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/*
* Copyright Nick Thompson, 2017
* 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)
*/
#define BOOST_TEST_MODULE chebyshev_transform_test
#include <boost/cstdfloat.hpp>
#include <boost/type_index.hpp>
#include <boost/test/included/unit_test.hpp>
#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/math/special_functions/chebyshev.hpp>
#include <boost/math/special_functions/chebyshev_transform.hpp>
#include <boost/math/special_functions/sinc.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
#if !defined(TEST1) && !defined(TEST2) && !defined(TEST3) && !defined(TEST4)
# define TEST1
# define TEST2
# define TEST3
# define TEST4
#endif
using boost::multiprecision::cpp_bin_float_quad;
using boost::multiprecision::cpp_bin_float_50;
using boost::multiprecision::cpp_bin_float_100;
using boost::math::chebyshev_t;
using boost::math::chebyshev_t_prime;
using boost::math::chebyshev_u;
using boost::math::chebyshev_transform;
template<class Real>
void test_sin_chebyshev_transform()
{
using boost::math::chebyshev_transform;
using boost::math::constants::half_pi;
using std::sin;
using std::cos;
using std::abs;
Real tol = 10*std::numeric_limits<Real>::epsilon();
auto f = [](Real x) { return sin(x); };
Real a = 0;
Real b = 1;
chebyshev_transform<Real> cheb(f, a, b, tol);
Real x = a;
while (x < b)
{
Real s = sin(x);
Real c = cos(x);
if (abs(s) < tol)
{
BOOST_CHECK_SMALL(cheb(x), 100*tol);
BOOST_CHECK_CLOSE_FRACTION(c, cheb.prime(x), 100*tol);
}
else
{
BOOST_CHECK_CLOSE_FRACTION(s, cheb(x), 100*tol);
if (abs(c) < tol)
{
BOOST_CHECK_SMALL(cheb.prime(x), 100*tol);
}
else
{
BOOST_CHECK_CLOSE_FRACTION(c, cheb.prime(x), 100*tol);
}
}
x += static_cast<Real>(1)/static_cast<Real>(1 << 7);
}
Real Q = cheb.integrate();
BOOST_CHECK_CLOSE_FRACTION(1 - cos(static_cast<Real>(1)), Q, 100*tol);
}
template<class Real>
void test_sinc_chebyshev_transform()
{
using std::cos;
using std::sin;
using std::abs;
using boost::math::sinc_pi;
using boost::math::chebyshev_transform;
using boost::math::constants::half_pi;
Real tol = 500*std::numeric_limits<Real>::epsilon();
auto f = [](Real x) { return boost::math::sinc_pi(x); };
Real a = 0;
Real b = 1;
chebyshev_transform<Real> cheb(f, a, b, tol/50);
Real x = a;
while (x < b)
{
Real s = sinc_pi(x);
Real ds = (cos(x)-sinc_pi(x))/x;
if (x == 0) { ds = 0; }
if (s < tol)
{
BOOST_CHECK_SMALL(cheb(x), tol);
}
else
{
BOOST_CHECK_CLOSE_FRACTION(s, cheb(x), tol);
}
if (abs(ds) < tol)
{
BOOST_CHECK_SMALL(cheb.prime(x), 5 * tol);
}
else
{
BOOST_CHECK_CLOSE_FRACTION(ds, cheb.prime(x), 300*tol);
}
x += static_cast<Real>(1)/static_cast<Real>(1 << 7);
}
Real Q = cheb.integrate();
//NIntegrate[Sinc[x], {x, 0, 1}, WorkingPrecision -> 200, AccuracyGoal -> 150, PrecisionGoal -> 150, MaxRecursion -> 150]
Real Q_exp = boost::lexical_cast<Real>("0.94608307036718301494135331382317965781233795473811179047145477356668");
BOOST_CHECK_CLOSE_FRACTION(Q_exp, Q, tol);
}
//Examples taken from "Approximation Theory and Approximation Practice", by Trefethen
template<class Real>
void test_atap_examples()
{
using std::sin;
using boost::math::constants::half;
using boost::math::sinc_pi;
using boost::math::chebyshev_transform;
using boost::math::constants::half_pi;
Real tol = 10*std::numeric_limits<Real>::epsilon();
auto f1 = [](Real x) { return ((0 < x) - (x < 0)) - x/2; };
auto f2 = [](Real x) { Real t = sin(6*x); Real s = sin(x + exp(2*x));
Real u = (0 < s) - (s < 0);
return t + u; };
auto f3 = [](Real x) { return sin(6*x) + sin(60*exp(x)); };
auto f4 = [](Real x) { return 1/(1+1000*(x+half<Real>())*(x+half<Real>())) + 1/sqrt(1+1000*(x-.5)*(x-0.5));};
Real a = -1;
Real b = 1;
chebyshev_transform<Real> cheb1(f1, a, b);
chebyshev_transform<Real> cheb2(f2, a, b, tol);
//chebyshev_transform<Real> cheb3(f3, a, b, tol);
Real x = a;
while (x < b)
{
//Real s = f1(x);
if (sizeof(Real) == sizeof(float))
{
BOOST_CHECK_CLOSE_FRACTION(f1(x), cheb1(x), 4e-3);
}
else
{
BOOST_CHECK_CLOSE_FRACTION(f1(x), cheb1(x), 1.3e-5);
}
BOOST_CHECK_CLOSE_FRACTION(f2(x), cheb2(x), 6e-3);
//BOOST_CHECK_CLOSE_FRACTION(f3(x), cheb3(x), 100*tol);
x += static_cast<Real>(1)/static_cast<Real>(1 << 7);
}
}
//Validate that the Chebyshev polynomials are well approximated by the Chebyshev transform.
template<class Real>
void test_chebyshev_chebyshev_transform()
{
Real tol = 500*std::numeric_limits<Real>::epsilon();
// T_0 = 1:
auto t0 = [](Real) { return 1; };
chebyshev_transform<Real> cheb0(t0, -1, 1);
BOOST_CHECK_CLOSE_FRACTION(cheb0.coefficients()[0], 2, tol);
Real x = -1;
while (x < 1)
{
BOOST_CHECK_CLOSE_FRACTION(cheb0(x), 1, tol);
BOOST_CHECK_SMALL(cheb0.prime(x), tol);
x += static_cast<Real>(1)/static_cast<Real>(1 << 7);
}
// T_1 = x:
auto t1 = [](Real x) { return x; };
chebyshev_transform<Real> cheb1(t1, -1, 1);
BOOST_CHECK_CLOSE_FRACTION(cheb1.coefficients()[1], 1, tol);
x = -1;
while (x < 1)
{
if (x == 0)
{
BOOST_CHECK_SMALL(cheb1(x), tol);
}
else
{
BOOST_CHECK_CLOSE_FRACTION(cheb1(x), x, tol);
}
BOOST_CHECK_CLOSE_FRACTION(cheb1.prime(x), 1, tol);
x += static_cast<Real>(1)/static_cast<Real>(1 << 7);
}
auto t2 = [](Real x) { return 2*x*x-1; };
chebyshev_transform<Real> cheb2(t2, -1, 1);
BOOST_CHECK_CLOSE_FRACTION(cheb2.coefficients()[2], 1, tol);
x = -1;
while (x < 1)
{
BOOST_CHECK_CLOSE_FRACTION(cheb2(x), t2(x), tol);
if (x != 0)
{
BOOST_CHECK_CLOSE_FRACTION(cheb2.prime(x), 4*x, tol);
}
else
{
BOOST_CHECK_SMALL(cheb2.prime(x), tol);
}
x += static_cast<Real>(1)/static_cast<Real>(1 << 7);
}
}
BOOST_AUTO_TEST_CASE(chebyshev_transform_test)
{
#ifdef TEST1
test_chebyshev_chebyshev_transform<float>();
test_sin_chebyshev_transform<float>();
test_atap_examples<float>();
test_sinc_chebyshev_transform<float>();
#endif
#ifdef TEST2
test_chebyshev_chebyshev_transform<double>();
test_sin_chebyshev_transform<double>();
test_atap_examples<double>();
test_sinc_chebyshev_transform<double>();
#endif
#ifdef TEST3
test_chebyshev_chebyshev_transform<long double>();
test_sin_chebyshev_transform<long double>();
test_atap_examples<long double>();
test_sinc_chebyshev_transform<long double>();
#endif
#ifdef TEST4
#ifdef BOOST_HAS_FLOAT128
test_chebyshev_chebyshev_transform<__float128>();
test_sin_chebyshev_transform<__float128>();
test_atap_examples<__float128>();
test_sinc_chebyshev_transform<__float128>();
#endif
#endif
}
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