UNIFORM is a Mathematica library which return a sequence of uniformly distributed pseudorandom numbers.
The fundamental underlying random number generator in UNIFORM is based on a simple, old, and limited linear congruential random number generator originally used in the IBM System 360.
FORTRAN90 already has the random_number function, which can return pseudorandom numbers rapidly, in bulk, and generally with less correlation than UNIFORM provides.
However, this library makes it possible to compare certain computations that use uniform random numbers, written in C, C++, FORTRAN77, FORTRAN90, Mathematica, MATLAB or Python.
Various types of random data can be computed. The routine names are chosen to indicate the corresponding type:
In some cases, a one dimension vector or two dimensional array of values is to be generated, and part of the name will therefore include:
The underlying random numbers are generally defined over some unit interval or region. Routines are available which return these "unit" values, while other routines allow the user to specify limits between which the unit values are rescaled. The name of a routine will usually include a tag suggestig which is the case:
The random number generator embodied here is not very sophisticated. It will not have the best properties of distribution, noncorrelation and long period. It is not the purpose of this library to achieve such worthy goals. This is simply a reasonably portable library that can be implemented in various languages, on various machines, and for which it is possible, for instance, to regard the output as a function of the seed, and moreover, to work directly with the sequence of seeds, if necessary.
In order for the package to be accessible, the package file must be placed in the appropriate place. A typical place is the "Applications" subdirectory of the "User Base Directory". These are directories set up by Mathematica. You can find out where the User Base Directory is by the Mathematica command:
$UserBaseDirectory
Then you need to copy the package file to the "Applications"
subdirectory of that directory.
Once the new package has been placed, you should probably run Mathematica and direct it to rebuild the Help database. This will serve to update Mathematica's internal information so that it can explain how the functions in the package are called.
To use the Uniform functions, the user must first load the package, with the command
<< Uniform.m
after which, for the duration of the Mathematica session, the
user can invoke the functions with commands like
new_seed = I4Uniform01[12345]
or
r4 = R4Uniform01[12345]
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
UNIFORM is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a Mathematica version and a MATLAB version and a Python version.
You can go up one level to the Mathematica packages and notebooks.