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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 <iostream>
#include <boost/core/demangle.hpp>
#include <boost/hana/for_each.hpp>
#include <boost/hana/ext/std/integer_sequence.hpp>
#include <boost/multiprecision/float128.hpp>
#include <boost/math/special_functions/daubechies_scaling.hpp>
#include <boost/math/tools/ulps_plot.hpp>
#include <quicksvg/graph_fn.hpp>
using boost::multiprecision::float128;
constexpr const int GRAPH_WIDTH = 300;
template<typename Real, int p>
void plot_phi(int grid_refinements = -1)
{
auto phi = boost::math::daubechies_scaling<Real, p>();
if (grid_refinements >= 0)
{
phi = boost::math::daubechies_scaling<Real, p>(grid_refinements);
}
Real a = 0;
Real b = phi.support().second;
std::string title = "Daubechies " + std::to_string(p) + " scaling function";
title = "";
std::string filename = "daubechies_" + std::to_string(p) + "_scaling.svg";
int samples = 1024;
quicksvg::graph_fn daub(a, b, title, filename, samples, GRAPH_WIDTH);
daub.set_gridlines(8, 2*p-1);
daub.set_stroke_width(1);
daub.add_fn(phi);
daub.write_all();
}
template<typename Real, int p>
void plot_dphi(int grid_refinements = -1)
{
auto phi = boost::math::daubechies_scaling<Real, p>();
if (grid_refinements >= 0)
{
phi = boost::math::daubechies_scaling<Real, p>(grid_refinements);
}
Real a = 0;
Real b = phi.support().second;
std::string title = "Daubechies " + std::to_string(p) + " scaling function derivative";
title = "";
std::string filename = "daubechies_" + std::to_string(p) + "_scaling_prime.svg";
int samples = 1024;
quicksvg::graph_fn daub(a, b, title, filename, samples, GRAPH_WIDTH);
daub.set_stroke_width(1);
daub.set_gridlines(8, 2*p-1);
auto dphi = [phi](Real x)->Real { return phi.prime(x); };
daub.add_fn(dphi);
daub.write_all();
}
template<typename Real, int p>
void plot_convergence()
{
auto phi0 = boost::math::daubechies_scaling<Real, p>(0);
Real a = 0;
Real b = phi0.support().second;
std::string title = "Daubechies " + std::to_string(p) + " scaling at 0 (green), 1 (orange), 2 (red), and 24 (blue) grid refinements";
title = "";
std::string filename = "daubechies_" + std::to_string(p) + "_scaling_convergence.svg";
quicksvg::graph_fn daub(a, b, title, filename, 1024, 900);
daub.set_stroke_width(1);
daub.set_gridlines(8, 2*p-1);
daub.add_fn(phi0, "green");
auto phi1 = boost::math::daubechies_scaling<Real, p>(1);
daub.add_fn(phi1, "orange");
auto phi2 = boost::math::daubechies_scaling<Real, p>(2);
daub.add_fn(phi2, "red");
auto phi21 = boost::math::daubechies_scaling<Real, p>(21);
daub.add_fn(phi21);
daub.write_all();
}
template<typename Real, int p>
void plot_condition_number()
{
using std::abs;
using std::log;
static_assert(p >= 3, "p = 2 is not differentiable, so condition numbers cannot be effectively evaluated.");
auto phi = boost::math::daubechies_scaling<Real, p>();
Real a = std::sqrt(std::numeric_limits<Real>::epsilon());
Real b = phi.support().second - 1000*std::sqrt(std::numeric_limits<Real>::epsilon());
std::string title = "log10 of condition number of function evaluation for Daubechies " + std::to_string(p) + " scaling function.";
title = "";
std::string filename = "daubechies_" + std::to_string(p) + "_scaling_condition_number.svg";
quicksvg::graph_fn daub(a, b, title, filename, 2048, GRAPH_WIDTH);
daub.set_stroke_width(1);
daub.set_gridlines(8, 2*p-1);
auto cond = [&phi](Real x)
{
Real y = phi(x);
Real dydx = phi.prime(x);
Real z = abs(x*dydx/y);
using std::isnan;
if (z==0)
{
return Real(-1);
}
if (isnan(z))
{
// Graphing libraries don't like nan's:
return Real(1);
}
return log10(z);
};
daub.add_fn(cond);
daub.write_all();
}
template<typename CoarseReal, typename PreciseReal, int p, class PhiPrecise>
void do_ulp(int coarse_refinements, PhiPrecise phi_precise)
{
auto phi_coarse = boost::math::daubechies_scaling<CoarseReal, p>(coarse_refinements);
std::string title = std::to_string(p) + " vanishing moment ULP plot at " + std::to_string(coarse_refinements) + " refinements and " + boost::core::demangle(typeid(CoarseReal).name()) + " precision";
title = "";
std::string filename = "daubechies_" + std::to_string(p) + "_" + boost::core::demangle(typeid(CoarseReal).name()) + "_" + std::to_string(coarse_refinements) + "_refinements.svg";
int samples = 20000;
int clip = 10;
int horizontal_lines = 8;
int vertical_lines = 2*p - 1;
auto [a, b] = phi_coarse.support();
auto plot = boost::math::tools::ulps_plot<decltype(phi_precise), PreciseReal, CoarseReal>(phi_precise, a, b, samples);
plot.clip(clip).width(GRAPH_WIDTH).horizontal_lines(horizontal_lines).vertical_lines(vertical_lines).ulp_envelope(false);
plot.background_color("white").font_color("black");
plot.add_fn(phi_coarse);
plot.write(filename);
}
int main()
{
boost::hana::for_each(std::make_index_sequence<18>(), [&](auto i){ plot_phi<double, i+2>(); });
boost::hana::for_each(std::make_index_sequence<17>(), [&](auto i){ plot_dphi<double, i+3>(); });
boost::hana::for_each(std::make_index_sequence<17>(), [&](auto i){ plot_condition_number<double, i+3>(); });
boost::hana::for_each(std::make_index_sequence<18>(), [&](auto i){ plot_convergence<double, i+2>(); });
using PreciseReal = float128;
using CoarseReal = double;
int precise_refinements = 23;
constexpr const int p = 8;
std::cout << "Computing precise scaling function in " << boost::core::demangle(typeid(PreciseReal).name()) << " precision.\n";
auto phi_precise = boost::math::daubechies_scaling<PreciseReal, p>(precise_refinements);
std::cout << "Beginning comparison with functions computed in " << boost::core::demangle(typeid(CoarseReal).name()) << " precision.\n";
for (int i = 7; i <= precise_refinements-1; ++i)
{
std::cout << "\tCoarse refinement " << i << "\n";
do_ulp<CoarseReal, PreciseReal, p>(i, phi_precise);
}
}
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