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tanh_sinh_test_errors.cpp
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tanh_sinh_test_errors.cpp
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/*
Copyright John Maddock 2021.
Derived in part from machine translation of "tanh-sinh integrator version 5"
Copyright © 2010, 2020 Graeme Dennes
https://newtonexcelbach.com/2020/10/29/numerical-integration-with-tanh-sinh-quadrature-v-5-0/
This program is free software : you can redistribute itand /or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program.If not, see < https://www.gnu.org/licenses/>.
*/
#include "tanh_sinh_test_cases.hpp"
#include <boost/math/quadrature/tanh_sinh.hpp>
#include <boost/math/special_functions/relative_difference.hpp>
#include <iostream>
#include <iomanip>
//#define TEST_QTHSH
unsigned calls = 0;
template <>
void log_test_call(const double&)
{
++calls;
}
template <class F, class Real>
Real qthsh(F f, Real a, Real b, int n, Real eps, Real* perror)
{
BOOST_MATH_STD_USING
Real c = (a + b) / 2; // center (mean)
Real d = (b - a) / 2; // half distance
Real s = f(c);
Real v, h = 2;
int k = 0;
if (n <= 0) // use default levels n=6
n = 6; // 6 is optimal, 7 just as good taking longer
if (eps <= 0) // use default eps=1E-9
eps = 1E-9;
do {
Real p = 0, q, fp = 0, fm = 0, t, eh;
h /= 2;
t = eh = exp(h);
if (k > 0)
eh *= eh;
do {
Real u = exp(1 / t - t); // = exp(-2*sinh(j*h)) = 1/exp(sinh(j*h))^2
Real r = 2 * u / (1 + u); // = 1 - tanh(sinh(j*h))
Real w = (t + 1 / t) * r / (1 + u); // = cosh(j*h)/cosh(sinh(j*h))^2
Real x = d * r;
if (a + x > a) { // if too close to a then reuse previous fp
Real y = f(a + x);
if (boost::math::isfinite(y))
fp = y; // if f(x) is finite, add to the local sum
}
if (b - x < b) { // if too close to b then reuse previous fm
Real y = f(b - x);
if (boost::math::isfinite(y))
fm = y; // if f(x) is finite, add to the local sum
}
q = w * (fp + fm);
p += q;
t *= eh;
} while (fabs(q) > eps * fabs(p));
v = 2 * s;
s += p;
++k;
} while (fabs(v - s) > 10 * eps * fabs(s) && k <= n);
*perror = fabs(v - s) / (fabs(s) + eps);
return d * s * h; // result with estimated relative error e
}
int main()
{
std::pair<const test_entry*, const test_entry*> p = get_tests();
boost::math::quadrature::tanh_sinh<double> integrator;
double tolerance = 1e-9;
double error = 0;
int index = 1;
std::cout << " N Result #Calls ErrorEstimate ErrorFound\n";
for (const test_entry* pos = p.first; pos != p.second; ++pos, ++index)
{
try {
double result = integrator.integrate(pos->proc, pos->a, pos->b, tolerance, &error);
std::cout << std::setw(4) << std::right << index
<< std::setw(25) << std::scientific << std::right << std::setprecision(17) << result
<< std::setw(10) << std::right << calls
<< std::setw(15) << std::right << std::setprecision(4) << error
<< std::setw(15) << std::right << std::setprecision(4) << boost::math::relative_difference(result, pos->exact_result) << std::endl;
}
catch (const boost::math::evaluation_error&)
{
std::cout << std::setw(4) << std::right << index
<< std::right << std::setw(20) << "EXCEPTION!!" << std::endl;
}
calls = 0;
}
#ifdef TEST_QTHSH
std::cout << "\n\nTesting qthsh at " << tolerance << std::endl << std::endl;
std::cout << "\n\n N Result #Calls ErrorEstimate ErrorFound\n";
index = 1;
for (const test_entry* pos = p.first; pos != p.second; ++pos, ++index)
{
try {
double result = qthsh(pos->proc, pos->a, pos->b, 15, tolerance, &error);
std::cout << std::setw(4) << std::right << index
<< std::setw(25) << std::scientific << std::right << std::setprecision(17) << result
<< std::setw(10) << std::right << calls
<< std::setw(15) << std::right << std::setprecision(4) << error
<< std::setw(15) << std::right << std::setprecision(4) << boost::math::relative_difference(result, pos->exact_result) << std::endl;
}
catch (const boost::math::evaluation_error&)
{
std::cout << std::setw(4) << std::right << index
<< std::right << std::setw(20) << "EXCEPTION!!" << std::endl;
}
calls = 0;
}
//
// Internally, qthsh multiplies the tolerance by 10 to obtain a termination condition.
// Boost just uses tolerance directly as the termination condition.
// So add this comparison to level up the playing field and compare like with like:
//
std::cout << "\n\nTesting qthsh at " << (tolerance / 10) << std::endl << std::endl;
std::cout << "\n\n N Result #Calls ErrorEstimate ErrorFound\n";
index = 1;
for (const test_entry* pos = p.first; pos != p.second; ++pos, ++index)
{
try {
double result = qthsh(pos->proc, pos->a, pos->b, 15, tolerance / 10, &error);
std::cout << std::setw(4) << std::right << index
<< std::setw(25) << std::scientific << std::right << std::setprecision(17) << result
<< std::setw(10) << std::right << calls
<< std::setw(15) << std::right << std::setprecision(4) << error
<< std::setw(15) << std::right << std::setprecision(4) << boost::math::relative_difference(result, pos->exact_result) << std::endl;
}
catch (const boost::math::evaluation_error&)
{
std::cout << std::setw(4) << std::right << index
<< std::right << std::setw(20) << "EXCEPTION!!" << std::endl;
}
calls = 0;
}
#endif
}