Performs a second-degree fit of data. More...

#include <SimpleFits.h>

Inheritance diagram for lar::util::QuadraticFit< T >:

Public Types
using	FitParameters_t = std::array< Data_t, NParams >
	type of set of fit parameters More...

using	FitMatrix_t = std::array< Data_t, sqr(NParams)>

using	Data_t = typename Base_t::Data_t
	type of the data More...

Public Types inherited from lar::util::details::SimplePolyFitterBase< T, 2U >
using	Data_t = typename Base_t::Data_t
	type of the data More...

using	FitParameters_t = typename Interface_t::FitParameters_t
	type of set of fit parameters More...

using	FitMatrix_t = typename Interface_t::FitMatrix_t
	type of matrix for covariance (a std::array) More...

Public Types inherited from lar::util::details::SimpleFitterInterface< T, D+1 >
using	Data_t = T
	type of the data More...

using	MatrixOps = FastMatrixOperations< Data_t, NParams >

using	FitParameters_t = std::array< Data_t, NParams >
	type of set of fit parameters More...

using	FitMatrix_t = typename MatrixOps::Matrix_t
	type of matrix for covariance (a std::array) More...

Public Types inherited from lar::util::details::SimplePolyFitterDataBase< T, D >
using	Data_t = typename Collector_t::Data_t
	type of the data More...

using	Measurement_t = typename Collector_t::Measurement_t
	type of measurement without uncertainty More...

using	MeasurementAndUncertainty_t = typename Collector_t::MeasurementAndUncertainty_t
	type of measurement with uncertainty More...

Public Member Functions
virtual Data_t	ChiSquare () const override
	Returns the $\chi^{2}$ of the fit. More...

Public Member Functions inherited from lar::util::details::SimplePolyFitterBase< T, 2U >
virtual bool	isValid () const override
	Returns if the fit has valid results. More...

bool	FillResults (FitParameters_t &params, FitMatrix_t &Xmat, Data_t &det, FitMatrix_t &Smat) const override
	Fills the specified parameters. More...

bool	FillResults (FitParameters_t &params, FitParameters_t &paramerrors, FitMatrix_t &Xmat, Data_t &det, FitMatrix_t &Smat) const override
	Fills the specified parameters. More...

bool	FillResults (FitParameters_t &params, FitParameters_t &paramerrors) const override
	Fills the specified parameters. More...

virtual Data_t	Evaluate (Data_t x) const override
	Evaluates the fitted function at the specified point. More...

virtual FitParameters_t	FitParameters () const override
	Computes and returns all the parameters of the fit result. More...

virtual FitParameters_t	FitParameterErrors () const override
	Computes and returns all the parameter errors of the fit result. More...

virtual FitMatrix_t	FitParameterCovariance () const override
	Computes and returns all the covariance matrix of the fit result. More...

virtual Data_t	FitParameter (unsigned int n) const override
	Returns the parameter n of the fit result. More...

virtual Data_t	FitParameterError (unsigned int n) const override
	Returns the error on parameter n of the fit result. More...

virtual int	NDF () const override
	Returns the degrees of freedom in the determination of the fit. More...

Public Member Functions inherited from lar::util::details::SimpleFitterInterface< T, D+1 >
virtual	~SimpleFitterInterface ()=default
	Virtual destructor: compiler's default. More...

virtual bool	FillResults (FitParameters_t &params, FitMatrix_t &Xmat, Data_t &det, FitMatrix_t &Smat) const =0
	Fills the specified parameters. More...

virtual bool	FillResults (FitParameters_t &params, FitParameters_t &paramerrors, FitMatrix_t &Xmat, Data_t &det, FitMatrix_t &Smat) const =0
	Fills the specified parameters. More...

virtual Data_t	Evaluate (Data_t x) const =0
	Evaluates the fitted function at the specified point. More...

Data_t	operator() (Data_t x) const
	Evaluates the fitted function; alias of Evaluate() More...

Public Member Functions inherited from lar::util::details::SimplePolyFitterDataBase< T, D >
void	clear ()
	Clears all the statistics. More...

template<typename Stream >
void	PrintStats (Stream &out) const
	Prints the collected statistics into a stream. More...

bool	add (Data_t x, Data_t y, Data_t sy=Data_t(1.0))

bool	add (Measurement_t value, Data_t sy=Data_t(1.0))

bool	add (MeasurementAndUncertainty_t value)

template<typename Iter >
void	add_without_uncertainty (Iter begin, Iter end)

template<typename Iter , typename Pred >
void	add_without_uncertainty (Iter begin, Iter end, Pred extractor)

template<typename Cont , typename Pred >
void	add_without_uncertainty (Cont cont, Pred extractor)

template<typename Cont >
void	add_without_uncertainty (Cont cont)

template<typename VIter , typename UIter , typename VPred , typename UPred = identity>
unsigned int	add_with_uncertainty (VIter begin_value, VIter end_value, UIter begin_uncertainty, VPred value_extractor, UPred uncertainty_extractor=UPred())

template<typename Iter >
unsigned int	add_with_uncertainty (Iter begin, Iter end)

template<typename Cont >
unsigned int	add_with_uncertainty (Cont cont)

int	N () const

Data_t	AverageUncertainty () const

Protected Member Functions

Data_t	I () const
	Aliases. More...

Data_t	X () const

Data_t	X2 () const

Data_t	X3 () const

Data_t	X4 () const

Data_t	Y () const

Data_t	XY () const

Data_t	X2Y () const

Data_t	Y2 () const

Protected Member Functions inherited from lar::util::details::SimplePolyFitterBase< T, 2U >
virtual FitParameters_t	FitParameterErrors (FitMatrix_t const &Smat) const
	Computes and returns all the parameter errors of the fit result. More...

virtual FitMatrix_t	MakeMatrixX () const
	Fills and returns the matrix of x^n sum coefficients ( { x^(i+j) } ) More...

virtual FitParameters_t	MakeMatrixY () const
	Fills and returns the matrix (vector) of x^n y sum coefficients. More...

virtual FitParameters_t	FitParameters (FitMatrix_t const &Xmat) const
	Returns the fitted parameters using the provided information. More...

virtual FitParameters_t	FitParameters (FitMatrix_t const &Smat, Data_t) const

virtual Data_t	Param (unsigned int n, FitMatrix_t const &Xmat) const
	Computes a single fit parameter using the given information. More...

virtual Data_t	Param (unsigned int n, FitMatrix_t const &Xmat, Data_t detXmat) const

Protected Member Functions inherited from lar::util::details::SimpleFitterInterface< T, D+1 >
virtual Data_t	Determinant (FitMatrix_t const &mat) const
	Computes the determinant of a matrix. More...

virtual FitMatrix_t	InvertMatrix (FitMatrix_t const &mat, Data_t det) const
	Computes the inverse of a matrix (using provided determinant) More...

virtual FitMatrix_t	InvertMatrix (FitMatrix_t const &mat) const
	Computes the inverse of a matrix. More...

virtual FitParameters_t	MatrixProduct (FitMatrix_t const &mat, FitParameters_t const &vec) const
	Computes the product of a FitMatrix_t and a FitParameters_t. More...

Protected Member Functions inherited from lar::util::details::SimplePolyFitterDataBase< T, D >
Data_t	XN (unsigned int n) const
	Returns the weighted sum of x^n. More...

Data_t	XNY (unsigned int n) const
	Returns the weighted sum of x^n y. More...

Private Types
using	Base_t = details::SimplePolyFitterBase< T, 2U >

Additional Inherited Members
Static Public Member Functions inherited from lar::util::details::SimplePolyFitterBase< T, 2U >
static FitParameters_t	ExtractParameterErrors (FitMatrix_t const &Smat)
	Extracts parameter errors from diagonal of the covarriance matrix. More...

Static Public Member Functions inherited from lar::util::details::SimpleFitterInterface< T, D+1 >
static constexpr Data_t	sqr (Data_t v)
	Returns the square of the specified data value. More...

static constexpr Data_t	cube (Data_t v)
	Returns the cube of the specified data value. More...

Static Public Member Functions inherited from lar::util::details::SimplePolyFitterDataBase< T, D >
template<typename V >
static constexpr V	sqr (V const &v)
	Returns the square of the specified value. More...

Static Public Attributes inherited from lar::util::details::SimplePolyFitterBase< T, 2U >
static constexpr unsigned int	Degree
	Degree of the fit. More...

static constexpr unsigned int	NParams
	Number of parameters in the fit. More...

Static Public Attributes inherited from lar::util::details::SimpleFitterInterface< T, D+1 >
static constexpr unsigned int	NParams
	Number of parameters in the fit. More...

Static Public Attributes inherited from lar::util::details::SimplePolyFitterDataBase< T, D >
static constexpr unsigned int	Degree = Collector_t::Degree
	Degree of the fit. More...

Protected Attributes inherited from lar::util::details::SimplePolyFitterDataBase< T, D >
Collector_t	stats
	statistics collected from fit data input More...

Detailed Description

template<typename T>
class lar::util::QuadraticFit< T >

Performs a second-degree fit of data.

Template Parameters

T	type of the quantities
W	type of the weight (as T by default)

The quadratic fit connects measurements $( y_{i} \pm \sigma_{y,i} )$ with a parameter $( x_{i} )$ not affected by uncertainty. The returned parameters describe a quadratic curve $f(x) = a_{0} + a_{1} x + a_{2} x^{2}$ obtained by minimization of $\chi^{2} = \sum_{i} \frac{ \left(y_{i} - f(x_{i}) \right)^{2} }{ \sigma^{2}_{y,i} }$

This saves having to link to ROOT for the simplest cases.

This simple quadratic fitter does not store any result: each time a result is requested, it is computed anew. In particular that is true also for ChiSquare(), that requires the full parameters set and therefore reruns the full fit (FitParameters()) and for the covariance matrix of the parameters.

Definition at line 953 of file SimpleFits.h.

Member Typedef Documentation

template<typename T>

using lar::util::QuadraticFit< T >::Base_t = details::SimplePolyFitterBase<T, 2U>

private

Definition at line 954 of file SimpleFits.h.

template<typename T>

using lar::util::details::SimplePolyFitterBase< T, D >::Data_t = typename Base_t::Data_t

type of the data

Definition at line 653 of file SimpleFits.h.

template<typename T>

using lar::util::QuadraticFit< T >::FitMatrix_t = std::array<Data_t, sqr(NParams)>

Definition at line 971 of file SimpleFits.h.

template<typename T>

using lar::util::QuadraticFit< T >::FitParameters_t = std::array<Data_t, NParams>

type of set of fit parameters

Definition at line 970 of file SimpleFits.h.

Member Function Documentation

template<typename T >

auto lar::util::QuadraticFit< T >::ChiSquare ( ) const

overridevirtual

Returns the $\chi^{2}$ of the fit.

Returns: the $\chi^{2}$ of the fit (not divided by NDF())

Reimplemented from lar::util::details::SimplePolyFitterBase< T, 2U >.

Definition at line 1771 of file SimpleFits.h.

 {
   FitParameters_t a = this->FitParameters();
   return Y2()           - Data_t(2) *        (a[0]*Y() + a[1]*XY() + a[2]*X2Y())
        + sqr(a[0])*I()  + Data_t(2) * a[0] * (           a[1]*X()  + a[2]*X2() )
        + sqr(a[1])*X2() + Data_t(2) * a[1] * (                       a[2]*X3() )
        + sqr(a[2])*X4();
 } // QuadraticFit<T>::ChiSquare()