Class for interpolating the inverse of a 1-dimensional function. More...

#include <G4INCLInvFInterpolationTable.hh>

Inheritance diagram for G4INCL::InvFInterpolationTable:

Public Types
typedef G4double(*const	ManipulatorFunc) (const G4double)
	Typedef to simplify the syntax of inverseCDFTable. More...

Public Member Functions
std::vector< G4double >	getNodeAbscissae () const

std::vector< G4double >	getNodeValues () const

unsigned int	getNumberOfNodes () const

virtual G4double	getXMaximum () const
	Return the maximum allowed value of the independent variable. More...

virtual G4double	getXMinimum () const
	Return the minimum allowed value of the independent variable. More...

virtual G4double	integrate (const G4double x0, const G4double x1, const G4double step=-1.) const
	Integrate the function between two values. More...

InterpolationTable *	inverseCDFTable (ManipulatorFunc fWrap=0, const G4int nNodes=60) const
	Return a pointer to the inverse of the CDF of this function. More...

	InvFInterpolationTable (IFunction1D const &f, const unsigned int nNodes=30)

G4double	operator() (const G4double x) const
	Compute the value of the function. More...

IFunction1D *	primitive () const
	Return a pointer to the (numerical) primitive to this function. More...

std::string	print () const

virtual	~InvFInterpolationTable ()

Protected Member Functions
void	initDerivatives ()
	Initialise the values of the node derivatives. More...

Protected Attributes
std::vector< InterpolationNode >	nodes
	Interpolating nodes. More...

G4double	xMax
	Maximum value of the independent variable. More...

G4double	xMin
	Minimum value of the independent variable. More...

Static Private Attributes
static const G4double	integrationCoefficients []
	Coefficients for numerical integration. More...

Detailed Description

Class for interpolating the inverse of a 1-dimensional function.

Definition at line 56 of file G4INCLInvFInterpolationTable.hh.

Member Typedef Documentation

◆ ManipulatorFunc

typedef G4double(*const G4INCL::IFunction1D::ManipulatorFunc) (const G4double)

inherited

Typedef to simplify the syntax of inverseCDFTable.

Definition at line 93 of file G4INCLIFunction1D.hh.

Constructor & Destructor Documentation

◆ InvFInterpolationTable()

G4INCL::InvFInterpolationTable::InvFInterpolationTable	(	IFunction1D const &	f,
		const unsigned int	nNodes = `30`
	)

Definition at line 52 of file G4INCLInvFInterpolationTable.cc.

                                                                                                {
// assert(nNodes>2);
 
    const G4double x0 = f.getXMinimum();
    const G4double x1 = f.getXMaximum();
 
    // Build the nodes
    G4double last = f(x0);
    InterpolationNode firstNode(last, x0, 0.);
    nodes.push_back(firstNode);
    G4int skippedNodes = 0;
    for(unsigned i = 1; i < nNodes; i++) {
      const G4double xi = x0 + i*(x1-x0)/((G4double)(nNodes-1));
      // Make sure that the x vector is sorted (corresponding to a monotonous
      // function)
      const G4double value = f(xi);
      if(value <= last) {
        ++skippedNodes;
        continue;
      }
      InterpolationNode node(value, xi, 0.);
      nodes.push_back(node);
      last = value;
    }
 
// assert(nNodes==nodes.size()+skippedNodes);
 
    // Initialise the "derivative" values
    initDerivatives();
  }

References G4INCL::IFunction1D::getXMaximum(), G4INCL::IFunction1D::getXMinimum(), G4INCL::InterpolationTable::initDerivatives(), and G4INCL::InterpolationTable::nodes.

◆ ~InvFInterpolationTable()

virtual G4INCL::InvFInterpolationTable::~InvFInterpolationTable ( )

inlinevirtual

Definition at line 59 of file G4INCLInvFInterpolationTable.hh.

59{}

Member Function Documentation

◆ getNodeAbscissae()

std::vector< G4double > G4INCL::InterpolationTable::getNodeAbscissae ( ) const

inherited

Definition at line 67 of file G4INCLInterpolationTable.cc.

                                                                 {
    std::vector<G4double> x(nodes.size());
    std::transform(nodes.begin(), nodes.end(), x.begin(),
                   std::mem_fn(&InterpolationNode::getX));
    return x;
  }

References G4INCL::InterpolationNode::getX(), G4INCL::InterpolationTable::nodes, and G4coutFormatters::anonymous_namespace{G4coutFormatters.cc}::transform().

◆ getNodeValues()

std::vector< G4double > G4INCL::InterpolationTable::getNodeValues ( ) const

inherited

Definition at line 74 of file G4INCLInterpolationTable.cc.

                                                              {
    std::vector<G4double> y(nodes.size());
    std::transform(nodes.begin(), nodes.end(), y.begin(),
                   std::mem_fn(&InterpolationNode::getY));
    return y;
  }

References G4INCL::InterpolationNode::getY(), G4INCL::InterpolationTable::nodes, and G4coutFormatters::anonymous_namespace{G4coutFormatters.cc}::transform().

◆ getNumberOfNodes()

unsigned int G4INCL::InterpolationTable::getNumberOfNodes ( ) const

inlineinherited

Definition at line 111 of file G4INCLInterpolationTable.hh.

111{ return nodes.size(); }

References G4INCL::InterpolationTable::nodes.

◆ getXMaximum()

virtual G4double G4INCL::IFunction1D::getXMaximum ( ) const

inlinevirtualinherited

Return the maximum allowed value of the independent variable.

Definition at line 75 of file G4INCLIFunction1D.hh.

75{ return xMax; }

G4INCL::IFunction1D::xMax

G4double xMax

Maximum value of the independent variable.

Definition: G4INCLIFunction1D.hh:106

References G4INCL::IFunction1D::xMax.

Referenced by G4INCL::IFunction1D::inverseCDFTable(), InvFInterpolationTable(), and G4INCL::IFunction1D::primitive().

◆ getXMinimum()

virtual G4double G4INCL::IFunction1D::getXMinimum ( ) const

inlinevirtualinherited

Return the minimum allowed value of the independent variable.

Definition at line 72 of file G4INCLIFunction1D.hh.

72{ return xMin; }

G4INCL::IFunction1D::xMin

G4double xMin

Minimum value of the independent variable.

Definition: G4INCLIFunction1D.hh:104

References G4INCL::IFunction1D::xMin.

Referenced by G4INCL::IFunction1D::inverseCDFTable(), InvFInterpolationTable(), and G4INCL::IFunction1D::primitive().

◆ initDerivatives()

void G4INCL::InterpolationTable::initDerivatives ( )

protectedinherited

Initialise the values of the node derivatives.

Definition at line 81 of file G4INCLInterpolationTable.cc.

                                           {
    for(unsigned i = 0; i < nodes.size()-1; i++) {
      if((nodes.at(i+1).getX() - nodes.at(i).getX()) == 0.0) // Safeguard against division by zero
        nodes[i].setYPrime(0.0);
      else
        nodes[i].setYPrime((nodes.at(i+1).getY() - nodes.at(i).getY())/(nodes.at(i+1).getX() - nodes.at(i).getX()));
    }
    nodes.back().setYPrime(nodes.at(nodes.size()-2).getYPrime()); // Duplicate the last value
  }

References G4INCL::InterpolationTable::nodes.

Referenced by G4INCL::InterpolationTable::InterpolationTable(), and InvFInterpolationTable().

◆ integrate()

G4double G4INCL::IFunction1D::integrate	(	const G4double	x0,
		const G4double	x1,
		const G4double	step = `-1.`
	)		const

virtualinherited

Integrate the function between two values.

Parameters

x0	lower integration bound
x1	upper integration bound
step	largest integration step size; if <0, 45 steps will be used

Returns: $\int_{x_0}^{x_1} f(x) dx$

Definition at line 66 of file G4INCLIFunction1D.cc.

                                                                                                 {
    G4double xi = std::max(x0, xMin);
    G4double xa = std::min(x1, xMax);
    G4double sign;
 
    if(x1 <= x0) {
      sign = -1.0;
      std::swap(xi, xa);
    } else
      sign = 1.0;
 
    const G4double interval = xa - xi;
 
    G4int nIntervals;
    if(step<0.) {
      nIntervals = 45;
    } else {
      nIntervals = G4int(interval/step);
 
      // Round up nIntervals to the closest multiple of 9
      G4int remainder = nIntervals % 9;
      if (remainder != 0)
        nIntervals += 9 - remainder;
 
      nIntervals = std::max(nIntervals, 9);
    }
 
    const G4double dx = interval/nIntervals;
    G4double result = (operator()(xi) + operator()(xa)) * integrationCoefficients[0]/2;
    for(G4int j = 1; j<nIntervals; ++j) {
      const G4double x = xi + interval*G4double(j)/G4double(nIntervals);
      const unsigned index = j%9;
      result += operator()(x) * integrationCoefficients[index];
    }
 
    return result*dx*sign;
 
  }

References G4INCL::IFunction1D::integrationCoefficients, G4INCL::Math::max(), G4INCL::Math::min(), G4INCL::IFunction1D::operator()(), G4INCL::Math::sign(), G4INCL::IFunction1D::xMax, and G4INCL::IFunction1D::xMin.

◆ inverseCDFTable()

InterpolationTable * G4INCL::IFunction1D::inverseCDFTable	(	IFunction1D::ManipulatorFunc	fWrap = `0`,
		const G4int	nNodes = `60`
	)		const

inherited

Return a pointer to the inverse of the CDF of this function.

The function parameter fWrap is wrapped around the return value of operator(). If fWrap=NULL (default), fWrap=identity.

Definition at line 123 of file G4INCLIFunction1D.cc.

                                                                                                             {
    class InverseCDF : public IFunction1D {
      public:
        InverseCDF(IFunction1D const * const f, ManipulatorFunc fw) :
          IFunction1D(f->getXMinimum(), f->getXMaximum()),
          theFunction(f),
          normalisation(1./theFunction->integrate(xMin,xMax)),
          fWrap(fw)
      {}
 
        G4double operator()(const G4double x) const {
          if(fWrap)
            return fWrap(std::min(1., normalisation * theFunction->integrate(xMin,x)));
          else
            return std::min(1., normalisation * theFunction->integrate(xMin,x));
        }
      private:
        IFunction1D const * const theFunction;
        const G4double normalisation;
        ManipulatorFunc fWrap;
    } *theInverseCDF = new InverseCDF(this, fWrap);
 
    InterpolationTable *theTable = new InvFInterpolationTable(*theInverseCDF, nNodes);
    delete theInverseCDF;
    return theTable;
  }

References G4INCL::IFunction1D::getXMaximum(), G4INCL::IFunction1D::getXMinimum(), G4INCL::IFunction1D::IFunction1D(), G4INCL::Math::min(), G4INCL::IFunction1D::operator()(), G4INCL::IFunction1D::xMax, and G4INCL::IFunction1D::xMin.

Referenced by G4INCL::NuclearDensityFactory::createPCDFTable(), G4INCL::NuclearDensityFactory::createRCDFTable(), and G4INCL::NuclearDensityFactory::createRPCorrelationTable().

◆ operator()()

G4double G4INCL::InterpolationTable::operator() ( const G4double x ) const

virtualinherited

Compute the value of the function.

Implements G4INCL::IFunction1D.

Definition at line 91 of file G4INCLInterpolationTable.cc.

                                                                {
    // Find the relevant interpolation bin
    InterpolationNode xNode(x,0.,0.);
    std::vector<InterpolationNode>::const_iterator iter =
      std::lower_bound(nodes.begin(), nodes.end(), xNode);
 
    if(iter==nodes.begin())
      return nodes.front().getY();
 
    if(iter==nodes.end())
      return nodes.back().getY();
 
    std::vector<InterpolationNode>::const_iterator previousIter = iter - 1;
    const G4double dx = x - previousIter->getX();
    return previousIter->getY() + previousIter->getYPrime()*dx;
  }

References G4INCL::InterpolationTable::nodes.

◆ primitive()

IFunction1D * G4INCL::IFunction1D::primitive ( ) const

inherited

Return a pointer to the (numerical) primitive to this function.

Definition at line 105 of file G4INCLIFunction1D.cc.

                                            {
    class Primitive : public IFunction1D {
      public:
        Primitive(IFunction1D const * const f) :
          IFunction1D(f->getXMinimum(), f->getXMaximum()),
          theFunction(f)
      {}
 
        G4double operator()(const G4double x) const {
          return theFunction->integrate(xMin,x);
        }
      private:
        IFunction1D const * const theFunction;
    } *thePrimitive = new Primitive(this);
 
    return thePrimitive;
  }

References G4INCL::IFunction1D::getXMaximum(), G4INCL::IFunction1D::getXMinimum(), G4INCL::IFunction1D::IFunction1D(), G4INCL::IFunction1D::operator()(), Primitive, and G4INCL::IFunction1D::xMin.

◆ print()

std::string G4INCL::InterpolationTable::print ( ) const

inherited

Definition at line 108 of file G4INCLInterpolationTable.cc.

                                            {
    std::string message;
    for(std::vector<InterpolationNode>::const_iterator n=nodes.begin(), e=nodes.end(); n!=e; ++n)
      message += n->print();
    return message;
  }

References CLHEP::detail::n, and G4INCL::InterpolationTable::nodes.

Referenced by G4INCL::NuclearDensityFactory::createPCDFTable(), G4INCL::NuclearDensityFactory::createRCDFTable(), and G4INCL::NuclearDensityFactory::createRPCorrelationTable().

Field Documentation

◆ integrationCoefficients

const G4double G4INCL::IFunction1D::integrationCoefficients

staticprivateinherited

Initial value:

= {
*95.0/288.0,
0/240.0,
0/30.0,
0/720.0,
0/160.0,
0/160.0,
0/720.0,
0/30.0,
0/240.0,
  }

Coefficients for numerical integration.

Definition at line 110 of file G4INCLIFunction1D.hh.

Referenced by G4INCL::IFunction1D::integrate().

◆ nodes

std::vector<InterpolationNode> G4INCL::InterpolationTable::nodes

protectedinherited

Interpolating nodes.

Definition at line 128 of file G4INCLInterpolationTable.hh.

Referenced by G4INCL::InterpolationTable::getNodeAbscissae(), G4INCL::InterpolationTable::getNodeValues(), G4INCL::InterpolationTable::getNumberOfNodes(), G4INCL::InterpolationTable::initDerivatives(), G4INCL::InterpolationTable::InterpolationTable(), InvFInterpolationTable(), G4INCL::InterpolationTable::operator()(), and G4INCL::InterpolationTable::print().

◆ xMax

G4double G4INCL::IFunction1D::xMax

protectedinherited

Maximum value of the independent variable.

Definition at line 106 of file G4INCLIFunction1D.hh.

Referenced by G4INCL::IFunction1D::getXMaximum(), G4INCL::IFunction1D::integrate(), and G4INCL::IFunction1D::inverseCDFTable().

◆ xMin

G4double G4INCL::IFunction1D::xMin

protectedinherited

Minimum value of the independent variable.

Definition at line 104 of file G4INCLIFunction1D.hh.

Referenced by G4INCL::IFunction1D::getXMinimum(), G4INCL::IFunction1D::integrate(), G4INCL::IFunction1D::inverseCDFTable(), and G4INCL::IFunction1D::primitive().

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

source/processes/hadronic/models/inclxx/utils/include/G4INCLInvFInterpolationTable.hh
source/processes/hadronic/models/inclxx/utils/src/G4INCLInvFInterpolationTable.cc

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ ManipulatorFunc

Constructor & Destructor Documentation

◆ InvFInterpolationTable()

◆ ~InvFInterpolationTable()

Member Function Documentation

◆ getNodeAbscissae()

◆ getNodeValues()

◆ getNumberOfNodes()

◆ getXMaximum()

◆ getXMinimum()

◆ initDerivatives()

◆ integrate()

◆ inverseCDFTable()

◆ operator()()

◆ primitive()

◆ print()

Field Documentation

◆ integrationCoefficients

◆ nodes

◆ xMax

◆ xMin