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

All 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.
`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