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math/test/quintic_hermite_test.cpp

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/*
* Copyright Nick Thompson, 2020
* 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 <boost/random/uniform_real.hpp>
#include <boost/random/mersenne_twister.hpp>
#include <boost/math/interpolators/quintic_hermite.hpp>
#include <boost/circular_buffer.hpp>
#ifdef BOOST_HAS_FLOAT128
#include <boost/multiprecision/float128.hpp>
using boost::multiprecision::float128;
#endif
using boost::math::interpolators::quintic_hermite;
template<typename Real>
void test_constant()
{
std::vector<Real> x{0,1,2,3, 9, 22, 81};
std::vector<Real> y(x.size());
std::vector<Real> dydx(x.size(), 0);
std::vector<Real> d2ydx2(x.size(), 0);
for (auto & t : y) {
t = 7;
}
auto qh = quintic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
for (Real t = 0; t <= 81; t += 0.25) {
CHECK_ULP_CLOSE(Real(7), qh(t), 24);
CHECK_ULP_CLOSE(Real(0), qh.prime(t), 24);
}
}
template<typename Real>
void test_linear()
{
std::vector<Real> x{0,1,2,3, 4,5,6,7,8,9};
std::vector<Real> y = x;
std::vector<Real> dydx(x.size(), 1);
std::vector<Real> d2ydx2(x.size(), 0);
auto qh = quintic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
for (Real t = 0; t <= 9; t += 0.25) {
CHECK_ULP_CLOSE(Real(t), qh(t), 2);
CHECK_ULP_CLOSE(Real(1), qh.prime(t), 2);
}
boost::random::mt19937 rng;
boost::random::uniform_real_distribution<Real> dis(0.5,1);
x.resize(512);
x[0] = dis(rng);
Real xmin = x[0];
for (size_t i = 1; i < x.size(); ++i) {
x[i] = x[i-1] + dis(rng);
}
Real xmax = x.back();
y = x;
dydx.resize(x.size(), 1);
d2ydx2.resize(x.size(), 0);
qh = quintic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
for (Real t = xmin; t <= xmax; t += 0.125) {
CHECK_ULP_CLOSE(Real(t), qh(t), 2);
}
}
template<typename Real>
void test_quadratic()
{
std::vector<Real> x{0,1,2,3, 4,5,6,7,8,9};
std::vector<Real> y(x.size());
for (size_t i = 0; i < y.size(); ++i)
{
y[i] = x[i]*x[i]/2;
}
std::vector<Real> dydx(x.size());
for (size_t i = 0; i < y.size(); ++i) {
dydx[i] = x[i];
}
std::vector<Real> d2ydx2(x.size(), 1);
auto qh = quintic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
for (Real t = 0; t <= 9; t += 0.0078125) {
CHECK_ULP_CLOSE(Real(t*t)/2, qh(t), 2);
CHECK_ULP_CLOSE(t, qh.prime(t), 2);
}
boost::random::mt19937 rng;
boost::random::uniform_real_distribution<Real> dis(0.5,1);
x.resize(8);
x[0] = dis(rng);
Real xmin = x[0];
for (size_t i = 1; i < x.size(); ++i) {
x[i] = x[i-1] + dis(rng);
}
Real xmax = x.back();
y.resize(x.size());
for (size_t i = 0; i < y.size(); ++i)
{
y[i] = x[i]*x[i]/2;
}
dydx.resize(x.size());
for (size_t i = 0; i < y.size(); ++i) {
dydx[i] = x[i];
}
d2ydx2.resize(x.size(), 1);
qh = quintic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
for (Real t = xmin; t <= xmax; t += 0.125) {
CHECK_ULP_CLOSE(Real(t*t)/2, qh(t), 4);
}
}
template<typename Real>
void test_cubic()
{
std::vector<Real> x{0,1,2,3, 4,5,6,7,8,9};
std::vector<Real> y(x.size());
for (size_t i = 0; i < y.size(); ++i)
{
y[i] = x[i]*x[i]*x[i]/6;
}
std::vector<Real> dydx(x.size());
for (size_t i = 0; i < y.size(); ++i) {
dydx[i] = x[i]*x[i]/2;
}
std::vector<Real> d2ydx2(x.size());
for (size_t i = 0; i < y.size(); ++i) {
d2ydx2[i] = x[i];
}
auto qh = quintic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
for (Real t = 0; t <= 9; t += 0.0078125) {
CHECK_ULP_CLOSE(Real(t*t*t)/6, qh(t), 10);
}
}
template<typename Real>
void test_quartic()
{
std::vector<Real> x{0,1,2,3, 4,5,6,7,8,9, 10, 11};
std::vector<Real> y(x.size());
for (size_t i = 0; i < y.size(); ++i)
{
y[i] = x[i]*x[i]*x[i]*x[i]/24;
}
std::vector<Real> dydx(x.size());
for (size_t i = 0; i < y.size(); ++i) {
dydx[i] = x[i]*x[i]*x[i]/6;
}
std::vector<Real> d2ydx2(x.size());
for (size_t i = 0; i < y.size(); ++i) {
d2ydx2[i] = x[i]*x[i]/2;
}
auto qh = quintic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
for (Real t = 1; t <= 11; t += 0.0078125) {
CHECK_ULP_CLOSE(Real(t*t*t*t)/24, qh(t), 100);
}
}
template<typename Real>
void test_interpolation_condition()
{
for (size_t n = 4; n < 50; ++n) {
std::vector<Real> x(n);
std::vector<Real> y(n);
std::vector<Real> dydx(n);
std::vector<Real> d2ydx2(n);
boost::random::mt19937 rd;
boost::random::uniform_real_distribution<Real> dis(0,1);
Real x0 = dis(rd);
x[0] = x0;
y[0] = dis(rd);
for (size_t i = 1; i < n; ++i) {
x[i] = x[i-1] + dis(rd);
y[i] = dis(rd);
dydx[i] = dis(rd);
d2ydx2[i] = dis(rd);
}
auto x_copy = x;
auto y_copy = y;
auto dydx_copy = dydx;
auto d2ydx2_copy = d2ydx2;
auto s = quintic_hermite(std::move(x_copy), std::move(y_copy), std::move(dydx_copy), std::move(d2ydx2_copy));
//std::cout << "s = " << s << "\n";
for (size_t i = 0; i < x.size(); ++i) {
CHECK_ULP_CLOSE(y[i], s(x[i]), 2);
CHECK_ULP_CLOSE(dydx[i], s.prime(x[i]), 2);
}
}
}
int main()
{
test_constant<float>();
test_linear<float>();
test_quadratic<float>();
test_cubic<float>();
test_quartic<float>();
test_interpolation_condition<float>();
test_constant<double>();
test_linear<double>();
test_quadratic<double>();
test_cubic<double>();
test_quartic<double>();
test_interpolation_condition<double>();
test_constant<long double>();
test_linear<long double>();
test_quadratic<long double>();
test_cubic<long double>();
test_quartic<long double>();
test_interpolation_condition<long double>();
#ifdef BOOST_HAS_FLOAT128
test_constant<float128>();
test_linear<float128>();
test_quadratic<float128>();
test_cubic<float128>();
test_quartic<float128>();
test_interpolation_condition<float128>();
#endif
return boost::math::test::report_errors();
}
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