Gabriele Cosmo
225 lines
6.5 KiB
Plaintext
225 lines
6.5 KiB
Plaintext
//
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// ********************************************************************
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// * License and Disclaimer *
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// * *
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// * The Geant4 software is copyright of the Copyright Holders of *
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// * the Geant4 Collaboration. It is provided under the terms and *
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// * conditions of the Geant4 Software License, included in the file *
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// * LICENSE and available at http://cern.ch/geant4/license . These *
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// * include a list of copyright holders. *
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// * *
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// * Neither the authors of this software system, nor their employing *
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// * institutes,nor the agencies providing financial support for this *
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// * work make any representation or warranty, express or implied, *
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// * regarding this software system or assume any liability for its *
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// * use. Please see the license in the file LICENSE and URL above *
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// * for the full disclaimer and the limitation of liability. *
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// * *
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// * This code implementation is the result of the scientific and *
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// * technical work of the GEANT4 collaboration. *
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// * By using, copying, modifying or distributing the software (or *
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// * any work based on the software) you agree to acknowledge its *
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// * use in resulting scientific publications, and indicate your *
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// * acceptance of all terms of the Geant4 Software license. *
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// ********************************************************************
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//
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// G4PolynomialSolver inline methods implementation
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//
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// Author: E.Medernach, 19.12.2000 - First implementation
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// --------------------------------------------------------------------
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#define POLEPSILON 1e-12
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#define POLINFINITY 9.0E99
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#define ITERATION 12 // 20 But 8 is really enough for Newton with a good guess
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template <class T, class F>
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G4PolynomialSolver<T, F>::G4PolynomialSolver(T* typeF, F func, F deriv,
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G4double precision)
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{
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Precision = precision;
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FunctionClass = typeF;
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Function = func;
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Derivative = deriv;
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}
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template <class T, class F>
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G4PolynomialSolver<T, F>::~G4PolynomialSolver()
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{}
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template <class T, class F>
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G4double G4PolynomialSolver<T, F>::solve(G4double IntervalMin,
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G4double IntervalMax)
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{
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return Newton(IntervalMin, IntervalMax);
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}
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/* If we want to be general this could work for any
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polynomial of order more that 4 if we find the (ORDER + 1)
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control points
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*/
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#define NBBEZIER 5
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template <class T, class F>
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G4int G4PolynomialSolver<T, F>::BezierClipping(/*T* typeF,F func,F deriv,*/
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G4double* IntervalMin,
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G4double* IntervalMax)
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{
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/** BezierClipping is a clipping interval Newton method **/
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/** It works by clipping the area where the polynomial is **/
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G4double P[NBBEZIER][2], D[2];
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G4double NewMin, NewMax;
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G4int IntervalIsVoid = 1;
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/*** Calculating Control Points ***/
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/* We see the polynomial as a Bezier curve for some control points to find */
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/*
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For 5 control points (polynomial of degree 4) this is:
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0 p0 = F((*IntervalMin))
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1/4 p1 = F((*IntervalMin)) + ((*IntervalMax) - (*IntervalMin))/4
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* F'((*IntervalMin))
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2/4 p2 = 1/6 * (16*F(((*IntervalMax) + (*IntervalMin))/2)
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- (p0 + 4*p1 + 4*p3 + p4))
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3/4 p3 = F((*IntervalMax)) - ((*IntervalMax) - (*IntervalMin))/4
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* F'((*IntervalMax))
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1 p4 = F((*IntervalMax))
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*/
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/* x,y,z,dx,dy,dz are constant during searching */
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D[0] = (FunctionClass->*Derivative)(*IntervalMin);
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P[0][0] = (*IntervalMin);
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P[0][1] = (FunctionClass->*Function)(*IntervalMin);
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if(std::fabs(P[0][1]) < Precision)
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{
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return 1;
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}
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if(((*IntervalMax) - (*IntervalMin)) < POLEPSILON)
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{
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return 1;
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}
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P[1][0] = (*IntervalMin) + ((*IntervalMax) - (*IntervalMin)) / 4;
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P[1][1] = P[0][1] + (((*IntervalMax) - (*IntervalMin)) / 4.0) * D[0];
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D[1] = (FunctionClass->*Derivative)(*IntervalMax);
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P[4][0] = (*IntervalMax);
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P[4][1] = (FunctionClass->*Function)(*IntervalMax);
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P[3][0] = (*IntervalMax) - ((*IntervalMax) - (*IntervalMin)) / 4;
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P[3][1] = P[4][1] - ((*IntervalMax) - (*IntervalMin)) / 4 * D[1];
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P[2][0] = ((*IntervalMax) + (*IntervalMin)) / 2;
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P[2][1] =
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(16 * (FunctionClass->*Function)(((*IntervalMax) + (*IntervalMin)) / 2) -
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(P[0][1] + 4 * P[1][1] + 4 * P[3][1] + P[4][1])) /
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6;
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{
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G4double Intersection;
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G4int i, j;
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NewMin = (*IntervalMax);
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NewMax = (*IntervalMin);
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for(i = 0; i < 5; ++i)
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for(j = i + 1; j < 5; ++j)
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{
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/* there is an intersection only if each have different signs */
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if(((P[j][1] > -Precision) && (P[i][1] < Precision)) ||
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((P[j][1] < Precision) && (P[i][1] > -Precision)))
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{
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IntervalIsVoid = 0;
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Intersection =
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P[j][0] - P[j][1] * ((P[i][0] - P[j][0]) / (P[i][1] - P[j][1]));
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if(Intersection < NewMin)
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{
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NewMin = Intersection;
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}
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if(Intersection > NewMax)
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{
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NewMax = Intersection;
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}
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}
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}
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if(IntervalIsVoid != 1)
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{
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(*IntervalMax) = NewMax;
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(*IntervalMin) = NewMin;
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}
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}
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if(IntervalIsVoid == 1)
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{
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return -1;
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}
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return 0;
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}
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template <class T, class F>
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G4double G4PolynomialSolver<T, F>::Newton(G4double IntervalMin,
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G4double IntervalMax)
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{
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/* So now we have a good guess and an interval where
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if there are an intersection the root must be */
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G4double Value = 0;
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G4double Gradient = 0;
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G4double Lambda;
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G4int i = 0;
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G4int j = 0;
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/* Reduce interval before applying Newton Method */
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{
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G4int NewtonIsSafe;
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while((NewtonIsSafe = BezierClipping(&IntervalMin, &IntervalMax)) == 0)
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;
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if(NewtonIsSafe == -1)
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{
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return POLINFINITY;
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}
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}
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Lambda = IntervalMin;
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Value = (FunctionClass->*Function)(Lambda);
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// while ((std::fabs(Value) > Precision)) {
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while(j != -1)
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{
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Value = (FunctionClass->*Function)(Lambda);
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Gradient = (FunctionClass->*Derivative)(Lambda);
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Lambda = Lambda - Value / Gradient;
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if(std::fabs(Value) <= Precision)
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{
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++j;
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if(j == 2)
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{
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j = -1;
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}
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}
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else
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{
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++i;
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if(i > ITERATION)
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return POLINFINITY;
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}
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}
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return Lambda;
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}
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