[Boost-commit] svn:boost r50075 - sandbox/math_toolkit/libs/math/example

Subject: [Boost-commit] svn:boost r50075 - sandbox/math_toolkit/libs/math/example
From: pbristow_at_[hidden]
Date: 2008-12-02 12:16:04

Author: pbristow
Date: 2008-12-02 12:16:03 EST (Tue, 02 Dec 2008)
New Revision: 50075
URL: http://svn.boost.org/trac/boost/changeset/50075

Log:
A very noddy example for Laplace distribution.  Better ideas?
Added:
   sandbox/math_toolkit/libs/math/example/laplace_example.cpp   (contents, props changed)

Added: sandbox/math_toolkit/libs/math/example/laplace_example.cpp
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/example/laplace_example.cpp	2008-12-02 12:16:03 EST (Tue, 02 Dec 2008)
@@ -0,0 +1,171 @@
+// laplace_example.cpp
+
+// Copyright Paul A. Bristow 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)
+
+// Example of using laplace (& comparing with normal) distribution.
+
+// Note that this file contains Quickbook mark-up as well as code
+// and comments, don't change any of the special comment mark-ups!
+
+//[laplace_example1
+/*`
+First we need some includes to access the laplace & normal distributions
+(and some std output of course).
+*/
+
+#include <boost/math/distributions/laplace.hpp> // for laplace_distribution
+  using boost::math::laplace; // typedef provides default type is double.
+#include <boost/math/distributions/normal.hpp> // for normal_distribution
+  using boost::math::normal; // typedef provides default type is double.
+
+#include <iostream>
+  using std::cout; using std::endl; using std::left; using std::showpoint; using std::noshowpoint;
+#include <iomanip>
+  using std::setw; using std::setprecision;
+#include <limits>
+  using std::numeric_limits;
+
+int main()
+{
+  cout << "Example: Laplace distribution." << endl;
+
+  try
+  {
+    { // Traditional tables and values.
+/*`Let's start by printing some traditional tables.
+*/      
+      double step = 1.; // in z 
+      double range = 4; // min and max z = -range to +range.
+      //int precision = 17; // traditional tables are only computed to much lower precision.
+      int precision = 4; // traditional table at much lower precision.
+      int width = 10; // for use with setw.
+
+      // Construct standard laplace & normal distributions l & s
+        normal s; // (default location or mean = zero, and scale or standard deviation = unity)
+        cout << "Standard normal distribution, mean or location = "<< s.location()
+          << ", standard deviation or scale = " << s.scale() << endl;
+        laplace l; // (default mean = zero, and standard deviation = unity)
+        cout << "Laplace normal distribution, location = "<< l.location()
+          << ", scale = " << l.scale() << endl;
+
+/*` First the probability distribution function (pdf).
+*/
+      cout << "Probability distribution function values" << endl;
+      cout << " z  PDF  normal     laplace    (difference)" << endl;
+      cout.precision(5);
+      for (double z = -range; z < range + step; z += step)
+      {
+        cout << left << setprecision(3) << setw(6) << z << " " 
+          << setprecision(precision) << setw(width) << pdf(s, z) << "  "
+          << setprecision(precision) << setw(width) << pdf(l, z)<<  "  ("
+          << setprecision(precision) << setw(width) << pdf(l, z) - pdf(s, z) // difference.
+          << ")" << endl;
+      }
+      cout.precision(6); // default
+/*`Notice how the laplace is less at z = 1 , but has 'fatter' tails at 2 and 3. 
+
+   And the area under the normal curve from -[infin] up to z,
+   the cumulative distribution function (cdf).
+*/
+      // For a standard distribution 
+      cout << "Standard location = "<< s.location()
+        << ", scale = " << s.scale() << endl;
+      cout << "Integral (area under the curve) from - infinity up to z " << endl;
+      cout << " z  CDF  normal     laplace    (difference)" << endl;
+      for (double z = -range; z < range + step; z += step)
+      {
+        cout << left << setprecision(3) << setw(6) << z << " " 
+          << setprecision(precision) << setw(width) << cdf(s, z) << "  "
+          << setprecision(precision) << setw(width) << cdf(l, z) <<  "  ("
+          << setprecision(precision) << setw(width) << cdf(l, z) - cdf(s, z) // difference.
+          << ")" << endl;
+      }
+      cout.precision(6); // default
+
+/*`
+Pretty-printing a traditional 2-dimensional table is left as an exercise for the student,
+but why bother now that the Boost Math Toolkit lets you write
+*/
+    double z = 2.; 
+    cout << "Area for gaussian z = " << z << " is " << cdf(s, z) << endl; // to get the area for z.
+    cout << "Area for laplace z = " << z << " is " << cdf(l, z) << endl; // 
+/*`
+Correspondingly, we can obtain the traditional 'critical' values for significance levels.
+For the 95% confidence level, the significance level usually called alpha,
+is 0.05 = 1 - 0.95 (for a one-sided test), so we can write
+*/
+     cout << "95% of gaussian area has a z below " << quantile(s, 0.95) << endl;
+     cout << "95% of laplace area has a z below " << quantile(l, 0.95) << endl;
+   // 95% of area has a z below 1.64485
+   // 95% of laplace area has a z below 2.30259
+/*`and a two-sided test (a comparison between two levels, rather than a one-sided test)
+
+*/
+     cout << "95% of gaussian area has a z between " << quantile(s, 0.975)
+       << " and " << -quantile(s, 0.975) << endl;
+     cout << "95% of laplace area has a z between " << quantile(l, 0.975)
+       << " and " << -quantile(l, 0.975) << endl;
+   // 95% of area has a z between 1.95996 and -1.95996
+   // 95% of laplace area has a z between 2.99573 and -2.99573
+/*`Notice how much wider z has to be to enclose 95% of the area.
+*/
+  }
+//] [/[laplace_example1]
+  }
+  catch(const std::exception& e)
+  { // Always useful to include try & catch blocks because default policies 
+    // are to throw exceptions on arguments that cause errors like underflow, overflow. 
+    // Lacking try & catch blocks, the program will abort without a message below,
+    // which may give some helpful clues as to the cause of the exception.
+    std::cout <<
+      "\n""Message from thrown exception was:\n   " << e.what() << std::endl;
+  }
+  return 0;
+}  // int main()
+
+
+/*
+
+Output is:
+
+Example: Laplace distribution.
+Standard normal distribution, mean or location = 0, standard deviation or scale = 1
+Laplace normal distribution, location = 0, scale = 1
+Probability distribution function values
+ z  PDF  normal     laplace    (difference)
+-4     0.0001338   0.009158    (0.009024  )
+-3     0.004432    0.02489     (0.02046   )
+-2     0.05399     0.06767     (0.01368   )
+-1     0.242       0.1839      (-0.05803  )
+0      0.3989      0.5         (0.1011    )
+1      0.242       0.1839      (-0.05803  )
+2      0.05399     0.06767     (0.01368   )
+3      0.004432    0.02489     (0.02046   )
+4      0.0001338   0.009158    (0.009024  )
+Standard location = 0, scale = 1
+Integral (area under the curve) from - infinity up to z 
+ z  CDF  normal     laplace    (difference)
+-4     3.167e-005  0.009158    (0.009126  )
+-3     0.00135     0.02489     (0.02354   )
+-2     0.02275     0.06767     (0.04492   )
+-1     0.1587      0.1839      (0.02528   )
+0      0.5         0.5         (0         )
+1      0.8413      0.8161      (-0.02528  )
+2      0.9772      0.9323      (-0.04492  )
+3      0.9987      0.9751      (-0.02354  )
+4      1           0.9908      (-0.009126 )
+Area for gaussian z = 2 is 0.97725
+Area for laplace z = 2 is 0.932332
+95% of gaussian area has a z below 1.64485
+95% of laplace area has a z below 2.30259
+95% of gaussian area has a z between 1.95996 and -1.95996
+95% of laplace area has a z between 2.99573 and -2.99573
+
+
+*/
+