allows you to create a random number stream. This is useful for several
reasons. For example, you might want to generate random values without
affecting the state of the global stream. You might want separate
sources of randomness in a simulation. Or you may need to use a different
generator algorithm than the one MATLAB® software uses at startup.
you can create your own stream, set the writable properties, and use
it to generate random numbers. You can control the stream you create
the same way you control the global stream. You can even replace the
global stream with the stream you create.
To create a stream, use the
myStream=RandStream('mlfg6331_64'); rand(myStream,1,5) ans = 0.6530 0.8147 0.7167 0.8615 0.0764
The random stream
myStream acts separately
from the global stream. The functions
continue to draw from the global stream, and will not affect the results
You can make
myStream the global stream using
RandStream.setGlobalStream(myStream) RandStream.getGlobalStream ans = mlfg6331_64 random stream (current global stream) Seed: 0 NormalTransform: Ziggurat RandStream.getGlobalStream==myStream ans = 1
You may want to return to a previous part of a simulation. A
random stream can be controlled by having it jump to fixed checkpoints,
called substreams. The
Substream property allows
you to jump back and forth among multiple substreams. To use the
create a stream using a generator that supports substreams. (See Choosing
a Random Number Generator for
a list of generator algorithms and their properties.)
The initial value of
Substream is 1.
stream.Substream ans = 1
Substreams are useful in serial computation. Substreams can recreate all or part of a simulation by returning to a particular checkpoint in stream. For example, they can be used in loops.
for i=1:5 stream.Substream=i; rand(1,i) end ans = 0.6530 ans = 0.3364 0.8265 ans = 0.9539 0.6446 0.4913 ans = 0.0244 0.5134 0.6305 0.6534 ans = 0.3323 0.9296 0.5767 0.1233 0.6934
Each of these substreams can reproduce its loop iteration. For example, you can return to the 5th substream. The result will return the same values as the 5th output above.
stream.Substream=5; rand(1,5) ans = 0.3323 0.9296 0.5767 0.1233 0.6934
MATLAB software offers six generator algorithms. The following
table summarizes the key properties of the available generator algorithms
and the keywords used to create them. To return a list of all the
available generator algorithms, use the
|Keyword||Generator||Multiple Stream and Substream Support||Approximate Period In Full Precision|
|Mersenne twister (default)||No|
|SIMD-oriented fast Mersenne twister||No|
|Multiplicative congruential generator||No|
|Multiplicative lagged Fibonacci generator||Yes|
|Combined multiple recursive generator||Yes|
|Shift-register generator summed with linear congruential generator||No|
|Modified subtract with borrow generator||No|
Some of the generators (
provide for backwards compatibility with earlier versions of MATLAB.
Two generators (
provide explicit support for parallel random number generation. The
remaining generators (
are designed primarily for sequential applications. Depending on the
application, some generators may be faster or return values with more
Another reason for the choice of generators has to do with applications. All pseudorandom number generators are based on deterministic algorithms, and all will fail a sufficiently specific statistical test for randomness. One way to check the results of a Monte Carlo simulation is to rerun the simulation with two or more different generator algorithms, and MATLAB software's choice of generators provide you with the means to do that. Although it is unlikely that your results will differ by more than Monte Carlo sampling error when using different generators, there are examples in the literature where this kind of validation has turned up flaws in a particular generator algorithm (see  for an example).
A 32-bit multiplicative congruential generator, as described
in , with multiplier , modulo . This generator has a period
of and does not support multiple
streams or substreams. Each
U(0,1) value is created
using a single 32-bit integer from the generator; the possible values
are all multiples of strictly within
used by default for
mcg16807 streams is the polar
algorithm (described in ).
Note: This generator is identical to the one used beginning in MATLAB Version
4 by both the
A 64-bit multiplicative lagged Fibonacci generator, as described
in , with lags , . This generator is similar to
the MLFG implemented in the SPRNG package. It has a period of approximately . It supports up to parallel streams, via parameterization,
and substreams each of length . Each
is created using one 64-bit integer from the generator; the possible
values are all multiples of strictly
within the interval (0,1). The
used by default for
mlfg6331_64 streams is the
ziggurat algorithm ,
but with the
mlfg6331_64 generator underneath.
A 32-bit combined multiple recursive generator, as described
in . This generator
is similar to the CMRG implemented in the RngStreams package. It has
a period of , and supports up to parallel streams, via sequence
splitting, and substreams each
of length . Each
is created using two 32-bit integers from the generator; the possible
values are multiples of strictly within
the interval (0,1). The
randn algorithm used
by default for
mrg32k3a streams is the ziggurat
but with the
mrg32k3a generator underneath.
The Mersenne Twister, as described in ,
has period and each U(0,1) value is created
using two 32-bit integers. The possible values are multiples of in the interval (0,1). This
generator does not support multiple streams or substreams. The
used by default for
mt19937ar streams is the ziggurat
but with the
mt19937ar generator underneath. Note:
This generator is identical to the one used by the
beginning in MATLAB Version 7, activated by
The Double precision SIMD-oriented Fast Mersenne Twister, as described in , is a faster implementation of the Mersenne Twister algorithm. The period is and the possible values are multiples of in the interval (0,1). The generator produces double precision values in [1,2) natively, which are transformed to create U(0,1) values. This generator does not support multiple streams or substreams.
Marsaglia's SHR3 shift-register generator summed with a linear
congruential generator with multiplier , addend , and modulus . SHR3 is a 3-shift-register
generator defined as , where is the identity operator, is the left shift operator,
and R is the right shift operator. The combined generator
(the SHR3 part is described in )
has a period of approximately .
This generator does not support multiple streams or substreams. Each
U(0,1) value is created using one 32-bit integer from the generator;
the possible values are all multiples of strictly within the interval
randn algorithm used by default for
is the earlier form of the ziggurat algorithm , but
shr3cong generator underneath. This generator
is identical to the one used by the
beginning in MATLAB Version 5, activated using
A modified Subtract-with-Borrow generator, as described in . This
generator is similar to an additive lagged Fibonacci generator with
lags 27 and 12, but is modified to have a much longer period of approximately . The generator works natively
in double precision to create U(0,1) values, and all values in the
open interval (0,1) are possible. The
used by default for
swb2712 streams is the ziggurat
but with the
swb2712 generator underneath. Note:
This generator is identical to the one used by the rand function beginning
in MATLAB Version 5, activated using
Computes a normal random variate by applying the standard normal inverse cumulative distribution function to a uniform random variate. Exactly one uniform value is consumed per normal value.
The polar rejection algorithm, as described in . Approximately 1.27 uniform values are consumed per normal value, on average.
The ziggurat algorithm, as described in . Approximately 2.02 uniform values are consumed per normal value, on average.
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