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 JFIT_LOCAL::JTypedef_t< JModel_t >::parameter_type	parameter_type
	Data type of fit parameter.

Public Member Functions
	JGandalf ()
	Default constructor.

template<class JFunction_t , class T , class ... Args>
result_type	operator() (const JFunction_t &fit, T __begin, T __end, Args ...args)
	Multi-dimensional fit of multiple data sets.

Public Attributes
std::vector< parameter_type >	parameters
	fit parameters

int	numberOfIterations
	number of iterations

double	lambda
	control parameter

JModel_t	value
	value

JModel_t	error
	error

JMATH::JMatrixNS	V
	Hesse matrix.

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

static double	EPSILON = 1.0e-3
	maximal distance to minimum

static bool	EPSILON_ABSOLUTE = false
	set epsilon to absolute difference instead of relative

static double	LAMBDA_MIN = 0.01
	minimal value control parameter

static double	LAMBDA_MAX = 100.0
	maximal value control parameter

static double	LAMBDA_UP = 10.0
	multiplication factor control parameter

static double	LAMBDA_DOWN = 10.0
	multiplication factor control parameter

static double	PIVOT = std::numeric_limits<double>::epsilon()
	minimal value diagonal element of Hesse matrix

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

Private Member Functions
void	reset ()
	Reset current parameters.

template<class JFunction_t , class T , class ... Args>
void	update (const JFunction_t &fit, T __begin, T __end, Args ...args)
	Recursive method to update current parameters.

template<class JFunction_t >
void	update (const JFunction_t &fit)
	Termination method to update current parameters.

Static Private Member Functions
static double	get (const JModel_t &model, double JModel_t::*parameter)
	Read/write access to parameter value by data member.

static double &	get (JModel_t &model, double JModel_t::*parameter)
	Read/write access to parameter value by data member.

static double	get (const JModel_t &model, const size_t index)
	Read/write access to parameter value by index.

static double &	get (JModel_t &model, const size_t index)
	Read/write access to parameter value by index.

static double	get (const JModel_t &model, const int index)
	Read/write access to parameter value by index.

static double &	get (JModel_t &model, const int index)
	Read/write access to parameter value by index.

Private Attributes
std::vector< double >	h

JMATH::JVectorND	x

struct {

result_type result

}	current

struct {

JModel_t value

result_type result

}	previous

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 capabilities.

The data member JGandalf::value corresponds to the start c.q. 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::V.
The data member JGandalf::parameters constitutes a list of those parameters of the model that should actually be fitted.
For this, the model should contain the type definition for parameter_type.
Normally, this type definition corresponds to a pointer to a data member of the model.
If not defined, the parameters are assumed to be data members of type double.
Alternatively, the type definition can be size_t or int.
In that case, the model should provide for the element access operator[].
The first template parameter in the function operator should provide for an implementation of the actual fit function.
This function should return the data type JGandalf::result_type.
This data structure comprises the values of the chi2 and the gradient for a given data point.
The function operator returns the minimal chi2 and summed gradient of all data points.

Definition at line 85 of file JGandalf.hh.

Member Typedef Documentation

◆ parameter_type

template<class JModel_t >

JFIT_LOCAL::JTypedef_t<JModel_t>::parameter_type JFIT::JGandalf< JModel_t >::parameter_type

Data type of fit parameter.

Definition at line 96 of file JGandalf.hh.

Constructor & Destructor Documentation

◆ JGandalf()

template<class JModel_t >

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

inline

Default constructor.

Definition at line 144 of file JGandalf.hh.

145 {}

Member Function Documentation

◆ operator()()

template<class JModel_t >

template<class JFunction_t , class T , class ... Args>

result_type JFIT::JGandalf< JModel_t >::operator()	(	const JFunction_t &	fit,
		T	__begin,
		T	__end,
		Args ...	args )

inline

Multi-dimensional fit of multiple data sets.

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

Parameters

fit	fit function
__begin	begin of data
__end	end of data
args	optional data

Returns: chi2 and gradient

Definition at line 161 of file JGandalf.hh.

    {
      using namespace std;
      using namespace JPP;
 
      // note that all model values should be assigned to the start value of the model before use
      // because the actual list of model parameters can vary from fit to fit
      // (e.g. if model consists of a container).
 
      const size_t N = parameters.size();
 
      V.resize(N);
      h.resize(N);
      x.resize(N);
 
      previous.result.chi2 = numeric_limits<double>::max();
 
      current.result.chi2     = numeric_limits<double>::max();
      current.result.gradient = value;
      current.result.gradient = zero;
 
      error     = value;
      error     = zero;
 
      lambda    = LAMBDA_MIN;
 
      for (numberOfIterations = 0; numberOfIterations != MAXIMUM_ITERATIONS; ++numberOfIterations) {
 
        DEBUG("step:     " << numberOfIterations << endl);
 
        reset();
 
        update(fit, __begin, __end, args...);
 
        DEBUG("lambda:   " << FIXED(12,5) << lambda              << endl);
        DEBUG("chi2:     " << FIXED(12,5) << current.result.chi2 << endl);
 
        if (current.result.chi2 < previous.result.chi2) {
 
          if (numberOfIterations != 0) {
 
            const double tolerance = EPSILON * (EPSILON_ABSOLUTE ? 1.0 : fabs(previous.result.chi2)); 
 
            if (fabs(previous.result.chi2 - current.result.chi2) <= tolerance) {
 
              // normal end
 
              const result_type result = current.result;
 
              reset();
 
              update(fit, __begin, __end, args...);
 
              try {
                V.invert();
              }
              catch (const exception& error) {}
 
              for (size_t i = 0; i != N; ++i) {
                get(error, parameters[i]) = sqrt(V(i,i));
              }
 
              return result;
            }
 
            if (lambda > LAMBDA_MIN) {
              lambda /= LAMBDA_DOWN;
            }
          }
 
          // store current values
 
          previous.value  = value;
          previous.result = current.result;
 
        } else {
 
          value   = previous.value;                                 // restore value
 
          lambda *= LAMBDA_UP;
          
          if (lambda > LAMBDA_MAX) {
            break;
          }
 
          reset();
 
          update(fit, __begin, __end, args...);
        }
 
        DEBUG("Hesse matrix:" << endl << V << endl);
 
        // force definite positiveness
 
        for (size_t i = 0; i != N; ++i) {
 
          if (V(i,i) < PIVOT) {
            V(i,i) = PIVOT;
          }
 
          h[i] = 1.0 / sqrt(V(i,i));
        }
 
        // normalisation
        
        for (size_t row = 0; row != N; ++row) {
          for (size_t col = 0; col != row; ++col) {
            V(row,col) *= h[row] * h[col];
            V(col,row)  = V(row,col);
          }
        }
        
        for (size_t i = 0; i != N; ++i) {
          V(i,i) = 1.0 + lambda;
        }
 
        // solve A x = b
 
        for (size_t col = 0; col != N; ++col) {
          x[col] = h[col] * get(current.result.gradient, parameters[col]);
        }
 
        try {
          V.solve(x);
        }
        catch (const exception& error) {
 
          ERROR("JGandalf: " << error.what() << endl << V << endl);
 
          break;
        }
 
        // update value
 
        for (size_t row = 0; row != N; ++row) {
 
          DEBUG("u[" << noshowpos << setw(3) << row << "] = " << showpos << FIXED(15,5) << get(value, parameters[row]));
 
          get(value, parameters[row]) -= h[row] * x[row];
 
          DEBUG(" -> " << FIXED(15,5) << get(value, parameters[row]) << noshowpos << endl);
        }
 
        model(value);
      }
 
      // abnormal end
 
      const result_type result = previous.result;
 
      value   = previous.value;                                     // restore value
 
      reset();
 
      update(fit, __begin, __end, args...);
 
      try {
        V.invert();
      }
      catch (const exception& error) {}
 
      for (size_t i = 0; i != N; ++i) {
        get(error, parameters[i]) = sqrt(V(i,i));
      }
 
      return result;
    }

◆ reset()

template<class JModel_t >

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

inlineprivate

Reset current parameters.

Definition at line 350 of file JGandalf.hh.

    {
      using namespace JPP;
 
      current.result.chi2     = 0.0;
      current.result.gradient = zero;
 
      V.reset();          
    }

◆ update() [1/2]

template<class JModel_t >

template<class JFunction_t , class T , class ... Args>

void JFIT::JGandalf< JModel_t >::update	(	const JFunction_t &	fit,
		T	__begin,
		T	__end,
		Args ...	args )

inlineprivate

Recursive method to update current parameters.

Parameters

fit	fit function
__begin	begin of data
__end	end of data
args	optional data

Definition at line 370 of file JGandalf.hh.

    {
      for (T i = __begin; i != __end; ++i) {
 
        const result_type& result = fit(value, *i);
 
        current.result.chi2     += result.chi2;
        current.result.gradient += result.gradient;
 
        for (size_t row = 0; row != parameters.size(); ++row) {
          for (size_t col = row; col != parameters.size(); ++col) {
            V(row,col) += get(result.gradient, parameters[row]) * get(result.gradient, parameters[col]);
          }
        }
      }
 
      update(fit, args...);
    }

◆ update() [2/2]

template<class JModel_t >

template<class JFunction_t >

void JFIT::JGandalf< JModel_t >::update ( const JFunction_t & fit )

inlineprivate

Termination method to update current parameters.

Parameters

fit	fit function

Definition at line 396 of file JGandalf.hh.

    {
      for (size_t row = 0; row != parameters.size(); ++row) {
        for (size_t col = 0; col != row; ++col) {
          V(row,col) = V(col,row);
        }
      }
    }

◆ get() [1/6]

template<class JModel_t >

static double JFIT::JGandalf< JModel_t >::get	(	const JModel_t &	model,
		double JModel_t::*	parameter )

inlinestaticprivate

Read/write access to parameter value by data member.

Parameters

model	model
parameter	parameter

Returns: value

Definition at line 413 of file JGandalf.hh.

    {
      return model.*parameter;
    }

◆ get() [2/6]

template<class JModel_t >

static double & JFIT::JGandalf< JModel_t >::get	(	JModel_t &	model,
		double JModel_t::*	parameter )

inlinestaticprivate

Read/write access to parameter value by data member.

Parameters

model	model
parameter	parameter

Returns: value

Definition at line 426 of file JGandalf.hh.

    {
      return model.*parameter;
    }

◆ get() [3/6]

template<class JModel_t >

static double JFIT::JGandalf< JModel_t >::get	(	const JModel_t &	model,
		const size_t	index )

inlinestaticprivate

Read/write access to parameter value by index.

Parameters

model	model
index	index

Returns: value

Definition at line 439 of file JGandalf.hh.

    {
      return model[index];
    }

◆ get() [4/6]

template<class JModel_t >

static double & JFIT::JGandalf< JModel_t >::get	(	JModel_t &	model,
		const size_t	index )

inlinestaticprivate

Read/write access to parameter value by index.

Parameters

model	model
index	index

Returns: value

Definition at line 452 of file JGandalf.hh.

    {
      return model[index];
    }

◆ get() [5/6]

template<class JModel_t >

static double JFIT::JGandalf< JModel_t >::get	(	const JModel_t &	model,
		const int	index )

inlinestaticprivate

Read/write access to parameter value by index.

Parameters

model	model
index	index

Returns: value

Definition at line 465 of file JGandalf.hh.

    {
      return model[index];
    }

◆ get() [6/6]

template<class JModel_t >

static double & JFIT::JGandalf< JModel_t >::get	(	JModel_t &	model,
		const int	index )

inlinestaticprivate

Read/write access to parameter value by index.

Parameters

model	model
index	index

Returns: value

Definition at line 478 of file JGandalf.hh.

    {
      return model[index];
    }

Member Data Documentation

◆ MAXIMUM_ITERATIONS

template<class JModel_t >

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

static

maximal number of iterations

maximal number of iterations.

Definition at line 330 of file JGandalf.hh.

◆ EPSILON

template<class JModel_t >

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

static

maximal distance to minimum

maximal distance to minimum.

Definition at line 331 of file JGandalf.hh.

◆ EPSILON_ABSOLUTE

template<class JModel_t >

bool JFIT::JGandalf< JModel_t >::EPSILON_ABSOLUTE = false

static

set epsilon to absolute difference instead of relative

set epsilon to absolute difference instead of relative.

Definition at line 332 of file JGandalf.hh.

◆ LAMBDA_MIN

template<class JModel_t >

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

static

minimal value control parameter

Definition at line 333 of file JGandalf.hh.

◆ LAMBDA_MAX

template<class JModel_t >

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

static

maximal value control parameter

Definition at line 334 of file JGandalf.hh.

◆ LAMBDA_UP

template<class JModel_t >

double JFIT::JGandalf< JModel_t >::LAMBDA_UP = 10.0

static

multiplication factor control parameter

Definition at line 335 of file JGandalf.hh.

◆ LAMBDA_DOWN

template<class JModel_t >

double JFIT::JGandalf< JModel_t >::LAMBDA_DOWN = 10.0

static

multiplication factor control parameter

Definition at line 336 of file JGandalf.hh.

◆ PIVOT

template<class JModel_t >

double JFIT::JGandalf< JModel_t >::PIVOT = std::numeric_limits<double>::epsilon()

static

minimal value diagonal element of Hesse matrix

minimal value diagonal element of matrix

Definition at line 337 of file JGandalf.hh.

◆ parameters

template<class JModel_t >

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

fit parameters

Definition at line 339 of file JGandalf.hh.

◆ numberOfIterations

template<class JModel_t >

int JFIT::JGandalf< JModel_t >::numberOfIterations

number of iterations

Definition at line 340 of file JGandalf.hh.

◆ lambda

template<class JModel_t >

double JFIT::JGandalf< JModel_t >::lambda

control parameter

Definition at line 341 of file JGandalf.hh.

◆ value

template<class JModel_t >

JModel_t JFIT::JGandalf< JModel_t >::value

value

Definition at line 342 of file JGandalf.hh.

◆ error

template<class JModel_t >

JModel_t JFIT::JGandalf< JModel_t >::error

error

Definition at line 343 of file JGandalf.hh.

◆ V

template<class JModel_t >

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

Hesse matrix.

Definition at line 344 of file JGandalf.hh.

◆ h

template<class JModel_t >

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

private

Definition at line 483 of file JGandalf.hh.

◆ x

template<class JModel_t >

JMATH::JVectorND JFIT::JGandalf< JModel_t >::x

private

Definition at line 484 of file JGandalf.hh.

◆ result

template<class JModel_t >

result_type JFIT::JGandalf< JModel_t >::result

Definition at line 487 of file JGandalf.hh.

◆ [struct]

struct { ... } JFIT::JGandalf< JModel_t >::current

◆ [struct]

struct { ... } JFIT::JGandalf< JModel_t >::previous

◆ 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:

JGandalf.hh

Classes

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Private Member Functions

Static Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ parameter_type

Constructor & Destructor Documentation

◆ JGandalf()

Member Function Documentation

◆ operator()()

◆ reset()

◆ update() [1/2]

◆ update() [2/2]

◆ get() [1/6]

◆ get() [2/6]

◆ get() [3/6]

◆ get() [4/6]

◆ get() [5/6]

◆ get() [6/6]

Member Data Documentation

◆ MAXIMUM_ITERATIONS

◆ EPSILON

◆ EPSILON_ABSOLUTE

◆ LAMBDA_MIN

◆ LAMBDA_MAX

◆ LAMBDA_UP

◆ LAMBDA_DOWN

◆ PIVOT

◆ parameters

◆ numberOfIterations

◆ lambda

◆ value

◆ error

◆ V

◆ h

◆ x

◆ result

◆ [struct]

◆ [struct]

◆ debug