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// test_find_scale.cpp
// Copyright John Maddock 2007.
// Copyright Paul A. Bristow 2007.
// 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)
// Basic sanity test for find_scale function.
// Default distribution domain error policy is
// #define BOOST_MATH_DOMAIN_ERROR_POLICY throw_on_error
#include <pch.hpp>
#include <boost/math/tools/test.hpp>
#include <boost/math/concepts/real_concept.hpp> // for real_concept
#include <boost/math/distributions/normal.hpp> // for normal_distribution
using boost::math::normal; // Default type double.
using boost::math::normal_distribution; // All floating-point types.
#include <boost/math/distributions/cauchy.hpp> // for cauchy_distribution
using boost::math::cauchy;
#include <boost/math/distributions/pareto.hpp> // for cauchy_distribution
using boost::math::pareto;
#include <boost/math/distributions/find_scale.hpp>
using boost::math::find_scale;
using boost::math::complement;// will be needed by users who want complement,
#include <boost/math/policies/policy.hpp>
using boost::math::policies::policy;
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp> // for test_main
#include <boost/test/tools/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE_FRACTION, BOOST_CHECK_EQUAL...
#include <iostream>
#include <iomanip>
using std::cout; using std::endl; using std::fixed;
using std::right; using std::left; using std::showpoint;
using std::showpos; using std::setw; using std::setprecision;
#include <limits>
using std::numeric_limits;
template <class RealType> // Any floating-point type RealType.
void test_spots(RealType)
{ // Parameter only provides the type, float, double... value ignored.
// Basic sanity checks, test data may be to double precision only
// so set tolerance to 100 eps expressed as a fraction,
// or 100 eps of type double expressed as a fraction,
// whichever is the larger.
RealType tolerance = (std::max)
(boost::math::tools::epsilon<RealType>(),
static_cast<RealType>(std::numeric_limits<double>::epsilon()));
tolerance *= 100; // 100 eps as a fraction.
cout << "Tolerance for type " << typeid(RealType).name() << " is "
<< setprecision(3) << tolerance << " (or " << tolerance * 100 << "%)." << endl;
BOOST_MATH_CHECK_THROW( // Probability outside 0 to 1.
find_scale<normal_distribution<RealType> >(
static_cast<RealType>(0.), static_cast<RealType>(-1.), static_cast<RealType>(0.) ),
std::domain_error);
normal_distribution<RealType> n; // standard N(0,1)
BOOST_CHECK_EQUAL(n.location(), 0); // aka mean.
BOOST_CHECK_EQUAL(n.scale(), 1); // aka standard_deviation.
// Check for 'bad' arguments.
BOOST_MATH_CHECK_THROW(find_scale<normal>(0., -1., 0.), std::domain_error); // p below 0 to 1.
BOOST_MATH_CHECK_THROW(find_scale<normal>(0., 2., 0.), std::domain_error); // p above 0 to 1.
BOOST_MATH_CHECK_THROW(find_scale<normal>(numeric_limits<double>::infinity(), 0.5, 0.),
std::domain_error); // z not finite.
BOOST_MATH_CHECK_THROW(find_scale<normal>(numeric_limits<double>::quiet_NaN(), -1., 0.),
std::domain_error); // z not finite
BOOST_MATH_CHECK_THROW(find_scale<normal>(0., -1., numeric_limits<double>::quiet_NaN()),
std::domain_error); // scale not finite
BOOST_MATH_CHECK_THROW(find_scale<normal>(complement(0., -1., 0.)), std::domain_error); // p below 0 to 1.
BOOST_MATH_CHECK_THROW(find_scale<normal>(complement(0., 2., 0.)), std::domain_error); // p above 0 to 1.
BOOST_MATH_CHECK_THROW(find_scale<normal>(complement(numeric_limits<double>::infinity(), 0.5, 0.)),
std::domain_error); // z not finite.
BOOST_MATH_CHECK_THROW(find_scale<normal>(complement(numeric_limits<double>::quiet_NaN(), -1., 0.)),
std::domain_error); // z not finite
BOOST_MATH_CHECK_THROW(find_scale<normal>(complement(0., -1., numeric_limits<double>::quiet_NaN())),
std::domain_error); // scale not finite
BOOST_MATH_CHECK_THROW(find_scale<normal>(complement(0., -1., 0.)), std::domain_error); // p below 0 to 1.
// Check for ab-use with unsuitable distribution(s), for example,
// pareto distribution (and most others) can't be used with find_scale (or find_location)
// because they lack the scale and location attributes.
// BOOST_MATH_CHECK_THROW(find_scale<pareto>(0., 0.5, 0.), std::domain_error);
// correctly fails to compile in find_scale() at
// static_assert(::boost::math::tools::is_scaled_distribution<Dist>::value);
// Check doesn't throw when an ignore_error for domain_error policy is used.
using boost::math::policies::policy;
using boost::math::policies::domain_error;
using boost::math::policies::ignore_error;
// Define a (bad?) policy to ignore domain errors ('bad' arguments):
typedef policy<domain_error<ignore_error> > ignore_domain_policy;
// Using a typedef is convenient, especially if it is re-used.
#ifndef BOOST_NO_EXCEPTIONS
BOOST_CHECK_NO_THROW(find_scale<normal>(0, -1, 1,
ignore_domain_policy())); // probability outside [0, 1]
BOOST_CHECK_NO_THROW(find_scale<normal>(numeric_limits<double>::infinity(), -1, 1,
ignore_domain_policy())); // z not finite.
BOOST_CHECK_NO_THROW(find_scale<normal>(complement(0, -1, 1, ignore_domain_policy()))); // probability outside [0, 1]
BOOST_CHECK_NO_THROW(find_scale<normal>(complement(numeric_limits<double>::infinity(), -1, 1,
ignore_domain_policy()))); // z not finite.
#endif
RealType l = 0.; // standard normal distribution.
RealType sd = static_cast<RealType>(1); // normal default standard deviation = 1.
normal_distribution<RealType> n01(l, sd); // mean(location) = 0, standard_deviation (scale) = 1.
RealType z = static_cast<RealType>(-2); // z to give prob p
//cout << "Standard normal distribution with standard deviation = " << sd
// << " has " << "fraction <= " << z << " = " << cdf(n01, z) << endl;
// Standard normal distribution with standard deviation = 1 has fraction <= -2 = 0.0227501
//normal_distribution<RealType> np001pc(l, sd); // Same mean(location) but with standard_deviation (scale) changed.
//cout << "Normal distribution with standard deviation = " << s
// << " has " << "fraction <= " << z << " = " << cdf(np001pc, z) << endl;
// Find scale to give a probability p (0.001) of z (-2)
RealType p = static_cast<RealType>(0.001); // only 0.1% to be below z (-2).
// location (mean) remains at zero.
RealType s = find_scale<normal_distribution<RealType> >(z, p, l);
//cout << "Mean " << l << ", z " << z << ", p " << p
// << ", sd " << sd << ", find_scale " << s
// << ", difference in sd " << s - sd << endl;
// Mean 0, z -2, p 0.001, sd 1, find_scale 0.64720053440907599, difference in sd -0.352799
cout.precision(17);
BOOST_CHECK_CLOSE_FRACTION(s, static_cast<RealType>(0.64720053440907599L), tolerance);
normal_distribution<RealType> np001pc(l, s); // Same mean(location) but with standard_deviation (scale) changed.
//cout << "Normal distribution with standard deviation = " << s
// << " has " << "fraction <= " << z << " = " << cdf(np001pc, z) << endl;
// Normal distribution with standard deviation = 0.647201 has fraction <= -2 = 0.001
// Check cdf such that only fraction p really is below changed standard deviation s.
BOOST_CHECK_CLOSE_FRACTION(p, cdf(np001pc, z), tolerance);
// Check that some policies can be applied (though results not used here).
s = find_scale<normal_distribution<RealType> >(z, p, l, policy<>()); // Default policy, needs using boost::math::policies::policy;
s = find_scale<normal_distribution<RealType> >(z, p, l, boost::math::policies::policy<>()); // Default policy, fully specified.
s = find_scale<normal_distribution<RealType> >(z, p, l, ignore_domain_policy()); // find_scale with new policy, using typedef.
s = find_scale<normal_distribution<RealType> >(z, p, l, policy<domain_error<ignore_error> >()); // New policy, without typedef.
// Check that can use the complement version too.
RealType q = 1 - p; // complement.
s = find_scale<normal_distribution<RealType> >(complement(z, q, l)); // Implicit default policy.
BOOST_CHECK_CLOSE_FRACTION(s, static_cast<RealType>(0.64720053440907599L), tolerance);
s = find_scale<normal_distribution<RealType> >(complement(z, q, l, policy<>())); // Explicit default policy.
BOOST_CHECK_CLOSE_FRACTION(s, static_cast<RealType>(0.64720053440907599L), tolerance);
normal_distribution<RealType> np95pc(l, s); // Same mean(location) but with new standard_deviation (scale).
//cout << "Mean " << l << ", z " << z << ", q " << q
//<< ", sd " << sd << ", find_scale " << s
//<< ", difference in sd " << s - sd << endl;
//cout << "Normal distribution with standard deviation = " << s
// << " has " << "fraction <= " << z << " = " << cdf(np001pc, z) << endl;
BOOST_CHECK_CLOSE_FRACTION(q, cdf(complement(np95pc, z)), tolerance);
} // template <class RealType>void test_spots(RealType)
BOOST_AUTO_TEST_CASE( test_main )
{
// 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.
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_spots(0.0L); // Test long double.
#if !BOOST_WORKAROUND(BOOST_BORLANDC, BOOST_TESTED_AT(0x0582)) && !defined(BOOST_MATH_NO_REAL_CONCEPT_TESTS)
test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
#endif
#else
std::cout << "<note>The long double tests have been disabled on this platform "
"either because the long double overloads of the usual math functions are "
"not available at all, or because they are too inaccurate for these tests "
"to pass.</note>" << std::endl;
#endif
} // BOOST_AUTO_TEST_CASE( test_main )
/*
Output is:
Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_find_scale.exe"
Running 1 test case...
Tolerance for type float is 1.19e-005 (or 0.00119%).
Tolerance for type double is 2.22e-014 (or 2.22e-012%).
Tolerance for type long double is 2.22e-014 (or 2.22e-012%).
Tolerance for type class boost::math::concepts::real_concept is 2.22e-014 (or 2.22e-012%).
*** No errors detected
*/
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