PolynomialFunctionNewtonForm (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.analysis.polynomials.PolynomialFunctionNewtonForm

All Implemented Interfaces:

UnivariateDifferentiableFunction, UnivariateFunction
```
public class PolynomialFunctionNewtonForm
extends 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 and Description

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

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

Method Summary

Methods
Modifier and Type	Method and 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.
`DerivativeStructure`	`value(DerivativeStructure t)` Simple mathematical function.
`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.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - 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 Detail
  - 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 Detail

PolynomialFunctionNewtonForm

Method Detail

value

value

degree

getNewtonCoefficients

getCenters

getCoefficients

evaluate

computeCoefficients

verifyInputArray