// @(#)root/mathmore:$Id$
// Authors: B. List 29.4.2010

 /**********************************************************************
  *                                                                    *
  * Copyright (c) 2004 ROOT Foundation,  CERN/PH-SFT                   *
  *                                                                    *
  * This library 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.             *
  *                                                                    *
  * 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   *
  * General Public License for more details.                           *
  *                                                                    *
  * You should have received a copy of the GNU General Public License  *
  * along with this library (see file COPYING); if not, write          *
  * to the Free Software Foundation, Inc., 59 Temple Place, Suite      *
  * 330, Boston, MA 02111-1307 USA, or contact the author.             *
  *                                                                    *
  **********************************************************************/

// Header file for class VavilovFast
//
// Created by: blist  at Thu Apr 29 11:19:00 2010
//
// Last update: Thu Apr 29 11:19:00 2010
//
#ifndef ROOT_Math_VavilovFast
#define ROOT_Math_VavilovFast


/**
   @ingroup StatFunc
 */


#include "Math/Vavilov.h"

namespace ROOT {
namespace Math {

//____________________________________________________________________________
/**
   Class describing a Vavilov distribution.

   The probability density function of the Vavilov distribution
   as function of Landau's parameter is given by:
  \f[ p(\lambda_L; \kappa, \beta^2) =
  \frac{1}{2 \pi i}\int_{c-i\infty}^{c+i\infty} \phi(s) e^{\lambda_L s} ds\f]
   where \f$\phi(s) = e^{C} e^{\psi(s)}\f$
   with  \f$ C = \kappa (1+\beta^2 \gamma )\f$
   and \f$\psi(s)= s \ln \kappa + (s+\beta^2 \kappa)
               \cdot \left ( \int \limits_{0}^{1}
               \frac{1 - e^{\frac{-st}{\kappa}}}{t} \,d t- \gamma \right )
               - \kappa \, e^{\frac{-s}{\kappa}}\f$.
   \f$ \gamma = 0.5772156649\dots\f$ is Euler's constant.

   For the class VavilovFast,
   Pdf returns the Vavilov distribution as function of Landau's parameter
   \f$\lambda_L = \lambda_V/\kappa  - \ln \kappa\f$,
   which is the convention used in the CERNLIB routines, and in the tables
   by S.M. Seltzer and M.J. Berger: Energy loss stragglin of protons and mesons:
   Tabulation of the Vavilov distribution, pp 187-203
   in: National Research Council (U.S.), Committee on Nuclear Science:
   Studies in penetration of charged particles in matter,
   Nat. Akad. Sci. Publication 1133,
   Nucl. Sci. Series Report No. 39,
   Washington (Nat. Akad. Sci.) 1964, 388 pp.
   Available from
   <A HREF="http://books.google.de/books?id=kmMrAAAAYAAJ&lpg=PP9&pg=PA187#v=onepage&q&f=false">Google books</A>

   Therefore, for small values of \f$\kappa < 0.01\f$,
   pdf approaches the Landau distribution.

   For values \f$\kappa > 10\f$, the Gauss approximation should be used
   with \f$\mu\f$ and \f$\sigma\f$ given by Vavilov::mean(kappa, beta2)
   and sqrt(Vavilov::variance(kappa, beta2).

   For values \f$\kappa > 10\f$, the Gauss approximation should be used
   with \f$\mu\f$ and \f$\sigma\f$ given by Vavilov::mean(kappa, beta2)
   and sqrt(Vavilov::variance(kappa, beta2).

   The original Vavilov pdf is obtained by
   v.Pdf(lambdaV/kappa-log(kappa))/kappa.

   For detailed description see
   A. Rotondi and P. Montagna, Fast calculation of Vavilov distribution,
   <A HREF="http://dx.doi.org/10.1016/0168-583X(90)90749-K">Nucl. Instr. and Meth. B47 (1990) 215-224</A>,
   which has been implemented in
   <A HREF="http://wwwasdoc.web.cern.ch/wwwasdoc/shortwrupsdir/g115/top.html">
   CERNLIB (G115)</A>.

   The class stores coefficients needed to calculate \f$p(\lambda; \kappa, \beta^2)\f$
   for fixed values of \f$\kappa\f$ and \f$\beta^2\f$.
   Changing these values is computationally expensive.

   The parameter \f$\kappa\f$ must be in the range \f$0.01 \le \kappa \le 12\f$.

   The parameter \f$\beta^2\f$ must be in the range \f$0 \le \beta^2 \le 1\f$.

   Average times on a Pentium Core2 Duo P8400 2.26GHz:
   - 9.9us per call to SetKappaBeta2 or constructor
   - 0.095us per call to Pdf, Cdf
   - 3.7us per first call to Quantile after SetKappaBeta2 or constructor
   - 0.137us per subsequent call to Quantile

   Benno List, June 2010

   @ingroup StatFunc
 */


class VavilovFast: public Vavilov {

public:


   /**
      Initialize an object to calculate the Vavilov distribution

       @param kappa The parameter \f$\kappa\f$, which must be in the range \f$0.01 \le \kappa \le 12 \f$
       @param beta2 The parameter \f$\beta^2\f$, which must be in the range \f$0 \le \beta^2 \le 1 \f$
   */

  VavilovFast(double kappa=1, double beta2=1);


   /**
     Destructor
   */
   virtual ~VavilovFast();


public:

   /**
       Evaluate the Vavilov probability density function

       @param x The Landau parameter \f$x = \lambda_L\f$
   */
   double Pdf (double x) const;

   /**
       Evaluate the Vavilov probability density function,
       and set kappa and beta2, if necessary

       @param x The Landau parameter \f$x = \lambda_L\f$
       @param kappa The parameter \f$\kappa\f$, which must be in the range \f$0.01 \le \kappa \le 12 \f$
       @param beta2 The parameter \f$\beta^2\f$, which must be in the range \f$0 \le \beta^2 \le 1 \f$
   */
   double Pdf (double x, double kappa, double beta2);

   /**
       Evaluate the Vavilov cummulative probability density function

       @param x The Landau parameter \f$x = \lambda_L\f$
   */
   double Cdf (double x) const;

   /**
       Evaluate the Vavilov cummulative probability density function,
       and set kappa and beta2, if necessary

       @param x The Landau parameter \f$x = \lambda_L\f$
       @param kappa The parameter \f$\kappa\f$, which must be in the range \f$0.01 \le \kappa \le 12 \f$
       @param beta2 The parameter \f$\beta^2\f$, which must be in the range \f$0 \le \beta^2 \le 1 \f$
   */
   double Cdf (double x, double kappa, double beta2);

   /**
       Evaluate the Vavilov complementary cummulative probability density function

       @param x The Landau parameter \f$x = \lambda_L\f$
   */
   double Cdf_c (double x) const;

   /**
       Evaluate the Vavilov complementary cummulative probability density function,
       and set kappa and beta2, if necessary

       @param x The Landau parameter \f$x = \lambda_L\f$
       @param kappa The parameter \f$\kappa\f$, which must be in the range \f$0.01 \le \kappa \le 12 \f$
       @param beta2 The parameter \f$\beta^2\f$, which must be in the range \f$0 \le \beta^2 \le 1 \f$
   */
   double Cdf_c (double x, double kappa, double beta2);

   /**
       Evaluate the inverse of the Vavilov cummulative probability density function

       @param z The argument \f$z\f$, which must be in the range \f$0 \le z \le 1\f$
   */
   double Quantile (double z) const;

   /**
       Evaluate the inverse of the Vavilov cummulative probability density function,
       and set kappa and beta2, if necessary

       @param z The argument \f$z\f$, which must be in the range \f$0 \le z \le 1\f$
       @param kappa The parameter \f$\kappa\f$, which must be in the range \f$0.01 \le \kappa \le 12 \f$
       @param beta2 The parameter \f$\beta^2\f$, which must be in the range \f$0 \le \beta^2 \le 1 \f$
   */
   double Quantile (double z, double kappa, double beta2);

   /**
       Evaluate the inverse of the complementary Vavilov cummulative probability density function

       @param z The argument \f$z\f$, which must be in the range \f$0 \le z \le 1\f$
   */
   double Quantile_c (double z) const;

   /**
       Evaluate the inverse of the complementary Vavilov cummulative probability density function,
       and set kappa and beta2, if necessary

       @param z The argument \f$z\f$, which must be in the range \f$0 \le z \le 1\f$
       @param kappa The parameter \f$\kappa\f$, which must be in the range \f$0.01 \le \kappa \le 12 \f$
       @param beta2 The parameter \f$\beta^2\f$, which must be in the range \f$0 \le \beta^2 \le 1 \f$
   */
   double Quantile_c (double z, double kappa, double beta2);

   /**
      Change \f$\kappa\f$ and \f$\beta^2\f$ and recalculate coefficients if necessary

       @param kappa The parameter \f$\kappa\f$, which must be in the range \f$0.01 \le \kappa \le 12 \f$
       @param beta2 The parameter \f$\beta^2\f$, which must be in the range \f$0 \le \beta^2 \le 1 \f$
   */
   virtual void SetKappaBeta2 (double kappa, double beta2);

   /**
      Return the minimum value of \f$\lambda\f$ for which \f$p(\lambda; \kappa, \beta^2)\f$
      is nonzero in the current approximation
   */
   virtual double GetLambdaMin() const;

   /**
      Return the maximum value of \f$\lambda\f$ for which \f$p(\lambda; \kappa, \beta^2)\f$
      is nonzero in the current approximation
   */
   virtual double GetLambdaMax() const;

   /**
      Return the current value of \f$\kappa\f$
   */
   virtual double GetKappa()     const;

   /**
      Return the current value of \f$\beta^2\f$
   */
   virtual double GetBeta2()     const;

   /**
      Returns a static instance of class VavilovFast
   */
   static VavilovFast *GetInstance();

   /**
      Returns a static instance of class VavilovFast,
      and sets the values of kappa and beta2

       @param kappa The parameter \f$\kappa\f$, which must be in the range \f$0.01 \le \kappa \le 12 \f$
       @param beta2 The parameter \f$\beta^2\f$, which must be in the range \f$0 \le \beta^2 \le 1 \f$
   */
   static VavilovFast *GetInstance(double kappa, double beta2);


private:
   double fKappa;
   double fBeta2;

   double fAC[14];
   double fHC[9];
   double fWCM[201];
   int    fItype;
   int    fNpt;

   static VavilovFast *fgInstance;

};

   /**
       The Vavilov probability density function

       @param x The Landau parameter \f$x = \lambda_L\f$
       @param kappa The parameter \f$\kappa\f$, which must be in the range \f$0.01 \le \kappa \le 12 \f$
       @param beta2 The parameter \f$\beta^2\f$, which must be in the range \f$0 \le \beta^2 \le 1 \f$

       @ingroup PdfFunc
   */
double vavilov_fast_pdf (double x, double kappa, double beta2);

   /**
       The Vavilov cummulative probability density function

       @param x The Landau parameter \f$x = \lambda_L\f$
       @param kappa The parameter \f$\kappa\f$, which must be in the range \f$0.01 \le \kappa \le 12 \f$
       @param beta2 The parameter \f$\beta^2\f$, which must be in the range \f$0 \le \beta^2 \le 1 \f$

       @ingroup ProbFunc
   */
double vavilov_fast_cdf (double x, double kappa, double beta2);

   /**
       The Vavilov complementary cummulative probability density function

       @param x The Landau parameter \f$x = \lambda_L\f$
       @param kappa The parameter \f$\kappa\f$, which must be in the range \f$0.01 \le \kappa \le 12 \f$
       @param beta2 The parameter \f$\beta^2\f$, which must be in the range \f$0 \le \beta^2 \le 1 \f$

       @ingroup ProbFunc
   */
double vavilov_fast_cdf_c (double x, double kappa, double beta2);

   /**
       The inverse of the Vavilov cummulative probability density function

       @param z The argument \f$z\f$, which must be in the range \f$0 \le z \le 1\f$
       @param kappa The parameter \f$\kappa\f$, which must be in the range \f$0.01 \le \kappa \le 12 \f$
       @param beta2 The parameter \f$\beta^2\f$, which must be in the range \f$0 \le \beta^2 \le 1 \f$

      @ingroup QuantFunc
   */
double vavilov_fast_quantile (double z, double kappa, double beta2);

   /**
       The inverse of the complementary Vavilov cummulative probability density function

       @param z The argument \f$z\f$, which must be in the range \f$0 \le z \le 1\f$
       @param kappa The parameter \f$\kappa\f$, which must be in the range \f$0.01 \le \kappa \le 12 \f$
       @param beta2 The parameter \f$\beta^2\f$, which must be in the range \f$0 \le \beta^2 \le 1 \f$

      @ingroup QuantFunc
   */
double vavilov_fast_quantile_c (double z, double kappa, double beta2);

} // namespace Math
} // namespace ROOT

#endif /* ROOT_Math_VavilovFast */
 VavilovFast.h:1
 VavilovFast.h:2
 VavilovFast.h:3
 VavilovFast.h:4
 VavilovFast.h:5
 VavilovFast.h:6
 VavilovFast.h:7
 VavilovFast.h:8
 VavilovFast.h:9
 VavilovFast.h:10
 VavilovFast.h:11
 VavilovFast.h:12
 VavilovFast.h:13
 VavilovFast.h:14
 VavilovFast.h:15
 VavilovFast.h:16
 VavilovFast.h:17
 VavilovFast.h:18
 VavilovFast.h:19
 VavilovFast.h:20
 VavilovFast.h:21
 VavilovFast.h:22
 VavilovFast.h:23
 VavilovFast.h:24
 VavilovFast.h:25
 VavilovFast.h:26
 VavilovFast.h:27
 VavilovFast.h:28
 VavilovFast.h:29
 VavilovFast.h:30
 VavilovFast.h:31
 VavilovFast.h:32
 VavilovFast.h:33
 VavilovFast.h:34
 VavilovFast.h:35
 VavilovFast.h:36
 VavilovFast.h:37
 VavilovFast.h:38
 VavilovFast.h:39
 VavilovFast.h:40
 VavilovFast.h:41
 VavilovFast.h:42
 VavilovFast.h:43
 VavilovFast.h:44
 VavilovFast.h:45
 VavilovFast.h:46
 VavilovFast.h:47
 VavilovFast.h:48
 VavilovFast.h:49
 VavilovFast.h:50
 VavilovFast.h:51
 VavilovFast.h:52
 VavilovFast.h:53
 VavilovFast.h:54
 VavilovFast.h:55
 VavilovFast.h:56
 VavilovFast.h:57
 VavilovFast.h:58
 VavilovFast.h:59
 VavilovFast.h:60
 VavilovFast.h:61
 VavilovFast.h:62
 VavilovFast.h:63
 VavilovFast.h:64
 VavilovFast.h:65
 VavilovFast.h:66
 VavilovFast.h:67
 VavilovFast.h:68
 VavilovFast.h:69
 VavilovFast.h:70
 VavilovFast.h:71
 VavilovFast.h:72
 VavilovFast.h:73
 VavilovFast.h:74
 VavilovFast.h:75
 VavilovFast.h:76
 VavilovFast.h:77
 VavilovFast.h:78
 VavilovFast.h:79
 VavilovFast.h:80
 VavilovFast.h:81
 VavilovFast.h:82
 VavilovFast.h:83
 VavilovFast.h:84
 VavilovFast.h:85
 VavilovFast.h:86
 VavilovFast.h:87
 VavilovFast.h:88
 VavilovFast.h:89
 VavilovFast.h:90
 VavilovFast.h:91
 VavilovFast.h:92
 VavilovFast.h:93
 VavilovFast.h:94
 VavilovFast.h:95
 VavilovFast.h:96
 VavilovFast.h:97
 VavilovFast.h:98
 VavilovFast.h:99
 VavilovFast.h:100
 VavilovFast.h:101
 VavilovFast.h:102
 VavilovFast.h:103
 VavilovFast.h:104
 VavilovFast.h:105
 VavilovFast.h:106
 VavilovFast.h:107
 VavilovFast.h:108
 VavilovFast.h:109
 VavilovFast.h:110
 VavilovFast.h:111
 VavilovFast.h:112
 VavilovFast.h:113
 VavilovFast.h:114
 VavilovFast.h:115
 VavilovFast.h:116
 VavilovFast.h:117
 VavilovFast.h:118
 VavilovFast.h:119
 VavilovFast.h:120
 VavilovFast.h:121
 VavilovFast.h:122
 VavilovFast.h:123
 VavilovFast.h:124
 VavilovFast.h:125
 VavilovFast.h:126
 VavilovFast.h:127
 VavilovFast.h:128
 VavilovFast.h:129
 VavilovFast.h:130
 VavilovFast.h:131
 VavilovFast.h:132
 VavilovFast.h:133
 VavilovFast.h:134
 VavilovFast.h:135
 VavilovFast.h:136
 VavilovFast.h:137
 VavilovFast.h:138
 VavilovFast.h:139
 VavilovFast.h:140
 VavilovFast.h:141
 VavilovFast.h:142
 VavilovFast.h:143
 VavilovFast.h:144
 VavilovFast.h:145
 VavilovFast.h:146
 VavilovFast.h:147
 VavilovFast.h:148
 VavilovFast.h:149
 VavilovFast.h:150
 VavilovFast.h:151
 VavilovFast.h:152
 VavilovFast.h:153
 VavilovFast.h:154
 VavilovFast.h:155
 VavilovFast.h:156
 VavilovFast.h:157
 VavilovFast.h:158
 VavilovFast.h:159
 VavilovFast.h:160
 VavilovFast.h:161
 VavilovFast.h:162
 VavilovFast.h:163
 VavilovFast.h:164
 VavilovFast.h:165
 VavilovFast.h:166
 VavilovFast.h:167
 VavilovFast.h:168
 VavilovFast.h:169
 VavilovFast.h:170
 VavilovFast.h:171
 VavilovFast.h:172
 VavilovFast.h:173
 VavilovFast.h:174
 VavilovFast.h:175
 VavilovFast.h:176
 VavilovFast.h:177
 VavilovFast.h:178
 VavilovFast.h:179
 VavilovFast.h:180
 VavilovFast.h:181
 VavilovFast.h:182
 VavilovFast.h:183
 VavilovFast.h:184
 VavilovFast.h:185
 VavilovFast.h:186
 VavilovFast.h:187
 VavilovFast.h:188
 VavilovFast.h:189
 VavilovFast.h:190
 VavilovFast.h:191
 VavilovFast.h:192
 VavilovFast.h:193
 VavilovFast.h:194
 VavilovFast.h:195
 VavilovFast.h:196
 VavilovFast.h:197
 VavilovFast.h:198
 VavilovFast.h:199
 VavilovFast.h:200
 VavilovFast.h:201
 VavilovFast.h:202
 VavilovFast.h:203
 VavilovFast.h:204
 VavilovFast.h:205
 VavilovFast.h:206
 VavilovFast.h:207
 VavilovFast.h:208
 VavilovFast.h:209
 VavilovFast.h:210
 VavilovFast.h:211
 VavilovFast.h:212
 VavilovFast.h:213
 VavilovFast.h:214
 VavilovFast.h:215
 VavilovFast.h:216
 VavilovFast.h:217
 VavilovFast.h:218
 VavilovFast.h:219
 VavilovFast.h:220
 VavilovFast.h:221
 VavilovFast.h:222
 VavilovFast.h:223
 VavilovFast.h:224
 VavilovFast.h:225
 VavilovFast.h:226
 VavilovFast.h:227
 VavilovFast.h:228
 VavilovFast.h:229
 VavilovFast.h:230
 VavilovFast.h:231
 VavilovFast.h:232
 VavilovFast.h:233
 VavilovFast.h:234
 VavilovFast.h:235
 VavilovFast.h:236
 VavilovFast.h:237
 VavilovFast.h:238
 VavilovFast.h:239
 VavilovFast.h:240
 VavilovFast.h:241
 VavilovFast.h:242
 VavilovFast.h:243
 VavilovFast.h:244
 VavilovFast.h:245
 VavilovFast.h:246
 VavilovFast.h:247
 VavilovFast.h:248
 VavilovFast.h:249
 VavilovFast.h:250
 VavilovFast.h:251
 VavilovFast.h:252
 VavilovFast.h:253
 VavilovFast.h:254
 VavilovFast.h:255
 VavilovFast.h:256
 VavilovFast.h:257
 VavilovFast.h:258
 VavilovFast.h:259
 VavilovFast.h:260
 VavilovFast.h:261
 VavilovFast.h:262
 VavilovFast.h:263
 VavilovFast.h:264
 VavilovFast.h:265
 VavilovFast.h:266
 VavilovFast.h:267
 VavilovFast.h:268
 VavilovFast.h:269
 VavilovFast.h:270
 VavilovFast.h:271
 VavilovFast.h:272
 VavilovFast.h:273
 VavilovFast.h:274
 VavilovFast.h:275
 VavilovFast.h:276
 VavilovFast.h:277
 VavilovFast.h:278
 VavilovFast.h:279
 VavilovFast.h:280
 VavilovFast.h:281
 VavilovFast.h:282
 VavilovFast.h:283
 VavilovFast.h:284
 VavilovFast.h:285
 VavilovFast.h:286
 VavilovFast.h:287
 VavilovFast.h:288
 VavilovFast.h:289
 VavilovFast.h:290
 VavilovFast.h:291
 VavilovFast.h:292
 VavilovFast.h:293
 VavilovFast.h:294
 VavilovFast.h:295
 VavilovFast.h:296
 VavilovFast.h:297
 VavilovFast.h:298
 VavilovFast.h:299
 VavilovFast.h:300
 VavilovFast.h:301
 VavilovFast.h:302
 VavilovFast.h:303
 VavilovFast.h:304
 VavilovFast.h:305
 VavilovFast.h:306
 VavilovFast.h:307
 VavilovFast.h:308
 VavilovFast.h:309
 VavilovFast.h:310
 VavilovFast.h:311
 VavilovFast.h:312
 VavilovFast.h:313
 VavilovFast.h:314
 VavilovFast.h:315
 VavilovFast.h:316
 VavilovFast.h:317
 VavilovFast.h:318
 VavilovFast.h:319
 VavilovFast.h:320
 VavilovFast.h:321
 VavilovFast.h:322
 VavilovFast.h:323
 VavilovFast.h:324
 VavilovFast.h:325
 VavilovFast.h:326
 VavilovFast.h:327
 VavilovFast.h:328
 VavilovFast.h:329
 VavilovFast.h:330
 VavilovFast.h:331
 VavilovFast.h:332
 VavilovFast.h:333
 VavilovFast.h:334
 VavilovFast.h:335
 VavilovFast.h:336
 VavilovFast.h:337
 VavilovFast.h:338
 VavilovFast.h:339
 VavilovFast.h:340
 VavilovFast.h:341