Class PolynomialFunctionNewtonForm
java.lang.Object
org.apache.commons.math.analysis.polynomials.PolynomialFunctionNewtonForm
- All Implemented Interfaces:
UnivariateRealFunction
Implements the representation of a real polynomial function in
Newton Form. For reference, see Elementary Numerical Analysis,
ISBN 0070124477, chapter 2.
The formula of polynomial in Newton form is p(x) = a[0] + a[1](x-c[0]) + a[2](x-c[0])(x-c[1]) + ... + a[n](x-c[0])(x-c[1])...(x-c[n-1]) Note that the length of a[] is one more than the length of c[]
- Since:
- 1.2
- Version:
- $Revision: 1073498 $ $Date: 2011-02-22 21:57:26 +0100 (mar. 22 févr. 2011) $
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Constructor Summary
ConstructorsConstructorDescriptionPolynomialFunctionNewtonForm
(double[] a, double[] c) Construct a Newton polynomial with the given a[] and c[]. -
Method Summary
Modifier and TypeMethodDescriptionprotected void
Calculate the normal polynomial coefficients given the Newton form.int
degree()
Returns the degree of the polynomial.static double
evaluate
(double[] a, double[] c, double z) Evaluate the Newton polynomial using nested multiplication.double[]
Returns a copy of the centers array.double[]
Returns a copy of the coefficients array.double[]
Returns a copy of coefficients in Newton form formula.double
value
(double z) Calculate the function value at the given point.protected static void
verifyInputArray
(double[] a, double[] c) Verifies that the input arrays are valid.
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Constructor Details
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PolynomialFunctionNewtonForm
Construct a Newton polynomial with the given a[] and c[]. The order of centers are important in that if c[] shuffle, then values of a[] would completely change, not just a permutation of old a[].The constructor makes copy of the input arrays and assigns them.
- Parameters:
a
- the coefficients in Newton form formulac
- the centers- Throws:
IllegalArgumentException
- if input arrays are not valid
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Method Details
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value
Calculate the function value at the given point.- Specified by:
value
in interfaceUnivariateRealFunction
- Parameters:
z
- the point at which the function value is to be computed- Returns:
- the function value
- Throws:
FunctionEvaluationException
- if a runtime error occurs- See Also:
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degree
public int degree()Returns the degree of the polynomial.- Returns:
- the degree of the polynomial
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getNewtonCoefficients
public double[] getNewtonCoefficients()Returns a copy of coefficients in Newton form formula.Changes made to the returned copy will not affect the polynomial.
- Returns:
- a fresh copy of coefficients in Newton form formula
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getCenters
public double[] getCenters()Returns a copy of the centers array.Changes made to the returned copy will not affect the polynomial.
- Returns:
- a fresh copy of the centers array
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getCoefficients
public double[] getCoefficients()Returns a copy of the coefficients array.Changes made to the returned copy will not affect the polynomial.
- Returns:
- a fresh copy of the coefficients array
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evaluate
public static double evaluate(double[] a, double[] c, double z) throws FunctionEvaluationException, IllegalArgumentException Evaluate the Newton polynomial using nested multiplication. It is also called Horner's Rule and takes O(N) time.- Parameters:
a
- the coefficients in Newton form formulac
- the centersz
- the point at which the function value is to be computed- Returns:
- the function value
- Throws:
FunctionEvaluationException
- if a runtime error occursIllegalArgumentException
- if inputs are not valid
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computeCoefficients
protected void computeCoefficients()Calculate the normal polynomial coefficients given the Newton form. It also uses nested multiplication but takes O(N^2) time. -
verifyInputArray
Verifies that the input arrays are valid.The centers must be distinct for interpolation purposes, but not for general use. Thus it is not verified here.
- Parameters:
a
- the coefficients in Newton form formulac
- the centers- Throws:
IllegalArgumentException
- if not valid- See Also:
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