Chris@16: //  Copyright John Maddock 2007.
Chris@16: //  Copyright Paul A. Bristow 2007.
Chris@16: 
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_STATS_FIND_SCALE_HPP
Chris@16: #define BOOST_STATS_FIND_SCALE_HPP
Chris@16: 
Chris@16: #include <boost/math/distributions/fwd.hpp> // for all distribution signatures.
Chris@16: #include <boost/math/distributions/complement.hpp>
Chris@16: #include <boost/math/policies/policy.hpp>
Chris@16: // using boost::math::policies::policy;
Chris@16: #include <boost/math/tools/traits.hpp>
Chris@16: #include <boost/static_assert.hpp>
Chris@16: #include <boost/math/special_functions/fpclassify.hpp>
Chris@16: #include <boost/math/policies/error_handling.hpp>
Chris@16: // using boost::math::complement; // will be needed by users who want complement,
Chris@16: // but NOT placed here to avoid putting it in global scope.
Chris@16: 
Chris@16: namespace boost
Chris@16: {
Chris@16:   namespace math
Chris@16:   {
Chris@16:     // Function to find location of random variable z
Chris@16:     // to give probability p (given scale)
Chris@16:     // Applies to normal, lognormal, extreme value, Cauchy, (and symmetrical triangular),
Chris@16:     // distributions that have scale.
Chris@16:     // BOOST_STATIC_ASSERTs, see below, are used to enforce this.
Chris@16: 
Chris@16:     template <class Dist, class Policy>
Chris@16:     inline
Chris@16:       typename Dist::value_type find_scale( // For example, normal mean.
Chris@16:       typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p.
Chris@16:       // For example, a nominal minimum acceptable weight z, so that p * 100 % are > z
Chris@16:       typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z.
Chris@16:       typename Dist::value_type location, // location parameter, for example, normal distribution mean.
Chris@16:       const Policy& pol 
Chris@16:       )
Chris@16:     {
Chris@16: #if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590))
Chris@16:       BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value); 
Chris@16:       BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value); 
Chris@16: #endif
Chris@16:       static const char* function = "boost::math::find_scale<Dist, Policy>(%1%, %1%, %1%, Policy)";
Chris@16: 
Chris@16:       if(!(boost::math::isfinite)(p) || (p < 0) || (p > 1))
Chris@16:       {
Chris@16:         return policies::raise_domain_error<typename Dist::value_type>(
Chris@16:           function, "Probability parameter was %1%, but must be >= 0 and <= 1!", p, pol);
Chris@16:       }
Chris@16:       if(!(boost::math::isfinite)(z))
Chris@16:       {
Chris@16:         return policies::raise_domain_error<typename Dist::value_type>(
Chris@16:           function, "find_scale z parameter was %1%, but must be finite!", z, pol);
Chris@16:       }
Chris@16:       if(!(boost::math::isfinite)(location))
Chris@16:       {
Chris@16:         return policies::raise_domain_error<typename Dist::value_type>(
Chris@16:           function, "find_scale location parameter was %1%, but must be finite!", location, pol);
Chris@16:       }
Chris@16: 
Chris@16:       //cout << "z " << z << ", p " << p << ",  quantile(Dist(), p) "
Chris@16:       //<< quantile(Dist(), p) << ", z - mean " << z - location 
Chris@16:       //<<", sd " << (z - location)  / quantile(Dist(), p) << endl;
Chris@16: 
Chris@16:       //quantile(N01, 0.001) -3.09023
Chris@16:       //quantile(N01, 0.01) -2.32635
Chris@16:       //quantile(N01, 0.05) -1.64485
Chris@16:       //quantile(N01, 0.333333) -0.430728
Chris@16:       //quantile(N01, 0.5) 0  
Chris@16:       //quantile(N01, 0.666667) 0.430728
Chris@16:       //quantile(N01, 0.9) 1.28155
Chris@16:       //quantile(N01, 0.95) 1.64485
Chris@16:       //quantile(N01, 0.99) 2.32635
Chris@16:       //quantile(N01, 0.999) 3.09023
Chris@16: 
Chris@16:       typename Dist::value_type result = 
Chris@16:         (z - location)  // difference between desired x and current location.
Chris@16:         / quantile(Dist(), p); // standard distribution.
Chris@16: 
Chris@16:       if (result <= 0)
Chris@16:       { // If policy isn't to throw, return the scale <= 0.
Chris@16:         policies::raise_evaluation_error<typename Dist::value_type>(function,
Chris@16:           "Computed scale (%1%) is <= 0!" " Was the complement intended?",
Chris@16:           result, Policy());
Chris@16:       }
Chris@16:       return result;
Chris@16:     } // template <class Dist, class Policy> find_scale
Chris@16: 
Chris@16:     template <class Dist>
Chris@16:     inline // with default policy.
Chris@16:       typename Dist::value_type find_scale( // For example, normal mean.
Chris@16:       typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p.
Chris@16:       // For example, a nominal minimum acceptable z, so that p * 100 % are > z
Chris@16:       typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z.
Chris@16:       typename Dist::value_type location) // location parameter, for example, mean.
Chris@16:     { // Forward to find_scale using the default policy.
Chris@16:       return (find_scale<Dist>(z, p, location, policies::policy<>()));
Chris@16:     } // find_scale
Chris@16: 
Chris@16:     template <class Dist, class Real1, class Real2, class Real3, class Policy>
Chris@16:     inline typename Dist::value_type find_scale(
Chris@16:       complemented4_type<Real1, Real2, Real3, Policy> const& c)
Chris@16:     {
Chris@16:       //cout << "cparam1 q " << c.param1 // q
Chris@16:       //  << ", c.dist z " << c.dist // z
Chris@16:       //  << ", c.param2 l " << c.param2 // l
Chris@16:       //  << ", quantile (Dist(), c.param1 = q) "
Chris@16:       //  << quantile(Dist(), c.param1) //q
Chris@16:       //  << endl;
Chris@16: 
Chris@16: #if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590))
Chris@16:       BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value); 
Chris@16:       BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value); 
Chris@16: #endif
Chris@16:       static const char* function = "boost::math::find_scale<Dist, Policy>(complement(%1%, %1%, %1%, Policy))";
Chris@16: 
Chris@16:       // Checks on arguments, as not complemented version,
Chris@16:       // Explicit policy.
Chris@16:       typename Dist::value_type q = c.param1;
Chris@16:       if(!(boost::math::isfinite)(q) || (q < 0) || (q > 1))
Chris@16:       {
Chris@16:         return policies::raise_domain_error<typename Dist::value_type>(
Chris@16:           function, "Probability parameter was %1%, but must be >= 0 and <= 1!", q, c.param3);
Chris@16:       }
Chris@16:       typename Dist::value_type z = c.dist;
Chris@16:       if(!(boost::math::isfinite)(z))
Chris@16:       {
Chris@16:         return policies::raise_domain_error<typename Dist::value_type>(
Chris@16:           function, "find_scale z parameter was %1%, but must be finite!", z, c.param3);
Chris@16:       }
Chris@16:       typename Dist::value_type location = c.param2;
Chris@16:       if(!(boost::math::isfinite)(location))
Chris@16:       {
Chris@16:         return policies::raise_domain_error<typename Dist::value_type>(
Chris@16:           function, "find_scale location parameter was %1%, but must be finite!", location, c.param3);
Chris@16:       }
Chris@16: 
Chris@16:       typename Dist::value_type result = 
Chris@16:         (c.dist - c.param2)  // difference between desired x and current location.
Chris@16:         / quantile(complement(Dist(), c.param1));
Chris@16:       //     (  z    - location) / (quantile(complement(Dist(),  q)) 
Chris@16:       if (result <= 0)
Chris@16:       { // If policy isn't to throw, return the scale <= 0.
Chris@16:         policies::raise_evaluation_error<typename Dist::value_type>(function,
Chris@16:           "Computed scale (%1%) is <= 0!" " Was the complement intended?",
Chris@16:           result, Policy());
Chris@16:       }
Chris@16:       return result;
Chris@16:     } // template <class Dist, class Policy, class Real1, class Real2, class Real3> typename Dist::value_type find_scale
Chris@16: 
Chris@16:     // So the user can start from the complement q = (1 - p) of the probability p,
Chris@16:     // for example, s = find_scale<normal>(complement(z, q, l));
Chris@16: 
Chris@16:     template <class Dist, class Real1, class Real2, class Real3>
Chris@16:     inline typename Dist::value_type find_scale(
Chris@16:       complemented3_type<Real1, Real2, Real3> const& c)
Chris@16:     {
Chris@16:       //cout << "cparam1 q " << c.param1 // q
Chris@16:       //  << ", c.dist z " << c.dist // z
Chris@16:       //  << ", c.param2 l " << c.param2 // l
Chris@16:       //  << ", quantile (Dist(), c.param1 = q) "
Chris@16:       //  << quantile(Dist(), c.param1) //q
Chris@16:       //  << endl;
Chris@16: 
Chris@16: #if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590))
Chris@16:       BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value); 
Chris@16:       BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value); 
Chris@16: #endif
Chris@16:       static const char* function = "boost::math::find_scale<Dist, Policy>(complement(%1%, %1%, %1%, Policy))";
Chris@16: 
Chris@16:       // Checks on arguments, as not complemented version,
Chris@16:       // default policy policies::policy<>().
Chris@16:       typename Dist::value_type q = c.param1;
Chris@16:       if(!(boost::math::isfinite)(q) || (q < 0) || (q > 1))
Chris@16:       {
Chris@16:         return policies::raise_domain_error<typename Dist::value_type>(
Chris@16:           function, "Probability parameter was %1%, but must be >= 0 and <= 1!", q, policies::policy<>());
Chris@16:       }
Chris@16:       typename Dist::value_type z = c.dist;
Chris@16:       if(!(boost::math::isfinite)(z))
Chris@16:       {
Chris@16:         return policies::raise_domain_error<typename Dist::value_type>(
Chris@16:           function, "find_scale z parameter was %1%, but must be finite!", z, policies::policy<>());
Chris@16:       }
Chris@16:       typename Dist::value_type location = c.param2;
Chris@16:       if(!(boost::math::isfinite)(location))
Chris@16:       {
Chris@16:         return policies::raise_domain_error<typename Dist::value_type>(
Chris@16:           function, "find_scale location parameter was %1%, but must be finite!", location, policies::policy<>());
Chris@16:       }
Chris@16: 
Chris@16:       typename Dist::value_type result = 
Chris@16:         (z - location)  // difference between desired x and current location.
Chris@16:         / quantile(complement(Dist(), q));
Chris@16:       //     (  z    - location) / (quantile(complement(Dist(),  q)) 
Chris@16:       if (result <= 0)
Chris@16:       { // If policy isn't to throw, return the scale <= 0.
Chris@16:         policies::raise_evaluation_error<typename Dist::value_type>(function,
Chris@16:           "Computed scale (%1%) is <= 0!" " Was the complement intended?",
Chris@16:           result, policies::policy<>()); // This is only the default policy - also Want a version with Policy here.
Chris@16:       }
Chris@16:       return result;
Chris@16:     } // template <class Dist, class Real1, class Real2, class Real3> typename Dist::value_type find_scale
Chris@16: 
Chris@16:   } // namespace boost
Chris@16: } // namespace math
Chris@16: 
Chris@16: #endif // BOOST_STATS_FIND_SCALE_HPP