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 FORTRAN77 version and
a FORTRAN90 version and
a Mathematica 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 Mdimensional 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:

Paul Bratley, Bennett Fox, Linus Schrage,
A Guide to Simulation,
Second Edition,
Springer, 1987,
ISBN: 0387964673,
LC: QA76.9.C65.B73.

Bennett Fox,
Algorithm 647:
Implementation and Relative Efficiency of Quasirandom
Sequence Generators,
ACM Transactions on Mathematical Software,
Volume 12, Number 4, December 1986, pages 362376.

Donald Knuth,
The Art of Computer Programming,
Volume 2, Seminumerical Algorithms,
Third Edition,
Addison Wesley, 1997,
ISBN: 0201896842,
LC: QA76.6.K64.

Pierre LEcuyer,
Random Number Generation,
in Handbook of Simulation,
edited by Jerry Banks,
Wiley, 1998,
ISBN: 0471134031,
LC: T57.62.H37.

Peter Lewis, Allen Goodman, James Miller,
A PseudoRandom Number Generator for the System/360,
IBM Systems Journal,
Volume 8, Number 2, 1969, pages 136143.

Stephen Park, Keith Miller,
Random Number Generators: Good Ones are Hard to Find,
Communications of the ACM,
Volume 31, Number 10, October 1988, pages 11921201.

Eric Weisstein,
CRC Concise Encyclopedia of Mathematics,
CRC Press, 2002,
Second edition,
ISBN: 1584883472,
LC: QA5.W45.

Barry Wilkinson, Michael Allen,
Parallel Programming:
Techniques and Applications Using Networked Workstations and
Parallel Computers,
Prentice Hall,
ISBN: 0131405632,
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 "Nth power" of a linear congruential generator.

lcrg_evaluate.py,
evaluates an LCRG, y = ( A * x + B ) mod C.

lcrg_seed.py,
computes the Nth 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:
You can go up one level to
the PYTHON source codes.
Last revised on 06 December 2014.