polyfit.h File Reference

Polynomial fitting using the least squares method (Gauss-Newton for linear models) and evaluating polynomial function. More...

#include <stdexcept>
#include <Eigen/Eigen>

Go to the source code of this file.

Functions
template<typename Derived>
const Eigen::MatrixX< typename Derived::PlainObject::Scalar >	sablib::Vandermonde (const Eigen::MatrixBase< Derived > &x, const unsigned int polyorder)
	Generates a Vandermonde matrix for a given vector and polynomial order.
template<typename Derived>
const Derived::PlainObject	sablib::PolyFit (const Eigen::MatrixX< typename Derived::PlainObject::Scalar > &V, const Eigen::MatrixBase< Derived > &y)
	Solves the polynomial least squares fitting problem using a pre-calculated Vandermonde matrix.
template<typename Derived>
const Derived::PlainObject	sablib::PolyFit (const Eigen::MatrixBase< Derived > &x, const Eigen::MatrixBase< Derived > &y, const unsigned int polyorder)
	Fits a polynomial of a specified order to the given data points.
template<typename Derived>
const Derived::PlainObject	sablib::PolyVal (const Eigen::MatrixBase< Derived > &coeff, const Eigen::MatrixX< typename Derived::PlainObject::Scalar > &V)
	Evaluates the polynomial at specified points using a pre-calculated Vandermonde matrix.
template<typename Derived>
const Derived::PlainObject	sablib::PolyVal (const Eigen::MatrixBase< Derived > &coeff, const Eigen::MatrixBase< Derived > &x)
	Evaluates the polynomial at specified x-coordinates.
template<typename Derived>
const Derived::PlainObject::Scalar	sablib::PolyVal (const Eigen::MatrixBase< Derived > &coeff, const typename Derived::PlainObject::Scalar x)
	Evaluates the polynomial at single specified x-coordinate.

Detailed Description

Polynomial fitting using the least squares method (Gauss-Newton for linear models) and evaluating polynomial function.

Author

Izadori

Definition in file polyfit.h.

Function Documentation

PolyFit() [1/2]

template<typename Derived>

const Derived::PlainObject sablib::PolyFit	(	const Eigen::MatrixBase< Derived > &	x,
		const Eigen::MatrixBase< Derived > &	y,
		const unsigned int	polyorder )

Fits a polynomial of a specified order to the given data points.

This function uses the normal equations, which is the Gauss-Newton method applied to a linear model.

Parameters

x	The x-coordinates of the data points.
y	The y-coordinates of the data points.
polyorder	The order of the polynomial to fit.

Returns

The coefficients of the fitted polynomial (from lowest to highest order).

Exceptions

std::invalid_argument

If x and y sizes differ or if polyorder is too high for the number of points.

Definition at line 95 of file polyfit.h.

PolyFit() [2/2]

template<typename Derived>

const Derived::PlainObject sablib::PolyFit	(	const Eigen::MatrixX< typename Derived::PlainObject::Scalar > &	V,
		const Eigen::MatrixBase< Derived > &	y )

Solves the polynomial least squares fitting problem using a pre-calculated Vandermonde matrix.

Parameters

V	The Vandermonde matrix.
y	The target vector of data points.

Returns

The coefficients of the fitted polynomial.

Exceptions

std::invalid_argument

If the number of rows in V does not match the size of y.

Definition at line 66 of file polyfit.h.

PolyVal() [1/3]

template<typename Derived>

const Derived::PlainObject sablib::PolyVal	(	const Eigen::MatrixBase< Derived > &	coeff,
		const Eigen::MatrixBase< Derived > &	x )

Evaluates the polynomial at specified x-coordinates.

Parameters

coeff	The coefficients of the polynomial.
x	The x-coordinates where the polynomial will be evaluated.

Returns

The evaluated values.

Definition at line 151 of file polyfit.h.

PolyVal() [2/3]

template<typename Derived>

const Derived::PlainObject sablib::PolyVal	(	const Eigen::MatrixBase< Derived > &	coeff,
		const Eigen::MatrixX< typename Derived::PlainObject::Scalar > &	V )

Evaluates the polynomial at specified points using a pre-calculated Vandermonde matrix.

Parameters

coeff	The coefficients of the polynomial.
V	The Vandermonde matrix.

Returns

The evaluated values.

Exceptions

std::invalid_argument

If the length of coeff is zero or the number of columns in V does not match the size of coeff.

Definition at line 122 of file polyfit.h.

PolyVal() [3/3]

template<typename Derived>

const Derived::PlainObject::Scalar sablib::PolyVal	(	const Eigen::MatrixBase< Derived > &	coeff,
		const typename Derived::PlainObject::Scalar	x )

Evaluates the polynomial at single specified x-coordinate.

Parameters

coeff	The coefficients of the polynomial.
x	The x-coordinate where the polynomial will be evaluated.

Returns

The evaluated value.

Exceptions

std::invalid_argument

If the length of coeff is zero.

Definition at line 170 of file polyfit.h.

Vandermonde()

template<typename Derived>

const Eigen::MatrixX< typename Derived::PlainObject::Scalar > sablib::Vandermonde	(	const Eigen::MatrixBase< Derived > &	x,
		const unsigned int	polyorder )

Generates a Vandermonde matrix for a given vector and polynomial order.

Parameters

x	The input vector of data points.
polyorder	The order of the polynomial (columns in the matrix will be polyorder + 1).

Returns

The generated Vandermonde matrix.

Exceptions

std::invalid_argument

If the length of x is zero or polyorder is zero.

Definition at line 25 of file polyfit.h.