| 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 | //
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| 28 | // Author: Luciano Pandola (Luciano.Pandola@cern.ch)
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| 29 | //
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| 30 | // History:
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| 31 | // -----------
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| 32 | // 17 Feb 2003 LP Created
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| 33 | // 17 Dec 2003 LP Removed memory leak
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| 34 | // 17 Mar 2004 LP Removed unnecessary calls to std::pow(a,b)
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| 35 | //
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| 36 | // -------------------------------------------------------------------
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| 37 |
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| 38 | #include "G4PenelopeInterpolator.hh"
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| 39 | #include "G4DataVector.hh"
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| 40 |
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| 41 | G4PenelopeInterpolator::G4PenelopeInterpolator(G4double* pX,G4double* pY,G4int nOfData,G4double S1,G4double SN) :
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| 42 | a(0),b(0),c(0),d(0),x(0),y(0)
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| 43 | {
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| 44 | // pX = X grid points (ascending order)
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| 45 | // pY = corresponding function values
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| 46 | // nOfData = number of points in the grid > 4
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| 47 | // S1 and S2 = second derivatives at X[0] and X[nOfData-1]
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| 48 | a = new G4DataVector;
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| 49 | b = new G4DataVector;
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| 50 | c = new G4DataVector;
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| 51 | d = new G4DataVector;
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| 52 |
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| 53 | if (nOfData < 4 )
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| 54 | {
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| 55 | G4String excep = "Spline interpolation cannot be performed with less than 4 points";
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| 56 | G4Exception(excep);
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| 57 | }
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| 58 |
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| 59 | G4int N1=nOfData-1;
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| 60 | G4int N2=nOfData-2;
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| 61 | G4int i;
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| 62 | G4int k=0;
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| 63 | G4DataVector A(N1),B(N2),D(nOfData);//auxiliary arrays
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| 64 | A.clear();
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| 65 | B.clear();
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| 66 | D.clear();
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| 67 | for (i=0;i<N1;i++){
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| 68 | if ((pX[i+1]-pX[i]) < 1.0e-13)
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| 69 | {
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| 70 | G4String excep = "Spline x values not in increasing order";
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| 71 | G4Exception(excep);
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| 72 | }
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| 73 | A.push_back(pX[i+1]-pX[i]);
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| 74 | D.push_back((pY[i+1]-pY[i])/A[i]);
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| 75 | }
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| 76 |
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| 77 | //Symmetric coefficient matrix
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| 78 | for (i=0;i<N2;i++){
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| 79 | B.push_back(2.0*(A[i]+A[i+1]));
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| 80 | k=N1-i-1;
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| 81 | D[k]=6.0*(D[k]-D[k-1]);
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| 82 | }
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| 83 | D[1]=D[1]-A[0]*S1;
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| 84 | D[N1-1]=D[N1-1]-A[N1-1]*SN;
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| 85 |
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| 86 | //Gauss solution of the tridiagonal system
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| 87 | for (i=1;i<N2;i++){
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| 88 | G4double R=A[i]/B[i-1];
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| 89 | B[i]=B[i]-R*A[i];
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| 90 | D[i+1]=D[i+1]-R*D[i];
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| 91 | }
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| 92 |
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| 93 | //The sigma coefficients are stored in array D
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| 94 | D[N1-1]=D[N1-1]/B[N2-1];
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| 95 | for (i=1;i<N2;i++){
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| 96 | k=N1-i-1;
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| 97 | D[k]=(D[k]-A[k]*D[k+1])/B[k-1];
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| 98 | }
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| 99 | D.push_back(SN);
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| 100 |
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| 101 | //Spline coefficients
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| 102 | G4double SI1=S1;
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| 103 | G4double SI=0,H=0,HI=0;
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| 104 | G4double store=0;
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| 105 | G4double help1=0;
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| 106 | G4double help2=0;
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| 107 |
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| 108 | for (i=0;i<N1;i++){
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| 109 | SI=SI1;
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| 110 | SI1=D[i+1];
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| 111 | H=A[i];
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| 112 | HI=1.0/H;
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| 113 | help1 = pX[i+1]*pX[i+1]*pX[i+1];
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| 114 | help2 = pX[i]*pX[i]*pX[i];
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| 115 | store=HI*(SI*help1-SI1*help2)/6.0+HI*(pY[i]*pX[i+1]-pY[i+1]*pX[i])+
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| 116 | H*(SI1*pX[i]-SI*pX[i+1])/6.0;
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| 117 | a->push_back(store);
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| 118 | store=(HI/2.0)*(SI1*(pX[i]*pX[i])-SI*(pX[i+1]*pX[i+1]))+HI*(pY[i+1]-pY[i])+(H/6.0)*(SI-SI1);
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| 119 | b->push_back(store);
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| 120 | store=(HI/2.0)*(SI*pX[i+1]-SI1*pX[i]);
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| 121 | c->push_back(store);
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| 122 | store=(HI/6.0)*(SI1-SI);
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| 123 | d->push_back(store);
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| 124 | }
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| 125 | //Natural cubic spline for x > x[nOfData-1]
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| 126 | G4double FN=pY[nOfData-1];
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| 127 | store=(*b)[N1-1]+pX[nOfData-1]*(2.0*(*c)[N1-1]+pX[nOfData-1]*3.0*(*d)[N1-1]);
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| 128 | a->push_back(FN-pX[nOfData-1]*store);
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| 129 | b->push_back(store);
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| 130 | c->push_back(0.0);
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| 131 | d->push_back(0.0);
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| 132 |
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| 133 | x = new G4DataVector;
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| 134 | y = new G4DataVector;
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| 135 |
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| 136 | for (i=0;i<nOfData;i++){
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| 137 | x->push_back(pX[i]);
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| 138 | y->push_back(pY[i]);
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| 139 | }
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| 140 | return;
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| 141 | }
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| 142 |
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| 143 | G4PenelopeInterpolator::~G4PenelopeInterpolator()
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| 144 | {
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| 145 | delete a;
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| 146 | delete b;
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| 147 | delete c;
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| 148 | delete d;
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| 149 | delete x;
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| 150 | delete y;
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| 151 | }
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| 152 |
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| 153 | G4double G4PenelopeInterpolator::CubicSplineInterpolation(G4double xx)
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| 154 | {
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| 155 | G4double interp=0;
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| 156 | G4int index = FindBin(xx);
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| 157 | interp=(*a)[index]+xx*((*b)[index]+xx*((*c)[index]+xx*(*d)[index]));
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| 158 | return interp;
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| 159 | }
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| 160 |
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| 161 | G4double G4PenelopeInterpolator::FirstDerivative(G4double xx)
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| 162 | {
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| 163 | G4double interp=0;
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| 164 | G4int index = FindBin(xx);
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| 165 | interp=(*b)[index]+xx*((*c)[index]*2.0+xx*(*d)[index]*3.0);
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| 166 | return interp;
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| 167 | }
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| 168 |
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| 169 | G4double G4PenelopeInterpolator::CalculateMomentum(G4double UpperLimit,
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| 170 | G4int MomentumOrder)
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| 171 | {
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| 172 | G4int i;
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| 173 | G4int nOfData = (G4int) x->size();
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| 174 | const G4double eps=1.0e-35;
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| 175 | if (MomentumOrder < -1) G4Exception("Calculate Momentum: error 0");
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| 176 | if (nOfData < 2) G4Exception("Calculate Momentum: error 1");
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| 177 | if ((*x)[0]<0) G4Exception("Calculate Momentum: error 2");
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| 178 | for (i=1;i<nOfData;i++)
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| 179 | {
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| 180 | if ((*x)[i]<0) G4Exception("Calculate Momentum: error 3");
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| 181 | if ((*x)[i] < (*x)[i-1]) G4Exception ("Calculate Momentum: error 4");
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| 182 | }
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| 183 |
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| 184 | G4double RMom=0.0;
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| 185 | if (UpperLimit < (*x)[0]) return RMom;
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| 186 | G4int iend=0;
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| 187 | G4double xt=std::min(UpperLimit,(*x)[nOfData-1]);
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| 188 | G4double x1,x2,y1,y2;
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| 189 | G4double xtc,dx,dy,a1,b1,ds;
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| 190 | for (i=0;i<(nOfData-1);i++){
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| 191 | x1=std::max((*x)[i],eps);
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| 192 | y1=(*y)[i];
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| 193 | x2=std::max((*x)[i+1],eps);
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| 194 | y2=(*y)[i+1];
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| 195 | if (xt < x2)
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| 196 | {
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| 197 | xtc=xt;
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| 198 | iend=1;
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| 199 | }
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| 200 | else
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| 201 | {
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| 202 | xtc=x2;
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| 203 | }
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| 204 | dx=x2-x1;
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| 205 | dy=y2-y1;
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| 206 | if (std::abs(dx) > (1e-14*std::abs(dy)))
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| 207 | {
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| 208 | b1=dy/dx;
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| 209 | a1=y1-b1*x1;
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| 210 | if (MomentumOrder == -1)
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| 211 | {
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| 212 | ds=a1*std::log(xtc/x1)+b1*(xtc-x1);
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| 213 | }
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| 214 | else
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| 215 | {
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| 216 | ds=a1*(std::pow(xtc,MomentumOrder+1)-std::pow(x1,MomentumOrder+1))/ ((G4double) (MomentumOrder+1))+
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| 217 | b1*(std::pow(xtc,MomentumOrder+2)-std::pow(x1,MomentumOrder+2))/((G4double) (MomentumOrder+2));
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| 218 | }
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| 219 | }
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| 220 | else
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| 221 | {
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| 222 | ds=0.5*(y1+y2)*std::pow((xtc-x1),MomentumOrder);
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| 223 | }
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| 224 | RMom += ds;
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| 225 | if (iend != 0) return RMom;
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| 226 | }
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| 227 | return RMom;
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| 228 | }
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| 229 |
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| 230 | G4int G4PenelopeInterpolator::FindBin(G4double xx)
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| 231 | {
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| 232 | //Finds the interval x[i],x[i+1] which contains the value xx
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| 233 |
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| 234 | G4int nbOfPoints=x->size();
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| 235 |
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| 236 | if (xx > (*x)[nbOfPoints-1])
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| 237 | {
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| 238 | return (nbOfPoints-1);
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| 239 | }
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| 240 | if (xx < (*x)[0])
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| 241 | {
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| 242 | return 0;
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| 243 | }
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| 244 | G4int i=0,i1=nbOfPoints-1;
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| 245 | do{
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| 246 | G4int it=(i+i1)/2;
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| 247 | if (xx > (*x)[it])
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| 248 | {
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| 249 | i=it;
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| 250 | }
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| 251 | else
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| 252 | {
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| 253 | i1=it;
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| 254 | }
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| 255 | } while((i1-i) > 1);
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| 256 | return i;
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| 257 | }
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| 258 |
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| 259 |
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| 260 |
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| 261 |
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