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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 <random>
#include <boost/math/interpolators/pchip.hpp>
#include <boost/circular_buffer.hpp>
#include <boost/assert.hpp>
#ifdef BOOST_HAS_FLOAT128
#include <boost/multiprecision/float128.hpp>
using boost::multiprecision::float128;
#endif
#if __has_include(<stdfloat>)
# include <stdfloat>
#endif
using boost::math::interpolators::pchip;
template<typename Real>
void test_constant()
{
std::vector<Real> x{0,1,2,3, 9, 22, 81};
std::vector<Real> y(x.size());
for (auto & t : y) {
t = 7;
}
auto x_copy = x;
auto y_copy = y;
auto pchip_spline = pchip(std::move(x_copy), std::move(y_copy));
//std::cout << "Constant value pchip spline = " << pchip_spline << "\n";
for (Real t = x[0]; t <= x.back(); t += Real(0.25)) {
CHECK_ULP_CLOSE(Real(7), pchip_spline(t), 2);
CHECK_ULP_CLOSE(Real(0), pchip_spline.prime(t), 2);
}
boost::circular_buffer<Real> x_buf(x.size());
for (auto & t : x) {
x_buf.push_back(t);
}
boost::circular_buffer<Real> y_buf(x.size());
for (auto & t : y) {
y_buf.push_back(t);
}
auto circular_pchip_spline = pchip(std::move(x_buf), std::move(y_buf));
for (Real t = x[0]; t <= x.back(); t += Real(0.25)) {
CHECK_ULP_CLOSE(Real(7), circular_pchip_spline(t), 2);
CHECK_ULP_CLOSE(Real(0), pchip_spline.prime(t), 2);
}
circular_pchip_spline.push_back(x.back() + 1, 7);
CHECK_ULP_CLOSE(Real(0), circular_pchip_spline.prime(x.back()+1), 2);
}
template<typename Real>
void test_linear()
{
std::vector<Real> x{0,1,2,3};
std::vector<Real> y{0,1,2,3};
auto x_copy = x;
auto y_copy = y;
auto pchip_spline = pchip(std::move(x_copy), std::move(y_copy));
CHECK_ULP_CLOSE(y[0], pchip_spline(x[0]), 0);
CHECK_ULP_CLOSE(Real(1)/Real(2), pchip_spline(Real(1)/Real(2)), 10);
CHECK_ULP_CLOSE(y[1], pchip_spline(x[1]), 0);
CHECK_ULP_CLOSE(Real(3)/Real(2), pchip_spline(Real(3)/Real(2)), 10);
CHECK_ULP_CLOSE(y[2], pchip_spline(x[2]), 0);
CHECK_ULP_CLOSE(Real(5)/Real(2), pchip_spline(Real(5)/Real(2)), 10);
CHECK_ULP_CLOSE(y[3], pchip_spline(x[3]), 0);
x.resize(45);
y.resize(45);
for (size_t i = 0; i < x.size(); ++i) {
x[i] = i;
y[i] = i;
}
x_copy = x;
y_copy = y;
pchip_spline = pchip(std::move(x_copy), std::move(y_copy));
for (Real t = 0; t < x.back(); t += Real(0.5)) {
CHECK_ULP_CLOSE(t, pchip_spline(t), 0);
CHECK_ULP_CLOSE(Real(1), pchip_spline.prime(t), 0);
}
x_copy = x;
y_copy = y;
// Test endpoint derivatives:
pchip_spline = pchip(std::move(x_copy), std::move(y_copy), Real(1), Real(1));
for (Real t = 0; t < x.back(); t += Real(0.5)) {
CHECK_ULP_CLOSE(t, pchip_spline(t), 0);
CHECK_ULP_CLOSE(Real(1), pchip_spline.prime(t), 0);
}
boost::circular_buffer<Real> x_buf(x.size());
for (auto & t : x) {
x_buf.push_back(t);
}
boost::circular_buffer<Real> y_buf(x.size());
for (auto & t : y) {
y_buf.push_back(t);
}
auto circular_pchip_spline = pchip(std::move(x_buf), std::move(y_buf));
for (Real t = x[0]; t <= x.back(); t += Real(0.25)) {
CHECK_ULP_CLOSE(t, circular_pchip_spline(t), 2);
CHECK_ULP_CLOSE(Real(1), circular_pchip_spline.prime(t), 2);
}
circular_pchip_spline.push_back(x.back() + 1, y.back()+1);
CHECK_ULP_CLOSE(Real(y.back() + 1), circular_pchip_spline(Real(x.back()+1)), 2);
CHECK_ULP_CLOSE(Real(1), circular_pchip_spline.prime(Real(x.back()+1)), 2);
}
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::default_random_engine rd;
std::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);
}
auto x_copy = x;
auto y_copy = y;
auto s = pchip(std::move(x_copy), std::move(y_copy));
//std::cout << "s = " << s << "\n";
for (size_t i = 0; i < x.size(); ++i) {
CHECK_ULP_CLOSE(y[i], s(x[i]), 2);
}
x_copy = x;
y_copy = y;
// The interpolation condition is not affected by the endpoint derivatives, even though these derivatives might be super weird:
s = pchip(std::move(x_copy), std::move(y_copy), Real(0), Real(0));
//std::cout << "s = " << s << "\n";
for (size_t i = 0; i < x.size(); ++i) {
CHECK_ULP_CLOSE(y[i], s(x[i]), 2);
}
}
}
template<typename Real>
void test_monotonicity()
{
for (size_t n = 4; n < 50; ++n) {
std::vector<Real> x(n);
std::vector<Real> y(n);
std::default_random_engine rd;
std::uniform_real_distribution<Real> dis(0,1);
Real x0 = dis(rd);
x[0] = x0;
y[0] = dis(rd);
// Monotone increasing:
for (size_t i = 1; i < n; ++i) {
x[i] = x[i-1] + dis(rd);
y[i] = y[i-1] + dis(rd);
}
auto x_copy = x;
auto y_copy = y;
auto s = pchip(std::move(x_copy), std::move(y_copy));
//std::cout << "s = " << s << "\n";
for (size_t i = 0; i < x.size() - 1; ++i) {
Real tmin = x[i];
Real tmax = x[i+1];
Real val = y[i];
CHECK_ULP_CLOSE(y[i], s(x[i]), 2);
for (Real t = tmin; t < tmax; t += (tmax-tmin)/16) {
Real greater_val = s(t);
BOOST_ASSERT(val <= greater_val);
val = greater_val;
}
}
x[0] = dis(rd);
y[0] = dis(rd);
// Monotone decreasing:
for (size_t i = 1; i < n; ++i) {
x[i] = x[i-1] + dis(rd);
y[i] = y[i-1] - dis(rd);
}
x_copy = x;
y_copy = y;
s = pchip(std::move(x_copy), std::move(y_copy));
//std::cout << "s = " << s << "\n";
for (size_t i = 0; i < x.size() - 1; ++i) {
Real tmin = x[i];
Real tmax = x[i+1];
Real val = y[i];
CHECK_ULP_CLOSE(y[i], s(x[i]), 2);
for (Real t = tmin; t < tmax; t += (tmax-tmin)/16) {
Real lesser_val = s(t);
BOOST_ASSERT(val >= lesser_val);
val = lesser_val;
}
}
}
}
int main()
{
#if (__GNUC__ > 7) || defined(_MSC_VER) || defined(__clang__)
#ifdef __STDCPP_FLOAT32_T__
test_constant<std::float32_t>();
test_linear<std::float32_t>();
test_interpolation_condition<std::float32_t>();
test_monotonicity<std::float32_t>();
#else
test_constant<float>();
test_linear<float>();
test_interpolation_condition<float>();
test_monotonicity<float>();
#endif
#ifdef __STDCPP_FLOAT64_T__
test_constant<std::float64_t>();
test_linear<std::float64_t>();
test_interpolation_condition<std::float64_t>();
test_monotonicity<std::float64_t>();
#else
test_constant<double>();
test_linear<double>();
test_interpolation_condition<double>();
test_monotonicity<double>();
#endif
test_constant<long double>();
test_linear<long double>();
test_interpolation_condition<long double>();
test_monotonicity<long double>();
#ifdef BOOST_HAS_FLOAT128
test_constant<float128>();
test_linear<float128>();
#endif
#endif
return boost::math::test::report_errors();
}
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