[1199] | 1 | // |
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| 2 | // ******************************************************************** |
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| 3 | // * License and Disclaimer * |
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| 4 | // * * |
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| 5 | // * The Geant4 software is copyright of the Copyright Holders of * |
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| 6 | // * the Geant4 Collaboration. It is provided under the terms and * |
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| 7 | // * conditions of the Geant4 Software License, included in the file * |
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| 8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
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| 9 | // * include a list of copyright holders. * |
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| 10 | // * * |
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| 11 | // * Neither the authors of this software system, nor their employing * |
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| 12 | // * institutes,nor the agencies providing financial support for this * |
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| 13 | // * work make any representation or warranty, express or implied, * |
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| 14 | // * regarding this software system or assume any liability for its * |
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| 15 | // * use. Please see the license in the file LICENSE and URL above * |
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| 16 | // * for the full disclaimer and the limitation of liability. * |
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| 17 | // * * |
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| 18 | // * This code implementation is the result of the scientific and * |
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| 19 | // * technical work of the GEANT4 collaboration. * |
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| 20 | // * By using, copying, modifying or distributing the software (or * |
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| 21 | // * any work based on the software) you agree to acknowledge its * |
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| 22 | // * use in resulting scientific publications, and indicate your * |
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| 23 | // * acceptance of all terms of the Geant4 Software license. * |
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| 24 | // ******************************************************************** |
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| 25 | // |
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| 26 | // |
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| 27 | // $Id: G4IntegratorTest.cc,v 1.10 2006/08/21 12:24:32 gcosmo Exp $ |
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| 28 | // GEANT4 tag $Name: geant4-09-02-ref-02 $ |
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| 29 | // |
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| 30 | // Test program for G4Integrator class. The function std::exp(-x)*std::cos(x) is |
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| 31 | // integrated between zero and two pi. The exact result is 0.499066278634 |
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| 32 | // |
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| 33 | // History: |
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| 34 | // |
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| 35 | // 05.04.97 V.Grichine, first implementation |
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| 36 | // 04.09.99 V.Grichine, integration of member function from a class and main, |
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| 37 | // as well as integration of global scope functions |
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| 38 | |
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| 39 | #include "G4ios.hh" |
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| 40 | #include "globals.hh" |
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| 41 | #include "G4SimpleIntegration.hh" |
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| 42 | #include "G4Integrator.hh" |
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| 43 | |
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| 44 | G4double GlobalFunction( G4double x ){ return std::exp(-x)*std::cos(x) ; } |
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| 45 | |
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| 46 | G4double GlobalCos( G4double x ){ return std::cos(x) ; } |
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| 47 | |
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| 48 | G4double GlobalHermite(G4double x){ return x*x*std::cos(x) ; } |
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| 49 | |
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| 50 | |
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| 51 | G4double fY; |
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| 52 | G4int fN = 100; |
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| 53 | |
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| 54 | G4double X1 = -3.25/5.; |
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| 55 | G4double X2 = 3.25/5.; |
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| 56 | |
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| 57 | G4double Y1 = -7.5/5.; |
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| 58 | G4double Y2 = 7.5/5.; |
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| 59 | |
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| 60 | G4double Harp(G4double x) |
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| 61 | { |
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| 62 | |
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| 63 | G4double tmp = std::sqrt(1 + x*x + fY*fY); |
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| 64 | tmp *= 1 + x*x + fY*fY ; |
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| 65 | return 1/tmp; |
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| 66 | } |
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| 67 | |
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| 68 | |
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| 69 | G4double HarpX(G4double y) |
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| 70 | { |
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| 71 | fY = y; |
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| 72 | G4SimpleIntegration myIntegrand(Harp); |
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| 73 | return myIntegrand.Simpson(X1,X2,fN); |
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| 74 | // return myIntegrand.Gauss(X1,X2,fN); |
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| 75 | } |
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| 76 | |
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| 77 | |
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| 78 | |
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| 79 | |
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| 80 | |
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| 81 | |
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| 82 | G4double HarpY() |
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| 83 | { |
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| 84 | // G4int i; |
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| 85 | G4SimpleIntegration myIntegrand(HarpX); |
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| 86 | // G4double sum =0.; |
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| 87 | // for(i = 0; i < fN; i++) |
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| 88 | G4double result = myIntegrand.Simpson(Y1,Y2,fN); |
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| 89 | return result/twopi; |
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| 90 | |
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| 91 | } |
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| 92 | |
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| 93 | class B |
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| 94 | { |
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| 95 | typedef G4double (B::* PBmem)(G4double); |
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| 96 | |
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| 97 | public: |
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| 98 | |
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| 99 | B(){;} |
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| 100 | |
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| 101 | ~B(){;} |
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| 102 | |
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| 103 | G4double TestFunction(G4double x){ return std::exp(-x)*std::cos(x) ; } |
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| 104 | |
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| 105 | G4double CosFunction(G4double x) { return std::cos(x) ; } |
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| 106 | |
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| 107 | G4double TestHermite(G4double x){ return x*x*std::cos(x) ; } |
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| 108 | |
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| 109 | G4double HarpX(G4double); |
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| 110 | G4double HarpY(G4double); |
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| 111 | |
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| 112 | |
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| 113 | void Integrand() ; |
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| 114 | |
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| 115 | }; |
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| 116 | |
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| 117 | |
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| 118 | void B::Integrand() |
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| 119 | { |
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| 120 | G4int i, n ; |
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| 121 | G4double pTolerance; |
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| 122 | G4double simpson1=0., simpson2=0. ; |
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| 123 | G4double legendre1=0., legendre2=0. ; |
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| 124 | G4double chebyshev1=0., chebyshev2=0. ; |
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| 125 | G4double adaptg1=0., adaptg2=0.; |
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| 126 | G4double a = 0.0 ; |
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| 127 | G4double b = twopi ; |
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| 128 | |
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| 129 | G4SimpleIntegration myIntegrand(GlobalFunction) ; |
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| 130 | |
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| 131 | G4Integrator<B,PBmem> integral; |
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| 132 | |
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| 133 | B bbb ; |
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| 134 | |
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| 135 | G4cout<<"Iter" |
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| 136 | <<"\t"<<"Simpson "<<"\t"<<"Simpson " |
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| 137 | <<"\t"<<"Legendre"<<"\t"<<"Legendre" |
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| 138 | <<"\t"<<"Chebyshev"<<"\t"<<"Chebyshev"<<G4endl ; |
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| 139 | |
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| 140 | for(i=1;i<=20;i++) |
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| 141 | { |
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| 142 | n = 2*i ; |
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| 143 | |
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| 144 | simpson1 = integral.Simpson(this,&B::TestFunction,a,b,n) ; |
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| 145 | legendre1 = integral.Legendre(this,&B::TestFunction,a,b,n) ; |
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| 146 | simpson2 = integral.Simpson(bbb,&B::TestFunction,a,b,n) ; |
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| 147 | legendre2 = integral.Legendre(bbb,&B::TestFunction,a,b,n) ; |
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| 148 | chebyshev1 = integral.Chebyshev(this,&B::TestFunction,a,b,n) ; |
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| 149 | chebyshev2 = integral.Chebyshev(bbb,&B::TestFunction,a,b,n) ; |
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| 150 | |
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| 151 | G4cout<<n |
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| 152 | <<"\t"<<simpson1<<"\t"<<simpson2 |
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| 153 | <<"\t"<<legendre1<<"\t"<<legendre2 |
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| 154 | <<"\t"<<chebyshev1<<"\t"<<chebyshev2<<G4endl ; |
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| 155 | } |
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| 156 | G4cout<<G4endl ; |
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| 157 | |
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| 158 | for(i=0;i<8;i++) |
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| 159 | { |
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| 160 | pTolerance = std::pow(10.0,-i) ; |
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| 161 | adaptg1 = integral.AdaptiveGauss(bbb,&B::TestFunction,a,b,pTolerance) ; |
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| 162 | adaptg2 = integral.AdaptiveGauss(this,&B::TestFunction,a,b,pTolerance) ; |
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| 163 | G4cout<<pTolerance<<"\t"<<adaptg1<<"\t"<<adaptg2<<G4endl; |
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| 164 | } |
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| 165 | for(i=1;i<20;i++) |
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| 166 | { |
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| 167 | n = 1*i ; |
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| 168 | G4double laguerre1=0., laguerre2=0.; |
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| 169 | laguerre1 = integral.Laguerre(bbb,&B::CosFunction,0.0,n) ; |
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| 170 | laguerre2 = integral.Laguerre(this,&B::CosFunction,0.0,n) ; |
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| 171 | G4cout<<"n = "<<n<<"\t"<<"exact = 0.5 " |
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| 172 | <<" and n-point GaussLaguerre = " |
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| 173 | <<laguerre1<<"\t"<<laguerre2<<G4endl ; |
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| 174 | } |
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| 175 | for(i=1;i<20;i++) |
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| 176 | { |
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| 177 | n = 1*i ; |
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| 178 | G4double hermite1=0., hermite2=0; |
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| 179 | G4double exactH = 2*0.125*std::sqrt(pi)*std::exp(-0.25) ; |
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| 180 | hermite1 = integral.Hermite(bbb,&B::TestHermite,n) ; |
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| 181 | hermite2 = integral.Hermite(this,&B::TestHermite,n) ; |
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| 182 | G4cout<<"n = "<<n<<"\t"<<"exact = "<<exactH |
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| 183 | <<" and n-point GaussHermite = " |
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| 184 | <<hermite1<<"\t"<<hermite2<<G4endl ; |
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| 185 | } |
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| 186 | G4double exactJ = pi*0.4400505857 ; |
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| 187 | |
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| 188 | for(i=1;i<20;i++) |
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| 189 | { |
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| 190 | n = 1*i ; |
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| 191 | G4double jacobi1=0., jacobi2=0.; |
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| 192 | jacobi1 = integral.Jacobi(bbb,&B::CosFunction,0.5,0.5,n) ; |
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| 193 | jacobi2 = integral.Jacobi(this,&B::CosFunction,0.5,0.5,n) ; |
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| 194 | G4cout<<"n = "<<n<<"\t"<<"exact = "<<exactJ |
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| 195 | <<" and n-point Gauss-Jacobi = " |
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| 196 | <<jacobi1<<"\t"<<jacobi2<<G4endl ; |
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| 197 | } |
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| 198 | } |
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| 199 | |
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| 200 | |
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| 201 | int main() |
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| 202 | { |
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| 203 | B myIntegration ; |
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| 204 | |
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| 205 | myIntegration.Integrand() ; |
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| 206 | |
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| 207 | G4Integrator<B,function> iii ; |
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| 208 | G4int i, n ; |
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| 209 | G4double a = 0.0 ; |
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| 210 | G4double b = twopi ; |
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| 211 | G4double simpson3,legendre,legendre10,legendre96,chebyshev ; |
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| 212 | |
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| 213 | G4cout<<"Global function integration"<<G4endl ; |
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| 214 | G4cout<<"n = "<<"\t"<<"Simpson"<<"\t" |
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| 215 | <<"\t"<<"Legendre""\t"<<"Chebyshev"<<G4endl ; |
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| 216 | for(i=1;i<=30;i++) |
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| 217 | { |
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| 218 | n = 2*i ; |
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| 219 | simpson3 = iii.Simpson(GlobalFunction,a,b,n) ; |
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| 220 | legendre = iii.Legendre(GlobalFunction,a,b,n) ; |
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| 221 | chebyshev = iii.Chebyshev(GlobalFunction,a,b,n) ; |
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| 222 | G4cout<<n<<"\t"<<simpson3<<"\t"<<legendre<<"\t"<<chebyshev<<G4endl ; |
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| 223 | } |
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| 224 | legendre10 = iii.Legendre10(GlobalFunction,a,b) ; |
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| 225 | legendre96 = iii.Legendre96(GlobalFunction,a,b) ; |
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| 226 | G4cout<<"Legendre 10 points = "<<"\t"<<legendre10<<G4endl ; |
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| 227 | G4cout<<"Legendre 96 points = "<<"\t"<<legendre96<<G4endl ; |
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| 228 | |
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| 229 | for(i=0;i<8;i++) |
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| 230 | { |
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| 231 | G4double pTolerance = std::pow(10.0,-i) ; |
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| 232 | G4double adaptg = iii.AdaptiveGauss(GlobalFunction,a,b,pTolerance) ; |
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| 233 | G4cout<<pTolerance<<"\t"<<adaptg<<G4endl; |
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| 234 | } |
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| 235 | for(i=1;i<20;i++) |
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| 236 | { |
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| 237 | n = 1*i ; |
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| 238 | G4double laguerre = iii.Laguerre(GlobalCos,0.0,n) ; |
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| 239 | G4cout<<"n = "<<n<<"\t"<<"exact = 0.5 " |
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| 240 | <<" and n-point Laguerre = " |
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| 241 | <<laguerre<<G4endl ; |
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| 242 | } |
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| 243 | for(i=1;i<20;i++) |
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| 244 | { |
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| 245 | n = 1*i ; |
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| 246 | G4double exactH = 2*0.125*std::sqrt(pi)*std::exp(-0.25) ; |
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| 247 | G4double hermite = iii.Hermite(GlobalHermite,n) ; |
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| 248 | G4cout<<"n = "<<n<<"\t"<<"exact = "<<exactH |
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| 249 | <<" and n-point Hermite = " |
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| 250 | <<hermite<<G4endl ; |
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| 251 | } |
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| 252 | G4double exactJ = pi*0.4400505857 ; |
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| 253 | |
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| 254 | for(i=1;i<20;i++) |
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| 255 | { |
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| 256 | n = 1*i ; |
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| 257 | G4double jacobi = iii.Jacobi(GlobalCos,0.5,0.5,n) ; |
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| 258 | G4cout<<"n = "<<n<<"\t"<<"exact = "<<exactJ |
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| 259 | <<" and n-point Jacobi = " |
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| 260 | <<jacobi<<G4endl ; |
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| 261 | } |
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| 262 | |
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| 263 | |
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| 264 | |
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| 265 | G4cout<<"Ivanchenko integral = "<<HarpY()<<G4endl; |
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| 266 | |
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| 267 | |
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| 268 | return 0; |
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| 269 | } |
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