287 lines
8.7 KiB
C++
287 lines
8.7 KiB
C++
// Copyright Paul A. Bristow 2017
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// Copyright John Z. Maddock 2017
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// Distributed under the Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt or
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// copy at http ://www.boost.org/LICENSE_1_0.txt).
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/*! \brief Graph showing use of Lambert W function.
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\details
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Both Lambert W0 and W-1 branches can be shown on one graph.
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But useful to have another graph for larger values of argument z.
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Need two separate graphs for Lambert W0 and -1 prime because
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the sensible ranges and axes are too different.
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One would get too small LambertW0 in top right and W-1 in bottom left.
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*/
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#include <boost/math/special_functions/lambert_w.hpp>
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using boost::math::lambert_w0;
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using boost::math::lambert_wm1;
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using boost::math::lambert_w0_prime;
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using boost::math::lambert_wm1_prime;
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#include <boost/math/special_functions.hpp>
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using boost::math::isfinite;
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#include <boost/svg_plot/svg_2d_plot.hpp>
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using namespace boost::svg;
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#include <boost/svg_plot/show_2d_settings.hpp>
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using boost::svg::show_2d_plot_settings;
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#include <iostream>
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// using std::cout;
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// using std::endl;
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#include <exception>
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#include <stdexcept>
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#include <string>
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#include <array>
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#include <vector>
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#include <utility>
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using std::pair;
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#include <map>
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using std::map;
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#include <set>
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using std::multiset;
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#include <limits>
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using std::numeric_limits;
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#include <cmath> //
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/*!
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*/
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int main()
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{
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try
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{
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std::cout << "Lambert W graph example." << std::endl;
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//[lambert_w_graph_1
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//] [/lambert_w_graph_1]
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{
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std::map<const double, double> wm1s; // Lambert W-1 branch values.
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std::map<const double, double> w0s; // Lambert W0 branch values.
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std::cout.precision(std::numeric_limits<double>::max_digits10);
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int count = 0;
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for (double z = -0.36787944117144232159552377016146086744581113103176804; z < 2.8; z += 0.001)
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{
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double w0 = lambert_w0(z);
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w0s[z] = w0;
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// std::cout << "z " << z << ", w = " << w0 << std::endl;
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count++;
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}
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std::cout << "points " << count << std::endl;
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count = 0;
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for (double z = -0.3678794411714423215955237701614608727; z < -0.001; z += 0.001)
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{
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double wm1 = lambert_wm1(z);
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wm1s[z] = wm1;
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count++;
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}
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std::cout << "points " << count << std::endl;
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svg_2d_plot data_plot;
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data_plot.title("Lambert W function.")
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.x_size(400)
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.y_size(300)
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.legend_on(true)
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.legend_lines(true)
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.x_label("z")
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.y_label("W")
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.x_range(-1, 3.)
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.y_range(-4., +1.)
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.x_major_interval(1.)
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.y_major_interval(1.)
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.x_major_grid_on(true)
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.y_major_grid_on(true)
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//.x_values_on(true)
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//.y_values_on(true)
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.y_values_rotation(horizontal)
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//.plot_window_on(true)
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.x_values_precision(3)
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.y_values_precision(3)
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.coord_precision(4) // Needed to avoid stepping on curves.
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.copyright_holder("Paul A. Bristow")
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.copyright_date("2018")
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//.background_border_color(black);
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;
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data_plot.plot(w0s, "W0 branch").line_color(red).shape(none).line_on(true).bezier_on(false).line_width(1);
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data_plot.plot(wm1s, "W-1 branch").line_color(blue).shape(none).line_on(true).bezier_on(false).line_width(1);
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data_plot.write("./lambert_w_graph");
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show_2d_plot_settings(data_plot); // For plot diagnosis only.
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} // small z Lambert W
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{ // bigger argument z Lambert W
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std::map<const double, double> w0s_big; // Lambert W0 branch values for large z and W.
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std::map<const double, double> wm1s_big; // Lambert W-1 branch values for small z and large -W.
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int count = 0;
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for (double z = -0.3678794411714423215955237701614608727; z < 10000.; z += 50.)
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{
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double w0 = lambert_w0(z);
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w0s_big[z] = w0;
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count++;
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}
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std::cout << "points " << count << std::endl;
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count = 0;
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for (double z = -0.3678794411714423215955237701614608727; z < -0.001; z += 0.001)
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{
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double wm1 = lambert_wm1(z);
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wm1s_big[z] = wm1;
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count++;
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}
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std::cout << "Lambert W0 large z argument points = " << count << std::endl;
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svg_2d_plot data_plot2;
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data_plot2.title("Lambert W0 function for larger z.")
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.x_size(400)
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.y_size(300)
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.legend_on(false)
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.x_label("z")
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.y_label("W")
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//.x_label_on(true)
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//.y_label_on(true)
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//.xy_values_on(false)
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.x_range(-1, 10000.)
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.y_range(-1., +8.)
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.x_major_interval(2000.)
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.y_major_interval(1.)
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.x_major_grid_on(true)
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.y_major_grid_on(true)
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//.x_values_on(true)
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//.y_values_on(true)
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.y_values_rotation(horizontal)
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//.plot_window_on(true)
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.x_values_precision(3)
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.y_values_precision(3)
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.coord_precision(4) // Needed to avoid stepping on curves.
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.copyright_holder("Paul A. Bristow")
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.copyright_date("2018")
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//.background_border_color(black);
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;
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data_plot2.plot(w0s_big, "W0 branch").line_color(red).shape(none).line_on(true).bezier_on(false).line_width(1);
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// data_plot2.plot(wm1s_big, "W-1 branch").line_color(blue).shape(none).line_on(true).bezier_on(false).line_width(1);
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// This wouldn't show anything useful.
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data_plot2.write("./lambert_w_graph_big_w");
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} // Big argument z Lambert W
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{ // Lambert W0 Derivative plots
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// std::map<const double, double> wm1ps; // Lambert W-1 prime branch values.
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std::map<const double, double> w0ps; // Lambert W0 prime branch values.
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std::cout.precision(std::numeric_limits<double>::max_digits10);
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int count = 0;
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for (double z = -0.36; z < 3.; z += 0.001)
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{
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double w0p = lambert_w0_prime(z);
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w0ps[z] = w0p;
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// std::cout << "z " << z << ", w0 = " << w0 << std::endl;
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count++;
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}
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std::cout << "points " << count << std::endl;
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//count = 0;
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//for (double z = -0.36; z < -0.1; z += 0.001)
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//{
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// double wm1p = lambert_wm1_prime(z);
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// std::cout << "z " << z << ", w-1 = " << wm1p << std::endl;
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// wm1ps[z] = wm1p;
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// count++;
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//}
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//std::cout << "points " << count << std::endl;
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svg_2d_plot data_plotp;
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data_plotp.title("Lambert W0 prime function.")
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.x_size(400)
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.y_size(300)
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.legend_on(false)
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.x_label("z")
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.y_label("W0'")
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.x_range(-0.3, +1.)
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.y_range(0., +5.)
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.x_major_interval(0.2)
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.y_major_interval(2.)
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.x_major_grid_on(true)
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.y_major_grid_on(true)
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.y_values_rotation(horizontal)
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.x_values_precision(3)
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.y_values_precision(3)
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.coord_precision(4) // Needed to avoid stepping on curves.
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.copyright_holder("Paul A. Bristow")
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.copyright_date("2018")
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;
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// derivative of N[productlog(0, x), 55] at x=0 to 10
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// Plot[D[N[ProductLog[0, x], 55], x], {x, 0, 10}]
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// Plot[ProductLog[x]/(x + x ProductLog[x]), {x, 0, 10}]
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data_plotp.plot(w0ps, "W0 prime branch").line_color(red).shape(none).line_on(true).bezier_on(false).line_width(1);
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data_plotp.write("./lambert_w0_prime_graph");
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} // Lambert W0 Derivative plots
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{ // Lambert Wm1 Derivative plots
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std::map<const double, double> wm1ps; // Lambert W-1 prime branch values.
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std::cout.precision(std::numeric_limits<double>::max_digits10);
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int count = 0;
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for (double z = -0.3678; z < -0.00001; z += 0.001)
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{
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double wm1p = lambert_wm1_prime(z);
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// std::cout << "z " << z << ", w-1 = " << wm1p << std::endl;
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wm1ps[z] = wm1p;
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count++;
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}
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std::cout << "Lambert W-1 prime points = " << count << std::endl;
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svg_2d_plot data_plotp;
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data_plotp.title("Lambert W-1 prime function.")
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.x_size(400)
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.y_size(300)
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.legend_on(false)
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.x_label("z")
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.y_label("W-1'")
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.x_range(-0.4, +0.01)
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.x_major_interval(0.1)
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.y_range(-20., -5.)
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.y_major_interval(5.)
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.x_major_grid_on(true)
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.y_major_grid_on(true)
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.y_values_rotation(horizontal)
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.x_values_precision(3)
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.y_values_precision(3)
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.coord_precision(4) // Needed to avoid stepping on curves.
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.copyright_holder("Paul A. Bristow")
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.copyright_date("2018")
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;
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// derivative of N[productlog(0, x), 55] at x=0 to 10
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// Plot[D[N[ProductLog[0, x], 55], x], {x, 0, 10}]
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// Plot[ProductLog[x]/(x + x ProductLog[x]), {x, 0, 10}]
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data_plotp.plot(wm1ps, "W-1 prime branch").line_color(blue).shape(none).line_on(true).bezier_on(false).line_width(1);
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data_plotp.write("./lambert_wm1_prime_graph");
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} // Lambert W-1 prime graph
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} // try
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catch (std::exception& ex)
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{
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std::cout << ex.what() << std::endl;
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}
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} // int main()
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/*
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//[lambert_w_graph_1_output
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//] [/lambert_w_graph_1_output]
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*/
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