org.apache.commons.math.analysis
Class PolynomialSplineFunction

java.lang.Object
  extended by org.apache.commons.math.analysis.PolynomialSplineFunction
All Implemented Interfaces:
java.io.Serializable, DifferentiableUnivariateRealFunction, UnivariateRealFunction

public class PolynomialSplineFunction
extends java.lang.Object
implements DifferentiableUnivariateRealFunction, java.io.Serializable

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])

Version:
$Revision: 348761 $ $Date: 2005-11-24 09:04:20 -0700 (Thu, 24 Nov 2005) $
See Also:
Serialized Form

Field Summary
private  double[] knots
          Spline segment interval delimiters (knots).
private  int n
          Number of spline segments = number of polynomials = number of partition points - 1
private  PolynomialFunction[] polynomials
          The polynomial functions that make up the spline.
private static long serialVersionUID
          Serializable version identifier
 
Constructor Summary
PolynomialSplineFunction(double[] knots, PolynomialFunction[] polynomials)
          Construct a polynomial spline function with the given segment delimiters and interpolating polynomials.
 
Method Summary
 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.
private static boolean isStrictlyIncreasing(double[] x)
          Determines if the given array is ordered in a strictly increasing fashion.
 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
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

serialVersionUID

private static final long serialVersionUID
Serializable version identifier

See Also:
Constant Field Values

knots

private double[] knots
Spline segment interval delimiters (knots). Size is n+1 for n segments.


polynomials

private PolynomialFunction[] polynomials
The polynomial functions that make up the spline. The first element determines the value of the spline over the first subinterval, the second over the second, etc. Spline function values are determined by evaluating these functions at (x - knot[i]) where i is the knot segment to which x belongs.


n

private int n
Number of spline segments = number of polynomials = number of partition points - 1

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 FunctionEvaluationException
Compute the value for the function.

Throws FunctionEvaluationException if v is outside of the domain of the function. The domain is [smallest knot, largest knot].

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:
FunctionEvaluationException - 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

isStrictlyIncreasing

private static boolean isStrictlyIncreasing(double[] x)
Determines if the given array is ordered in a strictly increasing fashion.

Parameters:
x - the array to examine.
Returns:
true if the elements in x are ordered in a stricly increasing manner. false, otherwise.