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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) },
- { SC_(1.951913356781005859375000000000000000000), SC_(2.982279586791992187500000000000000000000e1), SC_(9.532412719726562500000000000000000000000e1), SC_(9.999887200477040810758641857663267864056e-1), SC_(1.127995229591892413581423367321359444282e-5) },
- { SC_(1.951913356781005859375000000000000000000), SC_(3.152261734008789062500000000000000000000e1), SC_(1.338981170654296875000000000000000000000e2), SC_(9.999999981716438903356424143868590809089e-1), SC_(1.828356109664357585613140919091144116655e-9) },
- { SC_(1.951913356781005859375000000000000000000), SC_(3.423733520507812500000000000000000000000e1), SC_(1.809462280273437500000000000000000000000e2), SC_(9.999999999999779223507784210789075338814e-1), SC_(2.207764922157892109246611863427962135540e-14) },
- { SC_(1.951913356781005859375000000000000000000), SC_(3.477303314208984375000000000000000000000e1), SC_(3.672494649887084960937500000000000000000), SC_(1.917873016822970354862321861326583012994e-5), SC_(9.999808212698317702964513767813867341699e-1) },
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