Polynomial (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.functions.Polynomial

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable, MathFunction, MathFunctionWithDerivative, MathFunctionWithFirstDerivative, MathFunctionWithIntegral

Direct Known Subclasses:

LeastSquares, PolInterp
```
public class Polynomial
extends java.lang.Object
implements MathFunction, MathFunctionWithFirstDerivative, MathFunctionWithDerivative, MathFunctionWithIntegral, java.io.Serializable, java.lang.Cloneable
```
Represents a polynomial of degree n in power form. Such a polynomial is of the form

p(x) = c₀ + c₁x + ^... + c_nxⁿ,
where c₀,…, c_n are the coefficients of the polynomial.

See Also:
Serialized Form

Constructor Summary

Constructors
Constructor and Description

Polynomial(double... coeff)
Constructs a new polynomial with coefficients coeff.

Constructors
Constructor and Description
`Polynomial(double... coeff)` Constructs a new polynomial with coefficients `coeff`.

Method Summary

Methods
Modifier and Type	Method and Description
`Polynomial`	`clone()`
`double`	`derivative(double x)` Computes (or estimates) the first derivative of the function at point `x`.
`double`	`derivative(double x, int n)` Computes (or estimates) the nth derivative of the function at point `x`.
`Polynomial`	`derivativePolynomial(int n)` Returns a polynomial corresponding to the nth derivative of this polynomial.
`double`	`evaluate(double x)` Returns the value of the function evaluated at x.
`double`	`getCoefficient(int i)` Returns the ith coefficient of the polynomial.
`double[]`	`getCoefficients()` Returns an array containing the coefficients of the polynomial.
`int`	`getDegree()` Returns the degree of this polynomial.
`double`	`integral(double a, double b)` Computes (or estimates) the integral of the function over the interval [a, b].
`Polynomial`	`integralPolynomial(double c)` Returns a polynomial representing the integral of this polynomial.
`void`	`setCoefficients(double... coeff)` Sets the array of coefficients of this polynomial to `coeff`.
`java.lang.String`	`toString()`

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

- Constructor Detail
  - Polynomial
```
public Polynomial(double... coeff)
```
    Constructs a new polynomial with coefficients coeff. The value of coeff[i] in this array corresponds to c_i.
    
    Parameters:
    coeff - the coefficients of the polynomial.
    
    Throws:
    
    java.lang.NullPointerException - if coeff is null.
    
    java.lang.IllegalArgumentException - if the length of coeff is 0.
- Method Detail
  - getDegree
```
public int getDegree()
```
    Returns the degree of this polynomial.
    
    Returns:
    the degree of this polynomial.
  - getCoefficients
```
public double[] getCoefficients()
```
    Returns an array containing the coefficients of the polynomial.
    
    Returns:
    the array of coefficients.
  - getCoefficient
```
public double getCoefficient(int i)
```
    Returns the ith coefficient of the polynomial.
    
    Returns:
    the array of coefficients.
  - setCoefficients
```
public void setCoefficients(double... coeff)
```
    Sets the array of coefficients of this polynomial to coeff.
    
    Parameters:
    coeff - the new array of coefficients.
    
    Throws:
    
    java.lang.NullPointerException - if coeff is null.
    
    java.lang.IllegalArgumentException - if the length of coeff is 0.
  - evaluate
```
public double evaluate(double x)
```
    Description copied from interface: MathFunction
    
    Returns the value of the function evaluated at x.
    
    Specified by:
    
    evaluate in interface MathFunction
    
    Parameters:
    x - value at which the distribution function is evaluated
    
    Returns:
    function evaluated at x
  - derivative
```
public double derivative(double x)
```
    Description copied from interface: MathFunctionWithFirstDerivative
    
    Computes (or estimates) the first derivative of the function at point x.
    
    Specified by:
    
    derivative in interface MathFunctionWithFirstDerivative
    
    Parameters:
    x - the point to evaluate the derivative to.
    
    Returns:
    the value of the derivative.
  - derivative
```
public double derivative(double x,
                int n)
```
    Description copied from interface: MathFunctionWithDerivative
    
    Computes (or estimates) the nth derivative of the function at point x. For n = 0, this returns the result of evaluate.
    
    Specified by:
    
    derivative in interface MathFunctionWithDerivative
    
    Parameters:
    x - the point to evaluate the derivate to.
    n - the order of the derivative.
    
    Returns:
    the resulting derivative.
  - derivativePolynomial
```
public Polynomial derivativePolynomial(int n)
```
    Returns a polynomial corresponding to the nth derivative of this polynomial.
    
    Parameters:
    n - the degree of the derivative.
    
    Returns:
    the derivative.
  - integral
```
public double integral(double a,
              double b)
```
    Description copied from interface: MathFunctionWithIntegral
    
    Computes (or estimates) the integral of the function over the interval [a, b].
    
    Specified by:
    
    integral in interface MathFunctionWithIntegral
    
    Parameters:
    a - the starting point of the interval.
    b - the ending point of the interval.
    
    Returns:
    the value of the integral.
  - integralPolynomial
```
public Polynomial integralPolynomial(double c)
```
    Returns a polynomial representing the integral of this polynomial. This integral is of the form
    
    ∫p(x)dx = c + c₀x + $\displaystyle {\frac{{c_1 x^2}}{2}}$ + ^... + $\displaystyle {\frac{{c_n x^{n+1}}}{{n+1}}}$ ,
    where c is a user-defined constant.
    
    Parameters:
    c - the constant for the integral.
    
    Returns:
    the polynomial representing the integral.
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object
  - clone
```
public Polynomial clone()
```
    Overrides:
    
    clone in class java.lang.Object

Class Polynomial

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

Polynomial

Method Detail

getDegree

getCoefficients

getCoefficient

setCoefficients

evaluate

derivative

derivative

derivativePolynomial

integral

integralPolynomial

toString

clone