Function
org.jscience.mathematics.function

Class Function<X,Y>

  • All Implemented Interfaces:
    Serializable, javolution.lang.Realtime
    Direct Known Subclasses:
    DiscreteFunction, Polynomial, RationalFunction


    public abstract class Function<X,Y>extends Objectimplements 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:

             // Defines local variables.         Variable.Local<Rational> varX = new Variable.Local<Rational>("x");         Variable.Local<Rational> varY = new Variable.Local<Rational>("y");                  // f(x, y) =  x\xc2\xb2 + x\xc2\xb7y + 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) = x\xc2\xb2-x+1, f(x,y)= x\xc2\xb7y) but the general function instance might tabulate the values, solve an equation, etc.

    See Also:
    Wikipedia: Functions (mathematics), Serialized Form
    • Method Summary

      Methods 
      Modifier and TypeMethod 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.
      booleanequals(Object obj)
      Indicates if this function is equals to the specified object.
      abstract Yevaluate()
      Evaluates this function using its variables current values.
      Yevaluate(X... args)
      Evaluates this function for the specified arguments values (convenience method).
      Yevaluate(X arg)
      Evaluates this function for the specified argument value (convenience method).
      Variable<X>getVariable(String symbol)
      Retrieves the variable from this function having the specified symbol (convenience method).
      abstract List<Variable<X>>getVariables()
      Returns a lexically ordered list of the variables (or arguments) for this function (empty list for constant functions).
      inthashCode()
      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.
      StringtoString()
      Returns the text representation of this function as a java.lang.String.
      abstract javolution.text.TexttoText()
      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).
    • Method Detail

      • getVariables

        public abstract 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(Object obj)
        Indicates if this function is equals to the specified object.
        Overrides:
        equals in class 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 Object
        Returns:
        this function hash code.
      • getVariable

        public final Variable<X> getVariable(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:
        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\xc2\xb7dv]
        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 \xc2\xb7 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:
        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 String toString()
        Returns the text representation of this function as a java.lang.String.
        Overrides:
        toString in class Object
        Returns:
        toText().toString()

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