1 | // |
---|
2 | // ******************************************************************** |
---|
3 | // * License and Disclaimer * |
---|
4 | // * * |
---|
5 | // * The Geant4 software is copyright of the Copyright Holders of * |
---|
6 | // * the Geant4 Collaboration. It is provided under the terms and * |
---|
7 | // * conditions of the Geant4 Software License, included in the file * |
---|
8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
---|
9 | // * include a list of copyright holders. * |
---|
10 | // * * |
---|
11 | // * Neither the authors of this software system, nor their employing * |
---|
12 | // * institutes,nor the agencies providing financial support for this * |
---|
13 | // * work make any representation or warranty, express or implied, * |
---|
14 | // * regarding this software system or assume any liability for its * |
---|
15 | // * use. Please see the license in the file LICENSE and URL above * |
---|
16 | // * for the full disclaimer and the limitation of liability. * |
---|
17 | // * * |
---|
18 | // * This code implementation is the result of the scientific and * |
---|
19 | // * technical work of the GEANT4 collaboration. * |
---|
20 | // * By using, copying, modifying or distributing the software (or * |
---|
21 | // * any work based on the software) you agree to acknowledge its * |
---|
22 | // * use in resulting scientific publications, and indicate your * |
---|
23 | // * acceptance of all terms of the Geant4 Software license. * |
---|
24 | // ******************************************************************** |
---|
25 | // |
---|
26 | // |
---|
27 | // $Id: testGaussianQuadrature.cc,v 1.6 2006/06/29 19:00:37 gunter Exp $ |
---|
28 | // GEANT4 tag $Name: geant4-09-02-ref-02 $ |
---|
29 | // |
---|
30 | // Test program for G4GaussianQuadrature class. The function std::exp(-x)*std::cos(x) is |
---|
31 | // integrated between zero and two pi. The true result is 0.499066278634 |
---|
32 | // |
---|
33 | |
---|
34 | #include "G4ios.hh" |
---|
35 | #include "globals.hh" |
---|
36 | // #include "G4VGaussianQuadrature.hh" |
---|
37 | #include "G4GaussChebyshevQ.hh" |
---|
38 | #include "G4GaussHermiteQ.hh" |
---|
39 | #include "G4GaussJacobiQ.hh" |
---|
40 | #include "G4GaussLaguerreQ.hh" |
---|
41 | #include "G4GaussLegendreQ.hh" |
---|
42 | |
---|
43 | G4double TestChebyshev(G4double x) |
---|
44 | { |
---|
45 | return std::sqrt(1-x*x)*std::cos(x) ; |
---|
46 | } |
---|
47 | |
---|
48 | G4double TestFunction(G4double x) |
---|
49 | { |
---|
50 | return std::exp(-x)*std::cos(x) ; |
---|
51 | } |
---|
52 | |
---|
53 | G4double TestHermite(G4double x) |
---|
54 | { |
---|
55 | return x*x*std::cos(x) ; |
---|
56 | } |
---|
57 | |
---|
58 | G4double CosFunction(G4double x) |
---|
59 | { |
---|
60 | return std::cos(x) ; |
---|
61 | } |
---|
62 | |
---|
63 | int main() |
---|
64 | { |
---|
65 | G4int i, n = 20; |
---|
66 | // G4double pTolerance ; |
---|
67 | G4double a = -1.0 ; |
---|
68 | G4double b = 1.0 ; |
---|
69 | // G4double true = pi*0.4400505857 ; |
---|
70 | for(i=1;i<20;i++) |
---|
71 | { |
---|
72 | n = 1*i ; |
---|
73 | G4GaussChebyshevQ myChebyshev(TestChebyshev,n) ; |
---|
74 | G4cout<<"n = "<<n<<"\t"<<"true = "<<true<<" and n-point Gauss-Chebyshev = " |
---|
75 | <<myChebyshev.Integral(a,b)<<G4endl ; |
---|
76 | } |
---|
77 | // G4double true = pi*0.4400505857 ; |
---|
78 | for(i=1;i<20;i++) |
---|
79 | { |
---|
80 | n = 1*i ; |
---|
81 | G4GaussJacobiQ myJacobi(CosFunction,0.5,0.5,n) ; |
---|
82 | G4cout<<"n = "<<n<<"\t"<<"true = "<<true<<" and n-point Gauss-Jacobi = " |
---|
83 | <<myJacobi.Integral()<<G4endl ; |
---|
84 | } |
---|
85 | G4double true = 2*0.125*std::sqrt(pi)*std::exp(-0.25) ; |
---|
86 | for(i=1;i<20;i++) |
---|
87 | { |
---|
88 | n = 1*i ; |
---|
89 | G4GaussHermiteQ myHermite(TestHermite,n) ; |
---|
90 | G4cout<<"n = "<<n<<"\t"<<"true = "<<true<<" and n-point GaussHermite = " |
---|
91 | <<myHermite.Integral()<<G4endl ; |
---|
92 | } |
---|
93 | /* ******************* |
---|
94 | G4GaussianQuadrature myHermite(n) ; |
---|
95 | for(i=0;i<(n+1)/2;i++) |
---|
96 | { |
---|
97 | G4cout<<i<<"\t"<<myHermite.GetAbscissa(i)<<"\t" |
---|
98 | <<myHermite.GetWeight(i)<<G4endl ; |
---|
99 | } |
---|
100 | G4GaussianQuadrature myLaguerre(0.0,n) ; |
---|
101 | for(i=0;i<n;i++) |
---|
102 | { |
---|
103 | G4cout<<i<<"\t"<<myLaguerre.GetAbscissa(i)<<"\t" |
---|
104 | <<myLaguerre.GetWeight(i)<<G4endl ; |
---|
105 | } |
---|
106 | */ ///////////////////////////////////// |
---|
107 | for(i=1;i<20;i++) |
---|
108 | { |
---|
109 | n = 1*i ; |
---|
110 | G4GaussLaguerreQ myLaguerre(CosFunction,0.0,n) ; |
---|
111 | G4cout<<"n = "<<n<<"\t"<<"true = 0.5 "<<" and n-point GaussLaguerre = " |
---|
112 | <<myLaguerre.Integral()<<G4endl ; |
---|
113 | } |
---|
114 | G4GaussLegendreQ myIntegrand(TestFunction) ; |
---|
115 | G4cout<<"true is 0.499066278634 "<<" and QuickGaussLegendre is "<< |
---|
116 | myIntegrand.QuickIntegral(0,2*pi)<<G4endl ; |
---|
117 | G4cout<<"true is 0.499066278634 "<<" and AccurateGaussLegendre is "<< |
---|
118 | myIntegrand.AccurateIntegral(0,2*pi)<<G4endl ; |
---|
119 | |
---|
120 | |
---|
121 | for(i=1;i<20;i++) |
---|
122 | { |
---|
123 | n = 8*i ; |
---|
124 | G4GaussLegendreQ myLegendre(TestFunction, n) ; |
---|
125 | G4cout<<myLegendre.GetNumber()<< |
---|
126 | "true is 0.5 "<<" and n-point GaussLegendre is " |
---|
127 | <<myLegendre.Integral(0,200*pi)<<G4endl ; |
---|
128 | } |
---|
129 | /* ************************************************** |
---|
130 | |
---|
131 | */ ///////////////////////////////////// |
---|
132 | return 0; |
---|
133 | } |
---|