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1// @(#)root/mathcore:$Id$
2// Author: Federico Carminati 22/04/2004
5 * Copyright (C) 1995-2004, 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_TComplex
13#define ROOT_TComplex
16// //
17// TComplex //
18// //
21#include "TMath.h"
23#include "Rtypes.h"
26class TComplex {
29 Double_t fRe; // real part
30 Double_t fIm; // imaginary part
33 // ctors and dtors
34 TComplex(): fRe(0), fIm(0) {}
35 TComplex(Double_t re, Double_t im=0, Bool_t polar=kFALSE);
36 virtual ~TComplex() {}
38 // constants
39 static TComplex I() {return TComplex(0,1);}
40 static TComplex One() {return TComplex(1,0);}
42 // getters and setters
43 Double_t Re() const {return fRe;}
44 Double_t Im() const {return fIm;}
45 Double_t Rho() const {return TMath::Sqrt(fRe*fRe+fIm*fIm);}
46 Double_t Rho2() const {return fRe*fRe+fIm*fIm;}
47 Double_t Theta() const {return (fIm||fRe)?TMath::ATan2(fIm,fRe):0;}
49 { if (polar) { fRe = x*TMath::Cos(y); fIm = x*TMath::Sin(y); }
50 else { fRe = x; fIm = y; } return *this; }
52 // Simple operators complex - complex
54 {return TComplex(fRe*c.fRe-fIm*c.fIm,fRe*c.fIm+fIm*c.fRe);}
56 {return TComplex(fRe+c.fRe, fIm+c.fIm);}
58 {return TComplex(fRe*c.fRe+fIm*c.fIm,-fRe*c.fIm+fIm*c.fRe)/c.Rho2();}
60 {return TComplex(fRe-c.fRe, fIm-c.fIm);}
63 {return ((*this) = (*this) * c);}
65 {return ((*this) = (*this) + c);}
67 {return ((*this) = (*this) / c);}
69 {return ((*this) = (*this) - c);}
72 {return TComplex(-fRe,-fIm);}
74 {return *this;}
76 // Simple operators complex - double
78 {return TComplex(fRe*c,fIm*c);}
80 {return TComplex(fRe+c, fIm);}
82 {return TComplex(fRe/c,fIm/c);}
84 {return TComplex(fRe-c, fIm);}
86 // Simple operators double - complex
88 {return TComplex(d*c.fRe,d*c.fIm);}
90 {return TComplex(d+c.fRe, c.fIm);}
92 {return TComplex(d*c.fRe,-d*c.fIm)/c.Rho2();}
94 {return TComplex(d-c.fRe, -c.fIm);}
96 // Convertors
97 operator Double_t () const {return fRe;}
98 operator Float_t () const {return static_cast<Float_t>(fRe);}
99 operator Int_t () const {return static_cast<Int_t>(fRe);}
101 // TMath:: extensions
102 static TComplex Sqrt(const TComplex &c)
103 {return TComplex(TMath::Sqrt(c.Rho()),0.5*c.Theta(),kTRUE);}
105 static TComplex Exp(const TComplex &c)
106 {return TComplex(TMath::Exp(c.fRe),c.fIm,kTRUE);}
107 static TComplex Log(const TComplex &c)
108 {return TComplex(0.5*TMath::Log(c.Rho2()),c.Theta());}
109 static TComplex Log2(const TComplex &c)
110 {return Log(c)/TMath::Log(2);}
111 static TComplex Log10(const TComplex &c)
112 {return Log(c)/TMath::Log(10);}
114 static TComplex Sin(const TComplex &c)
115 {return TComplex(TMath::Sin(c.fRe)*TMath::CosH(c.fIm),
116 TMath::Cos(c.fRe)*TMath::SinH(c.fIm));}
117 static TComplex Cos(const TComplex &c)
118 {return TComplex(TMath::Cos(c.fRe)*TMath::CosH(c.fIm),
119 -TMath::Sin(c.fRe)*TMath::SinH(c.fIm));}
120 static TComplex Tan(const TComplex &c)
121 {TComplex cc=Cos(c); return Sin(c)*Conjugate(cc)/cc.Rho2();}
123 static TComplex ASin(const TComplex &c)
124 {return -I()*Log(I()*c+TMath::Sign(1.,c.Im())*Sqrt(1.-c*c));}
125 static TComplex ACos(const TComplex &c)
126 {return -I()*Log(c+TMath::Sign(1.,c.Im())*Sqrt(c*c-1.));}
127 static TComplex ATan(const TComplex &c)
128 {return -0.5*I()*Log((1.+I()*c)/(1.-I()*c));}
130 static TComplex SinH(const TComplex &c)
131 {return TComplex(TMath::SinH(c.fRe)*TMath::Cos(c.fIm),
132 TMath::CosH(c.fRe)*TMath::Sin(c.fIm));}
133 static TComplex CosH(const TComplex &c)
134 {return TComplex(TMath::CosH(c.fRe)*TMath::Cos(c.fIm),
135 TMath::SinH(c.fRe)*TMath::Sin(c.fIm));}
136 static TComplex TanH(const TComplex &c)
137 {TComplex cc=CosH(c); return SinH(c)*Conjugate(cc)/cc.Rho2();}
139 static TComplex ASinH(const TComplex &c)
140 {return Log(c+TMath::Sign(1.,c.Im())*Sqrt(c*c+1.));}
141 static TComplex ACosH(const TComplex &c)
142 {return Log(c+TMath::Sign(1.,c.Im())*Sqrt(c*c-1.));}
143 static TComplex ATanH(const TComplex &c)
144 {return 0.5*Log((1.+c)/(1.-c));}
146 static Double_t Abs(const TComplex &c)
147 {return c.Rho();}
149 static TComplex Power(const TComplex& x, const TComplex& y)
150 {Double_t lrho=TMath::Log(x.Rho());
151 Double_t theta=x.Theta();
152 return TComplex(TMath::Exp(lrho*y.Re()-theta*y.Im()),
153 lrho*y.Im()+theta*y.Re(),kTRUE);}
155 {return TComplex(TMath::Power(x.Rho(),y),x.Theta()*y,kTRUE);}
158 Double_t theta=(x>0)?0:TMath::Pi();
159 return TComplex(TMath::Exp(lrho*y.Re()-theta*y.Im()),
160 lrho*y.Im()+theta*y.Re(),kTRUE);}
161 static TComplex Power(const TComplex& x, Int_t y)
162 {return TComplex(TMath::Power(x.Rho(),y),x.Theta()*y,kTRUE);}
164 static Int_t Finite(const TComplex& c)
165 {return TMath::Min(TMath::Finite(c.Re()),TMath::Finite(c.Im()));}
166 static Int_t IsNaN(const TComplex& c)
167 {return TMath::IsNaN(c.Re()) || TMath::IsNaN(c.Im());}
169 static TComplex Min(const TComplex &a, const TComplex &b)
170 {return a.Rho()<=b.Rho()?a:b;}
171 static TComplex Max(const TComplex &a, const TComplex &b)
172 {return a.Rho()>=b.Rho()?a:b;}
174 {return TComplex(1.,c.Theta(),kTRUE);}
176 {return TComplex(c.Re(),-c.Im());}
177 static TComplex Range(const TComplex &lb, const TComplex &ub, const TComplex &c)
178 {return Max(lb,Min(c,ub));}
180 // I/O
181 friend std::ostream& operator<<(std::ostream& out, const TComplex& c);
182 friend std::istream& operator>>(std::istream& in, TComplex& c);
184 ClassDef(TComplex,1) //Complex Class
187namespace cling {
188std::string printValue(TComplex *c);
#define d(i)
Definition: RSha256.hxx:102
#define b(i)
Definition: RSha256.hxx:100
#define c(i)
Definition: RSha256.hxx:101
int Int_t
Definition: RtypesCore.h:43
const Bool_t kFALSE
Definition: RtypesCore.h:90
bool Bool_t
Definition: RtypesCore.h:61
double Double_t
Definition: RtypesCore.h:57
float Float_t
Definition: RtypesCore.h:55
const Bool_t kTRUE
Definition: RtypesCore.h:89
#define ClassDef(name, id)
Definition: Rtypes.h:322
static TComplex Max(const TComplex &a, const TComplex &b)
Definition: TComplex.h:171
Double_t fRe
Definition: TComplex.h:29
Double_t Im() const
Definition: TComplex.h:44
virtual ~TComplex()
Definition: TComplex.h:36
Double_t fIm
Definition: TComplex.h:30
static TComplex Power(const TComplex &x, Double_t y)
Definition: TComplex.h:154
static TComplex ACos(const TComplex &c)
Definition: TComplex.h:125
static TComplex Power(Double_t x, const TComplex &y)
Definition: TComplex.h:156
static TComplex I()
Definition: TComplex.h:39
friend std::istream & operator>>(std::istream &in, TComplex &c)
Definition: TComplex.cxx:50
TComplex operator+()
Definition: TComplex.h:73
Double_t Re() const
Definition: TComplex.h:43
static TComplex ATan(const TComplex &c)
Definition: TComplex.h:127
static TComplex Log2(const TComplex &c)
Definition: TComplex.h:109
static TComplex Sqrt(const TComplex &c)
Definition: TComplex.h:102
TComplex operator-()
Definition: TComplex.h:71
TComplex operator/=(const TComplex &c)
Definition: TComplex.h:66
TComplex operator*=(const TComplex &c)
Definition: TComplex.h:62
TComplex operator/(const TComplex &c) const
Definition: TComplex.h:57
static TComplex CosH(const TComplex &c)
Definition: TComplex.h:133
static TComplex ACosH(const TComplex &c)
Definition: TComplex.h:141
TComplex operator-=(const TComplex &c)
Definition: TComplex.h:68
static TComplex Cos(const TComplex &c)
Definition: TComplex.h:117
static TComplex Power(const TComplex &x, const TComplex &y)
Definition: TComplex.h:149
static TComplex Log(const TComplex &c)
Definition: TComplex.h:107
Double_t Rho2() const
Definition: TComplex.h:46
friend std::ostream & operator<<(std::ostream &out, const TComplex &c)
Definition: TComplex.cxx:42
static TComplex Sin(const TComplex &c)
Definition: TComplex.h:114
static TComplex One()
Definition: TComplex.h:40
static TComplex Conjugate(const TComplex &c)
Definition: TComplex.h:175
Double_t Theta() const
Definition: TComplex.h:47
TComplex operator+=(const TComplex &c)
Definition: TComplex.h:64
static TComplex SinH(const TComplex &c)
Definition: TComplex.h:130
static TComplex TanH(const TComplex &c)
Definition: TComplex.h:136
static TComplex ASin(const TComplex &c)
Definition: TComplex.h:123
static TComplex Log10(const TComplex &c)
Definition: TComplex.h:111
static TComplex Range(const TComplex &lb, const TComplex &ub, const TComplex &c)
Definition: TComplex.h:177
static Int_t Finite(const TComplex &c)
Definition: TComplex.h:164
static TComplex Tan(const TComplex &c)
Definition: TComplex.h:120
Double_t Rho() const
Definition: TComplex.h:45
TComplex operator*(const TComplex &c) const
Definition: TComplex.h:53
static TComplex Normalize(const TComplex &c)
Definition: TComplex.h:173
static TComplex Min(const TComplex &a, const TComplex &b)
Definition: TComplex.h:169
static TComplex Power(const TComplex &x, Int_t y)
Definition: TComplex.h:161
static TComplex Exp(const TComplex &c)
Definition: TComplex.h:105
static Int_t IsNaN(const TComplex &c)
Definition: TComplex.h:166
static Double_t Abs(const TComplex &c)
Definition: TComplex.h:146
TComplex operator()(Double_t x, Double_t y, Bool_t polar=kFALSE)
Definition: TComplex.h:48
static TComplex ASinH(const TComplex &c)
Definition: TComplex.h:139
Definition: TComplex.h:34
static TComplex ATanH(const TComplex &c)
Definition: TComplex.h:143
Double_t y[n]
Definition: legend1.C:17
Double_t x[n]
Definition: legend1.C:17
Double_t CosH(Double_t)
Definition: TMath.h:643
Bool_t IsNaN(Double_t x)
Definition: TMath.h:882
Double_t Exp(Double_t x)
Definition: TMath.h:717
T1 Sign(T1 a, T2 b)
Definition: TMathBase.h:165
Int_t Finite(Double_t x)
Check if it is finite with a mask in order to be consistent in presence of fast math.
Definition: TMath.h:761
Double_t ATan2(Double_t y, Double_t x)
Definition: TMath.h:669
Double_t Log(Double_t x)
Definition: TMath.h:750
Double_t Sqrt(Double_t x)
Definition: TMath.h:681
LongDouble_t Power(LongDouble_t x, LongDouble_t y)
Definition: TMath.h:725
Short_t Min(Short_t a, Short_t b)
Definition: TMathBase.h:180
Double_t Cos(Double_t)
Definition: TMath.h:631
constexpr Double_t Pi()
Definition: TMath.h:38
Double_t Sin(Double_t)
Definition: TMath.h:627
Short_t Abs(Short_t d)
Definition: TMathBase.h:120
Double_t SinH(Double_t)
Definition: TMath.h:639
auto * a
Definition: textangle.C:12