1 // Copyright Paul A. Bristow 2017
2 // Copyright John Z. Maddock 2017
3
4 // Distributed under the Boost Software License, Version 1.0.
5 // (See accompanying file LICENSE_1_0.txt or
6 // copy at http ://www.boost.org/LICENSE_1_0.txt).
7
8 /*! \brief Graph showing use of Lambert W function.
9
10 \details
11
12 Both Lambert W0 and W-1 branches can be shown on one graph.
13 But useful to have another graph for larger values of argument z.
14 Need two separate graphs for Lambert W0 and -1 prime because
15 the sensible ranges and axes are too different.
16
17 One would get too small LambertW0 in top right and W-1 in bottom left.
18
19 */
20
21 #include <boost/math/special_functions/lambert_w.hpp>
22 using boost::math::lambert_w0;
23 using boost::math::lambert_wm1;
24 using boost::math::lambert_w0_prime;
25 using boost::math::lambert_wm1_prime;
26
27 #include <boost/math/special_functions.hpp>
28 using boost::math::isfinite;
29 #include <boost/svg_plot/svg_2d_plot.hpp>
30 using namespace boost::svg;
31 #include <boost/svg_plot/show_2d_settings.hpp>
32 using boost::svg::show_2d_plot_settings;
33
34 #include <iostream>
35 // using std::cout;
36 // using std::endl;
37 #include <exception>
38 #include <stdexcept>
39 #include <string>
40 #include <array>
41 #include <vector>
42 #include <utility>
43 using std::pair;
44 #include <map>
45 using std::map;
46 #include <set>
47 using std::multiset;
48 #include <limits>
49 using std::numeric_limits;
50 #include <cmath> //
51
52 /*!
53 */
main()54 int main()
55 {
56 try
57 {
58 std::cout << "Lambert W graph example." << std::endl;
59
60 //[lambert_w_graph_1
61 //] [/lambert_w_graph_1]
62 {
63 std::map<const double, double> wm1s; // Lambert W-1 branch values.
64 std::map<const double, double> w0s; // Lambert W0 branch values.
65
66 std::cout.precision(std::numeric_limits<double>::max_digits10);
67
68 int count = 0;
69 for (double z = -0.36787944117144232159552377016146086744581113103176804; z < 2.8; z += 0.001)
70 {
71 double w0 = lambert_w0(z);
72 w0s[z] = w0;
73 // std::cout << "z " << z << ", w = " << w0 << std::endl;
74 count++;
75 }
76 std::cout << "points " << count << std::endl;
77
78 count = 0;
79 for (double z = -0.3678794411714423215955237701614608727; z < -0.001; z += 0.001)
80 {
81 double wm1 = lambert_wm1(z);
82 wm1s[z] = wm1;
83 count++;
84 }
85 std::cout << "points " << count << std::endl;
86
87 svg_2d_plot data_plot;
88 data_plot.title("Lambert W function.")
89 .x_size(400)
90 .y_size(300)
91 .legend_on(true)
92 .legend_lines(true)
93 .x_label("z")
94 .y_label("W")
95 .x_range(-1, 3.)
96 .y_range(-4., +1.)
97 .x_major_interval(1.)
98 .y_major_interval(1.)
99 .x_major_grid_on(true)
100 .y_major_grid_on(true)
101 //.x_values_on(true)
102 //.y_values_on(true)
103 .y_values_rotation(horizontal)
104 //.plot_window_on(true)
105 .x_values_precision(3)
106 .y_values_precision(3)
107 .coord_precision(4) // Needed to avoid stepping on curves.
108 .copyright_holder("Paul A. Bristow")
109 .copyright_date("2018")
110 //.background_border_color(black);
111 ;
112 data_plot.plot(w0s, "W0 branch").line_color(red).shape(none).line_on(true).bezier_on(false).line_width(1);
113 data_plot.plot(wm1s, "W-1 branch").line_color(blue).shape(none).line_on(true).bezier_on(false).line_width(1);
114 data_plot.write("./lambert_w_graph");
115
116 show_2d_plot_settings(data_plot); // For plot diagnosis only.
117
118 } // small z Lambert W
119
120 { // bigger argument z Lambert W
121
122 std::map<const double, double> w0s_big; // Lambert W0 branch values for large z and W.
123 std::map<const double, double> wm1s_big; // Lambert W-1 branch values for small z and large -W.
124 int count = 0;
125 for (double z = -0.3678794411714423215955237701614608727; z < 10000.; z += 50.)
126 {
127 double w0 = lambert_w0(z);
128 w0s_big[z] = w0;
129 count++;
130 }
131 std::cout << "points " << count << std::endl;
132
133 count = 0;
134 for (double z = -0.3678794411714423215955237701614608727; z < -0.001; z += 0.001)
135 {
136 double wm1 = lambert_wm1(z);
137 wm1s_big[z] = wm1;
138 count++;
139 }
140 std::cout << "Lambert W0 large z argument points = " << count << std::endl;
141
142 svg_2d_plot data_plot2;
143 data_plot2.title("Lambert W0 function for larger z.")
144 .x_size(400)
145 .y_size(300)
146 .legend_on(false)
147 .x_label("z")
148 .y_label("W")
149 //.x_label_on(true)
150 //.y_label_on(true)
151 //.xy_values_on(false)
152 .x_range(-1, 10000.)
153 .y_range(-1., +8.)
154 .x_major_interval(2000.)
155 .y_major_interval(1.)
156 .x_major_grid_on(true)
157 .y_major_grid_on(true)
158 //.x_values_on(true)
159 //.y_values_on(true)
160 .y_values_rotation(horizontal)
161 //.plot_window_on(true)
162 .x_values_precision(3)
163 .y_values_precision(3)
164 .coord_precision(4) // Needed to avoid stepping on curves.
165 .copyright_holder("Paul A. Bristow")
166 .copyright_date("2018")
167 //.background_border_color(black);
168 ;
169
170 data_plot2.plot(w0s_big, "W0 branch").line_color(red).shape(none).line_on(true).bezier_on(false).line_width(1);
171 // data_plot2.plot(wm1s_big, "W-1 branch").line_color(blue).shape(none).line_on(true).bezier_on(false).line_width(1);
172 // This wouldn't show anything useful.
173 data_plot2.write("./lambert_w_graph_big_w");
174 } // Big argument z Lambert W
175
176 { // Lambert W0 Derivative plots
177
178 // std::map<const double, double> wm1ps; // Lambert W-1 prime branch values.
179 std::map<const double, double> w0ps; // Lambert W0 prime branch values.
180
181 std::cout.precision(std::numeric_limits<double>::max_digits10);
182
183 int count = 0;
184 for (double z = -0.36; z < 3.; z += 0.001)
185 {
186 double w0p = lambert_w0_prime(z);
187 w0ps[z] = w0p;
188 // std::cout << "z " << z << ", w0 = " << w0 << std::endl;
189 count++;
190 }
191 std::cout << "points " << count << std::endl;
192
193 //count = 0;
194 //for (double z = -0.36; z < -0.1; z += 0.001)
195 //{
196 // double wm1p = lambert_wm1_prime(z);
197 // std::cout << "z " << z << ", w-1 = " << wm1p << std::endl;
198 // wm1ps[z] = wm1p;
199 // count++;
200 //}
201 //std::cout << "points " << count << std::endl;
202
203 svg_2d_plot data_plotp;
204 data_plotp.title("Lambert W0 prime function.")
205 .x_size(400)
206 .y_size(300)
207 .legend_on(false)
208 .x_label("z")
209 .y_label("W0'")
210 .x_range(-0.3, +1.)
211 .y_range(0., +5.)
212 .x_major_interval(0.2)
213 .y_major_interval(2.)
214 .x_major_grid_on(true)
215 .y_major_grid_on(true)
216 .y_values_rotation(horizontal)
217 .x_values_precision(3)
218 .y_values_precision(3)
219 .coord_precision(4) // Needed to avoid stepping on curves.
220 .copyright_holder("Paul A. Bristow")
221 .copyright_date("2018")
222 ;
223
224 // derivative of N[productlog(0, x), 55] at x=0 to 10
225 // Plot[D[N[ProductLog[0, x], 55], x], {x, 0, 10}]
226 // Plot[ProductLog[x]/(x + x ProductLog[x]), {x, 0, 10}]
227 data_plotp.plot(w0ps, "W0 prime branch").line_color(red).shape(none).line_on(true).bezier_on(false).line_width(1);
228 data_plotp.write("./lambert_w0_prime_graph");
229 } // Lambert W0 Derivative plots
230
231 { // Lambert Wm1 Derivative plots
232
233 std::map<const double, double> wm1ps; // Lambert W-1 prime branch values.
234
235 std::cout.precision(std::numeric_limits<double>::max_digits10);
236
237 int count = 0;
238 for (double z = -0.3678; z < -0.00001; z += 0.001)
239 {
240 double wm1p = lambert_wm1_prime(z);
241 // std::cout << "z " << z << ", w-1 = " << wm1p << std::endl;
242 wm1ps[z] = wm1p;
243 count++;
244 }
245 std::cout << "Lambert W-1 prime points = " << count << std::endl;
246
247 svg_2d_plot data_plotp;
248 data_plotp.title("Lambert W-1 prime function.")
249 .x_size(400)
250 .y_size(300)
251 .legend_on(false)
252 .x_label("z")
253 .y_label("W-1'")
254 .x_range(-0.4, +0.01)
255 .x_major_interval(0.1)
256 .y_range(-20., -5.)
257 .y_major_interval(5.)
258 .x_major_grid_on(true)
259 .y_major_grid_on(true)
260 .y_values_rotation(horizontal)
261 .x_values_precision(3)
262 .y_values_precision(3)
263 .coord_precision(4) // Needed to avoid stepping on curves.
264 .copyright_holder("Paul A. Bristow")
265 .copyright_date("2018")
266 ;
267
268 // derivative of N[productlog(0, x), 55] at x=0 to 10
269 // Plot[D[N[ProductLog[0, x], 55], x], {x, 0, 10}]
270 // Plot[ProductLog[x]/(x + x ProductLog[x]), {x, 0, 10}]
271 data_plotp.plot(wm1ps, "W-1 prime branch").line_color(blue).shape(none).line_on(true).bezier_on(false).line_width(1);
272 data_plotp.write("./lambert_wm1_prime_graph");
273 } // Lambert W-1 prime graph
274 } // try
275 catch (std::exception& ex)
276 {
277 std::cout << ex.what() << std::endl;
278 }
279 } // int main()
280
281 /*
282
283 //[lambert_w_graph_1_output
284
285 //] [/lambert_w_graph_1_output]
286 */
287