poisson_randomdev.h

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/*
 *  poisson_randomdev.h
 *
 *  This file is part of NEST.
 *
 *  Copyright (C) 2004 The NEST Initiative
 *
 *  NEST is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  NEST is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with NEST.  If not, see <http://www.gnu.org/licenses/>.
 *
 */

#ifndef POISSON_RANDOMDEV_H
#define  POISSON_RANDOMDEV_H

#include <cmath>
#include <vector>

#include "randomgen.h"
#include "randomdev.h"
#include "lockptr.h" 

/************************************************************/
/* Class PoissonRNG                                         */
/*                                                          */
/* Generates an RNG which returns Poisson(x; lambda)        */
/* distributed random numbers out of an RNG which returns   */
/* uniformly distributed random numbers:                    */
/*                                                          */
/*    p(n) = (lambda^n / n!) exp(-lambda)  , n = 0, 1, ...  */ 
/*                                                          */
/* Arguments:                                               */
/*  - pointer to an RNG                                     */
/*  - parameters lambda (optional, default = 1)             */
/*                                                          */
/* Algorithm: Ahrens & Dieter [1]                           */
/*  - table lookup for lambda < 10                          */
/*  - involved rejection scheme based on normal random dev  */
/*    otherwise                                             */
/*  - answer to [2], Sec 3.4.1, exercise 8                  */
/*  - changing lambda involves some costly computations     */
/*                                                          */
/* Verification:                                            */
/*  - 60 different lambda, 0.01 .. 100                      */
/*  - 10.000.000 numbers generated per lambda               */
/*  - mt19937 as uniform rng source                         */
/*  - chi^2 test on batches of 10000 numbers                */
/*  - Kolmogorov-Smirnov test on chi^2 test scores          */
/*  - lambda == 0.01 critical, most likely due problems     */
/*    with test (just two bins in chi^2 test)               */
/*  - lambda == 20 failed KS test once, passed on second    */
/*    set of 10^7 numbers generated with different seed     */
/*                                                          */
/* References:                                              */
/* [1] J H Ahrens, U Dieter, ACM TOMS 8:163-179(1982)       */
/* [2] D E Knuth, The Art of Computer Programming, vol 2.   */
/*                                                          */
/* Author:                                                  */
/*  Hans Ekkehard Plesser                                   */
/*                                                          */
/* History:                                                 */
/*  3.0 HEP, 2003-05-23 Ahrens & Dieter algorithm           */
/*  2.0 HEP, 2002-07-09 (for librandom 2.0)                 */
/*                                                          */
/* To do:                                                   */
/*  - some of the numerics has only floating point accuracy */
/*    should be improved to double.                         */

/************************************************************/

namespace librandom {

/*BeginDocumentation
Name: rdevdict::poisson - poisson random deviate generator
Description:
   Generates poisson distributed random numbers.

   p(n) = (lambda^n / n!) exp(-lambda)  , n = 0, 1, ...  
    
Parameters:
   lambda - distribution parameter, lambda

SeeAlso: CreateRDV, RandomArray, rdevdict
Author: Hans Ekkehard Plesser
*/
  
  class PoissonRandomDev : public RandomDev
  {
    RngPtr r;       // pointer to underlying uniform RNG
    
  public:


    // accept only lockPTRs for initialization,
    // otherwise creation of a lock ptr would 
    // occur as side effect---might be unhealthy
    PoissonRandomDev(RngPtr, double lambda = 0.0);
    PoissonRandomDev(double lambda = 0.0);      // for threaded environments

    void set_lambda(double); 

    void set_status(const DictionaryDatum&); 

    void get_status(DictionaryDatum&) const; 

    using RandomDev::operator();
    using RandomDev::ldev;

    long ldev(RngPtr) const;   
    bool has_ldev() const { return true; }

    double operator()(RngPtr) const;     

  private:
    void init_();   

    double mu_;     

    // quantities for case A, steps N, I, S
    double s_;        
    double d_;        
    unsigned long L_; 

    // quantities for case A, step H 
    double c_;        

    // quantities for case A, function F
    double om_;        
    double c0_;
    double c1_;
    double c2_;
    double c3_;

    static const unsigned n_tab_;     
    std::vector<double> P_;           

    static const unsigned fact_[];    

    static const double   a_[];       
    static const unsigned n_a_;       

    void proc_f_(const unsigned k, double &px, double &py, 
         double &fx, double &fy) const;

  };

}

inline
double librandom::PoissonRandomDev::operator()(RngPtr rthrd) const
{ 
  return static_cast<double>(ldev(rthrd)); 
}

# endif