mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2024-11-22 20:28:42 -05:00
304 lines
8.9 KiB
C++
304 lines
8.9 KiB
C++
// (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;
|
|
}
|
|
|
|
|