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...
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... | |
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 [107], [110], [122] 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.
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
.
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.
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.)
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 |
Implemented in PointSet.DefaultPointSetIterator, RandMrg, RandomStreamWithCache, InverseGaussianProcessMSH.NonRandomStream, RandomStreamBase, BakerTransformedStream, AntitheticStream, and TruncatedRandomStream.
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.
The generators programmed in SSJ never return the values 0 or 1.
Implemented in DigitalNet.DigitalNetIterator, PointSet.DefaultPointSetIterator, RandMrg, RandomStreamWithCache, InverseGaussianProcessMSH.NonRandomStream, RandomStreamBase, BakerTransformedStream, AntitheticStream, and TruncatedRandomStream.
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.
(Calls nextDouble
once.)
i | smallest integer that can be generated |
j | greatest integer that can be generated |
Implemented in PointSet.DefaultPointSetIterator, RandMrg, LFSR258, LFSR113, RandomStreamWithCache, InverseGaussianProcessMSH.NonRandomStream, RandomStreamBase, BakerTransformedStream, AntitheticStream, and TruncatedRandomStream.
String toString | ( | ) |
Returns a string containing the current state of this stream.
Implemented in F2NL607, RandMrg, GenF2w32, LFSR258, LFSR113, MRG31k3p, WELL1024, WELL512, InverseGaussianProcessMSH.NonRandomStream, MRG32k3a, RandRijndael, MRG32k3aL, WELL607, MT19937, RandomStreamBase, BakerTransformedStream, and AntitheticStream.