#include <BaseNumericalRandomGenerator.h>

Inheritance diagram for BaseNumericalRandomGenerator:

Public Member Functions
	BaseNumericalRandomGenerator (double xmin=0., double xmax=1., int n=1000, int iter=6)

virtual double	function (double x)=0

double	generate (RandomEngineAndDistribution const *) const
	The random generation according to function() More...

double	generateExp (RandomEngineAndDistribution const *) const

double	generateLin (RandomEngineAndDistribution const *) const

void	initialize ()
	The initialization (numerical integarion, inversion) More...

bool	setSubInterval (double x1, double x2)
	To shoot in a given interval. More...

virtual	~BaseNumericalRandomGenerator ()
	Default destructor. More...

Protected Attributes
double	deltar

std::vector< double >	f

int	iter

int	n

double	rmin

std::vector< double >	sampling

double	xmax

double	xmin

Private Attributes
int	m

Detailed Description

Definition at line 27 of file BaseNumericalRandomGenerator.h.

Constructor & Destructor Documentation

BaseNumericalRandomGenerator::BaseNumericalRandomGenerator	(	double	xmin = `0.`,
		double	xmax = `1.`,
		int	n = `1000`,
		int	iter = `6`
	)

Constructor that perform the necessary integration and inversion steps xmin and xmax are the generation bounds, n is the internal table size and iter is the number of iterations for the numerical part.

Definition at line 7 of file BaseNumericalRandomGenerator.cc.

References f, and sampling.

                                                               :
   xmin(xmin), xmax(xmax), n(n), iter(iter) 
 {
   f.resize(n);
   sampling.resize(n);
 }

virtual BaseNumericalRandomGenerator::~BaseNumericalRandomGenerator ( )

inlinevirtual

Default destructor.

Definition at line 40 of file BaseNumericalRandomGenerator.h.

40 {}

Member Function Documentation

virtual double BaseNumericalRandomGenerator::function ( double x )

pure virtual

Implemented in HistogramGenerator, GammaNumericalGenerator, and LandauFluctuationGenerator.

double BaseNumericalRandomGenerator::generate ( RandomEngineAndDistribution const * random ) const

The random generation according to function()

Definition at line 82 of file BaseNumericalRandomGenerator.cc.

References deltar, RandomEngineAndDistribution::flatShoot(), i, alignCSCRings::r, rmin, alignCSCRings::s, and sampling.

Referenced by GammaNumericalGenerator::gamma(), and LandauFluctuationGenerator::landau().

                                                                                       {
 
   double r=rmin+deltar*random->flatShoot();
   int i=(int)r;
   double s=r-(double)i;
   //  cout << " i,r,s = " << i << " " << r << " " << s << endl;
   return sampling[i]+s*(sampling[i+1]-sampling[i]);
 
 }

double BaseNumericalRandomGenerator::generateExp ( RandomEngineAndDistribution const * random ) const

The random generation according to function(), refined to generate as an exponential in each of the intervals

Definition at line 93 of file BaseNumericalRandomGenerator.cc.

References a, b, deltar, create_public_lumi_plots::exp, f, RandomEngineAndDistribution::flatShoot(), i, cmsBatch::log, alignCSCRings::r, rmin, and sampling.

Referenced by GammaNumericalGenerator::gamma_exp().

                                                                                          {
 
   double r=rmin+deltar*random->flatShoot();
   int i=(int)r;
   //  double s=r-(double)i;
   //  cout << " i,r,s = " << i << " " << r << " " << s << endl;
   double b = -std::log(f[i+1]/f[i]) / (sampling[i+1]-sampling[i]);
   double a = f[i] * std::exp(b*sampling[i]);
 
   double umin = -a/b*std::exp(-b*sampling[i]);
   double umax = -a/b*std::exp(-b*sampling[i+1]);
   double u= (umax-umin) * random->flatShoot() + umin;
 
   return -std::log(-b/a*u) / b;
 
 }

double BaseNumericalRandomGenerator::generateLin ( RandomEngineAndDistribution const * random ) const

The random generation according to function(), refined to generate as a linear function in each of the intervals

Definition at line 111 of file BaseNumericalRandomGenerator.cc.

References a, b, deltar, f, RandomEngineAndDistribution::flatShoot(), i, alignCSCRings::r, rmin, sampling, and mathSSE::sqrt().

Referenced by GammaNumericalGenerator::gamma_lin().

                                                                                          {
 
   double r=rmin+deltar*random->flatShoot();
   int i=(int)r;
   //  double s=r-(double)i;
   //  cout << " i,r,s = " << i << " " << r << " " << s << endl;
   double a = (f[i+1]-f[i]) / (sampling[i+1]-sampling[i]);
   double b = f[i] - a*sampling[i];
 
   double umin = a*sampling[i]*sampling[i]/2. + b*sampling[i];
   double umax = a*sampling[i+1]*sampling[i+1]/2. + b*sampling[i+1];
   double u= (umax-umin) * random->flatShoot() + umin;
 
   return (-b+std::sqrt(b*b+2.*a*u))/a;
 
 }

void BaseNumericalRandomGenerator::initialize ( )

The initialization (numerical integarion, inversion)

Definition at line 16 of file BaseNumericalRandomGenerator.cc.

References a, deltar, f, i, iter, relval_steps::k, m, n, alignCSCRings::r, rmin, sampling, xmax, xmin, y, and z.

Referenced by GammaNumericalGenerator::GammaNumericalGenerator(), HistogramGenerator::HistogramGenerator(), and LandauFluctuationGenerator::LandauFluctuationGenerator().

                                          {
   
   m = n-1;
   rmin = 0.;
   deltar = (double)m-rmin;
 
   std::vector<double> a,y,z,xnew;
   a.resize(n);
   y.resize(n);
   z.resize(n);
   xnew.resize(n);
 
   double sig1 = 0.;
 
   // Initialize sampling
   double du = (xmax-xmin)/(float)m;
   sampling[0] = xmin;
   for (int i=1; i<n; ++i) 
     sampling[i] = sampling[i-1] + du;
 
   // Starting point for iterations
   for (int it=0; it<iter; ++it) { 
     
     // Calculate function values
     for (int i=0; i<n; ++i )
       f[i] = function(sampling[i]);
 
     // Calculate bin areas
     for (int i=0; i<m; ++i )
       a[i] = (sampling[i+1]-sampling[i]) * (f[i+1]+f[i]) / 2.;
 
     // Calculate cumulative spectrum Y values
     y[0]=0.;
     for (int i=1; i<n; ++i )
       y[i] = y[i-1] + a[i-1];
 
     // Put equidistant points on y scale
     double dz = y[n-1]/(float)m;
     z[0]=0;
     for (int i=1; i<n; ++i ) 
       z[i] = z[i-1] + dz; 
 
     // Determine spacinf of Z points in between Y points
     // From this, determine new X values and finally replace old values
     xnew[0] = sampling[0];
     xnew[n-1] = sampling[n-1];
     int k=0; 
     for ( int i=1; i<m; ++i ) { 
       while ( y[k+1] < z[i] ) ++k;
       double r = (z[i]-y[k]) / (y[k+1]-y[k]);
       xnew[i] = sampling[k] + (sampling[k+1]-sampling[k])*r;
     }
 
     for ( int i=0; i<n; ++i )
       sampling[i] = xnew[i];
 
     sig1 = sig1 + y[m];
     // std::cout << "BaseNumericalRandomGenerator::Iteration # " << it+1 
     // << " Integral = " << sig1/(float)(it+1) 
     // << std::endl;
 
   }
 
 }

bool BaseNumericalRandomGenerator::setSubInterval	(	double	x1,
		double	x2
	)

To shoot in a given interval.

Definition at line 129 of file BaseNumericalRandomGenerator.cc.

References deltar, rmin, sampling, tmp, and xmax.

                                                                     {
   if(x1<xmin||x2>xmax) return false;
   if(x1>x2)
     {
       double tmp=x1;
       x1=x2;
       x2=tmp;
     }
   
   unsigned ibin=1;
   for(;ibin<(unsigned)n&&x1>sampling[ibin];++ibin);
   unsigned ibin1=ibin;
   for(;ibin<(unsigned)n&&x2>sampling[ibin];++ibin);
   unsigned ibin2=ibin;
 
   //  cout << sampling[ibin1-1] << " " << x1 << " " << sampling[ibin1] << endl;
   // cout << sampling[ibin2-1] << " " << x2 << " " << sampling[ibin2] << endl;
 
   rmin = ibin1+(x1-sampling[ibin1])/(sampling[ibin1]-sampling[ibin1-1]);
   deltar= ibin2+(x2-sampling[ibin2])/(sampling[ibin2]-sampling[ibin2-1]) - rmin;
   //  cout << rmin << " " << deltar << endl;
   return true;
 }