umontreal.iro.lecuyer.functions

Class Polynomial

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.

Method Summary

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 + + ^... + ,

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