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<html>
<head>
<title>
UNIFORM - Uniform Random Number Generation
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
UNIFORM <br> Uniform Random Number Generation
</h1>
<hr>
<p>
<b>UNIFORM</b>
is a FORTRAN90 library which
returns a sequence of uniformly distributed pseudorandom numbers.
</p>
<p>
The fundamental underlying random number generator in <b>UNIFORM</b>
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!
</p>
<p>
FORTRAN90 already has the <b>random_number</b> function, which can
return pseudorandom numbers rapidly, in bulk, and generally with
less correlation than <b>UNIFORM</b> provides.
</p>
<p>
However, this library makes it possible to compare certain computations
that use uniform random numbers, written in C, C++, FORTRAN77,
FORTRAN90, Mathematica or MATLAB.
</p>
<p>
Various types of random data can be computed. The routine names
are chosen to indicate the corresponding type:
<ul>
<li>
<b>C4</b>, complex ( kind = 4 )
</li>
<li>
<b>C8</b>, complex ( kind = 8 )
</li>
<li>
<b>CH</b>, character
</li>
<li>
<b>I4</b>, integer ( kind = 4 )
</li>
<li>
<b>I8</b>, integer ( kind = 8 )
</li>
<li>
<b>L</b>, logical
</li>
<li>
<b>R4</b>, real ( kind = 4 )
</li>
<li>
<b>R8</b>, real ( kind = 8 )
</li>
</ul>
</p>
<p>
In some cases, a one dimensional vector or two dimensional
array of values is to be generated, and part of the name
will therefore include:
<ul>
<li>
<b>VEC</b>, vector;
</li>
<li>
<b>MAT</b>, a matrix of data;
</li>
</ul>
</p>
<p>
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:
<ul>
<li>
<b>01</b>, the data that is being returned lies in a
unit interval or region;
</li>
</ul>
</p>
<p>
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.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>UNIFORM</b> is available in
<a href = "../../c_src/uniform/uniform.html">a C version</a> and
<a href = "../../cpp_src/uniform/uniform.html">a C++ version</a> and
<a href = "../../f77_src/uniform/uniform.html">a FORTRAN77 version</a> and
<a href = "../../f_src/uniform/uniform.html">a FORTRAN90 version</a> and
<a href = "../../math_src/uniform/uniform.html">a Mathematica version</a> and
<a href = "../../m_src/uniform/uniform.html">a MATLAB version</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/asa183/asa183.html">
ASA183</a>,
a FORTRAN90 library which
implements the Wichman-Hill pseudorandom number generator.
</p>
<p>
<a href = "../../f_src/cvt/cvt.html">
CVT</a>,
a FORTRAN90 library which
computes elements of a Centroidal Voronoi Tessellation.
</p>
<p>
<a href = "../../f_src/faure/faure.html">
FAURE</a>,
a FORTRAN90 library which
computes elements of a Faure quasirandom sequence.
</p>
<p>
<a href = "../../f_src/f90_random/f90_random.html">
F90_RANDOM</a>,
FORTRAN90 programs which
illustrate the use of Fortran's random number generator routines.
</p>
<p>
<a href = "../../f_src/grid/grid.html">
GRID</a>,
a FORTRAN90 library which
computes elements of a grid dataset.
</p>
<p>
<a href = "../../f_src/halton/halton.html">
HALTON</a>,
a FORTRAN90 library which
computes elements of a Halton quasirandom sequence.
</p>
<p>
<a href = "../../f_src/hammersley/hammersley.html">
HAMMERSLEY</a>,
a FORTRAN90 library which
computes elements of a Hammersley quasirandom sequence.
</p>
<p>
<a href = "../../f_src/hex_grid/hex_grid.html">
HEX_GRID</a>,
a FORTRAN90 library which
computes elements of a hexagonal grid dataset.
</p>
<p>
<a href = "../../f_src/hex_grid_angle/hex_grid_angle.html">
HEX_GRID_ANGLE</a>,
a FORTRAN90 library which
computes elements of an angled hexagonal grid dataset.
</p>
<p>
<a href = "../../f_src/ieee_uniform/ieee_uniform.html">
IEEE_UNIFORM</a>,
a FORTRAN90 library which
tries to uniformly sample the discrete set of values that represent the
legal IEEE real numbers;
</p>
<p>
<a href = "../../f_src/ihs/ihs.html">
IHS</a>,
a FORTRAN90 library which
computes elements of an improved distributed Latin hypercube dataset.
</p>
<p>
<a href = "../../f_src/latin_center/latin_center.html">
LATIN_CENTER</a>,
a FORTRAN90 library which
computes elements of a Latin Hypercube dataset, choosing center points.
</p>
<p>
<a href = "../../f_src/latin_edge/latin_edge.html">
LATIN_EDGE</a>,
a FORTRAN90 library which
computes elements of a Latin Hypercube dataset, choosing edge points.
</p>
<p>
<a href = "../../f_src/latin_random/latin_random.html">
LATIN_RANDOM</a>,
a FORTRAN90 library which
computes elements of a Latin Hypercube dataset, choosing points at random.
</p>
<p>
<a href = "../../f_src/lattice_rule/lattice_rule.html">
LATTICE_RULE</a>,
a FORTRAN90 library which
approximates multidimensional integrals using lattice rules.
</p>
<p>
<a href = "../../f_src/lcvt/lcvt.html">
LCVT</a>,
a FORTRAN90 library which
computes a latinized Centroidal Voronoi Tessellation.
</p>
<p>
<a href = "../../f_src/niederreiter2/niederreiter2.html">
NIEDERREITER2</a>,
a FORTRAN90 library which
computes elements of a Niederreiter quasirandom sequence with base 2.
</p>
<p>
<a href = "../../f_src/normal/normal.html">
NORMAL</a>,
a FORTRAN90 library which
computes elements of a sequence of pseudorandom normally distributed values.
</p>
<p>
<a href = "../../f_src/randlc/randlc.html">
RANDLC</a>,
a FORTRAN90 library which
generates a sequence of pseudorandom numbers,
used by the NAS Benchmark programs.
</p>
<p>
<a href = "../../f_src/random_mpi/random_mpi.html">
RANDOM_MPI</a>,
a FORTRAN90 program which
demonstrates one way to generate the same sequence of random numbers
for both sequential execution and parallel execution under MPI.
</p>
<p>
<a href = "../../f_src/sobol/sobol.html">
SOBOL</a>,
a FORTRAN90 library which
computes elements of a Sobol quasirandom sequence.
</p>
<p>
<a href = "../../f_src/uniform_dataset/uniform_dataset.html">
UNIFORM_DATASET</a>,
a FORTRAN90 program which
generates a dataset of uniform pseudorandom values and writes them to a file.
</p>
<p>
<a href = "../../f_src/van_der_corput/van_der_corput.html">
VAN_DER_CORPUT</a>,
a FORTRAN90 library which
computes elements of a van der Corput quasirandom sequence.
</p>
<p>
<a href = "../../f_src/ziggurat/ziggurat.html">
ZIGGURAT</a>,
a FORTRAN90 program which
generates points from a uniform, normal or exponential distribution, using
the ziggurat method.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Paul Bratley, Bennett Fox, Linus Schrage,<br>
A Guide to Simulation,<br>
Second Edition,<br>
Springer, 1987,<br>
ISBN: 0387964673,<br>
LC: QA76.9.C65.B73.
</li>
<li>
Bennett Fox,<br>
Algorithm 647:
Implementation and Relative Efficiency of Quasirandom
Sequence Generators,<br>
ACM Transactions on Mathematical Software,<br>
Volume 12, Number 4, December 1986, pages 362-376.
</li>
<li>
Donald Knuth,<br>
The Art of Computer Programming,<br>
Volume 2, Seminumerical Algorithms,<br>
Third Edition,<br>
Addison Wesley, 1997,<br>
ISBN: 0201896842,<br>
LC: QA76.6.K64.
</li>
<li>
Pierre LEcuyer,<br>
Random Number Generation,<br>
in Handbook of Simulation,<br>
edited by Jerry Banks,<br>
Wiley, 1998,<br>
ISBN: 0471134031,<br>
LC: T57.62.H37.
</li>
<li>
Peter Lewis, Allen Goodman, James Miller,<br>
A Pseudo-Random Number Generator for the System/360,<br>
IBM Systems Journal,<br>
Volume 8, Number 2, 1969, pages 136-143.
</li>
<li>
Stephen Park, Keith Miller,<br>
Random Number Generators: Good Ones are Hard to Find,<br>
Communications of the ACM,<br>
Volume 31, Number 10, October 1988, pages 1192-1201.
</li>
<li>
Eric Weisstein,<br>
CRC Concise Encyclopedia of Mathematics,<br>
CRC Press, 2002,<br>
Second edition,<br>
ISBN: 1584883472,<br>
LC: QA5.W45.
</li>
<li>
Barry Wilkinson, Michael Allen,<br>
Parallel Programming:
Techniques and Applications Using Networked Workstations and Parallel Computers,<br>
Prentice Hall,<br>
ISBN: 0-13-140563-2,<br>
LC: QA76.642.W54.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "uniform.f90">uniform.f90</a>,
the source code.
</li>
<li>
<a href = "uniform.sh">uniform.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "uniform_prb.f90">uniform_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "uniform_prb.sh">uniform_prb.sh</a>,
commands to compile, link and run the sample calling program.
</li>
<li>
<a href = "uniform_prb_output.txt">uniform_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>C4_UNIFORM_01</b> returns a unit pseudorandom C4.
</li>
<li>
<b>C4MAT_UNIFORM_01</b> returns a unit pseudorandom C4MAT.
</li>
<li>
<b>C4VEC_UNIFORM_01</b> returns a unit pseudorandom C4VEC.
</li>
<li>
<b>C8_UNIFORM_01</b> returns a unit pseudorandom C8.
</li>
<li>
<b>C8MAT_UNIFORM_01</b> returns a unit pseudorandom C8MAT.
</li>
<li>
<b>C8VEC_UNIFORM_01</b> returns a unit pseudorandom C8VEC.
</li>
<li>
<b>CH_UNIFORM</b> returns a scaled pseudorandom CH.
</li>
<li>
<b>CONGRUENCE</b> solves a congruence of the form ( A * X = C ) mod B.
</li>
<li>
<b>GET_SEED</b> returns a seed for the random number generator.
</li>
<li>
<b>I4_GCD</b> finds the greatest common divisor of two I4's.
</li>
<li>
<b>I4_HUGE</b> returns a "huge" I4.
</li>
<li>
<b>I4_SEED_ADVANCE</b> "advances" the seed.
</li>
<li>
<b>I4_UNIFORM</b> returns a scaled pseudorandom I4.
</li>
<li>
<b>I4_UNIFORM_0I</b> returns a pseudorandom I4.
</li>
<li>
<b>I4MAT_UNIFORM</b> returns a scaled pseudorandom I4MAT.
</li>
<li>
<b>I4VEC_UNIFORM</b> returns a scaled pseudorandom I4VEC.
</li>
<li>
<b>I8_UNIFORM</b> returns a scaled pseudorandom I8.
</li>
<li>
<b>L_UNIFORM</b> returns a pseudorandom L.
</li>
<li>
<b>LCRG_ANBN</b> computes the "N-th power" of a linear congruential generator.
</li>
<li>
<b>LCRG_EVALUATE</b> evaluates an LCRG, y = ( A * x + B ) mod C.
</li>
<li>
<b>LCRG_SEED</b> computes the N-th seed of a linear congruential generator.
</li>
<li>
<b>LMAT_UNIFORM</b> returns a pseudorandom LMAT.
</li>
<li>
<b>LVEC_UNIFORM</b> returns a pseudorandom LVEC.
</li>
<li>
<b>POWER_MOD</b> computes ( A^N ) mod M.
</li>
<li>
<b>R4_UNIFORM</b> returns a scaled pseudorandom R4.
</li>
<li>
<b>R4_UNIFORM_01</b> returns a unit pseudorandom R4.
</li>
<li>
<b>R4MAT_UNIFORM</b> returns a scaled pseudorandom R4MAT.
</li>
<li>
<b>R4MAT_UNIFORM_01</b> returns a unit pseudorandom R4MAT.
</li>
<li>
<b>R4VEC_UNIFORM</b> returns a scaled pseudorandom R4VEC.
</li>
<li>
<b>R4VEC_UNIFORM_01</b> returns a unit pseudorandom R4VEC.
</li>
<li>
<b>R8_UNIFORM</b> returns a scaled pseudorandom R8.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8COL_UNIFORM</b> fills an R8COL with scaled pseudorandom numbers.
</li>
<li>
<b>R8I8_UNIFORM</b> returns a scaled pseudorandom R8 using an I8 seed.
</li>
<li>
<b>R8I8_UNIFORM_01</b> returns a unit pseudorandom R8 using an I8 seed.
</li>
<li>
<b>R8MAT_UNIFORM</b> returns a scaled pseudorandom R8MAT.
</li>
<li>
<b>R8MAT_UNIFORM_01</b> returns a unit pseudorandom R8MAT.
</li>
<li>
<b>R8ROW_UNIFORM</b> fills an R8ROW with scaled pseudorandom numbers.
</li>
<li>
<b>R8VEC_UNIFORM</b> returns a scaled pseudorandom R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_01</b> returns a unit pseudorandom R8VEC.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 15 January 2012.
</i>
<!-- John Burkardt -->
</body>
</html>