summaryrefslogtreecommitdiffstats
path: root/src/boost/libs/math/tools/ibeta_data.cpp
diff options
context:
space:
mode:
Diffstat (limited to 'src/boost/libs/math/tools/ibeta_data.cpp')
-rw-r--r--src/boost/libs/math/tools/ibeta_data.cpp303
1 files changed, 303 insertions, 0 deletions
diff --git a/src/boost/libs/math/tools/ibeta_data.cpp b/src/boost/libs/math/tools/ibeta_data.cpp
new file mode 100644
index 00000000..667365ec
--- /dev/null
+++ b/src/boost/libs/math/tools/ibeta_data.cpp
@@ -0,0 +1,303 @@
+// (C) Copyright John Maddock 2006.
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0. (See accompanying file
+// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include <boost/math/special_functions/gamma.hpp>
+#include <boost/math/special_functions/beta.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/lexical_cast.hpp>
+#include <fstream>
+#include <map>
+#include <boost/math/tools/test_data.hpp>
+#include <boost/random.hpp>
+#include "mp_t.hpp"
+
+using namespace boost::math::tools;
+using namespace boost::math;
+using namespace std;
+
+template <class T>
+struct ibeta_fraction1_t
+{
+ typedef std::pair<T, T> result_type;
+
+ ibeta_fraction1_t(T a_, T b_, T x_) : a(a_), b(b_), x(x_), k(1) {}
+
+ result_type operator()()
+ {
+ T aN;
+ if(k & 1)
+ {
+ int m = (k - 1) / 2;
+ aN = -(a + m) * (a + b + m) * x;
+ aN /= a + 2*m;
+ aN /= a + 2*m + 1;
+ }
+ else
+ {
+ int m = k / 2;
+ aN = m * (b - m) *x;
+ aN /= a + 2*m - 1;
+ aN /= a + 2*m;
+ }
+ ++k;
+ return std::make_pair(aN, T(1));
+ }
+
+private:
+ T a, b, x;
+ int k;
+};
+
+//
+// This function caches previous calls to beta
+// just so we can speed things up a bit:
+//
+template <class T>
+T get_beta(T a, T b)
+{
+ static std::map<std::pair<T, T>, T> m;
+
+ if(a < b)
+ std::swap(a, b);
+
+ std::pair<T, T> p(a, b);
+ typename std::map<std::pair<T, T>, T>::const_iterator i = m.find(p);
+ if(i != m.end())
+ return i->second;
+
+ T r = beta(a, b);
+ p.first = a;
+ p.second = b;
+ m[p] = r;
+
+ return r;
+}
+
+//
+// compute the continued fraction:
+//
+template <class T>
+T get_ibeta_fraction1(T a, T b, T x)
+{
+ ibeta_fraction1_t<T> f(a, b, x);
+ T fract = boost::math::tools::continued_fraction_a(f, boost::math::policies::digits<T, boost::math::policies::policy<> >());
+ T denom = (a * (fract + 1));
+ T num = pow(x, a) * pow(1 - x, b);
+ if(num == 0)
+ return 0;
+ else if(denom == 0)
+ return -1;
+ return num / denom;
+}
+//
+// calculate the incomplete beta from the fraction:
+//
+template <class T>
+std::pair<T,T> ibeta_fraction1(T a, T b, T x)
+{
+ T bet = get_beta(a, b);
+ if(x > ((a+1)/(a+b+2)))
+ {
+ T fract = get_ibeta_fraction1(b, a, 1-x);
+ if(fract/bet > 0.75)
+ {
+ fract = get_ibeta_fraction1(a, b, x);
+ return std::make_pair(fract, bet - fract);
+ }
+ return std::make_pair(bet - fract, fract);
+ }
+ T fract = get_ibeta_fraction1(a, b, x);
+ if(fract/bet > 0.75)
+ {
+ fract = get_ibeta_fraction1(b, a, 1-x);
+ return std::make_pair(bet - fract, fract);
+ }
+ return std::make_pair(fract, bet - fract);
+
+}
+//
+// calculate the regularised incomplete beta from the fraction:
+//
+template <class T>
+std::pair<T,T> ibeta_fraction1_regular(T a, T b, T x)
+{
+ T bet = get_beta(a, b);
+ if(x > ((a+1)/(a+b+2)))
+ {
+ T fract = get_ibeta_fraction1(b, a, 1-x);
+ if(fract == 0)
+ bet = 1; // normalise so we don't get 0/0
+ else if(bet == 0)
+ return std::make_pair(T(-1), T(-1)); // Yikes!!
+ if(fract / bet > 0.75)
+ {
+ fract = get_ibeta_fraction1(a, b, x);
+ return std::make_pair(fract / bet, 1 - (fract / bet));
+ }
+ return std::make_pair(1 - (fract / bet), fract / bet);
+ }
+ T fract = get_ibeta_fraction1(a, b, x);
+ if(fract / bet > 0.75)
+ {
+ fract = get_ibeta_fraction1(b, a, 1-x);
+ return std::make_pair(1 - (fract / bet), fract / bet);
+ }
+ return std::make_pair(fract / bet, 1 - (fract / bet));
+}
+
+//
+// we absolutely must trunctate the input values to float
+// precision: we have to be certain that the input values
+// can be represented exactly in whatever width floating
+// point type we are testing, otherwise the output will
+// necessarily be off.
+//
+float external_f;
+float force_truncate(const float* f)
+{
+ external_f = *f;
+ return external_f;
+}
+
+float truncate_to_float(mp_t r)
+{
+ float f = boost::math::tools::real_cast<float>(r);
+ return force_truncate(&f);
+}
+
+boost::mt19937 rnd;
+boost::uniform_real<float> ur_a(1.0F, 5.0F);
+boost::variate_generator<boost::mt19937, boost::uniform_real<float> > gen(rnd, ur_a);
+boost::uniform_real<float> ur_a2(0.0F, 100.0F);
+boost::variate_generator<boost::mt19937, boost::uniform_real<float> > gen2(rnd, ur_a2);
+
+struct beta_data_generator
+{
+ boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t, mp_t, mp_t> operator()(mp_t ap, mp_t bp, mp_t x_)
+ {
+ float a = truncate_to_float(real_cast<float>(gen() * pow(mp_t(10), ap)));
+ float b = truncate_to_float(real_cast<float>(gen() * pow(mp_t(10), bp)));
+ float x = truncate_to_float(real_cast<float>(x_));
+ std::cout << a << " " << b << " " << x << std::endl;
+ std::pair<mp_t, mp_t> ib_full = ibeta_fraction1(mp_t(a), mp_t(b), mp_t(x));
+ std::pair<mp_t, mp_t> ib_reg = ibeta_fraction1_regular(mp_t(a), mp_t(b), mp_t(x));
+ return boost::math::make_tuple(a, b, x, ib_full.first, ib_full.second, ib_reg.first, ib_reg.second);
+ }
+};
+
+// medium sized values:
+struct beta_data_generator_medium
+{
+ boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t, mp_t, mp_t> operator()(mp_t x_)
+ {
+ mp_t a = gen2();
+ mp_t b = gen2();
+ mp_t x = x_;
+ a = ConvPrec(a, 22);
+ b = ConvPrec(b, 22);
+ x = ConvPrec(x, 22);
+ std::cout << a << " " << b << " " << x << std::endl;
+ //mp_t exp_beta = boost::math::beta(a, b, x);
+ std::pair<mp_t, mp_t> ib_full = ibeta_fraction1(mp_t(a), mp_t(b), mp_t(x));
+ /*exp_beta = boost::math::tools::relative_error(ib_full.first, exp_beta);
+ if(exp_beta > 1e-40)
+ {
+ std::cout << exp_beta << std::endl;
+ }*/
+ std::pair<mp_t, mp_t> ib_reg = ibeta_fraction1_regular(mp_t(a), mp_t(b), mp_t(x));
+ return boost::math::make_tuple(a, b, x, ib_full.first, ib_full.second, ib_reg.first, ib_reg.second);
+ }
+};
+
+struct beta_data_generator_small
+{
+ boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t, mp_t, mp_t> operator()(mp_t x_)
+ {
+ float a = truncate_to_float(gen2()/10);
+ float b = truncate_to_float(gen2()/10);
+ float x = truncate_to_float(real_cast<float>(x_));
+ std::cout << a << " " << b << " " << x << std::endl;
+ std::pair<mp_t, mp_t> ib_full = ibeta_fraction1(mp_t(a), mp_t(b), mp_t(x));
+ std::pair<mp_t, mp_t> ib_reg = ibeta_fraction1_regular(mp_t(a), mp_t(b), mp_t(x));
+ return boost::math::make_tuple(a, b, x, ib_full.first, ib_full.second, ib_reg.first, ib_reg.second);
+ }
+};
+
+struct beta_data_generator_int
+{
+ boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t, mp_t, mp_t> operator()(mp_t a, mp_t b, mp_t x_)
+ {
+ float x = truncate_to_float(real_cast<float>(x_));
+ std::cout << a << " " << b << " " << x << std::endl;
+ std::pair<mp_t, mp_t> ib_full = ibeta_fraction1(a, b, mp_t(x));
+ std::pair<mp_t, mp_t> ib_reg = ibeta_fraction1_regular(a, b, mp_t(x));
+ return boost::math::make_tuple(a, b, x, ib_full.first, ib_full.second, ib_reg.first, ib_reg.second);
+ }
+};
+
+int main(int, char* [])
+{
+ parameter_info<mp_t> arg1, arg2, arg3, arg4, arg5;
+ test_data<mp_t> data;
+
+ std::cout << "Welcome.\n"
+ "This program will generate spot tests for the incomplete beta functions:\n"
+ " beta(a, b, x) and ibeta(a, b, x)\n\n"
+ "This is not an interactive program be prepared for a long wait!!!\n\n";
+
+ arg1 = make_periodic_param(mp_t(-5), mp_t(6), 11);
+ arg2 = make_periodic_param(mp_t(-5), mp_t(6), 11);
+ arg3 = make_random_param(mp_t(0.0001), mp_t(1), 10);
+ arg4 = make_random_param(mp_t(0.0001), mp_t(1), 100 /*500*/);
+ arg5 = make_periodic_param(mp_t(1), mp_t(41), 10);
+
+ arg1.type |= dummy_param;
+ arg2.type |= dummy_param;
+ arg3.type |= dummy_param;
+ arg4.type |= dummy_param;
+ arg5.type |= dummy_param;
+
+ // comment out all but one of the following when running
+ // or this program will take forever to complete!
+ //data.insert(beta_data_generator(), arg1, arg2, arg3);
+ //data.insert(beta_data_generator_medium(), arg4);
+ //data.insert(beta_data_generator_small(), arg4);
+ data.insert(beta_data_generator_int(), arg5, arg5, arg3);
+
+ test_data<mp_t>::const_iterator i, j;
+ i = data.begin();
+ j = data.end();
+ while(i != j)
+ {
+ mp_t v1 = beta((*i)[0], (*i)[1], (*i)[2]);
+ mp_t v2 = relative_error(v1, (*i)[3]);
+ std::string s = boost::lexical_cast<std::string>((*i)[3]);
+ mp_t v3 = boost::lexical_cast<mp_t>(s);
+ mp_t v4 = relative_error(v3, (*i)[3]);
+ if(v2 > 1e-40)
+ {
+ std::cout << v2 << std::endl;
+ }
+ if(v4 > 1e-60)
+ {
+ std::cout << v4 << std::endl;
+ }
+ ++ i;
+ }
+
+ std::cout << "Enter name of test data file [default=ibeta_data.ipp]";
+ std::string line;
+ std::getline(std::cin, line);
+ boost::algorithm::trim(line);
+ if(line == "")
+ line = "ibeta_data.ipp";
+ std::ofstream ofs(line.c_str());
+ ofs << std::scientific << std::setprecision(40);
+ write_code(ofs, data, "ibeta_data");
+
+ return 0;
+}
+
+
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-21 12:31:29 +0000