G4DataInterpolation Class Reference

#include <G4DataInterpolation.hh>

Public Member Functions
	G4DataInterpolation (G4double pX[], G4double pY[], G4int number)
	G4DataInterpolation (G4double pX[], G4double pY[], G4int number, G4double pFirstDerStart, G4double pFirstDerFinish)
	~G4DataInterpolation ()
G4double	PolynomInterpolation (G4double pX, G4double &deltaY) const
void	PolIntCoefficient (G4double cof[]) const
G4double	RationalPolInterpolation (G4double pX, G4double &deltaY) const
G4double	CubicSplineInterpolation (G4double pX) const
G4double	FastCubicSpline (G4double pX, G4int index) const
G4int	LocateArgument (G4double pX) const
void	CorrelatedSearch (G4double pX, G4int &index) const

Detailed Description

Definition at line 116 of file G4DataInterpolation.hh.

Constructor & Destructor Documentation

G4DataInterpolation::G4DataInterpolation	(	G4double	pX[],
		G4double	pY[],
		G4int	number
	)

Definition at line 36 of file G4DataInterpolation.cc.

   : fArgument(new G4double[number]),
     fFunction(new G4double[number]),
     fSecondDerivative(0),
     fNumber(number)
{
   for(G4int i=0;i<fNumber;i++)
   {
      fArgument[i] = pX[i] ;
      fFunction[i] = pY[i] ;
   }
} 

G4DataInterpolation::G4DataInterpolation	(	G4double	pX[],
		G4double	pY[],
		G4int	number,
		G4double	pFirstDerStart,
		G4double	pFirstDerFinish
	)

Definition at line 58 of file G4DataInterpolation.cc.

   : fArgument(new G4double[number]),
     fFunction(new G4double[number]),
     fSecondDerivative(new G4double[number]),
     fNumber(number)
{
   G4int i=0 ;
   G4double p=0.0, qn=0.0, sig=0.0, un=0.0 ;
   const G4double maxDerivative = 0.99e30 ;
   G4double* u = new G4double[fNumber - 1] ;

   for(i=0;i<fNumber;i++)
   {
      fArgument[i] = pX[i] ;
      fFunction[i] = pY[i] ;
   }
   if(pFirstDerStart > maxDerivative)
   {
      fSecondDerivative[0] = 0.0 ;
      u[0] = 0.0 ;
   }
   else
   {
      fSecondDerivative[0] = -0.5 ;
      u[0] = (3.0/(fArgument[1]-fArgument[0]))
           * ((fFunction[1]-fFunction[0])/(fArgument[1]-fArgument[0])
           - pFirstDerStart) ;
   }
   
   // Decomposition loop for tridiagonal algorithm. fSecondDerivative[i]
   // and u[i] are used for temporary storage of the decomposed factors.
   
   for(i=1;i<fNumber-1;i++)
   {
      sig = (fArgument[i]-fArgument[i-1])/(fArgument[i+1]-fArgument[i-1]) ;
      p = sig*fSecondDerivative[i-1] + 2.0 ;
      fSecondDerivative[i] = (sig - 1.0)/p ;
      u[i] = (fFunction[i+1]-fFunction[i])/(fArgument[i+1]-fArgument[i]) -
             (fFunction[i]-fFunction[i-1])/(fArgument[i]-fArgument[i-1]) ;
      u[i] =(6.0*u[i]/(fArgument[i+1]-fArgument[i-1]) - sig*u[i-1])/p ;
   }
   if(pFirstDerFinish > maxDerivative)
   {
      qn = 0.0 ;
      un = 0.0 ;
   }
   else
   {
      qn = 0.5 ;
      un = (3.0/(fArgument[fNumber-1]-fArgument[fNumber-2]))
         * (pFirstDerFinish - (fFunction[fNumber-1]-fFunction[fNumber-2])
         / (fArgument[fNumber-1]-fArgument[fNumber-2])) ;
   }
   fSecondDerivative[fNumber-1] = (un - qn*u[fNumber-2])/
                                  (qn*fSecondDerivative[fNumber-2] + 1.0) ;
   
   // The backsubstitution loop for the triagonal algorithm of solving
   // a linear system of equations.
   
   for(G4int k=fNumber-2;k>=0;k--)
   {
      fSecondDerivative[k] = fSecondDerivative[k]*fSecondDerivative[k+1] + u[k];
   }
   delete[] u ;
} 

G4DataInterpolation::~G4DataInterpolation

(

)

Definition at line 133 of file G4DataInterpolation.cc.

{
   delete [] fArgument ;
   delete [] fFunction ;
   if(fSecondDerivative)  { delete [] fSecondDerivative; }
}

Member Function Documentation

void G4DataInterpolation::CorrelatedSearch	(	G4double	pX,
		G4int &	index
	)		const

Definition at line 414 of file G4DataInterpolation.cc.

{
   G4int kHigh=0, k=0, Increment=0 ;
   // ascend = true for ascending order of table, false otherwise
   G4bool ascend = (fArgument[fNumber-1] >= fArgument[0]) ;
   if(index < 0 || index > fNumber-1)
   {
      index = -1 ;
      kHigh = fNumber ;
   }
   else
   {
      Increment = 1 ;   //   What value would be the best ?
      if((pX >= fArgument[index]) == ascend)
      {
         if(index == fNumber -1)
         {
            index = fNumber ;
            return ;
         }
         kHigh = index + 1 ;
         while((pX >= fArgument[kHigh]) == ascend)
         {
            index = kHigh ;
            Increment += Increment ;      // double the Increment
            kHigh = index + Increment ;
            if(kHigh > (fNumber - 1))
            {
               kHigh = fNumber ;
               break ;
            }
         }
      }
      else
      {
         if(index == 0)
         {
            index = -1 ;
            return ;
         }
         kHigh = index-- ;
         while((pX < fArgument[index]) == ascend)
         {
            kHigh = index ;
            Increment <<= 1 ;      // double the Increment
            if(Increment >= kHigh)
            {
               index = -1 ;
               break ;
            }
            else
            {
               index = kHigh - Increment ;
            }
         }
      }        // Value bracketed
   }
   // final bisection searching

   while((kHigh - index) != 1)
   {
      k = (kHigh + index) >> 1 ;
      if((pX >= fArgument[k]) == ascend)
      {
         index = k ;
      }
      else
      {
         kHigh = k ;
      }
   }
   if (!(pX != fArgument[fNumber-1]))
   {
      index = fNumber - 2 ;
   }
   if (!(pX != fArgument[0]))
   {
      index = 0 ;
   }
   return ;
}

G4double G4DataInterpolation::CubicSplineInterpolation

(

G4double

pX

)

const

Definition at line 311 of file G4DataInterpolation.cc.

{
   G4int kLow=0, kHigh=fNumber-1, k=0 ;
   
   // Searching in the table by means of bisection method. 
   // fArgument must be monotonic, either increasing or decreasing
   
   while((kHigh - kLow) > 1)
   {
      k = (kHigh + kLow) >> 1 ; // compute midpoint 'bisection'
      if(fArgument[k] > pX)
      {
         kHigh = k ;
      }
      else
      {
         kLow = k ;
      }
   }        // kLow and kHigh now bracket the input value of pX
   G4double deltaHL = fArgument[kHigh] - fArgument[kLow] ;
   if (!(deltaHL != 0.0))
   {
      G4Exception("G4DataInterpolation::CubicSplineInterpolation()",
                  "Error", FatalException, "Bad fArgument input !") ;
   }
   G4double a = (fArgument[kHigh] - pX)/deltaHL ;
   G4double b = (pX - fArgument[kLow])/deltaHL ;
   
   // Final evaluation of cubic spline polynomial for return
   
   return a*fFunction[kLow] + b*fFunction[kHigh] + 
          ((a*a*a - a)*fSecondDerivative[kLow] +
           (b*b*b - b)*fSecondDerivative[kHigh])*deltaHL*deltaHL/6.0  ;
}

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G4double G4DataInterpolation::FastCubicSpline	(	G4double	pX,
		G4int	index
	)		const

Definition at line 353 of file G4DataInterpolation.cc.

{
   G4double delta = fArgument[index+1] - fArgument[index] ;
   if (!(delta != 0.0))
   {
      G4Exception("G4DataInterpolation::FastCubicSpline()",
                  "Error", FatalException, "Bad fArgument input !") ;
   }
   G4double a = (fArgument[index+1] - pX)/delta ;
   G4double b = (pX - fArgument[index])/delta ;
   
   // Final evaluation of cubic spline polynomial for return
   
   return a*fFunction[index] + b*fFunction[index+1] + 
          ((a*a*a - a)*fSecondDerivative[index] +
           (b*b*b - b)*fSecondDerivative[index+1])*delta*delta/6.0  ;
}

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G4int G4DataInterpolation::LocateArgument

(

G4double

pX

)

const

Definition at line 378 of file G4DataInterpolation.cc.

{
   G4int kLow=-1, kHigh=fNumber, k=0 ; 
   G4bool ascend=(fArgument[fNumber-1] >= fArgument[0]) ;
   while((kHigh - kLow) > 1)
   {
      k = (kHigh + kLow) >> 1 ; // compute midpoint 'bisection'
      if( (pX >= fArgument[k]) == ascend)
      {
         kLow = k ;
      }
      else
      {
         kHigh = k ;
      }
   }
   if (!(pX != fArgument[0]))
   {
      return 1 ;
   }
   else if (!(pX != fArgument[fNumber-1]))
   {
      return fNumber - 2 ;
   }
   else  return kLow ;
}

void G4DataInterpolation::PolIntCoefficient

(

G4double

cof[]

)

const

Definition at line 202 of file G4DataInterpolation.cc.

{
   G4int i=0, j=0 ;
   G4double factor;
   G4double reducedY=0.0, mult=1.0 ;
   G4double* tempArgument = new G4double[fNumber] ;
   
   for(i=0;i<fNumber;i++)
   {
      tempArgument[i] = cof[i] = 0.0 ;
   }
   tempArgument[fNumber-1] = -fArgument[0] ;
   
   for(i=1;i<fNumber;i++)
   {
      for(j=fNumber-1-i;j<fNumber-1;j++)
      {
         tempArgument[j] -= fArgument[i]*tempArgument[j+1] ;
      }
      tempArgument[fNumber-1] -= fArgument[i] ;
   }
   for(i=0;i<fNumber;i++)
   {
      factor = fNumber ;
      for(j=fNumber-1;j>=1;j--)
      {
         factor = j*tempArgument[j] + factor*fArgument[i] ;
      }
      reducedY = fFunction[i]/factor ;
      mult = 1.0 ;
      for(j=fNumber-1;j>=0;j--)
      {
         cof[j] += mult*reducedY ;
         mult = tempArgument[j] + mult*fArgument[i] ;
      }
   }
   delete[] tempArgument ;
}

G4double G4DataInterpolation::PolynomInterpolation	(	G4double	pX,
		G4double &	deltaY
	)		const

Definition at line 148 of file G4DataInterpolation.cc.

{
   G4int i=0, j=1, k=0 ;
   G4double mult=0.0, difi=0.0, deltaLow=0.0, deltaUp=0.0, cd=0.0, y=0.0 ;
   G4double* c = new G4double[fNumber] ;
   G4double* d = new G4double[fNumber] ;
   G4double diff = std::fabs(pX-fArgument[0]) ;
   for(i=0;i<fNumber;i++)
   {
      difi = std::fabs(pX-fArgument[i]) ;
      if(difi <diff)
      {
         k = i ;
         diff = difi ;
      }
      c[i] = fFunction[i] ;
      d[i] = fFunction[i] ;   
   }
   y = fFunction[k--] ;     
   for(j=1;j<fNumber;j++)
   {
      for(i=0;i<fNumber-j;i++)
      {
         deltaLow = fArgument[i] - pX ;
         deltaUp = fArgument[i+j] - pX ;
         cd = c[i+1] - d[i] ;
         mult = deltaLow - deltaUp ;
         if (!(mult != 0.0))
         {
            G4Exception("G4DataInterpolation::PolynomInterpolation()",
                        "Error", FatalException, "Coincident nodes !") ;
         }
         mult  = cd/mult ;
         d[i] = deltaUp*mult ;
         c[i] = deltaLow*mult ;
      }
      y += (deltaY = (2*k < (fNumber - j -1) ? c[k+1] : d[k--] )) ;
   }
   delete[] c ;
   delete[] d ;
   
   return y ;
}

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G4double G4DataInterpolation::RationalPolInterpolation	(	G4double	pX,
		G4double &	deltaY
	)		const

Definition at line 249 of file G4DataInterpolation.cc.

{
   G4int i=0, j=1, k=0 ;
   const G4double tolerance = 1.6e-24 ;
   G4double mult=0.0, difi=0.0, cd=0.0, y=0.0, cof=0.0 ;
   G4double* c = new G4double[fNumber] ;
   G4double* d = new G4double[fNumber] ;
   G4double diff = std::fabs(pX-fArgument[0]) ;
   for(i=0;i<fNumber;i++)
   {
      difi = std::fabs(pX-fArgument[i]) ;
      if (!(difi != 0.0))
      {
         y = fFunction[i] ;
         deltaY = 0.0 ;
         delete[] c ;
         delete[] d ;
         return y ;
      }
      else if(difi < diff)
      {
         k = i ;
         diff = difi ;
      }
      c[i] = fFunction[i] ;
      d[i] = fFunction[i] + tolerance ;   // to prevent rare zero/zero cases
   }
   y = fFunction[k--] ;    
   for(j=1;j<fNumber;j++)
   {
      for(i=0;i<fNumber-j;i++)
      {
         cd  = c[i+1] - d[i] ;
         difi  = fArgument[i+j] - pX ;
         cof  = (fArgument[i] - pX)*d[i]/difi ;
         mult = cof - c[i+1] ;
         if (!(mult != 0.0))    // function to be interpolated has pole at pX
         {
            G4Exception("G4DataInterpolation::RationalPolInterpolation()",
                        "Error", FatalException, "Coincident nodes !") ;
         }
         mult  = cd/mult ;
         d[i] = c[i+1]*mult ;
         c[i] = cof*mult ;
      }
      y += (deltaY = (2*k < (fNumber - j - 1) ? c[k+1] : d[k--] )) ;
   }
   delete[] c ;
   delete[] d ;
   
   return y ;
}

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---

The documentation for this class was generated from the following files:

• geant4.10.03.p01/source/global/HEPNumerics/include/G4DataInterpolation.hh
• geant4.10.03.p01/source/global/HEPNumerics/src/G4DataInterpolation.cc