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Initial commit of a program to plot PDF graphs.

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[SVN r42891]
This commit is contained in:
John Maddock
2008-01-21 11:27:56 +00:00
parent 88fc5d269d
commit 5eed81e70b
1 changed files with 374 additions and 0 deletions
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doc/sf_and_dist/graphs/dist_graphs.cpp Normal file
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// (C) Copyright John Maddock 2008.
// 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)
#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
#include <boost/math/distributions.hpp>
#include <boost/math/tools/roots.hpp>
#include <boost/svg_plot/svg_2d_plot.hpp>
#include <list>
#include <map>
#include <string>
template <class Dist>
struct value_finder
{
value_finder(Dist const& d, typename Dist::value_type v)
: m_dist(d), m_value(v) {}
inline typename Dist::value_type operator()(const typename Dist::value_type& x)
{
return pdf(m_dist, x) - m_value;
}
private:
Dist m_dist;
typename Dist::value_type m_value;
};
template <class Dist>
class distribution_plotter
{
public:
distribution_plotter() : m_min_x(0), m_max_x(0), m_min_y(0), m_max_y(0) {}
void add(const Dist& d, const std::string& name)
{
//
// Add to our list for later:
//
m_distributions.push_back(std::make_pair(name, d));
//
// Get the extent:
//
double a, b;
std::tr1::tie(a, b) = support(d);
//
// PDF maximimum is at the mode:
//
double mod;
try
{
mod = mode(d);
}
catch(const std::domain_error& )
{
mod = a;
}
if(mod <= a)
{
if(a)
mod = a * (1 + 1e-2);
else
mod = 1e-2;
}
double peek_y = pdf(d, mod);
double min_y = peek_y / 20;
//
// If the extent is "infinite" then find out how large it
// has to be for the PDF to decay to min_y:
//
if(a <= -(std::numeric_limits<double>::max)())
{
boost::uintmax_t max_iter = 500;
double guess = mod;
if((pdf(d, 0) > min_y) || (guess == 0))
guess = -1e-3;
a = boost::math::tools::bracket_and_solve_root(
value_finder<Dist>(d, min_y),
guess,
8.0,
true,
boost::math::tools::eps_tolerance<double>(10),
max_iter).first;
}
if(b >= (std::numeric_limits<double>::max)())
{
boost::uintmax_t max_iter = 500;
double guess = mod;
if(a <= 0)
if((pdf(d, 0) > min_y) || (guess == 0))
guess = 1e-3;
b = boost::math::tools::bracket_and_solve_root(
value_finder<Dist>(d, min_y),
guess,
8.0,
false,
boost::math::tools::eps_tolerance<double>(10),
max_iter).first;
}
//
// Recalculate peek_y and location of mod so that
// it's not too close to one end of the graph:
// otherwise we may be shooting off to infinity.
//
if(mod <= a + (b-a)/50)
{
mod = a + (b-a)/50;
}
if(mod >= b - (b-a)/50)
{
mod = b - (b-a)/50;
}
peek_y = pdf(d, mod);
//
// Now set our limits:
//
if(peek_y > m_max_y)
m_max_y = peek_y;
if(m_max_x == m_min_x)
{
m_max_x = b;
m_min_x = a;
}
else
{
if(a < m_min_x)
m_min_x = a;
if(b > m_max_x)
m_max_x = b;
}
}
void plot(const std::string& title, const std::string& file)
{
using namespace boost::svg;
static const svg_color colors[5] =
{
darkblue,
darkred,
darkgreen,
darkorange,
chartreuse
};
svg_2d_plot plot;
plot.image_size(750, 400);
plot.title_font_size(20);
plot.legend_title_font_size(15);
plot.title(title);
plot.legend_on(true).title_on(true);
//plot.x_major_labels_on(true).y_major_labels_on(true);
double x_delta = (m_max_x - m_min_x) / 10;
double y_delta = (m_max_y - m_min_y) / 10;
plot.x_range(m_min_x, m_max_x)
.y_range(m_min_y, m_max_y + y_delta);
plot.x_label_on(true).x_label("Random Variable");
plot.y_label_on(true).y_label("Probability");
plot.plot_border_color(lightslategray).legend_border_color(lightslategray).background_border_color(lightslategray);
//
// 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);
int color_index = 0;
for(std::list<std::pair<std::string, Dist> >::const_iterator i = m_distributions.begin();
i != m_distributions.end(); ++i)
{
double x = m_min_x;
double interval = (m_max_x - m_min_x) / 1000;
std::map<double, double> data;
while(x <= m_max_x)
{
data[x] = pdf(i->second, x);
x += interval;
}
plot.plot(data, i->first)
.line_on(true)
.line_color(colors[color_index])
.line_width(0.5)
.shape(none);
++color_index;
color_index = color_index % (sizeof(colors)/sizeof(colors[0]));
}
plot.write(file);
}
private:
std::list<std::pair<std::string, Dist> > m_distributions;
double m_min_x, m_max_x, m_min_y, m_max_y;
};
int main()
{
distribution_plotter<boost::math::gamma_distribution<> >
gamma_plotter;
gamma_plotter.add(boost::math::gamma_distribution<>(1), "shape = 0.5");
gamma_plotter.add(boost::math::gamma_distribution<>(2), "shape = 1");
gamma_plotter.add(boost::math::gamma_distribution<>(4), "shape = 3");
gamma_plotter.plot("Gamma Distribution PDF With Scale = 1", "gamma1_pdf.svg");
distribution_plotter<boost::math::gamma_distribution<> >
gamma_plotter2;
gamma_plotter2.add(boost::math::gamma_distribution<>(2, 0.5), "scale = 2");
gamma_plotter2.add(boost::math::gamma_distribution<>(2, 1), "scale = 0.5");
gamma_plotter2.add(boost::math::gamma_distribution<>(2, 2), "scale = 2");
gamma_plotter2.plot("Gamma Distribution PDF With Shape = 2", "gamma2_pdf.svg");
distribution_plotter<boost::math::normal>
normal_plotter;
normal_plotter.add(boost::math::normal(0, 1), "&#x3BC; = 0, &#x3C3; = 1");
normal_plotter.add(boost::math::normal(0, 0.5), "&#x3BC; = 0, &#x3C3; = 0.5");
normal_plotter.add(boost::math::normal(0, 2), "&#x3BC; = 0, &#x3C3; = 2");
normal_plotter.add(boost::math::normal(-1, 1), "&#x3BC; = -1, &#x3C3; = 1");
normal_plotter.add(boost::math::normal(1, 1), "&#x3BC; = 1, &#x3C3; = 1");
normal_plotter.plot("Normal Distribution PDF", "normal_pdf.svg");
distribution_plotter<boost::math::non_central_chi_squared>
nc_cs_plotter;
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 0), "v=20, l=0");
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 1), "v=20, l=1");
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 5), "v=20, l=5");
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 10), "v=20, l=10");
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 20), "v=20, l=20");
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 100), "v=20, l=100");
nc_cs_plotter.plot("Non Central Chi Squared PDF", "nccs_pdf.svg");
distribution_plotter<boost::math::beta_distribution<> >
beta_plotter;
beta_plotter.add(boost::math::beta_distribution<>(0.5, 0.5), "alpha=0.5, beta=0.5");
beta_plotter.add(boost::math::beta_distribution<>(5, 1), "alpha=5, beta=1");
beta_plotter.add(boost::math::beta_distribution<>(1, 3), "alpha=1, beta=3");
beta_plotter.add(boost::math::beta_distribution<>(2, 2), "alpha=2, beta=2");
beta_plotter.add(boost::math::beta_distribution<>(2, 5), "alpha=2, beta=5");
beta_plotter.plot("Beta Distribution PDF", "beta_pdf.svg");
distribution_plotter<boost::math::cauchy_distribution<> >
cauchy_plotter;
cauchy_plotter.add(boost::math::cauchy_distribution<>(-5, 1), "location = -5");
cauchy_plotter.add(boost::math::cauchy_distribution<>(0, 1), "location = 0");
cauchy_plotter.add(boost::math::cauchy_distribution<>(5, 1), "location = 5");
cauchy_plotter.plot("Cauchy Distribution PDF (scale = 1)", "cauchy_pdf1.svg");
distribution_plotter<boost::math::cauchy_distribution<> >
cauchy_plotter2;
cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 0.5), "scale = 0.5");
cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 1), "scale = 1");
cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 2), "scale = 2");
cauchy_plotter2.plot("Cauchy Distribution PDF (location = 0)", "cauchy_pdf2.svg");
distribution_plotter<boost::math::chi_squared_distribution<> >
chi_squared_plotter;
chi_squared_plotter.add(boost::math::chi_squared_distribution<>(1), "v=1");
chi_squared_plotter.add(boost::math::chi_squared_distribution<>(2), "v=2");
chi_squared_plotter.add(boost::math::chi_squared_distribution<>(5), "v=5");
chi_squared_plotter.plot("Chi Squared Distribution PDF", "chi_squared_pdf.svg");
distribution_plotter<boost::math::exponential_distribution<> >
exponential_plotter;
exponential_plotter.add(boost::math::exponential_distribution<>(0.5), "&#x3BB;=1");
exponential_plotter.add(boost::math::exponential_distribution<>(1), "&#x3BB;=2");
exponential_plotter.add(boost::math::exponential_distribution<>(2), "&#x3BB;=5");
exponential_plotter.plot("Exponential Distribution PDF", "exponential_pdf.svg");
distribution_plotter<boost::math::extreme_value_distribution<> >
extreme_value_plotter;
extreme_value_plotter.add(boost::math::extreme_value_distribution<>(-5), "location=1");
extreme_value_plotter.add(boost::math::extreme_value_distribution<>(0), "location=2");
extreme_value_plotter.add(boost::math::extreme_value_distribution<>(5), "location=5");
extreme_value_plotter.plot("Extreme Value Distribution PDF (shape=1)", "extreme_value_pdf1.svg");
distribution_plotter<boost::math::extreme_value_distribution<> >
extreme_value_plotter2;
extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 0.5), "shape=0.5");
extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 1), "shape=1");
extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 2), "shape=2");
extreme_value_plotter2.plot("Extreme Value Distribution PDF (location=0)", "extreme_value_pdf2.svg");
distribution_plotter<boost::math::fisher_f_distribution<> >
fisher_f_plotter;
fisher_f_plotter.add(boost::math::fisher_f_distribution<>(4, 4), "n=4, m=4");
fisher_f_plotter.add(boost::math::fisher_f_distribution<>(10, 4), "n=10, m=4");
fisher_f_plotter.add(boost::math::fisher_f_distribution<>(10, 10), "n=10, m=10");
fisher_f_plotter.add(boost::math::fisher_f_distribution<>(4, 10), "n=4, m=10");
fisher_f_plotter.plot("F Distribution PDF", "fisher_f_pdf.svg");
distribution_plotter<boost::math::lognormal_distribution<> >
lognormal_plotter;
lognormal_plotter.add(boost::math::lognormal_distribution<>(-1), "location=-1");
lognormal_plotter.add(boost::math::lognormal_distribution<>(0), "location=0");
lognormal_plotter.add(boost::math::lognormal_distribution<>(1), "location=1");
lognormal_plotter.plot("Lognormal Distribution PDF (scale=1)", "lognormal_pdf1.svg");
distribution_plotter<boost::math::lognormal_distribution<> >
lognormal_plotter2;
lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 0.5), "scale=0.5");
lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 1), "scale=1");
lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 2), "scale=2");
lognormal_plotter2.plot("Lognormal Distribution PDF (location=0)", "lognormal_pdf2.svg");
distribution_plotter<boost::math::pareto_distribution<> >
pareto_plotter;
pareto_plotter.add(boost::math::pareto_distribution<>(1), "location=1");
pareto_plotter.add(boost::math::pareto_distribution<>(2), "location=2");
pareto_plotter.add(boost::math::pareto_distribution<>(3), "location=3");
pareto_plotter.plot("Pareto Distribution PDF (scale=1)", "pareto_pdf1.svg");
distribution_plotter<boost::math::pareto_distribution<> >
pareto_plotter2;
pareto_plotter2.add(boost::math::pareto_distribution<>(1, 0.5), "scale=0.5");
pareto_plotter2.add(boost::math::pareto_distribution<>(1, 1), "scale=1");
pareto_plotter2.add(boost::math::pareto_distribution<>(1, 2), "scale=2");
pareto_plotter2.plot("Pareto Distribution PDF (location=1)", "pareto_pdf2.svg");
distribution_plotter<boost::math::rayleigh_distribution<> >
rayleigh_plotter;
rayleigh_plotter.add(boost::math::rayleigh_distribution<>(0.5), "&#x3C3;=0.5");
rayleigh_plotter.add(boost::math::rayleigh_distribution<>(1), "&#x3C3;=1");
rayleigh_plotter.add(boost::math::rayleigh_distribution<>(2), "&#x3C3;=2");
rayleigh_plotter.add(boost::math::rayleigh_distribution<>(4), "&#x3C3;=4");
rayleigh_plotter.add(boost::math::rayleigh_distribution<>(10), "&#x3C3;=10");
rayleigh_plotter.plot("Rayleigh Distribution PDF", "rayleigh_pdf.svg");
distribution_plotter<boost::math::triangular_distribution<> >
triangular_plotter;
triangular_plotter.add(boost::math::triangular_distribution<>(-1,0,1), "{-1,0,1}");
triangular_plotter.add(boost::math::triangular_distribution<>(0,1,1), "{0,1,1}");
triangular_plotter.add(boost::math::triangular_distribution<>(0,1,3), "{0,1,3}");
triangular_plotter.add(boost::math::triangular_distribution<>(0,0.5,1), "{0,0.5,1}");
triangular_plotter.add(boost::math::triangular_distribution<>(-2,0,3), "{-2,0,3}");
triangular_plotter.plot("Triangular Distribution PDF", "triangular_pdf.svg");
distribution_plotter<boost::math::students_t_distribution<> >
students_t_plotter;
students_t_plotter.add(boost::math::students_t_distribution<>(1), "v=1");
students_t_plotter.add(boost::math::students_t_distribution<>(5), "v=5");
students_t_plotter.add(boost::math::students_t_distribution<>(30), "v=30");
students_t_plotter.plot("Students T Distribution PDF", "students_t_pdf.svg");
distribution_plotter<boost::math::weibull_distribution<> >
weibull_plotter;
weibull_plotter.add(boost::math::weibull_distribution<>(0.2), "shape=0.2");
weibull_plotter.add(boost::math::weibull_distribution<>(1), "shape=1");
weibull_plotter.add(boost::math::weibull_distribution<>(5), "shape=5");
weibull_plotter.plot("Weibull Distribution PDF (scale=1)", "weibull_pdf1.svg");
distribution_plotter<boost::math::weibull_distribution<> >
weibull_plotter2;
weibull_plotter2.add(boost::math::weibull_distribution<>(3, 0.5), "scale=0.5");
weibull_plotter2.add(boost::math::weibull_distribution<>(3, 1), "scale=1");
weibull_plotter2.add(boost::math::weibull_distribution<>(3, 2), "scale=2");
weibull_plotter2.plot("weibull Distribution PDF (shape=3)", "weibull_pdf2.svg");
distribution_plotter<boost::math::uniform_distribution<> >
uniform_plotter;
uniform_plotter.add(boost::math::uniform_distribution<>(0, 1), "{0,1}");
uniform_plotter.add(boost::math::uniform_distribution<>(0, 3), "{0,3}");
uniform_plotter.add(boost::math::uniform_distribution<>(-2, 3), "{-2,3}");
uniform_plotter.add(boost::math::uniform_distribution<>(-1, 1), "{-1,1}");
uniform_plotter.plot("Uniform Distribution PDF", "uniform_pdf.svg");
}