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<html>
<head>
<title>
NORMAL - Normal Random Number Generators
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
NORMAL <br> Normal Random Number Generators
</h1>
<hr>
<p>
<b>NORMAL</b>
is a FORTRAN90 library which
returns a sequence of normally distributed pseudorandom numbers.
</p>
<p>
<b>NORMAL</b> is based on two simple ideas:
<ul>
<li>
the use of a fairly simple uniform pseudorandom number generator,
which can be implemented in software;
</li>
<li>
the use of the Box-Muller transformation to convert pairs of
uniformly distributed random values to pairs of normally distributed
random values.
</li>
</ul>
</p>
<p>
Using these ideas, it is not too hard to generate normal sequences
of real or complex values, of single or double precision. These
values can be generated as single quantities, vectors or matrices.
An associated seed actually determines the sequence. Varying
the seed will result in producing a different sequence.
</p>
<p>
The fundamental underlying random number generator used here
is based on a simple, old, and limited linear congruential random
number generator originally used in the IBM System 360.
</p>
<p>
This library makes it possible to compare certain computations
that use normal random numbers, written in C, C++, FORTRAN77,
FORTRAN90 or MATLAB.
</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>NORMAL</b> is available in
<a href = "../../c_src/normal/normal.html">a C version</a> and
<a href = "../../cpp_src/normal/normal.html">a C++ version</a> and
<a href = "../../f77_src/normal/normal.html">a FORTRAN77 version</a> and
<a href = "../../f_src/normal/normal.html">a FORTRAN90 version</a> and
<a href = "../../m_src/normal/normal.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/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/faure/faure.html">
FAURE</a>,
a FORTRAN90 library which
computes elements of a Faure quasirandom sequence.
</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/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_dataset/normal_dataset.html">
NORMAL_DATASET</a>,
a FORTRAN90 program which
generates a dataset of multivariate normal pseudorandom values and write them to a file.
</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/subpak/subpak.html">
SUBPAK</a>,
a FORTRAN90 library which
includes a routine <b>random_initialize</b> that can be used
to try to initialize the seed for the FORTRAN90 random number generator.
</p>
<p>
<a href = "../../f_src/uniform/uniform.html">
UNIFORM</a>,
a FORTRAN90 library which
computes elements of a uniformly distributed pseudorandom sequence.
</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>
<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, 1969, pages 136-143.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "normal.f90">normal.f90</a>,
the source code.
</li>
<li>
<a href = "normal.sh">normal.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "normal_prb.f90">normal_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "normal_prb.sh">normal_prb.sh</a>,
commands to compile, link and run the sample calling program.
</li>
<li>
<a href = "normal_prb_output.txt">normal_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>C4_NORMAL_01</b> returns a unit pseudonormal C4.
</li>
<li>
<b>C8_NORMAL_01</b> returns a unit pseudonormal C8.
</li>
<li>
<b>I4_HUGE</b> returns a "huge" I4.
</li>
<li>
<b>I4_NORMAL</b> returns a scaled pseudonormal I4.
</li>
<li>
<b>I8_NORMAL</b> returns a scaled pseudonormal I8.
</li>
<li>
<b>R4_NORMAL</b> returns a scaled pseudonormal R4.
</li>
<li>
<b>R4_NORMAL_01</b> returns a unit pseudonormal R4.
</li>
<li>
<b>R4_UNIFORM_01</b> returns a unit pseudorandom R4.
</li>
<li>
<b>R4VEC_NORMAL</b> returns a scaled pseudonormal R4VEC.
</li>
<li>
<b>R4VEC_UNIFORM_01</b> returns a unit pseudorandom R4VEC.
</li>
<li>
<b>R8_NORMAL</b> returns a scaled pseudonormal R8.
</li>
<li>
<b>R8_NORMAL_01</b> returns a unit pseudonormal R8.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8MAT_NORMAL</b> returns a scaled pseudonormal R8MAT.
</li>
<li>
<b>R8MAT_NORMAL_01</b> returns a unit pseudonormal R8MAT.
</li>
<li>
<b>R8VEC_NORMAL</b> returns a scaled pseudonormal R8VEC.
</li>
<li>
<b>R8VEC_NORMAL_01</b> returns a unit pseudonormal 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 02 February 2008.
</i>
<!-- John Burkardt -->
</body>
</html>