Random Class Reference
[Miscellaneous Tools]

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Detailed Description

The Mersenne Twister is a twisted generalized feedback shift-register generator of Matsumoto and Nishimura. The period of this generator is and it is equi-distributed in 623 dimensions for 32-bit numbers. The time performance of this generator is comparable to the commonly used generators.

This implementation is specialized for both 32-bit and 64-bit architectures. The generators differ sligthly in the initialization and generation phase so they produce two completly different sequences.

The generator gives back random numbers of serveral types. To get a random number from a range of a floating point type you can use one form of the operator() or the real() member function. If you want to get random number from the {0, 1, ..., n-1} integer range use the operator[] or the integer() method. And to get random number from the whole range of an integer type you can use the argumentless integer() or uinteger() functions. After all you can get random bool with equal chance of true and false or given probability of true result with the boolean() member functions.

      // The commented code is identical to the other
      double a = rnd();                     // [0.0, 1.0)
      // double a = rnd.real();             // [0.0, 1.0)
      double b = rnd(100.0);                // [0.0, 100.0)
      // double b = rnd.real(100.0);        // [0.0, 100.0)
      double c = rnd(1.0, 2.0);             // [1.0, 2.0)
      // double c = rnd.real(1.0, 2.0);     // [1.0, 2.0)
      int d = rnd[100000];                  // 0..99999
      // int d = rnd.integer(100000);       // 0..99999
      int e = rnd[6] + 1;                   // 1..6
      // int e = rnd.integer(1, 1 + 6);     // 1..6
      int b = rnd.uinteger<int>();          // 0 .. 2^31 - 1
      int c = rnd.integer<int>();           // - 2^31 .. 2^31 - 1
      bool g = rnd.boolean();               // P(g = true) = 0.5
      bool h = rnd.boolean(0.8);            // P(h = true) = 0.8

The lemon provides a global instance of the random number generator which name is rnd. Usually it is a good programming convenience to use this global generator to get random numbers.

Author:

Balazs Dezso

#include <lemon/random.h>

List of all members.

Public Member Functions
	Random ()
	Constructor.
template<typename Number >
	Random (Number seed)
	Constructor.
template<typename Iterator >
	Random (Iterator begin, Iterator end)
	Constructor.
	Random (const Random &other)
	Copy constructor.
Random &	operator= (const Random &other)
	Assign operator.
template<typename Number >
void	seed (Number seed)
	Seeding random sequence.
template<typename Iterator >
void	seed (Iterator begin, Iterator end)
	Seeding random sequence.
template<typename Number >
Number	real ()
	Returns a random real number from the range [0, 1).
template<typename Number >
Number	real (Number b)
	Returns a random real number the range [0, b).
template<typename Number >
Number	real (Number a, Number b)
	Returns a random real number from the range [a, b).
double	operator() ()
	Returns a random real number from the range [0, 1).
template<typename Number >
Number	operator() (Number b)
	Returns a random real number from the range [0, b).
template<typename Number >
Number	operator() (Number a, Number b)
	Returns a random real number from the range [a, b).
template<typename Number >
Number	integer (Number b)
	Returns a random integer from a range.
template<typename Number >
Number	integer (Number a, Number b)
	Returns a random integer from a range.
template<typename Number >
Number	operator[] (Number b)
	Returns a random integer from a range.
template<typename Number >
Number	uinteger ()
	Returns a random non-negative integer.
template<typename Number >
Number	integer ()
	Returns a random integer.
bool	boolean ()
	Returns a random bool.
Nonuniform distributions
bool	boolean (double p)
	Returns a random bool.
double	gauss ()
	Standard Gauss distribution.
double	gauss (double std_dev)
	Gauss distribution with given standard deviation and mean 0.
double	gauss (double mean, double std_dev)
	Gauss distribution with given mean and standard deviation.
double	exponential (double lambda=1.0)
	Exponential distribution with given mean.
double	gamma (int k)
double	gamma (double k, double theta=1.0)
	Gamma distribution with given shape and scale parameter.
Two dimensional distributions
dim2::Point< double >	disc ()
	Uniform distribution on the full unit circle.
dim2::Point< double >	gauss2 ()
	A kind of two dimensional Gauss distribution.
dim2::Point< double >	exponential2 ()
	A kind of two dimensional exponential distribution.

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Constructor & Destructor Documentation

Random

(

)

[inline]

Constructor with constant seeding.

Random

(

Number

seed

)

[inline]

Constructor with seed. The current number type will be converted to the architecture word type.

Random	(	Iterator	begin,
		Iterator	end
	)			[inline]

Constructor with array seeding. The given range should contain any number type and the numbers will be converted to the architecture word type.

Random

(

const Random &

other

)

[inline]

Copy constructor. The generated sequence will be identical to the other sequence. It can be used to save the current state of the generator and later use it to generate the same sequence.

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Member Function Documentation

Random& operator=

(

const Random &

other

)

[inline]

Assign operator. The generated sequence will be identical to the other sequence. It can be used to save the current state of the generator and later use it to generate the same sequence.

void seed

(

Number

seed

)

[inline]

Seeding the random sequence. The current number type will be converted to the architecture word type.

void seed	(	Iterator	begin,
		Iterator	end
	)			[inline]

Seeding the random sequence. The given range should contain any number type and the numbers will be converted to the architecture word type.

Number real

(

)

[inline]

It returns a random real number from the range [0, 1). The default Number type is double.

Number real

(

Number

b

)

[inline]

It returns a random real number from the range [0, b).

Number real	(	Number	a,
		Number	b
	)			[inline]

It returns a random real number from the range [a, b).

double operator()

(

)

[inline]

It returns a random double from the range [0, 1).

Number operator()

(

Number

b

)

[inline]

It returns a random real number from the range [0, b).

Number operator()	(	Number	a,
		Number	b
	)			[inline]

It returns a random real number from the range [a, b).

Number integer

(

Number

b

)

[inline]

It returns a random integer from the range {0, 1, ..., b - 1}.

Number integer	(	Number	a,
		Number	b
	)			[inline]

It returns a random integer from the range {a, a + 1, ..., b - 1}.

Number operator[]

(

Number

b

)

[inline]

It returns a random integer from the range {0, 1, ..., b - 1}.

Number uinteger

(

)

[inline]

It returns a random non-negative integer uniformly from the whole range of the current Number type. The default result type of this function is unsigned int.

Number integer

(

)

[inline]

It returns a random integer uniformly from the whole range of the current Number type. The default result type of this function is int.

bool boolean

(

)

[inline]

It returns a random bool. The generator holds a buffer for random bits. Every time when it become empty the generator makes a new random word and fill the buffer up.

bool boolean

(

double

p

)

[inline]

It returns a random bool with given probability of true result

double gauss

(

)

[inline]

Standard Gauss distribution.

Note:

The Cartesian form of the Box-Muller transformation is used to generate a random normal distribution.

Todo:

Consider using the "ziggurat" method instead.

double gauss

(

double

std_dev

)

[inline]

See also:

gauss()

double gauss	(	double	mean,
		double	std_dev
	)			[inline]

See also:

gauss()

double exponential

(

double

lambda = 1.0

)

[inline]

This function generates an exponential distribution random number with mean 1/lambda.

double gamma	(	double	k,
		double	theta = 1.0
	)			[inline]

This function generates a gamma distribution random number.

Parameters:

	k	shape parameter (k>0)
	theta	scale parameter

dim2::Point<double> gauss2

(

)

[inline]

This function provides a turning symmetric two-dimensional distribution. Both coordinates are of standard normal distribution, but they are not independent.

Note:

The coordinates are the two random variables provided by the Box-Muller method.

dim2::Point<double> exponential2

(

)

[inline]

This function provides a turning symmetric two-dimensional distribution. The x-coordinate is of conditionally exponential distribution with the condition that x is positive and y=0. If x is negative and y=0 then, -x is of exponential distribution. The same is true for the y-coordinate.