org.apache.commons.math.analysis.polynomials
Class PolynomialFunctionLagrangeForm

java.lang.Object
  org.apache.commons.math.analysis.polynomials.PolynomialFunctionLagrangeForm

All Implemented Interfaces:

UnivariateRealFunction

public class PolynomialFunctionLagrangeForm
extends Object
implements UnivariateRealFunction

Implements the representation of a real polynomial function in Lagrange Form. For reference, see Introduction to Numerical Analysis, ISBN 038795452X, chapter 2.

The approximated function should be smooth enough for Lagrange polynomial to work well. Otherwise, consider using splines instead.

Since:

1.2

Version:

$Revision: 1073498 $ $Date: 2011-02-22 21:57:26 +0100 (mar. 22 févr. 2011) $

Constructor Summary

PolynomialFunctionLagrangeForm(double[] x, double[] y)
Construct a Lagrange polynomial with the given abscissas and function values.

Method Summary

protected void	computeCoefficients() Calculate the coefficients of Lagrange polynomial from the interpolation data.
int	degree() Returns the degree of the polynomial.
static double	evaluate(double[] x, double[] y, double z) Evaluate the Lagrange polynomial using Neville's Algorithm.
double[]	getCoefficients() Returns a copy of the coefficients array.
double[]	getInterpolatingPoints() Returns a copy of the interpolating points array.
double[]	getInterpolatingValues() Returns a copy of the interpolating values array.
double	value(double z) Compute the value for the function.
static void	verifyInterpolationArray(double[] x, double[] y) Verifies that the interpolation arrays are valid.

Methods inherited from class java.lang.Object

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

Constructor Detail

PolynomialFunctionLagrangeForm

public PolynomialFunctionLagrangeForm(double[] x,
                                      double[] y)
                               throws IllegalArgumentException

Construct a Lagrange polynomial with the given abscissas and function values. The order of interpolating points are not important.

The constructor makes copy of the input arrays and assigns them.

Parameters:

x - interpolating points

y - function values at interpolating points

Throws:

IllegalArgumentException - if input arrays are not valid

Method Detail

value

public double value(double z)
             throws FunctionEvaluationException

Compute the value for the function.

Specified by:

value in interface UnivariateRealFunction

Parameters:

z - the point for which the function value should be computed

Returns:

the value

Throws:

FunctionEvaluationException - if the function evaluation fails

degree

public int degree()

Returns the degree of the polynomial.

Returns:

the degree of the polynomial

getInterpolatingPoints

public double[] getInterpolatingPoints()

Returns a copy of the interpolating points array.

Changes made to the returned copy will not affect the polynomial.

Returns:

a fresh copy of the interpolating points array

getInterpolatingValues

public double[] getInterpolatingValues()

Returns a copy of the interpolating values array.

Changes made to the returned copy will not affect the polynomial.

Returns:

a fresh copy of the interpolating values array

getCoefficients

public double[] getCoefficients()

Returns a copy of the coefficients array.

Changes made to the returned copy will not affect the polynomial.

Note that coefficients computation can be ill-conditioned. Use with caution and only when it is necessary.

Returns:

a fresh copy of the coefficients array

evaluate

public static double evaluate(double[] x,
                              double[] y,
                              double z)
                       throws DuplicateSampleAbscissaException,
                              IllegalArgumentException

Evaluate the Lagrange polynomial using Neville's Algorithm. It takes O(N^2) time.

This function is made public static so that users can call it directly without instantiating PolynomialFunctionLagrangeForm object.

Parameters:

x - the interpolating points array

y - the interpolating values array

z - the point at which the function value is to be computed

Returns:

the function value

Throws:

DuplicateSampleAbscissaException - if the sample has duplicate abscissas

IllegalArgumentException - if inputs are not valid

computeCoefficients

protected void computeCoefficients()
                            throws ArithmeticException

Calculate the coefficients of Lagrange polynomial from the interpolation data. It takes O(N^2) time.

Note this computation can be ill-conditioned. Use with caution and only when it is necessary.

Throws:

ArithmeticException - if any abscissas coincide

verifyInterpolationArray

public static void verifyInterpolationArray(double[] x,
                                            double[] y)
                                     throws IllegalArgumentException

Verifies that the interpolation arrays are valid.

The arrays features checked by this method are that both arrays have the same length and this length is at least 2.

The interpolating points must be distinct. However it is not verified here, it is checked in evaluate() and computeCoefficients().

Parameters:

x - the interpolating points array

y - the interpolating values array

Throws:

IllegalArgumentException - if not valid

See Also:

evaluate(double[], double[], double), computeCoefficients()