UNIFORM
A Uniform Random Number Generator
UNIFORM,
a MATLAB 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!
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, 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, a logical value.

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 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 FORTRAN90 version and
a MATLAB version and
a Python version.
Related Data and Programs:
ASA183,
a MATLAB library which
implements the WichmanHill random number generator (RNG).
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.
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.
RANDOM_SORTED,
a MATLAB library which
generates vectors of random values which are already sorted.
RANLIB,
a MATLAB library which
produces random samples from Probability Density Functions (PDF's),
including Beta, Chisquare Exponential, F, Gamma, Multivariate normal,
Noncentral chisquare, Noncentral F, Univariate normal, random permutations,
Real uniform, Binomial, Negative Binomial, Multinomial, Poisson
and Integer uniform,
by Barry Brown and James Lovato.
RNGLIB,
a MATLAB 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 MATLAB library which
computes elements of a Sobol quasirandom sequence.
uniform_test
VAN_DER_CORPUT,
a MATLAB library which
computes elements of a van der Corput quasirandom sequence.
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:

bvec_print.m,
prints a BVEC.

bvec_uniform.m,
returns a random BVEC (a binary vector).

c4_uniform_01.m,
returns a unit pseudorandom C4.

c4mat_print.m,
prints a C4MAT.

c4mat_print_some.m,
prints some of a C4MAT.

c4mat_uniform_01.m,
returns a unit pseudorandom C4MAT.

c4vec_print.m,
prints a C4VEC.

c4vec_uniform_01.m,
returns a unit pseudorandom C4VEC.

c8_uniform_01.m,
returns a unit pseudorandom C8.

c8mat_print.m,
prints a C8MAT.

c8mat_print_some.m,
prints some of a C8MAT.

c8mat_uniform_01.m,
returns an array of unit pseudorandom double precision
complex numbers.

c8vec_print.m,
prints a C8VEC.

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.

get_seed_test.m

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_sign.m,
returns the sign of an I4.

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_print.m,
prints an I4MAT;

i4mat_print_some.m,
prints some of an I4MAT;

i4mat_uniform_ab.m,
returns a scaled pseudorangom I4MAT.

i4vec_print.m,
prints an I4VEC.

i4vec_uniform_ab.m,
returns a scaled pseudorandom I4VEC.

l4_uniform.m,
returns a scaled random L4 (a logical value).

l4mat_print.m,
prints an L4MAT;

l4mat_print_some.m,
prints some of an L4MAT;

l4mat_uniform.m,
returns a random L4MAT (a logical matrix).

l4vec_print.m,
prints an L4VEC.

l4vec_uniform.m,
returns a random L4VEC (a logical vector).

lcrg_anbn.m,
computes the "Nth power" of a linear congruential generator.

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

lcrg_seed.m,
computes the Nth seed of a linear congruential random
number generator.

power_mod.m,
computes mod ( A^N, M ).

r4_uniform_01.m,
returns a unit pseudorandom R4.

r4_uniform_ab.m,
returns a scaled pseudorandom R4.

r4mat_print.m,
prints an R4MAT;

r4mat_print_some.m,
prints some of an R4MAT;

r4mat_uniform_01.m,
returns a unit pseudorandom R4MAT.

r4mat_uniform_ab.m,
returns a scaled pseudorandom R4MAT.

r4vec_print.m,
prints an R4VEC.

r4vec_uniform_01.m,
returns a unit pseudorandom R4VEC.

r4vec_uniform_ab.m,
returns a scaled pseudorandom R4VEC.

r8_uniform_01.m,
returns a unit pseudorandom R8.

r8_uniform_ab.m,
returns a scaled pseudorandom R8.

r8col_uniform_abvec.m,
fills an R8COL with scaled pseudorandom numbers.

r8mat_print.m,
prints an R8MAT;

r8mat_print_some.m,
prints some of an R8MAT;

r8mat_uniform_01.m,
returns a unit pseudorandom R8MAT.

r8mat_uniform_ab.m,
returns a scaled pseudorandom R8MAT.

r8row_uniform_abvec.m,
fills an R8ROW with scaled pseudorandom numbers.

r8vec_normal_01.m,
returns a unit normal random R8VEC.

r8vec_print.m,
prints an R8VEC.

r8vec_uniform_01.m,
returns a unit pseudorandom R8VEC.

r8vec_uniform_01_test.m

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.

s_len_trim.m,
returns the length of a string to the last nonblank.

timestamp.m,
prints the current YMDHMS date as a timestamp.
Last revised on 12 February 2019.