UNIFORM
A Uniform Random Number Generator

UNIFORM is a MATLAB library which returns 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. If you want state of the art random number generation, look elsewhere!

MATLAB already has the random function, and it is not the purpose of this library to replace it.

However, this library makes it possible to compare certain computations that use uniform random numbers, written in C, C++, FORTRAN77, FORTRAN90, Mathematica or MATLAB.

Various types of random data can be computed. The routine names are chosen to indicate the corresponding type:

• C4, complex ( single precision )
• C8, complex ( double precision )
• CH, character
• I4, integer ( single precision )
• I8, integer ( double precision )
• R4, real ( single precision )
• R8, real ( double precision )

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:

• VEC, vector;
• MAT, a matrix of data;

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. If a routine returns unit values, its name will include a special indicator:

• 01, the data that is being returned lies in a unit interval or region;

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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

CVT is a library of MATLAB routines which compute elements of a Centroidal Voronoi Tessellation.

FAURE is a library of MATLAB routines which compute elements of a Faure quasirandom sequence.

GRID is a library of MATLAB routines which compute elements of a grid dataset.

HALTON is a library of MATLAB routines which compute elements of a Halton quasirandom sequence.

HAMMERSLEY is a library of MATLAB routines which compute elements of a Hammersley quasirandom sequence.

HEX_GRID is a library of MATLAB routines which compute elements of a hexagonal grid dataset.

HEX_GRID_ANGLE is a library of FORTRAN90 routines which compute elements of an angled hexagonal grid dataset.

IHS is a library of MATLAB routines which compute elements of an improved distributed Latin hypercube dataset.

LATIN_CENTER is a library of MATLAB routines which compute elements of a Latin Hypercube dataset, choosing center points.

LATIN_EDGE is a library of MATLAB routines which compute elements of a Latin Hypercube dataset, choosing edge points.

LATIN_RANDOM is a library of MATLAB routines which compute elements of a Latin Hypercube dataset, choosing points at random.

LCVT is a library of MATLAB routines which compute a latinized Centroidal Voronoi Tessellation.

NIEDERREITER2 is a library of MATLAB routines which computes elements of a Niederreiter quasirandom sequence with base 2.

NORMAL is a MATLAB library which computes elements of a sequence of pseudorandom normally distributed values.

SOBOL is a library of MATLAB routines which compute elements of a Sobol quasirandom sequence.

UNIFORM is also available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a Mathematica version.

VAN_DER_CORPUT is a library of MATLAB routines which compute elements of a van der Corput quasirandom sequence.

Reference:

1. Paul Bratley, Bennett Fox, Linus Schrage,
   A Guide to Simulation,
   Second Edition,
   Springer, 1987,
   ISBN: 0387964673,
   LC: QA76.9.C65.B73.
2. Bennett Fox,
   Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators,
   ACM Transactions on Mathematical Software,
   Volume 12, Number 4, December 1986, pages 362-376.
3. Donald Knuth,
   The Art of Computer Programming,
   Volume 2, Seminumerical Algorithms,
   Third Edition,
   Addison Wesley, 1997,
   ISBN: 0201896842,
   LC: QA76.6.K64.
4. Pierre LEcuyer,
   Random Number Generation,
   in Handbook of Simulation,
   edited by Jerry Banks,
   Wiley, 1998,
   ISBN: 0471134031,
   LC: T57.62.H37.
5. Peter Lewis, Allen Goodman, James Miller,
   A Pseudo-Random Number Generator for the System/360,
   IBM Systems Journal,
   Volume 8, Number 2, 1969, pages 136-143.
6. Eric Weisstein,
   CRC Concise Encyclopedia of Mathematics,
   CRC Press, 2002,
   Second edition,
   ISBN: 1584883472,
   LC: QA5.W45.
7. Barry Wilkinson, Michael Allen,
   Parallel Programming: Techniques and Applications Using Networked Workstations and Parallel Computers,
   Prentice Hall,
   ISBN: 0-13-140563-2,
   LC: QA76.642.W54.

Tar File:

A GZIP'ed TAR file of the contents of this directory is available. This is only done as a convenience for users who want ALL the files, and don't want to download them individually. This is not a convenience for me, so don't be surprised if the tar file is somewhat out of date.

• uniform_m_src.tar.csh the commands used to create the GZIP'ed TAR file.
• uniform_m_src.tar.gz the GZIP'ed TAR file.

Source Code:

• c4_uniform_01.m, returns a unit pseudorandom C4.
• c4mat_uniform_01.m, returns a unit pseudorandom C4MAT.
• c4vec_uniform_01.m, returns a unit pseudorandom C4VEC.
• c8_uniform_01.m, returns a unit pseudorandom C8.
• c8mat_uniform_01.m, returns an array of unit pseudorandom double precision complex numbers.
• c8vec_uniform_01.m, returns a unit pseudorandom C8VEC.
• ch_uniform.m, returns a scaled pseudorandom CH.
• congruence.m, solves a congruence of the form A * X = C ( mod B ).
• get_seed.m, returns a random seed for the random number generator.
• i4_gcd.m, returns the greatest common divisor of two I4's.
• i4_huge.m, returns a huge I4.
• i4_seed_advance.m, "advances" the seed.
• i4_uniform.m, returns a scaled random I4.
• i4_uniform_0i.m, returns a pseudorandom I4 between 1 and 2^(31)-1.
• i4mat_uniform.m, returns a scaled pseudorangom I4MAT.
• i4vec_uniform.m, returns a scaled pseudorandom I4VEC.
• l_uniform.m, returns a scaled random L (a logical value).
• lcrg_anbn.m, computes the "N-th power" of a linear congruential generator.
• lcrg_evaluate.m, evaluates an LCRG, y = ( A * x + B ) mod C.
• lcrg_seed.m, computes the N-th seed of a linear congruential random number generator.
• lmat_uniform.m, returns a scaled random LMAT (a logical matrix).
• lvec_uniform.m, returns a scaled random LVEC (a logical vector).
• power_mod.m, computes mod ( A^N, M ).
• r4_uniform.m, returns a scaled pseudorandom R4.
• r4_uniform_01.m, returns a unit pseudorandom R4.
• r4mat_uniform_01.m, returns a unit pseudorandom R4MAT.
• r8_epsilon.m, returns the roundoff unit for R8 values.
• r8_uniform.m, returns a scaled pseudorandom R8.
• r8_uniform_01.m, returns a unit pseudorandom R8.
• r8mat_uniform.m, returns a scaled pseudorandom R8MAT.
• r8mat_uniform_01.m, returns a unit pseudorandom R8MAT.
• r8mat_uniform_write.m, writes a pseudorandom R8MAT to a file.
• r8vec_uniform.m, returns a scaled pseudorandom R8VEC.
• r8vec_uniform_01.m, returns a unit pseudorandom R8VEC.
• timestamp.m, prints the current YMDHMS date as a timestamp.
• timestring.m, copies the current YMDHMS date into a string.

Examples and Tests:

• uniform_test.m, a script that runs all the tests.
• uniform_test_output.txt, the output file.
• uniform_test01.m, tests C4_UNIFORM_01.
• uniform_test02.m, tests C4VEC_UNIFORM_01.
• uniform_test03.m, tests C8_UNIFORM_01.
• uniform_test04.m, tests C8VEC_UNIFORM_01.
• uniform_test05.m, tests CH_UNIFORM.
• uniform_test06.m, tests GET_SEED.
• uniform_test065.m, tests I4_SEED_ADVANCE.
• uniform_test07.m, tests I4_UNIFORM.
• uniform_test08.m, tests I4_UNIFORM.
• uniform_test09.m, tests I4_UNIFORM_0I.
• uniform_test10.m, tests I4VEC_UNIFORM.
• uniform_test11.m, tests I8_UNIFORM.
• uniform_test111.m, tests L_UNIFORM.
• uniform_test112.m, tests LVEC_UNIFORM.
• uniform_test118.m, tests LCRG_ANBN.
• uniform_test119.m, tests LCRG_ANBN.
• uniform_test12.m, demonstrates the use of LCRG_SEED.
• uniform_test13.m, tests R4_UNIFORM.
• uniform_test14.m, tests R4_UNIFORM_01.
• uniform_test15.m, tests R8_UNIFORM.
• uniform_test16.m, tests R8_UNIFORM_01.
• uniform_test17.m, tests R8_UNIFORM_01.
• uniform_test18.m, tests R8_UNIFORM_01.
• uniform_test19.m, tests R8_UNIFORM_01 and R8MAT_UNIFORM_01.
• uniform_test20.m, tests R8_UNIFORM_01 and R8VEC_UNIFORM_01.

You can go up one level to the MATLAB source codes.