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Reference Guide
Tools.h
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1// @(#)root/tmva $Id$
2// Author: Andreas Hoecker, Joerg Stelzer, Helge Voss, Kai Voss
3
4/**********************************************************************************
5 * Project: TMVA - a Root-integrated toolkit for multivariate data analysis *
6 * Package: TMVA *
7 * Class : Tools *
8 * Web : http://tmva.sourceforge.net *
9 * *
10 * Description: *
11 * Global auxiliary applications and data treatment routines *
12 * *
13 * Authors (alphabetical): *
14 * Andreas Hoecker <Andreas.Hocker@cern.ch> - CERN, Switzerland *
15 * Peter Speckmayer <peter.speckmayer@cern.ch> - CERN, Switzerland *
16 * Helge Voss <Helge.Voss@cern.ch> - MPI-K Heidelberg, Germany *
17 * Kai Voss <Kai.Voss@cern.ch> - U. of Victoria, Canada *
18 * *
19 * Copyright (c) 2005: *
20 * CERN, Switzerland *
21 * U. of Victoria, Canada *
22 * MPI-K Heidelberg, Germany *
23 * *
24 * Redistribution and use in source and binary forms, with or without *
25 * modification, are permitted according to the terms listed in LICENSE *
26 * (http://tmva.sourceforge.net/LICENSE) *
27 **********************************************************************************/
28
29#ifndef ROOT_TMVA_Tools
30#define ROOT_TMVA_Tools
31
32//////////////////////////////////////////////////////////////////////////
33// //
34// Tools (namespace) //
35// //
36// Global auxiliary applications and data treatment routines //
37// //
38//////////////////////////////////////////////////////////////////////////
39
40#include <vector>
41#include <sstream>
42#include <iostream>
43#include <iomanip>
44#if __cplusplus > 199711L
45#include <atomic>
46#endif
47
48#include "TXMLEngine.h"
49
50#include "TMatrixDSymfwd.h"
51
52#include "TMatrixDfwd.h"
53
54#include "TVectorDfwd.h"
55
56#include "TVectorDfwd.h"
57
58#include "TMVA/Types.h"
59
61
62#include "TString.h"
63
64#include "TMVA/MsgLogger.h"
65
66class TList;
67class TTree;
68class TH1;
69class TH2;
70class TH2F;
71class TSpline;
72class TXMLEngine;
73
74namespace TMVA {
75
76 class Event;
77 class PDF;
78 class MsgLogger;
79
80 class Tools {
81
82 private:
83
84 Tools();
85
86 public:
87
88 // destructor
89 ~Tools();
90
91 // accessor to single instance
92 static Tools& Instance();
93 static void DestroyInstance();
94
95
96 template <typename T> Double_t Mean(Long64_t n, const T *a, const Double_t *w=0);
97 template <typename Iterator, typename WeightIterator> Double_t Mean ( Iterator first, Iterator last, WeightIterator w);
98
99 template <typename T> Double_t RMS(Long64_t n, const T *a, const Double_t *w=0);
100 template <typename Iterator, typename WeightIterator> Double_t RMS(Iterator first, Iterator last, WeightIterator w);
101
102
103 // simple statistics operations on tree entries
104 void ComputeStat( const std::vector<TMVA::Event*>&,
105 std::vector<Float_t>*,
107 Double_t&, Double_t&, Double_t&, Int_t signalClass,
108 Bool_t norm = kFALSE );
109
110 // compute variance from sums
111 inline Double_t ComputeVariance( Double_t sumx2, Double_t sumx, Int_t nx );
112
113 // creates histograms normalized to one
114 TH1* projNormTH1F( TTree* theTree, const TString& theVarName,
115 const TString& name, Int_t nbins,
116 Double_t xmin, Double_t xmax, const TString& cut );
117
118 // normalize histogram by its integral
119 Double_t NormHist( TH1* theHist, Double_t norm = 1.0 );
120
121 // parser for TString phrase with items separated by a character
122 TList* ParseFormatLine( TString theString, const char * sep = ":" );
123
124 // parse option string for ANN methods
125 std::vector<Int_t>* ParseANNOptionString( TString theOptions, Int_t nvar,
126 std::vector<Int_t>* nodes );
127
128 // returns the square-root of a symmetric matrix: symMat = sqrtMat*sqrtMat
130
131 // returns the covariance matrix of of the different classes (and the sum)
132 // given the event sample
133 std::vector<TMatrixDSym*>* CalcCovarianceMatrices( const std::vector<Event*>& events, Int_t maxCls, VariableTransformBase* transformBase=0 );
134 std::vector<TMatrixDSym*>* CalcCovarianceMatrices( const std::vector<const Event*>& events, Int_t maxCls, VariableTransformBase* transformBase=0 );
135
136
137 // turns covariance into correlation matrix
138 const TMatrixD* GetCorrelationMatrix( const TMatrixD* covMat );
139
140 // check spline quality by comparison with initial histogram
141 Bool_t CheckSplines( const TH1*, const TSpline* );
142
143 // normalization of variable output
145
146 // return separation of two histograms
147 Double_t GetSeparation( TH1* S, TH1* B ) const;
148 Double_t GetSeparation( const PDF& pdfS, const PDF& pdfB ) const;
149
150 // vector rescaling
151 std::vector<Double_t> MVADiff( std::vector<Double_t>&, std::vector<Double_t>& );
152 void Scale( std::vector<Double_t>&, Double_t );
153 void Scale( std::vector<Float_t>&, Float_t );
154
155 // re-arrange a vector of arrays (vectors) in a way such that the first array
156 // is ordered, and the other arrays reshuffled accordingly
157 void UsefulSortDescending( std::vector< std::vector<Double_t> >&, std::vector<TString>* vs = 0 );
158 void UsefulSortAscending ( std::vector< std::vector<Double_t> >&, std::vector<TString>* vs = 0 );
159
160 void UsefulSortDescending( std::vector<Double_t>& );
161 void UsefulSortAscending ( std::vector<Double_t>& );
162
163 Int_t GetIndexMaxElement ( std::vector<Double_t>& );
164 Int_t GetIndexMinElement ( std::vector<Double_t>& );
165
166 // check if input string contains regular expression
168 TString ReplaceRegularExpressions( const TString& s, const TString& replace = "+" );
169
170 // routines for formatted output -----------------
171 void FormattedOutput( const std::vector<Double_t>&, const std::vector<TString>&,
172 const TString titleVars, const TString titleValues, MsgLogger& logger,
173 TString format = "%+1.3f" );
174 void FormattedOutput( const TMatrixD&, const std::vector<TString>&, MsgLogger& logger );
175 void FormattedOutput( const TMatrixD&, const std::vector<TString>& vert, const std::vector<TString>& horiz,
176 MsgLogger& logger );
177
178 void WriteFloatArbitraryPrecision( Float_t val, std::ostream& os );
179 void ReadFloatArbitraryPrecision ( Float_t& val, std::istream& is );
180
181 // for histogramming
182 TString GetXTitleWithUnit( const TString& title, const TString& unit );
183 TString GetYTitleWithUnit( const TH1& h, const TString& unit, Bool_t normalised );
184
185 // Mutual Information method for non-linear correlations estimates in 2D histogram
186 // Author: Moritz Backes, Geneva (2009)
188
189 // Correlation Ratio method for non-linear correlations estimates in 2D histogram
190 // Author: Moritz Backes, Geneva (2009)
192 TH2F* TransposeHist ( const TH2F& );
193
194 // check if "silent" or "verbose" option in configuration string
195 Bool_t CheckForSilentOption ( const TString& ) const;
196 Bool_t CheckForVerboseOption( const TString& ) const;
197
198 // color information
199 const TString& Color( const TString& );
200
201 // print welcome message (to be called from, eg, .TMVAlogon)
211
212 // print TMVA citation (to be called from, eg, .TMVAlogon)
217
218 void TMVAWelcomeMessage();
220 void TMVAVersionMessage( MsgLogger& logger );
221 void ROOTVersionMessage( MsgLogger& logger );
222
223 void TMVACitation( MsgLogger& logger, ECitation citType = kPlainText );
224
225 // string tools
226
227 std::vector<TString> SplitString( const TString& theOpt, const char separator ) const;
228
229 // variables
232 MsgLogger& Log() const { return *fLogger; }
233#if __cplusplus > 199711L
234 static std::atomic<Tools*> fgTools;
235#else
236 static Tools* fgTools;
237#endif
238
239 // xml tools
240
243 void WriteTMatrixDToXML ( void* node, const char* name, TMatrixD* mat );
244 void WriteTVectorDToXML ( void* node, const char* name, TVectorD* vec );
245 void ReadTMatrixDFromXML( void* node, const char* name, TMatrixD* mat );
246 void ReadTVectorDFromXML( void* node, const char* name, TVectorD* vec );
248
249 Bool_t HasAttr ( void* node, const char* attrname );
250 template<typename T>
251 inline void ReadAttr ( void* node, const char* , T& value );
252 void ReadAttr ( void* node, const char* attrname, TString& value );
253 void ReadAttr(void *node, const char *, float &value);
254 void ReadAttr(void *node, const char *, int &value);
255 void ReadAttr(void *node, const char *, short &value);
256
257 template<typename T>
258 void AddAttr ( void* node, const char* , const T& value, Int_t precision = 16 );
259 void AddAttr ( void* node, const char* attrname, const char* value );
260 void* AddChild ( void* parent, const char* childname, const char* content = 0, bool isRootNode = false );
261 Bool_t AddRawLine ( void* node, const char * raw );
262 Bool_t AddComment ( void* node, const char* comment );
263
264 void* GetParent( void* child);
265 void* GetChild ( void* parent, const char* childname=0 );
266 void* GetNextChild( void* prevchild, const char* childname=0 );
267 const char* GetContent ( void* node );
268 const char* GetName ( void* node );
269
272 void SetXMLEngineBufferSize(int buffer) { fXMLBufferSize = buffer; }
274
276
277 private:
278
279 int fXMLBufferSize = 10000000;
280 // utilities for correlation ratio
281 Double_t GetYMean_binX( const TH2& , Int_t bin_x );
282
283 }; // Common tools
284
285 Tools& gTools(); // global accessor
286
287 //
288 // Adapts a TRandom random number generator to the interface of the ones in the
289 // standard library (STL) so that TRandom derived generators can be used with
290 // STL algorithms such as `std::shuffle`.
291 //
292 // Example:
293 // ```
294 // std::vector<double> v {0, 1, 2, 3, 4, 5};
295 // TRandom3StdEngine rng(seed);
296 // std::shuffle(v.begin(), v.end(), rng);
297 // ```
298 //
299 // Or at a lower level:
300 // ```
301 // std::vector<double> v {0, 1, 2, 3, 4, 5};
302 // RandomGenerator<TRandom3> rng(seed);
303 // std::shuffle(v.begin(), v.end(), rng);
304 // ```
305 //
306 template <typename TRandomLike, typename UIntType = UInt_t, UIntType max_val = kMaxUInt>
308 public:
309 using result_type = UIntType;
310
311 RandomGenerator(UIntType s = 0) { fRandom.SetSeed(s); }
312
313 static constexpr UIntType min() { return 0; }
314 static constexpr UIntType max() { return max_val; }
315
316 void seed(UIntType s = 0) { fRandom.SetSeed(s); }
317
318 UIntType operator()() { return fRandom.Integer(max()); }
319
320 void discard(unsigned long long z)
321 {
322 double r;
323 for (unsigned long long i = 0; i < z; ++i)
324 r = fRandom.Rndm();
325 (void) r; /* avoid unused variable warning */
326 }
327
328 private:
329 TRandomLike fRandom; // random generator
330 };
331
332} // namespace TMVA
333
334////////////////////////////////////////////////////////////////////////////////
335/// read attribute from xml
336
337template<typename T> void TMVA::Tools::ReadAttr( void* node, const char* attrname, T& value )
338{
339 // read attribute from xml
340 const char *val = xmlengine().GetAttr(node, attrname);
341 if (val == 0) {
342 const char *nodename = xmlengine().GetNodeName(node);
343 Log() << kFATAL << "Trying to read non-existing attribute '" << attrname << "' from xml node '" << nodename << "'"
344 << Endl;
345 }
346 std::stringstream s(val);
347 // coverity[tainted_data_argument]
348 s >> value;
349}
350
351////////////////////////////////////////////////////////////////////////////////
352/// add attribute to xml
353
354template<typename T>
355void TMVA::Tools::AddAttr( void* node, const char* attrname, const T& value, Int_t precision )
356{
357 std::stringstream s;
358 s.precision( precision );
359 s << std::scientific << value;
360 AddAttr( node, attrname, s.str().c_str() );
361}
362
363////////////////////////////////////////////////////////////////////////////////
364/// compute variance from given sums
365
367{
368 if (nx<2) return 0;
369 return (sumx2 - ((sumx*sumx)/static_cast<Double_t>(nx)))/static_cast<Double_t>(nx-1);
370}
371
372#endif
ROOT::R::TRInterface & r
Definition: Object.C:4
#define d(i)
Definition: RSha256.hxx:102
#define h(i)
Definition: RSha256.hxx:106
int Int_t
Definition: RtypesCore.h:41
const Bool_t kFALSE
Definition: RtypesCore.h:88
long Long_t
Definition: RtypesCore.h:50
bool Bool_t
Definition: RtypesCore.h:59
double Double_t
Definition: RtypesCore.h:55
long long Long64_t
Definition: RtypesCore.h:69
float Float_t
Definition: RtypesCore.h:53
char name[80]
Definition: TGX11.cxx:109
float xmin
Definition: THbookFile.cxx:93
float xmax
Definition: THbookFile.cxx:93
typedef void((*Func_t)())
The TH1 histogram class.
Definition: TH1.h:56
2-D histogram with a float per channel (see TH1 documentation)}
Definition: TH2.h:248
Service class for 2-Dim histogram classes.
Definition: TH2.h:30
A doubly linked list.
Definition: TList.h:44
ostringstream derivative to redirect and format output
Definition: MsgLogger.h:59
PDF wrapper for histograms; uses user-defined spline interpolation.
Definition: PDF.h:63
UIntType operator()()
Definition: Tools.h:318
void discard(unsigned long long z)
Definition: Tools.h:320
TRandomLike fRandom
Definition: Tools.h:329
static constexpr UIntType max()
Definition: Tools.h:314
void seed(UIntType s=0)
Definition: Tools.h:316
RandomGenerator(UIntType s=0)
Definition: Tools.h:311
static constexpr UIntType min()
Definition: Tools.h:313
UIntType result_type
Definition: Tools.h:309
Global auxiliary applications and data treatment routines.
Definition: Tools.h:80
void ComputeStat(const std::vector< TMVA::Event * > &, std::vector< Float_t > *, Double_t &, Double_t &, Double_t &, Double_t &, Double_t &, Double_t &, Int_t signalClass, Bool_t norm=kFALSE)
sanity check
Definition: Tools.cxx:214
void * GetParent(void *child)
get parent node
Definition: Tools.cxx:1152
void FormattedOutput(const std::vector< Double_t > &, const std::vector< TString > &, const TString titleVars, const TString titleValues, MsgLogger &logger, TString format="%+1.3f")
formatted output of simple table
Definition: Tools.cxx:899
void UsefulSortDescending(std::vector< std::vector< Double_t > > &, std::vector< TString > *vs=0)
sort 2D vector (AND in parallel a TString vector) in such a way that the "first vector is sorted" and...
Definition: Tools.cxx:576
Bool_t HistoHasEquidistantBins(const TH1 &h)
Definition: Tools.cxx:1499
TList * ParseFormatLine(TString theString, const char *sep=":")
Parse the string and cut into labels separated by ":".
Definition: Tools.cxx:413
Double_t NormVariable(Double_t x, Double_t xmin, Double_t xmax)
normalise to output range: [-1, 1]
Definition: Tools.cxx:122
void WriteFloatArbitraryPrecision(Float_t val, std::ostream &os)
writes a float value with the available precision to a stream
Definition: Tools.cxx:1070
void * GetNextChild(void *prevchild, const char *childname=0)
XML helpers.
Definition: Tools.cxx:1174
TString GetYTitleWithUnit(const TH1 &h, const TString &unit, Bool_t normalised)
histogramming utility
Definition: Tools.cxx:1060
Double_t GetSeparation(TH1 *S, TH1 *B) const
compute "separation" defined as
Definition: Tools.cxx:133
static Tools & Instance()
Definition: Tools.cxx:75
TMatrixD * GetSQRootMatrix(TMatrixDSym *symMat)
square-root of symmetric matrix of course the resulting sqrtMat is also symmetric,...
Definition: Tools.cxx:283
std::vector< Double_t > MVADiff(std::vector< Double_t > &, std::vector< Double_t > &)
computes difference between two vectors
Definition: Tools.cxx:518
Int_t GetIndexMinElement(std::vector< Double_t > &)
find index of minimum entry in vector
Definition: Tools.cxx:777
TH1 * projNormTH1F(TTree *theTree, const TString &theVarName, const TString &name, Int_t nbins, Double_t xmin, Double_t xmax, const TString &cut)
projects variable from tree into normalised histogram
Definition: Tools.cxx:378
void ROOTVersionMessage(MsgLogger &logger)
prints the ROOT release number and date
Definition: Tools.cxx:1337
TString ReplaceRegularExpressions(const TString &s, const TString &replace="+")
replace regular expressions helper function to remove all occurrences "$!%^&()'<>?...
Definition: Tools.cxx:810
void * AddChild(void *parent, const char *childname, const char *content=0, bool isRootNode=false)
add child node
Definition: Tools.cxx:1136
void ReadTVectorDFromXML(void *node, const char *name, TVectorD *vec)
Definition: Tools.cxx:1279
TH1 * GetCumulativeDist(TH1 *h)
get the cumulative distribution of a histogram
Definition: Tools.cxx:1772
void ReadFloatArbitraryPrecision(Float_t &val, std::istream &is)
reads a float value with the available precision from a stream
Definition: Tools.cxx:1085
Bool_t AddRawLine(void *node, const char *raw)
XML helpers.
Definition: Tools.cxx:1202
~Tools()
destructor
Definition: Tools.cxx:113
Bool_t ContainsRegularExpression(const TString &s)
check if regular expression helper function to search for "$!%^&()'<>?= " in a string
Definition: Tools.cxx:796
static void DestroyInstance()
Definition: Tools.cxx:90
Double_t Mean(Long64_t n, const T *a, const Double_t *w=0)
Return the weighted mean of an array a with length n.
Definition: Tools.cxx:1703
Double_t GetMutualInformation(const TH2F &)
Mutual Information method for non-linear correlations estimates in 2D histogram Author: Moritz Backes...
Definition: Tools.cxx:601
std::vector< TString > SplitString(const TString &theOpt, const char separator) const
splits the option string at 'separator' and fills the list 'splitV' with the primitive strings
Definition: Tools.cxx:1211
MsgLogger & Log() const
Definition: Tools.h:232
const TString & Color(const TString &)
human readable color strings
Definition: Tools.cxx:840
TString StringFromDouble(Double_t d)
string tools
Definition: Tools.cxx:1245
int xmlenginebuffersize()
Definition: Tools.h:271
Bool_t CheckForVerboseOption(const TString &) const
check if verbosity "V" set in option
Definition: Tools.cxx:720
Double_t RMS(Long64_t n, const T *a, const Double_t *w=0)
Return the Standard Deviation of an array a with length n.
Definition: Tools.cxx:1759
const char * GetContent(void *node)
XML helpers.
Definition: Tools.cxx:1186
void * GetChild(void *parent, const char *childname=0)
get child node
Definition: Tools.cxx:1162
void WriteTVectorDToXML(void *node, const char *name, TVectorD *vec)
Definition: Tools.cxx:1271
Double_t ComputeVariance(Double_t sumx2, Double_t sumx, Int_t nx)
compute variance from given sums
Definition: Tools.h:366
TXMLEngine & xmlengine()
Definition: Tools.h:270
TXMLEngine * fXMLEngine
Definition: Tools.h:273
void Scale(std::vector< Double_t > &, Double_t)
scales double vector
Definition: Tools.cxx:531
Bool_t CheckSplines(const TH1 *, const TSpline *)
check quality of splining by comparing splines and histograms in each bin
Definition: Tools.cxx:491
const char * GetName(void *node)
XML helpers.
Definition: Tools.cxx:1194
const TMatrixD * GetCorrelationMatrix(const TMatrixD *covMat)
turns covariance into correlation matrix
Definition: Tools.cxx:336
void WriteTMatrixDToXML(void *node, const char *name, TMatrixD *mat)
XML helpers.
Definition: Tools.cxx:1255
MsgLogger * fLogger
Definition: Tools.h:231
Double_t GetCorrelationRatio(const TH2F &)
Compute Correlation Ratio of 2D histogram to estimate functional dependency between two variables Aut...
Definition: Tools.cxx:632
void ReadAttr(void *node, const char *, T &value)
read attribute from xml
Definition: Tools.h:337
Bool_t AddComment(void *node, const char *comment)
Definition: Tools.cxx:1144
void ReadTMatrixDFromXML(void *node, const char *name, TMatrixD *mat)
Definition: Tools.cxx:1288
TString GetXTitleWithUnit(const TString &title, const TString &unit)
histogramming utility
Definition: Tools.cxx:1052
void AddAttr(void *node, const char *, const T &value, Int_t precision=16)
add attribute to xml
Definition: Tools.h:355
@ kHtmlLink
Definition: Tools.h:216
@ kBibTeX
Definition: Tools.h:214
@ kPlainText
Definition: Tools.h:213
@ kLaTeX
Definition: Tools.h:215
TString StringFromInt(Long_t i)
string tools
Definition: Tools.cxx:1235
int fXMLBufferSize
Definition: Tools.h:279
Tools()
constructor
Definition: Tools.cxx:103
Double_t NormHist(TH1 *theHist, Double_t norm=1.0)
normalises histogram
Definition: Tools.cxx:395
std::vector< TMatrixDSym * > * CalcCovarianceMatrices(const std::vector< Event * > &events, Int_t maxCls, VariableTransformBase *transformBase=0)
compute covariance matrices
Definition: Tools.cxx:1526
Double_t GetYMean_binX(const TH2 &, Int_t bin_x)
Compute the mean in Y for a given bin X of a 2D histogram.
Definition: Tools.cxx:654
void TMVACitation(MsgLogger &logger, ECitation citType=kPlainText)
kinds of TMVA citation
Definition: Tools.cxx:1453
void TMVAVersionMessage(MsgLogger &logger)
prints the TMVA release number and date
Definition: Tools.cxx:1328
void TMVAWelcomeMessage()
direct output, eg, when starting ROOT session -> no use of Logger here
Definition: Tools.cxx:1314
std::vector< Int_t > * ParseANNOptionString(TString theOptions, Int_t nvar, std::vector< Int_t > *nodes)
parse option string for ANN methods default settings (should be defined in theOption string)
Definition: Tools.cxx:455
Int_t GetIndexMaxElement(std::vector< Double_t > &)
find index of maximum entry in vector
Definition: Tools.cxx:760
void SetXMLEngineBufferSize(int buffer)
Definition: Tools.h:272
TH2F * TransposeHist(const TH2F &)
Transpose quadratic histogram.
Definition: Tools.cxx:669
static Tools * fgTools
Definition: Tools.h:236
EWelcomeMessage
Definition: Tools.h:202
@ kSmall1WelcomeMsg
Definition: Tools.h:207
@ kSmall2WelcomeMsg
Definition: Tools.h:208
@ kLogoWelcomeMsg
Definition: Tools.h:206
@ kOriginalWelcomeMsgColor
Definition: Tools.h:209
@ kOriginalWelcomeMsgBW
Definition: Tools.h:210
@ kBlockWelcomeMsg
Definition: Tools.h:204
@ kStandardWelcomeMsg
Definition: Tools.h:202
@ kIsometricWelcomeMsg
Definition: Tools.h:203
@ kLeanWelcomeMsg
Definition: Tools.h:205
Bool_t HasAttr(void *node, const char *attrname)
add attribute from xml
Definition: Tools.cxx:1106
void UsefulSortAscending(std::vector< std::vector< Double_t > > &, std::vector< TString > *vs=0)
sort 2D vector (AND in parallel a TString vector) in such a way that the "first vector is sorted" and...
Definition: Tools.cxx:550
const TString fRegexp
Definition: Tools.h:230
Bool_t CheckForSilentOption(const TString &) const
check for "silence" option in configuration option string
Definition: Tools.cxx:703
Linear interpolation class.
Base class for spline implementation containing the Draw/Paint methods.
Definition: TSpline.h:22
Basic string class.
Definition: TString.h:131
A TTree represents a columnar dataset.
Definition: TTree.h:71
const char * GetNodeName(XMLNodePointer_t xmlnode)
returns name of xmlnode
const char * GetAttr(XMLNodePointer_t xmlnode, const char *name)
returns value of attribute for xmlnode
Definition: TXMLEngine.cxx:549
Double_t x[n]
Definition: legend1.C:17
const Int_t n
Definition: legend1.C:16
static double B[]
double T(double x)
Definition: ChebyshevPol.h:34
RooArgSet S(const RooAbsArg &v1)
static constexpr double s
create variable transformations
Tools & gTools()
MsgLogger & Endl(MsgLogger &ml)
Definition: MsgLogger.h:158
Definition: first.py:1
auto * m
Definition: textangle.C:8
auto * a
Definition: textangle.C:12