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Fix cardinal cubic b spline for std::float32_t

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This commit is contained in:
Matt Borland
2023-05-17 18:10:49 +02:00
parent 55eaf05b41
commit 00facdc1a9
2 changed files with 109 additions and 87 deletions
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2
include/boost/math/interpolators/detail/cardinal_cubic_b_spline_detail.hpp
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@@ -225,7 +225,7 @@ cardinal_cubic_b_spline_imp<Real>::cardinal_cubic_b_spline_imp(BidiIterator f, B
// mapsto
// 1 0 -1 | r0
// 0 1 1/2| (r1 - r0)/4
super_diagonal[1] = 0.5;
super_diagonal[1] = static_cast<Real>(0.5);
rhs[1] = (rhs[1] - rhs[0])/4;
// Now do a tridiagonal row reduction the standard way, until just before the last row:

194
test/cardinal_cubic_b_spline_test.cpp
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@@ -14,8 +14,13 @@
#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/math/interpolators/cardinal_cubic_b_spline.hpp>
#include <boost/math/interpolators/detail/cardinal_cubic_b_spline_detail.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
#if __has_include(<stdfloat>)
# include <stdfloat>
#endif
using boost::multiprecision::cpp_bin_float_50;
using boost::math::constants::third;
using boost::math::constants::half;
@@ -26,12 +31,12 @@ void test_b3_spline()
std::cout << "Testing evaluation of spline basis functions on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
// Outside the support:
Real eps = std::numeric_limits<Real>::epsilon();
BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline<Real>(2.5), (Real) 0);
BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline<Real>(-2.5), (Real) 0);
BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_prime<Real>(2.5), (Real) 0);
BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_prime<Real>(-2.5), (Real) 0);
BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_double_prime<Real>(2.5), (Real) 0);
BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_double_prime<Real>(-2.5), (Real) 0);
BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline<Real>(Real(2.5)), (Real) 0);
BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline<Real>(Real(-2.5)), (Real) 0);
BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_prime<Real>(Real(2.5)), (Real) 0);
BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_prime<Real>(Real(-2.5)), (Real) 0);
BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_double_prime<Real>(Real(2.5)), (Real) 0);
BOOST_CHECK_SMALL(boost::math::interpolators::detail::b3_spline_double_prime<Real>(Real(-2.5)), (Real) 0);
// On the boundary of support:
@@ -52,7 +57,7 @@ void test_b3_spline()
// Properties: B3 is an even function, B3' is an odd function.
for (size_t i = 1; i < 200; ++i)
{
Real arg = i*0.01;
Real arg = i*Real(0.01);
BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline<Real>(arg), boost::math::interpolators::detail::b3_spline<Real>(arg), eps);
BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline_prime<Real>(-arg), -boost::math::interpolators::detail::b3_spline_prime<Real>(arg), eps);
BOOST_CHECK_CLOSE(boost::math::interpolators::detail::b3_spline_double_prime<Real>(-arg), boost::math::interpolators::detail::b3_spline_double_prime<Real>(arg), eps);
@@ -76,8 +81,8 @@ void test_interpolation_condition()
v[i] = dis(gen);
}
Real step = 0.01;
Real a = 5;
Real step = static_cast<Real>(0.01);
Real a = Real(5);
boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), a, step);
for (size_t i = 0; i < v.size(); ++i)
@@ -99,21 +104,21 @@ void test_constant_function()
Real constant = 50.2;
for (size_t i = 0; i < v.size(); ++i)
{
v[i] = 50.2;
v[i] = Real(50.2);
}
Real step = 0.02;
Real step = static_cast<Real>(0.02);
Real a = 5;
boost::math::interpolators::cardinal_cubic_b_spline<Real> spline(v.data(), v.size(), a, step);
for (size_t i = 0; i < v.size(); ++i)
{
// Do not test at interpolation point; we already know it works there:
Real y = spline(i*step + a + 0.001);
Real y = spline(i*step + a + Real(0.001));
BOOST_CHECK_CLOSE(y, constant, 10*std::numeric_limits<Real>::epsilon());
Real y_prime = spline.prime(i*step + a + 0.002);
Real y_prime = spline.prime(i*step + a + Real(0.002));
BOOST_CHECK_SMALL(y_prime, 5000*std::numeric_limits<Real>::epsilon());
Real y_double_prime = spline.double_prime(i*step + a + 0.002);
Real y_double_prime = spline.double_prime(i*step + a + Real(0.002));
BOOST_CHECK_SMALL(y_double_prime, 5000*std::numeric_limits<Real>::epsilon());
}
@@ -123,9 +128,9 @@ void test_constant_function()
for (size_t i = 0; i < v.size(); ++i)
{
Real y = spline(i*step + a + 0.002);
Real y = spline(i*step + a + Real(0.002));
BOOST_CHECK_CLOSE(y, constant, std::numeric_limits<Real>::epsilon());
Real y_prime = spline.prime(i*step + a + 0.002);
Real y_prime = spline.prime(i*step + a + Real(0.002));
BOOST_CHECK_SMALL(y_prime, std::numeric_limits<Real>::epsilon());
}
@@ -137,9 +142,9 @@ void test_constant_function()
for (size_t i = 0; i < v.size(); ++i)
{
// Do not test at interpolation point; we already know it works there:
Real y = spline2(i*step + a + 0.001);
Real y = spline2(i*step + a + Real(0.001));
BOOST_CHECK_CLOSE(y, constant, 10 * std::numeric_limits<Real>::epsilon());
Real y_prime = spline2.prime(i*step + a + 0.002);
Real y_prime = spline2.prime(i*step + a + Real(0.002));
BOOST_CHECK_SMALL(y_prime, 5000 * std::numeric_limits<Real>::epsilon());
}
@@ -148,9 +153,9 @@ void test_constant_function()
for (size_t i = 0; i < v.size(); ++i)
{
Real y = spline2(i*step + a + 0.002);
Real y = spline2(i*step + a + Real(0.002));
BOOST_CHECK_CLOSE(y, constant, std::numeric_limits<Real>::epsilon());
Real y_prime = spline2.prime(i*step + a + 0.002);
Real y_prime = spline2.prime(i*step + a + Real(0.002));
BOOST_CHECK_SMALL(y_prime, std::numeric_limits<Real>::epsilon());
}
}
@@ -164,7 +169,7 @@ void test_affine_function()
std::vector<Real> v(500);
Real a = 10;
Real b = 8;
Real step = 0.005;
Real step = static_cast<Real>(0.005);
auto f = [a, b](Real x) { return a*x + b; };
for (size_t i = 0; i < v.size(); ++i)
@@ -176,7 +181,7 @@ void test_affine_function()
for (size_t i = 0; i < v.size() - 1; ++i)
{
Real arg = i*step + 0.0001;
Real arg = static_cast<Real>(i*step + Real(0.0001));
Real y = spline(arg);
BOOST_CHECK_CLOSE(y, f(arg), sqrt(std::numeric_limits<Real>::epsilon()));
Real y_prime = spline.prime(arg);
@@ -188,7 +193,7 @@ void test_affine_function()
for (size_t i = 0; i < v.size() - 1; ++i)
{
Real arg = i*step + 0.0001;
Real arg = static_cast<Real>(i*step + Real(0.0001));
Real y = spline(arg);
BOOST_CHECK_CLOSE(y, f(arg), sqrt(std::numeric_limits<Real>::epsilon()));
Real y_prime = spline.prime(arg);
@@ -203,10 +208,10 @@ void test_quadratic_function()
using std::sqrt;
std::cout << "Testing that quadratic functions are interpolated correctly by cubic b splines on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
std::vector<Real> v(500);
Real a = 1.2;
Real b = -3.4;
Real c = -8.6;
Real step = 0.01;
Real a = static_cast<Real>(1.2);
Real b = static_cast<Real>(-3.4);
Real c = static_cast<Real>(-8.6);
Real step = static_cast<Real>(0.01);
auto f = [a, b, c](Real x) { return a*x*x + b*x + c; };
for (size_t i = 0; i < v.size(); ++i)
@@ -218,11 +223,11 @@ void test_quadratic_function()
for (size_t i = 0; i < v.size() -1; ++i)
{
Real arg = i*step + 0.001;
Real arg = static_cast<Real>(i*step + Real(0.001));
Real y = spline(arg);
BOOST_CHECK_CLOSE(y, f(arg), 0.1);
BOOST_CHECK_CLOSE(y, f(arg), Real(0.1));
Real y_prime = spline.prime(arg);
BOOST_CHECK_CLOSE(y_prime, 2*a*arg + b, 2.0);
BOOST_CHECK_CLOSE(y_prime, 2*a*arg + b, Real(2.0));
}
}
@@ -233,9 +238,9 @@ void test_circ_conic_function()
using std::sqrt;
std::cout << "Testing that conic section of a circle is interpolated correctly by cubic b splines on type " << boost::typeindex::type_id<Real>().pretty_name() << '\n';
std::vector<Real> v(500);
Real cv = 0.1;
Real w = 2.0;
Real step = 2 * w / (v.size() - 1);
Real cv = Real(0.1);
Real w = Real(2.0);
Real step = Real(2 * w / (v.size() - 1));
auto f = [cv](Real x) { return cv * x * x / (1 + sqrt(1 - cv * cv * x * x)); };
auto df = [cv](Real x) { return cv * x / sqrt(1 - cv * cv * x * x); };
@@ -256,11 +261,11 @@ void test_circ_conic_function()
for (size_t i = 0; i < v.size() - 1; ++i)
{
Real arg = -w + i * step + 0.001;
Real arg = -w + i * step + Real(0.001);
Real y = spline(arg);
BOOST_CHECK_CLOSE(y, f(arg), 2.0);
BOOST_CHECK_CLOSE(y, f(arg), Real(2.0));
Real y_prime = spline.prime(arg);
BOOST_CHECK_CLOSE(y_prime, df(arg), 1.0);
BOOST_CHECK_CLOSE(y_prime, df(arg), Real(1.0));
}
}
@@ -272,7 +277,7 @@ void test_trig_function()
std::mt19937 gen;
std::vector<Real> v(500);
Real x0 = 1;
Real step = 0.125;
Real step = Real(0.125);
for (size_t i = 0; i < v.size(); ++i)
{
@@ -287,9 +292,9 @@ void test_trig_function()
{
Real x = abscissa(gen);
Real y = spline(x);
BOOST_CHECK_CLOSE(y, sin(x), 1.0);
BOOST_CHECK_CLOSE(y, Real(sin(x)), Real(1.0));
auto y_prime = spline.prime(x);
BOOST_CHECK_CLOSE(y_prime, cos(x), 2.0);
BOOST_CHECK_CLOSE(y_prime, Real(cos(x)), Real(2.0));
}
}
@@ -299,7 +304,8 @@ void test_copy_move()
std::cout << "Testing that copy/move operation succeed on cubic b spline\n";
std::vector<Real> v(500);
Real x0 = 1;
Real step = 0.125;
Real step = static_cast<Real>(0.125);
constexpr Real tol = Real(0.01);
for (size_t i = 0; i < v.size(); ++i)
{
@@ -312,22 +318,22 @@ void test_copy_move()
// Default constructor should compile so that splines can be member variables:
boost::math::interpolators::cardinal_cubic_b_spline<Real> d;
d = boost::math::interpolators::cardinal_cubic_b_spline<Real>(v.data(), v.size(), x0, step);
BOOST_CHECK_CLOSE(d(x0), sin(x0), 0.01);
BOOST_CHECK_CLOSE(d(x0), Real(sin(x0)), tol);
// Passing to lambda should compile:
auto f = [=](Real x) { return d(x); };
// Make sure this variable is used.
BOOST_CHECK_CLOSE(f(x0), sin(x0), 0.01);
BOOST_CHECK_CLOSE(f(x0), Real(sin(x0)), tol);
// Move operations should compile.
auto s = std::move(spline);
// Copy operations should compile:
boost::math::interpolators::cardinal_cubic_b_spline<Real> c = d;
BOOST_CHECK_CLOSE(c(x0), sin(x0), 0.01);
BOOST_CHECK_CLOSE(c(x0), Real(sin(x0)), tol);
// Test with std::bind:
auto h = std::bind(&boost::math::interpolators::cardinal_cubic_b_spline<double>::operator(), &s, std::placeholders::_1);
BOOST_CHECK_CLOSE(h(x0), sin(x0), 0.01);
auto h = std::bind(&boost::math::interpolators::cardinal_cubic_b_spline<Real>::operator(), &s, std::placeholders::_1);
BOOST_CHECK_CLOSE(h(x0), Real(sin(x0)), tol);
}
template<class Real>
@@ -336,7 +342,7 @@ void test_outside_interval()
std::cout << "Testing that the spline can be evaluated outside the interpolation interval\n";
std::vector<Real> v(400);
Real x0 = 1;
Real step = 0.125;
Real step = Real(0.125);
for (size_t i = 0; i < v.size(); ++i)
{
@@ -354,54 +360,70 @@ void test_outside_interval()
BOOST_AUTO_TEST_CASE(test_cubic_b_spline)
{
#ifdef __STDCPP_FLOAT32_T__
test_b3_spline<std::float32_t>();
test_interpolation_condition<std::float32_t>();
test_constant_function<std::float32_t>();
test_affine_function<std::float32_t>();
test_quadratic_function<std::float32_t>();
test_circ_conic_function<std::float32_t>();
test_trig_function<std::float32_t>();
#else
test_b3_spline<float>();
test_b3_spline<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_b3_spline<long double>();
#endif
test_b3_spline<cpp_bin_float_50>();
test_interpolation_condition<float>();
test_interpolation_condition<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_interpolation_condition<long double>();
#endif
test_interpolation_condition<cpp_bin_float_50>();
test_constant_function<float>();
test_constant_function<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_constant_function<long double>();
#endif
test_constant_function<cpp_bin_float_50>();
test_affine_function<float>();
test_affine_function<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_affine_function<long double>();
#endif
test_affine_function<cpp_bin_float_50>();
test_quadratic_function<float>();
test_quadratic_function<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_quadratic_function<long double>();
#endif
test_quadratic_function<cpp_bin_float_50>();
test_circ_conic_function<float>();
test_circ_conic_function<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_circ_conic_function<long double>();
#endif
test_trig_function<float>();
test_trig_function<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_trig_function<long double>();
#endif
test_trig_function<cpp_bin_float_50>();
#endif
#ifdef __STDCPP_FLOAT64_T__
test_b3_spline<std::float64_t>();
test_interpolation_condition<std::float64_t>();
test_constant_function<std::float64_t>();
test_affine_function<std::float64_t>();
test_quadratic_function<std::float64_t>();
test_circ_conic_function<std::float64_t>();
test_trig_function<std::float64_t>();
test_copy_move<std::float64_t>();
test_outside_interval<std::float64_t>();
#else
test_b3_spline<double>();
test_interpolation_condition<double>();
test_constant_function<double>();
test_affine_function<double>();
test_quadratic_function<double>();
test_circ_conic_function<double>();
test_trig_function<double>();
test_copy_move<double>();
test_outside_interval<double>();
#endif
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_b3_spline<long double>();
test_interpolation_condition<long double>();
test_constant_function<long double>();
test_affine_function<long double>();
test_quadratic_function<long double>();
test_circ_conic_function<long double>();
test_trig_function<long double>();
#endif
test_b3_spline<cpp_bin_float_50>();
test_interpolation_condition<cpp_bin_float_50>();
test_constant_function<cpp_bin_float_50>();
test_affine_function<cpp_bin_float_50>();
test_quadratic_function<cpp_bin_float_50>();
test_trig_function<cpp_bin_float_50>();
}