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G4GaussJacobiQ.cc
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28 #include "G4GaussJacobiQ.hh"
29 
30 
31 // -------------------------------------------------------------
32 //
33 // Constructor for Gauss-Jacobi integration method.
34 //
35 
36 G4GaussJacobiQ::G4GaussJacobiQ( function pFunction,
37  G4double alpha,
38  G4double beta,
39  G4int nJacobi )
40  : G4VGaussianQuadrature(pFunction)
41 
42 {
43  const G4double tolerance = 1.0e-12 ;
44  const G4double maxNumber = 12 ;
45  G4int i=1, k=1 ;
46  G4double root=0.;
47  G4double alphaBeta=0.0, alphaReduced=0.0, betaReduced=0.0,
48  root1=0.0, root2=0.0, root3=0.0 ;
49  G4double a=0.0, b=0.0, c=0.0,
50  newton1=0.0, newton2=0.0, newton3=0.0, newton0=0.0,
51  temp=0.0, rootTemp=0.0 ;
52 
53  fNumber = nJacobi ;
54  fAbscissa = new G4double[fNumber] ;
55  fWeight = new G4double[fNumber] ;
56 
57  for (i=1;i<=nJacobi;i++)
58  {
59  if (i == 1)
60  {
61  alphaReduced = alpha/nJacobi ;
62  betaReduced = beta/nJacobi ;
63  root1 = (1.0+alpha)*(2.78002/(4.0+nJacobi*nJacobi)+
64  0.767999*alphaReduced/nJacobi) ;
65  root2 = 1.0+1.48*alphaReduced+0.96002*betaReduced
66  + 0.451998*alphaReduced*alphaReduced
67  + 0.83001*alphaReduced*betaReduced ;
68  root = 1.0-root1/root2 ;
69  }
70  else if (i == 2)
71  {
72  root1=(4.1002+alpha)/((1.0+alpha)*(1.0+0.155998*alpha)) ;
73  root2=1.0+0.06*(nJacobi-8.0)*(1.0+0.12*alpha)/nJacobi ;
74  root3=1.0+0.012002*beta*(1.0+0.24997*std::fabs(alpha))/nJacobi ;
75  root -= (1.0-root)*root1*root2*root3 ;
76  }
77  else if (i == 3)
78  {
79  root1=(1.67001+0.27998*alpha)/(1.0+0.37002*alpha) ;
80  root2=1.0+0.22*(nJacobi-8.0)/nJacobi ;
81  root3=1.0+8.0*beta/((6.28001+beta)*nJacobi*nJacobi) ;
82  root -= (fAbscissa[0]-root)*root1*root2*root3 ;
83  }
84  else if (i == nJacobi-1)
85  {
86  root1=(1.0+0.235002*beta)/(0.766001+0.118998*beta) ;
87  root2=1.0/(1.0+0.639002*(nJacobi-4.0)/(1.0+0.71001*(nJacobi-4.0))) ;
88  root3=1.0/(1.0+20.0*alpha/((7.5+alpha)*nJacobi*nJacobi)) ;
89  root += (root-fAbscissa[nJacobi-4])*root1*root2*root3 ;
90  }
91  else if (i == nJacobi)
92  {
93  root1 = (1.0+0.37002*beta)/(1.67001+0.27998*beta) ;
94  root2 = 1.0/(1.0+0.22*(nJacobi-8.0)/nJacobi) ;
95  root3 = 1.0/(1.0+8.0*alpha/((6.28002+alpha)*nJacobi*nJacobi)) ;
96  root += (root-fAbscissa[nJacobi-3])*root1*root2*root3 ;
97  }
98  else
99  {
100  root = 3.0*fAbscissa[i-2]-3.0*fAbscissa[i-3]+fAbscissa[i-4] ;
101  }
102  alphaBeta = alpha + beta ;
103  for (k=1;k<=maxNumber;k++)
104  {
105  temp = 2.0 + alphaBeta ;
106  newton1 = (alpha-beta+temp*root)/2.0 ;
107  newton2 = 1.0 ;
108  for (G4int j=2;j<=nJacobi;j++)
109  {
110  newton3 = newton2 ;
111  newton2 = newton1 ;
112  temp = 2*j+alphaBeta ;
113  a = 2*j*(j+alphaBeta)*(temp-2.0) ;
114  b = (temp-1.0)*(alpha*alpha-beta*beta+temp*(temp-2.0)*root) ;
115  c = 2.0*(j-1+alpha)*(j-1+beta)*temp ;
116  newton1 = (b*newton2-c*newton3)/a ;
117  }
118  newton0 = (nJacobi*(alpha - beta - temp*root)*newton1 +
119  2.0*(nJacobi + alpha)*(nJacobi + beta)*newton2)/
120  (temp*(1.0 - root*root)) ;
121  rootTemp = root ;
122  root = rootTemp - newton1/newton0 ;
123  if (std::fabs(root-rootTemp) <= tolerance)
124  {
125  break ;
126  }
127  }
128  if (k > maxNumber)
129  {
130  G4Exception("G4GaussJacobiQ::G4GaussJacobiQ()", "OutOfRange",
131  FatalException, "Too many iterations in constructor.") ;
132  }
133  fAbscissa[i-1] = root ;
134  fWeight[i-1] = std::exp(GammaLogarithm((G4double)(alpha+nJacobi)) +
135  GammaLogarithm((G4double)(beta+nJacobi)) -
136  GammaLogarithm((G4double)(nJacobi+1.0)) -
137  GammaLogarithm((G4double)(nJacobi + alphaBeta + 1.0)))
138  *temp*std::pow(2.0,alphaBeta)/(newton0*newton2) ;
139  }
140 }
141 
142 
143 // ----------------------------------------------------------
144 //
145 // Gauss-Jacobi method for integration of
146 // ((1-x)^alpha)*((1+x)^beta)*pFunction(x)
147 // from minus unit to plus unit .
148 
149 
150 G4double
151 G4GaussJacobiQ::Integral() const
152 {
153  G4double integral = 0.0 ;
154  for(G4int i=0;i<fNumber;i++)
155  {
156  integral += fWeight[i]*fFunction(fAbscissa[i]) ;
157  }
158  return integral ;
159 }
160