org.jscience.mathematics.analysis.fitting
Class PolynomialFitter

java.lang.Object
  org.jscience.mathematics.analysis.fitting.AbstractCurveFitter
      org.jscience.mathematics.analysis.fitting.PolynomialFitter

All Implemented Interfaces:

java.io.Serializable, EstimationProblem

public class PolynomialFitter
extends AbstractCurveFitter
implements EstimationProblem, java.io.Serializable

This class implements a curve fitting specialized for polynomials.

Polynomial fitting is a very simple case of curve fitting. The estimated coefficients are the polynom coefficients. They are searched by a least square estimator.

This class is by no means optimized, neither in space nor in time performance.

See Also:

PolynomialCoefficient, Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class org.jscience.mathematics.analysis.fitting.AbstractCurveFitter

AbstractCurveFitter.FitMeasurement

Field Summary

Fields inherited from class org.jscience.mathematics.analysis.fitting.AbstractCurveFitter

coefficients, measurements

Constructor Summary

PolynomialFitter(int degree, int maxIterations, double convergence, double steadyStateThreshold, double epsilon)
Simple constructor.

PolynomialFitter(PolynomialCoefficient[] coefficients, int maxIterations, double convergence, double steadyStateThreshold, double epsilon)
Simple constructor.

Method Summary

double	partial(double x, EstimatedParameter p) Get the derivative of the function at x with respect to parameter p.
double	valueAt(double x) Get the value of the function at x according to the current parameters value.

Methods inherited from class org.jscience.mathematics.analysis.fitting.AbstractCurveFitter

addWeightedPair, fit, getAllParameters, getMeasurements, getUnboundParameters, sortMeasurements

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.jscience.mathematics.analysis.estimation.EstimationProblem

getAllParameters, getMeasurements, getUnboundParameters

Constructor Detail

PolynomialFitter

public PolynomialFitter(int degree,
                        int maxIterations,
                        double convergence,
                        double steadyStateThreshold,
                        double epsilon)

Simple constructor.

The polynomial fitter built this way are complete polynoms, ie. a n-degree polynom has n+1 coefficients. In order to build fitter for sparse polynoms (for example a x^20 - b x^30, on should first build the coefficients array and provide it to PolynomialFitter(PolynomialCoefficient[],int,double,double, double).

Parameters:

degree - maximal degree of the polynom

maxIterations - maximum number of iterations allowed

convergence - criterion threshold below which we do not need to improve the criterion anymore

steadyStateThreshold - steady state detection threshold, the problem has reached a steady state (read converged) if Math.abs (Jn - Jn-1) < Jn * convergence, where Jn and Jn-1 are the current and preceding criterion value (square sum of the weighted residuals of considered measurements).

epsilon - threshold under which the matrix of the linearized problem is considered singular (see SquareMatrix.solve).

PolynomialFitter

public PolynomialFitter(PolynomialCoefficient[] coefficients,
                        int maxIterations,
                        double convergence,
                        double steadyStateThreshold,
                        double epsilon)

Simple constructor.

This constructor can be used either when a first estimate of the coefficients is already known (which is of little interest because the fit cost is the same whether a first guess is known or not) or when one needs to handle sparse polynoms like a x^20 - b x^30.

Parameters:

coefficients - first estimate of the coefficients. A reference to this array is hold by the newly created object. Its elements will be adjusted during the fitting process and they will be set to the adjusted coefficients at the end.

maxIterations - maximum number of iterations allowed

convergence - criterion threshold below which we do not need to improve the criterion anymore

steadyStateThreshold - steady state detection threshold, the problem has reached a steady state (read converged) if Math.abs (Jn - Jn-1) < Jn * convergence, where Jn and Jn-1 are the current and preceding criterion value (square sum of the weighted residuals of considered measurements).

epsilon - threshold under which the matrix of the linearized problem is considered singular (see SquareMatrix.solve).

Method Detail

valueAt

public double valueAt(double x)

Get the value of the function at x according to the current parameters value.

Specified by:

valueAt in class AbstractCurveFitter

Parameters:

x - abscissa at which the theoretical value is requested

Returns:

theoretical value at x

partial

public double partial(double x,
                      EstimatedParameter p)

Get the derivative of the function at x with respect to parameter p.

Specified by:

partial in class AbstractCurveFitter

Parameters:

x - abscissa at which the partial derivative is requested

p - parameter with respect to which the derivative is requested

Returns:

partial derivative