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math/test/test_fisher.cpp
John Maddock 4341334b2b Updated accuracy in docs. 
Fixed test_fisher so it's gcc compatible (real_concept.hpp has to come first).


[SVN r3018]
2006-06-22 15:59:01 +00:00

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// Copyright Paul A. Bristow 2006.
// 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)
// test_fisher.cpp
// Basic sanity test for Fisher Cumulative Distribution Function.
#ifdef _MSC_VER
# pragma warning(disable: 4127) // conditional expression is constant.
# pragma warning(disable: 4100) // unreferenced formal parameter.
#endif
#include <boost/math/concepts/real_concept.hpp> // for real_concept
#include <boost/math/special_functions/fisher.hpp>
#include <boost/test/included/test_exec_monitor.hpp> // test_main
#include <boost/test/floating_point_comparison.hpp> // BOOST_CHECK_CLOSE
#include <limits>
using std::numeric_limits;
template <class FPT>
void test_spots(FPT)
{
// Basic sanity checks, tolerance is 6 decimal places
// expressed as a percentage (so -2) for BOOST_CHECK_CLOSE,
// One check per domain of the implementation:
int decdigits = numeric_limits<FPT>::digits10; // guaranteed for this type, eg 6 for float, 15 for double.
decdigits -= 0; // Perhaps allow some decimal digits margin of numerical error.
FPT tolerance = static_cast<FPT>(std::pow(10., -(decdigits-2))); // 1e-6 (as %)
tolerance *= 2; // Allow some small margin (2 means 1 least decimal digit?) of numerical error.
// Typically 2e-13% = 2e-15 as fraction for double.
// Whereas tolerance *= 1.5 fails thus
// difference between ::boost::math::fisher( static_cast<FPT>(1.), static_cast<FPT>(2.), static_cast<FPT>(6.5333333333333))
// {0.12500000000000022} and static_cast<FPT>(0.125){0.125} exceeds 1.5e-013%
// FPT tolerance = static_cast<FPT>(std::pow(10., -(4-2))); // 1e-4 (as %) OK with misc test values.
// PT tolerance = static_cast<FPT>(std::pow(10., -(6-2))); // 1e-6 (as %) fails for most values.
// This test only passes at 1e-5 because probability value is less accurate,
// a digit in 6th decimal place, although calculated using values from
// http://www.danielsoper.com/statcalc/calc04.aspx
// BUT I conclude that these values are only accurate to about 1e-4,
// so not very useful for testing!
/*
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(1.), // df1
static_cast<FPT>(1.), // df2
static_cast<FPT>(161.4476)), // F
static_cast<FPT>(0.05), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(2.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(19.0000)), // F
static_cast<FPT>(0.05), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(1.), // df1
static_cast<FPT>(10.), // df2
static_cast<FPT>(4.9646)), // F
static_cast<FPT>(0.05), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(1.), // df1
static_cast<FPT>(100.), // df2
static_cast<FPT>(3.9361)), // F
static_cast<FPT>(0.05), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(1.), // df1
static_cast<FPT>(1000000.), // df2
static_cast<FPT>(3.8415)), // F
static_cast<FPT>(0.05), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(10.), // df1
static_cast<FPT>(1.), // df2
static_cast<FPT>(241.8818)), // F
static_cast<FPT>(0.05), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(1.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(8.5263)), // F
static_cast<FPT>(0.1), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(1.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(18.5128)), // F
static_cast<FPT>(0.05), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(1.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(98.5025)), // F
static_cast<FPT>(0.01), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(1.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(998.4979)), // F
static_cast<FPT>(0.001), // probability.
tolerance);
*/
// http://www.vias.org/tmdatanaleng/cc_distri_calculator.html give some useful info,
// BUT the calculator link is broken.
// http://www.vias.org/simulations/simusoft_distcalc.html
// Distcalc version 1.2 Copyright 2002 H Lohninger, TU Wein
// H.Lohninger: Teach/Me Data Analysis, Springer-Verlag, Berlin-New York-Tokyo, 1999. ISBN 3-540-14743-8
// The Windows calculator is available zipped distcalc.exe for download at:
// http://www.vias.org/simulations/simu_stat.html
// This interactive Windows program was used to find some combination for which the
// result appears to be exact. No doubt this can be done analytically too,
// by mathematicians!
// Some combinations for which the result is 'exact', or at least is to 40 decimal digits.
// 40 decimal digits includes 128-bit significand User Defined Floating-Point types.
// These all pass tests at near epsilon accuracy for the floating-point type.
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(1.), // df1
static_cast<FPT>(2.), // df2
// static_cast<FPT>(0.6666666666666666666666666666666666667)), // F
static_cast<FPT>(2.)/static_cast<FPT>(3.) ), // F
static_cast<FPT>(0.5), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(1.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(1.6)), // F
static_cast<FPT>(0.333333333333333333333333333333333333), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(1.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(6.5333333333333333333333333333333333)), // F
static_cast<FPT>(0.125), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(2.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(1.)), // F
static_cast<FPT>(0.5), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(2.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(3.)), // F
static_cast<FPT>(0.25), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(2.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(3.)), // F
static_cast<FPT>(0.25), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(2.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(7.)), // F
static_cast<FPT>(0.125), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(2.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(9.)), // F
static_cast<FPT>(0.1), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(2.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(19.)), // F
static_cast<FPT>(0.05), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(2.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(29.)), // F
static_cast<FPT>(0.03333333333333333333333333333333333333333), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(2.), // df1
static_cast<FPT>(2.), // df2
static_cast<FPT>(99.)), // F
static_cast<FPT>(0.01), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(4.), // df1
static_cast<FPT>(4.), // df2
static_cast<FPT>(9.)), // F
static_cast<FPT>(0.028), // probability.
tolerance);
BOOST_CHECK_CLOSE(
::boost::math::fisher(
static_cast<FPT>(8.), // df1
static_cast<FPT>(8.), // df2
static_cast<FPT>(1.)), // F
static_cast<FPT>(0.5), // probability.
tolerance);
// These two don't pass at the 2 eps tolerance:
//BOOST_CHECK_CLOSE(
// ::boost::math::fisher(
// static_cast<FPT>(2.), // df1
// static_cast<FPT>(2.), // df2
// static_cast<FPT>(999.)), // F
// static_cast<FPT>(0.001), // probability.== 0.000999987125
//tolerance);
// And this even with 1 decimal digit tolerance.
// BOOST_CHECK_CLOSE(
// ::boost::math::fisher(
// static_cast<FPT>(2.), // df1
// static_cast<FPT>(2.), // df2
// static_cast<FPT>(9999.)), // F
// static_cast<FPT>(0.0001), // probability. == 0.000100016594 or 9.9999999999988987e-005
//tolerance);
//BOOST_CHECK_CLOSE(
// ::boost::math::fisher(
// static_cast<FPT>(2.), // df1
// static_cast<FPT>(7.), // df2
// static_cast<FPT>(99.)), // F
// static_cast<FPT>(0.00001), // probability.
//tolerance);
//BOOST_CHECK_CLOSE(
// ::boost::math::fisher(
// static_cast<FPT>(2.), // df1
// static_cast<FPT>(3.), // df2
// static_cast<FPT>(999.)), // F
// static_cast<FPT>(0.0000666666666666666666666666), // probability.
//tolerance);
// Also note limit cases for F(1, infinity) == normal distribution
// F(1, n2) == Student's t distribution
// F(n1, infinity) == Chisq distribution
// These might allow some further cross checks?
} // template <class FPT>void test_spots(FPT)
int test_main(int, char* [])
{
// Basic sanity-check spot values.
// (Parameter value, arbitrarily zero, only communicates the floating point type).
test_spots(0.0F); // Test float.
test_spots(0.0); // Test double.
test_spots(0.0L); // Test long double.
test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
return 0;
} // int test_main(int, char* [])
/*
Output:
1>------ Rebuild All started: Project: test_fisher, Configuration: Debug Win32 ------
1>Deleting intermediate and output files for project 'test_fisher', configuration 'Debug|Win32'
1>Compiling...
1>test_fisher.cpp
1>Linking...
1>Embedding manifest...
1>Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_fisher.exe"
1>Running 1 test case...
1>*** No errors detected
1>Build Time 0:06
1>Build log was saved at "file://i:\boost-06-05-03-1300\libs\math\test\Math_test\test_fisher\Debug\BuildLog.htm"
1>test_fisher - 0 error(s), 0 warning(s)
========== Rebuild All: 1 succeeded, 0 failed, 0 skipped ==========
*/
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