| Geant4 Cross Reference |
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25
26 #include "G4ios.hh"
27 #include "G4LegendrePolynomial.hh"
28 #include "G4Pow.hh"
29 #include "G4Exp.hh"
30 #include "G4Log.hh"
31
32 using namespace std;
33
34 G4double G4LegendrePolynomial::GetCoefficient(std::size_t i, std::size_t order)
35 {
36 if(order >= fCoefficients.size()) BuildUpToOrder(order);
37 if(order >= fCoefficients.size() ||
38 i/2 >= fCoefficients[order].size() ||
39 (i%2) != order %2) return 0;
40 return fCoefficients[order][i/2];
41 }
42
43 G4double G4LegendrePolynomial::EvalLegendrePoly(G4int order, G4double x)
44 {
45 // Call EvalAssocLegendrePoly with m=0
46 return (EvalAssocLegendrePoly(order,0,x));
47 }
48
49 G4double G4LegendrePolynomial::EvalAssocLegendrePoly(G4int l, G4int m, G4double x)
50 {
51 // Invalid calls --> 0. (Keeping for backward compatibility; should we throw instead?)
52 if (l<0 || m<-l || m>l) return 0.0;
53
54 // New check: g4pow doesn't handle integer arguments over 512.
55 // For us that means:
56 if ((l+m) > 512 || (l-m) > 512 || (2*m) > 512) return 0.0;
57
58 G4Pow* g4pow = G4Pow::GetInstance();
59 G4double x2 = x*x;
60
61 // hard-code the first few orders for speed
62 switch (l) {
63 case 0 :
64 return 1;
65 case 1 :
66 switch (m) {
67 case -1 : return 0.5 * sqrt(1.-x2);
68 case 0 : return x;
69 case 1 : return -sqrt(1.-x2);
70 };
71 break;
72 case 2 :
73 switch (m) {
74 case -2 : return 0.125 * (1.0 - x2);
75 case -1 : return 0.5 * x * sqrt(1.0 - x2);
76 case 0 : return 0.5*(3.*x2 - 1.);
77 case 1 : return -3.*x*sqrt(1.-x2);
78 case 2 : return 3.*(1.-x2);
79 };
80 break;
81 case 3 :
82 switch (m) {
83 case -3 : return (1.0/48.0) * (1.0 - x2) * sqrt(1.0 - x2);
84 case -2 : return 0.125 * x * (1.0 - x2);
85 case -1 : return 0.125 * (5.0 * x2 - 1.0) * sqrt(1.0 - x2);
86 case 0 : return 0.5*(5.*x*x2 - 3.*x);
87 case 1 : return -1.5*(5.*x2-1.)*sqrt(1.-x2);
88 case 2 : return 15.*x*(1.-x2);
89 case 3 : return -15.*(1.-x2)*sqrt(1.-x2);
90 };
91 break;
92 case 4 :
93 switch (m) {
94 case -4 : return (105.0/40320.0)*(1. - 2.*x2 + x2*x2);
95 case -3 : return (105.0/5040.0)*x*(1.-x2)*sqrt(1.-x2);
96 case -2 : return (15.0/720.0)*(7.*x2-1.)*(1.-x2);
97 case -1 : return 0.125*(7.*x*x2-3.*x)*sqrt(1.-x2);
98 case 0 : return 0.125*(35.*x2*x2 - 30.*x2 + 3.);
99 case 1 : return -2.5*(7.*x*x2-3.*x)*sqrt(1.-x2);
100 case 2 : return 7.5*(7.*x2-1.)*(1.-x2);
101 case 3 : return -105.*x*(1.-x2)*sqrt(1.-x2);
102 case 4 : return 105.*(1. - 2.*x2 + x2*x2);
103 };
104 break;
105 };
106
107 // if m<0, compute P[l,-m,x] and correct
108 if (m < 0)
109 {
110 G4double complementary_value = EvalAssocLegendrePoly(l, -m, x);
111 return complementary_value * (m%2==0 ? 1.0 : -1.0) * g4pow->factorial(l+m)/g4pow->factorial(l-m);
112 }
113
114 // Iteratively walk up from P[m,m,x] to P[l,m,x]
115
116 // prime the pump: P[l<m,m,x] = 0
117 G4double previous = 0.0;
118
119 // prime the pump: P[m,m,x]
120 G4double current;
121 if (m == 0) current = 1.0;
122 else if (m == 1) current = -sqrt((1.0 - (x2)));
123 else {
124 current = (m%2==0 ? 1.0 : -1.0) *
125 G4Exp(g4pow->logfactorial(2*m) - g4pow->logfactorial(m)) *
126 G4Exp(G4Log((1.0-(x2))*0.25)*0.5*G4double(m));
127 }
128
129 // Work up to P[l,m,x]
130 for(G4int i=m+1; i<=l; i++)
131 {
132 G4double next = (-(G4double(i+m-1))*previous + x*G4double(2*i-1)*current )/G4double(i-m);
133 previous = current;
134 current = next;
135 }
136
137 return current;
138 }
139
140 void G4LegendrePolynomial::BuildUpToOrder(std::size_t orderMax)
141 {
142 if(orderMax > 30) {
143 G4cout << "G4LegendrePolynomial::GetCoefficient(): "
144 << "I refuse to make a Legendre Polynomial of order "
145 << orderMax << G4endl;
146 return;
147 }
148 while(fCoefficients.size() < orderMax+1) { /* Loop checking, 30-Oct-2015, G.Folger */
149 std::size_t order = fCoefficients.size();
150 fCoefficients.resize(order+1);
151 if(order <= 1) fCoefficients[order].push_back(1.);
152 else {
153 for(std::size_t iCoeff = 0; iCoeff < order+1; ++iCoeff) {
154 if((order % 2) == (iCoeff % 2)) {
155 G4double coeff = 0;
156 if(iCoeff <= order-2) coeff -= fCoefficients[order-2][iCoeff/2]*G4double(order-1);
157 if(iCoeff > 0) coeff += fCoefficients[order-1][(iCoeff-1)/2]*G4double(2*order-1);
158 coeff /= G4double(order);
159 fCoefficients[order].push_back(coeff);
160 }
161 }
162 }
163 }
164 }
165
166