QuadraticRegression Class Reference

Estimates model parameters for a quadratic equation. More...

#include <OpenMS/ML/REGRESSION/QuadraticRegression.h>

Collaboration diagram for QuadraticRegression:

Public Member Functions
	QuadraticRegression ()
	Default constructor.
void	computeRegression (std::vector< double >::const_iterator x_begin, std::vector< double >::const_iterator x_end, std::vector< double >::const_iterator y_begin)
	Fit y = a + b*x + c*x^2 to unweighted 2D points.
void	computeRegressionWeighted (std::vector< double >::const_iterator x_begin, std::vector< double >::const_iterator x_end, std::vector< double >::const_iterator y_begin, std::vector< double >::const_iterator w_begin)
	Fit y = a + b*x + c*x^2 to weighted 2D points.
double	eval (double x) const
	Evaluate the fitted polynomial at x.
double	getA () const
	Constant term of the fitted polynomial.
double	getB () const
	Linear coefficient of the fitted polynomial.
double	getC () const
	Quadratic coefficient of the fitted polynomial.
double	getChiSquared () const
	Weighted residual sum of squares of the last successful fit.

Static Public Member Functions
static double	eval (double A, double B, double C, double x)
	Evaluate a quadratic polynomial at x using externally-supplied coefficients.

Protected Attributes
double	a_
	Constant term of the last successful fit.
double	b_
	Linear coefficient of the last successful fit.
double	c_
	Quadratic coefficient of the last successful fit.
double	chi_squared_
	Weighted residual sum of the last successful fit.

Detailed Description

Estimates model parameters for a quadratic equation.

Fits the coefficients of y = a + b*x + c*x^2 via the normal equations of a (weighted) least-squares problem. Both an unweighted (computeRegression) and a weighted (computeRegressionWeighted) overload are provided.

Once a fit is computed the coefficients and the chi-squared sum can be queried via getA / getB / getC / getChiSquared, and the resulting polynomial can be evaluated via eval. A static overload of eval is available for evaluating an externally-supplied (A,B,C) triple.

Before the first successful fit the coefficients and the chi-squared sum read back as 0.

Constructor & Destructor Documentation

QuadraticRegression()

QuadraticRegression

(

)

Default constructor.

Leaves all coefficients and the chi-squared sum at 0; the instance produces meaningful results only after the first successful call to computeRegression or computeRegressionWeighted.

Member Function Documentation

computeRegression()

void computeRegression	(	std::vector< double >::const_iterator	x_begin,
		std::vector< double >::const_iterator	x_end,
		std::vector< double >::const_iterator	y_begin
	)

Fit y = a + b*x + c*x^2 to unweighted 2D points.

Equivalent to calling computeRegressionWeighted with a uniform weight of 1 for every point. On success the coefficients and getChiSquared are updated.

Parameters

[in]	x_begin	Iterator to the first x value.
[in]	x_end	Past-the-end iterator for the x range.
[in]	y_begin	Iterator to the first y value; the y range must contain at least std::distance(x_begin, x_end) elements.

Exceptions

Exception::UnableToFit

if the resulting linear system is singular (e.g. fewer than three distinct x values).

computeRegressionWeighted()

void computeRegressionWeighted	(	std::vector< double >::const_iterator	x_begin,
		std::vector< double >::const_iterator	x_end,
		std::vector< double >::const_iterator	y_begin,
		std::vector< double >::const_iterator	w_begin
	)

Fit y = a + b*x + c*x^2 to weighted 2D points.

Solves the weighted normal equations for the quadratic model. On success the coefficients and getChiSquared are updated.

Parameters

[in]	x_begin	Iterator to the first x value.
[in]	x_end	Past-the-end iterator for the x range.
[in]	y_begin	Iterator to the first y value; the y range must contain at least std::distance(x_begin, x_end) elements.
[in]	w_begin	Iterator to the first weight; the weight range must contain at least std::distance(x_begin, x_end) elements.

Exceptions

Exception::UnableToFit

if the resulting linear system is singular (e.g. fewer than three distinct x values).

eval() [1/2]

static double eval ( double  A, double  B, double  C, double  x  )

static

Evaluate a quadratic polynomial at x using externally-supplied coefficients.

Parameters

[in]	A	Constant term.
[in]	B	Linear coefficient.
[in]	C	Quadratic coefficient.
[in]	x	Input value.

Returns

A + B*x + C*x*x.

eval() [2/2]

double eval

(

double

x

)

const

Evaluate the fitted polynomial at x.

Parameters

[in]

x

Input value.

Returns

a + b*x + c*x^2 using the currently stored coefficients.

getA()

double getA

(

)

const

Constant term of the fitted polynomial.

Returns

a from the last successful fit (or 0 if no fit has been computed yet).

getB()

double getB

(

)

const

Linear coefficient of the fitted polynomial.

Returns

b from the last successful fit (or 0 if no fit has been computed yet).

getC()

double getC

(

)

const

Quadratic coefficient of the fitted polynomial.

Returns

c from the last successful fit (or 0 if no fit has been computed yet).

getChiSquared()

double getChiSquared

(

)

const

Weighted residual sum of squares of the last successful fit.

Returns

sum(weight * (y - a - b*x - c*x*x)^2) over the last fit's input points (or 0 if no fit has been computed yet).

Member Data Documentation

a_

double a_

protected

Constant term of the last successful fit.

b_

double b_

protected

Linear coefficient of the last successful fit.

c_

double c_

protected

Quadratic coefficient of the last successful fit.

chi_squared_

double chi_squared_

protected

Weighted residual sum of the last successful fit.