matrix_linear.cpp File Reference

Solving sets of linear equations through matrix algebra. More...

#include "Matrix.h"
#include "utilities.h"

Functions
double	linear_least_squares (int n1, int n2, double *x, double *y, double &a, double &b)
	Does a linear least squares fit between two vectors. More...
double	linear_least_squares (int n1, int n2, vector< double > &x, vector< double > &y, double &a, double &b)
double	fit_polynomial (int n, vector< double > &x, vector< double > &y, int order, vector< double > &coeff)
	Fits a data set to a polynomial function. More...
double	fit_polynomial (int n, double *x, double *y, int order, double *coeff)
	Fits a data set to a polynomial function. More...
Vector3< double >	fit_plane (Matrix a, vector< double > b)
	Solves for fitting a plane through a model. More...
vector< double >	fit_conic (vector< Vector3< double > > v)
	Solves for fitting a conic through a model. More...
vector< double >	fit_ellipse (vector< Vector3< double > > v)
	Solves for fitting a conic through a model. More...
vector< double >	fit_ellipse2 (vector< Vector3< double > > v)
	Solves for fitting a conic through a model. More...

Variables
int	verbose

Detailed Description

Solving sets of linear equations through matrix algebra.

Author

Bernard Heymann

Date

Created: 20000501

Modified: 20220216

Function Documentation

fit_conic()

vector< double > fit_conic

(

vector< Vector3< double > >

v

)

Solves for fitting a conic through a model.

Parameters

v	set of xy coordinates.

Returns

vector<double> 6 coefficients.

The conic is defined as:
    0 = c0 + c1*x + c2*y + c3*x2 + c4*x*y + c5*y2

fit_ellipse()

vector< double > fit_ellipse

(

vector< Vector3< double > >

v

)

Solves for fitting a conic through a model.

Parameters

v	set of xy coordinates.

Returns

vector<double> 6 coefficients.

The conic is defined as:
    0 = c0 + c1*x + c2*y + c3*x2 + c4*x*y + c5*y2

fit_ellipse2()

vector< double > fit_ellipse2

(

vector< Vector3< double > >

v

)

Solves for fitting a conic through a model.

Parameters

v	set of xy coordinates.

Returns

vector<double> 6 coefficients.

The conic is defined as:
    0 = c0 + c1*x + c2*y + c3*x2 + c4*x*y + c5*y2

fit_plane()

Vector3< double > fit_plane	(	Matrix	a,
		vector< double >	b
	)

Solves for fitting a plane through a model.

Parameters

a	3x3 matrix with cross-terms.
b	3 vector with averages.

Returns

Vector3<double> plane normal.

A plane is fit through the components and the normal calculated from:
    n•p = d
where n is the normal vector, p is a point in the plane, and d is the offset.

fit_polynomial() [1/2]

double fit_polynomial	(	int	n,
		double *	x,
		double *	y,
		int	order,
		double *	coeff
	)

Fits a data set to a polynomial function.

Parameters

n	number of data points.
*x	x array (at least order+1 values).
*y	y array (at least order+1 values).
order	polynomial order.
*coeff	array in which coefficients are returned (order+1 values) (if NULL, no coefficients returned).

Returns

double the deviation.

A polynomial of any order is fitted to the data using a least squares.
The polynomial is defined as:
    f(x) = a0 + a1*x + a2*x^2 + ...
The number of coefficients returned is the order plus one.
The deviation is defined as:
    R = sqrt(sum(y - f(x))^2/n)

fit_polynomial() [2/2]

double fit_polynomial	(	int	n,
		vector< double > &	x,
		vector< double > &	y,
		int	order,
		vector< double > &	coeff
	)

Fits a data set to a polynomial function.

Parameters

n	number of data points.
&x	x array (at least order+1 values).
&y	y array (at least order+1 values).
order	polynomial order.
&coeff	array in which coefficients are returned (order+1 values) (if NULL, no coefficients returned).

Returns

double the deviation.

A polynomial of any order is fitted to the data using a least squares.
The polynomial is defined as:
    f(x) = a0 + a1*x + a2*x^2 + ...
The number of coefficients returned is the order plus one.
The deviation is defined as:
    R = sqrt(sum(y - f(x))^2/n)

linear_least_squares() [1/2]

double linear_least_squares	(	int	n1,
		int	n2,
		double *	x,
		double *	y,
		double &	a,
		double &	b
	)

Does a linear least squares fit between two vectors.

Parameters

n1	the starting index in each vector (usually 0).
n2	the final index in each vector.
*x	x vector (at least n2+1 elements).
*y	y vector (at least n2+1 elements).
&a	the intercept.
&b	the slope.

Returns

double the correlation index.

The two input vectors must have elements between indices n1 and n2.

linear_least_squares() [2/2]

double linear_least_squares	(	int	n1,
		int	n2,
		vector< double > &	x,
		vector< double > &	y,
		double &	a,
		double &	b
	)

Variable Documentation

verbose

int verbose

extern