org.jscience.mathematics.functions
Class Function<X,Y>

java.lang.Object
  javolution.context.RealtimeObject
      org.jscience.mathematics.functions.Function<X,Y>

All Implemented Interfaces:

java.io.Serializable, Realtime, Immutable

Direct Known Subclasses:

DiscreteFunction, Polynomial, RationalFunction

public abstract class Function<X,Y>
extends RealtimeObject
implements Immutable, java.io.Serializable

This abstract class represents a mapping between two sets such that there is a unique element in the second set assigned to each element in the first set.

Functions can be discrete or continuous and multivariate functions (functions with multiple variables) are also supported as illustrated below:

         // Defines local variables.
         Variable.Local<Rational> varX = new Variable.Local<Rational>("x");
         Variable.Local<Rational> varY = new Variable.Local<Rational>("y");
         
         // f(x, y) =  x² + x·y + 1;
         Polynomial<Rational> x = Polynomial.valueOf(Rational.ONE, varX);
         Polynomial<Rational> y = Polynomial.valueOf(Rational.ONE, varY);
         Polynomial<Rational> fx_y = x.pow(2).plus(x.times(y)).plus(Rational.ONE);
         System.out.println("f(x,y) = " + fx_y);
 
         // Evaluates f(1,0) 
         System.out.println("f(1,0) = " + fx_y.evaluate(Rational.ONE, Rational.ZERO));
 
         // Calculates df(x,y)/dx
         System.out.println("df(x,y)/dx = " + fx_y.differentiate(varX));
          
         > f(x,y) = [1/1]x^2 + [1/1]xy + [1/1]
         > f(1,0) = 2/1
         > df(x,y)/dx = [2/1]x + [1/1]y
     

Functions are often given by formula (e.g. f(x) = x²-x+1, f(x,y)= x·y) but the general function instance might tabulate the values, solve an equation, etc.

Version:

3.1, April 1, 2006

Author:

Jean-Marie Dautelle

See Also:

Wikipedia: Functions (mathematics), Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class javolution.context.RealtimeObject

RealtimeObject.Factory<T extends RealtimeObject>

Nested classes/interfaces inherited from interface javolution.context.Realtime

Realtime.ObjectSpace

Constructor Summary

protected

Function() Default constructor.

Method Summary

<Z> Function<Z,Y>	compose(Function<Z,X> that) Returns the composition of this function with the one specified.
Function<X,Y>	differentiate(Variable<X> v) Returns the first derivative of this function with respect to the specified variable.
Function<X,Y>	divide(Function<X,Y> that) Returns the quotient of this function with the one specified.
boolean	equals(java.lang.Object obj) Indicates if this function is equals to the specified object.
abstract Y	evaluate() Evaluates this function using its variables current values.
Y	evaluate(X... args) Evaluates this function for the specified arguments values (convenience method).
Y	evaluate(X arg) Evaluates this function for the specified argument value (convenience method).
Variable<X>	getVariable(java.lang.String symbol) Retrieves the variable from this function having the specified symbol (convenience method).
abstract java.util.List<Variable<X>>	getVariables() Returns a lexically ordered list of the variables (or arguments) for this function (empty list for constant functions).
int	hashCode() Returns the hash code for this function (consistent with equals(Object).
Function<X,Y>	integrate(Variable<X> v) Returns an integral of this function with respect to the specified variable.
Function<X,Y>	minus(Function<X,Y> that) Returns the difference of this function with the one specified.
boolean	move(Realtime.ObjectSpace os) Moves this real-time object to the specified object space.
Function<X,Y>	plus(Function<X,Y> that) Returns the sum of this function with the one specified.
Function<X,Y>	pow(int n) Returns this function raised at the specified exponent.
Function<X,Y>	times(Function<X,Y> that) Returns the product of this function with the one specified.
Text	toText() Returns the textual representation of this real-time object (equivalent to toString except that the returned value can be allocated from the local context space).

Methods inherited from class javolution.context.RealtimeObject

export, isLocal, moveHeap, preserve, toString, unpreserve

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

Function

protected Function()

Default constructor.

Method Detail

getVariables

public abstract java.util.List<Variable<X>> getVariables()

Returns a lexically ordered list of the variables (or arguments) for this function (empty list for constant functions).

Returns:

this function current unset variables (sorted).

evaluate

public abstract Y evaluate()

Evaluates this function using its variables current values.

Returns:

the evaluation of this function.

Throws:

FunctionException - if any of this function's variable is not set.

equals

public boolean equals(java.lang.Object obj)

Indicates if this function is equals to the specified object.

Overrides:

equals in class java.lang.Object

Parameters:

obj - the object to be compared with.

Returns:

true if this function and the specified argument represent the same function; false otherwise.

hashCode

public int hashCode()

Returns the hash code for this function (consistent with equals(Object).

Overrides:

hashCode in class java.lang.Object

Returns:

this function hash code.

toText

public Text toText()

Returns the textual representation of this real-time object (equivalent to toString except that the returned value can be allocated from the local context space).

Specified by:

toText in interface Realtime

Overrides:

toText in class RealtimeObject

Returns:

this object's textual representation.

move

public boolean move(Realtime.ObjectSpace os)

Moves this real-time object to the specified object space.

Specified by:

move in interface Realtime

Overrides:

move in class RealtimeObject

Parameters:

os - the object space to move this real-time object to.

Returns:

true if the move has to be propagated to external real-time references; false otherwise.

getVariable

public final Variable<X> getVariable(java.lang.String symbol)

Retrieves the variable from this function having the specified symbol (convenience method).

Returns:

the variable having the specified symbol or null if none.

evaluate

public final Y evaluate(X arg)

Evaluates this function for the specified argument value (convenience method). The evaluation is performed in a LocalContext and can safely be called upon functions with global variables.

Parameters:

arg - the single variable value used for the evaluation.

Returns:

the evaluation of this function.

Throws:

FunctionException - if getVariables().size() != 1

evaluate

public final Y evaluate(X... args)

Evaluates this function for the specified arguments values (convenience method). The evaluation is performed in a LocalContext and can safely be called upon functions with global variables.

Parameters:

args - the variables values used for the evaluation.

Returns:

the evaluation of this function.

Throws:

java.lang.IllegalArgumentException - if args.length != getVariables().size())

compose

public <Z> Function<Z,Y> compose(Function<Z,X> that)

Returns the composition of this function with the one specified.

Parameters:

that - the function for which the return value is passed as argument to this function.

Returns:

the function (this o that)

Throws:

FunctionException - if this function is not monovariate.

differentiate

public Function<X,Y> differentiate(Variable<X> v)

Returns the first derivative of this function with respect to the specified variable.

Parameters:

v - the variable for which the derivative is calculated.

Returns:

d[this]/dv

Throws:

FunctionException - if the derivative is undefined.

See Also:

Derivative -- from MathWorld

integrate

public Function<X,Y> integrate(Variable<X> v)

Returns an integral of this function with respect to the specified variable.

Parameters:

v - the variable for which the integral is calculated.

Returns:

S[this·dv]

See Also:

Integral -- from MathWorld

plus

public Function<X,Y> plus(Function<X,Y> that)

Returns the sum of this function with the one specified.

Parameters:

that - the function to be added.

Returns:

this + that.

minus

public Function<X,Y> minus(Function<X,Y> that)

Returns the difference of this function with the one specified.

Parameters:

that - the function to be subtracted.

Returns:

this - that.

times

public Function<X,Y> times(Function<X,Y> that)

Returns the product of this function with the one specified.

Parameters:

that - the function multiplier.

Returns:

this · that.

divide

public Function<X,Y> divide(Function<X,Y> that)

Returns the quotient of this function with the one specified. Evaluation of this function may raise an exception if the function result is not a {

Parameters:

that - the function divisor.

Returns:

this / that.

pow

public Function<X,Y> pow(int n)

Returns this function raised at the specified exponent.

Parameters:

n - the exponent.

Returns:

thisn

Throws:

java.lang.IllegalArgumentException - if n <= 0