BCMath Namespace Reference

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Detailed Description

Some useful mathematic functions.

Author:

Daniel Kollar

Kevin Kröninger

Version:

1.0

Date:

08.2008 A namespace which encapsulates some mathematical functions necessary for BAT.

Functions
double	ApproxBinomial (int n, int k, double p)
double	ApproxLogFact (double x)
double	LogApproxBinomial (int n, int k, double p)
double	LogBinomFactor (int n, int k)
double	LogBreitWignerNonRel (double x, double mean, double Gamma, bool norm=false)
double	LogBreitWignerRel (double x, double mean, double Gamma)
double	LogFact (int n)
double	LogGaus (double x, double mean=0, double sigma=1, bool norm=false)
double	LogNoverK (int n, int k)
double	LogPoisson (double x, double par)
double	Max (double x, double y)
int	Max (int x, int y)
double	Min (double x, double y)
int	Min (int x, int y)
int	Nint (double x)
double	rms (int n, const double *a)

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Function Documentation

double BCMath::ApproxBinomial	(	int	n,
		int	k,
		double	p
	)

Calculates Binomial probability using approximations for factorial calculations if calculation for number greater than 20 required using the BCMath::ApproxLogFact function.

Definition at line 58 of file BCMath.cxx.

{
   return exp( BCMath::LogApproxBinomial(n, k, p) );
}

double BCMath::ApproxLogFact

(

double

x

)

Calculates natural logarithm of the n-factorial (n!) using Srinivasa Ramanujan approximation log(n!) = n*log(n) - n + log(n*(1.+4.*n*(1.+2.*n)))/6. + log(PI)/2. if n > 20. If n <= 20 it uses BCMath::LogFact to calculate it exactly.

Definition at line 109 of file BCMath.cxx.

{
   if(x>BCMATH_NFACT_ALIMIT)
      return x*log(x) - x + log(x*(1.+4.*x*(1.+2.*x)))/6. + log(M_PI)/2.;

   else
      return BCMath::LogFact((int)x);
}

double BCMath::LogApproxBinomial	(	int	n,
		int	k,
		double	p
	)

Calculates natural logarithm of the Binomial probability using approximations for factorial calculations if calculation for number greater than 20 required using the BCMath::ApproxLogFact function.

Definition at line 65 of file BCMath.cxx.

{
   // check p 
   if (p == 0)
      return -1e99; 

   else if (p == 1)
      return 0; 

   // switch parameters if n < k
   if(n<k)
   {
      int a=n;
      n=k;
      k=a;
   }

   return BCMath::LogBinomFactor(n,k) + (double)k*log(p) + (double)(n-k)*log(1.-p);
}

double BCMath::LogBinomFactor	(	int	n,
		int	k
	)

Calculates natural logarithm of the Binomial factor "n over k" using approximations for factorial calculations if calculation for number greater than 20 required using the BCMath::ApproxLogFact function. Even for large numbers the calculation is performed precisely, if n-k < 5

Definition at line 87 of file BCMath.cxx.

{
   // switch parameters if n < k
   if(n<k)
   {
      int a=n;
      n=k;
      k=a;
   }

   if(n==k || k==0) return 0.;
   if(k==1 || k==n-1) return log((double)n);

   // if no approximation needed
   if(n<BCMATH_NFACT_ALIMIT || (n-k)<5) return BCMath::LogNoverK(n,k);

   // calculate final log(n over k) using approximations if necessary
   return BCMath::ApproxLogFact((double)n) - BCMath::ApproxLogFact((double)k) - BCMath::ApproxLogFact((double)(n-k));
}

double BCMath::LogBreitWignerNonRel	(	double	x,
		double	mean,
		double	Gamma,
		bool	norm = false
	)

Definition at line 205 of file BCMath.cxx.

{
   double bw = log(Gamma) - log( (x - mean) * (x - mean) + Gamma * Gamma / 4.0);

   if (norm)
      bw -= log(2. * M_PI);

   return bw;
}

double BCMath::LogBreitWignerRel	(	double	x,
		double	mean,
		double	Gamma
	)

Definition at line 217 of file BCMath.cxx.

{
   return -log( (x*x - mean*mean) * (x*x - mean*mean) + mean*mean*Gamma*Gamma );
}

double BCMath::LogFact

(

int

n

)

Calculates natural logarithm of the n-factorial (n!)

Definition at line 119 of file BCMath.cxx.

{
   double ln = 0.;

   for(int i=1;i<=n;i++)
      ln += log((double)i);

   return ln;
}

double BCMath::LogGaus	(	double	x,
		double	mean = 0,
		double	sigma = 1,
		bool	norm = false
	)

Calculate the natural logarithm of a gaussian function with mean and sigma. If norm=true (default is false) the result is multiplied by the normalization constant, i.e. divided by sqrt(2*Pi)*sigma.

Definition at line 18 of file BCMath.cxx.

{
   // if we have a delta function, return fixed value
   if(sigma==0.)
      return 0;

   // if sigma is negative use absolute value
   if(sigma<0.)
      sigma *= -1.;

   double arg = (x-mean)/sigma;
   double result = -.5 * arg * arg;

   // check if we should add the normalization constant
   if(!norm)
      return result;

   // subtract the log of the denominator of the normalization constant
   // and return
   return result - log( sqrt( 2.* M_PI ) * sigma );
}

double BCMath::LogNoverK	(	int	n,
		int	k
	)

Calculates natural logarithm of the Binomial factor "n over k".

Definition at line 131 of file BCMath.cxx.

{
   // switch parameters if n < k
   if(n<k)
   {
      int a = n;
      n = k;
      k = a;
   }

   if(n==k || k==0) return 0.;
   if(k==1 || k==n-1) return log((double)n);

   int lmax = BCMath::Max(k,n-k);
   int lmin = BCMath::Min(k,n-k);

   double ln = 0.;

   for(int i=n;i>lmax;i--)
      ln += log((double)i);
   ln -= BCMath::LogFact(lmin);

   return ln;
}

double BCMath::LogPoisson	(	double	x,
		double	par
	)

Calculate the natural logarithm of a poisson distribution.

Definition at line 42 of file BCMath.cxx.

{
   if (par > 899)
      return BCMath::LogGaus(x,par,sqrt(par),true);

   if (x<0)
      return 0;

   if (x == 0.)
      return  -par;

   return x*log(par)-par-BCMath::ApproxLogFact(x);
}

double BCMath::Max	(	double	x,
		double	y
	)			[inline]

Definition at line 93 of file BCMath.h.

      { return x >= y ? x : y; }

int BCMath::Max	(	int	x,
		int	y
	)			[inline]

Returns the "greater or equal" of two numbers

Definition at line 90 of file BCMath.h.

      { return x >= y ? x : y; }

double BCMath::Min	(	double	x,
		double	y
	)			[inline]

Definition at line 102 of file BCMath.h.

   { return x <= y ? x : y; }

int BCMath::Min	(	int	x,
		int	y
	)			[inline]

Returns the "less or equal" of two numbers

Definition at line 99 of file BCMath.h.

      { return x <= y ? x : y; }

int BCMath::Nint

(

double

x

)

Returns the nearest integer of a double number.

Definition at line 158 of file BCMath.cxx.

{
   // round to integer
   int i;

   if (x >= 0)
   {
      i = (int)(x + .5);

      if (x + .5 == (double)i && i & 1)
         i--;
   }

   else
   {
      i = int(x - 0.5);

      if (x - 0.5 == double(i) && i & 1)
         i++;
   }

   return i;
}

double BCMath::rms	(	int	n,
		const double *	a
	)

Returns the rms of an array.

Definition at line 184 of file BCMath.cxx.

{
   if (n <= 0 || !a)
      return 0;

   double sum = 0., sum2 = 0.;

   for (int i = 0; i < n; i++)
   {
      sum  += a[i];
      sum2 += a[i] * a[i];
   }

   double n1 = 1./(double)n;
   double mean = sum * n1;

   return sqrt(fabs(sum2 * n1 - mean * mean));
}