MnParameterTransformation.cxx

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// @(#)root/minuit2:$Id$
// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei, E.G.P. Bos   2003-2017
 
/**********************************************************************
 *                                                                    *
 * Copyright (c) 2005 LCG ROOT Math team,  CERN/PH-SFT                *
 *                                                                    *
 **********************************************************************/
 
#include "Minuit2/MnParameterTransformation.h"
 
#include "Minuit2/MnMachinePrecision.h"
 
#include <cmath>
 
namespace ROOT {
 
namespace Minuit2 {
 
long double SinParameterTransformation::Int2ext(long double Value, long double Upper, long double Lower) const
{
   // transformation from  to internal (unlimited) to external values (limited by Lower/Upper )
   return Lower + 0.5 * (Upper - Lower) * (std::sin(Value) + 1.);
}
 
long double SinParameterTransformation::Ext2int(long double Value, long double Upper, long double Lower,
                                                const MnMachinePrecision &prec) const
{
   // transformation from external (limited by Lower/Upper )  to internal (unlimited) values given the lower/upper
   // limits
 
   long double piby2 = 2. * std::atan(1.);
   long double distnn = 8. * std::sqrt(prec.Eps2());
   long double vlimhi = piby2 - distnn;
   long double vlimlo = -piby2 + distnn;
 
   long double yy = 2. * (Value - Lower) / (Upper - Lower) - 1.;
   long double yy2 = yy * yy;
   if (yy2 > (1. - prec.Eps2())) {
      if (yy < 0.) {
         // Lower limit
         //       std::cout<<"SinParameterTransformation warning: is at its Lower allowed limit. "<<Value<<std::endl;
         return vlimlo;
      } else {
         // Upper limit
         //       std::cout<<"SinParameterTransformation warning: is at its Upper allowed limit."<<std::endl;
         return vlimhi;
      }
   } else {
      return std::asin(yy);
   }
}
 
long double SinParameterTransformation::DInt2Ext(long double Value, long double Upper, long double Lower) const
{
   // return the derivative of the transformation d Ext/ d Int
   return 0.5 * ((Upper - Lower) * std::cos(Value));
}
 
long double SinParameterTransformation::D2Int2Ext(long double Value, long double Upper, long double Lower) const
{
   // return the second derivative of the transformation d^2 Ext/ d Int^2
   return -0.5 * ((Upper - Lower) * std::sin(Value));
}
 
long double SinParameterTransformation::DExt2Int(long double Value, long double Upper, long double Lower) const
{
   // return the derivative of the transformation d Int/ d Ext
   return 1. / std::sqrt((Value - Lower) * (Upper - Value));
}
 
long double SqrtLowParameterTransformation::Int2ext(long double value, long double lower) const
{
   /// internal to external transformation
   long double val = lower - 1. + std::sqrt(value * value + 1.);
   return val;
}
 
long double
SqrtLowParameterTransformation::Ext2int(long double value, long double lower, const MnMachinePrecision &) const
{
   // external to internal transformation
   long double yy = value - lower + 1.;
   long double yy2 = yy * yy;
   if (yy2 < 1.)
      return 0;
   else
      return std::sqrt(yy2 - 1);
}
 
long double SqrtLowParameterTransformation::DInt2Ext(long double value, long double) const
{
   // derivative of internal to external transformation   :  d (Int2Ext) / d Int
   long double val = value / (std::sqrt(value * value + 1.));
   return val;
}
 
long double SqrtLowParameterTransformation::D2Int2Ext(long double value, long double) const
{
   // second derivative of internal to external transformation : d^2 (Int2Ext) / d Int^2
   long double val = std::pow(value * value + 1., -1.5);
   return val;
}
 
long double SqrtLowParameterTransformation::DExt2Int(long double value, long double lower) const
{
   // derivative of internal to external transformation   :  d (Ext2Int) / d Ext
   long double val = (value - lower + 1) / (std::sqrt((value - lower + 1) * (value - lower + 1) - 1.));
   return val;
}
 
long double SqrtUpParameterTransformation::Int2ext(long double value, long double upper) const
{
   // internal to external transformation
   long double val = upper + 1. - std::sqrt(value * value + 1.);
   return val;
}
 
long double
SqrtUpParameterTransformation::Ext2int(long double value, long double upper, const MnMachinePrecision &) const
{
   // external to internal transformation
   long double yy = upper - value + 1.;
   long double yy2 = yy * yy;
   if (yy2 < 1.)
      return 0;
   else
      return std::sqrt(yy2 - 1);
}
 
long double SqrtUpParameterTransformation::DInt2Ext(long double value, long double) const
{
   // derivative of internal to external transformation :  d (Int2Ext ) / d Int
   long double val = -value / (std::sqrt(value * value + 1.));
   return val;
}
 
long double SqrtUpParameterTransformation::D2Int2Ext(long double value, long double) const
{
   // second derivative of internal to external transformation : d^2 (Int2Ext) / d Int^2
   long double val = -std::pow(value * value + 1., -1.5);
   return val;
}
 
long double SqrtUpParameterTransformation::DExt2Int(long double value, long double upper) const
{
   // derivative of internal to external transformation :  d (Ext2Int ) / d Ext
   long double val = -(upper - value + 1) / (std::sqrt((upper - value + 1) * (upper - value + 1) - 1.));
   return val;
}
 
} // namespace Minuit2
 
} // namespace ROOT