Base class providing virtual fitting interface for polynomial fitters. More...

#include <SimpleFits.h>

Inheritance diagram for lar::util::details::SimplePolyFitterBase< T, D >:

Public Types
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 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...

Fitting
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 Data_t	ChiSquare () const override
	Returns the $\chi^{2}$ of the fit. 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 bool	FillResults (FitParameters_t &params, FitParameters_t &paramerrors) 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

Static Public Member Functions
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
static constexpr unsigned int	Degree = Base_t::Degree
	Degree of the fit. More...

static constexpr unsigned int	NParams = Interface_t::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 Member Functions
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	FitParameterErrors (FitMatrix_t const &Smat) const
	Computes and returns all the parameter errors of the fit result. 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	Interface_t = SimpleFitterInterface< T, D+1 >
	interface More...

using	Base_t = SimplePolyFitterDataBase< T, D >
	class storing input More...

Additional Inherited Members
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, unsigned int D>
class lar::util::details::SimplePolyFitterBase< T, D >

Base class providing virtual fitting interface for polynomial fitters.

Definition at line 637 of file SimpleFits.h.

Member Typedef Documentation

template<typename T, unsigned int D>

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

private

class storing input

Definition at line 642 of file SimpleFits.h.

template<typename T, unsigned int D>

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, unsigned int D>

using lar::util::details::SimplePolyFitterBase< T, D >::FitMatrix_t = typename Interface_t::FitMatrix_t

type of matrix for covariance (a std::array)

Definition at line 659 of file SimpleFits.h.

template<typename T, unsigned int D>

using lar::util::details::SimplePolyFitterBase< T, D >::FitParameters_t = typename Interface_t::FitParameters_t

type of set of fit parameters

Definition at line 656 of file SimpleFits.h.

template<typename T, unsigned int D>

using lar::util::details::SimplePolyFitterBase< T, D >::Interface_t = SimpleFitterInterface<T, D + 1>

private

interface

Definition at line 641 of file SimpleFits.h.

Member Function Documentation

template<typename T , unsigned int D>

auto lar::util::details::SimplePolyFitterBase< T, D >::ChiSquare ( ) const

overridevirtual

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

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

Implements lar::util::details::SimpleFitterInterface< T, D+1 >.

Reimplemented in lar::util::QuadraticFit< T >, and lar::util::LinearFit< T >.

Definition at line 1741 of file SimpleFits.h.

 {
   // the generic implementation of ChiSquare from sums is complex enough that
   // I freaked out
   throw std::logic_error
     ("SimplePolyFitterBase::ChiSquare() not implemented for generic fit");
 } // SimplePolyFitterBase<>::ChiSquare()

template<typename T , unsigned int D>

auto lar::util::details::SimplePolyFitterBase< T, D >::Evaluate ( Data_t x ) const

overridevirtual

Evaluates the fitted function at the specified point.

Parameters

x	the point where to evaluate the fit function

Returns: the value of the fit function

No check is performed whether the fit is valid.

Definition at line 1641 of file SimpleFits.h.

 {
   FitParameters_t params = FitParameters();
   unsigned int iParam = NParams - 1; // point to last parameter (highest degree)
   Data_t v = params[iParam];
   while (iParam > 0) v = v * x + params[--iParam];
   return v;
 } // SimplePolyFitterBase<>::Evaluate()

template<typename T , unsigned int D>

auto lar::util::details::SimplePolyFitterBase< T, D >::ExtractParameterErrors ( FitMatrix_t const & Smat )

static

Extracts parameter errors from diagonal of the covarriance matrix.

Definition at line 1715 of file SimpleFits.h.

 {
   FitParameters_t fit_errors;
   for (unsigned int iParam = 0; iParam <= Degree; ++iParam)
     fit_errors[iParam] = std::sqrt(Smat[iParam * (NParams + 1)]);
   return fit_errors;
 } // SimplePolyFitterBase<>::FitParameterErrors(FitMatrix_t)

template<typename T , unsigned int D>

bool lar::util::details::SimplePolyFitterBase< T, D >::FillResults	(	FitParameters_t &	params,
		FitMatrix_t &	Xmat,
		Data_t &	det,
		FitMatrix_t &	Smat
	)		const

override

Fills the specified parameters.

Parameters

params	the fitted values of the parameters
Xmat	the matrix of the x^n/s^2 sums
Smat	the covariance matrix
det	the determinant of Xmat

Returns: true if the fit is valid (i.e. if a unique solution exists)

Definition at line 1598 of file SimpleFits.h.

         {
 
   Xmat = MakeMatrixX();
   det = Determinant(Xmat);
   if (!std::isnormal(det)) {
     Smat.fill(Data_t(0));
     params.fill(Data_t(0));
     return false;
   }
   Smat = InvertMatrix(Xmat, det);
   params = FitParameters(Smat, det);
   return true;
 } // SimplePolyFitterBase<>::FillResults(params, matrices, determinant)

template<typename T , unsigned int D>

bool lar::util::details::SimplePolyFitterBase< T, D >::FillResults	(	FitParameters_t &	params,
		FitParameters_t &	paramerrors,
		FitMatrix_t &	Xmat,
		Data_t &	det,
		FitMatrix_t &	Smat
	)		const

override

Fills the specified parameters.

Parameters

params	the fitted values of the parameters
paramerrors	the uncertainty on the fitted parameters
Xmat	the matrix of the x^n/s^2 sums
Smat	the covariance matrix
det	the determinant of Xmat

Returns: true if the fit is valid (i.e. if a unique solution exists)

Definition at line 1617 of file SimpleFits.h.

         {
 
   if (!this->FillResults(params, Xmat, det, Smat)) return false;
   paramerrors = ExtractParameterErrors(Smat);
   return true;
 } // SimplePolyFitterBase<>::FillResults(params, errors, matrices, determinant)

template<typename T , unsigned int D>

bool lar::util::details::SimplePolyFitterBase< T, D >::FillResults	(	FitParameters_t &	params,
		FitParameters_t &	paramerrors
	)		const

override

Fills the specified parameters.

Parameters

params	the fitted values of the parameters
paramerrors	the uncertainty on the fitted parameters

Returns: true if the fit is valid (i.e. if a unique solution exists)

Definition at line 1629 of file SimpleFits.h.

         {
   // to compute the parameters, we need all the stuff;
   // we just keep it local and discard it in the end. Such a waste.
   FitMatrix_t Xmat, Smat;
   Data_t det;
   return FillResults(params, paramerrors, Xmat, det, Smat);
 } // SimplePolyFitterBase<>::FillResults(params, errors)

template<typename T , unsigned int D>

auto lar::util::details::SimplePolyFitterBase< T, D >::FitParameter ( unsigned int n ) const

inlineoverridevirtual

Returns the parameter n of the fit result.

Parameters

n	degree of the parameter; must be no larger than Degree

Returns: the parameter of the fit, in y/x^n units

Exceptions

std::range_error if there is no unique solution

Reimplemented from lar::util::details::SimpleFitterInterface< T, D+1 >.

Definition at line 1548 of file SimpleFits.h.

 {
   return Param(n, MakeMatrixX());
 } // SimplePolyFitterBase<>::FitParameter(unsigned int)

template<typename T , unsigned int D>

auto lar::util::details::SimplePolyFitterBase< T, D >::FitParameterCovariance ( ) const

overridevirtual

Computes and returns all the covariance matrix of the fit result.

Returns: the the covariance matrix of the fit

Exceptions

std::range_error if there is no unique solution

The matrix is symmetric, and stored in a linear way (say, first row, then second row).

Implements lar::util::details::SimpleFitterInterface< T, D+1 >.

Definition at line 1585 of file SimpleFits.h.

 {
   FitMatrix_t Xmat = MakeMatrixX();
   Data_t det = Determinant(Xmat);
   if (!std::isnormal(det)) {
     throw std::range_error
       ("SimplePolyFitterBase::FitParameterCovariance(): determinant 0 while fitting");
   }
   return InvertMatrix(Xmat, det);
 } // SimplePolyFitterBase<>::FitParameterCovariance()

template<typename T , unsigned int D>

auto lar::util::details::SimplePolyFitterBase< T, D >::FitParameterError ( unsigned int n ) const

overridevirtual

Returns the error on parameter n of the fit result.

Parameters

n	degree of the parameter; must be no larger than Degree

Returns: the error on the parameter of the fit, in y/x^n units

Exceptions

std::range_error if there is no unique solution

Reimplemented from lar::util::details::SimpleFitterInterface< T, D+1 >.

Definition at line 1556 of file SimpleFits.h.

 {
   if (n > Degree) return Data_t(0); // no parameter, no error
   return std::sqrt(FitParameterCovariance()[n * (NParams + 1)]);
 } // SimplePolyFitterBase<>::FitParameterError()

template<typename T , unsigned int D>

auto lar::util::details::SimplePolyFitterBase< T, D >::FitParameterErrors ( ) const

overridevirtual

Computes and returns all the parameter errors of the fit result.

Returns: the full set of parameter errors of the fit

Exceptions

std::range_error if there is no unique solution

Implements lar::util::details::SimpleFitterInterface< T, D+1 >.

Definition at line 1576 of file SimpleFits.h.

 {
   return FitParameterErrors(FitParameterCovariance());
 } // SimplePolyFitterBase<>::FitParameterErrors()

template<typename T, unsigned int D>

virtual FitParameters_t lar::util::details::SimplePolyFitterBase< T, D >::FitParameterErrors ( FitMatrix_t const & Smat ) const

inlineprotectedvirtual

Computes and returns all the parameter errors of the fit result.

Definition at line 798 of file SimpleFits.h.

799 { return ExtractParameterErrors(Smat); }

lar::util::details::SimplePolyFitterBase::ExtractParameterErrors

static FitParameters_t ExtractParameterErrors(FitMatrix_t const &Smat)

Extracts parameter errors from diagonal of the covarriance matrix.

Definition: SimpleFits.h:1715

template<typename T , unsigned int D>

auto lar::util::details::SimplePolyFitterBase< T, D >::FitParameters ( ) const

overridevirtual

Computes and returns all the parameters of the fit result.

Returns: the full set of parameters of the fit

Exceptions

std::range_error if there is no unique solution

Implements lar::util::details::SimpleFitterInterface< T, D+1 >.

Definition at line 1564 of file SimpleFits.h.

 {
   FitMatrix_t Xmat = MakeMatrixX();
   FitParameters_t fit_params;
   for (unsigned int iParam = 0; iParam < NParams; ++iParam)
     fit_params[iParam] = Param(iParam, Xmat);
   return fit_params;
 } // SimplePolyFitterBase<>::FitParameters()

template<typename T , unsigned int D>

auto lar::util::details::SimplePolyFitterBase< T, D >::FitParameters ( FitMatrix_t const & Xmat ) const

protectedvirtual

Returns the fitted parameters using the provided information.

Definition at line 1679 of file SimpleFits.h.

 {
   FitParameters_t fit_params;
   for (unsigned int iParam = 0; iParam < NParams; ++iParam)
     fit_params[iParam] = Param(iParam, Xmat);
   return fit_params;
 } // SimplePolyFitterBase<>::FitParameters(FitMatrix_t)

template<typename T , unsigned int D>

auto lar::util::details::SimplePolyFitterBase< T, D >::FitParameters	(	FitMatrix_t const &	Smat,
		Data_t
	)		const

protectedvirtual

Definition at line 1691 of file SimpleFits.h.

 {
   return MatrixProduct(Smat, MakeMatrixY());
 } // SimplePolyFitterBase<>::FitParameters(FitMatrix_t)

template<typename T , unsigned int D>

bool lar::util::details::SimplePolyFitterBase< T, D >::isValid ( ) const

inlineoverridevirtual

Returns if the fit has valid results.

Returns: if the fit has valid results

The fit has no valid results if:

insufficient data has been add()ed (no more than the fit Degree)
if input points are vertically aligned

Note that checking point 2 is expensive in terms of time.

Implements lar::util::details::SimpleFitterInterface< T, D+1 >.

Definition at line 1540 of file SimpleFits.h.

                                                                     {
   return (Base_t::N() > (int) Degree)
     && std::isnormal(Determinant(MakeMatrixX()));
 } // SimplePolyFitterBase<>::isValid()

template<typename T , unsigned int D>

auto lar::util::details::SimplePolyFitterBase< T, D >::MakeMatrixX ( ) const

protectedvirtual

Fills and returns the matrix of x^n sum coefficients ( { x^(i+j) } )

Definition at line 1654 of file SimpleFits.h.

 {
   FitMatrix_t Xmat;
   for (unsigned int i = 0; i < NParams; ++i) { // row
     for (unsigned int j = i; j < NParams; ++j) { // column
       Xmat[j * NParams + i] = Xmat[i * NParams + j] = Base_t::XN(i+j);
     } // for j
   } // for i
   return Xmat;
 } // SimplePolyFitterBase<>::MakeMatrixX()

template<typename T , unsigned int D>

auto lar::util::details::SimplePolyFitterBase< T, D >::MakeMatrixY ( ) const

protectedvirtual

Fills and returns the matrix (vector) of x^n y sum coefficients.

Definition at line 1668 of file SimpleFits.h.

 {
   FitParameters_t Ymat;
   for (unsigned int i = 0; i < NParams; ++i) Ymat[i] = Base_t::XNY(i);
   return Ymat;
 } // SimplePolyFitterBase<>::MakeMatrixY()

template<typename T, unsigned int D>

virtual int lar::util::details::SimplePolyFitterBase< T, D >::NDF ( ) const

inlineoverridevirtual

Returns the degrees of freedom in the determination of the fit.

Returns: the degrees of freedom in the determination of the fit

The return value may be 0 or negative if insufficient points have been added.

Implements lar::util::details::SimpleFitterInterface< T, D+1 >.

Definition at line 731 of file SimpleFits.h.

731 { return Base_t::N() - NParams; }

lar::util::details::SimplePolyFitterBase::NParams

static constexpr unsigned int NParams

Number of parameters in the fit.

Definition: SimpleFits.h:651

lar::util::details::SimplePolyFitterDataBase::N

int N() const

Definition: SimpleFits.h:427

template<typename T , unsigned int D>

auto lar::util::details::SimplePolyFitterBase< T, D >::Param	(	unsigned int	n,
		FitMatrix_t const &	Xmat
	)		const

protectedvirtual

Computes a single fit parameter using the given information.

Definition at line 1700 of file SimpleFits.h.

 {
   if (n > Degree) return Data_t(0); // no such a degree, its coefficient is 0
 
   Data_t detXmat = Determinant(Xmat);
   if (!std::isnormal(detXmat)) {
     throw std::range_error
       ("SimplePolyFitterBase::Param(): Determinant 0 while fitting");
   }
   return Param(n, Xmat, detXmat);
 } // SimplePolyFitterBase<>::Param(unsigned int, FitMatrix_t)

template<typename T , unsigned int D>

auto lar::util::details::SimplePolyFitterBase< T, D >::Param	(	unsigned int	n,
		FitMatrix_t const &	Xmat,
		Data_t	detXmat
	)		const

protectedvirtual

Definition at line 1727 of file SimpleFits.h.

 {
   if (n > Degree) return Data_t(0); // no such a degree, its coefficient is 0
   // XYmat is as Xmat...
   FitMatrix_t XYmat(Xmat);
   // ... except that the N-th column is replaced with { sum x^i y }
   for (unsigned int i = 0; i < NParams; ++i)
     XYmat[i * NParams + n] = Base_t::XNY(i);
 
   return Determinant(XYmat) / detXmat;
 } // SimplePolyFitterBase<>::Param(unsigned int, FitMatrix_t, Data_t)

Member Data Documentation

template<typename T, unsigned int D>

constexpr unsigned int lar::util::details::SimplePolyFitterBase< T, D >::Degree = Base_t::Degree

static

Degree of the fit.

Definition at line 648 of file SimpleFits.h.

template<typename T, unsigned int D>

constexpr unsigned int lar::util::details::SimplePolyFitterBase< T, D >::NParams = Interface_t::NParams

static

Number of parameters in the fit.

Definition at line 651 of file SimpleFits.h.

The documentation for this class was generated from the following file:

SimpleFits.h

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Private Types

Additional Inherited Members

Detailed Description

template<typename T, unsigned int D> class lar::util::details::SimplePolyFitterBase< T, D >

Member Typedef Documentation

Member Function Documentation

Member Data Documentation

template<typename T, unsigned int D>
class lar::util::details::SimplePolyFitterBase< T, D >