PolynomialFunction (Apache Commons Math 3.5 API)

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

All Implemented Interfaces:

Serializable, DifferentiableUnivariateFunction, UnivariateDifferentiableFunction, UnivariateFunction
```
public class PolynomialFunction
extends Object
implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction, Serializable
```
Immutable representation of a real polynomial function with real coefficients.
Horner's Method is used to evaluate the function.

See Also:
Serialized Form

Nested Class Summary

Nested Classes
Modifier and Type Class and Description

static class PolynomialFunction.Parametric
Dedicated parametric polynomial class.

Nested Classes
Modifier and Type	Class and Description
`static class`	`PolynomialFunction.Parametric` Dedicated parametric polynomial class.

Constructor Summary

Constructors
Constructor and Description

PolynomialFunction(double[] c)
Construct a polynomial with the given coefficients.

Constructors
Constructor and Description
`PolynomialFunction(double[] c)` Construct a polynomial with the given coefficients.

Method Summary

Methods
Modifier and Type	Method and Description
`PolynomialFunction`	`add(PolynomialFunction p)` Add a polynomial to the instance.
`int`	`degree()` Returns the degree of the polynomial.
`UnivariateFunction`	`derivative()` Returns the derivative as a `UnivariateFunction`.
`protected static double[]`	`differentiate(double[] coefficients)` Returns the coefficients of the derivative of the polynomial with the given coefficients.
`boolean`	`equals(Object obj)`
`protected static double`	`evaluate(double[] coefficients, double argument)` Uses Horner's Method to evaluate the polynomial with the given coefficients at the argument.
`double[]`	`getCoefficients()` Returns a copy of the coefficients array.
`int`	`hashCode()`
`PolynomialFunction`	`multiply(PolynomialFunction p)` Multiply the instance by a polynomial.
`PolynomialFunction`	`negate()` Negate the instance.
`PolynomialFunction`	`polynomialDerivative()` Returns the derivative as a `PolynomialFunction`.
`PolynomialFunction`	`subtract(PolynomialFunction p)` Subtract a polynomial from the instance.
`String`	`toString()` Returns a string representation of the polynomial.
`DerivativeStructure`	`value(DerivativeStructure t)` Simple mathematical function.
`double`	`value(double x)` Compute the value of the function for the given argument.

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

- Constructor Detail
  - PolynomialFunction
```
public PolynomialFunction(double[] c)
                   throws NullArgumentException,
                          NoDataException
```
    Construct a polynomial with the given coefficients. The first element of the coefficients array is the constant term. Higher degree coefficients follow in sequence. The degree of the resulting polynomial is the index of the last non-null element of the array, or 0 if all elements are null.
    The constructor makes a copy of the input array and assigns the copy to the coefficients property.
    
    Parameters:
    c - Polynomial coefficients.
    
    Throws:
    
    NullArgumentException - if c is null.
    
    NoDataException - if c is empty.
- Method Detail
  - value
```
public double value(double x)
```
    Compute the value of the function for the given argument.
    The value returned is
    coefficients[n] * x^n + ... + coefficients[1] * x + coefficients[0]
    
    Specified by:
    
    value in interface UnivariateFunction
    
    Parameters:
    x - Argument for which the function value should be computed.
    
    Returns:
    the value of the polynomial at the given point.
    See Also:
    UnivariateFunction.value(double)
  - degree
```
public int degree()
```
    Returns the degree of the polynomial.
    
    Returns:
    the degree of the polynomial.
  - getCoefficients
```
public double[] getCoefficients()
```
    Returns a copy of the coefficients array.
    Changes made to the returned copy will not affect the coefficients of the polynomial.
    
    Returns:
    a fresh copy of the coefficients array.
  - evaluate
```
protected static double evaluate(double[] coefficients,
              double argument)
                          throws NullArgumentException,
                                 NoDataException
```
    Uses Horner's Method to evaluate the polynomial with the given coefficients at the argument.
    
    Parameters:
    coefficients - Coefficients of the polynomial to evaluate.
    argument - Input value.
    
    Returns:
    the value of the polynomial.
    
    Throws:
    
    NoDataException - if coefficients is empty.
    
    NullArgumentException - if coefficients is null.
  - value
```
public DerivativeStructure value(DerivativeStructure t)
                          throws NullArgumentException,
                                 NoDataException
```
    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
    
    Throws:
    
    NoDataException - if coefficients is empty.
    
    NullArgumentException - if coefficients is null.
    Since:
    
    3.1
  - add
```
public PolynomialFunction add(PolynomialFunction p)
```
    Add a polynomial to the instance.
    
    Parameters:
    p - Polynomial to add.
    
    Returns:
    a new polynomial which is the sum of the instance and p.
  - subtract
```
public PolynomialFunction subtract(PolynomialFunction p)
```
    Subtract a polynomial from the instance.
    
    Parameters:
    p - Polynomial to subtract.
    
    Returns:
    a new polynomial which is the difference the instance minus p.
  - negate
```
public PolynomialFunction negate()
```
    Negate the instance.
    
    Returns:
    a new polynomial.
  - multiply
```
public PolynomialFunction multiply(PolynomialFunction p)
```
    Multiply the instance by a polynomial.
    
    Parameters:
    p - Polynomial to multiply by.
    
    Returns:
    a new polynomial.
  - differentiate
```
protected static double[] differentiate(double[] coefficients)
                                 throws NullArgumentException,
                                        NoDataException
```
    Returns the coefficients of the derivative of the polynomial with the given coefficients.
    
    Parameters:
    coefficients - Coefficients of the polynomial to differentiate.
    
    Returns:
    the coefficients of the derivative or null if coefficients has length 1.
    
    Throws:
    
    NoDataException - if coefficients is empty.
    
    NullArgumentException - if coefficients is null.
  - polynomialDerivative
```
public PolynomialFunction polynomialDerivative()
```
    Returns the derivative as a PolynomialFunction.
    
    Returns:
    the derivative polynomial.
  - derivative
```
public UnivariateFunction derivative()
```
    Returns the derivative as a UnivariateFunction.
    
    Specified by:
    
    derivative in interface DifferentiableUnivariateFunction
    
    Returns:
    the derivative function.
  - toString
```
public String toString()
```
    Returns a string representation of the polynomial.
    The representation is user oriented. Terms are displayed lowest degrees first. The multiplications signs, coefficients equals to one and null terms are not displayed (except if the polynomial is 0, in which case the 0 constant term is displayed). Addition of terms with negative coefficients are replaced by subtraction of terms with positive coefficients except for the first displayed term (i.e. we display -3 for a constant negative polynomial, but 1 - 3 x + x^2 if the negative coefficient is not the first one displayed).
    
    Overrides:
    
    toString in class Object
    
    Returns:
    a string representation of the polynomial.
  - hashCode
```
public int hashCode()
```
    Overrides:
    
    hashCode in class Object
  - equals
```
public boolean equals(Object obj)
```
    Overrides:
    
    equals in class Object

Class PolynomialFunction

Nested Class Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

PolynomialFunction

Method Detail

value

degree

getCoefficients

evaluate

value

add

subtract

negate

multiply

differentiate

polynomialDerivative

derivative

toString

hashCode

equals