Class PolynomialSplineFunction
- All Implemented Interfaces:
DifferentiableUnivariateRealFunction
,UnivariateRealFunction
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:
- The knot array is searched to find the segment to which
x
belongs. Ifx
is less than the smallest knot point or greater than the largest one, anIllegalArgumentException
is thrown. - Let
j
be the index of the largest knot point that is less than or equal tox
. The value returned is
polynomials[j](x - knot[j])
- Version:
- $Revision: 1037327 $ $Date: 2010-11-20 21:57:37 +0100 (sam. 20 nov. 2010) $
-
Constructor Summary
ConstructorsConstructorDescriptionPolynomialSplineFunction
(double[] knots, PolynomialFunction[] polynomials) Construct a polynomial spline function with the given segment delimiters and interpolating polynomials. -
Method Summary
Modifier and TypeMethodDescriptionReturns the derivative of the polynomial spline function as a UnivariateRealFunctiondouble[]
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.Returns a copy of the interpolating polynomials array.Returns the derivative of the polynomial spline function as a PolynomialSplineFunctiondouble
value
(double v) Compute the value for the function.
-
Constructor Details
-
PolynomialSplineFunction
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 delimiterspolynomials
- polynomial functions that make up the spline- Throws:
NullPointerException
- if either of the input arrays is nullIllegalArgumentException
- if knots has length less than 2,polynomials.length != knots.length - 1
, or the knots array is not strictly increasing.
-
-
Method Details
-
value
Compute the value for the function. SeePolynomialSplineFunction
for details on the algorithm for computing the value of the function.- Specified by:
value
in interfaceUnivariateRealFunction
- 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
Returns the derivative of the polynomial spline function as a UnivariateRealFunction- Specified by:
derivative
in interfaceDifferentiableUnivariateRealFunction
- Returns:
- the derivative function
-
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
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
-