Adding upstream version 14.2.21.upstream/14.2.21upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 286 insertions, 0 deletions

diff --git a/src/boost/libs/math/example/lambert_w_graph.cpp b/src/boost/libs/math/example/lambert_w_graph.cpp
new file mode 100644
index 00000000..3eb43f75
--- /dev/null
+++ b/src/boost/libs/math/example/lambert_w_graph.cpp
@@ -0,0 +1,286 @@
+// 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]
+   */