math.function

Class CubicFunction

java.lang.Object

math.function.AbstractFunction

math.function.CubicFunction

All Implemented Interfaces:

Function

public final class CubicFunction
extends AbstractFunction

A univariate polynomial function of degree 3.

Constructor Summary

Constructors

Constructor and Description
CubicFunction(double a, double b, double c, double d) Create a new cubic function using the given coefficients.
CubicFunction(Real a, Real b, Real c, Real d) Create a new cubic function using the given coefficients.

Method Summary

Modifier and Type	Method and Description
Real	a() retrieve the coefficient of the leading term of the polynomial.
double	at(double x) Compute and return the value of the function at the given point.
Real	at(Real point) Evaluate this function at the given point and return the result.
Real	b() retrieve the coefficient of the second degree term of the polynomial.
Real	c() retrieve the coefficient of the first degree term of the polynomial.
Real[]	coefficients() retrieve the coefficients of the polynomial.
double[]	coefficientsDbl() retrieve the coefficients of the polynomial as primitives.
Real	d() retrieve the constant term of the polynomial.
boolean	hasMaximum() Indicates if this function has a maximum or not.
boolean	hasMinimum() Indicates if this function has a minimum or not.
Real[]	localExtrema() retrieve the local extrema of this function.
Real[]	localExtremePoints() retrieve the points at which the local extrema of this function occur.
double	slopeAt(double x) Compute and return the slope at the given point.
String	toString()

Methods inherited from class math.function.AbstractFunction

functionEvaluations, slopeAt, slopeEvaluations

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

CubicFunction

public CubicFunction(Real a,
                     Real b,
                     Real c,
                     Real d)

Create a new cubic function using the given coefficients.

Parameters:

a - the coefficient of the leading term of the polynomial.

b - the coefficient of the second degree term of the polynomial.

c - the coefficient of the first degree term of the polynomial.

d - the constant term of the polynomial.

CubicFunction

public CubicFunction(double a,
                     double b,
                     double c,
                     double d)

Create a new cubic function using the given coefficients.

Parameters:

a - the coefficient of the leading term of the polynomial.

b - the coefficient of the second degree term of the polynomial.

c - the coefficient of the first degree term of the polynomial.

d - the constant term of the polynomial.

Method Detail

a

public Real a()

retrieve the coefficient of the leading term of the polynomial.

Returns:

the coefficient of the leading term of the polynomial.

b

public Real b()

retrieve the coefficient of the second degree term of the polynomial.

Returns:

the coefficient of the second degree term of the polynomial.

c

public Real c()

retrieve the coefficient of the first degree term of the polynomial.

Returns:

the coefficient of the first degree term of the polynomial.

d

public Real d()

retrieve the constant term of the polynomial.

Returns:

the constant term of the polynomial.

at

public Real at(Real point)

Evaluate this function at the given point and return the result.

Parameters:

point - the point to evaluate the function at.

Returns:

the value of this function at the given point.

at

public double at(double x)

Description copied from interface: Function

Compute and return the value of the function at the given point.

Parameters:

x - the point at which to evaluate the function.

Returns:

the value of the function at the given point.

slopeAt

public double slopeAt(double x)

Description copied from class: AbstractFunction

Compute and return the slope at the given point.

Overrides:

slopeAt in class AbstractFunction

Parameters:

x - an element of the function's domain.

Returns:

the slope of the function at the given point.

coefficients

public Real[] coefficients()

retrieve the coefficients of the polynomial.

Returns:

the coefficients of the polynomial.

coefficientsDbl

public double[] coefficientsDbl()

retrieve the coefficients of the polynomial as primitives.

Returns:

the coefficients of the polynomial as primitives.

localExtremePoints

public Real[] localExtremePoints()

retrieve the points at which the local extrema of this function occur.

Returns:

the points at which the local extrema of this function occur.

localExtrema

public Real[] localExtrema()

retrieve the local extrema of this function.

Returns:

the local extrema of this function.

hasMinimum

public boolean hasMinimum()

Indicates if this function has a minimum or not.

Returns:

true if this function has a minimum, false otherwise.

hasMaximum

public boolean hasMaximum()

Indicates if this function has a maximum or not.

Returns:

true if this function has a maximum, false otherwise.

toString

public String toString()

Overrides:

toString in class Object