UNIFORM
A Uniform Random Number Generator

UNIFORM is a Python library which returns a sequence of uniformly distributed pseudorandom numbers.

The fundamental underlying random number generator 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!

Python has the Random.random() function, which returns a random real number in the unit interval.

However, the UNIFORM 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:

• B, an integer binary value of 0 or 1.
• C4, complex ( single precision )
• C8, complex ( double precision )
• CH, character
• I4, integer ( single precision )
• L4, logical
• 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. The name of a routine will usually include a tag suggestig which is the case:

• 01, the data lies in a nit interval or region;
• AB, the data lies in a scaled 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 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 FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

HALTON, a Python library which computes elements of a Halton Quasi Monte Carlo (QMC) sequence, using a simple interface.

HAMMERSLEY, a Python library which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface.

LATIN_RANDOM, a Python program which computes elements of a Latin Hypercube dataset, choosing points at random.

NORMAL, a Python library which contains random number generators (RNG's) for normally distributed values.

PDFLIB, a Python library which evaluates Probability Density Functions (PDF's) and produces random samples from them, including beta, binomial, chi, exponential, gamma, inverse chi, inverse gamma, multinomial, normal, scaled inverse chi, and uniform.

PROB, a Python library which evaluates, samples, inverts, and characterizes a number of Probability Density Functions (PDF's) and Cumulative Density Functions (CDF's), including anglit, arcsin, benford, birthday, bernoulli, beta_binomial, beta, binomial, bradford, burr, cardiod, cauchy, chi, chi squared, circular, cosine, deranged, dipole, dirichlet mixture, discrete, empirical, english sentence and word length, error, exponential, extreme values, f, fisk, folded normal, frechet, gamma, generalized logistic, geometric, gompertz, gumbel, half normal, hypergeometric, inverse gaussian, laplace, levy, logistic, log normal, log series, log uniform, lorentz, maxwell, multinomial, nakagami, negative binomial, normal, pareto, planck, poisson, power, quasigeometric, rayleigh, reciprocal, runs, sech, semicircular, student t, triangle, uniform, von mises, weibull, zipf.

R8LIB, a Python library which contains many utility routines using double precision real (R8) arithmetic.

RANDLC, a Python library which implements a random number generator (RNG) used by the NAS Benchmark programs.

RANDOM_DATA, a Python library which uses a random number generator (RNG) to sample points corresponding to various probability density functions (PDF's), spatial dimensions, and geometries, including the M-dimensional cube, ellipsoid, simplex and sphere.

RANDOM_SORTED, a Python library which generates vectors of random values which are already sorted.

RNGLIB, a Python library which implements a random number generator (RNG) with splitting facilities, allowing multiple independent streams to be computed, by L'Ecuyer and Cote.

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

VAN_DER_CORPUT, a Python library which computes elements of a 1D van der Corput Quasi Monte Carlo (QMC) sequence using a simple interface.

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.py, returns a unit pseudorandom C4.
• c4mat_print.py, prints a C4MAT.
• c4mat_print_some.py, prints some of a C4MAT.
• c4mat_uniform_01.py, returns a unit pseudorandom C4MAT.
• c4vec_print.py, prints a C4VEC.
• c4vec_uniform_01.py, returns a unit pseudorandom C4VEC.
• c8_uniform_01.py, returns a unit pseudorandom C8.
• c8mat_print.py, prints a C8MAT.
• c8mat_print_some.py, prints some of a C8MAT.
• c8mat_uniform_01.py, returns an array of unit pseudorandom double precision complex numbers.
• c8vec_print.py, prints a C8VEC.
• c8vec_uniform_01.py, returns a unit pseudorandom C8VEC.
• ch_uniform_ab.py, returns a scaled pseudorandom CH.
• congruence.py, solves a congruence of the form A * X = C ( mod B ).
• get_seed.py, returns a random seed for the random number generator.
• i4_gcd.py, returns the greatest common divisor of two I4's.
• i4_huge.py, returns a huge I4.
• i4_modp.py, returns the nonnegative remainder of I4 division.
• i4_seed_advance.py, "advances" the seed.
• i4_sign.py, returns the sign of an I4.
• i4_uniform_0i.py, returns a pseudorandom I4 between 1 and 2^(31)-1.
• i4_uniform_ab.py, returns a scaled random I4 between A and B.
• i4mat_print.py, prints an I4MAT.
• i4mat_print_some.py, prints some of an I4MAT.
• i4mat_uniform_ab.py, returns a scaled pseudorangom I4MAT.
• i4vec_print.py, prints an I4VEC.
• i4vec_uniform_ab.py, returns a scaled pseudorandom I4VEC.
• l4_uniform.py, returns a scaled random L4 (a logical value).
• l4mat_print.py, prints an L4MAT.
• l4mat_print_some.py, prints some of an L4MAT.
• l4mat_uniform.py, returns a random L4MAT (a logical matrix).
• l4vec_print.py, prints an L4VEC.
• l4vec_uniform.py, returns a random L4VEC (a logical vector).
• lcrg_anbn.py, computes the "N-th power" of a linear congruential generator.
• lcrg_evaluate.py, evaluates an LCRG, y = ( A * x + B ) mod C.
• lcrg_seed.py, computes the N-th seed of a linear congruential random number generator.
• power_mod.py, computes mod ( A^N, M ).
• r4_uniform_01.py, returns a unit pseudorandom R4.
• r4_uniform_ab.py, returns a scaled pseudorandom R4.
• r4mat_print.py, prints an R4MAT.
• r4mat_print_some.py, prints some of an R4MAT.
• r4mat_uniform_ab.py, returns a scaled pseudorandom R4MAT.
• r4mat_uniform_01.py, returns a unit pseudorandom R4MAT.
• r4vec_print.py, prints an R4VEC.
• r4vec_uniform_01.py, returns a unit pseudorandom R4VEC.
• r4vec_uniform_ab.py, returns a scaled pseudorandom R4VEC.
• r8_uniform_01.py, returns a unit pseudorandom R8.
• r8_uniform_ab.py, returns a scaled pseudorandom R8.
• r8col_uniform_abvec.py, fills an R8COL with scaled pseudorandom numbers.
• r8mat_print.py, prints an R8MAT.
• r8mat_print_some.py, prints some of an R8MAT.
• r8mat_uniform_01.py, returns a unit pseudorandom R8MAT.
• r8mat_uniform_ab.py, returns a scaled pseudorandom R8MAT.
• r8row_uniform_abvec.py, fills an R8ROW with scaled pseudorandom numbers.
• r8vec_print.py, prints an R8VEC.
• r8vec_uniform_01.py, returns a unit pseudorandom R8VEC.
• r8vec_uniform_ab.py, returns a scaled pseudorandom R8VEC.
• r8vec_uniform_abvec.py, returns a scaled pseudorandom R8VEC.
• timestamp.py, prints the current YMDHMS date as a timestamp.

Examples and Tests:

• uniform_test.py, calls all the tests.
• uniform_test.sh, runs all the tests.
• uniform_test.txt, the output file.

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