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// (C) Copyright John Maddock 2006.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#include "mp_t.hpp"
#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>
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 truncate 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;
}
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