cern.jet.math

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 a^b.
• 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 a^b.
• Functions.bindArg2(Functions.pow,3) gives the function x³.
• Functions.bindArg1(Functions.pow,3) gives the function 3^x.
• Functions.swapArgs(Functions.pow) gives the function b^a.

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

Field Summary

Fields

Modifier and Type	Field and Description
static DoubleFunction	abs Function that returns Math.abs(a).
static DoubleFunction	acos Function that returns Math.acos(a).
static DoubleFunction	asin Function that returns Math.asin(a).
static DoubleFunction	atan Function that returns Math.atan(a).
static DoubleDoubleFunction	atan2 Function that returns Math.atan2(a,b).
static DoubleFunction	ceil Function that returns Math.ceil(a).
static DoubleDoubleFunction	compare Function that returns a < b ? -1 : a > b ? 1 : 0.
static DoubleFunction	cos Function that returns Math.cos(a).
static DoubleDoubleFunction	div Function that returns a / b.
static DoubleDoubleFunction	equals Function that returns a == b ? 1 : 0.
static DoubleFunction	exp Function that returns Math.exp(a).
static DoubleFunction	floor Function that returns Math.floor(a).
static Functions	functions Little trick to allow for "aliasing", that is, renaming this class.
static DoubleDoubleFunction	greater Function that returns a > b ? 1 : 0.
static DoubleFunction	identity Function that returns its argument.
static DoubleDoubleFunction	IEEEremainder Function that returns Math.IEEEremainder(a,b).
static DoubleFunction	inv Function that returns 1.0 / a.
static DoubleDoubleProcedure	isEqual Function that returns a == b.
static DoubleDoubleProcedure	isGreater Function that returns a > b.
static DoubleDoubleProcedure	isLess Function that returns a < b.
static DoubleDoubleFunction	less Function that returns a < b ? 1 : 0.
static DoubleDoubleFunction	lg Function that returns Math.log(a) / Math.log(b).
static DoubleFunction	log Function that returns Math.log(a).
static DoubleFunction	log2 Function that returns Math.log(a) / Math.log(2).
static DoubleDoubleFunction	max Function that returns Math.max(a,b).
static DoubleDoubleFunction	min Function that returns Math.min(a,b).
static DoubleDoubleFunction	minus Function that returns a - b.
static DoubleDoubleFunction	mod Function that returns a % b.
static DoubleDoubleFunction	mult Function that returns a * b.
static DoubleFunction	neg Function that returns -a.
static DoubleDoubleFunction	plus Function that returns a + b.
static DoubleDoubleFunction	plusAbs Function that returns Math.abs(a) + Math.abs(b).
static DoubleDoubleFunction	pow Function that returns Math.pow(a,b).
static DoubleFunction	rint Function that returns Math.rint(a).
static DoubleFunction	sign Function that returns a < 0 ? -1 : a > 0 ? 1 : 0.
static DoubleFunction	sin Function that returns Math.sin(a).
static DoubleFunction	sqrt Function that returns Math.sqrt(a).
static DoubleFunction	square Function that returns a * a.
static DoubleFunction	tan Function that returns Math.tan(a).

Method Summary

Modifier and Type	Method and Description
static DoubleFunction	between(double from, double to) Constructs a function that returns (from<=a && a<=to) ? 1 : 0.
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.
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.
static DoubleDoubleFunction	chain(DoubleDoubleFunction f, DoubleFunction g, DoubleFunction h) Constructs the function f( g(a), h(b) ).
static DoubleDoubleFunction	chain(DoubleFunction g, DoubleDoubleFunction h) Constructs the function g( h(a,b) ).
static DoubleFunction	chain(DoubleFunction g, DoubleFunction h) Constructs the function g( h(a) ).
static DoubleFunction	compare(double b) Constructs a function that returns a < b ? -1 : a > b ? 1 : 0.
static DoubleFunction	constant(double c) Constructs a function that returns the constant c.
static void	demo1() Demonstrates usage of this class.
static void	demo2(int size) Benchmarks and demonstrates usage of trivial and complex functions.
static DoubleFunction	div(double b) Constructs a function that returns a / b.
static DoubleFunction	equals(double b) Constructs a function that returns a == b ? 1 : 0.
static DoubleFunction	greater(double b) Constructs a function that returns a > b ? 1 : 0.
static DoubleFunction	IEEEremainder(double b) Constructs a function that returns Math.IEEEremainder(a,b).
static DoubleProcedure	isBetween(double from, double to) Constructs a function that returns from<=a && a<=to.
static DoubleProcedure	isEqual(double b) Constructs a function that returns a == b.
static DoubleProcedure	isGreater(double b) Constructs a function that returns a > b.
static DoubleProcedure	isLess(double b) Constructs a function that returns a < b.
static DoubleFunction	less(double b) Constructs a function that returns a < b ? 1 : 0.
static DoubleFunction	lg(double b) Constructs a function that returns Math.log(a) / Math.log(b).
static DoubleFunction	max(double b) Constructs a function that returns Math.max(a,b).
static DoubleFunction	min(double b) Constructs a function that returns Math.min(a,b).
static DoubleFunction	minus(double b) Constructs a function that returns a - b.
static DoubleDoubleFunction	minusMult(double constant) Constructs a function that returns a - b*constant.
static DoubleFunction	mod(double b) Constructs a function that returns a % b.
static DoubleFunction	mult(double b) Constructs a function that returns a * b.
static DoubleFunction	plus(double b) Constructs a function that returns a + b.
static DoubleDoubleFunction	plusMult(double constant) Constructs a function that returns a + b*constant.
static DoubleFunction	pow(double b) Constructs a function that returns Math.pow(a,b).
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).
static DoubleFunction	round(double precision) Constructs a function that returns the number rounded to the given precision; Math.rint(a/precision)*precision.
static DoubleDoubleFunction	swapArgs(DoubleDoubleFunction function) Constructs a function that returns function.apply(b,a), i.e.

Methods inherited from class java.lang.Object

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

Field Detail

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 < 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 < 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 < b.

isGreater

public static final DoubleDoubleProcedure isGreater

Function that returns a > b.

less

public static final DoubleDoubleFunction less

Function that returns a < 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).

Method Detail

between

public static DoubleFunction between(double from,
                                     double to)

Constructs a function that returns (from<=a && a<=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 < 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 from<=a && a<=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 < b. a is a variable, b is fixed.

less

public static DoubleFunction less(double b)

Constructs a function that returns a < 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.

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).