Gabriele Cosmo
506 lines
14 KiB
C++
506 lines
14 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: G4DataInterpolation.cc,v 1.5 2004/04/23 06:52:57 grichine Exp $
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// GEANT4 tag $Name: geant4-06-02 $
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//
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#include "G4DataInterpolation.hh"
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//////////////////////////////////////////////////////////////////////////////
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//
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// Constructor for initializing of fArgument, fFunction and fNumber data members
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G4DataInterpolation::G4DataInterpolation( G4double pX[],
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G4double pY[],
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G4int number ):
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fSecondDerivative (0)
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{
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G4int i ;
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fNumber = number ;
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fArgument = new G4double[fNumber] ;
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fFunction = new G4double[fNumber] ;
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for(i=0;i<fNumber;i++)
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{
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fArgument[i] = pX[i] ;
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fFunction[i] = pY[i] ;
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}
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}
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////////////////////////////////////////////////////////////////////////////
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//
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// Constructor for cubic spline interpolation. It creates the array
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// fSecondDerivative[0,...fNumber-1] which is used in this interpolation by
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// the function
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G4DataInterpolation::G4DataInterpolation( G4double pX[],
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G4double pY[],
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G4int number,
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G4double pFirstDerStart,
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G4double pFirstDerFinish )
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{
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G4int i, k ;
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G4double p, qn, sig, un ;
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const G4double maxDerivative = 0.99e30 ;
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fNumber = number ;
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fArgument = new G4double[fNumber] ;
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fFunction = new G4double[fNumber] ;
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fSecondDerivative = new G4double[fNumber] ;
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G4double* u = new G4double[fNumber - 1] ;
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for(i=0;i<fNumber;i++)
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{
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fArgument[i] = pX[i] ;
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fFunction[i] = pY[i] ;
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}
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if(pFirstDerStart > maxDerivative)
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{
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fSecondDerivative[0] = 0.0 ;
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u[0] = 0.0 ;
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}
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else
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{
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fSecondDerivative[0] = -0.5 ;
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u[0] = (3.0/(fArgument[1]-fArgument[0]))*
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((fFunction[1]-fFunction[0])/(fArgument[1]-fArgument[0]) -
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pFirstDerStart) ;
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}
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// Decomposition loop for tridiagonal algorithm. fSecondDerivative[i] and u[i]
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// are used for temporary storage of the decomposed factors.
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for(i=1;i<fNumber-1;i++)
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{
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sig = (fArgument[i]-fArgument[i-1])/(fArgument[i+1]-fArgument[i-1]) ;
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p = sig*fSecondDerivative[i-1] + 2.0 ;
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fSecondDerivative[i] = (sig - 1.0)/p ;
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u[i] = (fFunction[i+1]-fFunction[i])/(fArgument[i+1]-fArgument[i]) -
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(fFunction[i]-fFunction[i-1])/(fArgument[i]-fArgument[i-1]) ;
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u[i] =(6.0*u[i]/(fArgument[i+1]-fArgument[i-1]) - sig*u[i-1])/p ;
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}
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if(pFirstDerFinish > maxDerivative)
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{
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qn = 0.0 ;
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un = 0.0 ;
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}
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else
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{
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qn = 0.5 ;
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un =(3.0/(fArgument[fNumber-1]-fArgument[fNumber-2]))*(pFirstDerFinish -
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(fFunction[fNumber-1]-fFunction[fNumber-2])/
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(fArgument[fNumber-1]-fArgument[fNumber-2])) ;
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}
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fSecondDerivative[fNumber-1] = (un - qn*u[fNumber-2])/
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(qn*fSecondDerivative[fNumber-2] + 1.0) ;
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// The backsubstitution loop for the triagonal algorithm of solving a linear
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// system of equations.
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for(k=fNumber-2;k>=0;k--)
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{
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fSecondDerivative[k] = fSecondDerivative[k]*fSecondDerivative[k+1] + u[k] ;
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}
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delete[] u ;
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}
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////////////////////////////////////////////////////////////////////////////////////
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//
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// Destructor deletes dynamically created arrays for data members: fArgument,
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// fFunction and fSecondDerivative, all have dimension of fNumber
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G4DataInterpolation::~G4DataInterpolation()
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{
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delete[] fArgument ;
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delete[] fFunction ;
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if(fSecondDerivative) delete[] fSecondDerivative ;
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}
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////////////////////////////////////////////////////////////////////////////////////
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//
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// This function returns the value P(pX), where P(x) is polynom of fNumber-1 degree
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// such that P(fArgument[i]) = fFunction[i], for i = 0, ..., fNumber-1 . This is
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// Lagrange's form of interpolation and it is based on Neville's algorithm
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G4double
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G4DataInterpolation::PolynomInterpolation(G4double pX,
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G4double& deltaY ) const
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{
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G4int i, m, k = 0 ;
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G4double mult, diff, difi, deltaLow, deltaUp, cd, y ;
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G4double* c = new G4double[fNumber] ;
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G4double* d = new G4double[fNumber] ;
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diff = fabs(pX-fArgument[0]) ;
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for(i=0;i<fNumber;i++)
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{
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difi = fabs(pX-fArgument[i]) ;
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if(difi <diff)
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{
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k = i ;
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diff = difi ;
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}
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c[i] = fFunction[i] ;
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d[i] = fFunction[i] ;
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}
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y = fFunction[k--] ;
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for(m=1;m<fNumber;m++)
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{
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for(i=0;i<fNumber-m;i++)
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{
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deltaLow = fArgument[i] - pX ;
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deltaUp = fArgument[i+m] - pX ;
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cd = c[i+1] - d[i] ;
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mult = deltaLow - deltaUp ;
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if(mult == 0.0)
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{
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G4Exception
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("Coincident nodes in G4DataInterpolation::PolynomInterpolation") ;
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}
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mult = cd/mult ;
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d[i] = deltaUp*mult ;
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c[i] = deltaLow*mult ;
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}
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y += (deltaY = (2*k < (fNumber - m -1) ? c[k+1] : d[k--] )) ;
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}
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delete[] c ;
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delete[] d ;
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return y ;
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}
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////////////////////////////////////////////////////////////////////////////////
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//
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// Given arrays fArgument[0,..,fNumber-1] and fFunction[0,..,fNumber-1] , this
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// function calculates an array of coefficients. The coefficients don't provide
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// usually (fNumber>10) better accuracy for polynom interpolation, as compared with
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// PolynomInterpolation function. They could be used instead for derivate
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// calculations and some other applications.
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void
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G4DataInterpolation::PolIntCoefficient( G4double cof[]) const
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{
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G4int i, j ;
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G4double factor, reducedY, mult ;
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G4double* tempArgument = new G4double[fNumber] ;
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for(i=0;i<fNumber;i++)
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{
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tempArgument[i] = cof[i] = 0.0 ;
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}
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tempArgument[fNumber-1] = -fArgument[0] ;
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for(i=1;i<fNumber;i++)
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{
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for(j=fNumber-1-i;j<fNumber-1;j++)
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{
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tempArgument[j] -= fArgument[i]*tempArgument[j+1] ;
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}
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tempArgument[fNumber-1] -= fArgument[i] ;
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}
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for(i=0;i<fNumber;i++)
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{
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factor = fNumber ;
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for(j=fNumber-1;j>=1;j--)
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{
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factor = j*tempArgument[j] + factor*fArgument[i] ;
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}
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reducedY = fFunction[i]/factor ;
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mult = 1.0 ;
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for(j=fNumber-1;j>=0;j--)
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{
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cof[j] += mult*reducedY ;
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mult = tempArgument[j] + mult*fArgument[i] ;
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}
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}
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delete[] tempArgument ;
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}
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///////////////////////////////////////////////////////////////////////////////
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//
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// The function returns diagonal rational function (Bulirsch and Stoer algorithm
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// of Neville type) Pn(x)/Qm(x) where P and Q are polynoms.
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// Tests showed the method is not stable and hasn't advantage if compared with
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// polynomial interpolation ?!
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G4double
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G4DataInterpolation::RationalPolInterpolation(G4double pX,
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G4double& deltaY ) const
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{
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G4int i, m, k = 0 ;
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const G4double tolerance = 1.6e-24 ;
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G4double mult, difi, diff, cd, y, cof ;
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G4double* c = new G4double[fNumber] ;
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G4double* d = new G4double[fNumber] ;
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diff = fabs(pX-fArgument[0]) ;
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for(i=0;i<fNumber;i++)
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{
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difi = fabs(pX-fArgument[i]) ;
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if(difi == 0.0)
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{
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y = fFunction[i] ;
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deltaY = 0.0 ;
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delete[] c ;
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delete[] d ;
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return y ;
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}
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else if(difi < diff)
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{
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k = i ;
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diff = difi ;
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}
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c[i] = fFunction[i] ;
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d[i] = fFunction[i] + tolerance ; // to prevent rare zero/zero cases
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}
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y = fFunction[k--] ;
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for(m=1;m<fNumber;m++)
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{
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for(i=0;i<fNumber-m;i++)
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{
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cd = c[i+1] - d[i] ;
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difi = fArgument[i+m] - pX ;
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cof = (fArgument[i] - pX)*d[i]/difi ;
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mult = cof - c[i+1] ;
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if(mult == 0.0) // function to be interpolated has pole at pX
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{
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G4Exception("Error in G4DataInterpolation::RationalPolInterpolation") ;
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}
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mult = cd/mult ;
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d[i] = c[i+1]*mult ;
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c[i] = cof*mult ;
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}
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y += (deltaY = (2*k < (fNumber - m - 1) ? c[k+1] : d[k--] )) ;
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}
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delete[] c ;
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delete[] d ;
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return y ;
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}
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//////////////////////////////////////////////////////////////////////////////////
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//
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// Cubic spline interpolation in point pX for function given by the table:
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// fArgument, fFunction. The constructor, which creates fSecondDerivative, must be
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// called before. The function works optimal, if sequential calls are in random
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// values of pX.
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G4double
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G4DataInterpolation::CubicSplineInterpolation(G4double pX) const
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{
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G4int kLow, kHigh, k ;
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G4double deltaHL, a, b ;
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// Searching in the table by means of bisection method.
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// fArgument must be monotonic, either increasing or decreasing
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kLow = 0 ;
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kHigh = fNumber - 1 ;
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while((kHigh - kLow) > 1)
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{
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k = (kHigh + kLow) >> 1 ; // compute midpoint 'bisection'
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if(fArgument[k] > pX)
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{
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kHigh = k ;
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}
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else
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{
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kLow = k ;
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}
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} // kLow and kHigh now bracket the input value of pX
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deltaHL = fArgument[kHigh] - fArgument[kLow] ;
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if(deltaHL == 0.0)
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{
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G4Exception(
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"Bad fArgument input in G4DataInterpolation::CubicSplineInterpolation") ;
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}
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a = (fArgument[kHigh] - pX)/deltaHL ;
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b = (pX - fArgument[kLow])/deltaHL ;
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// Final evaluation of cubic spline polynomial for return
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return a*fFunction[kLow] + b*fFunction[kHigh] +
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((a*a*a - a)*fSecondDerivative[kLow] +
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(b*b*b - b)*fSecondDerivative[kHigh])*deltaHL*deltaHL/6.0 ;
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}
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///////////////////////////////////////////////////////////////////////////
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//
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// Return cubic spline interpolation in the point pX which is located between
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// fArgument[index] and fArgument[index+1]. It is usually called in sequence of
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// known from external analysis values of index.
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G4double
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G4DataInterpolation::FastCubicSpline(G4double pX,
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G4int index) const
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{
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G4double delta, a, b ;
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delta = fArgument[index+1] - fArgument[index] ;
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if(delta == 0.0)
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{
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G4Exception("Bad fArgument input in G4DataInterpolation::FastCubicSpline") ;
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}
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a = (fArgument[index+1] - pX)/delta ;
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b = (pX - fArgument[index])/delta ;
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// Final evaluation of cubic spline polynomial for return
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return a*fFunction[index] + b*fFunction[index+1] +
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((a*a*a - a)*fSecondDerivative[index] +
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(b*b*b - b)*fSecondDerivative[index+1])*delta*delta/6.0 ;
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}
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///////////////////////////////////////////////////////////////////////////////////
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//
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// Given argument pX, returns index k, so that pX bracketed by fArgument[k] and
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// fArgument[k+1]
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G4int
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G4DataInterpolation::LocateArgument(G4double pX) const
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{
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G4int kLow, kHigh, k ;
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G4bool ascend ;
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kLow = -1 ;
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kHigh = fNumber ;
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ascend = (fArgument[fNumber-1] >= fArgument[0]) ;
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while((kHigh - kLow) > 1)
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{
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k = (kHigh + kLow) >> 1 ; // compute midpoint 'bisection'
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if(pX >= fArgument[k] == ascend)
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{
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kLow = k ;
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}
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else
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{
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kHigh = k ;
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}
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}
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if(pX == fArgument[0])
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{
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return 1 ;
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}
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else if(pX == fArgument[fNumber-1])
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{
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return fNumber - 2 ;
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}
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else return kLow ;
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}
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/////////////////////////////////////////////////////////////////////////////////////
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//
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// Given a value pX, returns a value 'index' such that pX is between fArgument[index]
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// and fArgument[index+1]. fArgument MUST BE MONOTONIC, either increasing or
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// decreasing. If index = -1 or fNumber, this indicates that pX is out of range.
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// The value index on input is taken as the initial approximation for index on
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// output.
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void
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G4DataInterpolation::CorrelatedSearch( G4double pX,
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G4int& index ) const
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{
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G4int kHigh, k, Increment ;
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// ascend = true for ascending order of table, false otherwise
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G4bool ascend = (fArgument[fNumber-1] >= fArgument[0]) ;
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if(index < 0 || index > fNumber-1)
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{
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index = -1 ;
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kHigh = fNumber ;
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}
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else
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{
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Increment = 1 ; // What value would be the best ?
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if((pX >= fArgument[index]) == ascend)
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{
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if(index == fNumber -1)
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{
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index = fNumber ;
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return ;
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}
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kHigh = index + 1 ;
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while((pX >= fArgument[kHigh]) == ascend)
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{
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index = kHigh ;
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Increment += Increment ; // double the Increment
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kHigh = index + Increment ;
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if(kHigh > (fNumber - 1))
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{
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kHigh = fNumber ;
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break ;
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}
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}
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}
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else
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{
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if(index == 0)
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{
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index = -1 ;
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return ;
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}
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kHigh = index-- ;
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while((pX < fArgument[index]) == ascend)
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{
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kHigh = index ;
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Increment <<= 1 ; // double the Increment
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if(Increment >= kHigh)
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{
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index = -1 ;
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break ;
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}
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else
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{
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index = kHigh - Increment ;
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}
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}
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} // Value bracketed
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}
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// final bisection searching
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while((kHigh - index) != 1)
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{
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k = (kHigh + index) >> 1 ;
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if((pX >= fArgument[k]) == ascend)
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{
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index = k ;
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}
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else
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{
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kHigh = k ;
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}
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}
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if(pX == fArgument[fNumber-1])
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{
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index = fNumber - 2 ;
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}
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if(pX == fArgument[0])
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{
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index = 0 ;
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}
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return ;
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}
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//
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//
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//////////////////////////////////////////////////////////////////////////////////
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