Simple fit method based on Powell's algorithm, see reference: Numerical Recipes in C++, W.H. More...

#include <JSimplex.hh>

Inheritance diagram for JFIT::JSimplex< JModel_t >:

Public Types
typedef double	result_type

Public Member Functions
	JSimplex ()
	Default constructor.

template<class JFunction_t , class T >
double	operator() (const JFunction_t &fit, T __begin, T __end)
	Multi-dimensional fit.

template<class JFunction_t , class T >
double	operator() (const JFunction_t &fit, T __begin, T __end, const JModel_t &step)
	1D fit.

Public Attributes
JModel_t	value

std::vector< JModel_t >	step

int	numberOfIterations

Static Public Attributes
static int	MAXIMUM_ITERATIONS = 1000
	maximal number of iterations

static double	EPSILON = 1.0e-4
	maximal distance to minimum

static int	debug = 0
	debug level (default is off).

Private Member Functions
template<class JFunction_t , class T >
double	evaluate (const JFunction_t &fit, T __begin, T __end) const
	Evaluate chi2 for given data set.

Private Attributes
JModel_t	p0

JModel_t	p1

JModel_t	wall

Detailed Description

template<class JModel_t>
class JFIT::JSimplex< JModel_t >

Simple fit method based on Powell's algorithm, see reference: Numerical Recipes in C++, W.H.

Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Cambridge University Press.

The template argument refers to the model that should be fitted to the data. This data structure should have arithmetic capabalities.

The data member JSimplex::value corresponds to the start, current or final value of the model of the fit procedure. The data member JSimplex::step corresponds to the step directions. Note that the step directions may change during the fit. The template fit function should return the data type JGandalf::result_type which is composed of the values of the chi2 and gradient of a hit. The function operator returns the chi2 of the fit.

Definition at line 42 of file JSimplex.hh.

Member Typedef Documentation

◆ result_type

template<class JModel_t >

double JFIT::JSimplex< JModel_t >::result_type

Definition at line 47 of file JSimplex.hh.

Constructor & Destructor Documentation

◆ JSimplex()

template<class JModel_t >

JFIT::JSimplex< JModel_t >::JSimplex ( )

inline

Default constructor.

Definition at line 55 of file JSimplex.hh.

56 {}

Member Function Documentation

◆ operator()() [1/2]

template<class JModel_t >

template<class JFunction_t , class T >

double JFIT::JSimplex< JModel_t >::operator()	(	const JFunction_t &	fit,
		T	__begin,
		T	__end )

inline

Multi-dimensional fit.

The given fit function should return the equivalent of chi2 for the current value of the given model and a given data point.

Parameters

fit	fit function
__begin	begin of data
__end	end of data

Returns: chi2

Definition at line 71 of file JSimplex.hh.

    {
      using namespace std;
      using namespace JPP;
 
      double chi2_old = evaluate(fit, __begin, __end);
 
      const int N = step.size();
 
      if (N != 0) {
 
        p0   = value;
        p1   = value;
        wall = value;
 
        double chi2[N];
 
        numberOfIterations = 0;
 
        while (numberOfIterations != MAXIMUM_ITERATIONS) {
 
          DEBUG("old: " << FIXED(12,5) << chi2_old << endl);
 
          p0 = value;
 
          for (int i = 0; i != N; ++i) {
 
            DEBUG("step: " << i << ' ' << setw(5) << numberOfIterations << endl);
 
            chi2[i] = (*this)(fit, __begin, __end, step[i]);
          }
 
          // overall step direction of last iteration
 
          wall  = value;
          wall -= p0;
 
          const double chi2_new = (*this)(fit, __begin, __end, wall);
 
          DEBUG("new: " << FIXED(12,5) << chi2_new << endl);
 
 
          if (fabs(chi2_old - chi2_new) < EPSILON*fabs(chi2_old)) {
            return chi2_new;
          }
 
          // double overall step
 
          wall   = value;
          wall  -= p0;
          value += wall;
 
          const double fe = evaluate(fit, __begin, __end);
 
          value -= wall;
 
 
          for (int i = N-1; i != 0; --i) {
            chi2[i] = chi2[i-1] - chi2[i];
          }
 
          chi2[0] = chi2_old - chi2[0];
 
 
          double df = 0.0;
 
          for (int i = 0; i != N; ++i) {
            if (chi2[i] > df) {
              df = chi2[i];
            }
          }
 
          const double fn = chi2_new;
          const double f0 = chi2_old;
          const double ff = f0 - fn - df;
 
          // shift step directions
 
          if (fe < f0 && 2.0*(f0 - 2.0*fn + fe)*ff*ff < (f0-fe)*(f0-fe)*df) {
 
            for (int i = 0; i != N - 1; ++i) {
              step[i] = step[i+1];
            }
 
            step[N-1] = wall;
          }
 
          chi2_old = chi2_new;
        }
      }
 
      return chi2_old;
    }

◆ operator()() [2/2]

template<class JModel_t >

template<class JFunction_t , class T >

double JFIT::JSimplex< JModel_t >::operator()	(	const JFunction_t &	fit,
		T	__begin,
		T	__end,
		const JModel_t &	step )

inline

1D fit.

The given fit function should return the equivalent of chi2 for the current value of the given model and a given data point.

Parameters

fit	fit function
__begin	begin of data
__end	end of data
step	step direction

Definition at line 178 of file JSimplex.hh.

    {
      using namespace std;
      using namespace JPP;
 
      double lambda = 0.5;                                     // control parameter
      double factor = 1.0;                                     // multiplication factor
 
      double chi2_old = evaluate(fit, __begin, __end);
 
      for (int i = 0; numberOfIterations != MAXIMUM_ITERATIONS; ++numberOfIterations, ++i) {
 
        p1      = step;
        p1     *= lambda;
        value  += p1;
 
        const double chi2_new = evaluate(fit, __begin, __end);
 
        DEBUG("step: " << setw(3) << i << ' ' << FIXED(12,5) << chi2_old << ' ' << FIXED(12,5) << chi2_new << ' ' << FIXED(5,2) << lambda << endl);
 
        if (fabs(chi2_old - chi2_new) < EPSILON*fabs(chi2_old)) {
 
          if (chi2_new > chi2_old) {
 
            p1      = step;
            p1     *= lambda;
            value  -= p1;                                      // undo last step
 
            return chi2_old;
 
          } else {
 
            return chi2_new;
          }
        }
 
        if (chi2_new < chi2_old) {
 
          chi2_old = chi2_new;
 
        } else {
            
          p1      = step;
          p1     *= lambda;
          value  -=  p1;                                       // step back
          lambda  = -lambda;                                   // change direction
          
          if (i != 0) {
            factor = 0.5;                                      // reduce step size
          }
        }
        
        lambda = factor * lambda;
      }
 
      return chi2_old;
    }

◆ evaluate()

template<class JModel_t >

template<class JFunction_t , class T >

double JFIT::JSimplex< JModel_t >::evaluate	(	const JFunction_t &	fit,
		T	__begin,
		T	__end ) const

inlineprivate

Evaluate chi2 for given data set.

Parameters

fit	fit function
__begin	begin of data
__end	end of data

Definition at line 253 of file JSimplex.hh.

    {
      double chi2 = 0.0;
 
      for (T hit = __begin; hit != __end; ++hit) {
        chi2 += fit(value, *hit);
      }
 
      return chi2;
    }

Member Data Documentation

◆ MAXIMUM_ITERATIONS

template<class JModel_t >

int JFIT::JSimplex< JModel_t >::MAXIMUM_ITERATIONS = 1000

static

maximal number of iterations

maximal number of iterations.

Definition at line 237 of file JSimplex.hh.

◆ EPSILON

template<class JModel_t >

double JFIT::JSimplex< JModel_t >::EPSILON = 1.0e-4

static

maximal distance to minimum

maximal distance to minimum.

Definition at line 238 of file JSimplex.hh.

◆ value

template<class JModel_t >

JModel_t JFIT::JSimplex< JModel_t >::value

Definition at line 240 of file JSimplex.hh.

◆ step

template<class JModel_t >

std::vector<JModel_t> JFIT::JSimplex< JModel_t >::step

Definition at line 241 of file JSimplex.hh.

◆ numberOfIterations

template<class JModel_t >

int JFIT::JSimplex< JModel_t >::numberOfIterations

Definition at line 242 of file JSimplex.hh.

◆ p0

template<class JModel_t >

JModel_t JFIT::JSimplex< JModel_t >::p0

mutableprivate

Definition at line 264 of file JSimplex.hh.

◆ p1

template<class JModel_t >

JModel_t JFIT::JSimplex< JModel_t >::p1

mutableprivate

Definition at line 265 of file JSimplex.hh.

◆ wall

template<class JModel_t >

JModel_t JFIT::JSimplex< JModel_t >::wall

mutableprivate

Definition at line 266 of file JSimplex.hh.

◆ debug

template<class T >

int JEEP::JMessage< T >::debug = 0

staticinherited

debug level (default is off).

Definition at line 45 of file JMessage.hh.

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

JSimplex.hh

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ result_type

Constructor & Destructor Documentation

◆ JSimplex()

Member Function Documentation

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ evaluate()

Member Data Documentation

◆ MAXIMUM_ITERATIONS

◆ EPSILON

◆ value

◆ step

◆ numberOfIterations

◆ p0

◆ p1

◆ wall

◆ debug