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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 <numeric>
#include <utility>
#include <random>
#include <boost/core/demangle.hpp>
#include <boost/math/interpolators/whittaker_shannon.hpp>
#if __has_include(<stdfloat>)
# include <stdfloat>
#endif
using boost::math::interpolators::whittaker_shannon;
template<class Real>
void test_trivial()
{
Real t0 = 0;
Real h = Real(1)/Real(16);
std::vector<Real> v{Real(1.5)};
std::vector<Real> v_copy = v;
auto ws = whittaker_shannon<decltype(v)>(std::move(v), t0, h);
Real expected = 0;
if(!CHECK_MOLLIFIED_CLOSE(expected, ws.prime(0), 10*std::numeric_limits<Real>::epsilon())) {
std::cerr << " Problem occurred at abscissa " << 0 << "\n";
}
expected = -v_copy[0]/h;
if(!CHECK_MOLLIFIED_CLOSE(expected, ws.prime(h), 10*std::numeric_limits<Real>::epsilon())) {
std::cerr << " Problem occurred at abscissa " << 0 << "\n";
}
}
template<class Real>
void test_knots()
{
Real t0 = 0;
Real h = Real(1)/Real(16);
size_t n = 512;
std::vector<Real> v(n);
std::mt19937 gen(323723);
std::uniform_real_distribution<Real> dis(Real(1.0), Real(2.0));
for(size_t i = 0; i < n; ++i) {
v[i] = static_cast<Real>(dis(gen));
}
auto ws = whittaker_shannon<decltype(v)>(std::move(v), t0, h);
size_t i = 0;
while (i < n) {
Real t = t0 + i*h;
Real expected = ws[i];
Real computed = ws(t);
CHECK_ULP_CLOSE(expected, computed, 16);
++i;
}
}
template<class Real>
void test_bump()
{
using std::exp;
using std::abs;
using std::sqrt;
auto bump = [](Real x) { using std::exp; using std::abs; if (abs(x) >= 1) { return Real(0); } return exp(-Real(1)/(Real(1)-x*x)); };
auto bump_prime = [&bump](Real x) { Real z = 1-x*x; return -2*x*bump(x)/(z*z); };
Real t0 = -1;
size_t n = 2049;
Real h = Real(2)/Real(n-1);
std::vector<Real> v(n);
for(size_t i = 0; i < n; ++i) {
Real t = t0 + i*h;
v[i] = bump(t);
}
std::vector<Real> v_copy = v;
auto ws = whittaker_shannon<decltype(v)>(std::move(v), t0, h);
// Test the knots:
for(size_t i = v_copy.size()/4; i < 3*v_copy.size()/4; ++i) {
Real t = t0 + i*h;
Real expected = v_copy[i];
Real computed = ws(t);
if(!CHECK_MOLLIFIED_CLOSE(expected, computed, 10*std::numeric_limits<Real>::epsilon())) {
std::cerr << " Problem occurred at abscissa " << t << "\n";
}
Real expected_prime = bump_prime(t);
Real computed_prime = ws.prime(t);
if(!CHECK_MOLLIFIED_CLOSE(expected_prime, computed_prime, 1000*std::numeric_limits<Real>::epsilon())) {
std::cerr << " Problem occurred at abscissa " << t << "\n";
}
}
std::mt19937 gen(323723);
std::uniform_real_distribution<long double> dis(-0.85, 0.85);
size_t i = 0;
while (i++ < 1000)
{
Real t = static_cast<Real>(dis(gen));
Real expected = bump(t);
Real computed = ws(t);
if(!CHECK_MOLLIFIED_CLOSE(expected, computed, 10*std::numeric_limits<Real>::epsilon())) {
std::cerr << " Problem occurred at abscissa " << t << "\n";
}
Real expected_prime = bump_prime(t);
Real computed_prime = ws.prime(t);
if(!CHECK_MOLLIFIED_CLOSE(expected_prime, computed_prime, sqrt(std::numeric_limits<Real>::epsilon()))) {
std::cerr << " Problem occurred at abscissa " << t << "\n";
}
}
}
int main()
{
#ifdef __STDCPP_FLOAT32_T__
test_trivial<std::float32_t>();
test_knots<std::float32_t>();
#else
test_trivial<float>();
test_knots<float>();
#endif
#ifdef __STDCPP_FLOAT64_T__
test_trivial<std::float64_t>();
test_knots<std::float64_t>();
test_bump<std::float64_t>();
#else
test_trivial<double>();
test_knots<double>();
test_bump<double>();
#endif
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_knots<long double>();
#if LDBL_MANT_DIG <= 64
// Anything more precise than this fails for unknown reasons
test_bump<long double>();
#endif
#endif
return boost::math::test::report_errors();
}
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