         !detail::check_positive_x(
+            function,
+            x,
+            &r,
             Policy()))
                return r;
 
@@ -612,6 +904,12 @@
             function,
             l,
             &r,
+            Policy())
+            ||
+         !detail::check_positive_x(
+            function,
+            x,
+            &r,
             Policy()))
                return r;
 

Modified: sandbox/math_toolkit/libs/math/test/Jamfile.v2
==============================================================================
--- sandbox/math_toolkit/libs/math/test/Jamfile.v2	(original)
+++ sandbox/math_toolkit/libs/math/test/Jamfile.v2	2008-01-16 14:02:45 EST (Wed, 16 Jan 2008)
@@ -247,6 +247,30 @@
         : # requirements
               <define>TEST_REAL_CONCEPT
         : test_negative_binomial_real_concept ;
+run test_nc_chi_squared.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      <define>TEST_FLOAT
+        : test_nc_chi_squared_float ;
+run test_nc_chi_squared.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      <define>TEST_DOUBLE
+        : test_nc_chi_squared_double ;
+run test_nc_chi_squared.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      <define>TEST_LDOUBLE
+        : test_nc_chi_squared_long_double ;
+run test_nc_chi_squared.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      <define>TEST_REAL_CONCEPT
+        : test_nc_chi_squared_real_concept ;
 run test_normal.cpp ;
 run test_pareto.cpp ;
 run test_poisson.cpp  

Modified: sandbox/math_toolkit/libs/math/test/nccs.ipp
==============================================================================
--- sandbox/math_toolkit/libs/math/test/nccs.ipp	(original)
+++ sandbox/math_toolkit/libs/math/test/nccs.ipp	2008-01-16 14:02:45 EST (Wed, 16 Jan 2008)
@@ -1,81 +1,62 @@
 #define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
-   static const boost::array<boost::array<T, 5>, 6000> nccs = {{
+   static const boost::array<boost::array<T, 5>, 3200> nccs = {{
       { SC_(1.951913356781005859375000000000000000000), SC_(9.566968083381652832031250000000000000000e-1), SC_(2.908610105514526367187500000000000000000e-1), SC_(9.191713210042786241188236234883914114395e-2), SC_(9.080828678995721375881176376511608588560e-1) }, 
       { SC_(1.951913356781005859375000000000000000000), SC_(6.366568565368652343750000000000000000000), SC_(2.079620361328125000000000000000000000000), SC_(8.979177306921986952474050864260945461537e-2), SC_(9.102082269307801304752594913573905453846e-1) }, 
       { SC_(1.951913356781005859375000000000000000000), SC_(6.889215946197509765625000000000000000000), SC_(4.420564651489257812500000000000000000000), SC_(2.322522640917811378036214577533389504074e-1), SC_(7.677477359082188621963785422466610495926e-1) }, 
       { SC_(1.951913356781005859375000000000000000000), SC_(7.142335891723632812500000000000000000000), SC_(6.820687294006347656250000000000000000000), SC_(4.029439026943616888034033394094687890419e-1), SC_(5.970560973056383111965966605905312109581e-1) }, 
-      { SC_(1.951913356781005859375000000000000000000), SC_(7.288250446319580078125000000000000000000), SC_(8.316146850585937500000000000000000000000), SC_(5.038428377395773771758360212400971336315e-1), SC_(4.961571622604226228241639787599028663685e-1) }, 
-      { SC_(1.951913356781005859375000000000000000000), SC_(9.234277725219726562500000000000000000000), SC_(1.107432937622070312500000000000000000000e1), SC_(5.544105281575079014689864160160101377823e-1), SC_(4.455894718424920985310135839839898622177e-1) }, 
-      { SC_(1.951913356781005859375000000000000000000), SC_(1.024328517913818359375000000000000000000e1), SC_(1.218300342559814453125000000000000000000e1), SC_(5.577750867136484675075526897282128405956e-1), SC_(4.422249132863515324924473102717871594044e-1) }, 
-      { SC_(1.951913356781005859375000000000000000000), SC_(1.942635536193847656250000000000000000000e1), SC_(2.137826919555664062500000000000000000000e1), SC_(5.437263152350438819892533954754818163831e-1), SC_(4.562736847649561180107466045245181836169e-1) }, 
-      { SC_(1.951913356781005859375000000000000000000), SC_(1.950807952880859375000000000000000000000e1), SC_(2.146213912963867187500000000000000000000e1), SC_(5.437336600869751102864733220798477851994e-1), SC_(4.562663399130248897135266779201522148006e-1) }, 
-      { SC_(1.951913356781005859375000000000000000000), SC_(2.197235107421875000000000000000000000000e1), SC_(2.394819068908691406250000000000000000000e1), SC_(5.422554060038592006097554113112438198162e-1), SC_(4.577445939961407993902445886887561801838e-1) }, 
-      { SC_(1.951913356781005859375000000000000000000), SC_(2.249290275573730468750000000000000000000e1), SC_(2.468926429748535156250000000000000000000e1), SC_(5.506952035548603506354200886700755078907e-1), SC_(4.493047964451396493645799113299244921093e-1) }, 
-      { SC_(1.951913356781005859375000000000000000000), SC_(2.503655242919921875000000000000000000000e1), SC_(2.968731307983398437500000000000000000000e1), SC_(6.380541278836940740846382394359979905332e-1), SC_(3.619458721163059259153617605640020094668e-1) }, 
-      { SC_(1.951913356781005859375000000000000000000), SC_(2.517932701110839843750000000000000000000e1), SC_(3.255749130249023437500000000000000000000e1), SC_(7.252831730256075994549684122751824434727e-1), SC_(2.747168269743924005450315877248175565273e-1) }, 
-      { SC_(1.951913356781005859375000000000000000000), SC_(2.539736366271972656250000000000000000000e1), SC_(3.555405807495117187500000000000000000000e1), SC_(7.984055633892103713314925646794327903921e-1), SC_(2.015944366107896286685074353205672096079e-1) }, 
-      { SC_(1.951913356781005859375000000000000000000), SC_(2.709540176391601562500000000000000000000e1), SC_(4.357097244262695312500000000000000000000e1), SC_(9.055957937261751262447611668825407833383e-1), SC_(9.440420627382487375523883311745921666175e-2) }, 
-      { SC_(1.951913356781005859375000000000000000000), SC_(2.837726783752441406250000000000000000000e1), SC_(6.065836334228515625000000000000000000000e1), SC_(9.915201802126919581349622062403211107638e-1), SC_(8.479819787308041865037793759678889236171e-3) }, 
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-      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.915013732910156250000000000000000000000e2), SC_(3.868892211914062500000000000000000000000e2), SC_(4.646066261400716931329423411881118174560e-1), SC_(5.353933738599283068670576588118881825440e-1) }, 
-      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.918984832763671875000000000000000000000e2), SC_(3.908031005859375000000000000000000000000e2), SC_(5.057862246880519715190448594999293253585e-1), SC_(4.942137753119480284809551405000706746415e-1) }, 
-      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.929777069091796875000000000000000000000e2), SC_(3.922734985351562500000000000000000000000e2), SC_(5.103401564073109179202650004553723208057e-1), SC_(4.896598435926890820797349995446276791943e-1) }, 
-      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.935389862060546875000000000000000000000e2), SC_(3.928740539550781250000000000000000000000e2), SC_(5.107899529574641160919830486462544902796e-1), SC_(4.892100470425358839080169513537455097204e-1) }, 
-      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.937735595703125000000000000000000000000e2), SC_(3.934624633789062500000000000000000000000e2), SC_(5.149017264305247681133769667501871765435e-1), SC_(4.850982735694752318866230332498128234565e-1) }, 
-      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.941185607910156250000000000000000000000e2), SC_(3.973485107421875000000000000000000000000e2), SC_(5.557736535299754577238739897676765663797e-1), SC_(4.442263464700245422761260102323234336203e-1) }, 
-      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.962219390869140625000000000000000000000e2), SC_(4.350695495605468750000000000000000000000e2), SC_(8.734208067641611058089718811855438820161e-1), SC_(1.265791932358388941910281188144561179839e-1) }, 
-      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.985762634277343750000000000000000000000e2), SC_(4.774465026855468750000000000000000000000e2), SC_(9.862961785274749388734229563401456908532e-1), SC_(1.370382147252506112657704365985430914680e-2) }, 
-      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.988137054443359375000000000000000000000e2), SC_(5.175422973632812500000000000000000000000e2), SC_(9.993515745877044169890527883106015017448e-1), SC_(6.484254122955830109472116893984982552481e-4) }, 
-      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.992922668457031250000000000000000000000e2), SC_(5.978820800781250000000000000000000000000e2), SC_(9.999998412058642981462624294362836802506e-1), SC_(1.587941357018537375705637163197494372068e-7) }
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.451677856445312500000000000000000000000e2), SC_(4.478026428222656250000000000000000000000e2), SC_(9.989298174363830482551903570127157560119e-1), SC_(1.070182563616951744809642987284243988141e-3) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.481294555664062500000000000000000000000e2), SC_(5.211378784179687500000000000000000000000e2), SC_(9.999994797904691860176751277865619206758e-1), SC_(5.202095308139823248722134380793241867631e-7) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.486264953613281250000000000000000000000e2), SC_(6.958446044921875000000000000000000000000e2), SC_(9.999999999999999996045263399197254490884e-1), SC_(3.954736600802745509115943800189889355831e-19) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.515480346679687500000000000000000000000e2), SC_(1.052531494140625000000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(6.601257805885150289909120658456231227750e-54) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.527500000000000000000000000000000000000e2), SC_(1.408183227539062500000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(1.000237582081951046145742432553355955693e-96) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.584414672851562500000000000000000000000e2), SC_(1.788686401367187500000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(5.957827315427703908759646403474290650064e-146) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.594559783935546875000000000000000000000e2), SC_(3.587517929077148437500000000000000000000e1), SC_(1.356176082172300107520771145977600912607e-69), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.595857238769531250000000000000000000000e2), SC_(8.972038269042968750000000000000000000000e1), SC_(8.216070643082009610897966985030390252065e-34), SC_(9.999999999999999999999999999999991783929e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.596211700439453125000000000000000000000e2), SC_(1.794584960937500000000000000000000000000e2), SC_(7.166324162989548688114040163345096606824e-12), SC_(9.999999999928336758370104513118859598367e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.600560913085937500000000000000000000000e2), SC_(2.695139160156250000000000000000000000000e2), SC_(1.327523249276128325865905450265666297728e-3), SC_(9.986724767507238716741340945497343337023e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.629447326660156250000000000000000000000e2), SC_(3.260164794921875000000000000000000000000e2), SC_(1.301004072687408931880643785374331713448e-1), SC_(8.698995927312591068119356214625668286552e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.643806610107421875000000000000000000000e2), SC_(3.600397033691406250000000000000000000000e2), SC_(4.660182128381547289926298172432381841274e-1), SC_(5.339817871618452710073701827567618158726e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.646915740966796875000000000000000000000e2), SC_(3.636233825683593750000000000000000000000e2), SC_(5.062665303560026040030081445813429265462e-1), SC_(4.937334696439973959969918554186570734538e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.670017089843750000000000000000000000000e2), SC_(3.662975158691406250000000000000000000000e2), SC_(5.106973005574084169848510356025972361947e-1), SC_(4.893026994425915830151489643974027638053e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.698258666992187500000000000000000000000e2), SC_(3.691585998535156250000000000000000000000e2), SC_(5.111052702424046835457855804537903702324e-1), SC_(4.888947297575953164542144195462096297676e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.744857635498046875000000000000000000000e2), SC_(3.741553649902343750000000000000000000000e2), SC_(5.150887834143480940075807657281644704146e-1), SC_(4.849112165856519059924192342718355295854e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.756861267089843750000000000000000000000e2), SC_(3.787317504882812500000000000000000000000e2), SC_(5.553201941675350167646371773361318286268e-1), SC_(4.446798058324649832353628226638681713732e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.811583862304687500000000000000000000000e2), SC_(4.184996337890625000000000000000000000000e2), SC_(8.705310827199552808744555344825350400779e-1), SC_(1.294689172800447191255444655174649599221e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.826751708984375000000000000000000000000e2), SC_(4.583652038574218750000000000000000000000e2), SC_(9.852368357723595013366611071898316886584e-1), SC_(1.476316422764049866333889281016831134165e-2) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.831471099853515625000000000000000000000e2), SC_(4.971757812500000000000000000000000000000e2), SC_(9.992475277030363823098749022492933911247e-1), SC_(7.524722969636176901250977507066088753398e-4) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.867986450195312500000000000000000000000e2), SC_(5.791416625976562500000000000000000000000e2), SC_(9.999997868073928052689964204548628458249e-1), SC_(2.131926071947310035795451371541751186443e-7) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.900444183349609375000000000000000000000e2), SC_(7.786804199218750000000000000000000000000e2), SC_(9.999999999999999999842890448735225215767e-1), SC_(1.571095512647747842332431001488736906025e-20) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.914333953857421875000000000000000000000e2), SC_(1.172187500000000000000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(3.535476598966853255870979872762898186893e-58) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.915013732910156250000000000000000000000e2), SC_(1.563188720703125000000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(1.503818272229840966678812511638176571203e-104) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.918984832763671875000000000000000000000e2), SC_(1.955971435546875000000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(2.310477211914576555408738212352063615286e-156) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.929777069091796875000000000000000000000e2), SC_(3.922735214233398437500000000000000000000e1), SC_(5.529022449107786967054709588291909745351e-72), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.935389862060546875000000000000000000000e2), SC_(9.820869445800781250000000000000000000000e1), SC_(3.003464474651918107665338937597739013444e-35), SC_(9.999999999999999999999999999999999699654e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.937735595703125000000000000000000000000e2), SC_(1.965346832275390625000000000000000000000e2), SC_(2.080463495775573742672052667674087592048e-12), SC_(9.999999999979195365042244262573279473323e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.941185607910156250000000000000000000000e2), SC_(2.950607910156250000000000000000000000000e2), SC_(9.973915776745850702522937113932704987176e-4), SC_(9.990026084223254149297477062886067295013e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.962219390869140625000000000000000000000e2), SC_(3.559659729003906250000000000000000000000e2), SC_(1.231238558149305651892248029845975246239e-1), SC_(8.768761441850694348107751970154024753761e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.985762634277343750000000000000000000000e2), SC_(3.938933410644531250000000000000000000000e2), SC_(4.642429596210990429025849224204611903317e-1), SC_(5.357570403789009570974150775795388096683e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.988137054443359375000000000000000000000e2), SC_(3.977113952636718750000000000000000000000e2), SC_(5.056692632383849664727396199463872273040e-1), SC_(4.943307367616150335272603800536127726960e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.992922668457031250000000000000000000000e2), SC_(3.985880737304687500000000000000000000000e2), SC_(5.102581793845303603671068481454659458711e-1), SC_(4.897418206154696396328931518545340541289e-1) }
    }};
 #undef SC_
 

Modified: sandbox/math_toolkit/libs/math/test/test_nc_chi_squared.cpp
==============================================================================
--- sandbox/math_toolkit/libs/math/test/test_nc_chi_squared.cpp	(original)
+++ sandbox/math_toolkit/libs/math/test/test_nc_chi_squared.cpp	2008-01-16 14:02:45 EST (Wed, 16 Jan 2008)
@@ -7,8 +7,20 @@
 // (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_chi_squared.hpp> // for chi_squared_distribution
+#include <boost/math/special_functions/cbrt.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
 
@@ -31,21 +43,87 @@
          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] << " , " << data[i][5] << " } " << std::endl;\
+         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
+      "[^|]*", 350, 100);                  // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      largest_type,                     // test type(s)
+      "[^|]*large[^|]*",                   // test data group
+      "[^|]*", 10000, 3000);                  // 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)
 {
    // Formula direct from 
    // http://mathworld.wolfram.com/NoncentralChi-SquaredDistribution.html
    // with no simplification:
-   RealType r = -(x+lam)/2 + log(x) * (v-1)/2 + log(lam) / 2;
-   r -= log(lam * x) * v/4;
-   r = exp(r) / 2;
-   r *= boost::math::cyl_bessel_i(v/2 - 1, sqrt(lam * x));
-   return r;
+   RealType sum, term, prefix(1);
+   RealType eps = boost::math::tools::epsilon<RealType>();
+   term = sum = pdf(boost::math::chi_squared_distribution<RealType>(v), x);
+   for(int i = 1;; ++i)
+   {
+      prefix *= lam / (2 * i);
+      term = prefix * pdf(boost::math::chi_squared_distribution<RealType>(v + 2 * i), x);
+      sum += term;
+      if(term / sum < eps)
+         break;
+   }
+   return sum * exp(-lam/2);
 }
 
 template <class RealType>
@@ -60,20 +138,32 @@
    boost::math::non_central_chi_squared_distribution<RealType> dist(df, ncp);
    BOOST_CHECK_CLOSE(
       cdf(dist, cs), P, tol);
-   BOOST_CHECK_CLOSE(
-      pdf(dist, cs), naive_pdf(dist.degrees_of_freedom(), ncp, cs), 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 free of error:
+      // 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);
+            quantile(dist, P), cs, tol * 10);
       BOOST_CHECK_CLOSE(
-            quantile(complement(dist, Q)), cs, tol);
+            quantile(complement(dist, Q)), cs, tol * 10);
+      BOOST_CHECK_CLOSE(
+         dist.find_degrees_of_freedom(ncp, cs, P), df, tol * 10);
+      BOOST_CHECK_CLOSE(
+         dist.find_degrees_of_freedom(boost::math::complement(ncp, cs, Q)), df, tol * 10);
+      BOOST_CHECK_CLOSE(
+         dist.find_non_centrality(df, cs, P), ncp, tol * 10);
+      BOOST_CHECK_CLOSE(
+         dist.find_non_centrality(boost::math::complement(df, cs, Q)), ncp, tol * 10);
    }
 }
 
@@ -90,6 +180,8 @@
    //
    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;
 
@@ -140,7 +232,7 @@
       static_cast<RealType>(38.56038),   // Chi Squared statistic
       static_cast<RealType>(0.8519497361859118e-1),       // Probability of result (CDF), P
       static_cast<RealType>(1-0.8519497361859118e-1),           // Q = 1 - P
-      tolerance);
+      tolerance * 2);
    test_spot(
       static_cast<RealType>(100),   // degrees of freedom
       static_cast<RealType>(16),   // non centrality
@@ -205,16 +297,14 @@
    BOOST_CHECK_CLOSE(
       coefficient_of_variation(dist)
       , standard_deviation(dist) / mean(dist), tol2);
-#if 0
    // mode:
    BOOST_CHECK_CLOSE(
       mode(dist)
-      , static_cast<RealType>(6), tol2);
-#endif
+      , static_cast<RealType>(17.184201151792944), sqrt(tolerance));
    BOOST_CHECK_CLOSE(
       median(dist), 
       quantile(
-      non_central_chi_squared_distribution<RealType>(
+      boost::math::non_central_chi_squared_distribution<RealType>(
          static_cast<RealType>(8),
          static_cast<RealType>(12)),
       static_cast<RealType>(0.5)), static_cast<RealType>(tol2));
@@ -290,6 +380,13 @@
    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;
 
    //
@@ -329,17 +426,65 @@
          value_type pt = data[i][2];
          BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
       }
+      //
+      // Sanity check mode as well, 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_chi_squared_distribution<value_type>(data[i][0], data[i][1]));
+         value_type p = pdf(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), m);
+         BOOST_CHECK_EX(pdf(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), m * (1 + sqrt(precision))) <= p, i);
+         BOOST_CHECK_EX(pdf(boost::math::non_central_chi_squared_distribution<value_type>(data[i][0], data[i][1]), m * (1 - sqrt(precision))) <= 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:
+      //
+      if(boost::math::tools::digits<value_type>() > 50)
+      {
+         try{
+            if((data[i][3] < 0.99) && (data[i][3] != 0))
+            {
+               BOOST_CHECK_CLOSE_EX(
+                  boost::math::non_central_chi_squared_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_chi_squared_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_chi_squared_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_chi_squared_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)
 {
-#if 0
 #include "nccs.ipp"
     do_test_nc_chi_squared(nccs, type_name, "Non Central Chi Squared, medium parameters");
     quantile_sanity_check(nccs, type_name, "Non Central Chi Squared, medium parameters");
-#endif
+
 #include "nccs_big.ipp"
     do_test_nc_chi_squared(nccs_big, type_name, "Non Central Chi Squared, large parameters");
     quantile_sanity_check(nccs_big, type_name, "Non Central Chi Squared, large parameters");
@@ -349,31 +494,41 @@
 {
    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* [])
 
-/*
-
-
-*/
-
-
-