public class PolynomialFunctionNewtonForm extends Object implements UnivariateRealFunction
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[]
Constructor and Description |
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PolynomialFunctionNewtonForm(double[] a,
double[] c)
Construct a Newton polynomial with the given a[] and c[].
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Modifier and Type | Method and Description |
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protected void |
computeCoefficients()
Calculate the normal polynomial coefficients given the Newton form.
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int |
degree()
Returns the degree of the polynomial.
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static double |
evaluate(double[] a,
double[] c,
double z)
Evaluate the Newton polynomial using nested multiplication.
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double[] |
getCenters()
Returns a copy of the centers array.
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double[] |
getCoefficients()
Returns a copy of the coefficients array.
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double[] |
getNewtonCoefficients()
Returns a copy of coefficients in Newton form formula.
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double |
value(double z)
Calculate the function value at the given point.
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protected static void |
verifyInputArray(double[] a,
double[] c)
Verifies that the input arrays are valid.
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public PolynomialFunctionNewtonForm(double[] a, double[] c) throws IllegalArgumentException
The constructor makes copy of the input arrays and assigns them.
a
- the coefficients in Newton form formulac
- the centersIllegalArgumentException
- if input arrays are not validpublic double value(double z) throws FunctionEvaluationException
value
in interface UnivariateRealFunction
z
- the point at which the function value is to be computedFunctionEvaluationException
- if a runtime error occursUnivariateRealFunction.value(double)
public int degree()
public double[] getNewtonCoefficients()
Changes made to the returned copy will not affect the polynomial.
public double[] getCenters()
Changes made to the returned copy will not affect the polynomial.
public double[] getCoefficients()
Changes made to the returned copy will not affect the polynomial.
public static double evaluate(double[] a, double[] c, double z) throws FunctionEvaluationException, IllegalArgumentException
a
- the coefficients in Newton form formulac
- the centersz
- the point at which the function value is to be computedFunctionEvaluationException
- if a runtime error occursIllegalArgumentException
- if inputs are not validprotected void computeCoefficients()
protected static void verifyInputArray(double[] a, double[] c) throws IllegalArgumentException
The centers must be distinct for interpolation purposes, but not for general use. Thus it is not verified here.
a
- the coefficients in Newton form formulac
- the centersIllegalArgumentException
- if not validDividedDifferenceInterpolator.computeDividedDifference(double[],
double[])
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