java.lang.Object

org.apache.commons.math4.analysis.polynomials.PolynomialFunctionNewtonForm

All Implemented Interfaces:: UnivariateDifferentiableFunction, UnivariateFunction

public class PolynomialFunctionNewtonForm
extends java.lang.Object
implements UnivariateDifferentiableFunction

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

Constructor Summary

Constructors

Constructor Description

PolynomialFunctionNewtonForm(double[] a, double[] c)
Construct a Newton polynomial with the given a[] and c[].

Method Summary

Modifier and Type	Method	Description
`protected void`	`computeCoefficients()`	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[]`	`getCenters()`	Returns a copy of the centers array.
`double[]`	`getCoefficients()`	Returns a copy of the coefficients array.
`double[]`	`getNewtonCoefficients()`	Returns a copy of coefficients in Newton form formula.
`double`	`value(double z)`	Calculate the function value at the given point.
`DerivativeStructure`	`value(DerivativeStructure t)`	Simple mathematical function.
`protected static void`	`verifyInputArray(double[] a, double[] c)`	Verifies that the input arrays are valid.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details
- PolynomialFunctionNewtonForm
  
  public PolynomialFunctionNewtonForm(double[] a, double[] c) throws NullArgumentException, NoDataException, DimensionMismatchException
  
  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 - Coefficients in Newton form formula.
  
  c - Centers.
  
  Throws:
  
  NullArgumentException - if any argument is null.
  
  NoDataException - if any array has zero length.
  
  DimensionMismatchException - if the size difference between a and c is not equal to 1.
Method Details
- value
  
  public double value(double z)
  
  Calculate the function value at the given point.
  
  Specified by:
  
  value in interface UnivariateFunction
  
  Parameters:
  
  z - Point at which the function value is to be computed.
  
  Returns:
  
  the function value.
- value
  
  public DerivativeStructure value(DerivativeStructure t)
  
  Simple mathematical function.
  UnivariateDifferentiableFunction classes compute both the value and the first derivative of the function.
  
  Specified by:
  
  value in interface UnivariateDifferentiableFunction
  
  Parameters:
  
  t - function input value
  
  Returns:
  
  function result
  
  Since:
  
  3.1
- degree
  
  public int degree()
  
  Returns the degree of the polynomial.
  
  Returns:
  
  the degree of the polynomial
- 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
- 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.
- 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.
- evaluate
  
  public static double evaluate(double[] a, double[] c, double z) throws NullArgumentException, DimensionMismatchException, NoDataException
  
  Evaluate the Newton polynomial using nested multiplication. It is also called Horner's Rule and takes O(N) time.
  
  Parameters:
  
  a - Coefficients in Newton form formula.
  
  c - Centers.
  
  z - Point at which the function value is to be computed.
  
  Returns:
  
  the function value.
  
  Throws:
  
  NullArgumentException - if any argument is null.
  
  NoDataException - if any array has zero length.
  
  DimensionMismatchException - if the size difference between a and c is not equal to 1.
- 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
  
  protected static void verifyInputArray(double[] a, double[] c) throws NullArgumentException, NoDataException, DimensionMismatchException
  
  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 formula
  
  c - the centers
  
  Throws:
  
  NullArgumentException - if any argument is null.
  
  NoDataException - if any array has zero length.
  
  DimensionMismatchException - if the size difference between a and c is not equal to 1.
  
  See Also:
  
  DividedDifferenceInterpolator.computeDividedDifference(double[], double[])

Class PolynomialFunctionNewtonForm

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Details

Method Details