public class PolynomialSplineFunction extends java.lang.Object implements DifferentiableUnivariateRealFunction
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:
x
belongs. If x
is less than the smallest knot point or greater
than the largest one, an IllegalArgumentException
is thrown.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 and Description 

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

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.

public PolynomialSplineFunction(double[] knots, PolynomialFunction[] polynomials)
The constructor copies both arrays and assigns the copies to the knots and polynomials properties, respectively.
knots
 spline segment interval delimiterspolynomials
 polynomial functions that make up the splinejava.lang.NullPointerException
 if either of the input arrays is nulljava.lang.IllegalArgumentException
 if knots has length less than 2,
polynomials.length != knots.length  1
, or the knots array
is not strictly increasing.public double value(double v) throws ArgumentOutsideDomainException
PolynomialSplineFunction
for details on the algorithm for
computing the value of the function.value
in interface UnivariateRealFunction
v
 the point for which the function value should be computedArgumentOutsideDomainException
 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)public UnivariateRealFunction derivative()
derivative
in interface DifferentiableUnivariateRealFunction
public PolynomialSplineFunction polynomialSplineDerivative()
public int getN()
public PolynomialFunction[] getPolynomials()
Returns a fresh copy of the array. Changes made to the copy will not affect the polynomials property.
public double[] getKnots()
Returns a fresh copy of the array. Changes made to the copy will not affect the knots property.
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