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.
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
is computed as follows:
xis less than the smallest knot point or greater than the largest one, an
jbe 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|
Construct a polynomial spline function with the given segment delimiters and interpolating polynomials.
|Modifier and Type||Method and Description|
Returns the derivative of the polynomial spline function as a UnivariateRealFunction
Returns an array copy of the knot points.
Returns the number of spline segments = the number of polynomials = the number of knot points - 1.
Returns a copy of the interpolating polynomials array.
Returns the derivative of the polynomial spline function as a PolynomialSplineFunction
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 delimiters
polynomials- polynomial functions that make up the spline
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.
public double value(double v) throws ArgumentOutsideDomainException
PolynomialSplineFunctionfor details on the algorithm for computing the value of the function.
v- the point for which the function value should be computed
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)
public UnivariateRealFunction derivative()
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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