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+/* boost random/non_central_chi_squared_distribution.hpp header file
+ *
+ * Copyright Thijs van den Berg 2014
+ * 
+ * Distributed under 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)
+ *
+ * See http://www.boost.org for most recent version including documentation.
+ *
+ * $Id$
+ */
+
+#ifndef BOOST_RANDOM_NON_CENTRAL_CHI_SQUARED_DISTRIBUTION_HPP
+#define BOOST_RANDOM_NON_CENTRAL_CHI_SQUARED_DISTRIBUTION_HPP
+
+#include <boost/config/no_tr1/cmath.hpp>
+#include <iosfwd>
+#include <istream>
+#include <boost/limits.hpp>
+#include <boost/random/detail/config.hpp>
+#include <boost/random/detail/operators.hpp>
+#include <boost/random/uniform_real_distribution.hpp>
+#include <boost/random/normal_distribution.hpp>
+#include <boost/random/chi_squared_distribution.hpp>
+#include <boost/random/poisson_distribution.hpp>
+
+namespace boost {
+namespace random {
+
+/**
+ * The noncentral chi-squared distribution is a real valued distribution with
+ * two parameter, @c k and @c lambda.  The distribution produces values > 0.
+ *
+ * This is the distribution of the sum of squares of k Normal distributed
+ * variates each with variance one and \f$\lambda\f$ the sum of squares of the
+ * normal means.
+ *
+ * The distribution function is
+ * \f$\displaystyle P(x) = \frac{1}{2} e^{-(x+\lambda)/2} \left( \frac{x}{\lambda} \right)^{k/4-1/2} I_{k/2-1}( \sqrt{\lambda x} )\f$.
+ *  where  \f$\displaystyle I_\nu(z)\f$ is a modified Bessel function of the
+ * first kind.
+ *
+ * The algorithm is taken from
+ *
+ *  @blockquote
+ *  "Monte Carlo Methods in Financial Engineering", Paul Glasserman,
+ *  2003, XIII, 596 p, Stochastic Modelling and Applied Probability, Vol. 53,
+ *  ISBN 978-0-387-21617-1, p 124, Fig. 3.5.
+ *  @endblockquote
+ */
+template <typename RealType = double>
+class non_central_chi_squared_distribution {
+public:
+    typedef RealType result_type;
+    typedef RealType input_type;
+    
+    class param_type {
+    public:
+        typedef non_central_chi_squared_distribution distribution_type;
+        
+        /**
+         * Constructs the parameters of a non_central_chi_squared_distribution.
+         * @c k and @c lambda are the parameter of the distribution.
+         *
+         * Requires: k > 0 && lambda > 0
+         */
+        explicit
+        param_type(RealType k_arg = RealType(1), RealType lambda_arg = RealType(1))
+        : _k(k_arg), _lambda(lambda_arg)
+        {
+            BOOST_ASSERT(k_arg > RealType(0));
+            BOOST_ASSERT(lambda_arg > RealType(0));
+        }
+        
+        /** Returns the @c k parameter of the distribution */
+        RealType k() const { return _k; }
+        
+        /** Returns the @c lambda parameter of the distribution */
+        RealType lambda() const { return _lambda; }
+
+        /** Writes the parameters of the distribution to a @c std::ostream. */
+        BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
+        {
+            os << parm._k << ' ' << parm._lambda;
+            return os;
+        }
+        
+        /** Reads the parameters of the distribution from a @c std::istream. */
+        BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
+        {
+            is >> parm._k >> std::ws >> parm._lambda;
+            return is;
+        }
+
+        /** Returns true if the parameters have the same values. */
+        BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
+        { return lhs._k == rhs._k && lhs._lambda == rhs._lambda; }
+        
+        /** Returns true if the parameters have different values. */
+        BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
+        
+    private:
+        RealType _k;
+        RealType _lambda;
+    };
+
+    /**
+     * Construct a @c non_central_chi_squared_distribution object. @c k and
+     * @c lambda are the parameter of the distribution.
+     *
+     * Requires: k > 0 && lambda > 0
+     */
+    explicit
+    non_central_chi_squared_distribution(RealType k_arg = RealType(1), RealType lambda_arg = RealType(1))
+      : _param(k_arg, lambda_arg)
+    {
+        BOOST_ASSERT(k_arg > RealType(0));
+        BOOST_ASSERT(lambda_arg > RealType(0));
+    }
+
+    /**
+     * Construct a @c non_central_chi_squared_distribution object from the parameter.
+     */
+    explicit
+    non_central_chi_squared_distribution(const param_type& parm)
+      : _param( parm )
+    { }
+    
+    /**
+     * Returns a random variate distributed according to the
+     * non central chi squared distribution specified by @c param.
+     */
+    template<typename URNG>
+    RealType operator()(URNG& eng, const param_type& parm) const
+    { return non_central_chi_squared_distribution(parm)(eng); }
+    
+    /**
+     * Returns a random variate distributed according to the
+     * non central chi squared distribution.
+     */
+    template<typename URNG> 
+    RealType operator()(URNG& eng) 
+    {
+        using std::sqrt;
+        if (_param.k() > 1) {
+            boost::random::normal_distribution<RealType> n_dist;
+            boost::random::chi_squared_distribution<RealType> c_dist(_param.k() - RealType(1));
+            RealType _z = n_dist(eng);
+            RealType _x = c_dist(eng);
+            RealType term1 = _z + sqrt(_param.lambda());
+            return term1*term1 + _x;
+        }
+        else {
+            boost::random::poisson_distribution<> p_dist(_param.lambda()/RealType(2));
+            boost::random::poisson_distribution<>::result_type _p = p_dist(eng);
+            boost::random::chi_squared_distribution<RealType> c_dist(_param.k() + RealType(2)*_p);
+            return c_dist(eng);
+        }
+    }
+
+    /** Returns the @c k parameter of the distribution. */
+    RealType k() const { return _param.k(); }
+    
+    /** Returns the @c lambda parameter of the distribution. */
+    RealType lambda() const { return _param.lambda(); }
+    
+    /** Returns the parameters of the distribution. */
+    param_type param() const { return _param; }
+    
+    /** Sets parameters of the distribution. */
+    void param(const param_type& parm) { _param = parm; }
+    
+    /** Resets the distribution, so that subsequent uses does not depend on values already produced by it.*/
+    void reset() {}
+    
+    /** Returns the smallest value that the distribution can produce. */
+    RealType min BOOST_PREVENT_MACRO_SUBSTITUTION() const
+    { return RealType(0); }
+    
+    /** Returns the largest value that the distribution can produce. */
+    RealType max BOOST_PREVENT_MACRO_SUBSTITUTION() const
+    { return (std::numeric_limits<RealType>::infinity)(); }
+
+    /** Writes the parameters of the distribution to a @c std::ostream. */
+    BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, non_central_chi_squared_distribution, dist)
+    {
+        os << dist.param();
+        return os;
+    }
+    
+    /** reads the parameters of the distribution from a @c std::istream. */
+    BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, non_central_chi_squared_distribution, dist)
+    {
+        param_type parm;
+        if(is >> parm) {
+            dist.param(parm);
+        }
+        return is;
+    }
+
+    /** Returns true if two distributions have the same parameters and produce 
+        the same sequence of random numbers given equal generators.*/
+    BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(non_central_chi_squared_distribution, lhs, rhs)
+    { return lhs.param() == rhs.param(); }
+    
+    /** Returns true if two distributions have different parameters and/or can produce 
+       different sequences of random numbers given equal generators.*/
+    BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(non_central_chi_squared_distribution)
+    
+private:
+
+    /// @cond show_private
+    param_type  _param;
+    /// @endcond
+};
+
+} // namespace random
+} // namespace boost
+
+#endif