public class PolynomialSplineFunction extends Object implements UnivariateDifferentiableFunction
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|
Get an array copy of the knot points.
Get the number of spline segments.
Get a copy of the interpolating polynomials array.
Indicates whether a point is within the interpolation range.
Get the derivative of the polynomial spline function.
Simple mathematical function.
Compute the value for the function.
public PolynomialSplineFunction(double knots, PolynomialFunction polynomials) throws NullArgumentException, NumberIsTooSmallException, DimensionMismatchException, NonMonotonicSequenceException
knots- Spline segment interval delimiters.
polynomials- Polynomial functions that make up the spline.
NullArgumentException- if either of the input arrays is
NumberIsTooSmallException- if knots has length less than 2.
polynomials.length != knots.length - 1.
NonMonotonicSequenceException- if the
knotsarray is not strictly increasing.
public double value(double v)
PolynomialSplineFunctionfor details on the algorithm for computing the value of the function.
v- Point for which the function value should be computed.
vis outside of the domain of the spline function (smaller than the smallest knot point or larger than the largest knot point).
public DerivativeStructure value(DerivativeStructure t)
UnivariateDifferentiableFunction classes compute both the
value and the first derivative of the function.
public int getN()
public PolynomialFunction getPolynomials()
public double getKnots()
public boolean isValidPoint(double x)
xis a valid point.
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