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Please see the license in the file LICENSE and URL above * 16 // * for the full disclaimer and the limitatio 16 // * for the full disclaimer and the limitation of liability. * 17 // * 17 // * * 18 // * This code implementation is the result 18 // * This code implementation is the result of the scientific and * 19 // * technical work of the GEANT4 collaboratio 19 // * technical work of the GEANT4 collaboration. * 20 // * By using, copying, modifying or distri 20 // * By using, copying, modifying or distributing the software (or * 21 // * any work based on the software) you ag 21 // * any work based on the software) you agree to acknowledge its * 22 // * use in resulting scientific publicati 22 // * use in resulting scientific publications, and indicate your * 23 // * acceptance of all terms of the Geant4 Sof 23 // * acceptance of all terms of the Geant4 Software license. * 24 // ******************************************* 24 // ******************************************************************** 25 // 25 // 26 // G4GaussLaguerreQ class implementation << 27 // 26 // 28 // Author: V.Grichine, 13.05.1997 << 27 // 29 // ------------------------------------------- << 30 << 31 #include "G4GaussLaguerreQ.hh" 28 #include "G4GaussLaguerreQ.hh" 32 29 >> 30 >> 31 33 // ------------------------------------------- 32 // ------------------------------------------------------------ 34 // 33 // 35 // Constructor for Gauss-Laguerre quadrature m 34 // Constructor for Gauss-Laguerre quadrature method: integral from zero to 36 // infinity of std::pow(x,alpha)*std::exp(-x)* 35 // infinity of std::pow(x,alpha)*std::exp(-x)*f(x). 37 // The value of nLaguerre sets the accuracy. 36 // The value of nLaguerre sets the accuracy. 38 // The constructor creates arrays fAbscissa[0, << 37 // The constructor creates arrays fAbscissa[0,..,nLaguerre-1] and 39 // fWeight[0,..,nLaguerre-1] . << 38 // fWeight[0,..,nLaguerre-1] . 40 // 39 // 41 40 42 G4GaussLaguerreQ::G4GaussLaguerreQ(function pF << 41 G4GaussLaguerreQ::G4GaussLaguerreQ( function pFunction, 43 G4int nLagu << 42 G4double alpha, 44 : G4VGaussianQuadrature(pFunction) << 43 G4int nLaguerre ) >> 44 : G4VGaussianQuadrature(pFunction) 45 { 45 { 46 const G4double tolerance = 1.0e-10; << 46 const G4double tolerance = 1.0e-10 ; 47 const G4int maxNumber = 12; << 47 const G4int maxNumber = 12 ; 48 G4int i = 1, k = 1; << 48 G4int i=1, k=1 ; 49 G4double newton0 = 0.0, newton1 = 0.0, temp1 << 49 G4double newton0=0.0, newton1=0.0, 50 temp = 0.0, cofi = 0.0; << 50 temp1=0.0, temp2=0.0, temp3=0.0, temp=0.0, cofi=0.0 ; 51 << 51 52 fNumber = nLaguerre; << 52 fNumber = nLaguerre ; 53 fAbscissa = new G4double[fNumber]; << 53 fAbscissa = new G4double[fNumber] ; 54 fWeight = new G4double[fNumber]; << 54 fWeight = new G4double[fNumber] ; 55 << 55 56 for(i = 1; i <= fNumber; ++i) // Loop over << 56 for(i=1;i<=fNumber;i++) // Loop over the desired roots 57 { << 57 { 58 if(i == 1) << 58 if(i == 1) 59 { << 59 { 60 newton0 = (1.0 + alpha) * (3.0 + 0.92 * << 60 newton0 = (1.0 + alpha)*(3.0 + 0.92*alpha) 61 (1.0 + 2.4 * fNumber + 1.8 * a << 61 / (1.0 + 2.4*fNumber + 1.8*alpha) ; 62 } << 62 } 63 else if(i == 2) << 63 else if(i == 2) 64 { << 64 { 65 newton0 += (15.0 + 6.25 * alpha) / (1.0 << 65 newton0 += (15.0 + 6.25*alpha)/(1.0 + 0.9*alpha + 2.5*fNumber) ; 66 } << 66 } 67 else << 67 else 68 { << 68 { 69 cofi = i - 2; << 69 cofi = i - 2 ; 70 newton0 += ((1.0 + 2.55 * cofi) / (1.9 * << 70 newton0 += ((1.0+2.55*cofi)/(1.9*cofi) 71 1.26 * cofi * alpha / (1.0 + << 71 + 1.26*cofi*alpha/(1.0+3.5*cofi)) 72 (newton0 - fAbscissa[i - 3]) << 72 * (newton0 - fAbscissa[i-3])/(1.0 + 0.3*alpha) ; 73 } << 73 } 74 for(k = 1; k <= maxNumber; ++k) << 74 for(k=1;k<=maxNumber;k++) 75 { << 76 temp1 = 1.0; << 77 temp2 = 0.0; << 78 for(G4int j = 1; j <= fNumber; ++j) << 79 { 75 { 80 temp3 = temp2; << 76 temp1 = 1.0 ; 81 temp2 = temp1; << 77 temp2 = 0.0 ; 82 temp1 = << 78 for(G4int j=1;j<=fNumber;j++) 83 ((2 * j - 1 + alpha - newton0) * tem << 79 { >> 80 temp3 = temp2 ; >> 81 temp2 = temp1 ; >> 82 temp1 = ((2*j - 1 + alpha - newton0)*temp2 >> 83 - (j - 1 + alpha)*temp3)/j ; >> 84 } >> 85 temp = (fNumber*temp1 - (fNumber +alpha)*temp2)/newton0 ; >> 86 newton1 = newton0 ; >> 87 newton0 = newton1 - temp1/temp ; >> 88 if(std::fabs(newton0 - newton1) <= tolerance) >> 89 { >> 90 break ; >> 91 } 84 } 92 } 85 temp = (fNumber * temp1 - (fNumber + << 93 if(k > maxNumber) 86 newton1 = newton0; << 87 newton0 = newton1 - temp1 / temp; << 88 if(std::fabs(newton0 - newton1) <= toler << 89 { 94 { 90 break; << 95 G4Exception("G4GaussLaguerreQ::G4GaussLaguerreQ()", >> 96 "OutOfRange", FatalException, >> 97 "Too many iterations in Gauss-Laguerre constructor") ; 91 } 98 } 92 } << 99 93 if(k > maxNumber) << 100 fAbscissa[i-1] = newton0 ; 94 { << 101 fWeight[i-1] = -std::exp(GammaLogarithm(alpha + fNumber) 95 G4Exception("G4GaussLaguerreQ::G4GaussLa << 102 - GammaLogarithm((G4double)fNumber))/(temp*fNumber*temp2) ; 96 FatalException, << 103 } 97 "Too many iterations in Gaus << 98 } << 99 << 100 fAbscissa[i - 1] = newton0; << 101 fWeight[i - 1] = -std::exp(GammaLogarith << 102 GammaLogarithm( << 103 (temp * fNumber * temp2); << 104 } << 105 } 104 } 106 105 107 // ------------------------------------------- 106 // ----------------------------------------------------------------- 108 // 107 // 109 // Gauss-Laguerre method for integration of 108 // Gauss-Laguerre method for integration of 110 // std::pow(x,alpha)*std::exp(-x)*pFunction(x) 109 // std::pow(x,alpha)*std::exp(-x)*pFunction(x) 111 // from zero up to infinity. pFunction is eval 110 // from zero up to infinity. pFunction is evaluated in fNumber points 112 // for which fAbscissa[i] and fWeight[i] array 111 // for which fAbscissa[i] and fWeight[i] arrays were created in 113 // G4VGaussianQuadrature(double,int) construct 112 // G4VGaussianQuadrature(double,int) constructor 114 113 115 G4double G4GaussLaguerreQ::Integral() const << 114 G4double >> 115 G4GaussLaguerreQ::Integral() const 116 { 116 { 117 G4double integral = 0.0; << 117 G4double integral = 0.0 ; 118 for(G4int i = 0; i < fNumber; ++i) << 118 for(G4int i=0;i<fNumber;i++) 119 { << 119 { 120 integral += fWeight[i] * fFunction(fAbscis << 120 integral += fWeight[i]*fFunction(fAbscissa[i]) ; 121 } << 121 } 122 return integral; << 122 return integral ; 123 } 123 } 124 124