#include <vdgl_ortho_regress.h>

Inheritance diagram for vdgl_ortho_regress:

Public Member Functions
void	reset ()
	vdgl_ortho_regress ()
	~vdgl_ortho_regress ()
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 :

Detailed Description

Definition at line 21 of file vdgl_ortho_regress.h.

Constructor & Destructor Documentation

vdgl_ortho_regress::vdgl_ortho_regress ( ) [inline]

Definition at line 34 of file vdgl_ortho_regress.h.

vdgl_ortho_regress::~vdgl_ortho_regress ( ) [inline]

Definition at line 36 of file vdgl_ortho_regress.h.

Member Function Documentation

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

Definition at line 38 of file vdgl_ortho_regress.h.

void vdgl_ortho_regress::add_points	(	double const *	x,
		double const *	y,
		unsigned	n
	)

Definition at line 14 of file vdgl_ortho_regress.cxx.

void vdgl_ortho_regress::add_points	(	float const *	x,
		float const *	y,
		unsigned	n
	)

Definition at line 19 of file vdgl_ortho_regress.cxx.

double vdgl_ortho_regress::cost	(	double	a,
		double	b,
		double	c
	)		const

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.

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

Definition at line 58 of file vdgl_ortho_regress.h.

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

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]`

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]`

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.