Function

java.lang.Object
- org.jscience.mathematics.function.Function<X,Y>

All Implemented Interfaces:

java.io.Serializable, javolution.lang.Realtime

Direct Known Subclasses:

DiscreteFunction, Polynomial, RationalFunction
```
public abstract class Function<X,Y>
extends java.lang.Object
implements java.io.Serializable, javolution.lang.Realtime
```
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:[code] // Defines local variables. Variable.Local varX = new Variable.Local("x"); Variable.Local varY = new Variable.Local("y"); // f(x, y) = x² + x·y + 1; Polynomial x = Polynomial.valueOf(Rational.ONE, varX); Polynomial y = Polynomial.valueOf(Rational.ONE, varY); Polynomial 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 [/code]

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

Method Summary

All Methods Instance Methods Abstract Methods Concrete Methods
Modifier and Type	Method and Description
`<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.
`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.
`java.lang.String`	`toString()` Returns the text representation of this function as a `java.lang.String`.
`abstract javolution.text.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 java.lang.Object
getClass, notify, notifyAll, wait, wait, wait

- 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.
  - 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
  - toText
```
public abstract javolution.text.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 javolution.lang.Realtime
    
    Returns:
    
    this object's textual representation.
  - toString
```
public final java.lang.String toString()
```
    Returns the text representation of this function as a java.lang.String.
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    toText().toString()

Class Function<X,Y>

Method Summary

Methods inherited from class java.lang.Object

Method Detail

getVariables

evaluate

equals

hashCode

getVariable

evaluate

evaluate

compose

differentiate

integrate

plus

minus

times

divide

pow

toText

toString