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This commit is contained in:
Gabriele Cosmo
2020-06-26 10:23:25 +02:00
parent c02c370437
commit 67ba86d073
1871 changed files with 174422 additions and 131884 deletions
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source/global/HEPNumerics/src/G4SimpleIntegration.cc
+106 -133
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@@ -23,161 +23,134 @@
// * acceptance of all terms of the Geant4 Software license. *
// ********************************************************************
//
// G4SimpleIntegration class implementation
//
//
// Implementation file for simple integration methods
//
// Author: V.Grichine, 26.03.1997
// --------------------------------------------------------------------
#include "globals.hh"
#include "G4SimpleIntegration.hh"
#include "globals.hh"
G4SimpleIntegration::G4SimpleIntegration(function pFunction)
: fFunction(pFunction)
{}
G4SimpleIntegration::G4SimpleIntegration( function pFunction )
: fFunction(pFunction),
fTolerance(.0001),
fMaxDepth(100)
G4SimpleIntegration::G4SimpleIntegration(function pFunction,
G4double pTolerance)
: fFunction(pFunction)
, fTolerance(pTolerance)
{}
G4SimpleIntegration::~G4SimpleIntegration() {}
// Simple integration methods
G4double G4SimpleIntegration::Trapezoidal(G4double xInitial, G4double xFinal,
G4int iterationNumber)
{
G4double Step = (xFinal - xInitial) / iterationNumber;
G4double mean = (fFunction(xInitial) + fFunction(xFinal)) * 0.5;
G4double x = xInitial;
for(G4int i = 1; i < iterationNumber; ++i)
{
x += Step;
mean += fFunction(x);
}
return mean * Step;
}
G4SimpleIntegration::G4SimpleIntegration( function pFunction,
G4double pTolerance)
: fFunction(pFunction),
fTolerance(pTolerance),
fMaxDepth(100)
G4double G4SimpleIntegration::MidPoint(G4double xInitial, G4double xFinal,
G4int iterationNumber)
{
G4double Step = (xFinal - xInitial) / iterationNumber;
G4double x = xInitial + 0.5 * Step;
G4double mean = fFunction(x);
for(G4int i = 1; i < iterationNumber; ++i)
{
x += Step;
mean += fFunction(x);
}
return mean * Step;
}
G4SimpleIntegration::~G4SimpleIntegration()
G4double G4SimpleIntegration::Gauss(G4double xInitial, G4double xFinal,
G4int iterationNumber)
{
}
// Simple integration methods
G4double
G4SimpleIntegration::Trapezoidal(G4double xInitial,
G4double xFinal,
G4int iterationNumber )
{
G4double Step = (xFinal - xInitial)/iterationNumber ;
G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ;
G4double x = xInitial ;
for(G4int i=1;i<iterationNumber;i++)
{
x += Step ;
mean += fFunction(x) ;
}
return mean*Step ;
G4double x = 0.;
static const G4double root = 1.0 / std::sqrt(3.0);
G4double Step = (xFinal - xInitial) / (2.0 * iterationNumber);
G4double delta = Step * root;
G4double mean = 0.0;
for(G4int i = 0; i < iterationNumber; ++i)
{
x = (2 * i + 1) * Step;
mean += (fFunction(x + delta) + fFunction(x - delta));
}
return mean * Step;
}
G4double
G4SimpleIntegration::MidPoint(G4double xInitial,
G4double xFinal,
G4int iterationNumber )
G4double G4SimpleIntegration::Simpson(G4double xInitial, G4double xFinal,
G4int iterationNumber)
{
G4double Step = (xFinal - xInitial)/iterationNumber ;
G4double x = xInitial + 0.5*Step;
G4double mean = fFunction(x) ;
for(G4int i=1;i<iterationNumber;i++)
{
x += Step ;
mean += fFunction(x) ;
}
return mean*Step ;
G4double Step = (xFinal - xInitial) / iterationNumber;
G4double x = xInitial;
G4double xPlus = xInitial + 0.5 * Step;
G4double mean = (fFunction(xInitial) + fFunction(xFinal)) * 0.5;
G4double sum = fFunction(xPlus);
for(G4int i = 1; i < iterationNumber; ++i)
{
x += Step;
xPlus += Step;
mean += fFunction(x);
sum += fFunction(xPlus);
}
mean += 2.0 * sum;
return mean * Step / 3.0;
}
G4double
G4SimpleIntegration::Gauss(G4double xInitial,
G4double xFinal,
G4int iterationNumber )
// Adaptive Gauss integration
G4double G4SimpleIntegration::AdaptGaussIntegration(G4double xInitial,
G4double xFinal)
{
G4double x=0.;
static const G4double root = 1.0/std::sqrt(3.0) ;
G4double Step = (xFinal - xInitial)/(2.0*iterationNumber) ;
G4double delta = Step*root ;
G4double mean = 0.0 ;
for(G4int i=0;i<iterationNumber;i++)
{
x = (2*i + 1)*Step ;
mean += (fFunction(x+delta) + fFunction(x-delta)) ;
}
return mean*Step ;
G4int depth = 0;
G4double sum = 0.0;
AdaptGauss(xInitial, xFinal, sum, depth);
return sum;
}
G4double
G4SimpleIntegration::Simpson(G4double xInitial,
G4double xFinal,
G4int iterationNumber )
G4double G4SimpleIntegration::Gauss(G4double xInitial, G4double xFinal)
{
G4double Step = (xFinal - xInitial)/iterationNumber ;
G4double x = xInitial ;
G4double xPlus = xInitial + 0.5*Step ;
G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ;
G4double sum = fFunction(xPlus) ;
for(G4int i=1;i<iterationNumber;i++)
{
x += Step ;
xPlus += Step ;
mean += fFunction(x) ;
sum += fFunction(xPlus) ;
}
mean += 2.0*sum ;
return mean*Step/3.0 ;
static const G4double root = 1.0 / std::sqrt(3.0);
G4double xMean = (xInitial + xFinal) / 2.0;
G4double Step = (xFinal - xInitial) / 2.0;
G4double delta = Step * root;
G4double sum = (fFunction(xMean + delta) + fFunction(xMean - delta));
return sum * Step;
}
// Adaptive Gauss integration
G4double
G4SimpleIntegration::AdaptGaussIntegration( G4double xInitial,
G4double xFinal )
void G4SimpleIntegration::AdaptGauss(G4double xInitial, G4double xFinal,
G4double& sum, G4int& depth)
{
G4int depth = 0 ;
G4double sum = 0.0 ;
AdaptGauss(xInitial,xFinal,sum,depth) ;
return sum ;
}
G4double
G4SimpleIntegration::Gauss( G4double xInitial,
G4double xFinal )
{
static const G4double root = 1.0/std::sqrt(3.0) ;
G4double xMean = (xInitial + xFinal)/2.0 ;
G4double Step = (xFinal - xInitial)/2.0 ;
G4double delta = Step*root ;
G4double sum = (fFunction(xMean + delta) + fFunction(xMean - delta)) ;
return sum*Step ;
}
void
G4SimpleIntegration::AdaptGauss( G4double xInitial,
G4double xFinal,
G4double& sum,
G4int& depth )
{
if(depth >fMaxDepth)
{
G4Exception("G4SimpleIntegration::AdaptGauss()", "Error",
FatalException, "Function varies too rapidly !") ;
}
G4double xMean = (xInitial + xFinal)/2.0 ;
G4double leftHalf = Gauss(xInitial,xMean) ;
G4double rightHalf = Gauss(xMean,xFinal) ;
G4double full = Gauss(xInitial,xFinal) ;
if(std::fabs(leftHalf+rightHalf-full) < fTolerance)
{
sum += full ;
}
else
{
depth++ ;
AdaptGauss(xInitial,xMean,sum,depth) ;
AdaptGauss(xMean,xFinal,sum,depth) ;
}
if(depth > fMaxDepth)
{
G4Exception("G4SimpleIntegration::AdaptGauss()", "Error", FatalException,
"Function varies too rapidly !");
}
G4double xMean = (xInitial + xFinal) / 2.0;
G4double leftHalf = Gauss(xInitial, xMean);
G4double rightHalf = Gauss(xMean, xFinal);
G4double full = Gauss(xInitial, xFinal);
if(std::fabs(leftHalf + rightHalf - full) < fTolerance)
{
sum += full;
}
else
{
++depth;
AdaptGauss(xInitial, xMean, sum, depth);
AdaptGauss(xMean, xFinal, sum, depth);
}
}