PolynomialSplineFunction (Commons MATH 2.2)

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])
Version:

$Revision: 1037327 $ $Date: 2010-11-20 21:57:37 +0100 (sam. 20 nov. 2010) $

Field Summary

Fields
Modifier and Type	Field and Description
`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.

Constructor Summary

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

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and 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.
`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
  - knots
```
private final double[] knots
```
    Spline segment interval delimiters (knots). Size is n+1 for n segments.
  - polynomials
```
private final 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 final 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 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
  - 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.

Class PolynomialSplineFunction

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

knots

polynomials

n

Constructor Detail

PolynomialSplineFunction

Method Detail

value

derivative

polynomialSplineDerivative

getN

getPolynomials

getKnots

isStrictlyIncreasing