JFIT::JGandalf< JModel_t > Class Template Reference

Fit method based on the Levenberg-Marquardt method. More...

#include <JGandalf.hh>

Inheritance diagram for JFIT::JGandalf< JModel_t >:

Classes
struct	result_type
	Data structure for return value of fit function. More...

Public Types
typedef JModel_t::parameter_type	parameter_type
	Data type of fit parameter. More...

Public Member Functions
	JGandalf ()
	Default constructor. More...
template<class JFunction_t , class T1 , class T2 >
double	operator() (const JFunction_t &fit, T1 __begin1, T1 __end1, T2 __begin2, T2 __end2)
	Multi-dimensional fit of two data sets. More...
template<class JFunction_t , class T >
double	operator() (const JFunction_t &fit, T __begin, T __end)
	Multi-dimensional fit of one data set. More...

Public Attributes
double	lambda
JModel_t	value
JModel_t	error
std::vector< parameter_type >	parameters
int	numberOfIterations
JMATH::JMatrixNS	H

Static Public Attributes
static int	MAXIMUM_ITERATIONS = 1000
	maximal number of iterations More...
static double	EPSILON = 1.0e-4
	maximal distance to minimum More...
static double	LAMBDA_MIN = 0.01
	minimal value control parameter More...
static double	LAMBDA_MAX = 100.0
	maximal value control parameter More...
static double	LAMBDA_UP = 9.0
	multiplication factor control parameter More...
static double	LAMBDA_DOWN = 11.0
	multiplication factor control parameter More...
static double	PIVOT = 1.0e-3
	minimal value diagonal element of matrix More...
static int	debug = 0
	debug level (default is off). More...

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

Private Attributes
double	chi2
JModel_t	gradient
JModel_t	previous
std::vector< double >	h

Detailed Description

template<class JModel_t>
class JFIT::JGandalf< JModel_t >

Fit method based on the Levenberg-Marquardt method.

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

The data member JGandalf::value corresponds to the start or final value of the model of the fit procedure and JGandalf::error to the uncertainties. The co-variance matrix is stored in data member JGandalf::H. The data member JGandalf::parameters is a list of pointers to those data members of the model that should be fitted. 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 data point, respectively. The function operator returns the chi2 of the fit.

Definition at line 45 of file JGandalf.hh.

Member Typedef Documentation

template<class JModel_t>

typedef JModel_t::parameter_type JFIT::JGandalf< JModel_t >::parameter_type

Data type of fit parameter.

Definition at line 56 of file JGandalf.hh.

Constructor & Destructor Documentation

template<class JModel_t>

JFIT::JGandalf< JModel_t >::JGandalf ( )

inline

Default constructor.

Definition at line 104 of file JGandalf.hh.

    {}

Member Function Documentation

template<class JModel_t>

template<class JFunction_t , class T1 , class T2 >

double JFIT::JGandalf< JModel_t >::operator() ( const JFunction_t &  fit, T1  __begin1, T1  __end1, T2  __begin2, T2  __end2  )

inline

Multi-dimensional fit of two data sets.

The fit function should return the equivalent of chi2 for the current value of the model and the given data point as well as the partial derivatives.

Parameters

fit	fit function
__begin1	begin of first data set
__end1	end of first data set
__begin2	begin of second data set
__end2	end of second data set

Returns

chi2

Definition at line 122 of file JGandalf.hh.

    {
      using namespace std;

      const int N = parameters.size();

      H.resize(N);
      h.resize(N);

      previous  = value;
      error     = JModel_t();
      lambda    = LAMBDA_MIN;

      double chi2_old = numeric_limits<double>::max();

      for (numberOfIterations = 0; numberOfIterations != MAXIMUM_ITERATIONS; ++numberOfIterations) {

        DEBUG("step:     " << numberOfIterations << endl);

        reset();

        evaluate(fit, __begin1, __end1);
        evaluate(fit, __begin2, __end2);

        DEBUG("lambda:   " << SCIENTIFIC(12,5) << lambda << endl);
        DEBUG("chi2:     " << FIXED     (12,5) << chi2   << endl);

        if (chi2 < chi2_old) {

          if (numberOfIterations != 0) {

            if (fabs(chi2_old - chi2) < EPSILON*fabs(chi2_old)) {
              return chi2;
            }

            lambda /= LAMBDA_DOWN;
          }

          chi2_old = chi2;
          previous = value;

        } else {

          value   = previous;
          lambda *= LAMBDA_UP;
            
          if (lambda > LAMBDA_MAX) {
            return chi2_old;                                   // no improvement found
          }

          reset();
          
          evaluate(fit, __begin1, __end1);
          evaluate(fit, __begin2, __end2);
        }

        DEBUG("Hesse matrix:" << endl);
        DEBUG(H << endl);


        // force definite positiveness

        for (int i = 0; i != N; ++i) {

          if (H(i,i) < PIVOT) {
            H(i,i) = PIVOT;
          }

          h[i] = 1.0 / sqrt(H(i,i));
        }


        // normalisation

        for (int i = 0; i != N; ++i) {
          for (int j = 0; j != i; ++j) {
            H(j,i) *= h[i] * h[j];
            H(i,j)  = H(j,i);
          }
        }
        
        for (int i = 0; i != N; ++i) {
          H(i,i) = 1.0 + lambda;
        }

        
        try {
          H.invert();
        }
        catch (const JException& error) {
          ERROR("JGandalf: " << error.what() << endl);
          return chi2_old;
        }
        
        
        for (int i = 0; i != N; ++i) {

          DEBUG("u[" << noshowpos << i << "] = " << showpos << FIXED(15,5) << value.*parameters[i]);

          for (int j = 0; j != N; ++j) {
            value.*parameters[i] -= H(i,j) * gradient.*parameters[j] * h[i] * h[j];
          }

          DEBUG(' ' << FIXED(15,5) << value.*parameters[i] << noshowpos << endl);

          error.*parameters[i] = h[i];
        }
      }

      return chi2_old;
    }

template<class JModel_t>

template<class JFunction_t , class T >

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

inline

Multi-dimensional fit of one data set.

The fit function should return the equivalent of chi2 for the current value of the model and the given data point as well as the partial derivatives.

Parameters

fit	fit function
__begin	begin of data
__end	end of data

Returns

chi2

Definition at line 249 of file JGandalf.hh.

    {
      return (*this)(fit, __begin, __end, __end, __end);
    }

template<class JModel_t>

void JFIT::JGandalf< JModel_t >::reset ( )

inlineprivate

Reset.

Definition at line 275 of file JGandalf.hh.

    {
      chi2     = 0.0;      
      gradient = JModel_t();

      H.reset();          
    }

template<class JModel_t>

template<class JFunction_t , class T >

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

inlineprivate

Evaluate fit for given data set.

Parameters

fit	fit function
__begin	begin of data
__end	end of data

Definition at line 292 of file JGandalf.hh.

    {
      for (T hit = __begin; hit != __end; ++hit) {
          
        const result_type& result = fit(value, *hit);

        chi2     += result.chi2;
        gradient += result.gradient;
        
        for (unsigned int i = 0; i != parameters.size(); ++i) {
          for (unsigned int j = i; j != parameters.size(); ++j) {
            H(i,j) += result.gradient.*parameters[i] * result.gradient.*parameters[j];
          }
        }
      }
    }

Member Data Documentation

template<class JModel_t>

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

static

maximal number of iterations

maximal number of iterations.

Definition at line 255 of file JGandalf.hh.

template<class JModel_t>

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

static

maximal distance to minimum

maximal distance to minimum.

Definition at line 256 of file JGandalf.hh.

template<class JModel_t>

double JFIT::JGandalf< JModel_t >::LAMBDA_MIN = 0.01

static

minimal value control parameter

Definition at line 257 of file JGandalf.hh.

template<class JModel_t>

double JFIT::JGandalf< JModel_t >::LAMBDA_MAX = 100.0

static

maximal value control parameter

Definition at line 258 of file JGandalf.hh.

template<class JModel_t>

double JFIT::JGandalf< JModel_t >::LAMBDA_UP = 9.0

static

multiplication factor control parameter

Definition at line 259 of file JGandalf.hh.

template<class JModel_t>

double JFIT::JGandalf< JModel_t >::LAMBDA_DOWN = 11.0

static

multiplication factor control parameter

Definition at line 260 of file JGandalf.hh.

template<class JModel_t>

double JFIT::JGandalf< JModel_t >::PIVOT = 1.0e-3

static

minimal value diagonal element of matrix

Definition at line 261 of file JGandalf.hh.

template<class JModel_t>

double JFIT::JGandalf< JModel_t >::lambda

Definition at line 264 of file JGandalf.hh.

template<class JModel_t>

JModel_t JFIT::JGandalf< JModel_t >::value

Definition at line 265 of file JGandalf.hh.

template<class JModel_t>

JModel_t JFIT::JGandalf< JModel_t >::error

Definition at line 266 of file JGandalf.hh.

template<class JModel_t>

std::vector<parameter_type> JFIT::JGandalf< JModel_t >::parameters

Definition at line 267 of file JGandalf.hh.

template<class JModel_t>

int JFIT::JGandalf< JModel_t >::numberOfIterations

Definition at line 268 of file JGandalf.hh.

template<class JModel_t>

JMATH::JMatrixNS JFIT::JGandalf< JModel_t >::H

Definition at line 269 of file JGandalf.hh.

template<class JModel_t>

double JFIT::JGandalf< JModel_t >::chi2

private

Definition at line 309 of file JGandalf.hh.

template<class JModel_t>

JModel_t JFIT::JGandalf< JModel_t >::gradient

private

Definition at line 310 of file JGandalf.hh.

template<class JModel_t>

JModel_t JFIT::JGandalf< JModel_t >::previous

private

Definition at line 311 of file JGandalf.hh.

template<class JModel_t>

std::vector<double> JFIT::JGandalf< JModel_t >::h

private

Definition at line 312 of file JGandalf.hh.

template<class T>

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

staticinherited

debug level (default is off).

Definition at line 43 of file JMessage.hh.

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

• JGandalf.hh