DGtal::SimpleLinearRegression Class Reference

Description of class 'SimpleLinearRegression'. More...

#include <DGtal/math/SimpleLinearRegression.h>

Public Member Functions
	~SimpleLinearRegression ()
	SimpleLinearRegression (double eps_zero=1e-8)
void	clear ()
template<class XIterator , class YIterator >
void	addSamples (XIterator begin_x, XIterator end_x, YIterator begin_y)
void	addSample (const double x, const double y)
bool	computeRegression ()
double	slope () const
double	intercept () const
double	estimateY (double x) const
double	estimateVariance () const
std::pair< double, double >	trustIntervalForY (const double x, const double a) const
void	setEpsilonZero (const double aEpsilonZero)
double	epsilonZero () const
double	size () const
void	selfDisplay (std::ostream &that_stream) const
bool	isValid () const

Private Member Functions
	SimpleLinearRegression (const SimpleLinearRegression &other)
SimpleLinearRegression &	operator= (const SimpleLinearRegression &other)

Private Attributes
double	myEpsilonZero
	Epsilon zero value. More...
unsigned int	myN
	Number of samples. More...
std::vector< double >	myY
	Ordinate values of sample points. More...
std::vector< double >	myX
	Abscissa values of sample points. More...
double	myB [2]
std::vector< double >	myU
double	mySumX
double	mySumX2
double	mySumY
double	mySumXY
double	myD
double	myNormU2

Detailed Description

Description of class 'SimpleLinearRegression'.

Aim: Represents a simple linear regression model with 1 regressor constant and 1 variable regressor and n data: Y = X B + U, where U follows Gaussian law N(0, sigma^2 I_n). Y, U are n-vectors, B is a 2-vector, X is the nx2-matrix [(1 x1) ... (1 xn) ] with rank 2.

This class can compute the linear regression coefficients and also performs some tests to check if the data corresponds to a linear model.

Note

backport from ImaGene.

Definition at line 73 of file SimpleLinearRegression.h.

Constructor & Destructor Documentation

~SimpleLinearRegression()

DGtal::SimpleLinearRegression::~SimpleLinearRegression

(

)

Destructor.

SimpleLinearRegression() [1/2]

DGtal::SimpleLinearRegression::SimpleLinearRegression

(

double

eps_zero = 1e-8

)

Constructor. The object is empty (and invalid for regression).

Parameters

eps_zero

the value below which the absolute value of the determinant is considered null.

SimpleLinearRegression() [2/2]

DGtal::SimpleLinearRegression::SimpleLinearRegression ( const SimpleLinearRegression &  other )

private

Copy constructor.

Parameters

other

the object to clone. Forbidden by default.

Member Function Documentation

addSample()

void DGtal::SimpleLinearRegression::addSample	(	const double	x,
		const double	y
	)

Adds the sample (y,x). Does not compute immediately the regression. See 'computeRegression' for computing the regression with the current samples.

Parameters

x	the x data.
y	the y data.

See also

computeRegression

Referenced by DGtal::OrderedLinearRegression::backwardSLR(), DGtal::OrderedLinearRegression::forwardSLR(), and testSimpleRegression().

addSamples()

template<class XIterator , class YIterator >

void DGtal::SimpleLinearRegression::addSamples	(	XIterator	begin_x,
		XIterator	end_x,
		YIterator	begin_y
	)

Adds the samples (y,x). Does not compute immediately the regression. See 'computeRegression' for computing the regression with the current samples.

Parameters

begin_x	an iterator on the first x-data
end_x	an iterator after the last x-data
begin_y	an iterator on the first y-data

See also

computeRegression

Referenced by DGtal::OrderedLinearRegression::backwardSLR(), DGtal::OrderedLinearRegression::forwardSLR(), testSimpleRegression2(), testSimpleRegression3(), and testSimpleRegressionOrdered().

clear()

void DGtal::SimpleLinearRegression::clear

(

)

Clear all datas.

Referenced by DGtal::OrderedLinearRegression::backwardSLR(), and DGtal::OrderedLinearRegression::forwardSLR().

computeRegression()

bool DGtal::SimpleLinearRegression::computeRegression

(

)

Computes the regression of the current parameters.

Returns

'true' if the regression was valid (non null number of samples, rank of X is 2), 'false' otherwise.

Referenced by DGtal::OrderedLinearRegression::backwardSLR(), DGtal::OrderedLinearRegression::forwardSLR(), testSimpleRegression(), testSimpleRegression2(), testSimpleRegression3(), and testSimpleRegressionOrdered().

epsilonZero()

double DGtal::SimpleLinearRegression::epsilonZero ( ) const

inline

Returns

the epsilon zero value.

Definition at line 190 of file SimpleLinearRegression.h.

    {
      return myEpsilonZero;
    }

References myEpsilonZero.

estimateVariance()

double DGtal::SimpleLinearRegression::estimateVariance

(

)

const

Returns

the current estimation of the variance of the Gaussian perturbation (i.e. variance of U).

estimateY()

double DGtal::SimpleLinearRegression::estimateY

(

double

x

)

const

Given a new x, predicts its y (hat{y}) according to the linear regression model.

Parameters

x	any value.

Returns

the estimated y value, ie hat{y} = B0 + B1*x.

intercept()

double DGtal::SimpleLinearRegression::intercept

(

)

const

Returns

the intercept of the linear regression (B0 in Y=B0+B1*X).

Referenced by testSimpleRegression(), testSimpleRegression2(), and testSimpleRegression3().

isValid()

bool DGtal::SimpleLinearRegression::isValid

(

)

const

Checks the validity/consistency of the object.

Returns

'true' if the object is valid, 'false' otherwise.

operator=()

SimpleLinearRegression& DGtal::SimpleLinearRegression::operator= ( const SimpleLinearRegression &  other )

private

Assignment.

Parameters

other

the object to copy.

Returns

a reference on 'this'. Forbidden by default.

selfDisplay()

void DGtal::SimpleLinearRegression::selfDisplay

(

std::ostream &

that_stream

)

const

Writes/Displays the object on an output stream.

Parameters

that_stream

the output stream where the object is written.

setEpsilonZero()

void DGtal::SimpleLinearRegression::setEpsilonZero ( const double  aEpsilonZero )

inline

Set the epsilon zero value, value below which the absolute value of the determinant is considered null.

Parameters

aEpsilonZero

the epsilon zero value.

Definition at line 181 of file SimpleLinearRegression.h.

    {
      myEpsilonZero = aEpsilonZero;
    }

References myEpsilonZero.

Referenced by DGtal::OrderedLinearRegression::backwardSLR(), and DGtal::OrderedLinearRegression::forwardSLR().

size()

double DGtal::SimpleLinearRegression::size ( ) const

inline

Returns

the number of samples.

Definition at line 199 of file SimpleLinearRegression.h.

    {
      return myN;
    }

References myN.

Referenced by testSimpleRegressionOrdered().

slope()

double DGtal::SimpleLinearRegression::slope

(

)

const

Returns

the slope of the linear regression (B1 in Y=B0+B1*X).

Referenced by testSimpleRegression(), testSimpleRegression2(), testSimpleRegression3(), and testSimpleRegressionOrdered().

trustIntervalForY()

std::pair<double,double> DGtal::SimpleLinearRegression::trustIntervalForY	(	const double	x,
		const double	a
	)		const

Given a test confidence value (1-[a]), return the expected interval of value for Y, given a new [x], so that the model is still linear. One may thus check if a new pair (y,x) is still in the current linear model or not.

Parameters

x	any x value.
a	the expected confidence value for the test (a=0.05 means 95% of confidence).

Returns

the expected interval [min_y, max_y] such that any value y within confirms the current linear model.

Referenced by DGtal::OrderedLinearRegression::backwardSLR(), and DGtal::OrderedLinearRegression::forwardSLR().

Field Documentation

myB

double DGtal::SimpleLinearRegression::myB[2]

private

Linear regression line parameters [0] is the intercept and [1] the slope.

Definition at line 237 of file SimpleLinearRegression.h.

myD

double DGtal::SimpleLinearRegression::myD

private

Definition at line 245 of file SimpleLinearRegression.h.

myEpsilonZero

double DGtal::SimpleLinearRegression::myEpsilonZero

private

Epsilon zero value.

Definition at line 224 of file SimpleLinearRegression.h.

Referenced by epsilonZero(), and setEpsilonZero().

myN

unsigned int DGtal::SimpleLinearRegression::myN

private

Number of samples.

Definition at line 227 of file SimpleLinearRegression.h.

Referenced by size().

myNormU2

double DGtal::SimpleLinearRegression::myNormU2

private

Definition at line 246 of file SimpleLinearRegression.h.

mySumX

double DGtal::SimpleLinearRegression::mySumX

private

Definition at line 241 of file SimpleLinearRegression.h.

mySumX2

double DGtal::SimpleLinearRegression::mySumX2

private

Definition at line 242 of file SimpleLinearRegression.h.

mySumXY

double DGtal::SimpleLinearRegression::mySumXY

private

Definition at line 244 of file SimpleLinearRegression.h.

mySumY

double DGtal::SimpleLinearRegression::mySumY

private

Definition at line 243 of file SimpleLinearRegression.h.

myU

std::vector<double> DGtal::SimpleLinearRegression::myU

private

Definition at line 240 of file SimpleLinearRegression.h.

myX

std::vector<double> DGtal::SimpleLinearRegression::myX

private

Abscissa values of sample points.

Definition at line 233 of file SimpleLinearRegression.h.

myY

std::vector<double> DGtal::SimpleLinearRegression::myY

private

Ordinate values of sample points.

Definition at line 230 of file SimpleLinearRegression.h.

---

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

• SimpleLinearRegression.h