JFIT Namespace Reference

Auxiliary classes and methods for linear and iterative data regression. More...

Classes
class	JEnergy
	Data structure for fit of energy. More...
struct	JRegressor< JEnergy >
	Regressor function object for fit of muon energy. More...
class	JEstimator
	Template definition of linear fit. More...
class	JGandalf
	Fit method based on the Levenberg-Marquardt method. More...
struct	JParameter_t
	Auxiliary data structure for fit parameter. More...
struct	JModifier_t
	Auxiliary data structure for editable parameter. More...
struct	JGradient
	Conjugate gradient fit. More...
struct	JK40
	Auxiliary class for handling light yields due to K40 decays. More...
struct	JK40Hit
	Auxiliary class for simultaneously handling light yields and response of module. More...
class	JEstimator< JLegendre< JOrdinate_t, N > >
	Linear fit of Legendre polynomial. More...
class	JLine1Z
	Data structure for fit of straight line paralel to z-axis. More...
class	JEstimator< JLine1Z >
	Linear fit of straight line parallel to z-axis to set of hits (objects with position and time). More...
class	JLine3EZ
	Data structure for fit of straight line in positive z-direction with energy. More...
class	JLine3Z
	Data structure for fit of straight line in positive z-direction. More...
struct	JRegressor< JLine3Z, JSimplex >
	Regressor function object for JLine3Z fit using JSimplex minimiser. More...
struct	JRegressor< JLine3Z, JGandalf >
	Regressor function object for JLine3Z fit using JGandalf minimiser. More...
class	JMatrixNZ
	Determination of the co-variance matrix of hits for a track along z-axis (JFIT::JLine1Z). More...
struct	JMEstimator
	Interface for maximum likelihood estimator (M-estimator). More...
struct	JMEstimatorNormal
	Normal M-estimator. More...
struct	JMEstimatorLorentzian
	Lorentzian M-estimator. More...
struct	JMEstimatorLinear
	Linear M-estimator. More...
struct	JMEstimatorNull
	Null M-estimator. More...
struct	JMEstimatorTukey
	Tukey's biweight M-estimator. More...
struct	JMEstimatorNormalWithBackground
	Normal M-estimator with background. More...
struct	JModel
	Auxiliary class to match data points with given model. More...
struct	JModel< JLine1Z >
	Template specialisation of class JModel to match hit with muon trajectory along z-axis. More...
struct	JModel< JEnergy >
	Template specialisation of class JModel to match hit with muon energy. More...
struct	JModel< JPoint4D >
	Template specialisation of class JModel to match hit with bright point. More...
struct	JNPE
	Auxiliary class for handling various light yields. More...
struct	JNPEHit
	Auxiliary class for simultaneously handling light yields and response of PMT. More...
struct	JPMTW0
	Auxiliary class for handling PMT geometry, rate and response. More...
class	JPoint3D
	Data structure for position fit. More...
class	JEstimator< JPoint3D >
	Linear fit of crossing point (position) between axes (objects with position and direction). More...
class	JPoint4D
	Data structure for vertex fit. More...
class	JEstimator< JPoint4D >
	Linear fit of bright point (position and time) between hits (objects with position and time). More...
struct	JRegressor< JPoint4D, JSimplex >
	Regressor function object for JPoint4D fit using JSimplex minimiser. More...
class	JAbstractMinimiser
	Abstract minimiser. More...
struct	JRegressor
	Template definition of a data regressor of given model. More...
struct	JAbstractRegressor
	Abstract class for global fit method. More...
class	JSimplex
	Simple fit method based on Powell's algorithm, see reference: Numerical Recipes in C++, W.H. More...
struct	JRegressorHelper
	Template data structure for PDF tables. More...
struct	JRegressorHelper< JLine3Z, JGandalf >
	Template specialisation for PDF tables. More...
struct	JRegressorStorage
	Template data structure for storage for PDF tables. More...
struct	JRegressorStorage< JLine3Z, JGandalf >
	Template specialisation for storage for PDF tables. More...
class	JShower3EZ
	Data structure for fit of straight line in positive z-direction with energy. More...
struct	JRegressor< JShower3EZ, JSimplex >
	Regressor function object for JShower3EZ fit using JSimplex minimiser. More...
struct	JRegressor< JShower3EZ, JGandalf >
	Regressor function object for JShower3EZ fit using JGandalf minimiser. More...
class	JShower3Z
	Data structure for cascade in positive z-direction. More...
struct	JRegressor< JShowerEH, JSimplex >
	Regressor function object for JShowerEH fit using JSimplex minimiser. More...
struct	JRegressor< JPoint4D, JGandalf >
	Regressor function object for JPoint4D fit using JGandalf minimiser. More...
class	JShowerEH
	Data structure for fit of straight line in positive z-direction with energy. More...
struct	JRegressor< JEnergy, JSimplex >
	Regressor function object for JShower3EZ fit using JSimplex minimiser. More...
struct	JShowerNPE
	Auxiliary class for handling EM shower light yield. More...
struct	JShowerNPEHit
	Auxiliary class for simultaneously handling light yields and response of PMT. More...
class	JVectorNZ
	Determination of the time residual vector of hits for a track along z-axis (JFIT::JLine1Z). More...
class	JEnergyCorrection
	Auxiliary class for correction of energy determined by JEnergy.cc. More...
class	JFit
	Data structure for track fit results with history and optional associated values. More...
class	JEvt
	Data structure for set of track fit results. More...
struct	JEvent
	Auxiliary class for historical event. More...
struct	JHistory
	Container for historical events. More...
class	JShowerEnergyCorrection
	Auxiliary class for correction of energy determined by JShowerEnergy.cc. More...

Typedefs
typedef JTOOLS::JRange< double >	JZRange

Enumerations
enum	JMEstimator_t {   EM_NORMAL = 0, EM_LORENTZIAN = 1, EM_LINEAR = 2, EM_NULL = 3,   EM_TUKEY = 4, EM_NORMALWITHBACKGROUND = 5 }
	Definition of the various M-Estimators available to use. More...

Functions
double	getP (const double expval, bool hit)
	Get Poisson probability to observe a hit or not for given expectation value for the number of hits. More...
double	getChi2 (const double P)
	Get chi2 corresponding to given probability. More...
double	getChi2 (const double expval, bool hit)
	Get chi2 to observe a hit or not for given expectation value for the number of hits. More...
template<class JModel_t , class JHit_t >
double	getChi2 (const JModel_t &model, const JHit_t &hit, const double sigma)
	Determine chi2 of a hit for a given model and time resolution. More...
template<class JModel_t , class T >
double	getChi2 (const JModel_t &model, T __begin, T __end, const double sigma)
	Determine chi2 of data for given model and time resolution. More...
double	getChi2 (const JVectorNZ &Y, const JMatrixNZ &V)
	Determine chi2 using full covariance matrix. More...
template<class T >
double	getChi2 (const JLine1Z &track, T __begin, T __end, const JMatrixNZ &V)
	Determine chi2 of data for given track using full covariance matrix. More...
template<class T >
double	getChi2 (const JLine1Z &track, T __begin, T __end, const double alpha, const double sigma)
	Determine chi2 of data for given track and angular and time resolution. More...
double	getChi2 (const JVectorNZ &Y, const JMatrixNZ &V, const int i)
	Determine difference between chi2 with and without hit using full covariance matrix. More...
template<class JModel_t , class JFit_t , class T >
double	getChi2 (const JModel_t &model, const JFit_t &fit, T __begin, T __end)
	Get chi2 of data for given model and fit function. More...
double	getProbability (const size_t N, const size_t M, const JK40Rates &R_Hz, const double T_ns)
	Get probability due to random background. More...
JMEstimator *	getMEstimator (const int type)
	Get M-Estimator. More...

Detailed Description

Auxiliary classes and methods for linear and iterative data regression.

Author

mdejong

adomi

lquinn

mdejong, adomi

Typedef Documentation

typedef JTOOLS::JRange<double> JFIT::JZRange

Definition at line 21 of file JFit/JModel.hh.

Enumeration Type Documentation

enum JFIT::JMEstimator_t

Definition of the various M-Estimators available to use.

Enumerator
EM_NORMAL
EM_LORENTZIAN
EM_LINEAR
EM_NULL
EM_TUKEY
EM_NORMALWITHBACKGROUND

Definition at line 185 of file JMEstimator.hh.

                     {
    EM_NORMAL                 = 0,
    EM_LORENTZIAN             = 1,
    EM_LINEAR                 = 2,
    EM_NULL                   = 3,
    EM_TUKEY                  = 4,
    EM_NORMALWITHBACKGROUND   = 5
  };

Function Documentation

double JFIT::getP ( const double  expval, bool  hit  )

inline

Get Poisson probability to observe a hit or not for given expectation value for the number of hits.

Parameters

expval	expectation value
hit	hit

Returns

probability

Definition at line 41 of file JFitToolkit.hh.

  {
    if (hit)
      return -expm1(-expval);       // 1 - P(0)
    else
      return exp(-expval);          // P(0)
  }

double JFIT::getChi2 ( const double  P )

inline

Get chi2 corresponding to given probability.

Parameters

P	probability

Returns

chi2

Definition at line 56 of file JFitToolkit.hh.

  {
    return -log(P);
  }

double JFIT::getChi2 ( const double  expval, bool  hit  )

inline

Get chi2 to observe a hit or not for given expectation value for the number of hits.

Parameters

expval	expectation value
hit	hit

Returns

probability

Definition at line 69 of file JFitToolkit.hh.

  {
    if (hit)
      return -log1p(-exp(-expval));
    else
      return expval;
  }

template<class JModel_t , class JHit_t >

double JFIT::getChi2 ( const JModel_t &  model, const JHit_t &  hit, const double  sigma  )

inline

Determine chi2 of a hit for a given model and time resolution.

The template argument JModel_t refers to a data structure which should provide for the following method:

  double getT(const JHit_t& hit) const;    // get expected time of hit

Parameters

model	model
hit	hit
sigma	sigma

Returns

chi2

Definition at line 93 of file JFitToolkit.hh.

  {
    const double ds = (hit.getT() - model.getT(hit)) / sigma;

    return ds * ds;
  }

template<class JModel_t , class T >

double JFIT::getChi2 ( const JModel_t &  model, T  __begin, T  __end, const double  sigma  )

inline

Determine chi2 of data for given model and time resolution.

The template argument JModel_t refers to a data structure which should provide for the following method:

  double getT(const value_type& hit) const;    // expected time of hit

where value_type corresponds to the value type if the input data.

Parameters

model	model
__begin	begin of data
__end	end of data
sigma	time resolution [ns]

Returns

chi2

Definition at line 118 of file JFitToolkit.hh.

  {
    double chi2 = 0.0;

    for (T hit = __begin; hit != __end; ++hit) {
      chi2 += getChi2(model, *hit, sigma);
    }

    return chi2;
  }

double JFIT::getChi2 ( const JVectorNZ &  Y, const JMatrixNZ &  V  )

inline

Determine chi2 using full covariance matrix.

Parameters

Y	residuals
V	covariance matrix

Returns

chi2

Definition at line 137 of file JFitToolkit.hh.

  {
    return V.getDot(Y);
  }

template<class T >

double JFIT::getChi2 ( const JLine1Z &  track, T  __begin, T  __end, const JMatrixNZ &  V  )

inline

Determine chi2 of data for given track using full covariance matrix.

Parameters

track	track
__begin	begin of data
__end	end of data
V	covariance matrix

Returns

chi2

Definition at line 154 of file JFitToolkit.hh.

  {
    const JVectorNZ Y(track, __begin, __end);

    return getChi2(Y, V);
  }

template<class T >

double JFIT::getChi2 ( const JLine1Z &  track, T  __begin, T  __end, const double  alpha, const double  sigma  )

inline

Determine chi2 of data for given track and angular and time resolution.

Parameters

track	track
__begin	begin of data
__end	end of data
alpha	angular resolution [deg]
sigma	time resolution [ns]

Returns

chi2

Definition at line 176 of file JFitToolkit.hh.

  {
    JMatrixNZ V(track, __begin, __end, alpha, sigma);

    V.invert();

    return getChi2(track, __begin, __end, V);
  }

double JFIT::getChi2 ( const JVectorNZ &  Y, const JMatrixNZ &  V, const int  i  )

inline

Determine difference between chi2 with and without hit using full covariance matrix.

Parameters

Y	residuals
V	covariance matrix
i	index of excluded hit

Returns

chi2

Definition at line 194 of file JFitToolkit.hh.

  {
    double chi2 = 0.0;

    for (size_t j = 0; j != V.size(); ++j) {
      chi2 += V(i,j) * Y[j];
    }

    return chi2*chi2 / V(i,i);
  }

template<class JModel_t , class JFit_t , class T >

double JFIT::getChi2 ( const JModel_t &  model, const JFit_t &  fit, T  __begin, T  __end  )

inline

Get chi2 of data for given model and fit function.

The template argument JFit_t refers to a data structure which should provide for the function object operator:

  double operator()(const JModel_t& model, const value_type&) const;    // chi2

where JModel_t refers to the given model and value_type to the value type if the input data. The return value should correspond to the chi2 of the hit.

Parameters

model	model
fit	fit function
__begin	begin of data
__end	end of data

Definition at line 227 of file JFitToolkit.hh.

  {
    double chi2 = 0.0;

    for (T hit = __begin; hit != __end; ++hit) {
      chi2 += fit(model, *hit);
    }

    return chi2;
  }

double JFIT::getProbability ( const size_t  N, const size_t  M, const JK40Rates &  R_Hz, const double  T_ns  )

inline

Get probability due to random background.

Parameters

N	number of active PMTs
M	multiplicity of hits
R_Hz	rates [Hz]
T_ns	time window [ns]

Returns

probability

Definition at line 248 of file JFitToolkit.hh.

  {
    using namespace JPP;

    if (N == 0) {
      return (M == 0 ? 1.0 : 0.0);
    }

    const double T =  T_ns * 1.0e-9;
    const double p = -expm1(-R_Hz.getSinglesRate() * N * T);    // 1 - P(0) due to singles rate
    
    double P = 0.0;

    for (multiplicity_type i = R_Hz.getLowerL1Multiplicity(); i <= R_Hz.getUpperL1Multiplicity(); ++i) {
      P -= expm1(-R_Hz.getMultiplesRate(i) * T);                // 1 - P(0) due to multiples rates
    }

    P *= (1.0 + p);                                             // 1 - P(0) due to multiples rates M-1 combined with singles rate
    
    return (poisson(M, R_Hz.getSinglesRate() * N * T)  -                 // P(M) due to singles rate
            expm1(-R_Hz.getMultiplesRate(M)      * T)  -                 // P(M) due to multiples rate
            expm1(-R_Hz.getMultiplesRate(M-1)    * T) * p) / (1.0 + P);  // P(M-1) * P(1) due to multiples rate combined with singles rate
  }

JMEstimator* JFIT::getMEstimator ( const int  type )

inline

Get M-Estimator.

Note that for M-estimators with an additional parameter, defaults are used.

Parameters

type

type

Returns

pointer to newly created M-Estimator (may be NULL)

Definition at line 203 of file JMEstimator.hh.

  {
    switch (type) {

    case EM_NORMAL:
      return new JMEstimatorNormal();

    case EM_LORENTZIAN:
      return new JMEstimatorLorentzian();

    case EM_LINEAR:
      return new JMEstimatorLinear();

    case EM_NULL:
      return new JMEstimatorNull();

    case EM_TUKEY:
      return new JMEstimatorTukey(5.0);

    case EM_NORMALWITHBACKGROUND:
      return new JMEstimatorNormalWithBackground(1.0e-5);

    default:
      return NULL;
    }
  }