Regressor function object for JLine3Z fit using JGandalf minimiser. More...

#include <JLine3ZRegressor.hh>

Inheritance diagram for JFIT::JRegressor< JLine3Z, JGandalf >:

Public Types
typedef JTOOLS::JSplineFunction1S_t	JFunction1D_t

typedef JTOOLS::JMAPLIST < JTOOLS::JPolint1FunctionalMap, JTOOLS::JPolint0FunctionalGridMap, JTOOLS::JPolint0FunctionalGridMap > ::maplist	JPDFMaplist_t

typedef JPHYSICS::JPDFTable < JFunction1D_t, JPDFMaplist_t >	JPDF_t
	time dependent PDF More...

typedef JTOOLS::JMAPLIST < JTOOLS::JPolint1FunctionalMapH, JTOOLS::JPolint1FunctionalGridMap, JTOOLS::JPolint1FunctionalGridMap > ::maplist	JNPEMaplist_t

typedef JPHYSICS::JNPETable < double, double, JNPEMaplist_t >	JNPE_t
	time integrated PDF More...

typedef JGandalf< JLine3Z >	minimiser_type

typedef JRegressor< JLine3Z, JGandalf >	regressor_type

typedef minimiser_type::result_type	result_type

typedef JLine3Z::parameter_type	parameter_type
	Data type of fit parameter. More...

Public Member Functions
	JRegressor ()
	Default constructor. More...

	JRegressor (const std::string &fileDescriptor, const double TTS, const int numberOfPoints=25, const double epsilon=1.0e-10)
	Constructor. More...

template<class JHit_t >
result_type	operator() (const JLine3Z &track, const JHit_t &hit) const
	Fit function. More...

result_type	operator() (const JLine3Z &track, const JPMTW0 &pmt) 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 E, const double R, const double theta, const double phi, const double t1) const
	Get signal hypothesis value for time differentiated PDF. More...

JNPE_t::result_type	getH0 (const double R_Hz) const
	Get background hypothesis value for time integrated PDF. More...

JNPE_t::result_type	getH1 (const double E, const double R, const double theta, const double phi) const
	Get signal hypothesis value for time integrated PDF. More...

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

void	setRmax (const double Rmax)
	Set maximal road width of PDF. More...

result_type	operator() (const JLine3Z &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 multiple data sets. More...

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

JNPE_t	npe [NUMBER_OF_PDFS]
	PDF. More...

double	E_GeV
	Energy of muon at vertex [GeV]. More...

JLANG::JSharedPointer < JMEstimator >	estimator
	M-Estimator function. More...

std::vector< parameter_type >	parameters
	fit parameters More...

int	numberOfIterations
	number of iterations More...

double	lambda
	control parameter More...

JLine3Z	value
	value More...

JLine3Z	error
	error More...

JMATH::JMatrixNS	V
	Hesse matrix. More...

result_type	result

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 double	Rmin_m = 0.1
	Minimal distance of [m]. More...

static const int	NUMBER_OF_PDFS = 6

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 Hesse matrix More...

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

Detailed Description

template<>
struct JFIT::JRegressor< JLine3Z, JGandalf >

Regressor function object for JLine3Z fit using JGandalf minimiser.

Definition at line 111 of file JLine3ZRegressor.hh.

Member Typedef Documentation

typedef JTOOLS::JSplineFunction1S_t JFIT::JRegressor< JLine3Z, JGandalf >::JFunction1D_t

Definition at line 116 of file JLine3ZRegressor.hh.

typedef JTOOLS::JMAPLIST<JTOOLS::JPolint1FunctionalMap, JTOOLS::JPolint0FunctionalGridMap, JTOOLS::JPolint0FunctionalGridMap>::maplist JFIT::JRegressor< JLine3Z, JGandalf >::JPDFMaplist_t

Definition at line 119 of file JLine3ZRegressor.hh.

typedef JPHYSICS::JPDFTable<JFunction1D_t, JPDFMaplist_t> JFIT::JRegressor< JLine3Z, JGandalf >::JPDF_t

time dependent PDF

Definition at line 120 of file JLine3ZRegressor.hh.

typedef JTOOLS::JMAPLIST<JTOOLS::JPolint1FunctionalMapH, JTOOLS::JPolint1FunctionalGridMap, JTOOLS::JPolint1FunctionalGridMap>::maplist JFIT::JRegressor< JLine3Z, JGandalf >::JNPEMaplist_t

Definition at line 124 of file JLine3ZRegressor.hh.

typedef JPHYSICS::JNPETable<double, double, JNPEMaplist_t> JFIT::JRegressor< JLine3Z, JGandalf >::JNPE_t

time integrated PDF

Definition at line 125 of file JLine3ZRegressor.hh.

typedef JGandalf <JLine3Z > JFIT::JAbstractRegressor< JLine3Z , JGandalf >::minimiser_type

inherited

Definition at line 78 of file JRegressor.hh.

typedef JRegressor<JLine3Z , JGandalf > JFIT::JAbstractRegressor< JLine3Z , JGandalf >::regressor_type

inherited

Definition at line 79 of file JRegressor.hh.

typedef minimiser_type::result_type JFIT::JAbstractRegressor< JLine3Z , JGandalf >::result_type

inherited

Definition at line 80 of file JRegressor.hh.

typedef JLine3Z ::parameter_type JFIT::JGandalf< JLine3Z >::parameter_type

inherited

Data type of fit parameter.

Definition at line 63 of file JGandalf.hh.

Constructor & Destructor Documentation

JFIT::JRegressor< JLine3Z, JGandalf >::JRegressor ( )

inline

Default constructor.

Definition at line 130 of file JLine3ZRegressor.hh.

131 {};

JFIT::JRegressor< JLine3Z, JGandalf >::JRegressor	(	const std::string &	fileDescriptor,
		const double	TTS,
		const int	numberOfPoints = `25`,
		const double	epsilon = `1.0e-10`
	)

inline

Constructor.

The PDF file descriptor should contain the wild card character JPHYSICS::WILD_CARD which will be replaced by the corresponding PDF types listed in JRegressor<JLine3Z, JGandalf>::pdf_t.

The TTS corresponds to the additional time smearing applied to the PDFs.

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 147 of file JLine3ZRegressor.hh.

                                                             :
       E_GeV(0.0),
       estimator(new JMEstimatorNormal())
     {
       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);
         }
 
         npe[ i ] = JNPE_t(pdf[i]);
       }
     }

Member Function Documentation

template<class JHit_t >

result_type JFIT::JRegressor< JLine3Z, JGandalf >::operator()	(	const JLine3Z &	track,
		const JHit_t &	hit
	)		const

inline

Fit function.

This method is used to determine the chi2 and gradient of given hit with respect to trajectory of muon.

The template argument JHit_t 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

track	track
hit	hit

Returns: chi2 and gradient

Definition at line 217 of file JLine3ZRegressor.hh.

     {
       using namespace JPP;
       
       JPosition3D  D(hit.getX(),  hit.getY(),  hit.getZ());
       JDirection3D U(hit.getDX(), hit.getDY(), hit.getDZ());
 
       D.sub(track.getPosition());
 
       const double z  = D.getDot(track.getDirection());
       const double x  = D.getX()  -  z * track.getDX();
       const double y  = D.getY()  -  z * track.getDY();
       const double R2 = D.getLengthSquared() - z*z;
       const double R  = (R2 > Rmin_m*Rmin_m ? sqrt(R2) : Rmin_m);
 
       const double t1 = track.getT() + (z + R * getTanThetaC()) * getInverseSpeedOfLight();
 
       U.rotate(JRotation3Z(-atan2(y,x)));                  // rotate PMT axis to x-z plane
 
       const double theta = U.getTheta();
       const double phi   = fabs(U.getPhi());
 
       const double E  = gWater.getE(E_GeV, z);
       const double dt = T_ns.constrain(hit.getT()  -  t1);
 
       JPDF_t::result_type H0 = getH0(hit.getR(), dt);
       JPDF_t::result_type H1 = getH1(E, R, theta, phi, dt);
 
       if (H1.V >= Vmax_npe) {
         H1 *= Vmax_npe / H1.V;
       }
 
       H1 += H0;                                                                                      // signal + background
 
       result_type result;
 
       result.chi2     = H1.getChi2() - H0.getChi2();                                                 // Likelihood ratio
 
       const double wc = 1.0  -  getTanThetaC() * z / R;                                              // d(ct1)/d(z)
 
       result.gradient = JLine3Z(JLine1Z(JPosition3D(-getTanThetaC() * D.getX() / R,                  // d(ct1)/d(x)
                                                     -getTanThetaC() * D.getY() / R,                  // d(ct1)/d(y)
                                                     0.0),
                                         getSpeedOfLight()),                                          // d(ct1)/d(t)
                                 JVersor3Z(wc * (D.getX() - D.getZ()*track.getDX()/track.getDZ()),    // d(ct1)/d(dx)
                                           wc * (D.getY() - D.getZ()*track.getDY()/track.getDZ())));  // d(ct1)/d(dy)
       
       result.gradient.mul(getInverseSpeedOfLight() * (H1.getDerivativeOfChi2() -
                                                       H0.getDerivativeOfChi2()));                    // x d(chi2)/d(ct1)
 
       return result;
     }

result_type JFIT::JRegressor< JLine3Z, JGandalf >::operator()	(	const JLine3Z &	track,
		const JPMTW0 &	pmt
	)		const

inline

Fit function.

This method is used to determine the chi2 and gradient of given PMT with respect to trajectory of muon.

Parameters

track	track
pmt	pmt

Returns: chi2 and gradient

Definition at line 279 of file JLine3ZRegressor.hh.

     {
       using namespace JGEOMETRY3D;
       using namespace JPHYSICS;
       
       JPosition3D  D(pmt.getPosition());
       JDirection3D U(pmt.getDirection());
 
       D.sub(track.getPosition());
 
       const double z  = D.getDot(track.getDirection());
       const double x  = D.getX()  -  z * track.getDX();
       const double y  = D.getY()  -  z * track.getDY();
       const double R2 = D.getLengthSquared() - z*z;
       const double R  = (R2 > Rmin_m*Rmin_m ? sqrt(R2) : Rmin_m);
 
       U.rotate(JRotation3Z(-atan2(y,x)));                  // rotate PMT axis to x-z plane
 
       const double theta = U.getTheta();
       const double phi   = fabs(U.getPhi());
 
       const double E  = gWater.getE(E_GeV, z);
 
       JNPE_t::result_type H0 = getH0(pmt.getR());
       JNPE_t::result_type H1 = getH1(E, R, theta, phi);
 
       if (H1.f >= Vmax_npe) {
         H1 *= Vmax_npe / H1.f;
       }
 
       H1 += H0;
 
       const bool   hit = pmt.getN() != 0;
       const double u   = H1.getChi2(hit);
 
       result_type result;
 
       result.chi2     = estimator->getRho(u);
 
       result.gradient = JLine3Z(JLine1Z(JPosition3D(-D.getX() / R,   // d(R)/d(x)
                                                     -D.getY() / R,   // d(R)/d(y)
                                                     0.0),
                                         0.0),
                                 JVersor3Z(-z * D.getX() / R,         // d(R)/d(dx)
                                           -z * D.getY() / R));       // d(R)/d(dy)
 
       result.gradient.mul(estimator->getPsi(u));
       result.gradient.mul(H1.getDerivativeOfChi2(hit));              // x d(chi2)/d(R)
 
       return result;
     }

JPDF_t::result_type JFIT::JRegressor< JLine3Z, 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 339 of file JLine3ZRegressor.hh.

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

JPDF_t::result_type JFIT::JRegressor< JLine3Z, JGandalf >::getH1	(	const double	E,
		const double	R,
		const double	theta,
		const double	phi,
		const double	t1
	)		const

inline

Get signal hypothesis value for time differentiated PDF.

Parameters

E	muon energy at minimum distance of approach [GeV]
R	minimum distance of approach [m]
theta	PMT zenith angle [rad]
phi	PMT azimuth angle [rad]
t1	arrival time relative to Cherenkov hypothesis [ns]

Returns: hypothesis value

Definition at line 356 of file JLine3ZRegressor.hh.

     {
       using namespace std;
       using namespace JPP;
 
       JPDF_t::result_type h1 = zero;
 
       for (int i = 0; i != NUMBER_OF_PDFS; ++i) {
 
         if (!pdf[i].empty() && R <= pdf[i].getXmax()) {
 
           JPDF_t::result_type y1 = pdf[i](max(R, pdf[i].getXmin()), theta, phi, t1);
           
           // safety measures
           
           if (y1.f <= 0.0) {
             y1.f  = 0.0;
             y1.fp = 0.0;
           }
           
           if (y1.v <= 0.0) {
             y1.v  = 0.0;
           }
           
           // energy dependence
           
           if        (is_deltarays(pdf_t[i])) {
             y1 *= getDeltaRaysFromMuon(E);
           } else if (is_bremsstrahlung(pdf_t[i])) {
             y1 *= E;
           }
           
           h1 += y1;
         }
       }
 
       return h1;
     }

JNPE_t::result_type JFIT::JRegressor< JLine3Z, JGandalf >::getH0 ( const double R_Hz ) const

inline

Get background hypothesis value for time integrated PDF.

Parameters

R_Hz rate [Hz]

Returns: hypothesis value

Definition at line 406 of file JLine3ZRegressor.hh.

     {
       return JNPE_t::result_type(R_Hz * 1e-9 * T_ns.getLength(), 0.0);
     }

JNPE_t::result_type JFIT::JRegressor< JLine3Z, JGandalf >::getH1	(	const double	E,
		const double	R,
		const double	theta,
		const double	phi
	)		const

inline

Get signal hypothesis value for time integrated PDF.

Parameters

E	muon energy at minimum distance of approach [GeV]
R	minimum distance of approach [m]
theta	PMT zenith angle [rad]
phi	PMT azimuth angle [rad]

Returns: hypothesis value

Definition at line 421 of file JLine3ZRegressor.hh.

     {
       using namespace std;
       using namespace JPP;
 
       JNPE_t::result_type h1 = JMATH::zero;
         
       for (int i = 0; i != NUMBER_OF_PDFS; ++i) {
 
         if (!npe[i].empty() && R <= npe[i].getXmax()) {
 
           try {
 
             JNPE_t::result_type y1 = npe[i](max(R, npe[i].getXmin()), theta, phi);
           
             // safety measures
             
             if (y1.f > 0.0) {
             
               // energy dependence
             
               if        (is_deltarays(pdf_t[i])) {
                 y1 *= getDeltaRaysFromMuon(E);
               } else if (is_bremsstrahlung(pdf_t[i])) {
                 y1 *= E;
               }
           
               h1 += y1;
             }
           }
           catch(JException& error) {
             ERROR(error << endl);
           }
         }
       }
 
       return h1;
     }

double JFIT::JRegressor< JLine3Z, JGandalf >::getRmax ( ) const

inline

Get maximal road width of PDF.

Returns: road width [m]

Definition at line 469 of file JLine3ZRegressor.hh.

     {
       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;
     }

void JFIT::JRegressor< JLine3Z, JGandalf >::setRmax ( const double Rmax )

inline

Set maximal road width of PDF.

Parameters

Rmax	road width [m]

Definition at line 488 of file JLine3ZRegressor.hh.

     {
       for (int i = 0; i != NUMBER_OF_PDFS; ++i) {
         if (!pdf[i].empty()) {
           pdf[i].compress(JTOOLS::JRange<typename JFunction1D_t::abscissa_type>(0.0, Rmax));
         }
       }
     }

result_type JFIT::JAbstractRegressor< JLine3Z , JGandalf >::operator()	(	const JLine3Z &	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< JLine3Z >::operator()	(	const JFunction_t &	fit,
		T	__begin,
		T	__end,
		Args...	args
	)

inlineinherited

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

Definition at line 128 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);
 
       previous.result.chi2 = numeric_limits<double>::max();
 
       previous.V.resize(N);
 
       current.result.chi2     = numeric_limits<double>::max();
       current.result.gradient = value;
       current.result.gradient = zero;
 
       current.V.resize(N);
 
       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) {
 
             if (fabs(previous.result.chi2 - current.result.chi2) < EPSILON*fabs(previous.result.chi2)) {
               return current.result;                                // normal end
             }
 
             if (lambda > LAMBDA_MIN) {
               lambda /= LAMBDA_DOWN;
             }
 
             // store current values
 
             previous.value  = value;
             previous.error  = error;
             previous.result = current.result;
             
             previous.V.swap(V);
           }
 
         } else {
 
           value   = previous.value;                                 // restore value
 
           lambda *= LAMBDA_UP;
           
           if (lambda > LAMBDA_MAX) {
             break;
           }
 
           reset();
 
           update(fit, __begin, __end, args...);
         }
 
 
         V.swap(current.V);
 
         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;
         }
 
 
         // invert Hesse matrix
 
         try {
           V.invert();
         }
         catch (const JException& error) {
 
           ERROR("JGandalf: " << error.what() << endl << V << endl);
 
           break;
         }
 
 
         // update value and error       
         
         for (size_t row = 0; row != N; ++row) {
 
           DEBUG("u[" << noshowpos << row << "] = " << showpos << FIXED(15,5) << get(value, parameters[row]));
 
           for (size_t col = 0; col != N; ++col) {
 
             V(row,col) *= h[row] * h[col];
 
             get(value, parameters[row]) -= V(row,col) * get(current.result.gradient, parameters[col]);
           }
           
           DEBUG(" -> " << FIXED(15,5) << get(value, parameters[row]) << noshowpos << endl);
 
           get(error, parameters[row]) = h[row];
         }
       }
 
       // abnormal end
 
       value   = previous.value;                                     // restore value
       error   = previous.error;                                     // restore error
 
       V.swap(previous.V);                                           // restore Hesse matrix
 
       return previous.result;
     }

Member Data Documentation

JTimeRange JFIT::JRegressor< JLine3Z, JGandalf >::T_ns

static

Time window with respect to Cherenkov hypothesis [ns].

Default values.

Definition at line 498 of file JLine3ZRegressor.hh.

double JFIT::JRegressor< JLine3Z, JGandalf >::Vmax_npe = std::numeric_limits<double>::max()

static

Maximal integral of PDF [npe].

Definition at line 499 of file JLine3ZRegressor.hh.

double JFIT::JRegressor< JLine3Z, JGandalf >::Rmin_m = 0.1

static

Minimal distance of [m].

Definition at line 500 of file JLine3ZRegressor.hh.

const int JFIT::JRegressor< JLine3Z, JGandalf >::NUMBER_OF_PDFS = 6

static

Definition at line 502 of file JLine3ZRegressor.hh.

const JPDFType_t JFIT::JRegressor< JLine3Z, JGandalf >::pdf_t

static

Initial value:

= { DIRECT_LIGHT_FROM_MUON,
                                                              SCATTERED_LIGHT_FROM_MUON,
                                                              DIRECT_LIGHT_FROM_DELTARAYS,
                                                              SCATTERED_LIGHT_FROM_DELTARAYS,
                                                              DIRECT_LIGHT_FROM_EMSHOWERS,
                                                              SCATTERED_LIGHT_FROM_EMSHOWERS }