RandGamma.cc

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// $Id:$
// -*- C++ -*-
//
// -----------------------------------------------------------------------
//                             HEP Random
//                          --- RandGamma ---
//                      class implementation file
// -----------------------------------------------------------------------

// =======================================================================
// John Marraffino - Created: 12th May 1998
// M Fischler      - put and get to/from streams 12/13/04
// M Fischler         - put/get to/from streams uses pairs of ulongs when
//                      + storing doubles avoid problems with precision 
//                      4/14/05
// =======================================================================

#include "CLHEP/Random/RandGamma.h"
#include "CLHEP/Random/DoubConv.h"
#include <cmath>        // for std::log()

namespace CLHEP {

std::string RandGamma::name() const {return "RandGamma";}
HepRandomEngine & RandGamma::engine() {return *localEngine;}

RandGamma::~RandGamma() {
}

double RandGamma::shoot( HepRandomEngine *anEngine,  double k,
                                                        double lambda ) {
  return genGamma( anEngine, k, lambda );
}

double RandGamma::shoot( double k, double lambda ) {
  HepRandomEngine *anEngine = HepRandom::getTheEngine();
  return genGamma( anEngine, k, lambda );
}

double RandGamma::fire( double k, double lambda ) {
  return genGamma( localEngine.get(), k, lambda );
}

void RandGamma::shootArray( const int size, double* vect,
                            double k, double lambda )
{
  for( double* v = vect; v != vect + size; ++v )
    *v = shoot(k,lambda);
}

void RandGamma::shootArray( HepRandomEngine* anEngine,
                            const int size, double* vect,
                            double k, double lambda )
{
  for( double* v = vect; v != vect + size; ++v )
    *v = shoot(anEngine,k,lambda);
}

void RandGamma::fireArray( const int size, double* vect)
{
  for( double* v = vect; v != vect + size; ++v )
    *v = fire(defaultK,defaultLambda);
}

void RandGamma::fireArray( const int size, double* vect,
                           double k, double lambda )
{
  for( double* v = vect; v != vect + size; ++v )
    *v = fire(k,lambda);
}

double RandGamma::genGamma( HepRandomEngine *anEngine,
                               double a, double lambda ) {
/*************************************************************************
 *         Gamma Distribution - Rejection algorithm gs combined with     *
 *                              Acceptance complement method gd          *
 *************************************************************************/

static double aa = -1.0, aaa = -1.0, b, c, d, e, r, s, si, ss, q0,
       q1 = 0.0416666664, q2 =  0.0208333723, q3 = 0.0079849875,
       q4 = 0.0015746717, q5 = -0.0003349403, q6 = 0.0003340332,
       q7 = 0.0006053049, q8 = -0.0004701849, q9 = 0.0001710320,
       a1 = 0.333333333,  a2 = -0.249999949,  a3 = 0.199999867,
       a4 =-0.166677482,  a5 =  0.142873973,  a6 =-0.124385581,
       a7 = 0.110368310,  a8 = -0.112750886,  a9 = 0.104089866,
       e1 = 1.000000000,  e2 =  0.499999994,  e3 = 0.166666848,
       e4 = 0.041664508,  e5 =  0.008345522,  e6 = 0.001353826,
       e7 = 0.000247453;

double gds,p,q,t,sign_u,u,v,w,x;
double v1,v2,v12;

// Check for invalid input values

 if( a <= 0.0 ) return (-1.0);
 if( lambda <= 0.0 ) return (-1.0);

 if (a < 1.0)
   {          // CASE A: Acceptance rejection algorithm gs
    b = 1.0 + 0.36788794412 * a;       // Step 1
    for(;;)
      {
       p = b * anEngine->flat();
       if (p <= 1.0)
          {                            // Step 2. Case gds <= 1
           gds = std::exp(std::log(p) / a);
           if (std::log(anEngine->flat()) <= -gds) return(gds/lambda);
          }
       else
          {                            // Step 3. Case gds > 1
           gds = - std::log ((b - p) / a);
           if (std::log(anEngine->flat()) <= ((a - 1.0) * std::log(gds))) return(gds/lambda);
          }
      }
   }
 else
   {          // CASE B: Acceptance complement algorithm gd
    if (a != aa)
       {                               // Step 1. Preparations
        aa = a;
        ss = a - 0.5;
        s = std::sqrt(ss);
        d = 5.656854249 - 12.0 * s;
       }
                                              // Step 2. Normal deviate
    do {
      v1 = 2.0 * anEngine->flat() - 1.0;
      v2 = 2.0 * anEngine->flat() - 1.0;
      v12 = v1*v1 + v2*v2;
    } while ( v12 > 1.0 );
    t = v1*std::sqrt(-2.0*std::log(v12)/v12);
    x = s + 0.5 * t;
    gds = x * x;
    if (t >= 0.0) return(gds/lambda);         // Immediate acceptance

    u = anEngine->flat();            // Step 3. Uniform random number
    if (d * u <= t * t * t) return(gds/lambda); // Squeeze acceptance

    if (a != aaa)
       {                               // Step 4. Set-up for hat case
        aaa = a;
        r = 1.0 / a;
        q0 = ((((((((q9 * r + q8) * r + q7) * r + q6) * r + q5) * r + q4) *
                          r + q3) * r + q2) * r + q1) * r;
        if (a > 3.686)
           {
            if (a > 13.022)
               {
                b = 1.77;
                si = 0.75;
                c = 0.1515 / s;
               }
            else
               {
                b = 1.654 + 0.0076 * ss;
                si = 1.68 / s + 0.275;
                c = 0.062 / s + 0.024;
               }
           }
        else
           {
            b = 0.463 + s - 0.178 * ss;
            si = 1.235;
            c = 0.195 / s - 0.079 + 0.016 * s;
           }
       }
    if (x > 0.0)                       // Step 5. Calculation of q
       {
        v = t / (s + s);               // Step 6.
        if (std::fabs(v) > 0.25)
           {
            q = q0 - s * t + 0.25 * t * t + (ss + ss) * std::log(1.0 + v);
           }
        else
           {
            q = q0 + 0.5 * t * t * ((((((((a9 * v + a8) * v + a7) * v + a6) *
                            v + a5) * v + a4) * v + a3) * v + a2) * v + a1) * v;
           }                // Step 7. Quotient acceptance
        if (std::log(1.0 - u) <= q) return(gds/lambda);
       }

    for(;;)
       {                    // Step 8. Double exponential deviate t
        do
        {
         e = -std::log(anEngine->flat());
         u = anEngine->flat();
         u = u + u - 1.0;
         sign_u = (u > 0)? 1.0 : -1.0;
         t = b + (e * si) * sign_u;
        }
        while (t <= -0.71874483771719);   // Step 9. Rejection of t
        v = t / (s + s);                  // Step 10. New q(t)
        if (std::fabs(v) > 0.25)
           {
            q = q0 - s * t + 0.25 * t * t + (ss + ss) * std::log(1.0 + v);
           }
        else
           {
            q = q0 + 0.5 * t * t * ((((((((a9 * v + a8) * v + a7) * v + a6) *
                            v + a5) * v + a4) * v + a3) * v + a2) * v + a1) * v;
           }
        if (q <= 0.0) continue;           // Step 11.
        if (q > 0.5)
           {
            w = std::exp(q) - 1.0;
           }
        else
           {
            w = ((((((e7 * q + e6) * q + e5) * q + e4) * q + e3) * q + e2) *
                                     q + e1) * q;
           }                    // Step 12. Hat acceptance
        if ( c * u * sign_u <= w * std::exp(e - 0.5 * t * t))
           {
            x = s + 0.5 * t;
            return(x*x/lambda);
           }
       }
   }
}

std::ostream & RandGamma::put ( std::ostream & os ) const {
  int pr=os.precision(20);
  std::vector<unsigned long> t(2);
  os << " " << name() << "\n";
  os << "Uvec" << "\n";
  t = DoubConv::dto2longs(defaultK);
  os << defaultK << " " << t[0] << " " << t[1] << "\n";
  t = DoubConv::dto2longs(defaultLambda);
  os << defaultLambda << " " << t[0] << " " << t[1] << "\n";
  os.precision(pr);
  return os;
}

std::istream & RandGamma::get ( std::istream & is ) {
  std::string inName;
  is >> inName;
  if (inName != name()) {
    is.clear(std::ios::badbit | is.rdstate());
    std::cerr << "Mismatch when expecting to read state of a "
              << name() << " distribution\n"
              << "Name found was " << inName
              << "\nistream is left in the badbit state\n";
    return is;
  }
  if (possibleKeywordInput(is, "Uvec", defaultK)) {
    std::vector<unsigned long> t(2);
    is >> defaultK >> t[0] >> t[1]; defaultK = DoubConv::longs2double(t); 
    is >> defaultLambda>>t[0]>>t[1]; defaultLambda = DoubConv::longs2double(t); 
    return is;
  }
  // is >> defaultK encompassed by possibleKeywordInput
  is >> defaultLambda;
  return is;
}

}  // namespace CLHEP