Class FieldPolynomialSplineFunction<T extends CalculusFieldElement<T>>
 Type Parameters:
T
 the type of the field elements
 All Implemented Interfaces:
CalculusFieldUnivariateFunction<T>
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 ispolynomials[j](x  knot[j])
 Since:
 1.5

Constructor Summary
ConstructorDescriptionFieldPolynomialSplineFunction
(T[] knots, FieldPolynomialFunction<T>[] polynomials) Construct a polynomial spline function with the given segment delimiters and interpolating polynomials. 
Method Summary
Modifier and TypeMethodDescriptiongetField()
Get theField
to which the instance belongs.T[]
getKnots()
Get an array copy of the knot points.int
getN()
Get the number of spline segments.Get a copy of the interpolating polynomials array.boolean
isValidPoint
(T x) Indicates whether a point is within the interpolation range.Get the derivative of the polynomial spline function.value
(double v) Compute the value for the function.Compute the value for the function.

Constructor Details

FieldPolynomialSplineFunction
public FieldPolynomialSplineFunction(T[] knots, FieldPolynomialFunction<T>[] polynomials) throws MathIllegalArgumentException, NullArgumentException 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:
NullArgumentException
 if either of the input arrays isnull
.MathIllegalArgumentException
 if knots has length less than 2.MathIllegalArgumentException
 ifpolynomials.length != knots.length  1
.MathIllegalArgumentException
 if theknots
array is not strictly increasing.


Method Details

getField
Get theField
to which the instance belongs. Returns:
Field
to which the instance belongs

value
Compute the value for the function. SeeFieldPolynomialSplineFunction
for details on the algorithm for computing the value of the function. Parameters:
v
 Point for which the function value should be computed. Returns:
 the value.
 Throws:
MathIllegalArgumentException
 ifv
is outside of the domain of the spline function (smaller than the smallest knot point or larger than the largest knot point).

value
Compute the value for the function. SeeFieldPolynomialSplineFunction
for details on the algorithm for computing the value of the function. Specified by:
value
in interfaceCalculusFieldUnivariateFunction<T extends CalculusFieldElement<T>>
 Parameters:
v
 Point for which the function value should be computed. Returns:
 the value.
 Throws:
MathIllegalArgumentException
 ifv
is outside of the domain of the spline function (smaller than the smallest knot point or larger than the largest knot point).

getN
public int getN()Get the number of spline segments. It is also the number of polynomials and the number of knot points  1. Returns:
 the number of spline segments.

getPolynomials
Get a copy of the interpolating polynomials array. It returns a fresh copy of the array. Changes made to the copy will not affect the polynomials property. Returns:
 the interpolating polynomials.

getKnots
Get an array copy of the knot points. It returns a fresh copy of the array. Changes made to the copy will not affect the knots property. Returns:
 the knot points.

isValidPoint
Indicates whether a point is within the interpolation range. Parameters:
x
 Point. Returns:
true
ifx
is a valid point.

polynomialSplineDerivative
Get the derivative of the polynomial spline function. Returns:
 the derivative function.
