Class Functions

java.lang.Object
cern.jet.math.Functions
public class Functions extends Object
Function objects to be passed to generic methods. Contains the functions of Math as function objects, as well as a few more basic functions.

Function objects conveniently allow to express arbitrary functions in a generic manner. Essentially, a function object is an object that can perform a function on some arguments. It has a minimal interface: a method apply that takes the arguments, computes something and returns some result value. Function objects are comparable to function pointers in C used for call-backs.

Unary functions are of type DoubleFunction, binary functions of type DoubleDoubleFunction. All can be retrieved via public static final variables named after the function. Unary predicates are of type DoubleProcedure, binary predicates of type DoubleDoubleProcedure. All can be retrieved via public static final variables named isXXX.

Binary functions and predicates also exist as unary functions with the second argument being fixed to a constant. These are generated and retrieved via factory methods (again with the same name as the function). Example:

  • Functions.pow gives the function ab.
  • Functions.pow.apply(2,3)==8.
  • Functions.pow(3) gives the function a3.
  • Functions.pow(3).apply(2)==8.
More general, any binary function can be made an unary functions by fixing either the first or the second argument. See methods bindArg1(DoubleDoubleFunction,double) and bindArg2(DoubleDoubleFunction,double). The order of arguments can be swapped so that the first argument becomes the second and vice-versa. See method swapArgs(DoubleDoubleFunction). Example:
  • Functions.pow gives the function ab.
  • Functions.bindArg2(Functions.pow,3) gives the function x3.
  • Functions.bindArg1(Functions.pow,3) gives the function 3x.
  • Functions.swapArgs(Functions.pow) gives the function ba.

Even more general, functions can be chained (composed, assembled). Assume we have two unary functions g and h. The unary function g(h(a)) applying both in sequence can be generated via chain(DoubleFunction,DoubleFunction):

  • Functions.chain(g,h);
Assume further we have a binary function f. The binary function g(f(a,b)) can be generated via chain(DoubleFunction,DoubleDoubleFunction):
  • Functions.chain(g,f);
The binary function f(g(a),h(b)) can be generated via chain(DoubleDoubleFunction,DoubleFunction,DoubleFunction):
  • Functions.chain(f,g,h);
Arbitrarily complex functions can be composed from these building blocks. For example sin(a) + cos2(b) can be specified as follows:
  • chain(plus,sin,chain(square,cos));
or, of course, as 
new DoubleDoubleFunction() {
   public final double apply(double a, double b) { return Math.sin(a) + Math.pow(Math.cos(b),2); }
}

For aliasing see functions. Try this 

// should yield 1.4399560356056456 in all cases
double a = 0.5; 
double b = 0.2;
double v = Math.sin(a) + Math.pow(Math.cos(b),2);
System.out.println(v);
Functions F = Functions.functions;
DoubleDoubleFunction f = F.chain(F.plus,F.sin,F.chain(F.square,F.cos));
System.out.println(f.apply(a,b));
DoubleDoubleFunction g = new DoubleDoubleFunction() {
   public double apply(double a, double b) { return Math.sin(a) + Math.pow(Math.cos(b),2); }
};
System.out.println(g.apply(a,b));

Performance

Surprise. Using modern non-adaptive JITs such as SunJDK 1.2.2 (java -classic) there seems to be no or only moderate performance penalty in using function objects in a loop over traditional code in a loop. For complex nested function objects (e.g. F.chain(F.abs,F.chain(F.plus,F.sin,F.chain(F.square,F.cos)))) the penalty is zero, for trivial functions (e.g. F.plus) the penalty is often acceptable.
Iteration Performance [million function evaluations per second]
Pentium Pro 200 Mhz, SunJDK 1.2.2, NT, java -classic,
 

30000000 iterations

 3000000 iterations (10 times less)  
F.plus a+b F.chain(F.abs,F.chain(F.plus,F.sin,F.chain(F.square,F.cos))) Math.abs(Math.sin(a) + Math.pow(Math.cos(b),2))    
  10.8 29.6 0.43 0.35    
Version:
1.0, 09/24/99

  • Field Details

    • functions

      public static final Functions functions
      Little trick to allow for "aliasing", that is, renaming this class. Writing code like

      Functions.chain(Functions.plus,Functions.sin,Functions.chain(Functions.square,Functions.cos));

      is a bit awkward, to say the least. Using the aliasing you can instead write

      Functions F = Functions.functions;
      F.chain(F.plus,F.sin,F.chain(F.square,F.cos));

    • abs

      public static final DoubleFunction abs
      Function that returns Math.abs(a).

    • acos

      public static final DoubleFunction acos
      Function that returns Math.acos(a).

    • asin

      public static final DoubleFunction asin
      Function that returns Math.asin(a).

    • atan

      public static final DoubleFunction atan
      Function that returns Math.atan(a).

    • ceil

      public static final DoubleFunction ceil
      Function that returns Math.ceil(a).

    • cos

      public static final DoubleFunction cos
      Function that returns Math.cos(a).

    • exp

      public static final DoubleFunction exp
      Function that returns Math.exp(a).

    • floor

      public static final DoubleFunction floor
      Function that returns Math.floor(a).

    • identity

      public static final DoubleFunction identity
      Function that returns its argument.

    • inv

      public static final DoubleFunction inv
      Function that returns 1.0 / a.

    • log

      public static final DoubleFunction log
      Function that returns Math.log(a).

    • log2

      public static final DoubleFunction log2
      Function that returns Math.log(a) / Math.log(2).

    • neg

      public static final DoubleFunction neg
      Function that returns -a.

    • rint

      public static final DoubleFunction rint
      Function that returns Math.rint(a).

    • sign

      public static final DoubleFunction sign
      Function that returns a invalid input: '<' 0 ? -1 : a > 0 ? 1 : 0.

    • sin

      public static final DoubleFunction sin
      Function that returns Math.sin(a).

    • sqrt

      public static final DoubleFunction sqrt
      Function that returns Math.sqrt(a).

    • square

      public static final DoubleFunction square
      Function that returns a * a.

    • tan

      public static final DoubleFunction tan
      Function that returns Math.tan(a).

    • atan2

      public static final DoubleDoubleFunction atan2
      Function that returns Math.atan2(a,b).

    • compare

      public static final DoubleDoubleFunction compare
      Function that returns a invalid input: '<' b ? -1 : a > b ? 1 : 0.

    • div

      public static final DoubleDoubleFunction div
      Function that returns a / b.

    • equals

      public static final DoubleDoubleFunction equals
      Function that returns a == b ? 1 : 0.

    • greater

      public static final DoubleDoubleFunction greater
      Function that returns a > b ? 1 : 0.

    • IEEEremainder

      public static final DoubleDoubleFunction IEEEremainder
      Function that returns Math.IEEEremainder(a,b).

    • isEqual

      public static final DoubleDoubleProcedure isEqual
      Function that returns a == b.

    • isLess

      public static final DoubleDoubleProcedure isLess
      Function that returns a invalid input: '<' b.

    • isGreater

      public static final DoubleDoubleProcedure isGreater
      Function that returns a > b.

    • less

      public static final DoubleDoubleFunction less
      Function that returns a invalid input: '<' b ? 1 : 0.

    • lg

      public static final DoubleDoubleFunction lg
      Function that returns Math.log(a) / Math.log(b).

    • max

      public static final DoubleDoubleFunction max
      Function that returns Math.max(a,b).

    • min

      public static final DoubleDoubleFunction min
      Function that returns Math.min(a,b).

    • minus

      public static final DoubleDoubleFunction minus
      Function that returns a - b.

    • mod

      public static final DoubleDoubleFunction mod
      Function that returns a % b.

    • mult

      public static final DoubleDoubleFunction mult
      Function that returns a * b.

    • plus

      public static final DoubleDoubleFunction plus
      Function that returns a + b.

    • plusAbs

      public static final DoubleDoubleFunction plusAbs
      Function that returns Math.abs(a) + Math.abs(b).

    • pow

      public static final DoubleDoubleFunction pow
      Function that returns Math.pow(a,b).

  • Constructor Details

    • Functions

      protected Functions()
      Makes this class non instantiable, but still let's others inherit from it.

  • Method Details

    • between

      public static DoubleFunction between(double from, double to)
      Constructs a function that returns (frominvalid input: '<'=a invalid input: '&'invalid input: '&' ainvalid input: '<'=to) ? 1 : 0. a is a variable, from and to are fixed.

    • bindArg1

      public static DoubleFunction bindArg1(DoubleDoubleFunction function, double c)
      Constructs a unary function from a binary function with the first operand (argument) fixed to the given constant c. The second operand is variable (free).
      Parameters:
      function - a binary function taking operands in the form function.apply(c,var).
      Returns:
      the unary function function(c,var).

    • bindArg2

      public static DoubleFunction bindArg2(DoubleDoubleFunction function, double c)
      Constructs a unary function from a binary function with the second operand (argument) fixed to the given constant c. The first operand is variable (free).
      Parameters:
      function - a binary function taking operands in the form function.apply(var,c).
      Returns:
      the unary function function(var,c).

    • chain

      public static DoubleDoubleFunction chain(DoubleDoubleFunction f, DoubleFunction g, DoubleFunction h)
      Constructs the function f( g(a), h(b) ).
      Parameters:
      f - a binary function.
      g - a unary function.
      h - a unary function.
      Returns:
      the binary function f( g(a), h(b) ).

    • chain

      public static DoubleDoubleFunction chain(DoubleFunction g, DoubleDoubleFunction h)
      Constructs the function g( h(a,b) ).
      Parameters:
      g - a unary function.
      h - a binary function.
      Returns:
      the unary function g( h(a,b) ).

    • chain

      public static DoubleFunction chain(DoubleFunction g, DoubleFunction h)
      Constructs the function g( h(a) ).
      Parameters:
      g - a unary function.
      h - a unary function.
      Returns:
      the unary function g( h(a) ).

    • compare

      public static DoubleFunction compare(double b)
      Constructs a function that returns a invalid input: '<' b ? -1 : a > b ? 1 : 0. a is a variable, b is fixed.

    • constant

      public static DoubleFunction constant(double c)
      Constructs a function that returns the constant c.

    • demo1

      public static void demo1()
      Demonstrates usage of this class.

    • demo2

      public static void demo2(int size)
      Benchmarks and demonstrates usage of trivial and complex functions.

    • div

      public static DoubleFunction div(double b)
      Constructs a function that returns a / b. a is a variable, b is fixed.

    • equals

      public static DoubleFunction equals(double b)
      Constructs a function that returns a == b ? 1 : 0. a is a variable, b is fixed.

    • greater

      public static DoubleFunction greater(double b)
      Constructs a function that returns a > b ? 1 : 0. a is a variable, b is fixed.

    • IEEEremainder

      public static DoubleFunction IEEEremainder(double b)
      Constructs a function that returns Math.IEEEremainder(a,b). a is a variable, b is fixed.

    • isBetween

      public static DoubleProcedure isBetween(double from, double to)
      Constructs a function that returns frominvalid input: '<'=a invalid input: '&'invalid input: '&' ainvalid input: '<'=to. a is a variable, from and to are fixed.

    • isEqual

      public static DoubleProcedure isEqual(double b)
      Constructs a function that returns a == b. a is a variable, b is fixed.

    • isGreater

      public static DoubleProcedure isGreater(double b)
      Constructs a function that returns a > b. a is a variable, b is fixed.

    • isLess

      public static DoubleProcedure isLess(double b)
      Constructs a function that returns a invalid input: '<' b. a is a variable, b is fixed.

    • less

      public static DoubleFunction less(double b)
      Constructs a function that returns a invalid input: '<' b ? 1 : 0. a is a variable, b is fixed.

    • lg

      public static DoubleFunction lg(double b)
      Constructs a function that returns Math.log(a) / Math.log(b). a is a variable, b is fixed.

    • main

      protected static void main(String[] args)
      Tests various methods of this class.

    • max

      public static DoubleFunction max(double b)
      Constructs a function that returns Math.max(a,b). a is a variable, b is fixed.

    • min

      public static DoubleFunction min(double b)
      Constructs a function that returns Math.min(a,b). a is a variable, b is fixed.

    • minus

      public static DoubleFunction minus(double b)
      Constructs a function that returns a - b. a is a variable, b is fixed.

    • minusMult

      public static DoubleDoubleFunction minusMult(double constant)
      Constructs a function that returns a - b*constant. a and b are variables, constant is fixed.

    • mod

      public static DoubleFunction mod(double b)
      Constructs a function that returns a % b. a is a variable, b is fixed.

    • mult

      public static DoubleFunction mult(double b)
      Constructs a function that returns a * b. a is a variable, b is fixed.

    • plus

      public static DoubleFunction plus(double b)
      Constructs a function that returns a + b. a is a variable, b is fixed.

    • plusMult

      public static DoubleDoubleFunction plusMult(double constant)
      Constructs a function that returns a + b*constant. a and b are variables, constant is fixed.

    • pow

      public static DoubleFunction pow(double b)
      Constructs a function that returns Math.pow(a,b). a is a variable, b is fixed.

    • random

      public static DoubleFunction random()
      Constructs a function that returns a new uniform random number in the open unit interval (0.0,1.0) (excluding 0.0 and 1.0). Currently the engine is MersenneTwister and is seeded with the current time.

      Note that any random engine derived from RandomEngine and any random distribution derived from AbstractDistribution are function objects, because they implement the proper interfaces. Thus, if you are not happy with the default, just pass your favourite random generator to function evaluating methods.

    • round

      public static DoubleFunction round(double precision)
      Constructs a function that returns the number rounded to the given precision; Math.rint(a/precision)*precision. Examples: 
      precision = 0.01 rounds 0.012 --> 0.01, 0.018 --> 0.02
precision = 10   rounds 123   --> 120 , 127   --> 130

    • swapArgs

      public static DoubleDoubleFunction swapArgs(DoubleDoubleFunction function)
      Constructs a function that returns function.apply(b,a), i.e. applies the function with the first operand as second operand and the second operand as first operand.
      Parameters:
      function - a function taking operands in the form function.apply(a,b).
      Returns:
      the binary function function(b,a).