[u/mrichter/AliRoot.git] / FMD / flow / AliFMDFlowEfficiency.h

// -*- mode: C++ -*-
/* Copyright (C) 2007 Christian Holm Christensen <cholm@nbi.dk>
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public License
 * as published by the Free Software Foundation; either version 2.1 of
 * the License, or (at your option) any later version.
 *
 * This library 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
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
 * USA
 */
#ifndef ALIFMDFLOWEFFICIENCY_H
#define ALIFMDFLOWEFFICIENCY_H
#include <Rtypes.h>

/** @defgroup z_eff Efficiency calculations 
    @brief Functions to do efficiency calculations based on a
    Baysian analysis. 
*/
/** Namespace for efficency calculations 
    @ingroup z_eff */
namespace AliFMDFlowEfficiency 
{
  /** @{ 
      @ingroup z_eff */
  /** Calculate @f$ \log(\Gamma(z))\ \forall z>0@f$ 
      @param z Argument. 
      @return  @f$ \log(\Gamma(z))@f$ */ 
  Double_t LnGamma(Double_t z);
  
  /** Continued fraction evaluation by modified Lentz's method 
      used in calculation of incomplete  Beta function. 
      @param x argument. 
      @param a lower limit
      @param b upper limit
      @return incomplete Beta function evaluated at x */ 
  Double_t BetaCf(Double_t x, Double_t a, Double_t b);
  
  /** Calculates the incomplete Beta function @f$ I_x(a,b)@f$;
      this is the incomplete Beta function divided by the
      complete Beta function. 
      @param a Lower bound 
      @param b Upper bound 
      @param x Order 
      @return  @f$ I_x(a,b)@f$ */
  Double_t IBetaI(Double_t a, Double_t b, Double_t x);

  /** Calculates the fraction of the area under the curve 
      @f$ x^k (1-x)^{n-k}@f$ between @f$ x=a@f$ and @f$ x=b@f$ 
      @param a lower limit 
      @param b upper limit 
      @param k Parameter @f$ k@f$ 
      @param n Parameter @f$ n@f$ 
      @return The fraction under the curve */ 
  Double_t BetaAB(Double_t a, Double_t b, Int_t k, Int_t n);
  
  /** Integrates the Binomial distribution with parameters @a k and @a
      n, and determines the upper edge of the integration region, 
      starting at @a low, which contains probability content @a c.  If
      an upper limit is found, the value is returned. If no solution
      is found, -1 is returned. Check to see if there is any solution
      by verifying that the integral up to the maximum upper limit (1)
      is greater than c 
      @param low Where to start the integration from. 
      @param k   @a k parameter of the Binomial distribution. 
      @param n   @a N parameter of the Binomial distribution. 
      @param c   Wanted confidence limit (defaults to 68% - similar to
      @f$ 1\sigma@f$ of a Gaussian distribution)
      @return the upper limit of the confidence interval, or -1 in
      case of failure */
  Double_t SearchUpper(Double_t low, Int_t k, Int_t n, Double_t c=0.683);

  /** Integrates the Binomial distribution with parameters @a k and @a
      n, and determines the lower edge of the integration region, 
      ending at @a high, which contains probability content @a c.  If
      a lower limit is found, the value is returned. If no solution
      is found, -1 is returned. Check to see if there is any solution
      by verifying that the integral up to the maximum upper limit (1)
      is greater than c 
      @param high Where to end the integration at. 
      @param k    @a k parameter of the Binomial distribution. 
      @param n    @a N parameter of the Binomial distribution. 
      @param c    Wanted confidence limit (defaults to 68% - similar to
      @f$ 1\sigma@f$ of a Gaussian distribution) 
      @return the upper limit of the confidence interval, or -1 in
      case of failure */
  Double_t SearchLower(Double_t high, Int_t k, Int_t n, Double_t c=0.683);

  /** Numerical equation solver.  This includes root finding and
      minimum finding algorithms. Adapted from Numerical Recipes in
      C, 2nd edition. Translated to C++ by Marc Paterno
      @param ax   Left side of interval 
      @param bx   Middle of interval 
      @param cx   Right side of interval 
      @param tol  Tolerance 
      @param xmin On return, the value of @f$ x@f$ such that @f$
      f(x)@f$ i minimal. 
      @param k    Parameter of the Binomial distribution 
      @param n    Parameter of the Binomial distribution 
      @param c    Confidence level. 
      @return Minimum of @f$ f = f(x)@f$. */
  Double_t Brent(Double_t ax, Double_t bx, Double_t cx, Double_t& xmin, 
	       Int_t k, Int_t n, Double_t c=.683, Double_t tol=1e-9);
  
  /** Return the length of the interval starting at @a l that contains
      @a c of the @f$ x^k (1-x)^{n-k}@f$ distribution. If there is no
      sufficient interval starting at @a l, we return 2.0 
      @param l Lower bound 
      @param k Binomial parameter k 
      @param n Binomial parameter n 
      @param c Condifience level 
      @return Legnth of interval */
  Double_t Length(Double_t l, Int_t k, Int_t n, Double_t c=0.683);
    

  /** Calculate the shortest central confidence interval containing
      the required probability content @a c. Interval(low) returns the
      length of the interval starting at low that contains @a c
      probability. We use Brent's method, except in two special cases:
      when @a k=0, or when @a k=n 
      @author Marc Paterno
      @param k    Binomial parameter @a k 
      @param n    Binomial parameter @a n 
      @param low  On return, the lower limit
      @param high On return, the upper limit 
      @param c    Required confidence level (defaults to 68% - similar
      to @f$ 1\sigma@f$ of a Gaussian distribution)
      @return The mode */ 
  Double_t Interval(Int_t k, Int_t n, Double_t& low, Double_t& high, Double_t c=0.683);
  /** @} */
}


#endif
//
// EOF
//
Commit	Line	Data
39eefe19	1	// -- mode: C++ --
97e94238	2	/* Copyright (C) 2007 Christian Holm Christensen <cholm@nbi.dk>
	3	*
	4	* This library is free software; you can redistribute it and/or
	5	* modify it under the terms of the GNU Lesser General Public License
	6	* as published by the Free Software Foundation; either version 2.1 of
	7	* the License, or (at your option) any later version.
	8	*
	9	* This library is distributed in the hope that it will be useful, but
	10	* WITHOUT ANY WARRANTY; without even the implied warranty of
	11	* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
	12	* Lesser General Public License for more details.
	13	*
	14	* You should have received a copy of the GNU Lesser General Public
	15	* License along with this library; if not, write to the Free Software
	16	* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
	17	* USA
	18	*/
	19	#ifndef ALIFMDFLOWEFFICIENCY_H
	20	#define ALIFMDFLOWEFFICIENCY_H
39eefe19	21	#include <Rtypes.h>
	22
	23	/** @defgroup z_eff Efficiency calculations
	24	@brief Functions to do efficiency calculations based on a
	25	Baysian analysis.
	26	*/
	27	/** Namespace for efficency calculations
	28	@ingroup z_eff */
	29	namespace AliFMDFlowEfficiency
	30	{
	31	/** @{
	32	@ingroup z_eff */
	33	/** Calculate @f$ \log(\Gamma(z))\ \forall z>0@f$
	34	@param z Argument.
	35	@return @f$ \log(\Gamma(z))@f$ */
	36	Double_t LnGamma(Double_t z);
	37
	38	/** Continued fraction evaluation by modified Lentz's method
	39	used in calculation of incomplete Beta function.
	40	@param x argument.
	41	@param a lower limit
	42	@param b upper limit
	43	@return incomplete Beta function evaluated at x */
	44	Double_t BetaCf(Double_t x, Double_t a, Double_t b);
	45
	46	/** Calculates the incomplete Beta function @f$ I_x(a,b)@f$;
	47	this is the incomplete Beta function divided by the
	48	complete Beta function.
	49	@param a Lower bound
	50	@param b Upper bound
	51	@param x Order
	52	@return @f$ I_x(a,b)@f$ */
	53	Double_t IBetaI(Double_t a, Double_t b, Double_t x);
	54
	55	/** Calculates the fraction of the area under the curve
	56	@f$ x^k (1-x)^{n-k}@f$ between @f$ x=a@f$ and @f$ x=b@f$
	57	@param a lower limit
	58	@param b upper limit
	59	@param k Parameter @f$ k@f$
	60	@param n Parameter @f$ n@f$
	61	@return The fraction under the curve */
	62	Double_t BetaAB(Double_t a, Double_t b, Int_t k, Int_t n);
	63
	64	/** Integrates the Binomial distribution with parameters @a k and @a
	65	n, and determines the upper edge of the integration region,
	66	starting at @a low, which contains probability content @a c. If
	67	an upper limit is found, the value is returned. If no solution
	68	is found, -1 is returned. Check to see if there is any solution
	69	by verifying that the integral up to the maximum upper limit (1)
	70	is greater than c
	71	@param low Where to start the integration from.
	72	@param k @a k parameter of the Binomial distribution.
	73	@param n @a N parameter of the Binomial distribution.
	74	@param c Wanted confidence limit (defaults to 68% - similar to
	75	@f$ 1\sigma@f$ of a Gaussian distribution)
	76	@return the upper limit of the confidence interval, or -1 in
	77	case of failure */
	78	Double_t SearchUpper(Double_t low, Int_t k, Int_t n, Double_t c=0.683);
	79
	80	/** Integrates the Binomial distribution with parameters @a k and @a
	81	n, and determines the lower edge of the integration region,
	82	ending at @a high, which contains probability content @a c. If
	83	a lower limit is found, the value is returned. If no solution
	84	is found, -1 is returned. Check to see if there is any solution
85	by verifying that the integral up to the maximum upper limit (1)
86	is greater than c
87	@param high Where to end the integration at.
88	@param k @a k parameter of the Binomial distribution.
89	@param n @a N parameter of the Binomial distribution.
90	@param c Wanted confidence limit (defaults to 68% - similar to
91	@f$ 1\sigma@f$ of a Gaussian distribution)
92	@return the upper limit of the confidence interval, or -1 in
93	case of failure */
94	Double_t SearchLower(Double_t high, Int_t k, Int_t n, Double_t c=0.683);
95
96	/** Numerical equation solver. This includes root finding and
97	minimum finding algorithms. Adapted from Numerical Recipes in
98	C, 2nd edition. Translated to C++ by Marc Paterno
99	@param ax Left side of interval
100	@param bx Middle of interval
101	@param cx Right side of interval
102	@param tol Tolerance
103	@param xmin On return, the value of @f$ x@f$ such that @f$
104	f(x)@f$ i minimal.
105	@param k Parameter of the Binomial distribution
106	@param n Parameter of the Binomial distribution
107	@param c Confidence level.
108	@return Minimum of @f$ f = f(x)@f$. */
109	Double_t Brent(Double_t ax, Double_t bx, Double_t cx, Double_t& xmin,
110	Int_t k, Int_t n, Double_t c=.683, Double_t tol=1e-9);
111
112	/** Return the length of the interval starting at @a l that contains
113	@a c of the @f$ x^k (1-x)^{n-k}@f$ distribution. If there is no
114	sufficient interval starting at @a l, we return 2.0
115	@param l Lower bound
116	@param k Binomial parameter k
117	@param n Binomial parameter n
118	@param c Condifience level
119	@return Legnth of interval */
120	Double_t Length(Double_t l, Int_t k, Int_t n, Double_t c=0.683);
121
122
123	/** Calculate the shortest central confidence interval containing
124	the required probability content @a c. Interval(low) returns the
125	length of the interval starting at low that contains @a c
126	probability. We use Brent's method, except in two special cases:
127	when @a k=0, or when @a k=n
128	@author Marc Paterno
129	@param k Binomial parameter @a k
130	@param n Binomial parameter @a n
131	@param low On return, the lower limit
132	@param high On return, the upper limit
133	@param c Required confidence level (defaults to 68% - similar
134	to @f$ 1\sigma@f$ of a Gaussian distribution)
135	@return The mode */
136	Double_t Interval(Int_t k, Int_t n, Double_t& low, Double_t& high, Double_t c=0.683);
137	/** @} */
138	}
139
140
141	#endif
142	//
143	// EOF
144	//
145