This interface defines the basic structures to handle multiple streams of uniform (pseudo)random numbers and convenient tools to move around within and across these streams. More...

Inheritance diagram for RandomStream:

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Public Member Functions
void	resetStartStream ()
	Reinitializes the stream to its initial state \(I_g\): \(C_g\) and \(B_g\) are set to \(I_g\).

void	resetStartSubstream ()
	Reinitializes the stream to the beginning of its current substream: \(C_g\) is set to \(B_g\).

void	resetNextSubstream ()
	Reinitializes the stream to the beginning of its next substream: \(N_g\) is computed, and \(C_g\) and \(B_g\) are set to \(N_g\).

String	toString ()
	Returns a string containing the current state of this stream. More...

double	nextDouble ()
	Returns a (pseudo)random number from the uniform distribution over the interval \((0,1)\), using this stream, after advancing its state by one step. More...

void	nextArrayOfDouble (double[] u, int start, int n)
	Generates `n` (pseudo)random numbers from the uniform distribution and stores them into the array `u` starting at index `start`. More...

int	nextInt (int i, int j)
	Returns a (pseudo)random number from the discrete uniform distribution over the integers \(\{i,i+1,…,j\}\), using this stream. More...

void	nextArrayOfInt (int i, int j, int[] u, int start, int n)
	Generates `n` (pseudo)random numbers from the discrete uniform distribution over the integers \(\{i,i+1,…,j\}\), using this stream and stores the result in the array `u` starting at index `start`. More...

Detailed Description

This interface defines the basic structures to handle multiple streams of uniform (pseudo)random numbers and convenient tools to move around within and across these streams.

The actual random number generators (RNGs) are provided in classes that implement this RandomStream interface. Each stream of random numbers is an object of the class that implements this interface, and can be viewed as a virtual random number generator.

For each type of base RNG (i.e., each implementation of the RandomStream interface), the full period of the generator is cut into adjacent streams (or segments) of length \(Z\), and each of these streams is partitioned into \(V\) substreams of length \(W\), where \(Z = VW\). The values of \(V\) and \(W\) depend on the specific RNG, but are usually larger than \(2^{50}\). Thus, the distance \(Z\) between the starting points of two successive streams provided by an RNG usually exceeds \(2^{100}\). The initial seed of the RNG is the starting point of the first stream. It has a default value for each type of RNG, but this initial value can be changed by calling setPackageSeed for the corresponding class. Each time a new RandomStream is created, its starting point (initial seed) is computed automatically, \(Z\) steps ahead of the starting point of the previously created stream of the same type, and its current state is set equal to this starting point.

For each stream, one can advance by one step and generate one value, or go ahead to the beginning of the next substream within this stream, or go back to the beginning of the current substream, or to the beginning of the stream, or jump ahead or back by an arbitrary number of steps. Denote by \(C_g\) the current state of a stream \(g\), \(I_g\) its initial state, \(B_g\) the state at the beginning of the current substream, and \(N_g\) the state at the beginning of the next substream. The following diagram shows an example of a stream whose state is at the 6th value of the third substream, i.e., \(2W+5\) steps ahead of its initial state \(I_g\) and 5 steps ahead of its state \(B_g\). The form of the state of a stream depends on its type. For example, the state of a stream of class MRG32k3a is a vector of six 32-bit integers represented internally as floating-point numbers (in double).

The methods for manipulating the streams and generating random numbers are implemented differently for each type of RNG. The methods whose formal parameter types do not depend on the RNG type are specified in the interface RandomStream. The others (e.g., for setting the seeds) are given only in the classes that implement the specific RNG types.

See [118], [122], [137] for examples of situations where the multiple streams offered here are useful.

Methods for generating random variates from non-uniform distributions are provided in the umontreal.ssj.randvar package.

Member Function Documentation

◆ nextArrayOfDouble()

void nextArrayOfDouble	(	double []	u,
		int	start,
		int	n
	)

Generates n (pseudo)random numbers from the uniform distribution and stores them into the array u starting at index start.

Parameters

u	array that will contain the generated uniforms
start	starting index, in the array `u`, to write uniforms from
n	number of uniforms to generate

Implemented in PointSet.DefaultPointSetIterator, RandMrg, RandomStreamWithCache, InverseGaussianProcessMSH.NonRandomStream, RandomStreamBase, BakerTransformedStream, AntitheticStream, and TruncatedRandomStream.

◆ nextArrayOfInt()

void nextArrayOfInt	(	int	i,
		int	j,
		int []	u,
		int	start,
		int	n
	)

Generates n (pseudo)random numbers from the discrete uniform distribution over the integers \(\{i,i+1,…,j\}\), using this stream and stores the result in the array u starting at index start.

(Calls nextInt n times.)

Parameters

i	smallest integer that can be generated
j	greatest integer that can be generated
u	array that will contain the generated values
start	starting index, in the array `u`, to write integers from
n	number of values being generated