Computes a χ² from expectation function and data points. More...

#include "ChiSquareAccumulator.h"

Public Types
using	Function_t = F
	Type of function for the expectation. More...

using	Data_t = T
	Type of parameter and observed values. More...

Public Member Functions
unsigned int	N () const
	Returns the number of added points (it's not degrees of freedom yet!). More...

Data_t	expected (Data_t x) const
	Returns the expected value for the specified parameter. More...


	ChiSquareAccumulator (Function_t const &expected)
	Constructor: uses the specified expectation function. More...

Access to results
Data_t	chiSquare () const
	Returns the value of χ² currently accumulated. More...

Data_t	operator() () const
	Returns the value of χ² currently accumulated. More...

	operator Data_t () const
	Returns the value of χ² currently accumulated. More...

Data manipulation
void	add (Data_t x, Data_t y)
	Adds a data point to the χ². More...

void	add (Data_t x, Data_t y, Data_t s)
	Adds a data point to the χ². More...

void	clear ()
	Resets all the counts, starting from no data. More...

Static Private Member Functions
static Data_t	z (Data_t x, Data_t mu, Data_t sigma)
	Normal variable. More...

static Data_t	sqr (Data_t v)
	The usual square function. More...

Private Attributes
unsigned int	fN = 0U
	Number of data entries. More...

Data_t	fChiSq = 0.0
	Accumulated χ² value. More...

Function_t	fExpected
	Function for the expectation. More...

Detailed Description

template<typename F, typename T = double>
class lar::util::ChiSquareAccumulator< F, T >

Computes a χ² from expectation function and data points.

Template Parameters

F	type of the function
T	type of data

The formula used is the simple $\chi^{2} = \sum_{i} \left(\frac{y_{i} - e(x_{i})}{\sigma_{i}}\right)^{2}$ with each observed point being $( x_{i}, y_{i} \pm \sigma_{i} )$ and with $ e() $ the function describing the expectation (e.g. a fit result).

The parameter F must be usable as a unary functor, that is it must accept a single argument convertible from type Data_t (that is T), and return a value convertible back to type Data_t.

Example of usage:

double const a =  2.0;
double const b = -1.0;
auto f = [a,b](double x){ return a + b * x; };
lar::util::ChiSquareAccumulator<decltype(f)> chiSquare;
chiSquare.add(0.0, 1.0, 0.5); // add ( 0 ; 1.0 +/- 0.5 )
chiSquare.add(1.0, 1.0, 0.5); // add ( 1 ; 1.0 +/- 0.5 )
chiSquare.add(2.0, 1.0, 0.5); // add ( 2 ; 1.0 +/- 0.5 )
double const chi2value = chiSquare();
int degreesOfFreedom = int(chiSquare.N()) - 3;

will check three observations against the prediction of 2 - x, returning a chi2value of 8.0 and a degreesOfFreedom of 0 (note that the 3 degrees are manually subtracted).

Definition at line 53 of file ChiSquareAccumulator.h.

Member Typedef Documentation

template<typename F, typename T = double>

using lar::util::ChiSquareAccumulator< F, T >::Data_t = T

Type of parameter and observed values.

Definition at line 56 of file ChiSquareAccumulator.h.

template<typename F, typename T = double>

using lar::util::ChiSquareAccumulator< F, T >::Function_t = F

Type of function for the expectation.

Definition at line 55 of file ChiSquareAccumulator.h.

Constructor & Destructor Documentation

template<typename F, typename T = double>

lar::util::ChiSquareAccumulator< F, T >::ChiSquareAccumulator ( Function_t const & expected )

inline

Constructor: uses the specified expectation function.

Parameters

expected expectation function

The expectation function domain must be a single dimension of type Data_t.

Definition at line 66 of file ChiSquareAccumulator.h.

66 : fExpected(expected) {}

lar::util::ChiSquareAccumulator::fExpected

Function_t fExpected

Function for the expectation.

Definition: ChiSquareAccumulator.h:137

lar::util::ChiSquareAccumulator::expected

Data_t expected(Data_t x) const

Returns the expected value for the specified parameter.

Definition: ChiSquareAccumulator.h:84

Member Function Documentation

template<typename F, typename T = double>

void lar::util::ChiSquareAccumulator< F, T >::add	(	Data_t	x,
		Data_t	y
	)

inline

Adds a data point to the χ².

Parameters

x	parameter
y	observed data with the `x` parameter

The χ² is increased by $\left(y - e(x)\right)^{2}$ where e is the expectation function (expected()). The observed values are considered to have nominal uncertainty 1.

Definition at line 102 of file ChiSquareAccumulator.h.

References lar::util::ChiSquareAccumulator< F, T >::expected(), lar::util::ChiSquareAccumulator< F, T >::fChiSq, lar::util::ChiSquareAccumulator< F, T >::fN, and lar::util::ChiSquareAccumulator< F, T >::sqr().

       {
         fChiSq += sqr(y - expected(x));
         ++fN;
       }

template<typename F, typename T = double>

void lar::util::ChiSquareAccumulator< F, T >::add	(	Data_t	x,
		Data_t	y,
		Data_t	s
	)

inline

Adds a data point to the χ².

Parameters

x	parameter
y	observed data with the `x` parameter
s	uncertainty on the observed data (default: `1.0`)

The χ² is increased by $\left(\frac{y - e(x)}{s}\right)^{2}$ where e is the expectation function (expected()).

Definition at line 117 of file ChiSquareAccumulator.h.

References lar::util::ChiSquareAccumulator< F, T >::expected(), lar::util::ChiSquareAccumulator< F, T >::fChiSq, lar::util::ChiSquareAccumulator< F, T >::fN, lar::util::ChiSquareAccumulator< F, T >::sqr(), and lar::util::ChiSquareAccumulator< F, T >::z().

       {
         fChiSq += sqr(z(y, expected(x), s));
         ++fN;
       }

template<typename F, typename T = double>

Data_t lar::util::ChiSquareAccumulator< F, T >::chiSquare ( ) const

inline

Returns the value of χ² currently accumulated.

Definition at line 75 of file ChiSquareAccumulator.h.

References lar::util::ChiSquareAccumulator< F, T >::fChiSq.

Referenced by lar::util::ChiSquareAccumulator< F, T >::operator Data_t(), and lar::util::ChiSquareAccumulator< F, T >::operator()().

75 { return fChiSq; }

lar::util::ChiSquareAccumulator::fChiSq

Data_t fChiSq

Accumulated χ² value.

Definition: ChiSquareAccumulator.h:135

template<typename F, typename T = double>

void lar::util::ChiSquareAccumulator< F, T >::clear ( )

inline

Resets all the counts, starting from no data.

Definition at line 124 of file ChiSquareAccumulator.h.

References lar::util::ChiSquareAccumulator< F, T >::fChiSq, and lar::util::ChiSquareAccumulator< F, T >::fN.

       {
         fChiSq = Data_t{0};
         fN = 0U;
       }

template<typename F, typename T = double>

Data_t lar::util::ChiSquareAccumulator< F, T >::expected ( Data_t x ) const

inline

Returns the expected value for the specified parameter.

Definition at line 84 of file ChiSquareAccumulator.h.

References lar::util::ChiSquareAccumulator< F, T >::fExpected.

Referenced by lar::util::ChiSquareAccumulator< F, T >::add().

84 { return fExpected(x); }

x

Float_t x

Definition: compare.C:6

lar::util::ChiSquareAccumulator::fExpected

Function_t fExpected

Function for the expectation.

Definition: ChiSquareAccumulator.h:137

template<typename F, typename T = double>

unsigned int lar::util::ChiSquareAccumulator< F, T >::N ( ) const

inline

Returns the number of added points (it's not degrees of freedom yet!).

Definition at line 81 of file ChiSquareAccumulator.h.

References lar::util::ChiSquareAccumulator< F, T >::fN.

81 { return fN; }

lar::util::ChiSquareAccumulator::fN

unsigned int fN

Number of data entries.

Definition: ChiSquareAccumulator.h:134

template<typename F, typename T = double>

lar::util::ChiSquareAccumulator< F, T >::operator Data_t ( ) const

inline

Returns the value of χ² currently accumulated.

Definition at line 77 of file ChiSquareAccumulator.h.

References lar::util::ChiSquareAccumulator< F, T >::chiSquare().

77 { return chiSquare(); }

lar::util::ChiSquareAccumulator::chiSquare

Data_t chiSquare() const

Returns the value of χ² currently accumulated.

Definition: ChiSquareAccumulator.h:75

template<typename F, typename T = double>

Data_t lar::util::ChiSquareAccumulator< F, T >::operator() ( ) const

inline

Returns the value of χ² currently accumulated.

Definition at line 76 of file ChiSquareAccumulator.h.

References lar::util::ChiSquareAccumulator< F, T >::chiSquare().

76 { return chiSquare(); }

lar::util::ChiSquareAccumulator::chiSquare

Data_t chiSquare() const

Returns the value of χ² currently accumulated.

Definition: ChiSquareAccumulator.h:75

template<typename F, typename T = double>

static Data_t lar::util::ChiSquareAccumulator< F, T >::sqr ( Data_t v )

inlinestaticprivate

The usual square function.

Definition at line 143 of file ChiSquareAccumulator.h.

Referenced by lar::util::ChiSquareAccumulator< F, T >::add().

143 { return v * v; }

template<typename F, typename T = double>

static Data_t lar::util::ChiSquareAccumulator< F, T >::z	(	Data_t	x,
		Data_t	mu,
		Data_t	sigma
	)

inlinestaticprivate

Normal variable.

Definition at line 140 of file ChiSquareAccumulator.h.

Referenced by lar::util::ChiSquareAccumulator< F, T >::add().

140 { return (x - mu) / sigma; }

x

Float_t x

Definition: compare.C:6

Member Data Documentation

template<typename F, typename T = double>

Data_t lar::util::ChiSquareAccumulator< F, T >::fChiSq = 0.0

private

Accumulated χ² value.

Definition at line 135 of file ChiSquareAccumulator.h.

Referenced by lar::util::ChiSquareAccumulator< F, T >::add(), lar::util::ChiSquareAccumulator< F, T >::chiSquare(), and lar::util::ChiSquareAccumulator< F, T >::clear().

template<typename F, typename T = double>

Function_t lar::util::ChiSquareAccumulator< F, T >::fExpected

private

Function for the expectation.

Definition at line 137 of file ChiSquareAccumulator.h.

Referenced by lar::util::ChiSquareAccumulator< F, T >::expected().

template<typename F, typename T = double>

unsigned int lar::util::ChiSquareAccumulator< F, T >::fN = 0U

private

Number of data entries.

Definition at line 134 of file ChiSquareAccumulator.h.

Referenced by lar::util::ChiSquareAccumulator< F, T >::add(), lar::util::ChiSquareAccumulator< F, T >::clear(), and lar::util::ChiSquareAccumulator< F, T >::N().

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

lardata/v09_16_03/source/lardata/Utilities/ChiSquareAccumulator.h

Public Types

Public Member Functions

Static Private Member Functions

Private Attributes

Detailed Description

template<typename F, typename T = double> class lar::util::ChiSquareAccumulator< F, T >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename F, typename T = double>
class lar::util::ChiSquareAccumulator< F, T >