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/*
* Copyright Nick Thompson, 2019
* 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 "math_unit_test.hpp"
#include <vector>
#include <random>
#include <boost/math/constants/constants.hpp>
#include <boost/math/interpolators/cardinal_trigonometric.hpp>
#ifdef BOOST_HAS_FLOAT128
#include <boost/multiprecision/float128.hpp>
#endif
using std::sin;
using boost::math::constants::two_pi;
using boost::math::interpolators::cardinal_trigonometric;
template<class Real>
void test_constant()
{
Real t0 = 0;
Real h = 1;
for(size_t n = 1; n < 20; ++n)
{
Real c = 8;
std::vector<Real> v(n, c);
auto ct = cardinal_trigonometric<decltype(v)>(v, t0, h);
CHECK_ULP_CLOSE(c, ct(0.3), 3);
CHECK_ULP_CLOSE(c*h*n, ct.integrate(), 3);
CHECK_ULP_CLOSE(c*c*h*n, ct.squared_l2(), 3);
CHECK_MOLLIFIED_CLOSE(Real(0), ct.prime(0.8), 25*std::numeric_limits<Real>::epsilon());
CHECK_MOLLIFIED_CLOSE(Real(0), ct.double_prime(0.8), 25*std::numeric_limits<Real>::epsilon());
}
}
template<class Real>
void test_interpolation_condition()
{
std::mt19937 gen(1234);
std::uniform_real_distribution<Real> dis(1, 10);
for(size_t n = 1; n < 20; ++n) {
Real t0 = dis(gen);
Real h = dis(gen);
std::vector<Real> v(n);
for (size_t i = 0; i < n; ++i) {
v[i] = dis(gen);
}
auto ct = cardinal_trigonometric<decltype(v)>(v, t0, h);
for (size_t i = 0; i < n; ++i) {
Real arg = t0 + i*h;
Real expected = v[i];
Real computed = ct(arg);
if(!CHECK_ULP_CLOSE(expected, computed, 5*n))
{
std::cerr << " Samples: " << n << "\n";
}
}
}
}
#ifdef BOOST_HAS_FLOAT128
void test_constant_q()
{
__float128 t0 = 0;
__float128 h = 1;
for(size_t n = 1; n < 20; ++n)
{
__float128 c = 8;
std::vector<__float128> v(n, c);
auto ct = cardinal_trigonometric<decltype(v)>(v, t0, h);
CHECK_ULP_CLOSE(boost::multiprecision::float128(c), boost::multiprecision::float128(ct(0.3)), 3);
CHECK_ULP_CLOSE(boost::multiprecision::float128(c*h*n), boost::multiprecision::float128(ct.integrate()), 3);
}
}
#endif
template<class Real>
void test_sampled_sine()
{
using std::sin;
using std::cos;
for (unsigned n = 15; n < 50; ++n)
{
Real t0 = 0;
Real T = 1;
Real h = T/n;
std::vector<Real> v(n);
auto s = [&](Real t) { return sin(two_pi<Real>()*(t-t0)/T);};
auto s_prime = [&](Real t) { return two_pi<Real>()*cos(two_pi<Real>()*(t-t0)/T)/T;};
auto s_double_prime = [&](Real t) { return -two_pi<Real>()*two_pi<Real>()*sin(two_pi<Real>()*(t-t0)/T)/(T*T);};
for(size_t j = 0; j < v.size(); ++j)
{
Real t = t0 + j*h;
v[j] = s(t);
}
auto ct = cardinal_trigonometric<decltype(v)>(v, t0, h);
CHECK_ULP_CLOSE(T, ct.period(), 3);
std::mt19937 gen(1234);
std::uniform_real_distribution<Real> dist(0, 500);
unsigned j = 0;
while (j++ < 50) {
Real arg = dist(gen);
Real expected = s(arg);
Real computed = ct(arg);
CHECK_MOLLIFIED_CLOSE(expected, computed, std::numeric_limits<Real>::epsilon()*4000);
expected = s_prime(arg);
computed = ct.prime(arg);
CHECK_MOLLIFIED_CLOSE(expected, computed, 18000*std::numeric_limits<Real>::epsilon());
expected = s_double_prime(arg);
computed = ct.double_prime(arg);
CHECK_MOLLIFIED_CLOSE(expected, computed, 100000*std::numeric_limits<Real>::epsilon());
}
CHECK_MOLLIFIED_CLOSE(Real(0), ct.integrate(), std::numeric_limits<Real>::epsilon());
}
}
template<class Real>
void test_bump()
{
using std::exp;
using std::abs;
using std::sqrt;
using std::pow;
auto bump = [](Real x)->Real { if (abs(x) >= 1) { return Real(0); } return exp(-Real(1)/(Real(1)-x*x)); };
auto bump_prime = [](Real x)->Real {
if (abs(x) >= 1) { return Real(0); }
return -2*x*exp(-Real(1)/(Real(1)-x*x))/pow(1-x*x,2);
};
auto bump_double_prime = [](Real x)->Real {
if (abs(x) >= 1) { return Real(0); }
return (6*pow(x,4)-2)*exp(-Real(1)/(Real(1)-x*x))/pow(1-x*x,4);
};
Real t0 = -1;
size_t n = 4096;
Real h = Real(2)/Real(n);
std::vector<Real> v(n);
for(size_t i = 0; i < n; ++i)
{
Real t = t0 + i*h;
v[i] = bump(t);
}
auto ct = cardinal_trigonometric<decltype(v)>(v, t0, h);
std::mt19937 gen(323723);
std::uniform_real_distribution<long double> dis(-0.9, 0.9);
size_t i = 0;
while (i++ < 1000)
{
Real t = static_cast<Real>(dis(gen));
Real expected = bump(t);
Real computed = ct(t);
if(!CHECK_MOLLIFIED_CLOSE(expected, computed, 2*std::numeric_limits<Real>::epsilon())) {
std::cerr << " Problem occurred at abscissa " << t << "\n";
}
expected = bump_prime(t);
computed = ct.prime(t);
if(!CHECK_MOLLIFIED_CLOSE(expected, computed, 4000*std::numeric_limits<Real>::epsilon())) {
std::cerr << " Problem occurred at abscissa " << t << "\n";
}
expected = bump_double_prime(t);
computed = ct.double_prime(t);
if(!CHECK_MOLLIFIED_CLOSE(expected, computed, 4000*4000*std::numeric_limits<Real>::epsilon())) {
std::cerr << " Problem occurred at abscissa " << t << "\n";
}
}
// Wolfram Alpha:
// NIntegrate[Exp[-1/(1-x*x)],{x,-1,1}]
CHECK_ULP_CLOSE(Real(0.443993816168079437823L), ct.integrate(), 3);
// NIntegrate[Exp[-2/(1-x*x)],{x,-1,1}]
CHECK_ULP_CLOSE(Real(0.1330861208449942715569473279553285713625791551628130055345002588895389L), ct.squared_l2(), 1);
}
int main()
{
#ifdef TEST1
test_constant<float>();
test_sampled_sine<float>();
test_bump<float>();
test_interpolation_condition<float>();
#endif
#ifdef TEST2
test_constant<double>();
test_sampled_sine<double>();
test_bump<double>();
test_interpolation_condition<double>();
#endif
#ifdef TEST3
test_constant<long double>();
test_sampled_sine<long double>();
test_bump<long double>();
test_interpolation_condition<long double>();
#endif
#ifdef TEST4
#ifdef BOOST_HAS_FLOAT128
test_constant_q();
#endif
#endif
return boost::math::test::report_errors();
}
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