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RootFinder.cxx
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1 // @(#)root/tmva $Id$
2 // Author: Andreas Hoecker, Joerg Stelzer, Helge Voss
3 
4 /**********************************************************************************
5  * Project: TMVA - a Root-integrated toolkit for multivariate data analysis *
6  * Package: TMVA *
7  * Class : RootFinder *
8  * Web : http://tmva.sourceforge.net *
9  * *
10  * Description: *
11  * Implementation (see header file for description) *
12  * *
13  * Authors (alphabetical): *
14  * Andreas Hoecker <Andreas.Hocker@cern.ch> - CERN, Switzerland *
15  * Helge Voss <Helge.Voss@cern.ch> - MPI-K Heidelberg, Germany *
16  * Kai Voss <Kai.Voss@cern.ch> - U. of Victoria, Canada *
17  * *
18  * Copyright (c) 2005: *
19  * CERN, Switzerland *
20  * U. of Victoria, Canada *
21  * MPI-K Heidelberg, Germany *
22  * *
23  * Redistribution and use in source and binary forms, with or without *
24  * modification, are permitted according to the terms listed in LICENSE *
25  * (http://tmva.sourceforge.net/LICENSE) *
26  **********************************************************************************/
27 
28 /*! \class TMVA::RootFinder
29 \ingroup TMVA
30 Root finding using Brents algorithm (translated from CERNLIB function RZERO)
31 */
32 
33 #include "TMVA/RootFinder.h"
34 
35 #include "TMVA/MethodBase.h"
36 #include "TMVA/MsgLogger.h"
37 #include "TMVA/Types.h"
38 
39 #include "TMath.h"
40 #include "TObject.h"
41 
43 
44 ////////////////////////////////////////////////////////////////////////////////
45 /// constructor
46 
48  Double_t rootMin,
49  Double_t rootMax,
50  Int_t maxIterations,
51  Double_t absTolerance )
52 : fRootMin( rootMin ),
53  fRootMax( rootMax ),
54  fMaxIter( maxIterations ),
55  fAbsTol ( absTolerance ),
56  fLogger ( new MsgLogger("RootFinder") )
57 {
58  fMethod=method;
59 }
60 
61 ////////////////////////////////////////////////////////////////////////////////
62 /// destructor
63 
65 {
66  delete fLogger;
67 }
68 
69 ////////////////////////////////////////////////////////////////////////////////
70 /// Root finding using Brents algorithm; taken from CERNLIB function RZERO
71 
73 {
74  Double_t a = fRootMin, b = fRootMax;
75  Double_t fa = fMethod->GetValueForRoot( a ) - refValue;
76  Double_t fb = fMethod->GetValueForRoot( b ) - refValue;
77  if (fb*fa > 0) {
78  Log() << kWARNING << "<Root> initial interval w/o root: "
79  << "(a=" << a << ", b=" << b << "),"
80  << " (Eff_a=" << fMethod->GetValueForRoot( a )
81  << ", Eff_b=" << fMethod->GetValueForRoot( b ) << "), "
82  << "(fa=" << fa << ", fb=" << fb << "), "
83  << "refValue = " << refValue << Endl;
84  return 1;
85  }
86 
87  Bool_t ac_equal(kFALSE);
88  Double_t fc = fb;
89  Double_t c = 0, d = 0, e = 0;
90  for (Int_t iter= 0; iter <= fMaxIter; iter++) {
91  if ((fb < 0 && fc < 0) || (fb > 0 && fc > 0)) {
92 
93  // Rename a,b,c and adjust bounding interval d
94  ac_equal = kTRUE;
95  c = a; fc = fa;
96  d = b - a; e = b - a;
97  }
98 
99  if (TMath::Abs(fc) < TMath::Abs(fb)) {
100  ac_equal = kTRUE;
101  a = b; b = c; c = a;
102  fa = fb; fb = fc; fc = fa;
103  }
104 
105  Double_t tol = 0.5 * 2.2204460492503131e-16 * TMath::Abs(b);
106  Double_t m = 0.5 * (c - b);
107  if (fb == 0 || TMath::Abs(m) <= tol || TMath::Abs(fb) < fAbsTol) return b;
108 
109  // Bounds decreasing too slowly: use bisection
110  if (TMath::Abs (e) < tol || TMath::Abs (fa) <= TMath::Abs (fb)) { d = m; e = m; }
111  else {
112  // Attempt inverse cubic interpolation
113  Double_t p, q, r;
114  Double_t s = fb / fa;
115 
116  if (ac_equal) { p = 2 * m * s; q = 1 - s; }
117  else {
118  q = fa / fc; r = fb / fc;
119  p = s * (2 * m * q * (q - r) - (b - a) * (r - 1));
120  q = (q - 1) * (r - 1) * (s - 1);
121  }
122  // Check whether we are in bounds
123  if (p > 0) q = -q;
124  else p = -p;
125 
126  Double_t min1 = 3 * m * q - TMath::Abs (tol * q);
127  Double_t min2 = TMath::Abs (e * q);
128  if (2 * p < (min1 < min2 ? min1 : min2)) {
129  // Accept the interpolation
130  e = d; d = p / q;
131  }
132  else { d = m; e = m; } // Interpolation failed: use bisection.
133  }
134  // Move last best guess to a
135  a = b; fa = fb;
136  // Evaluate new trial root
137  if (TMath::Abs(d) > tol) b += d;
138  else b += (m > 0 ? +tol : -tol);
139 
140  fb = fMethod->GetValueForRoot( b ) - refValue;
141 
142  }
143 
144  // Return our best guess if we run out of iterations
145  Log() << kWARNING << "<Root> maximum iterations (" << fMaxIter
146  << ") reached before convergence" << Endl;
147 
148  return b;
149 }
MsgLogger & Endl(MsgLogger &ml)
Definition: MsgLogger.h:158
auto * m
Definition: textangle.C:8
Double_t Log(Double_t x)
Definition: TMath.h:750
Virtual base Class for all MVA method.
Definition: MethodBase.h:111
int Int_t
Definition: RtypesCore.h:41
bool Bool_t
Definition: RtypesCore.h:59
Short_t Abs(Short_t d)
Definition: TMathBase.h:120
MethodBase * fMethod
Definition: RootFinder.h:69
static struct mg_connection * fc(struct mg_context *ctx)
Definition: civetweb.c:3728
static constexpr double s
Double_t Root(Double_t refValue)
Root finding using Brents algorithm; taken from CERNLIB function RZERO.
Definition: RootFinder.cxx:72
ROOT::R::TRInterface & r
Definition: Object.C:4
auto * a
Definition: textangle.C:12
const Bool_t kFALSE
Definition: RtypesCore.h:88
RootFinder(MethodBase *method, Double_t rootMin, Double_t rootMax, Int_t maxIterations=100, Double_t absTolerance=0.0)
constructor
Definition: RootFinder.cxx:47
#define d(i)
Definition: RSha256.hxx:102
#define ClassImp(name)
Definition: Rtypes.h:365
double Double_t
Definition: RtypesCore.h:55
virtual ~RootFinder(void)
destructor
Definition: RootFinder.cxx:64
you should not use this method at all Int_t Int_t Double_t Double_t Double_t e
Definition: TRolke.cxx:630
ostringstream derivative to redirect and format output
Definition: MsgLogger.h:59
Root finding using Brents algorithm (translated from CERNLIB function RZERO)
Definition: RootFinder.h:48
you should not use this method at all Int_t Int_t Double_t Double_t Double_t Int_t Double_t Double_t Double_t Double_t b
Definition: TRolke.cxx:630
#define c(i)
Definition: RSha256.hxx:101
float * q
Definition: THbookFile.cxx:87
const Bool_t kTRUE
Definition: RtypesCore.h:87