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// @(#)root/mathmore:$Id$
// Author: L. Moneta 2009
// Implementation file for all the MinimizerVariableTransormation's
// (implementations taken from minuit2 classes)
#include "Math/MinimizerVariableTransformation.h"
#include <cmath>
#include <limits>
namespace ROOT {
namespace Math {
// implementations for the class SinVariableTransformation
double SinVariableTransformation::Int2ext(double value, double lower, double upper) const {
// transformation from internal (unlimited) to external values (limited by lower/upper )
return lower + 0.5*(upper - lower)*(std::sin(value) + 1.);
}
double SinVariableTransformation::Ext2int(double value, double lower, double upper) const {
// transformation from external (limited by lower/upper ) to internal (unlimited) values given the lower/upper limits
double piby2 = 2.*std::atan(1.);
static const double eps = std::numeric_limits<double>::epsilon();
double distnn = 8.*std::sqrt(eps);
double vlimhi = piby2 - distnn;
double vlimlo = -piby2 + distnn;
double yy = 2.*(value - lower)/(upper - lower) - 1.;
double yy2 = yy*yy;
if(yy2 > (1. - 8 * eps) ) {
if(yy < 0.) {
// lower limit
// std::cout<<"SinVariableTransformation warning: is at its lower allowed limit. "<<value<<std::endl;
return vlimlo;
} else {
// upper limit
// std::cout<<"SinVariableTransformation warning: is at its upper allowed limit."<<std::endl;
return vlimhi;
}
} else {
return std::asin(yy);
}
}
double SinVariableTransformation::DInt2Ext(double value, double lower, double upper) const {
// return the derivative of the internal to external transformation (Int2Ext) : d Int2Ext / d Int
return 0.5*((upper - lower)*std::cos(value));
}
// sqrt up
// implementations for the class SqrtUpVariableTransformation
double SqrtLowVariableTransformation::Int2ext(double value, double lower, double) const {
/// internal to external transformation
double val = lower - 1. + std::sqrt( value*value + 1.);
return val;
}
double SqrtLowVariableTransformation::Ext2int(double value, double lower, double ) const {
// external to internal transformation
double yy = value - lower + 1.;
double yy2 = yy*yy;
if (yy2 < 1. )
return 0;
else
return std::sqrt( yy2 -1);
}
double SqrtLowVariableTransformation::DInt2Ext(double value, double, double) const {
// derivative of internal to external transofrmation : d (Int2Ext) / d Int
double val = value/( std::sqrt( value*value + 1.) );
return val;
}
// sqrt up
// implementations for the class SqrtUpVariableTransformation
double SqrtUpVariableTransformation::Int2ext(double value, double upper, double) const {
// internal to external transformation
double val = upper + 1. - std::sqrt( value*value + 1.);
return val;
}
double SqrtUpVariableTransformation::Ext2int(double value, double upper, double ) const {
// external to internal transformation
double yy = upper - value + 1.;
double arg = yy*yy - 1;
return ( arg < 0 ) ? 0 : std::sqrt(arg);
}
double SqrtUpVariableTransformation::DInt2Ext(double value, double, double) const {
// derivative of internal to external transofrmation : d Ext / d Int
double val = - value/( std::sqrt( value*value + 1.) );
return val;
}
} // end namespace Math
} // end namespace ROOT
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