572 lines
16 KiB
Plaintext
572 lines
16 KiB
Plaintext
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// Copyright John Maddock 2007.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_DISTRIBUTIONS_DETAIL_INV_DISCRETE_QUANTILE
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#define BOOST_MATH_DISTRIBUTIONS_DETAIL_INV_DISCRETE_QUANTILE
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#include <algorithm>
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namespace boost{ namespace math{ namespace detail{
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//
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// Functor for root finding algorithm:
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//
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template <class Dist>
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struct distribution_quantile_finder
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{
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typedef typename Dist::value_type value_type;
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typedef typename Dist::policy_type policy_type;
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distribution_quantile_finder(const Dist d, value_type p, bool c)
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: dist(d), target(p), comp(c) {}
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value_type operator()(value_type const& x)
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{
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return comp ? value_type(target - cdf(complement(dist, x))) : value_type(cdf(dist, x) - target);
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}
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private:
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Dist dist;
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value_type target;
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bool comp;
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};
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//
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// The purpose of adjust_bounds, is to toggle the last bit of the
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// range so that both ends round to the same integer, if possible.
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// If they do both round the same then we terminate the search
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// for the root *very* quickly when finding an integer result.
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// At the point that this function is called we know that "a" is
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// below the root and "b" above it, so this change can not result
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// in the root no longer being bracketed.
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//
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template <class Real, class Tol>
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void adjust_bounds(Real& /* a */, Real& /* b */, Tol const& /* tol */){}
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template <class Real>
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void adjust_bounds(Real& /* a */, Real& b, tools::equal_floor const& /* tol */)
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{
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BOOST_MATH_STD_USING
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b -= tools::epsilon<Real>() * b;
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}
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template <class Real>
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void adjust_bounds(Real& a, Real& /* b */, tools::equal_ceil const& /* tol */)
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{
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BOOST_MATH_STD_USING
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a += tools::epsilon<Real>() * a;
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}
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template <class Real>
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void adjust_bounds(Real& a, Real& b, tools::equal_nearest_integer const& /* tol */)
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{
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BOOST_MATH_STD_USING
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a += tools::epsilon<Real>() * a;
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b -= tools::epsilon<Real>() * b;
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}
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//
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// This is where all the work is done:
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//
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template <class Dist, class Tolerance>
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typename Dist::value_type
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do_inverse_discrete_quantile(
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const Dist& dist,
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const typename Dist::value_type& p,
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bool comp,
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typename Dist::value_type guess,
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const typename Dist::value_type& multiplier,
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typename Dist::value_type adder,
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const Tolerance& tol,
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boost::uintmax_t& max_iter)
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{
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typedef typename Dist::value_type value_type;
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typedef typename Dist::policy_type policy_type;
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static const char* function = "boost::math::do_inverse_discrete_quantile<%1%>";
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BOOST_MATH_STD_USING
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distribution_quantile_finder<Dist> f(dist, p, comp);
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//
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// Max bounds of the distribution:
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//
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value_type min_bound, max_bound;
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boost::math::tie(min_bound, max_bound) = support(dist);
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if(guess > max_bound)
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guess = max_bound;
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if(guess < min_bound)
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guess = min_bound;
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value_type fa = f(guess);
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boost::uintmax_t count = max_iter - 1;
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value_type fb(fa), a(guess), b =0; // Compiler warning C4701: potentially uninitialized local variable 'b' used
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if(fa == 0)
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return guess;
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//
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// For small expected results, just use a linear search:
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//
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if(guess < 10)
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{
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b = a;
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while((a < 10) && (fa * fb >= 0))
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{
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if(fb <= 0)
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{
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a = b;
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b = a + 1;
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if(b > max_bound)
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b = max_bound;
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fb = f(b);
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--count;
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if(fb == 0)
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return b;
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if(a == b)
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return b; // can't go any higher!
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}
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else
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{
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b = a;
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a = (std::max)(value_type(b - 1), value_type(0));
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if(a < min_bound)
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a = min_bound;
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fa = f(a);
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--count;
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if(fa == 0)
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return a;
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if(a == b)
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return a; // We can't go any lower than this!
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}
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}
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}
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//
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// Try and bracket using a couple of additions first,
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// we're assuming that "guess" is likely to be accurate
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// to the nearest int or so:
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//
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else if(adder != 0)
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{
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//
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// If we're looking for a large result, then bump "adder" up
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// by a bit to increase our chances of bracketing the root:
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//
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//adder = (std::max)(adder, 0.001f * guess);
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if(fa < 0)
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{
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b = a + adder;
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if(b > max_bound)
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b = max_bound;
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}
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else
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{
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b = (std::max)(value_type(a - adder), value_type(0));
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if(b < min_bound)
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b = min_bound;
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}
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fb = f(b);
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--count;
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if(fb == 0)
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return b;
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if(count && (fa * fb >= 0))
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{
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//
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// We didn't bracket the root, try
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// once more:
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//
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a = b;
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fa = fb;
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if(fa < 0)
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{
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b = a + adder;
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if(b > max_bound)
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b = max_bound;
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}
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else
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{
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b = (std::max)(value_type(a - adder), value_type(0));
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if(b < min_bound)
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b = min_bound;
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}
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fb = f(b);
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--count;
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}
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if(a > b)
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{
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using std::swap;
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swap(a, b);
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swap(fa, fb);
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}
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}
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//
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// If the root hasn't been bracketed yet, try again
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// using the multiplier this time:
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//
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if((boost::math::sign)(fb) == (boost::math::sign)(fa))
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{
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if(fa < 0)
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{
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//
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// Zero is to the right of x2, so walk upwards
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// until we find it:
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//
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while(((boost::math::sign)(fb) == (boost::math::sign)(fa)) && (a != b))
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{
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if(count == 0)
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return policies::raise_evaluation_error(function, "Unable to bracket root, last nearest value was %1%", b, policy_type());
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a = b;
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fa = fb;
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b *= multiplier;
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if(b > max_bound)
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b = max_bound;
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fb = f(b);
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--count;
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BOOST_MATH_INSTRUMENT_CODE("a = " << a << " b = " << b << " fa = " << fa << " fb = " << fb << " count = " << count);
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}
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}
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else
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{
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//
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// Zero is to the left of a, so walk downwards
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// until we find it:
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//
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while(((boost::math::sign)(fb) == (boost::math::sign)(fa)) && (a != b))
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{
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if(fabs(a) < tools::min_value<value_type>())
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{
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// Escape route just in case the answer is zero!
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max_iter -= count;
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max_iter += 1;
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return 0;
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}
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if(count == 0)
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return policies::raise_evaluation_error(function, "Unable to bracket root, last nearest value was %1%", a, policy_type());
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b = a;
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fb = fa;
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a /= multiplier;
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if(a < min_bound)
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a = min_bound;
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fa = f(a);
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--count;
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BOOST_MATH_INSTRUMENT_CODE("a = " << a << " b = " << b << " fa = " << fa << " fb = " << fb << " count = " << count);
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}
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}
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}
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max_iter -= count;
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if(fa == 0)
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return a;
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if(fb == 0)
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return b;
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if(a == b)
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return b; // Ran out of bounds trying to bracket - there is no answer!
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//
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// Adjust bounds so that if we're looking for an integer
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// result, then both ends round the same way:
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//
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adjust_bounds(a, b, tol);
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//
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// We don't want zero or denorm lower bounds:
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//
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if(a < tools::min_value<value_type>())
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a = tools::min_value<value_type>();
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//
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// Go ahead and find the root:
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//
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std::pair<value_type, value_type> r = toms748_solve(f, a, b, fa, fb, tol, count, policy_type());
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max_iter += count;
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BOOST_MATH_INSTRUMENT_CODE("max_iter = " << max_iter << " count = " << count);
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return (r.first + r.second) / 2;
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}
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//
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// Some special routine for rounding up and down:
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// We want to check and see if we are very close to an integer, and if so test to see if
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// that integer is an exact root of the cdf. We do this because our root finder only
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// guarantees to find *a root*, and there can sometimes be many consecutive floating
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// point values which are all roots. This is especially true if the target probability
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// is very close 1.
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//
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template <class Dist>
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inline typename Dist::value_type round_to_floor(const Dist& d, typename Dist::value_type result, typename Dist::value_type p, bool c)
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{
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BOOST_MATH_STD_USING
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typename Dist::value_type cc = ceil(result);
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typename Dist::value_type pp = cc <= support(d).second ? c ? cdf(complement(d, cc)) : cdf(d, cc) : 1;
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if(pp == p)
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result = cc;
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else
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result = floor(result);
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//
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// Now find the smallest integer <= result for which we get an exact root:
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//
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while(result != 0)
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{
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cc = result - 1;
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if(cc < support(d).first)
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break;
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pp = c ? cdf(complement(d, cc)) : cdf(d, cc);
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if(pp == p)
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result = cc;
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else if(c ? pp > p : pp < p)
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break;
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result -= 1;
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}
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return result;
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}
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#ifdef BOOST_MSVC
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#pragma warning(push)
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#pragma warning(disable:4127)
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#endif
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template <class Dist>
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inline typename Dist::value_type round_to_ceil(const Dist& d, typename Dist::value_type result, typename Dist::value_type p, bool c)
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{
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BOOST_MATH_STD_USING
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typename Dist::value_type cc = floor(result);
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typename Dist::value_type pp = cc >= support(d).first ? c ? cdf(complement(d, cc)) : cdf(d, cc) : 0;
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if(pp == p)
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result = cc;
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else
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result = ceil(result);
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//
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// Now find the largest integer >= result for which we get an exact root:
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//
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while(true)
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{
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cc = result + 1;
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if(cc > support(d).second)
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break;
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pp = c ? cdf(complement(d, cc)) : cdf(d, cc);
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if(pp == p)
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result = cc;
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else if(c ? pp < p : pp > p)
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break;
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result += 1;
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}
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return result;
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}
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#ifdef BOOST_MSVC
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#pragma warning(pop)
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#endif
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//
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// Now finally are the public API functions.
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// There is one overload for each policy,
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// each one is responsible for selecting the correct
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// termination condition, and rounding the result
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// to an int where required.
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//
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template <class Dist>
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inline typename Dist::value_type
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inverse_discrete_quantile(
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const Dist& dist,
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typename Dist::value_type p,
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bool c,
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const typename Dist::value_type& guess,
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const typename Dist::value_type& multiplier,
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const typename Dist::value_type& adder,
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const policies::discrete_quantile<policies::real>&,
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boost::uintmax_t& max_iter)
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{
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if(p > 0.5)
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{
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p = 1 - p;
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c = !c;
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}
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typename Dist::value_type pp = c ? 1 - p : p;
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if(pp <= pdf(dist, 0))
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return 0;
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return do_inverse_discrete_quantile(
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dist,
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p,
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||
|
|
c,
|
||
|
|
guess,
|
||
|
|
multiplier,
|
||
|
|
adder,
|
||
|
|
tools::eps_tolerance<typename Dist::value_type>(policies::digits<typename Dist::value_type, typename Dist::policy_type>()),
|
||
|
|
max_iter);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class Dist>
|
||
|
|
inline typename Dist::value_type
|
||
|
|
inverse_discrete_quantile(
|
||
|
|
const Dist& dist,
|
||
|
|
const typename Dist::value_type& p,
|
||
|
|
bool c,
|
||
|
|
const typename Dist::value_type& guess,
|
||
|
|
const typename Dist::value_type& multiplier,
|
||
|
|
const typename Dist::value_type& adder,
|
||
|
|
const policies::discrete_quantile<policies::integer_round_outwards>&,
|
||
|
|
boost::uintmax_t& max_iter)
|
||
|
|
{
|
||
|
|
typedef typename Dist::value_type value_type;
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
typename Dist::value_type pp = c ? 1 - p : p;
|
||
|
|
if(pp <= pdf(dist, 0))
|
||
|
|
return 0;
|
||
|
|
//
|
||
|
|
// What happens next depends on whether we're looking for an
|
||
|
|
// upper or lower quantile:
|
||
|
|
//
|
||
|
|
if(pp < 0.5f)
|
||
|
|
return round_to_floor(dist, do_inverse_discrete_quantile(
|
||
|
|
dist,
|
||
|
|
p,
|
||
|
|
c,
|
||
|
|
(guess < 1 ? value_type(1) : (value_type)floor(guess)),
|
||
|
|
multiplier,
|
||
|
|
adder,
|
||
|
|
tools::equal_floor(),
|
||
|
|
max_iter), p, c);
|
||
|
|
// else:
|
||
|
|
return round_to_ceil(dist, do_inverse_discrete_quantile(
|
||
|
|
dist,
|
||
|
|
p,
|
||
|
|
c,
|
||
|
|
(value_type)ceil(guess),
|
||
|
|
multiplier,
|
||
|
|
adder,
|
||
|
|
tools::equal_ceil(),
|
||
|
|
max_iter), p, c);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class Dist>
|
||
|
|
inline typename Dist::value_type
|
||
|
|
inverse_discrete_quantile(
|
||
|
|
const Dist& dist,
|
||
|
|
const typename Dist::value_type& p,
|
||
|
|
bool c,
|
||
|
|
const typename Dist::value_type& guess,
|
||
|
|
const typename Dist::value_type& multiplier,
|
||
|
|
const typename Dist::value_type& adder,
|
||
|
|
const policies::discrete_quantile<policies::integer_round_inwards>&,
|
||
|
|
boost::uintmax_t& max_iter)
|
||
|
|
{
|
||
|
|
typedef typename Dist::value_type value_type;
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
typename Dist::value_type pp = c ? 1 - p : p;
|
||
|
|
if(pp <= pdf(dist, 0))
|
||
|
|
return 0;
|
||
|
|
//
|
||
|
|
// What happens next depends on whether we're looking for an
|
||
|
|
// upper or lower quantile:
|
||
|
|
//
|
||
|
|
if(pp < 0.5f)
|
||
|
|
return round_to_ceil(dist, do_inverse_discrete_quantile(
|
||
|
|
dist,
|
||
|
|
p,
|
||
|
|
c,
|
||
|
|
ceil(guess),
|
||
|
|
multiplier,
|
||
|
|
adder,
|
||
|
|
tools::equal_ceil(),
|
||
|
|
max_iter), p, c);
|
||
|
|
// else:
|
||
|
|
return round_to_floor(dist, do_inverse_discrete_quantile(
|
||
|
|
dist,
|
||
|
|
p,
|
||
|
|
c,
|
||
|
|
(guess < 1 ? value_type(1) : floor(guess)),
|
||
|
|
multiplier,
|
||
|
|
adder,
|
||
|
|
tools::equal_floor(),
|
||
|
|
max_iter), p, c);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class Dist>
|
||
|
|
inline typename Dist::value_type
|
||
|
|
inverse_discrete_quantile(
|
||
|
|
const Dist& dist,
|
||
|
|
const typename Dist::value_type& p,
|
||
|
|
bool c,
|
||
|
|
const typename Dist::value_type& guess,
|
||
|
|
const typename Dist::value_type& multiplier,
|
||
|
|
const typename Dist::value_type& adder,
|
||
|
|
const policies::discrete_quantile<policies::integer_round_down>&,
|
||
|
|
boost::uintmax_t& max_iter)
|
||
|
|
{
|
||
|
|
typedef typename Dist::value_type value_type;
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
typename Dist::value_type pp = c ? 1 - p : p;
|
||
|
|
if(pp <= pdf(dist, 0))
|
||
|
|
return 0;
|
||
|
|
return round_to_floor(dist, do_inverse_discrete_quantile(
|
||
|
|
dist,
|
||
|
|
p,
|
||
|
|
c,
|
||
|
|
(guess < 1 ? value_type(1) : floor(guess)),
|
||
|
|
multiplier,
|
||
|
|
adder,
|
||
|
|
tools::equal_floor(),
|
||
|
|
max_iter), p, c);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class Dist>
|
||
|
|
inline typename Dist::value_type
|
||
|
|
inverse_discrete_quantile(
|
||
|
|
const Dist& dist,
|
||
|
|
const typename Dist::value_type& p,
|
||
|
|
bool c,
|
||
|
|
const typename Dist::value_type& guess,
|
||
|
|
const typename Dist::value_type& multiplier,
|
||
|
|
const typename Dist::value_type& adder,
|
||
|
|
const policies::discrete_quantile<policies::integer_round_up>&,
|
||
|
|
boost::uintmax_t& max_iter)
|
||
|
|
{
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
typename Dist::value_type pp = c ? 1 - p : p;
|
||
|
|
if(pp <= pdf(dist, 0))
|
||
|
|
return 0;
|
||
|
|
return round_to_ceil(dist, do_inverse_discrete_quantile(
|
||
|
|
dist,
|
||
|
|
p,
|
||
|
|
c,
|
||
|
|
ceil(guess),
|
||
|
|
multiplier,
|
||
|
|
adder,
|
||
|
|
tools::equal_ceil(),
|
||
|
|
max_iter), p, c);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class Dist>
|
||
|
|
inline typename Dist::value_type
|
||
|
|
inverse_discrete_quantile(
|
||
|
|
const Dist& dist,
|
||
|
|
const typename Dist::value_type& p,
|
||
|
|
bool c,
|
||
|
|
const typename Dist::value_type& guess,
|
||
|
|
const typename Dist::value_type& multiplier,
|
||
|
|
const typename Dist::value_type& adder,
|
||
|
|
const policies::discrete_quantile<policies::integer_round_nearest>&,
|
||
|
|
boost::uintmax_t& max_iter)
|
||
|
|
{
|
||
|
|
typedef typename Dist::value_type value_type;
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
typename Dist::value_type pp = c ? 1 - p : p;
|
||
|
|
if(pp <= pdf(dist, 0))
|
||
|
|
return 0;
|
||
|
|
//
|
||
|
|
// Note that we adjust the guess to the nearest half-integer:
|
||
|
|
// this increase the chances that we will bracket the root
|
||
|
|
// with two results that both round to the same integer quickly.
|
||
|
|
//
|
||
|
|
return round_to_floor(dist, do_inverse_discrete_quantile(
|
||
|
|
dist,
|
||
|
|
p,
|
||
|
|
c,
|
||
|
|
(guess < 0.5f ? value_type(1.5f) : floor(guess + 0.5f) + 0.5f),
|
||
|
|
multiplier,
|
||
|
|
adder,
|
||
|
|
tools::equal_nearest_integer(),
|
||
|
|
max_iter) + 0.5f, p, c);
|
||
|
|
}
|
||
|
|
|
||
|
|
}}} // namespaces
|
||
|
|
|
||
|
|
#endif // BOOST_MATH_DISTRIBUTIONS_DETAIL_INV_DISCRETE_QUANTILE
|
||
|
|
|