767 lines
33 KiB
C++
767 lines
33 KiB
C++
// Copyright John Maddock 2008.
|
|
// Copyright Paul A. Bristow 2016
|
|
// Use, modification and distribution are subject to 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)
|
|
|
|
#ifdef _MSC_VER
|
|
# pragma warning (disable : 4127) // conditional expression is constant
|
|
# pragma warning (disable : 4180) // qualifier applied to function type has no meaning; ignored
|
|
# pragma warning (disable : 4503) // decorated name length exceeded, name was truncated
|
|
# pragma warning (disable : 4512) // assignment operator could not be generated
|
|
# pragma warning (disable : 4224) // nonstandard extension used : formal parameter 'function_ptr' was previously defined as a type
|
|
#endif
|
|
|
|
// #define BOOST_SVG_DIAGNOSTICS // define to provide diagnostic output from plotting.
|
|
|
|
#include <boost/math/special_functions.hpp>
|
|
#include <boost/math/tools/roots.hpp>
|
|
#include <boost/function.hpp>
|
|
#include <boost/bind.hpp>
|
|
|
|
#include <list>
|
|
#include <map>
|
|
#include <string>
|
|
#include <boost/svg_plot/svg_2d_plot.hpp>
|
|
#include <boost/svg_plot/show_2d_settings.hpp>
|
|
|
|
class function_arity1_plotter
|
|
{
|
|
public:
|
|
function_arity1_plotter() : m_min_x(0), m_max_x(0), m_min_y(0), m_max_y(0), m_has_legend(false) {}
|
|
|
|
//! Add a function to the plotter, compute the axes using range a to b and compute & add data points to map.
|
|
|
|
void add(boost::function<double(double)> f, double x_lo, double x_hi, const std::string& name)
|
|
{
|
|
std::cout << "Adding function " << name << ", x range " << x_lo << " to " << x_hi << std::endl;
|
|
if(name.size())
|
|
m_has_legend = true;
|
|
//
|
|
// Now set our x-axis limits:
|
|
if(m_max_x == m_min_x)
|
|
{
|
|
m_max_x = x_hi;
|
|
m_min_x = x_lo;
|
|
}
|
|
else
|
|
{
|
|
if(x_lo < m_min_x)
|
|
m_min_x = x_lo;
|
|
if(x_hi > m_max_x)
|
|
m_max_x = x_hi;
|
|
}
|
|
m_points.push_back(std::pair<std::string, std::map<double,double> >(name, std::map<double,double>()));
|
|
std::map<double,double>& points = m_points.rbegin()->second;
|
|
double interval = (x_hi - x_lo) / 200;
|
|
for(double x = x_lo; x <= x_hi; x += interval)
|
|
{
|
|
double y = f(x); // Evaluate the function.
|
|
// Set the Y axis limits if needed.
|
|
if((m_min_y == m_max_y) && (m_min_y == 0))
|
|
m_min_y = m_max_y = y;
|
|
if(m_min_y > y)
|
|
m_min_y = y;
|
|
if(m_max_y < y)
|
|
m_max_y = y;
|
|
points[x] = y; // Store the pair of points values.
|
|
} // for x
|
|
|
|
#ifdef BOOST_SVG_DIAGNOSTICS
|
|
std::cout << "Added function " << name
|
|
<< ", x range " << x_lo << " to " << x_hi
|
|
<< ", x min = " << m_min_x << ", x max = " << m_max_x
|
|
<< ", y min = " << m_min_y << ", y max = " << m_max_y
|
|
<< ", interval = " << interval
|
|
<< std::endl;
|
|
#endif
|
|
} // void add(boost::function<double(double)> f, double a, double b, const std::string& name)
|
|
|
|
//! Compute x and y min and max from a map of pre-computed data points.
|
|
void add(const std::map<double, double>& m, const std::string& name)
|
|
{
|
|
if (name.size() != 0)
|
|
{
|
|
m_has_legend = true;
|
|
}
|
|
m_points.push_back(std::pair<std::string, std::map<double,double> >(name, m));
|
|
|
|
std::map<double, double>::const_iterator i = m.begin();
|
|
while(i != m.end())
|
|
{
|
|
if((m_min_x == m_min_y) && (m_min_y == 0))
|
|
{
|
|
m_min_x = m_max_x = i->first;
|
|
}
|
|
if(i->first < m_min_x)
|
|
{
|
|
m_min_x = i->first;
|
|
}
|
|
if(i->first > m_max_x)
|
|
{
|
|
m_max_x = i->first;
|
|
}
|
|
|
|
if((m_min_y == m_max_y) && (m_min_y == 0))
|
|
{
|
|
m_min_y = m_max_y = i->second;
|
|
}
|
|
if(i->second < m_min_y)
|
|
{
|
|
m_min_y = i->second;
|
|
}
|
|
if(i->second > m_max_y)
|
|
{
|
|
m_max_y = i->second;
|
|
}
|
|
|
|
++i;
|
|
}
|
|
} // void add(const std::map<double, double>& m, const std::string& name)
|
|
|
|
//! Plot pre-computed m_points data for function.
|
|
void plot(const std::string& title, const std::string& file,
|
|
const std::string& x_lable = std::string(), const std::string& y_lable = std::string())
|
|
{
|
|
using namespace boost::svg;
|
|
|
|
static const svg_color colors[5] =
|
|
{ // Colors for plot curves, used in turn.
|
|
darkblue,
|
|
darkred,
|
|
darkgreen,
|
|
darkorange,
|
|
chartreuse
|
|
};
|
|
|
|
std::cout << "Plotting Special Function " << title << " to file " << file << std::endl;
|
|
|
|
svg_2d_plot plot;
|
|
plot.image_x_size(600);
|
|
plot.image_y_size(400);
|
|
plot.copyright_holder("John Maddock").copyright_date("2008").boost_license_on(true);
|
|
plot.coord_precision(4); // Could be 3 for smaller plots?
|
|
plot.title(title).title_font_size(20).title_on(true);
|
|
plot.legend_on(m_has_legend);
|
|
|
|
double x_delta = (m_max_x - m_min_x) / 50;
|
|
double y_delta = (m_max_y - m_min_y) / 50;
|
|
plot.x_range(m_min_x, m_max_x + x_delta)
|
|
.y_range(m_min_y, m_max_y + y_delta);
|
|
plot.x_label_on(true).x_label(x_lable);
|
|
plot.y_label_on(true).y_label(y_lable);
|
|
plot.y_major_grid_on(false).x_major_grid_on(false);
|
|
plot.x_num_minor_ticks(3);
|
|
plot.y_num_minor_ticks(3);
|
|
//
|
|
// Work out axis tick intervals:
|
|
double l = std::floor(std::log10((m_max_x - m_min_x) / 10) + 0.5);
|
|
double interval = std::pow(10.0, (int)l);
|
|
if(((m_max_x - m_min_x) / interval) > 10)
|
|
interval *= 5;
|
|
plot.x_major_interval(interval);
|
|
l = std::floor(std::log10((m_max_y - m_min_y) / 10) + 0.5);
|
|
interval = std::pow(10.0, (int)l);
|
|
if(((m_max_y - m_min_y) / interval) > 10)
|
|
interval *= 5;
|
|
plot.y_major_interval(interval);
|
|
plot.plot_window_on(true);
|
|
plot.plot_border_color(lightslategray)
|
|
.background_border_color(lightslategray)
|
|
.legend_border_color(lightslategray)
|
|
.legend_background_color(white);
|
|
|
|
int color_index = 0; // Cycle through the colors for each curve.
|
|
|
|
for(std::list<std::pair<std::string, std::map<double,double> > >::const_iterator i = m_points.begin();
|
|
i != m_points.end(); ++i)
|
|
{
|
|
plot.plot(i->second, i->first)
|
|
.line_on(true)
|
|
.line_color(colors[color_index])
|
|
.line_width(1.)
|
|
.shape(none);
|
|
if(i->first.size())
|
|
++color_index;
|
|
color_index = color_index % (sizeof(colors)/sizeof(colors[0]));
|
|
}
|
|
plot.write(file);
|
|
} // void plot(const std::string& title, const std::string& file,
|
|
|
|
void clear()
|
|
{
|
|
m_points.clear();
|
|
m_min_x = m_min_y = m_max_x = m_max_y = 0;
|
|
m_has_legend = false;
|
|
} // clear
|
|
|
|
private:
|
|
std::list<std::pair<std::string, std::map<double, double> > > m_points;
|
|
double m_min_x, m_max_x, m_min_y, m_max_y;
|
|
bool m_has_legend;
|
|
};
|
|
|
|
template <class F>
|
|
struct location_finder
|
|
{
|
|
location_finder(F _f, double t, double x0) : f(_f), target(t), x_off(x0){}
|
|
|
|
double operator()(double x)
|
|
{
|
|
try
|
|
{
|
|
return f(x + x_off) - target;
|
|
}
|
|
catch(const std::overflow_error&)
|
|
{
|
|
return boost::math::tools::max_value<double>();
|
|
}
|
|
catch(const std::domain_error&)
|
|
{
|
|
if(x + x_off == x_off)
|
|
return f(x_off + boost::math::tools::epsilon<double>() * x_off);
|
|
throw;
|
|
}
|
|
}
|
|
|
|
private:
|
|
F f;
|
|
double target;
|
|
double x_off;
|
|
};
|
|
|
|
template <class F>
|
|
double find_end_point(F f, double x0, double target, bool rising, double x_off = 0)
|
|
{
|
|
boost::math::tools::eps_tolerance<double> tol(50);
|
|
boost::uintmax_t max_iter = 1000;
|
|
return x_off + boost::math::tools::bracket_and_solve_root(
|
|
location_finder<F>(f, target, x_off),
|
|
x0,
|
|
1.5,
|
|
rising,
|
|
tol,
|
|
max_iter).first;
|
|
}
|
|
|
|
double sqrt1pm1(double x)
|
|
{
|
|
return boost::math::sqrt1pm1(x);
|
|
}
|
|
|
|
double lbeta(double a, double b)
|
|
{
|
|
return std::log(boost::math::beta(a, b));
|
|
}
|
|
|
|
int main()
|
|
{
|
|
try
|
|
{
|
|
function_arity1_plotter plot;
|
|
|
|
// Functions may have varying numbers and types of parameters.
|
|
// plot.add calls must use the appropriate function type.
|
|
// Not all function types may be used, so can ignore any warning like
|
|
// "C4101: 'f4': unreferenced local variable"
|
|
double(*f)(double); // Simplest function type, suits most functions.
|
|
double(*f2)(double, double);
|
|
double(*f2u)(unsigned, double);
|
|
double(*f2i)(int, double);
|
|
double(*f3)(double, double, double);
|
|
double(*f4)(double, double, double, double);
|
|
double max_val; // Hold evaluated value of function for use in find_end_point.
|
|
|
|
f = boost::math::zeta;
|
|
plot.add(f, find_end_point(f, 0.1, 40.0, false, 1.0), 10, "");
|
|
plot.add(f, -20, find_end_point(f, -0.1, -40.0, false, 1.0), "");
|
|
plot.plot("Zeta Function Over [-20,10]", "zeta1.svg", "z", "zeta(z)");
|
|
|
|
plot.clear();
|
|
plot.add(f, -14, 0, "");
|
|
plot.plot("Zeta Function Over [-14,0]", "zeta2.svg", "z", "zeta(z)");
|
|
|
|
f = boost::math::tgamma;
|
|
max_val = f(6);
|
|
plot.clear();
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false), 6, "");
|
|
plot.add(f, find_end_point(f, 0.1, -max_val, true, -1), find_end_point(f, -0.1, -max_val, false), "");
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false, -2), find_end_point(f, -0.1, max_val, true, -1), "");
|
|
plot.add(f, find_end_point(f, 0.1, -max_val, true, -3), find_end_point(f, -0.1, -max_val, false, -2), "");
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false, -4), find_end_point(f, -0.1, max_val, true, -3), "");
|
|
plot.plot("tgamma", "tgamma.svg", "z", "tgamma(z)");
|
|
|
|
f = boost::math::lgamma;
|
|
max_val = f(10);
|
|
plot.clear();
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false), 10, "");
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false, -1), find_end_point(f, -0.1, max_val, true), "");
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false, -2), find_end_point(f, -0.1, max_val, true, -1), "");
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false, -3), find_end_point(f, -0.1, max_val, true, -2), "");
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false, -4), find_end_point(f, -0.1, max_val, true, -3), "");
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false, -5), find_end_point(f, -0.1, max_val, true, -4), "");
|
|
plot.plot("lgamma", "lgamma.svg", "z", "lgamma(z)");
|
|
|
|
f = boost::math::digamma;
|
|
max_val = 10;
|
|
plot.clear();
|
|
plot.add(f, find_end_point(f, 0.1, -max_val, true), 10, "");
|
|
plot.add(f, find_end_point(f, 0.1, -max_val, true, -1), find_end_point(f, -0.1, max_val, true), "");
|
|
plot.add(f, find_end_point(f, 0.1, -max_val, true, -2), find_end_point(f, -0.1, max_val, true, -1), "");
|
|
plot.add(f, find_end_point(f, 0.1, -max_val, true, -3), find_end_point(f, -0.1, max_val, true, -2), "");
|
|
plot.add(f, find_end_point(f, 0.1, -max_val, true, -4), find_end_point(f, -0.1, max_val, true, -3), "");
|
|
plot.plot("digamma", "digamma.svg", "z", "digamma(z)");
|
|
|
|
|
|
f = boost::math::erf;
|
|
plot.clear();
|
|
plot.add(f, -3, 3, "erf");
|
|
plot.plot("erf", "erf.svg", "z", "erf(z)");
|
|
|
|
f = boost::math::erfc;
|
|
plot.clear();
|
|
plot.add(f, -3, 3, "erfc");
|
|
plot.plot("erfc", "erfc.svg", "z", "erfc(z)");
|
|
|
|
f = boost::math::erf_inv;
|
|
plot.clear();
|
|
plot.add(f, find_end_point(f, 0.1, -3, true, -1), find_end_point(f, -0.1, 3, true, 1), "");
|
|
plot.plot("erf_inv", "erf_inv.svg", "z", "erf_inv(z)");
|
|
f = boost::math::erfc_inv;
|
|
plot.clear();
|
|
plot.add(f, find_end_point(f, 0.1, 3, false), find_end_point(f, -0.1, -3, false, 2), "");
|
|
plot.plot("erfc_inv", "erfc_inv.svg", "z", "erfc_inv(z)");
|
|
|
|
f = boost::math::log1p;
|
|
plot.clear();
|
|
plot.add(f, find_end_point(f, 0.1, -10, true, -1), 10, "");
|
|
plot.plot("log1p", "log1p.svg", "z", "log1p(z)");
|
|
|
|
f = boost::math::expm1;
|
|
plot.clear();
|
|
plot.add(f, -4, 2, "");
|
|
plot.plot("expm1", "expm1.svg", "z", "expm1(z)");
|
|
|
|
f = boost::math::cbrt;
|
|
plot.clear();
|
|
plot.add(f, -10, 10, "");
|
|
plot.plot("cbrt", "cbrt.svg", "z", "cbrt(z)");
|
|
|
|
f = sqrt1pm1;
|
|
plot.clear();
|
|
plot.add(f, find_end_point(f, 0.1, -10, true, -1), 5, "");
|
|
plot.plot("sqrt1pm1", "sqrt1pm1.svg", "z", "sqrt1pm1(z)");
|
|
|
|
f2 = boost::math::powm1;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0.0001, _1), find_end_point(boost::bind(f2, 0.0001, _1), -1, 10, false), 5, "a=0.0001");
|
|
plot.add(boost::bind(f2, 0.001, _1), find_end_point(boost::bind(f2, 0.001, _1), -1, 10, false), 5, "a=0.001");
|
|
plot.add(boost::bind(f2, 0.01, _1), find_end_point(boost::bind(f2, 0.01, _1), -1, 10, false), 5, "a=0.01");
|
|
plot.add(boost::bind(f2, 0.1, _1), find_end_point(boost::bind(f2, 0.1, _1), -1, 10, false), 5, "a=0.1");
|
|
plot.add(boost::bind(f2, 0.75, _1), -5, 5, "a=0.75");
|
|
plot.add(boost::bind(f2, 1.25, _1), -5, 5, "a=1.25");
|
|
plot.plot("powm1", "powm1.svg", "z", "powm1(a, z)");
|
|
|
|
f = boost::math::sinc_pi;
|
|
plot.clear();
|
|
plot.add(f, -10, 10, "");
|
|
plot.plot("sinc_pi", "sinc_pi.svg", "z", "sinc_pi(z)");
|
|
|
|
f = boost::math::sinhc_pi;
|
|
plot.clear();
|
|
plot.add(f, -5, 5, "");
|
|
plot.plot("sinhc_pi", "sinhc_pi.svg", "z", "sinhc_pi(z)");
|
|
|
|
f = boost::math::acosh;
|
|
plot.clear();
|
|
plot.add(f, 1, 10, "acosh");
|
|
plot.plot("acosh", "acosh.svg", "z", "acosh(z)");
|
|
|
|
f = boost::math::asinh;
|
|
plot.clear();
|
|
plot.add(f, -10, 10, "");
|
|
plot.plot("asinh", "asinh.svg", "z", "asinh(z)");
|
|
|
|
f = boost::math::atanh;
|
|
plot.clear();
|
|
plot.add(f, find_end_point(f, 0.1, -5, true, -1), find_end_point(f, -0.1, 5, true, 1), "");
|
|
plot.plot("atanh", "atanh.svg", "z", "atanh(z)");
|
|
|
|
f2 = boost::math::tgamma_delta_ratio;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, _1, -0.5), 1, 40, "delta = -0.5");
|
|
plot.add(boost::bind(f2, _1, -0.2), 1, 40, "delta = -0.2");
|
|
plot.add(boost::bind(f2, _1, -0.1), 1, 40, "delta = -0.1");
|
|
plot.add(boost::bind(f2, _1, 0.1), 1, 40, "delta = 0.1");
|
|
plot.add(boost::bind(f2, _1, 0.2), 1, 40, "delta = 0.2");
|
|
plot.add(boost::bind(f2, _1, 0.5), 1, 40, "delta = 0.5");
|
|
plot.add(boost::bind(f2, _1, 1.0), 1, 40, "delta = 1.0");
|
|
plot.plot("tgamma_delta_ratio", "tgamma_delta_ratio.svg", "z", "tgamma_delta_ratio(delta, z)");
|
|
|
|
f2 = boost::math::gamma_p;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0.5, _1), 0, 20, "a = 0.5");
|
|
plot.add(boost::bind(f2, 1.0, _1), 0, 20, "a = 1.0");
|
|
plot.add(boost::bind(f2, 5.0, _1), 0, 20, "a = 5.0");
|
|
plot.add(boost::bind(f2, 10.0, _1), 0, 20, "a = 10.0");
|
|
plot.plot("gamma_p", "gamma_p.svg", "z", "gamma_p(a, z)");
|
|
|
|
f2 = boost::math::gamma_q;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0.5, _1), 0, 20, "a = 0.5");
|
|
plot.add(boost::bind(f2, 1.0, _1), 0, 20, "a = 1.0");
|
|
plot.add(boost::bind(f2, 5.0, _1), 0, 20, "a = 5.0");
|
|
plot.add(boost::bind(f2, 10.0, _1), 0, 20, "a = 10.0");
|
|
plot.plot("gamma_q", "gamma_q.svg", "z", "gamma_q(a, z)");
|
|
|
|
f2 = lbeta;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0.5, _1), 0.00001, 5, "a = 0.5");
|
|
plot.add(boost::bind(f2, 1.0, _1), 0.00001, 5, "a = 1.0");
|
|
plot.add(boost::bind(f2, 5.0, _1), 0.00001, 5, "a = 5.0");
|
|
plot.add(boost::bind(f2, 10.0, _1), 0.00001, 5, "a = 10.0");
|
|
plot.plot("beta", "beta.svg", "z", "log(beta(a, z))");
|
|
|
|
f = boost::math::expint;
|
|
max_val = f(4);
|
|
plot.clear();
|
|
plot.add(f, find_end_point(f, 0.1, -max_val, true), 4, "");
|
|
plot.add(f, -3, find_end_point(f, -0.1, -max_val, false), "");
|
|
plot.plot("Exponential Integral Ei", "expint_i.svg", "z", "expint(z)");
|
|
|
|
f2u = boost::math::expint;
|
|
max_val = 1;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2u, 1, _1), find_end_point(boost::bind(f2u, 1, _1), 0.1, max_val, false), 2, "n = 1 ");
|
|
plot.add(boost::bind(f2u, 2, _1), find_end_point(boost::bind(f2u, 2, _1), 0.1, max_val, false), 2, "n = 2 ");
|
|
plot.add(boost::bind(f2u, 3, _1), 0, 2, "n = 3 ");
|
|
plot.add(boost::bind(f2u, 4, _1), 0, 2, "n = 4 ");
|
|
plot.plot("Exponential Integral En", "expint2.svg", "z", "expint(n, z)");
|
|
|
|
f3 = boost::math::ibeta;
|
|
plot.clear();
|
|
plot.add(boost::bind(f3, 9, 1, _1), 0, 1, "a = 9, b = 1");
|
|
plot.add(boost::bind(f3, 7, 2, _1), 0, 1, "a = 7, b = 2");
|
|
plot.add(boost::bind(f3, 5, 5, _1), 0, 1, "a = 5, b = 5");
|
|
plot.add(boost::bind(f3, 2, 7, _1), 0, 1, "a = 2, b = 7");
|
|
plot.add(boost::bind(f3, 1, 9, _1), 0, 1, "a = 1, b = 9");
|
|
plot.plot("ibeta", "ibeta.svg", "z", "ibeta(a, b, z)");
|
|
|
|
f2i = boost::math::legendre_p;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2i, 1, _1), -1, 1, "l = 1");
|
|
plot.add(boost::bind(f2i, 2, _1), -1, 1, "l = 2");
|
|
plot.add(boost::bind(f2i, 3, _1), -1, 1, "l = 3");
|
|
plot.add(boost::bind(f2i, 4, _1), -1, 1, "l = 4");
|
|
plot.add(boost::bind(f2i, 5, _1), -1, 1, "l = 5");
|
|
plot.plot("Legendre Polynomials", "legendre_p.svg", "x", "legendre_p(l, x)");
|
|
|
|
f2u = boost::math::legendre_q;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2u, 1, _1), -0.95, 0.95, "l = 1");
|
|
plot.add(boost::bind(f2u, 2, _1), -0.95, 0.95, "l = 2");
|
|
plot.add(boost::bind(f2u, 3, _1), -0.95, 0.95, "l = 3");
|
|
plot.add(boost::bind(f2u, 4, _1), -0.95, 0.95, "l = 4");
|
|
plot.add(boost::bind(f2u, 5, _1), -0.95, 0.95, "l = 5");
|
|
plot.plot("Legendre Polynomials of the Second Kind", "legendre_q.svg", "x", "legendre_q(l, x)");
|
|
|
|
f2u = boost::math::laguerre;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2u, 0, _1), -5, 10, "n = 0");
|
|
plot.add(boost::bind(f2u, 1, _1), -5, 10, "n = 1");
|
|
plot.add(boost::bind(f2u, 2, _1),
|
|
find_end_point(boost::bind(f2u, 2, _1), -2, 20, false),
|
|
find_end_point(boost::bind(f2u, 2, _1), 4, 20, true),
|
|
"n = 2");
|
|
plot.add(boost::bind(f2u, 3, _1),
|
|
find_end_point(boost::bind(f2u, 3, _1), -2, 20, false),
|
|
find_end_point(boost::bind(f2u, 3, _1), 1, 20, false, 8),
|
|
"n = 3");
|
|
plot.add(boost::bind(f2u, 4, _1),
|
|
find_end_point(boost::bind(f2u, 4, _1), -2, 20, false),
|
|
find_end_point(boost::bind(f2u, 4, _1), 1, 20, true, 8),
|
|
"n = 4");
|
|
plot.add(boost::bind(f2u, 5, _1),
|
|
find_end_point(boost::bind(f2u, 5, _1), -2, 20, false),
|
|
find_end_point(boost::bind(f2u, 5, _1), 1, 20, true, 8),
|
|
"n = 5");
|
|
plot.plot("Laguerre Polynomials", "laguerre.svg", "x", "laguerre(n, x)");
|
|
|
|
f2u = boost::math::hermite;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2u, 0, _1), -1.8, 1.8, "n = 0");
|
|
plot.add(boost::bind(f2u, 1, _1), -1.8, 1.8, "n = 1");
|
|
plot.add(boost::bind(f2u, 2, _1), -1.8, 1.8, "n = 2");
|
|
plot.add(boost::bind(f2u, 3, _1), -1.8, 1.8, "n = 3");
|
|
plot.add(boost::bind(f2u, 4, _1), -1.8, 1.8, "n = 4");
|
|
plot.plot("Hermite Polynomials", "hermite.svg", "x", "hermite(n, x)");
|
|
|
|
f2 = boost::math::cyl_bessel_j;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), -20, 20, "v = 0");
|
|
plot.add(boost::bind(f2, 1, _1), -20, 20, "v = 1");
|
|
plot.add(boost::bind(f2, 2, _1), -20, 20, "v = 2");
|
|
plot.add(boost::bind(f2, 3, _1), -20, 20, "v = 3");
|
|
plot.add(boost::bind(f2, 4, _1), -20, 20, "v = 4");
|
|
plot.plot("Bessel J", "cyl_bessel_j.svg", "x", "cyl_bessel_j(v, x)");
|
|
|
|
f2 = boost::math::cyl_neumann;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), find_end_point(boost::bind(f2, 0, _1), 0.1, -5, true), 20, "v = 0");
|
|
plot.add(boost::bind(f2, 1, _1), find_end_point(boost::bind(f2, 1, _1), 0.1, -5, true), 20, "v = 1");
|
|
plot.add(boost::bind(f2, 2, _1), find_end_point(boost::bind(f2, 2, _1), 0.1, -5, true), 20, "v = 2");
|
|
plot.add(boost::bind(f2, 3, _1), find_end_point(boost::bind(f2, 3, _1), 0.1, -5, true), 20, "v = 3");
|
|
plot.add(boost::bind(f2, 4, _1), find_end_point(boost::bind(f2, 4, _1), 0.1, -5, true), 20, "v = 4");
|
|
plot.plot("Bessel Y", "cyl_neumann.svg", "x", "cyl_neumann(v, x)");
|
|
|
|
f2 = boost::math::cyl_bessel_i;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), find_end_point(boost::bind(f2, 0, _1), -0.1, 20, false), find_end_point(boost::bind(f2, 0, _1), 0.1, 20, true), "v = 0");
|
|
plot.add(boost::bind(f2, 2, _1), find_end_point(boost::bind(f2, 2, _1), -0.1, 20, false), find_end_point(boost::bind(f2, 2, _1), 0.1, 20, true), "v = 2");
|
|
plot.add(boost::bind(f2, 5, _1), find_end_point(boost::bind(f2, 5, _1), -0.1, -20, true), find_end_point(boost::bind(f2, 5, _1), 0.1, 20, true), "v = 5");
|
|
plot.add(boost::bind(f2, 7, _1), find_end_point(boost::bind(f2, 7, _1), -0.1, -20, true), find_end_point(boost::bind(f2, 7, _1), 0.1, 20, true), "v = 7");
|
|
plot.add(boost::bind(f2, 10, _1), find_end_point(boost::bind(f2, 10, _1), -0.1, 20, false), find_end_point(boost::bind(f2, 10, _1), 0.1, 20, true), "v = 10");
|
|
plot.plot("Bessel I", "cyl_bessel_i.svg", "x", "cyl_bessel_i(v, x)");
|
|
|
|
f2 = boost::math::cyl_bessel_k;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), find_end_point(boost::bind(f2, 0, _1), 0.1, 10, false), 10, "v = 0");
|
|
plot.add(boost::bind(f2, 2, _1), find_end_point(boost::bind(f2, 2, _1), 0.1, 10, false), 10, "v = 2");
|
|
plot.add(boost::bind(f2, 5, _1), find_end_point(boost::bind(f2, 5, _1), 0.1, 10, false), 10, "v = 5");
|
|
plot.add(boost::bind(f2, 7, _1), find_end_point(boost::bind(f2, 7, _1), 0.1, 10, false), 10, "v = 7");
|
|
plot.add(boost::bind(f2, 10, _1), find_end_point(boost::bind(f2, 10, _1), 0.1, 10, false), 10, "v = 10");
|
|
plot.plot("Bessel K", "cyl_bessel_k.svg", "x", "cyl_bessel_k(v, x)");
|
|
|
|
f2u = boost::math::sph_bessel;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2u, 0, _1), 0, 20, "v = 0");
|
|
plot.add(boost::bind(f2u, 2, _1), 0, 20, "v = 2");
|
|
plot.add(boost::bind(f2u, 5, _1), 0, 20, "v = 5");
|
|
plot.add(boost::bind(f2u, 7, _1), 0, 20, "v = 7");
|
|
plot.add(boost::bind(f2u, 10, _1), 0, 20, "v = 10");
|
|
plot.plot("Bessel j", "sph_bessel.svg", "x", "sph_bessel(v, x)");
|
|
|
|
f2u = boost::math::sph_neumann;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2u, 0, _1), find_end_point(boost::bind(f2u, 0, _1), 0.1, -5, true), 20, "v = 0");
|
|
plot.add(boost::bind(f2u, 2, _1), find_end_point(boost::bind(f2u, 2, _1), 0.1, -5, true), 20, "v = 2");
|
|
plot.add(boost::bind(f2u, 5, _1), find_end_point(boost::bind(f2u, 5, _1), 0.1, -5, true), 20, "v = 5");
|
|
plot.add(boost::bind(f2u, 7, _1), find_end_point(boost::bind(f2u, 7, _1), 0.1, -5, true), 20, "v = 7");
|
|
plot.add(boost::bind(f2u, 10, _1), find_end_point(boost::bind(f2u, 10, _1), 0.1, -5, true), 20, "v = 10");
|
|
plot.plot("Bessel y", "sph_neumann.svg", "x", "sph_neumann(v, x)");
|
|
|
|
f4 = boost::math::ellint_rj;
|
|
plot.clear();
|
|
plot.add(boost::bind(f4, _1, _1, _1, _1), find_end_point(boost::bind(f4, _1, _1, _1, _1), 0.1, 10, false), 4, "RJ");
|
|
f3 = boost::math::ellint_rf;
|
|
plot.add(boost::bind(f3, _1, _1, _1), find_end_point(boost::bind(f3, _1, _1, _1), 0.1, 10, false), 4, "RF");
|
|
plot.plot("Elliptic Integrals", "ellint_carlson.svg", "x", "");
|
|
|
|
f2 = boost::math::ellint_1;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, _1, 0.5), -0.9, 0.9, "φ=0.5");
|
|
plot.add(boost::bind(f2, _1, 0.75), -0.9, 0.9, "φ=0.75");
|
|
plot.add(boost::bind(f2, _1, 1.25), -0.9, 0.9, "φ=1.25");
|
|
plot.add(boost::bind(f2, _1, boost::math::constants::pi<double>() / 2), -0.9, 0.9, "φ=π/2");
|
|
plot.plot("Elliptic Of the First Kind", "ellint_1.svg", "k", "ellint_1(k, phi)");
|
|
|
|
f2 = boost::math::ellint_2;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, _1, 0.5), -1, 1, "φ=0.5");
|
|
plot.add(boost::bind(f2, _1, 0.75), -1, 1, "φ=0.75");
|
|
plot.add(boost::bind(f2, _1, 1.25), -1, 1, "φ=1.25");
|
|
plot.add(boost::bind(f2, _1, boost::math::constants::pi<double>() / 2), -1, 1, "φ=π/2");
|
|
plot.plot("Elliptic Of the Second Kind", "ellint_2.svg", "k", "ellint_2(k, phi)");
|
|
|
|
f3 = boost::math::ellint_3;
|
|
plot.clear();
|
|
plot.add(boost::bind(f3, _1, 0, 1.25), -1, 1, "n=0 φ=1.25");
|
|
plot.add(boost::bind(f3, _1, 0.5, 1.25), -1, 1, "n=0.5 φ=1.25");
|
|
plot.add(boost::bind(f3, _1, 0.25, boost::math::constants::pi<double>() / 2),
|
|
find_end_point(
|
|
boost::bind(f3, _1, 0.25, boost::math::constants::pi<double>() / 2),
|
|
0.5, 4, false, -1),
|
|
find_end_point(
|
|
boost::bind(f3, _1, 0.25, boost::math::constants::pi<double>() / 2),
|
|
-0.5, 4, true, 1), "n=0.25 φ=π/2");
|
|
plot.add(boost::bind(f3, _1, 0.75, boost::math::constants::pi<double>() / 2),
|
|
find_end_point(
|
|
boost::bind(f3, _1, 0.75, boost::math::constants::pi<double>() / 2),
|
|
0.5, 4, false, -1),
|
|
find_end_point(
|
|
boost::bind(f3, _1, 0.75, boost::math::constants::pi<double>() / 2),
|
|
-0.5, 4, true, 1), "n=0.75 φ=π/2");
|
|
plot.plot("Elliptic Of the Third Kind", "ellint_3.svg", "k", "ellint_3(k, n, phi)");
|
|
|
|
f2 = boost::math::jacobi_sn;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), -10, 10, "k=0");
|
|
plot.add(boost::bind(f2, 0.5, _1), -10, 10, "k=0.5");
|
|
plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75");
|
|
plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95");
|
|
plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1");
|
|
plot.plot("Jacobi Elliptic sn", "jacobi_sn.svg", "k", "jacobi_sn(k, u)");
|
|
|
|
f2 = boost::math::jacobi_cn;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), -10, 10, "k=0");
|
|
plot.add(boost::bind(f2, 0.5, _1), -10, 10, "k=0.5");
|
|
plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75");
|
|
plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95");
|
|
plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1");
|
|
plot.plot("Jacobi Elliptic cn", "jacobi_cn.svg", "k", "jacobi_cn(k, u)");
|
|
|
|
f2 = boost::math::jacobi_dn;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), -10, 10, "k=0");
|
|
plot.add(boost::bind(f2, 0.5, _1), -10, 10, "k=0.5");
|
|
plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75");
|
|
plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95");
|
|
plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1");
|
|
plot.plot("Jacobi Elliptic dn", "jacobi_dn.svg", "k", "jacobi_dn(k, u)");
|
|
|
|
f2 = boost::math::jacobi_cd;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), -10, 10, "k=0");
|
|
plot.add(boost::bind(f2, 0.5, _1), -10, 10, "k=0.5");
|
|
plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75");
|
|
plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95");
|
|
plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1");
|
|
plot.plot("Jacobi Elliptic cd", "jacobi_cd.svg", "k", "jacobi_cd(k, u)");
|
|
|
|
f2 = boost::math::jacobi_cs;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), 0.1, 3, "k=0");
|
|
plot.add(boost::bind(f2, 0.5, _1), 0.1, 3, "k=0.5");
|
|
plot.add(boost::bind(f2, 0.75, _1), 0.1, 3, "k=0.75");
|
|
plot.add(boost::bind(f2, 0.95, _1), 0.1, 3, "k=0.95");
|
|
plot.add(boost::bind(f2, 1, _1), 0.1, 3, "k=1");
|
|
plot.plot("Jacobi Elliptic cs", "jacobi_cs.svg", "k", "jacobi_cs(k, u)");
|
|
|
|
f2 = boost::math::jacobi_dc;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), -10, 10, "k=0");
|
|
plot.add(boost::bind(f2, 0.5, _1), -10, 10, "k=0.5");
|
|
plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75");
|
|
plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95");
|
|
plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1");
|
|
plot.plot("Jacobi Elliptic dc", "jacobi_dc.svg", "k", "jacobi_dc(k, u)");
|
|
|
|
f2 = boost::math::jacobi_ds;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), 0.1, 3, "k=0");
|
|
plot.add(boost::bind(f2, 0.5, _1), 0.1, 3, "k=0.5");
|
|
plot.add(boost::bind(f2, 0.75, _1), 0.1, 3, "k=0.75");
|
|
plot.add(boost::bind(f2, 0.95, _1), 0.1, 3, "k=0.95");
|
|
plot.add(boost::bind(f2, 1, _1), 0.1, 3, "k=1");
|
|
plot.plot("Jacobi Elliptic ds", "jacobi_ds.svg", "k", "jacobi_ds(k, u)");
|
|
|
|
f2 = boost::math::jacobi_nc;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), -5, 5, "k=0");
|
|
plot.add(boost::bind(f2, 0.5, _1), -5, 5, "k=0.5");
|
|
plot.add(boost::bind(f2, 0.75, _1), -5, 5, "k=0.75");
|
|
plot.add(boost::bind(f2, 0.95, _1), -5, 5, "k=0.95");
|
|
plot.add(boost::bind(f2, 1, _1), -5, 5, "k=1");
|
|
plot.plot("Jacobi Elliptic nc", "jacobi_nc.svg", "k", "jacobi_nc(k, u)");
|
|
|
|
f2 = boost::math::jacobi_ns;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), 0.1, 4, "k=0");
|
|
plot.add(boost::bind(f2, 0.5, _1), 0.1, 4, "k=0.5");
|
|
plot.add(boost::bind(f2, 0.75, _1), 0.1, 4, "k=0.75");
|
|
plot.add(boost::bind(f2, 0.95, _1), 0.1, 4, "k=0.95");
|
|
plot.add(boost::bind(f2, 1, _1), 0.1, 4, "k=1");
|
|
plot.plot("Jacobi Elliptic ns", "jacobi_ns.svg", "k", "jacobi_ns(k, u)");
|
|
|
|
f2 = boost::math::jacobi_nd;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), -2, 2, "k=0");
|
|
plot.add(boost::bind(f2, 0.5, _1), -2, 2, "k=0.5");
|
|
plot.add(boost::bind(f2, 0.75, _1), -2, 2, "k=0.75");
|
|
plot.add(boost::bind(f2, 0.95, _1), -2, 2, "k=0.95");
|
|
plot.add(boost::bind(f2, 1, _1), -2, 2, "k=1");
|
|
plot.plot("Jacobi Elliptic nd", "jacobi_nd.svg", "k", "jacobi_nd(k, u)");
|
|
|
|
f2 = boost::math::jacobi_sc;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), -5, 5, "k=0");
|
|
plot.add(boost::bind(f2, 0.5, _1), -5, 5, "k=0.5");
|
|
plot.add(boost::bind(f2, 0.75, _1), -5, 5, "k=0.75");
|
|
plot.add(boost::bind(f2, 0.95, _1), -5, 5, "k=0.95");
|
|
plot.add(boost::bind(f2, 1, _1), -5, 5, "k=1");
|
|
plot.plot("Jacobi Elliptic sc", "jacobi_sc.svg", "k", "jacobi_sc(k, u)");
|
|
|
|
f2 = boost::math::jacobi_sd;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2, 0, _1), -2.5, 2.5, "k=0");
|
|
plot.add(boost::bind(f2, 0.5, _1), -2.5, 2.5, "k=0.5");
|
|
plot.add(boost::bind(f2, 0.75, _1), -2.5, 2.5, "k=0.75");
|
|
plot.add(boost::bind(f2, 0.95, _1), -2.5, 2.5, "k=0.95");
|
|
plot.add(boost::bind(f2, 1, _1), -2.5, 2.5, "k=1");
|
|
plot.plot("Jacobi Elliptic sd", "jacobi_sd.svg", "k", "jacobi_sd(k, u)");
|
|
|
|
f = boost::math::airy_ai;
|
|
plot.clear();
|
|
plot.add(f, -20, 20, "");
|
|
plot.plot("Ai", "airy_ai.svg", "z", "airy_ai(z)");
|
|
|
|
f = boost::math::airy_bi;
|
|
plot.clear();
|
|
plot.add(f, -20, 3, "");
|
|
plot.plot("Bi", "airy_bi.svg", "z", "airy_bi(z)");
|
|
|
|
f = boost::math::airy_ai_prime;
|
|
plot.clear();
|
|
plot.add(f, -20, 20, "");
|
|
plot.plot("Ai'", "airy_aip.svg", "z", "airy_ai_prime(z)");
|
|
|
|
f = boost::math::airy_bi_prime;
|
|
plot.clear();
|
|
plot.add(f, -20, 3, "");
|
|
plot.plot("Bi'", "airy_bip.svg", "z", "airy_bi_prime(z)");
|
|
|
|
f = boost::math::trigamma;
|
|
max_val = 30;
|
|
plot.clear();
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false), 5, "");
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false, -1), find_end_point(f, -0.1, max_val, true), "");
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false, -2), find_end_point(f, -0.1, max_val, true, -1), "");
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false, -3), find_end_point(f, -0.1, max_val, true, -2), "");
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false, -4), find_end_point(f, -0.1, max_val, true, -3), "");
|
|
plot.add(f, find_end_point(f, 0.1, max_val, false, -5), find_end_point(f, -0.1, max_val, true, -4), "");
|
|
plot.plot("Trigamma", "trigamma.svg", "x", "trigamma(x)");
|
|
|
|
f2i = boost::math::polygamma;
|
|
max_val = -50;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true), 5, "");
|
|
plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -1), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true), "");
|
|
plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -2), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -1), "");
|
|
plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -3), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -2), "");
|
|
plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -4), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -3), "");
|
|
plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -5), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -4), "");
|
|
plot.add(boost::bind(f2i, 2, _1), find_end_point(boost::bind(f2i, 2, _1), 0.1, max_val, true, -6), find_end_point(boost::bind(f2i, 2, _1), -0.1, -max_val, true, -5), "");
|
|
plot.plot("Polygamma", "polygamma2.svg", "x", "polygamma(2, x)");
|
|
|
|
max_val = 800;
|
|
plot.clear();
|
|
plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false), 5, "");
|
|
plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -1), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true), "");
|
|
plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -2), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -1), "");
|
|
plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -3), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -2), "");
|
|
plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -4), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -3), "");
|
|
plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -5), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -4), "");
|
|
plot.add(boost::bind(f2i, 3, _1), find_end_point(boost::bind(f2i, 3, _1), 0.1, max_val, false, -6), find_end_point(boost::bind(f2i, 3, _1), -0.1, max_val, true, -5), "");
|
|
plot.plot("Polygamma", "polygamma3.svg", "x", "polygamma(3, x)");
|
|
|
|
|
|
}
|
|
catch (const std::exception& ex)
|
|
{
|
|
std::cout << ex.what() << std::endl;
|
|
}
|
|
return 0;
|
|
}
|
|
|