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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 <cmath>
#include <boost/math/special_functions/cardinal_b_spline.hpp>
#include <boost/math/interpolators/detail/cubic_b_spline_detail.hpp>
#ifdef BOOST_HAS_FLOAT128
#include <boost/multiprecision/float128.hpp>
using boost::multiprecision::float128;
#endif
using std::abs;
using boost::math::cardinal_b_spline;
using boost::math::cardinal_b_spline_prime;
using boost::math::forward_cardinal_b_spline;
using boost::math::cardinal_b_spline_double_prime;
template<class Real>
void test_box()
{
Real t = cardinal_b_spline<0>(Real(1.1));
Real expected = 0;
CHECK_ULP_CLOSE(expected, t, 0);
CHECK_ULP_CLOSE(expected, cardinal_b_spline_prime<0>(Real(1.1)), 0);
CHECK_EQUAL(cardinal_b_spline<0>(Real(0.5)), Real(0.5f));
CHECK_EQUAL(cardinal_b_spline_prime<0>(Real(0.5)), std::numeric_limits<Real>::infinity());
t = cardinal_b_spline<0>(Real(-1.1));
expected = 0;
CHECK_ULP_CLOSE(expected, t, 0);
Real h = Real(1)/Real(256);
for (t = -Real(1)/Real(2)+h; t < Real(1)/Real(2); t += h)
{
expected = 1;
CHECK_ULP_CLOSE(expected, cardinal_b_spline<0>(t), 0);
expected = 0;
CHECK_ULP_CLOSE(expected, cardinal_b_spline_prime<0>(Real(1.1)), 0);
}
for (t = h; t < 1; t += h)
{
expected = 1;
CHECK_ULP_CLOSE(expected, forward_cardinal_b_spline<0>(t), 0);
}
}
template<class Real>
void test_hat()
{
Real t = cardinal_b_spline<1>(Real(2.1));
Real expected = 0;
CHECK_ULP_CLOSE(expected, t, 0);
t = cardinal_b_spline<1>(Real(-2.1));
expected = 0;
CHECK_ULP_CLOSE(expected, t, 0);
Real h = Real(1)/Real(256);
for (t = -1; t <= 1; t += h)
{
expected = 1-abs(t);
if(!CHECK_ULP_CLOSE(expected, cardinal_b_spline<1>(t), 0) )
{
std::cerr << " Problem at t = " << t << "\n";
}
if (t == -Real(1)) {
if (!CHECK_ULP_CLOSE(Real(1)/Real(2), cardinal_b_spline_prime<1>(t), 0)) {
std::cout << " Problem at t = " << t << "\n";
}
}
else if (t == Real(1)) {
CHECK_ULP_CLOSE(-Real(1)/Real(2), cardinal_b_spline_prime<1>(t), 0);
}
else if (t < 0) {
CHECK_ULP_CLOSE(Real(1), cardinal_b_spline_prime<1>(t), 0);
}
else if (t == 0) {
CHECK_ULP_CLOSE(Real(0), cardinal_b_spline_prime<1>(t), 0);
}
else if (t > 0) {
CHECK_ULP_CLOSE(Real(-1), cardinal_b_spline_prime<1>(t), 0);
}
}
for (t = 0; t < 2; t += h)
{
expected = 1 - abs(t-1);
CHECK_ULP_CLOSE(expected, forward_cardinal_b_spline<1>(t), 0);
}
}
template<class Real>
void test_quadratic()
{
using std::abs;
auto b2 = [](Real x) {
Real absx = abs(x);
if (absx >= 3/Real(2)) {
return Real(0);
}
if (absx >= 1/Real(2)) {
Real t = absx - 3/Real(2);
return t*t/2;
}
Real t1 = absx - 1/Real(2);
Real t2 = absx + 1/Real(2);
return (2-t1*t1 -t2*t2)/2;
};
auto b2_prime = [&](Real x)->Real {
Real absx = abs(x);
Real signx = 1;
if (x < 0) {
signx = -1;
}
if (absx >= 3/Real(2)) {
return Real(0);
}
if (absx >= 1/Real(2)) {
return (absx - 3/Real(2))*signx;
}
return -2*absx*signx;
};
Real h = 1/Real(256);
for (Real t = -5; t <= 5; t += h) {
Real expected = b2(t);
CHECK_ULP_CLOSE(expected, cardinal_b_spline<2>(t), 0);
expected = b2_prime(t);
if (!CHECK_ULP_CLOSE(expected, cardinal_b_spline_prime<2>(t), 0))
{
std::cerr << " Problem at t = " << t << "\n";
}
}
}
template<class Real>
void test_cubic()
{
Real expected = Real(2)/Real(3);
Real computed = cardinal_b_spline<3, Real>(0);
CHECK_ULP_CLOSE(expected, computed, 0);
expected = Real(1)/Real(6);
computed = cardinal_b_spline<3, Real>(1);
CHECK_ULP_CLOSE(expected, computed, 0);
expected = Real(0);
computed = cardinal_b_spline<3, Real>(2);
CHECK_ULP_CLOSE(expected, computed, 0);
Real h = 1/Real(256);
for (Real t = -4; t <= 4; t += h) {
expected = boost::math::detail::b3_spline_prime<Real>(t);
computed = cardinal_b_spline_prime<3>(t);
CHECK_ULP_CLOSE(expected, computed, 0);
expected = boost::math::detail::b3_spline_double_prime<Real>(t);
computed = cardinal_b_spline_double_prime<3>(t);
if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
std::cerr << " Problem at t = " << t << "\n";
}
}
}
template<class Real>
void test_quintic()
{
Real expected = Real(11)/Real(20);
Real computed = cardinal_b_spline<5, Real>(0);
CHECK_ULP_CLOSE(expected, computed, 0);
expected = Real(13)/Real(60);
computed = cardinal_b_spline<5, Real>(1);
CHECK_ULP_CLOSE(expected, computed, 1);
expected = Real(1)/Real(120);
computed = cardinal_b_spline<5, Real>(2);
CHECK_ULP_CLOSE(expected, computed, 0);
expected = Real(0);
computed = cardinal_b_spline<5, Real>(3);
CHECK_ULP_CLOSE(expected, computed, 0);
}
template<unsigned n, typename Real>
void test_b_spline_derivatives()
{
Real h = 1/Real(256);
Real supp = (n+Real(1))/Real(2);
for (Real t = -supp - 1; t <= supp+1; t+= h)
{
Real expected = cardinal_b_spline<n-1>(t+Real(1)/Real(2)) - cardinal_b_spline<n-1>(t - Real(1)/Real(2));
Real computed = cardinal_b_spline_prime<n>(t);
CHECK_MOLLIFIED_CLOSE(expected, computed, std::numeric_limits<Real>::epsilon());
expected = cardinal_b_spline<n-2>(t+1) - 2*cardinal_b_spline<n-2>(t) + cardinal_b_spline<n-2>(t-1);
computed = cardinal_b_spline_double_prime<n>(t);
CHECK_MOLLIFIED_CLOSE(expected, computed, 2*std::numeric_limits<Real>::epsilon());
}
}
template<unsigned n, typename Real>
void test_partition_of_unity()
{
std::mt19937 gen(323723);
Real supp = (n+1.0)/2.0;
std::uniform_real_distribution<Real> dis(-supp, -supp+1);
for(size_t i = 0; i < 500; ++i) {
Real x = dis(gen);
Real one = 0;
while (x < supp) {
one += cardinal_b_spline<n>(x);
x += 1;
}
if(!CHECK_ULP_CLOSE(Real(1), one, n)) {
std::cerr << " Partition of unity failure at n = " << n << "\n";
}
}
}
int main()
{
test_box<float>();
test_box<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_box<long double>();
#endif
test_hat<float>();
test_hat<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_hat<long double>();
#endif
test_quadratic<float>();
test_quadratic<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_quadratic<long double>();
#endif
test_cubic<float>();
test_cubic<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_cubic<long double>();
#endif
test_quintic<float>();
test_quintic<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_quintic<long double>();
#endif
test_partition_of_unity<1, double>();
test_partition_of_unity<2, double>();
test_partition_of_unity<3, double>();
test_partition_of_unity<4, double>();
test_partition_of_unity<5, double>();
test_partition_of_unity<6, double>();
test_b_spline_derivatives<3, double>();
test_b_spline_derivatives<4, double>();
test_b_spline_derivatives<5, double>();
test_b_spline_derivatives<6, double>();
test_b_spline_derivatives<7, double>();
test_b_spline_derivatives<8, double>();
test_b_spline_derivatives<9, double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_b_spline_derivatives<3, long double>();
test_b_spline_derivatives<4, long double>();
test_b_spline_derivatives<5, long double>();
test_b_spline_derivatives<6, long double>();
test_b_spline_derivatives<7, long double>();
test_b_spline_derivatives<8, long double>();
test_b_spline_derivatives<9, long double>();
#endif
#ifdef BOOST_HAS_FLOAT128
test_box<float128>();
test_hat<float128>();
test_quadratic<float128>();
test_cubic<float128>();
test_quintic<float128>();
#endif
return boost::math::test::report_errors();
}
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