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 rand() 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.

Languages:

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

Related Data and Programs:

ASA183, a MATLAB library which implements the Wichman-Hill pseudorandom number generator.

CVT, a MATLAB library which computes elements of a Centroidal Voronoi Tessellation.

FAURE, a MATLAB library which computes elements of a Faure quasirandom sequence.

GRID, a MATLAB library which computes elements of a grid dataset.

HALTON, a MATLAB library which computes elements of a Halton quasirandom sequence.

HAMMERSLEY, a MATLAB library which computes elements of a Hammersley quasirandom sequence.

HEX_GRID, a MATLAB library which computes elements of a hexagonal grid dataset.

HEX_GRID_ANGLE, a FORTRAN90 library which computes elements of an angled hexagonal grid dataset.

IHS, a MATLAB library which computes elements of an improved distributed Latin hypercube dataset.

LATIN_CENTER, a MATLAB library which computes elements of a Latin Hypercube dataset, choosing center points.

LATIN_EDGE, a MATLAB library which computes elements of a Latin Hypercube dataset, choosing edge points.

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

LATTICE_RULE, a MATLAB library which approximates multidimensional integrals using lattice rules.

LCVT, a MATLAB library which computes a latinized Centroidal Voronoi Tessellation.

MATLAB_RANDOM, MATLAB programs which illustrate the use of Matlab's random number generators.

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

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

RANDLC, a MATLAB library which generates a sequence of pseudorandom numbers, used by the NAS Benchmark programs.

SOBOL, a MATLAB library which computes elements of a Sobol quasirandom sequence.

VAN_DER_CORPUT, a MATLAB library which computes 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. Stephen Park, Keith Miller,
   Random Number Generators: Good Ones are Hard to Find,
   Communications of the ACM,
   Volume 31, Number 10, October 1988, pages 1192-1201.
7. Eric Weisstein,
   CRC Concise Encyclopedia of Mathematics,
   CRC Press, 2002,
   Second edition,
   ISBN: 1584883472,
   LC: QA5.W45.
8. 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.

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_ab.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_0i.m, returns a pseudorandom I4 between 1 and 2^(31)-1.
• i4_uniform_ab.m, returns a scaled random I4 between A and B.
• i4mat_uniform_ab.m, returns a scaled pseudorangom I4MAT.
• i4vec_uniform_ab.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 random LMAT (a logical matrix).
• lvec_uniform.m, returns a random LVEC (a logical vector).
• power_mod.m, computes mod ( A^N, M ).
• r4_uniform_ab.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_uniform_ab.m, returns a scaled pseudorandom R8.
• r8_uniform_01.m, returns a unit pseudorandom R8.
• r8col_uniform_ab.m, fills an R8COL with scaled pseudorandom numbers.
• r8mat_uniform_01.m, returns a unit pseudorandom R8MAT.
• r8mat_uniform_ab.m, returns a scaled pseudorandom R8MAT.
• r8mat_uniform_abvec.m, returns a scaled pseudorandom R8MAT.
• r8row_uniform_ab.m, fills an R8ROW with scaled pseudorandom numbers.
• r8vec_uniform_01.m, returns a unit pseudorandom R8VEC.
• r8vec_uniform_ab.m, returns a scaled pseudorandom R8VEC.
• r8vec_uniform_abvec.m, returns a scaled pseudorandom R8VEC.
• r8vec_uniform_unit.m, returns a random unit vector.
• timestamp.m, prints the current YMDHMS date as a timestamp.

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.