123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286 |
- // Copyright Paul A. Bristow 2017
- // 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 use of Lambert W function.
- \details
- Both Lambert W0 and W-1 branches can be shown on one graph.
- But useful to have another graph for larger values of argument z.
- Need two separate graphs for Lambert W0 and -1 prime because
- the sensible ranges and axes are too different.
- One would get too small LambertW0 in top right and W-1 in bottom left.
- */
- #include <boost/math/special_functions/lambert_w.hpp>
- using boost::math::lambert_w0;
- using boost::math::lambert_wm1;
- using boost::math::lambert_w0_prime;
- using boost::math::lambert_wm1_prime;
- #include <boost/math/special_functions.hpp>
- using boost::math::isfinite;
- #include <boost/svg_plot/svg_2d_plot.hpp>
- using namespace boost::svg;
- #include <boost/svg_plot/show_2d_settings.hpp>
- using boost::svg::show_2d_plot_settings;
- #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> //
- /*!
- */
- int main()
- {
- try
- {
- std::cout << "Lambert W graph example." << std::endl;
- //[lambert_w_graph_1
- //] [/lambert_w_graph_1]
- {
- std::map<const double, double> wm1s; // Lambert W-1 branch values.
- std::map<const double, double> w0s; // Lambert W0 branch values.
- std::cout.precision(std::numeric_limits<double>::max_digits10);
- int count = 0;
- for (double z = -0.36787944117144232159552377016146086744581113103176804; z < 2.8; z += 0.001)
- {
- double w0 = lambert_w0(z);
- w0s[z] = w0;
- // std::cout << "z " << z << ", w = " << w0 << std::endl;
- count++;
- }
- std::cout << "points " << count << std::endl;
- count = 0;
- for (double z = -0.3678794411714423215955237701614608727; z < -0.001; z += 0.001)
- {
- double wm1 = lambert_wm1(z);
- wm1s[z] = wm1;
- count++;
- }
- std::cout << "points " << count << std::endl;
- svg_2d_plot data_plot;
- data_plot.title("Lambert W function.")
- .x_size(400)
- .y_size(300)
- .legend_on(true)
- .legend_lines(true)
- .x_label("z")
- .y_label("W")
- .x_range(-1, 3.)
- .y_range(-4., +1.)
- .x_major_interval(1.)
- .y_major_interval(1.)
- .x_major_grid_on(true)
- .y_major_grid_on(true)
- //.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(4) // Needed to avoid stepping on curves.
- .copyright_holder("Paul A. Bristow")
- .copyright_date("2018")
- //.background_border_color(black);
- ;
- data_plot.plot(w0s, "W0 branch").line_color(red).shape(none).line_on(true).bezier_on(false).line_width(1);
- data_plot.plot(wm1s, "W-1 branch").line_color(blue).shape(none).line_on(true).bezier_on(false).line_width(1);
- data_plot.write("./lambert_w_graph");
- show_2d_plot_settings(data_plot); // For plot diagnosis only.
- } // small z Lambert W
- { // bigger argument z Lambert W
- std::map<const double, double> w0s_big; // Lambert W0 branch values for large z and W.
- std::map<const double, double> wm1s_big; // Lambert W-1 branch values for small z and large -W.
- int count = 0;
- for (double z = -0.3678794411714423215955237701614608727; z < 10000.; z += 50.)
- {
- double w0 = lambert_w0(z);
- w0s_big[z] = w0;
- count++;
- }
- std::cout << "points " << count << std::endl;
- count = 0;
- for (double z = -0.3678794411714423215955237701614608727; z < -0.001; z += 0.001)
- {
- double wm1 = lambert_wm1(z);
- wm1s_big[z] = wm1;
- count++;
- }
- std::cout << "Lambert W0 large z argument points = " << count << std::endl;
- svg_2d_plot data_plot2;
- data_plot2.title("Lambert W0 function for larger z.")
- .x_size(400)
- .y_size(300)
- .legend_on(false)
- .x_label("z")
- .y_label("W")
- //.x_label_on(true)
- //.y_label_on(true)
- //.xy_values_on(false)
- .x_range(-1, 10000.)
- .y_range(-1., +8.)
- .x_major_interval(2000.)
- .y_major_interval(1.)
- .x_major_grid_on(true)
- .y_major_grid_on(true)
- //.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(4) // Needed to avoid stepping on curves.
- .copyright_holder("Paul A. Bristow")
- .copyright_date("2018")
- //.background_border_color(black);
- ;
- data_plot2.plot(w0s_big, "W0 branch").line_color(red).shape(none).line_on(true).bezier_on(false).line_width(1);
- // data_plot2.plot(wm1s_big, "W-1 branch").line_color(blue).shape(none).line_on(true).bezier_on(false).line_width(1);
- // This wouldn't show anything useful.
- data_plot2.write("./lambert_w_graph_big_w");
- } // Big argument z Lambert W
- { // Lambert W0 Derivative plots
- // std::map<const double, double> wm1ps; // Lambert W-1 prime branch values.
- std::map<const double, double> w0ps; // Lambert W0 prime branch values.
- std::cout.precision(std::numeric_limits<double>::max_digits10);
- int count = 0;
- for (double z = -0.36; z < 3.; z += 0.001)
- {
- double w0p = lambert_w0_prime(z);
- w0ps[z] = w0p;
- // std::cout << "z " << z << ", w0 = " << w0 << std::endl;
- count++;
- }
- std::cout << "points " << count << std::endl;
- //count = 0;
- //for (double z = -0.36; z < -0.1; z += 0.001)
- //{
- // double wm1p = lambert_wm1_prime(z);
- // std::cout << "z " << z << ", w-1 = " << wm1p << std::endl;
- // wm1ps[z] = wm1p;
- // count++;
- //}
- //std::cout << "points " << count << std::endl;
- svg_2d_plot data_plotp;
- data_plotp.title("Lambert W0 prime function.")
- .x_size(400)
- .y_size(300)
- .legend_on(false)
- .x_label("z")
- .y_label("W0'")
- .x_range(-0.3, +1.)
- .y_range(0., +5.)
- .x_major_interval(0.2)
- .y_major_interval(2.)
- .x_major_grid_on(true)
- .y_major_grid_on(true)
- .y_values_rotation(horizontal)
- .x_values_precision(3)
- .y_values_precision(3)
- .coord_precision(4) // Needed to avoid stepping on curves.
- .copyright_holder("Paul A. Bristow")
- .copyright_date("2018")
- ;
- // derivative of N[productlog(0, x), 55] at x=0 to 10
- // Plot[D[N[ProductLog[0, x], 55], x], {x, 0, 10}]
- // Plot[ProductLog[x]/(x + x ProductLog[x]), {x, 0, 10}]
- data_plotp.plot(w0ps, "W0 prime branch").line_color(red).shape(none).line_on(true).bezier_on(false).line_width(1);
- data_plotp.write("./lambert_w0_prime_graph");
- } // Lambert W0 Derivative plots
- { // Lambert Wm1 Derivative plots
- std::map<const double, double> wm1ps; // Lambert W-1 prime branch values.
- std::cout.precision(std::numeric_limits<double>::max_digits10);
- int count = 0;
- for (double z = -0.3678; z < -0.00001; z += 0.001)
- {
- double wm1p = lambert_wm1_prime(z);
- // std::cout << "z " << z << ", w-1 = " << wm1p << std::endl;
- wm1ps[z] = wm1p;
- count++;
- }
- std::cout << "Lambert W-1 prime points = " << count << std::endl;
- svg_2d_plot data_plotp;
- data_plotp.title("Lambert W-1 prime function.")
- .x_size(400)
- .y_size(300)
- .legend_on(false)
- .x_label("z")
- .y_label("W-1'")
- .x_range(-0.4, +0.01)
- .x_major_interval(0.1)
- .y_range(-20., -5.)
- .y_major_interval(5.)
- .x_major_grid_on(true)
- .y_major_grid_on(true)
- .y_values_rotation(horizontal)
- .x_values_precision(3)
- .y_values_precision(3)
- .coord_precision(4) // Needed to avoid stepping on curves.
- .copyright_holder("Paul A. Bristow")
- .copyright_date("2018")
- ;
- // derivative of N[productlog(0, x), 55] at x=0 to 10
- // Plot[D[N[ProductLog[0, x], 55], x], {x, 0, 10}]
- // Plot[ProductLog[x]/(x + x ProductLog[x]), {x, 0, 10}]
- data_plotp.plot(wm1ps, "W-1 prime branch").line_color(blue).shape(none).line_on(true).bezier_on(false).line_width(1);
- data_plotp.write("./lambert_wm1_prime_graph");
- } // Lambert W-1 prime graph
- } // try
- catch (std::exception& ex)
- {
- std::cout << ex.what() << std::endl;
- }
- } // int main()
- /*
- //[lambert_w_graph_1_output
- //] [/lambert_w_graph_1_output]
- */
|