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Cardinal B-splines

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NAThompson
2019-07-15 10:42:49 -04:00
parent f5cc5a1cc4
commit cfd5a353f6
3 changed files with 200 additions and 0 deletions
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1
test/Jamfile.v2
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@@ -902,6 +902,7 @@ test-suite misc :
[ run test_vector_barycentric_rational.cpp ../../test/build//boost_unit_test_framework : : : [ requires cxx11_smart_ptr cxx11_defaulted_functions cxx11_auto_declarations cxx11_unified_initialization_syntax ] [ check-target-builds ../../multiprecision/config//has_eigen : : <build>no ] ]
[ run test_constant_generate.cpp : : : release <define>USE_CPP_FLOAT=1 <exception-handling>off:<build>no ]
[ run test_cubic_b_spline.cpp ../../test/build//boost_unit_test_framework : : : [ requires cxx11_smart_ptr cxx11_defaulted_functions ] <debug-symbols>off <toolset>msvc:<cxxflags>/bigobj release ]
[ run cardinal_b_spline_test.cpp : : : [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
[ run whittaker_shannon_test.cpp : : : [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
[ run cardinal_quadratic_b_spline_test.cpp : : : [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
[ run catmull_rom_test.cpp ../../test/build//boost_unit_test_framework : : : <define>TEST=1 [ requires cxx11_hdr_array cxx11_hdr_initializer_list ] : catmull_rom_test_1 ]

197
test/cardinal_b_spline_test.cpp Normal file
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@@ -0,0 +1,197 @@
/*
* 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/special_functions/cardinal_b_spline.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::forward_cardinal_b_spline;
template<class Real>
void test_box()
{
Real t = cardinal_b_spline<0>(1.1);
Real expected = 0;
CHECK_ULP_CLOSE(expected, t, 0);
t = cardinal_b_spline<0>(-1.1);
expected = 0;
CHECK_ULP_CLOSE(expected, t, 0);
Real h = Real(1)/Real(256);
for (Real 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);
}
for (Real 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>(2.1);
Real expected = 0;
CHECK_ULP_CLOSE(expected, t, 0);
t = cardinal_b_spline<1>(-2.1);
expected = 0;
CHECK_ULP_CLOSE(expected, t, 0);
Real h = Real(1)/Real(256);
for (Real 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";
}
}
for (Real 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;
};
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);
}
}
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);
}
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_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(1, one, n)) {
std::cerr << " Partition of unity failure at n = " << n << "\n";
}
}
}
int main()
{
test_box<float>();
test_box<double>();
test_box<long double>();
test_hat<float>();
test_hat<double>();
test_hat<long double>();
test_quadratic<float>();
test_quadratic<double>();
test_quadratic<long double>();
test_cubic<float>();
test_cubic<double>();
test_cubic<long double>();
test_quintic<float>();
test_quintic<double>();
test_quintic<long double>();
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>();
#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();
}