#include <vdgl_OrthogRegress.h>

Inheritance diagram for vdgl_OrthogRegress:

Public Types
typedef vdgl_ortho_regress	base
Public Member Functions
	vdgl_OrthogRegress ()
	vdgl_OrthogRegress (double, double, double)
void	IncrByXY (double x, double y)
void	DecrByXY (double x, double y)
void	Fit ()
double	GetA () const
double	GetB () const
double	GetC () const
double	GetCost () const
double	GetEstCost () const
void	SetEstCost (double v)
void	Reset ()
void	reset ()
void	add_point (double x, double y)
void	add_points (double const , double const , unsigned)
void	add_points (float const , float const , unsigned)
void	remove_point (double x, double y)
void	remove_points (double const , double const , unsigned)
void	remove_points (float const , float const , unsigned)
double	cost (double a, double b, double c) const
	The problem is to minimize total squared distance to the line u.x + d = 0, ie.
double	rms_cost (double a, double b, double c) const
bool	fit (double a, double b, double *c) const
bool	fit_constrained (double x, double y, double a, double b, double *c) const
Public Attributes
unsigned	S1
double	Sx
double	Sy
double	Sxx
double	Sxy
double	Syy
Protected Member Functions
bool	fit (double &a, double &b, double &c) const
bool	fit_constrained (double x, double y, double &a, double &b, double &c) const
	The problem is to minimize total squared distance from a line passing through a given point x_0 :
Private Attributes
double	a_
double	b_
double	c_
double	est_

Detailed Description

Definition at line 16 of file vdgl_OrthogRegress.h.

Member Typedef Documentation

typedef vdgl_ortho_regress vdgl_OrthogRegress::base

Definition at line 21 of file vdgl_OrthogRegress.h.

Constructor & Destructor Documentation

vdgl_OrthogRegress::vdgl_OrthogRegress ( ) [inline]

Definition at line 22 of file vdgl_OrthogRegress.h.

vdgl_OrthogRegress::vdgl_OrthogRegress	(	double	,
		double	,
		double
	)		`[inline]`

Definition at line 23 of file vdgl_OrthogRegress.h.

Member Function Documentation

void vdgl_ortho_regress::add_point	(	double	x,
		double	y
	)		`[inline, inherited]`

Definition at line 38 of file vdgl_ortho_regress.h.

void vdgl_ortho_regress::add_points	(	double const *	x,
		double const *	y,
		unsigned	n
	)		`[inherited]`

Definition at line 14 of file vdgl_ortho_regress.cxx.

void vdgl_ortho_regress::add_points	(	float const *	x,
		float const *	y,
		unsigned	n
	)		`[inherited]`

Definition at line 19 of file vdgl_ortho_regress.cxx.

double vdgl_ortho_regress::cost	(	double	a,
		double	b,
		double	c
	)		const `[inherited]`

The problem is to minimize total squared distance to the line u.x + d = 0, ie.

: minimize | u.x_i + d |^2 subject to |u|=1

Writing x_i = xbar + y_i, where xbar is the centroid of the point set, the sum becomes | u.(x_i - xbar) |^2 + S1 | u.xbar + d |^2 , so that the optimal line must pass through the centroid. To find u, we find the eigenvector of the scatter matrix M = (x_i - xbar)*(x_i - xbar)^t which has least eigenvalue.

Definition at line 74 of file vdgl_ortho_regress.cxx.

void vdgl_OrthogRegress::DecrByXY	(	double	x,
		double	y
	)		`[inline]`

Definition at line 25 of file vdgl_OrthogRegress.h.

void vdgl_OrthogRegress::Fit ( ) [inline]

Definition at line 26 of file vdgl_OrthogRegress.h.

bool vdgl_ortho_regress::fit	(	double *	a,
		double *	b,
		double *	c
	)		const `[inline, inherited]`

Definition at line 58 of file vdgl_ortho_regress.h.

bool vdgl_ortho_regress::fit	(	double &	a,
		double &	b,
		double &	c
	)		const `[protected, inherited]`

Definition at line 79 of file vdgl_ortho_regress.cxx.

bool vdgl_ortho_regress::fit_constrained	(	double	x,
		double	y,
		double *	a,
		double *	b,
		double *	c
	)		const `[inline, inherited]`

Definition at line 60 of file vdgl_ortho_regress.h.

bool vdgl_ortho_regress::fit_constrained	(	double	x,
		double	y,
		double &	a,
		double &	b,
		double &	c
	)		const `[protected, inherited]`

The problem is to minimize total squared distance from a line passing through a given point x_0 :

minimize | u.x_i + d |^2 subject to |u|=1 u.x_0 + d = 0

But u.x_i + d = u.(x_i - x_0), so that we have to minimize u^t M u , where M = (x_i - x_0)*(x_i - x_0)^t. This is solved by taking the eigenvector of M of least eigenvalue.

Definition at line 106 of file vdgl_ortho_regress.cxx.

double vdgl_OrthogRegress::GetA ( ) const [inline]

Definition at line 27 of file vdgl_OrthogRegress.h.

double vdgl_OrthogRegress::GetB ( ) const [inline]

Definition at line 28 of file vdgl_OrthogRegress.h.

double vdgl_OrthogRegress::GetC ( ) const [inline]

Definition at line 29 of file vdgl_OrthogRegress.h.

double vdgl_OrthogRegress::GetCost ( ) const [inline]

Definition at line 30 of file vdgl_OrthogRegress.h.

double vdgl_OrthogRegress::GetEstCost ( ) const [inline]

Definition at line 31 of file vdgl_OrthogRegress.h.