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1// @(#)root/matrix:$Id$
2// Authors: Fons Rademakers, Eddy Offermann Nov 2003
5 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *
6 * All rights reserved. *
7 * *
8 * For the licensing terms see $ROOTSYS/LICENSE. *
9 * For the list of contributors see $ROOTSYS/README/CREDITS. *
10 *************************************************************************/
12#ifndef ROOT_TMatrixTSym
13#define ROOT_TMatrixTSym
16// //
17// TMatrixTSym //
18// //
19// Implementation of a symmetric matrix in the linear algebra package //
20// //
21// Note that in this implementation both matrix element m[i][j] and //
22// m[j][i] are updated and stored in memory . However, when making the //
23// object persistent only the upper right triangle is stored . //
24// //
27#include "TMatrixTBase.h"
28#include "TMatrixTUtils.h"
30template<class Element>class TMatrixT;
31template<class Element>class TMatrixTSymLazy;
32template<class Element>class TVectorT;
34template<class Element> class TMatrixTSym : public TMatrixTBase<Element> {
38 Element fDataStack[TMatrixTBase<Element>::kSizeMax]; //! data container
39 Element *fElements; //[fNelems] elements themselves
41 Element *New_m (Int_t size);
42 void Delete_m(Int_t size,Element*&);
43 Int_t Memcpy_m(Element *newp,const Element *oldp,Int_t copySize,
44 Int_t newSize,Int_t oldSize);
45 void Allocate(Int_t nrows,Int_t ncols,Int_t row_lwb = 0,Int_t col_lwb = 0,Int_t init = 0,
46 Int_t /*nr_nonzeros*/ = -1);
50 enum {kWorkMax = 100}; // size of work array
54 TMatrixTSym() { fElements = nullptr; }
55 explicit TMatrixTSym(Int_t nrows);
56 TMatrixTSym(Int_t row_lwb,Int_t row_upb);
57 TMatrixTSym(Int_t nrows,const Element *data,Option_t *option="");
58 TMatrixTSym(Int_t row_lwb,Int_t row_upb,const Element *data,Option_t *option="");
59 TMatrixTSym(const TMatrixTSym<Element> &another);
60 template <class Element2> TMatrixTSym(const TMatrixTSym<Element2> &another)
61 {
62 R__ASSERT(another.IsValid());
63 Allocate(another.GetNrows(),another.GetNcols(),another.GetRowLwb(),another.GetColLwb());
64 *this = another;
65 }
70 TMatrixTSym(const TMatrixTSymLazy<Element> &lazy_constructor);
74 // Elementary constructors
75 void TMult(const TMatrixT <Element> &a);
76 void TMult(const TMatrixTSym<Element> &a);
77 void Mult (const TMatrixTSym<Element> &a) { TMult(a); }
82 const Element *GetMatrixArray () const override;
83 Element *GetMatrixArray () override;
84 const Int_t *GetRowIndexArray() const override { return nullptr; }
85 Int_t *GetRowIndexArray() override { return nullptr; }
86 const Int_t *GetColIndexArray() const override { return nullptr; }
87 Int_t *GetColIndexArray() override { return nullptr; }
89 TMatrixTBase<Element> &SetRowIndexArray(Int_t * /*data*/) override { MayNotUse("SetRowIndexArray(Int_t *)"); return *this; }
90 TMatrixTBase<Element> &SetColIndexArray(Int_t * /*data*/) override { MayNotUse("SetColIndexArray(Int_t *)"); return *this; }
92 void Clear (Option_t * /*option*/ ="") override { if (this->fIsOwner) Delete_m(this->fNelems,fElements);
93 else fElements = nullptr;
94 this->fNelems = 0; }
95 Bool_t IsSymmetric() const override { return kTRUE; }
97 TMatrixTSym <Element> &Use (Int_t row_lwb,Int_t row_upb,Element *data);
98 const TMatrixTSym <Element> &Use (Int_t row_lwb,Int_t row_upb,const Element *data) const
99 { return (const TMatrixTSym<Element>&)
100 ((const_cast<TMatrixTSym<Element> *>(this))->Use(row_lwb,row_upb,const_cast<Element *>(data))); }
102 const TMatrixTSym <Element> &Use (Int_t nrows,const Element *data) const;
107 TMatrixTBase<Element> &GetSub (Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb,
108 TMatrixTBase<Element> &target,Option_t *option="S") const override;
109 TMatrixTSym <Element> GetSub (Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb,Option_t *option="S") const;
111 TMatrixTBase<Element> &SetSub (Int_t row_lwb,Int_t col_lwb,const TMatrixTBase<Element> &source) override;
113 TMatrixTBase<Element> &SetMatrixArray(const Element *data, Option_t *option="") override;
115 TMatrixTBase<Element> &Shift (Int_t row_shift,Int_t col_shift) override;
116 TMatrixTBase<Element> &ResizeTo (Int_t nrows,Int_t ncols,Int_t /*nr_nonzeros*/ =-1) override;
117 TMatrixTBase<Element> &ResizeTo (Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb,Int_t /*nr_nonzeros*/ =-1) override;
119 return ResizeTo(m.GetRowLwb(),m.GetRowUpb(),m.GetColLwb(),m.GetColUpb()); }
121 Double_t Determinant () const override;
122 void Determinant (Double_t &d1,Double_t &d2) const override;
124 TMatrixTSym<Element> &Invert (Double_t *det=nullptr);
127 inline TMatrixTSym<Element> &T () { return this->Transpose(*this); }
128 TMatrixTSym<Element> &Rank1Update (const TVectorT <Element> &v,Element alpha=1.0);
131 Element Similarity (const TVectorT <Element> &v) const;
134 // Either access a_ij as a(i,j)
135 inline Element operator()(Int_t rown,Int_t coln) const override;
136 inline Element &operator()(Int_t rown,Int_t coln) override;
138 // or as a[i][j]
139 inline const TMatrixTRow_const<Element> operator[](Int_t rown) const { return TMatrixTRow_const<Element>(*this,rown); }
140 inline TMatrixTRow <Element> operator[](Int_t rown) { return TMatrixTRow <Element>(*this,rown); }
144 template <class Element2> TMatrixTSym<Element> &operator= (const TMatrixTSym<Element2> &source)
145 {
146 if (!AreCompatible(*this,source)) {
147 Error("operator=(const TMatrixTSym2 &)","matrices not compatible");
148 return *this;
149 }
151 TObject::operator=(source);
152 const Element2 * const ps = source.GetMatrixArray();
153 Element * const pt = this->GetMatrixArray();
154 for (Int_t i = 0; i < this->fNelems; i++)
155 pt[i] = ps[i];
156 this->fTol = source.GetTol();
157 return *this;
158 }
160 TMatrixTSym<Element> &operator= (Element val);
161 TMatrixTSym<Element> &operator-=(Element val);
162 TMatrixTSym<Element> &operator+=(Element val);
163 TMatrixTSym<Element> &operator*=(Element val);
165 TMatrixTSym &operator+=(const TMatrixTSym &source);
166 TMatrixTSym &operator-=(const TMatrixTSym &source);
171 TMatrixTBase<Element> &Randomize (Element alpha,Element beta,Double_t &seed) override;
172 virtual TMatrixTSym <Element> &RandomizePD(Element alpha,Element beta,Double_t &seed);
174 const TMatrixT<Element> EigenVectors(TVectorT<Element> &eigenValues) const;
176 ClassDefOverride(TMatrixTSym,2) // Template of Symmetric Matrix class
178#ifndef __CINT__
179// When building with -fmodules, it instantiates all pending instantiations,
180// instead of delaying them until the end of the translation unit.
181// We 'got away with' probably because the use and the definition of the
182// explicit specialization do not occur in the same TU.
184// In case we are building with -fmodules, we need to forward declare the
185// specialization in order to compile the dictionary G__Matrix.cxx.
187#endif // __CINT__
189template <class Element> inline const Element *TMatrixTSym<Element>::GetMatrixArray() const { return fElements; }
190template <class Element> inline Element *TMatrixTSym<Element>::GetMatrixArray() { return fElements; }
192template <class Element> inline TMatrixTSym<Element> &TMatrixTSym<Element>::Use (Int_t nrows,Element *data) { return Use(0,nrows-1,data); }
193template <class Element> inline const TMatrixTSym<Element> &TMatrixTSym<Element>::Use (Int_t nrows,const Element *data) const
194 { return Use(0,nrows-1,data); }
196 { return Use(a.GetRowLwb(),a.GetRowUpb(),a.GetMatrixArray()); }
197template <class Element> inline const TMatrixTSym<Element> &TMatrixTSym<Element>::Use (const TMatrixTSym<Element> &a) const
198 { return Use(a.GetRowLwb(),a.GetRowUpb(),a.GetMatrixArray()); }
200template <class Element> inline TMatrixTSym<Element> TMatrixTSym<Element>::GetSub (Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb,
201 Option_t *option) const
202 {
204 this->GetSub(row_lwb,row_upb,col_lwb,col_upb,tmp,option);
205 return tmp;
206 }
208template <class Element> inline Element TMatrixTSym<Element>::operator()(Int_t rown,Int_t coln) const
210 R__ASSERT(this->IsValid());
211 const Int_t arown = rown-this->fRowLwb;
212 const Int_t acoln = coln-this->fColLwb;
213 if (arown >= this->fNrows || arown < 0) {
214 Error("operator()","Request row(%d) outside matrix range of %d - %d",rown,this->fRowLwb,this->fRowLwb+this->fNrows);
216 }
217 if (acoln >= this->fNcols || acoln < 0) {
218 Error("operator()","Request column(%d) outside matrix range of %d - %d",coln,this->fColLwb,this->fColLwb+this->fNcols);
220 }
221 return (fElements[arown*this->fNcols+acoln]);
224template <class Element> inline Element &TMatrixTSym<Element>::operator()(Int_t rown,Int_t coln)
226 R__ASSERT(this->IsValid());
227 const Int_t arown = rown-this->fRowLwb;
228 const Int_t acoln = coln-this->fColLwb;
229 if (arown >= this->fNrows || arown < 0) {
230 Error("operator()","Request row(%d) outside matrix range of %d - %d",rown,this->fRowLwb,this->fRowLwb+this->fNrows);
232 }
233 if (acoln >= this->fNcols || acoln < 0) {
234 Error("operator()","Request column(%d) outside matrix range of %d - %d",coln,this->fColLwb,this->fColLwb+this->fNcols);
236 }
237 return (fElements[arown*this->fNcols+acoln]);
240template <class Element> Bool_t operator== (const TMatrixTSym<Element> &source1,const TMatrixTSym<Element> &source2);
241template <class Element> TMatrixTSym<Element> operator+ (const TMatrixTSym<Element> &source1,const TMatrixTSym<Element> &source2);
242template <class Element> TMatrixTSym<Element> operator+ (const TMatrixTSym<Element> &source1, Element val);
243template <class Element> TMatrixTSym<Element> operator+ ( Element val ,const TMatrixTSym<Element> &source2);
244template <class Element> TMatrixTSym<Element> operator- (const TMatrixTSym<Element> &source1,const TMatrixTSym<Element> &source2);
245template <class Element> TMatrixTSym<Element> operator- (const TMatrixTSym<Element> &source1, Element val);
246template <class Element> TMatrixTSym<Element> operator- ( Element val ,const TMatrixTSym<Element> &source2);
247template <class Element> TMatrixTSym<Element> operator* (const TMatrixTSym<Element> &source, Element val );
248template <class Element> TMatrixTSym<Element> operator* ( Element val, const TMatrixTSym<Element> &source );
249// Preventing warnings with -Weffc++ in GCC since overloading the || and && operators was a design choice.
250#if (__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__) >= 40600
251#pragma GCC diagnostic push
252#pragma GCC diagnostic ignored "-Weffc++"
254template <class Element> TMatrixTSym<Element> operator&& (const TMatrixTSym<Element> &source1,const TMatrixTSym<Element> &source2);
255template <class Element> TMatrixTSym<Element> operator|| (const TMatrixTSym<Element> &source1,const TMatrixTSym<Element> &source2);
256#if (__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__) >= 40600
257#pragma GCC diagnostic pop
259template <class Element> TMatrixTSym<Element> operator> (const TMatrixTSym<Element> &source1,const TMatrixTSym<Element> &source2);
260template <class Element> TMatrixTSym<Element> operator>= (const TMatrixTSym<Element> &source1,const TMatrixTSym<Element> &source2);
261template <class Element> TMatrixTSym<Element> operator<= (const TMatrixTSym<Element> &source1,const TMatrixTSym<Element> &source2);
262template <class Element> TMatrixTSym<Element> operator< (const TMatrixTSym<Element> &source1,const TMatrixTSym<Element> &source2);
264template <class Element> TMatrixTSym<Element> &Add (TMatrixTSym<Element> &target, Element scalar,const TMatrixTSym<Element> &source);
266template <class Element> TMatrixTSym<Element> &ElementDiv (TMatrixTSym<Element> &target,const TMatrixTSym<Element> &source);
size_t size(const MatrixT &matrix)
retrieve the size of a square matrix
bool Bool_t
Definition: RtypesCore.h:63
int Int_t
Definition: RtypesCore.h:45
double Double_t
Definition: RtypesCore.h:59
const Bool_t kTRUE
Definition: RtypesCore.h:100
const char Option_t
Definition: RtypesCore.h:66
#define ClassDefOverride(name, id)
Definition: Rtypes.h:339
#define R__ASSERT(e)
Definition: TError.h:118
void Error(const char *location, const char *msgfmt,...)
Use this function in case an error occurred.
Definition: TError.cxx:188
Option_t Option_t option
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void data
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void char Point_t Rectangle_t WindowAttributes_t Float_t Float_t Float_t b
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void char Point_t Rectangle_t WindowAttributes_t Float_t Float_t Float_t Int_t Int_t UInt_t UInt_t Rectangle_t Int_t Int_t Window_t TString Int_t GCValues_t GetPrimarySelectionOwner GetDisplay GetScreen GetColormap GetNativeEvent const char const char dpyName wid window const char font_name cursor keysym reg const char only_if_exist regb h Point_t winding char text const char depth char const char Int_t count const char ColorStruct_t color const char Pixmap_t Pixmap_t PictureAttributes_t attr const char char ret_data h unsigned char height h Atom_t Int_t ULong_t ULong_t unsigned char prop_list Atom_t Atom_t target
TMatrixTSym< Element > & ElementDiv(TMatrixTSym< Element > &target, const TMatrixTSym< Element > &source)
Multiply target by the source, element-by-element.
TMatrixTSym< Element > operator<(const TMatrixTSym< Element > &source1, const TMatrixTSym< Element > &source2)
source1 < source2
TMatrixTSym< Element > operator+(const TMatrixTSym< Element > &source1, const TMatrixTSym< Element > &source2)
TMatrixTSym< Element > operator-(const TMatrixTSym< Element > &source1, const TMatrixTSym< Element > &source2)
TMatrixTSym< Element > & Add(TMatrixTSym< Element > &target, Element scalar, const TMatrixTSym< Element > &source)
Modify addition: target += scalar * source.
TMatrixTSym< Element > & ElementMult(TMatrixTSym< Element > &target, const TMatrixTSym< Element > &source)
Multiply target by the source, element-by-element.
TMatrixTSym< Element > operator>(const TMatrixTSym< Element > &source1, const TMatrixTSym< Element > &source2)
source1 > source2
TMatrixTSym< Element > operator>=(const TMatrixTSym< Element > &source1, const TMatrixTSym< Element > &source2)
source1 >= source2
TMatrixTSym< Element > operator<=(const TMatrixTSym< Element > &source1, const TMatrixTSym< Element > &source2)
source1 <= source2
TMatrixTSym< Element > operator||(const TMatrixTSym< Element > &source1, const TMatrixTSym< Element > &source2)
Logical Or.
TMatrixTSym< Element > operator*(const TMatrixTSym< Element > &source, Element val)
TMatrixTSym< Element > operator&&(const TMatrixTSym< Element > &source1, const TMatrixTSym< Element > &source2)
Logical AND.
Bool_t operator==(const TMatrixTSym< Element > &source1, const TMatrixTSym< Element > &source2)
Check to see if two matrices are identical.
TClass instances represent classes, structs and namespaces in the ROOT type system.
Definition: TClass.h:81
Definition: TMatrixTBase.h:84
Int_t GetNrows() const
Definition: TMatrixTBase.h:123
Bool_t fIsOwner
Definition: TMatrixTBase.h:100
Element fTol
Definition: TMatrixTBase.h:97
Int_t GetRowLwb() const
Definition: TMatrixTBase.h:121
Int_t GetColLwb() const
Definition: TMatrixTBase.h:124
static Element & NaNValue()
Bool_t IsValid() const
Definition: TMatrixTBase.h:146
Int_t GetNcols() const
Definition: TMatrixTBase.h:126
Element GetTol() const
Definition: TMatrixTBase.h:128
Definition: TMatrixTSym.h:34
TMatrixTSym< Element > GetSub(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, Option_t *option="S") const
Definition: TMatrixTSym.h:200
Element & operator()(Int_t rown, Int_t coln) override
Definition: TMatrixTSym.h:224
TMatrixTBase< Element > & ResizeTo(const TMatrixTSym< Element > &m)
Definition: TMatrixTSym.h:118
TMatrixTSym< Element > & operator*=(Element val)
Multiply every element of the matrix with val.
TMatrixTBase< Element > & ResizeTo(Int_t nrows, Int_t ncols, Int_t=-1) override
Set size of the matrix to nrows x ncols New dynamic elements are created, the overlapping part of the...
TMatrixTSym(const TMatrixTSym< Element2 > &another)
Definition: TMatrixTSym.h:60
TMatrixTRow< Element > operator[](Int_t rown)
Definition: TMatrixTSym.h:140
const Int_t * GetColIndexArray() const override
Definition: TMatrixTSym.h:86
TMatrixTSym< Element > & operator+=(Element val)
Add val to every element of the matrix.
const TMatrixTSym< Element > & Use(Int_t nrows, const Element *data) const
Definition: TMatrixTSym.h:193
const TMatrixTSym< Element > & Use(Int_t row_lwb, Int_t row_upb, const Element *data) const
Definition: TMatrixTSym.h:98
virtual TMatrixTSym< Element > & RandomizePD(Element alpha, Element beta, Double_t &seed)
randomize matrix element values but keep matrix symmetric positive definite
TMatrixTBase< Element > & Randomize(Element alpha, Element beta, Double_t &seed) override
randomize matrix element values but keep matrix symmetric
Int_t * GetRowIndexArray() override
Definition: TMatrixTSym.h:85
TMatrixTBase< Element > & SetColIndexArray(Int_t *) override
Definition: TMatrixTSym.h:90
TMatrixTSym< Element > & Transpose(const TMatrixTSym< Element > &source)
Transpose a matrix.
Element * New_m(Int_t size)
return data pointer .
TMatrixTSym< Element > & Use(Int_t nrows, Element *data)
Definition: TMatrixTSym.h:192
TMatrixTSym< Element > & Use(Int_t row_lwb, Int_t row_upb, Element *data)
const TMatrixTRow_const< Element > operator[](Int_t rown) const
Definition: TMatrixTSym.h:139
TMatrixTSym< Element > & Rank1Update(const TVectorT< Element > &v, Element alpha=1.0)
Perform a rank 1 operation on the matrix: A += alpha * v * v^T.
TMatrixTSym< Element > & Use(TMatrixTSym< Element > &a)
Definition: TMatrixTSym.h:195
TMatrixTSym< Element > & T()
Definition: TMatrixTSym.h:127
void Minus(const TMatrixTSym< Element > &a, const TMatrixTSym< Element > &b)
Symmetric matrix summation. Create a matrix C such that C = A + B.
void TMult(const TMatrixT< Element > &a)
Create a matrix C such that C = A' * A.
const Int_t * GetRowIndexArray() const override
Definition: TMatrixTSym.h:84
void Delete_m(Int_t size, Element *&)
delete data pointer m, if it was assigned on the heap
void Allocate(Int_t nrows, Int_t ncols, Int_t row_lwb=0, Int_t col_lwb=0, Int_t init=0, Int_t=-1)
Allocate new matrix.
Element * GetMatrixArray() override
Definition: TMatrixTSym.h:190
TMatrixTSym< Element > & GetSub(Int_t row_lwb, Int_t row_upb, TMatrixTSym< Element > &target, Option_t *option="S") const
Get submatrix [row_lwb..row_upb][row_lwb..row_upb]; The indexing range of the returned matrix depends...
Int_t Memcpy_m(Element *newp, const Element *oldp, Int_t copySize, Int_t newSize, Int_t oldSize)
copy copySize doubles from *oldp to *newp .
const TMatrixT< Element > EigenVectors(TVectorT< Element > &eigenValues) const
Return a matrix containing the eigen-vectors ordered by descending eigen-values.
TMatrixTSym< Element > & operator-=(Element val)
Subtract val from every element of the matrix.
Bool_t IsSymmetric() const override
Check whether matrix is symmetric.
Definition: TMatrixTSym.h:95
void Plus(const TMatrixTSym< Element > &a, const TMatrixTSym< Element > &b)
Symmetric matrix summation. Create a matrix C such that C = A + B.
Element fDataStack[TMatrixTBase< Element >::kSizeMax]
Definition: TMatrixTSym.h:38
TMatrixTSym< Element > & InvertFast(Double_t *det=nullptr)
Invert the matrix and calculate its determinant.
TMatrixTSym< Element > & SimilarityT(const TMatrixT< Element > &n)
Calculate B^T * (*this) * B , final matrix will be (ncolsb x ncolsb) It is more efficient than applyi...
static TClass * Class()
TMatrixTSym< Element > & Similarity(const TMatrixT< Element > &n)
Calculate B * (*this) * B^T , final matrix will be (nrowsb x nrowsb) This is a similarity transform w...
TMatrixTSym< Element > & operator=(const TMatrixTSym< Element > &source)
TMatrixTSym< Element > & SetSub(Int_t row_lwb, const TMatrixTBase< Element > &source)
Insert matrix source starting at [row_lwb][row_lwb], thereby overwriting the part [row_lwb....
TMatrixTBase< Element > & SetMatrixArray(const Element *data, Option_t *option="") override
Copy array data to matrix .
void Clear(Option_t *="") override
Definition: TMatrixTSym.h:92
void Mult(const TMatrixTSym< Element > &a)
Definition: TMatrixTSym.h:77
Element * fElements
data container
Definition: TMatrixTSym.h:39
TMatrixTBase< Element > & Shift(Int_t row_shift, Int_t col_shift) override
Shift the row index by adding row_shift and the column index by adding col_shift, respectively.
TMatrixTBase< Element > & Apply(const TElementActionT< Element > &action) override
Apply action to each matrix element.
~TMatrixTSym() override
Definition: TMatrixTSym.h:72
Double_t Determinant() const override
TMatrixTSym< Element > & Invert(Double_t *det=nullptr)
Invert the matrix and calculate its determinant Notice that the LU decomposition is used instead of B...
const TMatrixTSym< Element > & Use(const TMatrixTSym< Element > &a) const
Definition: TMatrixTSym.h:197
Element operator()(Int_t rown, Int_t coln) const override
Definition: TMatrixTSym.h:208
const Element * GetMatrixArray() const override
Definition: TMatrixTSym.h:189
TMatrixTBase< Element > & SetRowIndexArray(Int_t *) override
Definition: TMatrixTSym.h:89
Int_t * GetColIndexArray() override
Definition: TMatrixTSym.h:87
Definition: TMatrixT.h:39
TObject & operator=(const TObject &rhs)
TObject assignment operator.
Definition: TObject.h:298
void MayNotUse(const char *method) const
Use this method to signal that a method (defined in a base class) may not be called in a derived clas...
Definition: TObject.cxx:1023
virtual void Error(const char *method, const char *msgfmt,...) const
Issue error message.
Definition: TObject.cxx:970
Definition: TVectorT.h:27
TPaveText * pt
double beta(double x, double y)
Calculates the beta function.
const Int_t n
Definition: legend1.C:16
void init()
Inspect hardware capabilities, and load the optimal library for RooFit computations.
static constexpr double ps
Bool_t AreCompatible(const TMatrixTBase< Element1 > &m1, const TMatrixTBase< Element2 > &m2, Int_t verbose=0)
Check that matrice sm1 and m2 areboth valid and have identical shapes .
TMarker m
Definition: textangle.C:8
TArc a
Definition: textangle.C:12