Package org.apache.commons.math.analysis.polynomials

Class PolynomialSplineFunction

java.lang.Object

org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction

All Implemented Interfaces:

DifferentiableUnivariateRealFunction, UnivariateRealFunction

public class PolynomialSplineFunction
extends java.lang.Object
implements DifferentiableUnivariateRealFunction

Represents a polynomial spline function.

A polynomial spline function consists of a set of interpolating polynomials and an ascending array of domain knot points, determining the intervals over which the spline function is defined by the constituent polynomials. The polynomials are assumed to have been computed to match the values of another function at the knot points. The value consistency constraints are not currently enforced by PolynomialSplineFunction itself, but are assumed to hold among the polynomials and knot points passed to the constructor.

N.B.: The polynomials in the polynomials property must be centered on the knot points to compute the spline function values. See below.

The domain of the polynomial spline function is [smallest knot, largest knot]. Attempts to evaluate the function at values outside of this range generate IllegalArgumentExceptions.

The value of the polynomial spline function for an argument x is computed as follows:

1. The knot array is searched to find the segment to which x belongs. If x is less than the smallest knot point or greater than the largest one, an IllegalArgumentException is thrown.
2. Let j be the index of the largest knot point that is less than or equal to x. The value returned is
   polynomials[j](x - knot[j])

Constructor Summary

Constructors

Constructor	Description
PolynomialSplineFunction(double[] knots, PolynomialFunction[] polynomials)	Construct a polynomial spline function with the given segment delimiters and interpolating polynomials.

Method Summary

Modifier and Type	Method	Description
UnivariateRealFunction	derivative()	Returns the derivative of the polynomial spline function as a UnivariateRealFunction
double[]	getKnots()	Returns an array copy of the knot points.
int	getN()	Returns the number of spline segments = the number of polynomials = the number of knot points - 1.
PolynomialFunction[]	getPolynomials()	Returns a copy of the interpolating polynomials array.
PolynomialSplineFunction	polynomialSplineDerivative()	Returns the derivative of the polynomial spline function as a PolynomialSplineFunction
double	value(double v)	Compute the value for the function.

Methods inherited from class java.lang.Object

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

Constructor Detail

PolynomialSplineFunction

public PolynomialSplineFunction(double[] knots,
                                PolynomialFunction[] polynomials)

Construct a polynomial spline function with the given segment delimiters and interpolating polynomials.

The constructor copies both arrays and assigns the copies to the knots and polynomials properties, respectively.

Parameters:

knots - spline segment interval delimiters

polynomials - polynomial functions that make up the spline

Throws:

java.lang.NullPointerException - if either of the input arrays is null

java.lang.IllegalArgumentException - if knots has length less than 2, polynomials.length != knots.length - 1 , or the knots array is not strictly increasing.

Method Detail

value

public double value(double v)
             throws ArgumentOutsideDomainException

Compute the value for the function. See PolynomialSplineFunction for details on the algorithm for computing the value of the function.

Specified by:

value in interface UnivariateRealFunction

Parameters:

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

Returns:

the value

Throws:

ArgumentOutsideDomainException - if v is outside of the domain of of the spline function (less than the smallest knot point or greater than the largest knot point)

derivative

public UnivariateRealFunction derivative()

Returns the derivative of the polynomial spline function as a UnivariateRealFunction

Specified by:

derivative in interface DifferentiableUnivariateRealFunction

Returns:

the derivative function

polynomialSplineDerivative

public PolynomialSplineFunction polynomialSplineDerivative()

Returns the derivative of the polynomial spline function as a PolynomialSplineFunction

Returns:

the derivative function

getN

public int getN()

Returns the number of spline segments = the number of polynomials = the number of knot points - 1.

Returns:

the number of spline segments

getPolynomials

public PolynomialFunction[] getPolynomials()

Returns a copy of the interpolating polynomials array.

Returns a fresh copy of the array. Changes made to the copy will not affect the polynomials property.

Returns:

the interpolating polynomials

getKnots

public double[] getKnots()

Returns an array copy of the knot points.

Returns a fresh copy of the array. Changes made to the copy will not affect the knots property.

Returns:

the knot points