Gabriele Cosmo
289 lines
8.8 KiB
C++
289 lines
8.8 KiB
C++
//
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// ********************************************************************
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// * DISCLAIMER *
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// * *
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// * The following disclaimer summarizes all the specific disclaimers *
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// * of contributors to this software. The specific disclaimers,which *
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// * govern, are listed with their locations in: *
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// * http://cern.ch/geant4/license *
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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. *
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// * *
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// * This code implementation is the intellectual property of the *
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// * GEANT4 collaboration. *
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// * By copying, distributing or modifying the Program (or any work *
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// * based on the Program) you indicate your acceptance of this *
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// * statement, and all its terms. *
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// ********************************************************************
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//
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//
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// $Id: G4ChebyshevApproximation.cc,v 1.3 2001/07/11 10:00:41 gunter Exp $
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// GEANT4 tag $Name: geant4-05-00 $
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//
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#include "G4ChebyshevApproximation.hh"
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// Constructor for initialisation of the class data members. It creates the array
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// fChebyshevCof[0,...,fNumber-1], fNumber = n ; which consists of Chebyshev
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// coefficients describing the function pointed by pFunction. The values a and b
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// fixe the interval of validity of Chebyshev approximation.
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G4ChebyshevApproximation::G4ChebyshevApproximation( function pFunction,
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G4int n,
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G4double a,
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G4double b )
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{
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G4int i, j ;
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G4double rootSum, cof, cofj, weight ;
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fFunction = pFunction ;
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fNumber = n ;
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fDiff = 0.5*(b-a) ;
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fMean = 0.5*(b+a) ;
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fChebyshevCof = new G4double[fNumber] ;
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G4double* tempFunction = new G4double[fNumber] ;
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weight = 2.0/fNumber ;
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cof = 0.5*weight*pi ; // pi/n
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for (i=0;i<fNumber;i++)
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{
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rootSum = cos(cof*(i+0.5)) ;
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tempFunction[i]= fFunction(rootSum*fDiff+fMean) ;
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}
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for (j=0;j<fNumber;j++)
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{
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cofj = cof*j ;
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rootSum = 0.0 ;
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for (i=0;i<fNumber;i++)
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{
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rootSum += tempFunction[i]*cos(cofj*(i+0.5)) ;
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}
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fChebyshevCof[j] = weight*rootSum ;
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}
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delete[] tempFunction ;
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}
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// --------------------------------------------------------------------
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//
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// Constructor for creation of Chebyshev coefficients for m-derivative
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// from pFunction. The value of m ! MUST BE ! < n , because the result
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// array of fChebyshevCof will be of (n-m) size. The values a and b
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// fixe the interval of validity of Chebyshev approximation.
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G4ChebyshevApproximation::
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G4ChebyshevApproximation( function pFunction,
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G4int n,
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G4int m,
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G4double a,
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G4double b )
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{
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if(n <= m)
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{
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G4Exception
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("Invalid arguments in G4ChebyshevApproximation::G4ChebyshevApproximation") ;
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}
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G4int i, j ;
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G4double rootSum, cof, cofj, weight ;
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fFunction = pFunction ;
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fNumber = n ;
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fDiff = 0.5*(b-a) ;
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fMean = 0.5*(b+a) ;
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fChebyshevCof = new G4double[fNumber] ;
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G4double* tempFunction = new G4double[fNumber] ;
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weight = 2.0/fNumber ;
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cof = 0.5*weight*pi ; // pi/n
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for (i=0;i<fNumber;i++)
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{
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rootSum = cos(cof*(i+0.5)) ;
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tempFunction[i] = fFunction(rootSum*fDiff+fMean) ;
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}
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for (j=0;j<fNumber;j++)
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{
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cofj = cof*j ;
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rootSum = 0.0 ;
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for (i=0;i<fNumber;i++)
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{
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rootSum += tempFunction[i]*cos(cofj*(i+0.5)) ;
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}
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fChebyshevCof[j] = weight*rootSum ; // corresponds to pFunction
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}
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// Chebyshev coefficients for (m)-derivative of pFunction
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for(i=1;i<=m;i++)
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{
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DerivativeChebyshevCof(tempFunction) ;
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fNumber-- ;
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for(j=0;j<fNumber;j++)
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{
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fChebyshevCof[j] = tempFunction[j] ; // corresponds to (i)-derivative
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}
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}
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delete[] tempFunction ; // delete of dynamically allocated tempFunction
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}
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// ------------------------------------------------------
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//
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// Constructor for creation of Chebyshev coefficients for integral
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// from pFunction.
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G4ChebyshevApproximation::G4ChebyshevApproximation( function pFunction,
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G4double a,
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G4double b,
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G4int n )
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{
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G4int i,j;
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G4double rootSum, cof, cofj, weight ;
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fFunction = pFunction ;
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fNumber = n ;
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fDiff = 0.5*(b-a) ;
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fMean = 0.5*(b+a) ;
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fChebyshevCof = new G4double[fNumber] ;
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G4double* tempFunction = new G4double[fNumber] ;
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weight = 2.0/fNumber ;
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cof = 0.5*weight*pi ; // pi/n
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for (i=0;i<fNumber;i++)
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{
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rootSum = cos(cof*(i+0.5)) ;
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tempFunction[i]= fFunction(rootSum*fDiff+fMean) ;
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}
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for (j=0;j<fNumber;j++)
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{
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cofj = cof*j ;
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rootSum = 0.0 ;
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for (i=0;i<fNumber;i++)
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{
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rootSum += tempFunction[i]*cos(cofj*(i+0.5)) ;
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}
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fChebyshevCof[j] = weight*rootSum ; // corresponds to pFunction
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}
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// Chebyshev coefficients for integral of pFunction
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IntegralChebyshevCof(tempFunction) ;
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for(j=0;j<fNumber;j++)
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{
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fChebyshevCof[j] = tempFunction[j] ; // corresponds to integral
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}
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delete[] tempFunction ; // delete of dynamically allocated tempFunction
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}
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// ---------------------------------------------------------------
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//
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// Destructor deletes the array of Chebyshev coefficients
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G4ChebyshevApproximation::~G4ChebyshevApproximation()
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{
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delete[] fChebyshevCof ;
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}
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// ---------------------------------------------------------------
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//
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// Access function for Chebyshev coefficients
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//
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G4double
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G4ChebyshevApproximation::GetChebyshevCof(G4int number) const
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{
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if(number < 0 && number >= fNumber)
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{
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G4Exception
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("Argument out of range in G4ChebyshevApproximation::GetChebyshevCof") ;
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}
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return fChebyshevCof[number] ;
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}
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// --------------------------------------------------------------
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//
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// Evaluate the value of fFunction at the point x via the Chebyshev coefficients
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// fChebyshevCof[0,...,fNumber-1]
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G4double
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G4ChebyshevApproximation::ChebyshevEvaluation(G4double x) const
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{
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G4int i;
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G4double evaluate = 0.0, evaluate2 = 0.0, temp, xReduced, xReduced2 ;
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if ((x-fMean+fDiff)*(x-fMean-fDiff) > 0.0)
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{
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G4Exception("Invalid argument in G4ChebyshevApproximation::ChebyshevEvaluation");
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}
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xReduced = (x-fMean)/fDiff ;
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xReduced2 = 2.0*xReduced ;
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for (i=fNumber-1;i>=1;i--)
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{
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temp = evaluate ;
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evaluate = xReduced2*evaluate - evaluate2 + fChebyshevCof[i] ;
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evaluate2 = temp ;
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}
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return xReduced*evaluate - evaluate2 + 0.5*fChebyshevCof[0] ;
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}
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// ------------------------------------------------------------------
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//
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// Returns the array derCof[0,...,fNumber-2], the Chebyshev coefficients of the
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// derivative of the function whose coefficients are fChebyshevCof
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void
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G4ChebyshevApproximation::DerivativeChebyshevCof(G4double derCof[]) const
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{
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G4int i ;
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G4double cof = 1.0/fDiff ;
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derCof[fNumber-1] = 0.0 ;
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derCof[fNumber-2] = 2*(fNumber-1)*fChebyshevCof[fNumber-1] ;
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for(i=fNumber-3;i>=0;i--)
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{
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derCof[i] = derCof[i+2] + 2*(i+1)*fChebyshevCof[i+1] ;
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}
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for(i=0;i<fNumber;i++)
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{
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derCof[i] *= cof ;
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}
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}
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// ------------------------------------------------------------------------
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//
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// This function produces the array integralCof[0,...,fNumber-1] , the Chebyshev
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// coefficients of the integral of the function whose coefficients are
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// fChebyshevCof[]. The constant of integration is set so that the integral
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// vanishes at the point (fMean - fDiff), i.e. at the begining of the interval of
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// validity (we start the integration from this point).
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//
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void
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G4ChebyshevApproximation::IntegralChebyshevCof(G4double integralCof[]) const
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{
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G4int i ;
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G4double cof = 0.5*fDiff, sum = 0.0, factor = 1.0 ;
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for(i=1;i<fNumber-1;i++)
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{
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integralCof[i] = cof*(fChebyshevCof[i-1] - fChebyshevCof[i+1])/i ;
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sum += factor*integralCof[i] ;
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factor = -factor ;
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}
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integralCof[fNumber-1] = cof*fChebyshevCof[fNumber-2]/(fNumber-1) ;
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sum += factor*integralCof[fNumber-1] ;
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integralCof[0] = 2.0*sum ; // set the constant of integration
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}
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