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<html>
<head>
<title>
ODE_SWEEP_PARFOR - A Parallel MATLAB Function Using PARFOR
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
ODE_SWEEP_PARFOR <br> A Parallel MATLAB Function Using PARFOR
</h1>
<hr>
<p>
<b>ODE_SWEEP_PARFOR</b>
is a directory which
illustrates how a MATLAB function using the PARFOR statement
can be run in parallel.
</p>
<p>
Consider the parameterized second order differential equation:
<pre>
m x'' + b x' + k x = 0
</pre>
which represents the behavior of a spring mass system with a
mass of <b>m</b>, a spring constant of <b>k</b> and a damping
coefficient <b>b</b>.
</p>
<p>
We now suppose that we are interested in properties of the solution <b>x(t)</b>
over the time interval from 0 to 25 seconds, as we vary the physical properties
<b>b</b> and <b>k</b>. In particular, we would like to know the maximum value
of <b>x(t)</b> over the time interval for each choice of the physical parameters.
</p>
<p>
To answer this question, we must solve the ODE for each choice of the parameters.
Each solution is an independent computation, and one way to carry out the
computations in parallel is to use MATLAB's <b>parfor</b> statement.
</p>
<p>
The basic function has the form:
<blockquote>
function peakVals = ode_fun ( bVals, kVals )
</blockquote>
where
<ul>
<li>
bVals is an array of B values;
</li>
<li>
kVals is an array of K values;
</li>
<li>
peakVals is an array containing the maximum value of the ODE solution
for each combination of B and K.
</li>
</ul>
</p>
<p>
Depending on the situation, the function could be executed in parallel:
<ul>
<li>
interactively, and locally, using the <b>matlabpool</b> command;
</li>
<li>
indirectly, and locally, using the <b>batch</b> command;
</li>
<li>
indirectly, and on the Ithaca cluster, using the <b>batch</b> command;
</li>
<li>
indirectly, and on the FSU HPC cluster, using the <b>fsuClusterMatlab</b> command;
</li>
</ul>
</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>ODE_SWEEP_PARFOR</b> is available in
<a href = "../../m_src/ode_sweep_parfor/ode_sweep_parfor.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/collatz_parfor/collatz_parfor.html">
COLLATZ_PARFOR</a>,
a MATLAB program which
seeks the maximum Collatz sequence between 1 and N,
running in parallel using MATLAB's parfor feature.
</p>
<p>
<a href = "../../m_src/heated_plate_parfor/heated_plate_parfor.html">
HEATED_PLATE_PARFOR</a>,
a MATLAB program which
solves the steady (time independent) heat equation in a 2D
rectangular region, using MATLAB's parfor facility to run in parallel.
</p>
<p>
<a href = "../../m_src/hello_parfor/hello_parfor.html">
HELLO_PARFOR</a>,
a MATLAB program which
prints out "Hello, world!" multiple times, using MATLAB's parfor command
for parallel execution.
</p>
<p>
<a href = "../../m_src/high_card_parfor/high_card_parfor.html">
HIGH_CARD_PARFOR</a>,
a MATLAB program which
uses the parfor statement to compute in parallel the statistics for
a card game in which you are required to guess the location of the
highest card.
</p>
<p>
<a href = "../../m_src/matlab_parallel/matlab_parallel.html">
MATLAB_PARALLEL</a>,
programs which
illustrate "local" parallel programming on a single computer
with MATLAB's Parallel Computing Toolbox.
</p>
<p>
<a href = "../../m_src/matlab_random_parallel/matlab_random_parallel.html">
MATLAB_RANDOM_PARALLEL</a>,
MATLAB programs which
illustrate the use of Matlab's random number generator (RNG) functions
when using parallel features such as parfor or spmd.
</p>
<p>
<a href = "../../m_src/matrix_assemble_parfor/matrix_assemble_parfor.html">
MATRIX_ASSEMBLE_PARFOR</a>,
a MATLAB program which
demonstrates the parfor parallel programming
feature by assembling the Hilbert matrix in a parallel loop.
</p>
<p>
<a href = "../../m_src/md_parfor/md_parfor.html">
MD_PARFOR</a>,
a MATLAB program which
carries out a molecular dynamics simulation,
running in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../m_src/ode_sweep_serial/ode_sweep_serial.html">
ODE_SWEEP_SERIAL</a>,
a MATLAB program which
computes a grid of solutions to a parameterized system of
ordinary differential equations (ODE's).
</p>
<p>
<a href = "../../m_src/prime_parfor/prime_parfor.html">
PRIME_PARFOR</a>,
a MATLAB program which
counts the number of primes between 1 and N;
running in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../m_src/quad_parfor/quad_parfor.html">
QUAD_PARFOR</a>,
a MATLAB program which
estimates an integral using quadrature;
running in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../m_src/satisfy_parfor/satisfy_parfor.html">
SATISFY_PARFOR</a>,
a MATLAB program which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfiability problem,
running in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../m_src/sparse_parfor/sparse_parfor.html">
SPARSE_PARFOR</a>,
a MATLAB library which
demonstrates how a sparse matrix can be constructed by
evaluating individual blocks in parallel with the <b>parfor</b>
command, and then assembled (on a single processor) using the
<b>sparse()</b> command.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
The User's Guide for the Parallel Computing Toolbox is available at
<a href = "http://www.mathworks.com/access/helpdesk/help/pdf_doc/distcomp/distcomp.pdf">
http://www.mathworks.com/access/helpdesk/help/pdf_doc/distcomp/distcomp.pdf</a>
</p>
<p>
<ol>
<li>
Gaurav Sharma, Jos Martin,<br>
MATLAB: A Language for Parallel Computing,<br>
International Journal of Parallel Programming,<br>
Volume 37, Number 1, pages 3-36, February 2009.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "ode_fun.m">ode_fun.m</a>,
the function which performs the calculations.
</li>
<li>
<a href = "ode_system.m">ode_system.m</a>,
a function which redefines the second order ODE as a pair of first order
ODE's, suitable for treatment by MATLAB's ODE solvers.
</li>
<li>
<a href = "ode_display.m">ode_display.m</a>,
a script which displays a contour plot of the results of the parameter sweep.
</li>
<li>
<a href = "ode_display.png">ode_display.png</a>,
a surface plot of the data XMAX(B,K) computed by the program.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>ODE_POOL</b> executes the function locally and interactively.
<ul>
<li>
<a href = "ode_pool.m">ode_pool.m</a>
a script which uses the MATLABPOOL command to run the function locally and
interactively.
</li>
<li>
<a href = "ode_pool_output.txt">ode_pool_output.txt</a>
the output file.
</li>
</ul>
</p>
<p>
<b>ODE_BATCH_LOCAL</b> executes the function locally and noninteractively.
<ul>
<li>
<a href = "ode_script.m">ode_script.m</a>
a script which calls the function, necessary for the BATCH command.
</li>
<li>
<a href = "ode_batch_local.m">ode_batch_local.m</a>
a script which uses the BATCH command to run the function indirectly
and locally.
</li>
<li>
<a href = "ode_batch_local_output.txt">ode_batch_local_output.txt</a>
the output file.
</li>
</ul>
</p>
<p>
<b>ODE_FSU</b> executes the function on the FSU HPC cluster.
<ul>
<li>
<a href = "ode_fsu.m">ode_fsu.m</a>
a script which uses the fsuClusterMatlab command to run the function
indirectly on the FSU HPC cluster.
</li>
</ul>
</p>
<p>
<b>ODE_ITHACA</b> executes the function on the Virginia Tech Ithaca cluster.
<ul>
<li>
<a href = "ode_ithaca.m">ode_ithaca.m</a>
a script which runs the function on the Virginia Tech Ithaca cluster.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 26 March 2010.
</i>
<!-- John Burkardt -->
</body>
</html>