Regressor function object for JPoint4D fit using JGandalf minimiser. More...

#include <JShowerBrightPointRegressor.hh>

Inheritance diagram for JFIT::JRegressor< JPoint4D, JGandalf >:

Public Types
typedef JTOOLS::JSplineFunction1S_t	JFunction1D_t

typedef JTOOLS::JMAPLIST < JTOOLS::JPolint2FunctionalMap, JTOOLS::JPolint1FunctionalGridMap > ::maplist	JPDFMapList_t

typedef JPHYSICS::JPDFTable < JFunction1D_t, JPDFMapList_t >	JPDF_t

typedef JGandalf< JPoint4D >	minimiser_type

typedef JRegressor< JPoint4D, JGandalf >	regressor_type

typedef minimiser_type::result_type	result_type

typedef JPoint4D::parameter_type	parameter_type
	Data type of fit parameter. More...

Public Member Functions
	JRegressor (const std::string &fileDescriptor, const double TTS, const int numberOfPoints=25, const double epsilon=1.0e-10)
	Parameterized constructor. More...

result_type	operator() (const JPoint4D &vx, const JHitW0 &hit) const
	Fit function. More...

JPDF_t::result_type	getH0 (const double R_Hz, const double t1) const
	Get background hypothesis value for time differentiated PDF. More...

JPDF_t::result_type	getH1 (const double D, const double ct, const double t, const double E) const
	Get signal hypothesis value for bright point emission PDF. More...

double	getRmax () const
	Get maximal road width of PDF. More...

result_type	operator() (const JPoint4D &value, T __begin, T __end)
	Global fit. More...

result_type	operator() (const JFunction_t &fit, T __begin, T __end, Args...args)
	Multi-dimensional fit of two data sets. More...

Public Attributes
JPDF_t	pdf [NUMBER_OF_PDFS]
	PDF. More...

double	E_GeV
	Energy of the shower [GeV]. More...

double	lambda

JPoint4D	value

JPoint4D	error

std::vector< parameter_type >	parameters

int	numberOfIterations

JMATH::JMatrixNS	H

Static Public Attributes
static JTimeRange	T_ns
	Time window with respect to Cherenkov hypothesis [ns]. More...

static double	Vmax_npe = std::numeric_limits<double>::max()
	Maximal integral of PDF [npe]. More...

static const int	NUMBER_OF_PDFS = 2

static const JPDFType_t	pdf_t [NUMBER_OF_PDFS]
	PDF types. More...

static int	MAXIMUM_ITERATIONS
	maximal number of iterations More...

static double	EPSILON
	maximal distance to minimum More...

static double	LAMBDA_MIN
	minimal value control parameter More...

static double	LAMBDA_MAX
	maximal value control parameter More...

static double	LAMBDA_UP
	multiplication factor control parameter More...

static double	LAMBDA_DOWN
	multiplication factor control parameter More...

static double	PIVOT
	minimal value diagonal element of matrix More...

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

Detailed Description

template<>
struct JFIT::JRegressor< JPoint4D, JGandalf >

Regressor function object for JPoint4D fit using JGandalf minimiser.

Definition at line 44 of file JShowerBrightPointRegressor.hh.

Member Typedef Documentation

typedef JTOOLS::JSplineFunction1S_t JFIT::JRegressor< JPoint4D, JGandalf >::JFunction1D_t

Definition at line 49 of file JShowerBrightPointRegressor.hh.

typedef JTOOLS::JMAPLIST<JTOOLS::JPolint2FunctionalMap, JTOOLS::JPolint1FunctionalGridMap>::maplist JFIT::JRegressor< JPoint4D, JGandalf >::JPDFMapList_t

Definition at line 51 of file JShowerBrightPointRegressor.hh.

typedef JPHYSICS::JPDFTable<JFunction1D_t, JPDFMapList_t> JFIT::JRegressor< JPoint4D, JGandalf >::JPDF_t

Definition at line 52 of file JShowerBrightPointRegressor.hh.

typedef JGandalf <JPoint4D > JFIT::JAbstractRegressor< JPoint4D , JGandalf >::minimiser_type

inherited

Definition at line 78 of file JRegressor.hh.

typedef JRegressor<JPoint4D , JGandalf > JFIT::JAbstractRegressor< JPoint4D , JGandalf >::regressor_type

inherited

Definition at line 79 of file JRegressor.hh.

typedef minimiser_type::result_type JFIT::JAbstractRegressor< JPoint4D , JGandalf >::result_type

inherited

Definition at line 80 of file JRegressor.hh.

typedef JPoint4D ::parameter_type JFIT::JGandalf< JPoint4D >::parameter_type

inherited

Data type of fit parameter.

Definition at line 63 of file JGandalf.hh.

Constructor & Destructor Documentation

JFIT::JRegressor< JPoint4D, JGandalf >::JRegressor	(	const std::string &	fileDescriptor,
		const double	TTS,
		const int	numberOfPoints = `25`,
		const double	epsilon = `1.0e-10`
	)

inline

Parameterized constructor.

The PDF file descriptor should contain the wild card character JPHYSICS::WILD_CARD which will be replaced by the corresponding PDF types.

Parameters

fileDescriptor	PDF file descriptor
TTS	TTS [ns]
numberOfPoints	number of points for Gauss-Hermite integration of TTS
epsilon	precision for Gauss-Hermite integration of TTS

Definition at line 66 of file JShowerBrightPointRegressor.hh.

                                                            :
       E_GeV(0.0)
     {
       using namespace std;
       using namespace JPP;
       
       const JPDF_t::JSupervisor supervisor(new JPDF_t::JDefaultResult(JMATH::zero));
       
       for (int i = 0; i != NUMBER_OF_PDFS; ++i) {
         
         try {
 
           const string file_name = getFilename(fileDescriptor, pdf_t[i]);
           
           NOTICE("loading PDF from file " << file_name << "... " << flush);
 
           pdf[i].load(file_name.c_str());
 
           NOTICE("OK" << endl);
 
           pdf[i].setExceptionHandler(supervisor);
         }
         catch(const JException& error) {
           FATAL(error.what() << endl);
         }
       }
 
       // Add PDFs
       for (int i = 1; i < NUMBER_OF_PDFS; i += 2) {
   
         pdf[ i ].add(pdf[i-1]); 
 
         JPDF_t buffer;
 
         pdf[i-1].swap(buffer);
         
         if        (TTS > 0.0) {
           pdf[i].blur(TTS, numberOfPoints, epsilon);
         } else if (TTS < 0.0) {
           ERROR("Illegal value of TTS [ns]: " << TTS << endl);
         }
       }    
     }

Member Function Documentation

result_type JFIT::JRegressor< JPoint4D, JGandalf >::operator()	(	const JPoint4D &	vx,
		const JHitW0 &	hit
	)		const

inline

Fit function.

This method is used to determine the chi2 and gradient of given hit with respect a bright point emitting isotropically

JHitW0 refers to a data structure which should have the following member methods:

double getX(); // [m]
double getY(); // [m]
double getZ(); // [m]
double getDX(); // [u]
double getDY(); // [u]
double getDZ(); // [u]
double getT(); // [ns]

Parameters

vx	shower vertex
hit	hit

Returns: chi2 and gradient

Definition at line 130 of file JShowerBrightPointRegressor.hh.

     {      
       using namespace JPP;
 
       JPosition3D D(hit.getPosition());
       JDirection3D U(hit.getDirection());
 
       D.sub(vx.getPosition());
 
       double ct = U.getDot(D) / D.getLength();
       if (ct > +1.0) { ct = +1.0; }
       if (ct < -1.0) { ct = -1.0; }
 
       const double t = vx.getT() + (D.getLength() * getIndexOfRefraction() * getInverseSpeedOfLight());
 
       const double dt = T_ns.constrain(hit.getT() - t);
 
       JPDF_t::result_type H0 = getH0(hit.getR(), dt);  // getH0 = Get background hypothesis value 
       JPDF_t::result_type H1 = getH1(D.getLength(), ct, dt, E_GeV);  // getH1 = Get signal hypothesis value
 
       if (get_value(H1) >= Vmax_npe) {
         H1 *= Vmax_npe / get_value(H1);
       }
 
       H1 += H0;  // now H1 is signal + background
 
       result_type result;
       
       result.chi2 = H1.getChi2() - H0.getChi2();  // Likelihood ratio
 
       /*
        * Here it is evaluated: d(chi2)/d(ct) * d(ct)/d(x0,y0,z0,t0)
        */
       result.gradient = JPoint4D(JVector3D(-getIndexOfRefraction() * D.getX() / D.getLength(),    // d(ct)/d(x0) 
                                            -getIndexOfRefraction() * D.getY() / D.getLength(),    // d(ct)/d(y0) 
                                            -getIndexOfRefraction() * D.getZ() / D.getLength()),   // d(ct)/d(z0) 
                                  getSpeedOfLight());                                              // d(ct)/d(t0)
       
       result.gradient.mul(getInverseSpeedOfLight() * (H1.getDerivativeOfChi2() -
                                                       H0.getDerivativeOfChi2()));                 // x d(chi2)/d(ct1)
 
       return result;
 
     }

JPDF_t::result_type JFIT::JRegressor< JPoint4D, JGandalf >::getH0	(	const double	R_Hz,
		const double	t1
	)		const

inline

Get background hypothesis value for time differentiated PDF.

Parameters

R_Hz	rate [Hz]
t1	time [ns]

Returns: hypothesis value

Definition at line 182 of file JShowerBrightPointRegressor.hh.

     {
       using namespace JPP;
 
       return JPDF_t::result_type(R_Hz * 1e-9, t1, T_ns);
     }

JPDF_t::result_type JFIT::JRegressor< JPoint4D, JGandalf >::getH1	(	const double	D,
		const double	ct,
		const double	t,
		const double	E
	)		const

inline

Get signal hypothesis value for bright point emission PDF.

Parameters

D	HIT distance from shower vertex [m]
ct	cosine of the HIT angle
t	arrival time of the light
E	shower energy [GeV]

Returns: hypothesis value

Definition at line 199 of file JShowerBrightPointRegressor.hh.

     {
       using namespace JPP;
 
       JPDF_t::result_type h1 = JMATH::zero;
         
       for (int i = 0; i != NUMBER_OF_PDFS; ++i) {
 
         if (!pdf[i].empty() && D <= pdf[i].getXmax()) {
 
           try {
 
             JPDF_t::result_type y1 = E * pdf[i](std::max(D, pdf[i].getXmin()), ct, t);
           
             if (get_value(y1) > 0.0) {
               h1 += y1;
             }
           
           }
           catch(JLANG::JException& error) {
             ERROR(error << std::endl);
           }
         }
       }
 
       return h1;
     }

double JFIT::JRegressor< JPoint4D, JGandalf >::getRmax ( ) const

inline

Get maximal road width of PDF.

Returns: road width [m]

Definition at line 235 of file JShowerBrightPointRegressor.hh.

     {
       using namespace JPP;
 
       double xmax = 0.0;
 
       for (int i = 0; i != NUMBER_OF_PDFS; ++i) {
 
         if (!pdf[i].empty() && pdf[i].getXmax() > xmax) {
           xmax = pdf[i].getXmax();
         }
         
       }
 
       return xmax;
     }

result_type JFIT::JAbstractRegressor< JPoint4D , JGandalf >::operator()	(	const JPoint4D &	value,
		T	__begin,
		T	__end
	)

inlineinherited

Global fit.

Parameters

value	start value
__begin	begin of data set
__end	end of data set

Returns: chi2

Definition at line 92 of file JRegressor.hh.

     {
       static_cast<minimiser_type&>(*this).value = value;
 
       return static_cast<minimiser_type&>(*this)(static_cast<regressor_type&>(*this), __begin, __end);
     }

result_type JFIT::JGandalf< JPoint4D >::operator()	(	const JFunction_t &	fit,
		T	__begin,
		T	__end,
		Args...	args
	)

inlineinherited

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
__begin	begin of data
__end	end of data

Returns: chi2

Definition at line 127 of file JGandalf.hh.

     {
       using namespace std;
       using namespace JPP;
 
       const int N = parameters.size();
 
       H.resize(N);
       h.resize(N);
 
       previous  = value;
 
       successor.gradient = value;
       successor.gradient = zero;
 
       error     = value;
       error     = zero;
 
       lambda    = LAMBDA_MIN;
 
       result_type precessor = result_type(numeric_limits<double>::max(), value);
 
       for (numberOfIterations = 0; numberOfIterations != MAXIMUM_ITERATIONS; ++numberOfIterations) {
 
         DEBUG("step:     " << numberOfIterations << endl);
 
         reset();
 
         __evaluate__(fit, __begin, __end, args...);
 
         DEBUG("lambda:   " << SCIENTIFIC(12,5) << lambda         << endl);
         DEBUG("chi2:     " << FIXED     (12,5) << successor.chi2 << endl);
 
         if (successor.chi2 < precessor.chi2) {
 
           if (numberOfIterations != 0) {
 
             if (fabs(precessor.chi2 - successor.chi2) < EPSILON*fabs(precessor.chi2)) {
               return successor;
             }
 
             if (lambda > LAMBDA_MIN) {
               lambda /= LAMBDA_DOWN;
             }
           }
 
           precessor = successor;
           previous  = value;
 
         } else {
           
           value   = previous;
           lambda *= LAMBDA_UP;
           
           if (lambda > LAMBDA_MAX) {
             return precessor;                                   // no improvement found
           }
 
           reset();
           
           __evaluate__(fit, __begin, __end, args...);
         }
 
         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 precessor;
         }
         
         
         for (int i = 0; i != N; ++i) {
 
           DEBUG("u[" << noshowpos << i << "] = " << showpos << FIXED(15,5) << alias(value, parameters[i]));
 
           for (int j = 0; j != N; ++j) {
             alias(value, parameters[i]) -= H(i,j) * alias(successor.gradient, parameters[j]) * h[i] * h[j];
           }
           
           DEBUG(' ' << FIXED(15,5) << alias(value, parameters[i]) << noshowpos << endl);
 
           alias(error, parameters[i]) = h[i];
         }
       }
 
       return precessor;
     }