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// Copyright Paul A. Bristow 2017, 2018
// Copyright John Z. Maddock 2017
// Distributed under 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).
/*! \brief Graph showing differences of Lambert W function double from nearest representable values.
\details
*/
#include <boost/math/special_functions/lambert_w.hpp>
using boost::math::lambert_w0;
using boost::math::lambert_wm1;
#include <boost/math/special_functions.hpp>
using boost::math::isfinite;
#include <boost/svg_plot/svg_2d_plot.hpp>
using namespace boost::svg;
// For higher precision computation of Lambert W.
#include <boost/multiprecision/cpp_bin_float.hpp>
#include <boost/math/special_functions/next.hpp> // For float_distance.
using boost::math::float_distance;
#include <iostream>
// using std::cout;
// using std::endl;
#include <exception>
#include <stdexcept>
#include <string>
#include <array>
#include <vector>
#include <utility>
using std::pair;
#include <map>
using std::map;
#include <set>
using std::multiset;
#include <limits>
using std::numeric_limits;
#include <cmath> // exp
/*!
*/
int main()
{
try
{
std::cout << "Lambert W errors graph." << std::endl;
using boost::multiprecision::cpp_bin_float_50;
using boost::multiprecision::cpp_bin_float_quad;
typedef cpp_bin_float_quad HPT; // High precision type.
using boost::math::float_distance;
using boost::math::policies::precision;
using boost::math::policies::digits10;
using boost::math::policies::digits2;
using boost::math::policies::policy;
std::cout.precision(std::numeric_limits<double>::max_digits10);
//[lambert_w_graph_1
//] [/lambert_w_graph_1]
{
std::map<const double, double> w0s; // Lambert W0 branch values, default double precision, digits2 = 53.
std::map<const double, double> w0s_50; // Lambert W0 branch values digits2 = 50.
int max_distance = 0;
int total_distance = 0;
int count = 0;
const int bits = 7;
double min_z = -0.367879; // Close to singularity at -0.3678794411714423215955237701614608727 -exp(-1)
//double min_z = 0.06; // Above 0.05 switch point.
double max_z = 99.99;
double step_z = 0.05;
for (HPT z = min_z; z < max_z; z += step_z)
{
double zd = static_cast<double>(z);
double w0d = lambert_w0(zd); // double result from same default.
HPT w0_best = lambert_w0<HPT>(z);
double w0_best_d = static_cast<double>(w0_best); // reference result.
// w0s[zd] = (w0d - w0_best_d); // absolute difference.
// w0s[z] = 100 * (w0 - w0_best) / w0_best; // difference relative % .
w0s[zd] = float_distance<double>(w0d, w0_best_d); // difference in bits.
double fd = float_distance<double>(w0d, w0_best_d);
int distance = static_cast<int>(fd);
int abs_distance = abs(distance);
// std::cout << count << " " << zd << " " << w0d << " " << w0_best_d
// << ", Difference = " << w0d - w0_best_d << ", % = " << (w0d - w0_best_d) / w0d << ", Distance = " << distance << std::endl;
total_distance += abs_distance;
if (abs_distance > max_distance)
{
max_distance = abs_distance;
}
count++;
} // for z
std::cout << "points " << count << std::endl;
std::cout.precision(3);
std::cout << "max distance " << max_distance << ", total distances = " << total_distance
<< ", mean distance " << (float)total_distance / count << std::endl;
typedef std::map<const double, double>::const_iterator Map_Iterator;
/* for (std::map<const double, double>::const_iterator it = w0s.begin(); it != w0s.end(); ++it)
{
std::cout << " " << *(it) << "\n";
}
*/
svg_2d_plot data_plot_0; // <-0.368, -46> <-0.358, -4> <-0.348, 1>...
data_plot_0.title("Lambert W0 function differences from 'best' for double.")
.title_font_size(11)
.x_size(400)
.y_size(200)
.legend_on(false)
//.legend_font_weight(1)
.x_label("z")
.y_label("W0 difference (bits)")
//.x_label_on(true)
//.y_label_on(true)
//.xy_values_on(false)
.x_range(-1, 100.)
.y_range(-4., +4.)
.x_major_interval(10.)
.y_major_interval(2.)
.x_major_grid_on(true)
.y_major_grid_on(true)
.x_label_font_size(9)
.y_label_font_size(9)
//.x_values_on(true)
//.y_values_on(true)
.y_values_rotation(horizontal)
//.plot_window_on(true)
.x_values_precision(3)
.y_values_precision(3)
.coord_precision(3) // Needed to avoid stepping on curves.
//.coord_precision(4) // Needed to avoid stepping on curves.
.copyright_holder("Paul A. Bristow")
.copyright_date("2018")
//.background_border_color(black);
;
data_plot_0.plot(w0s, "W0 branch").line_color(red).shape(none).line_on(true).bezier_on(false).line_width(0.2);
//data_plot.plot(wm1s, "W-1 branch").line_color(blue).shape(none).line_on(true).bezier_on(false).line_width(1);
data_plot_0.write("./lambert_w0_errors_graph");
} // end W0 branch plot.
{ // Repeat for Lambert W-1 branch.
std::map<const double, double> wm1s; // Lambert W-1 branch values.
std::map<const double, double> wm1s_50; // Lambert Wm1 branch values digits2 = 50.
int max_distance = 0;
int total_distance = 0;
int count = 0;
const int bits = 7;
double min_z = -0.367879; // Close to singularity at -0.3678794411714423215955237701614608727 -exp(-1)
//double min_z = 0.06; // Above 0.05 switch point.
double max_z = -0.0001;
double step_z = 0.001;
for (HPT z = min_z; z < max_z; z += step_z)
{
if (z > max_z)
{
break;
}
double zd = static_cast<double>(z);
double wm1d = lambert_wm1(zd); // double result from same default.
HPT wm1_best = lambert_wm1<HPT>(z);
double wm1_best_d = static_cast<double>(wm1_best); // reference result.
// wm1s[zd] = (wm1d - wm1_best_d); // absolute difference.
// wm1s[z] = 100 * (wm1 - wm1_best) / wm1_best; // difference relative % .
wm1s[zd] = float_distance<double>(wm1d, wm1_best_d); // difference in bits.
double fd = float_distance<double>(wm1d, wm1_best_d);
int distance = static_cast<int>(fd);
int abs_distance = abs(distance);
//std::cout << count << " " << zd << " " << wm1d << " " << wm1_best_d
// << ", Difference = " << wm1d - wm1_best_d << ", % = " << (wm1d - wm1_best_d) / wm1d << ", Distance = " << distance << std::endl;
total_distance += abs_distance;
if (abs_distance > max_distance)
{
max_distance = abs_distance;
}
count++;
} // for z
std::cout << "points " << count << std::endl;
std::cout.precision(3);
std::cout << "max distance " << max_distance << ", total distances = " << total_distance
<< ", mean distance " << (float)total_distance / count << std::endl;
typedef std::map<const double, double>::const_iterator Map_Iterator;
/* for (std::map<const double, double>::const_iterator it = wm1s.begin(); it != wm1s.end(); ++it)
{
std::cout << " " << *(it) << "\n";
}
*/
svg_2d_plot data_plot_m1; // <-0.368, -46> <-0.358, -4> <-0.348, 1>...
data_plot_m1.title("Lambert W-1 function differences from 'best' for double.")
.title_font_size(11)
.x_size(400)
.y_size(200)
.legend_on(false)
//.legend_font_weight(1)
.x_label("z")
.y_label("W-1 difference (bits)")
.x_range(-0.39, +0.0001)
.y_range(-4., +4.)
.x_major_interval(0.1)
.y_major_interval(2.)
.x_major_grid_on(true)
.y_major_grid_on(true)
.x_label_font_size(9)
.y_label_font_size(9)
//.x_values_on(true)
//.y_values_on(true)
.y_values_rotation(horizontal)
//.plot_window_on(true)
.x_values_precision(3)
.y_values_precision(3)
.coord_precision(3) // Needed to avoid stepping on curves.
//.coord_precision(4) // Needed to avoid stepping on curves.
.copyright_holder("Paul A. Bristow")
.copyright_date("2018")
//.background_border_color(black);
;
data_plot_m1.plot(wm1s, "W-1 branch").line_color(darkblue).shape(none).line_on(true).bezier_on(false).line_width(0.2);
data_plot_m1.write("./lambert_wm1_errors_graph");
}
}
catch (std::exception& ex)
{
std::cout << ex.what() << std::endl;
}
} // int main()
/*
//[lambert_w_errors_graph_1_output
Lambert W errors graph.
points 2008
max distance 46, total distances = 717, mean distance 0.357
points 368
max distance 23, total distances = 329, mean distance 0.894
//] [/lambert_w_errors_graph_1_output]
*/
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