Polynomial regression. More...

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void	pprz_polyfit_float (float x, float y, int n, int p, float *c)
	Polynomial regression. More...

Detailed Description

Polynomial regression.

Definition in file pprz_polyfit_float.h.

Function Documentation

void pprz_polyfit_float	(	float *	x,
		float *	y,
		int	n,
		int	p,
		float *	c
	)

Polynomial regression.

Polynomial regression is a form of linear regression in which the relationship between the independent variable x and the dependent variable y is modelled as an nth order polynomial.

Considering the regression model:

$y_i = a_0 + a_1 x_i + ... + a_p x_i^p + \epsilon_i (i = 1 ... n)$

in matrix form

$y = Xa + \epsilon$

where

$X_{ij} = x_i^j (i = 1 ... n; j = 1 ... p)$

The vector of estimated polynomial regression coefficients using ordinary least squares estimation is

$a = (X' X)^{-1} X' y$

http://en.wikipedia.org/wiki/Polynomial_regression http://fr.wikipedia.org/wiki/R%C3%A9gression_polynomiale http://www.arachnoid.com/sage/polynomial.html

Parameters

[in]	x	pointer to the input array of independent variable X [n]
[in]	y	pointer to the input array of dependent variable Y [n]
[in]	n	number of input measurments
[in]	p	degree of the output polynomial
[out]	c	pointer to the output array of polynomial coefficients [p]

Polynomial regression is a form of linear regression in which the relationship between the independent variable x and the dependent variable y is modelled as an nth order polynomial.

Considering the regression model:

$y_i = c_0 + c_1 x_i + ... + c_p x_i^p + \epsilon_i (i = 1 ... n)$

in matrix form

$y = X.c + \epsilon$

where

$X_{ij} = x_i^j (i = 1 ... n; j = 1 ... p)$

The vector of estimated polynomial regression coefficients using ordinary least squares estimation is

$c = (X' X)^{-1} X' y$

http://en.wikipedia.org/wiki/Polynomial_regression http://fr.wikipedia.org/wiki/R%C3%A9gression_polynomiale http://www.arachnoid.com/sage/polynomial.html

Parameters

[in]	x	pointer to the input array of independent variable X [n]
[in]	y	pointer to the input array of dependent variable Y [n]
[in]	n	number of input measurments
[in]	p	degree of the output polynomial
[out]	c	pointer to the output array of polynomial coefficients [p+1]

Definition at line 63 of file pprz_polyfit_float.c.

References float_mat_zero(), float_vect_zero(), MAKE_MATRIX_PTR, pprz_svd_float(), and pprz_svd_solve_float().

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Detailed Description

Function Documentation