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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 <iomanip>
#include <iostream>
#include <cmath>
#include <cfloat>
#include <boost/core/demangle.hpp>
#include <boost/hana/for_each.hpp>
#include <boost/hana/ext/std/integer_sequence.hpp>
#include <boost/math/quadrature/wavelet_transforms.hpp>
#include <boost/math/tools/minima.hpp>
#include <boost/math/quadrature/trapezoidal.hpp>
#if __has_include(<stdfloat>)
# include <stdfloat>
#endif
#ifdef BOOST_HAS_FLOAT128
#include <boost/multiprecision/float128.hpp>
using boost::multiprecision::float128;
#endif
using boost::math::constants::pi;
using boost::math::constants::root_two;
using boost::math::quadrature::daubechies_wavelet_transform;
using boost::math::quadrature::trapezoidal;
template<typename Real, int p>
void test_wavelet_transform()
{
using std::abs;
std::cout << "Testing wavelet transform of " << p << " vanishing moment Daubechies wavelet on type " << boost::core::demangle(typeid(Real).name()) << "\n";
auto psi = boost::math::daubechies_wavelet<Real, p>();
auto abs_psi = [&psi](Real x) {
return abs(psi(x));
};
auto [a, b] = psi.support();
auto psil1 = trapezoidal(abs_psi, a, b, 100*std::numeric_limits<Real>::epsilon());
Real psi_sup_norm = 0;
for (double x = a; x < b; x += 0.00001)
{
Real y = psi(x);
if (std::abs(y) > psi_sup_norm)
{
psi_sup_norm = std::abs(y);
}
}
// An even function:
auto f = [](Real x) {
return std::exp(-abs(x));
};
Real fmax = 1;
Real fl2 = 1;
Real fl1 = 2;
auto Wf = daubechies_wavelet_transform(f, psi);
for (double s = 0; s < 10; s += 0.01)
{
Real w1 = Wf(s, 0.0);
Real w2 = Wf(-s, 0.0);
// Since f is an even function, we get w1 = w2:
CHECK_ULP_CLOSE(w1, w2, 12);
}
// The wavelet transform with respect to Daubechies wavelets
for (double s = -10; s < 10; s += 0.1)
{
for (double t = -10; t < 10; t+= 0.1)
{
Real w = Wf(s, t);
// Integral inequality:
Real r1 = sqrt(abs(s))*fmax*psil1;
if (!CHECK_LE(abs(w), r1))
{
std::cerr << " Integral inequality |W[f](s,t)| <= ||f||_infty ||psi||_1 is violated.\n";
}
if (!CHECK_LE(abs(w), fl2))
{
std::cerr << " Integral inequality | int f psi_s,t| <= ||f||_2 ||psi||_2 violated.\n";
}
Real r4 = sqrt(abs(s))*fl1*psi_sup_norm;
if (!CHECK_LE(abs(w), r4))
{
std::cerr << " Integral inequality |W[f](s,t)| <= sqrt(|s|)||f||_1 ||psi||_infty is violated.\n";
}
Real r5 = sqrt(abs(s))*fmax*psil1;
if (!CHECK_LE(abs(w), r5))
{
std::cerr << " Integral inequality |W[f](s,t)| <= sqrt(|s|)||f||_infty ||psi||_1 is violated.\n";
}
if (s != 0)
{
Real r2 = fl1*psi_sup_norm/sqrt(abs(s));
if(!CHECK_LE(abs(w), r2))
{
std::cerr << " Integral inequality |W[f](s,t)| <= ||f||_1 ||psi||_infty/sqrt(|s|) is violated.\n";
}
}
}
}
if (p > 5)
{
// Wavelet transform of a constant is zero.
// The quadrature sum is horribly ill-conditioned (technically infinite),
// so we'll only test on the more rapidly converging sums.
auto g = [](Real ) { return Real(7); };
auto Wg = daubechies_wavelet_transform(g, psi);
for (double s = -10; s < 10; s += 0.1)
{
for (double t = -10; t < 10; t+= 0.1)
{
Real w = Wg(s, t);
if (!CHECK_LE(abs(w), Real(10*sqrt(std::numeric_limits<Real>::epsilon()))))
{
std::cerr << " Wavelet transform of constant with respect to " << p << " vanishing moment Daubechies wavelet is insufficiently small\n";
}
}
}
// Wavelet transform of psi evaluated at s = 1, t = 0 is L2 norm of psi:
auto Wpsi = daubechies_wavelet_transform(psi, psi);
CHECK_MOLLIFIED_CLOSE(Real(1), Wpsi(1,0), Real(2*sqrt(std::numeric_limits<Real>::epsilon())));
}
}
int main()
{
try{
#ifdef __STDCPP_FLOAT64_T__
test_wavelet_transform<std::float64_t, 2>();
test_wavelet_transform<std::float64_t, 8>();
test_wavelet_transform<std::float64_t, 16>();
#else
test_wavelet_transform<double, 2>();
test_wavelet_transform<double, 8>();
test_wavelet_transform<double, 16>();
#endif
// All these tests pass, but the compilation takes too long on CI:
//boost::hana::for_each(std::make_index_sequence<17>(), [&](auto i) {
// test_wavelet_transform<double, i+3>();
//});
}
catch (std::bad_alloc const & e)
{
std::cerr << "Ran out of memory in wavelet transform test: " << e.what() << "\n";
// not much we can do about this, this test uses lots of memory!
}
return boost::math::test::report_errors();
}
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