// 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) | |
#ifndef BOOST_STATS_FIND_SCALE_HPP | |
#define BOOST_STATS_FIND_SCALE_HPP | |
#include <boost/math/distributions/fwd.hpp> // for all distribution signatures. | |
#include <boost/math/distributions/complement.hpp> | |
#include <boost/math/policies/policy.hpp> | |
// using boost::math::policies::policy; | |
#include <boost/math/tools/traits.hpp> | |
#include <boost/static_assert.hpp> | |
#include <boost/math/special_functions/fpclassify.hpp> | |
#include <boost/math/policies/error_handling.hpp> | |
// using boost::math::complement; // will be needed by users who want complement, | |
// but NOT placed here to avoid putting it in global scope. | |
namespace boost | |
{ | |
namespace math | |
{ | |
// Function to find location of random variable z | |
// to give probability p (given scale) | |
// Applies to normal, lognormal, extreme value, Cauchy, (and symmetrical triangular), | |
// distributions that have scale. | |
// BOOST_STATIC_ASSERTs, see below, are used to enforce this. | |
template <class Dist, class Policy> | |
inline | |
typename Dist::value_type find_scale( // For example, normal mean. | |
typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p. | |
// For example, a nominal minimum acceptable weight z, so that p * 100 % are > z | |
typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z. | |
typename Dist::value_type location, // location parameter, for example, normal distribution mean. | |
const Policy& pol | |
) | |
{ | |
#if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590)) | |
BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value); | |
BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value); | |
#endif | |
static const char* function = "boost::math::find_scale<Dist, Policy>(%1%, %1%, %1%, Policy)"; | |
if(!(boost::math::isfinite)(p) || (p < 0) || (p > 1)) | |
{ | |
return policies::raise_domain_error<typename Dist::value_type>( | |
function, "Probability parameter was %1%, but must be >= 0 and <= 1!", p, pol); | |
} | |
if(!(boost::math::isfinite)(z)) | |
{ | |
return policies::raise_domain_error<typename Dist::value_type>( | |
function, "find_scale z parameter was %1%, but must be finite!", z, pol); | |
} | |
if(!(boost::math::isfinite)(location)) | |
{ | |
return policies::raise_domain_error<typename Dist::value_type>( | |
function, "find_scale location parameter was %1%, but must be finite!", location, pol); | |
} | |
//cout << "z " << z << ", p " << p << ", quantile(Dist(), p) " | |
//<< quantile(Dist(), p) << ", z - mean " << z - location | |
//<<", sd " << (z - location) / quantile(Dist(), p) << endl; | |
//quantile(N01, 0.001) -3.09023 | |
//quantile(N01, 0.01) -2.32635 | |
//quantile(N01, 0.05) -1.64485 | |
//quantile(N01, 0.333333) -0.430728 | |
//quantile(N01, 0.5) 0 | |
//quantile(N01, 0.666667) 0.430728 | |
//quantile(N01, 0.9) 1.28155 | |
//quantile(N01, 0.95) 1.64485 | |
//quantile(N01, 0.99) 2.32635 | |
//quantile(N01, 0.999) 3.09023 | |
typename Dist::value_type result = | |
(z - location) // difference between desired x and current location. | |
/ quantile(Dist(), p); // standard distribution. | |
if (result <= 0) | |
{ // If policy isn't to throw, return the scale <= 0. | |
policies::raise_evaluation_error<typename Dist::value_type>(function, | |
"Computed scale (%1%) is <= 0!" " Was the complement intended?", | |
result, Policy()); | |
} | |
return result; | |
} // template <class Dist, class Policy> find_scale | |
template <class Dist> | |
inline // with default policy. | |
typename Dist::value_type find_scale( // For example, normal mean. | |
typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p. | |
// For example, a nominal minimum acceptable z, so that p * 100 % are > z | |
typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z. | |
typename Dist::value_type location) // location parameter, for example, mean. | |
{ // Forward to find_scale using the default policy. | |
return (find_scale<Dist>(z, p, location, policies::policy<>())); | |
} // find_scale | |
template <class Dist, class Real1, class Real2, class Real3, class Policy> | |
inline typename Dist::value_type find_scale( | |
complemented4_type<Real1, Real2, Real3, Policy> const& c) | |
{ | |
//cout << "cparam1 q " << c.param1 // q | |
// << ", c.dist z " << c.dist // z | |
// << ", c.param2 l " << c.param2 // l | |
// << ", quantile (Dist(), c.param1 = q) " | |
// << quantile(Dist(), c.param1) //q | |
// << endl; | |
#if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590)) | |
BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value); | |
BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value); | |
#endif | |
static const char* function = "boost::math::find_scale<Dist, Policy>(complement(%1%, %1%, %1%, Policy))"; | |
// Checks on arguments, as not complemented version, | |
// Explicit policy. | |
typename Dist::value_type q = c.param1; | |
if(!(boost::math::isfinite)(q) || (q < 0) || (q > 1)) | |
{ | |
return policies::raise_domain_error<typename Dist::value_type>( | |
function, "Probability parameter was %1%, but must be >= 0 and <= 1!", q, c.param3); | |
} | |
typename Dist::value_type z = c.dist; | |
if(!(boost::math::isfinite)(z)) | |
{ | |
return policies::raise_domain_error<typename Dist::value_type>( | |
function, "find_scale z parameter was %1%, but must be finite!", z, c.param3); | |
} | |
typename Dist::value_type location = c.param2; | |
if(!(boost::math::isfinite)(location)) | |
{ | |
return policies::raise_domain_error<typename Dist::value_type>( | |
function, "find_scale location parameter was %1%, but must be finite!", location, c.param3); | |
} | |
typename Dist::value_type result = | |
(c.dist - c.param2) // difference between desired x and current location. | |
/ quantile(complement(Dist(), c.param1)); | |
// ( z - location) / (quantile(complement(Dist(), q)) | |
if (result <= 0) | |
{ // If policy isn't to throw, return the scale <= 0. | |
policies::raise_evaluation_error<typename Dist::value_type>(function, | |
"Computed scale (%1%) is <= 0!" " Was the complement intended?", | |
result, Policy()); | |
} | |
return result; | |
} // template <class Dist, class Policy, class Real1, class Real2, class Real3> typename Dist::value_type find_scale | |
// So the user can start from the complement q = (1 - p) of the probability p, | |
// for example, s = find_scale<normal>(complement(z, q, l)); | |
template <class Dist, class Real1, class Real2, class Real3> | |
inline typename Dist::value_type find_scale( | |
complemented3_type<Real1, Real2, Real3> const& c) | |
{ | |
//cout << "cparam1 q " << c.param1 // q | |
// << ", c.dist z " << c.dist // z | |
// << ", c.param2 l " << c.param2 // l | |
// << ", quantile (Dist(), c.param1 = q) " | |
// << quantile(Dist(), c.param1) //q | |
// << endl; | |
#if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590)) | |
BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value); | |
BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value); | |
#endif | |
static const char* function = "boost::math::find_scale<Dist, Policy>(complement(%1%, %1%, %1%, Policy))"; | |
// Checks on arguments, as not complemented version, | |
// default policy policies::policy<>(). | |
typename Dist::value_type q = c.param1; | |
if(!(boost::math::isfinite)(q) || (q < 0) || (q > 1)) | |
{ | |
return policies::raise_domain_error<typename Dist::value_type>( | |
function, "Probability parameter was %1%, but must be >= 0 and <= 1!", q, policies::policy<>()); | |
} | |
typename Dist::value_type z = c.dist; | |
if(!(boost::math::isfinite)(z)) | |
{ | |
return policies::raise_domain_error<typename Dist::value_type>( | |
function, "find_scale z parameter was %1%, but must be finite!", z, policies::policy<>()); | |
} | |
typename Dist::value_type location = c.param2; | |
if(!(boost::math::isfinite)(location)) | |
{ | |
return policies::raise_domain_error<typename Dist::value_type>( | |
function, "find_scale location parameter was %1%, but must be finite!", location, policies::policy<>()); | |
} | |
typename Dist::value_type result = | |
(z - location) // difference between desired x and current location. | |
/ quantile(complement(Dist(), q)); | |
// ( z - location) / (quantile(complement(Dist(), q)) | |
if (result <= 0) | |
{ // If policy isn't to throw, return the scale <= 0. | |
policies::raise_evaluation_error<typename Dist::value_type>(function, | |
"Computed scale (%1%) is <= 0!" " Was the complement intended?", | |
result, policies::policy<>()); // This is only the default policy - also Want a version with Policy here. | |
} | |
return result; | |
} // template <class Dist, class Real1, class Real2, class Real3> typename Dist::value_type find_scale | |
} // namespace boost | |
} // namespace math | |
#endif // BOOST_STATS_FIND_SCALE_HPP |