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<html>
<head>
<title>
PRIME_SPMD - Counting Primes in Parallel using SPMD
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
PRIME_SPMD <br> Counting Primes in Parallel using SPMD
</h1>
<hr>
<p>
<b>PRIME_SPMD</b>
is a MATLAB program which
counts the number of primes between 1 and N,
executing in parallel using MATLAB's SPMD facility.
</p>
<p>
The algorithm is completely naive. For each integer I, it simply checks
whether any smaller J evenly divides it. The total amount of work
for a given N is thus roughly proportional to 1/2*N^2.
</p>
<p>
There is very little memory traffic and no communication, so this program
is a good test for the pure computational speedup offered by MATLAB's
Parallel Programming Toolbox.
</p>
<p>
The basic function has the form:
<blockquote>
function total = prime_fun ( n )
</blockquote>
where
<ul>
<li>
n, the largest integer to check.
</li>
<li>
total, the number of primes between 1 and n.
</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>PRIME_SPMD</b> is available in
<a href = "../../m_src/prime_spmd/prime_spmd.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/cell_detection_tasks/cell_detection_tasks.html">
CELL_DETECTION_TASKS</a>,
a MATLAB program which
creates modified versions of a sequence of gray-scale TIF files containing
images of cells; the process of each file is carried out independently,
using the "task" feature of MATLAB's parallel computing toolbox.
</p>
<p>
<a href = "../../m_src/cg_distributed/cg_distributed.html">
CG_DISTRIBUTED</a>,
a MATLAB program which
implements a version of the NAS CG conjugate gradient benchmark,
using distributed memory.
</p>
<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/contrast_spmd/contrast_spmd.html">
CONTRAST_SPMD</a>,
a MATLAB program which
demonstrates the SPMD parallel programming feature for image operations;
the client reads an image, the workers increase contrast over separate portions, and
the client assembles and displays the results.
</p>
<p>
<a href = "../../m_src/contrast2_spmd/contrast2_spmd.html">
CONTRAST2_SPMD</a>,
a MATLAB program which
demonstrates the SPMD parallel programming feature for image operations;
this improves the contrast_spmd program by allowing the workers to share some
data; this makes it possible to eliminate artificial "seams" in the processed
image.
</p>
<p>
<a href = "../../m_src/dijkstra_spmd/dijkstra_spmd.html">
DIJKSTRA_SPMD</a>,
a MATLAB program which
uses the SPMD feature to parallelize a simple example of Dijkstra's
minimum distance algorithm for graphs.
</p>
<p>
<a href = "../../m_src/face_spmd/face_spmd.html">
FACE_SPMD</a>,
a MATLAB program which
demonstrates the SPMD parallel programming feature;
the client has a 3D box that has been dissected into tetrahedrons.
Multiple workers cooperate to construct a list of the triangular faces
that lie on the boundaries of the box.
</p>
<p>
<a href = "../../m_src/fd2d_heat_explicit_spmd/fd2d_heat_explicit_spmd.html">
FD2D_HEAT_EXPLICIT_SPMD</a>,
a MATLAB program which
uses the finite difference method and explicit time stepping
to solve the time dependent heat equation in 2D. A black and white image
is used as the "initial condition". MATLAB's SPMD facility is used to
carry out the computation in parallel.
</p>
<p>
<a href = "../../m_src/fmincon_parallel/fmincon_parallel.html">
FMINCON_PARALLEL</a>,
a MATLAB program which
demonstrates the use of MATLAB's FMINCON constrained minimization
function, taking advantage of MATLAB's Parallel Computing Toolbox
for faster execution.
</p>
<p>
<a href = "../../m_src/image_denoise_spmd/image_denoise_spmd.html">
IMAGE_DENOISE_SPMD</a>,
a MATLAB program which
demonstrates the SPMD parallel programming feature for image operations;
the client reads an image, the workers process portions of it, and
the client assembles and displays the results.
</p>
<p>
<a href = "../../m_src/linear_solve_distributed/linear_solve_distributed.html">
LINEAR_SOLVE_DISTRIBUTED</a>
a MATLAB program which
solves a linear system <b>A*x=b</b> using MATLAB's <b>spmd</b> facility,
so that the matrix <b>A</b> is "distributed" across multiple MATLAB workers.
</p>
<p>
<a href = "../../m_src/matlab_parallel/matlab_parallel.html">
MATLAB_PARALLEL</a>,
MATLAB programs which
illustrate "local" parallel programming on a single computer
with MATLAB's Parallel Computing Toolbox.
</p>
<p>
<a href = "../../m_src/matrix_assemble_spmd/matrix_assemble_spmd.html">
MATRIX_ASSEMBLE_SPMD</a>,
a MATLAB program which
demonstrates the SPMD parallel programming feature by having each worker
assemble part of the Hilbert matrix, which is then combined into one
array by the client program.
</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_parfor/ode_sweep_parfor.html">
ODE_SWEEP_PARFOR</a>,
a MATLAB program which
demonstrates how the PARFOR command can be used to parallelize the computation
of a grid of solutions to a parameterized system of ODE's.
</p>
<p>
<a href = "../../m_src/plot_spmd/plot_spmd.html">
PLOT_SPMD</a>,
a MATLAB library which
demonstrates the SPMD parallel programming feature, by having a number
of labs compute parts of a sine plot, which is then displayed by the
client process.
</p>
<p>
<a href = "../../c_src/prime_openmp/prime_openmp.html">
PRIME_OPENMP</a>,
a C program which
counts the number of primes between 1 and N, using OpenMP for parallel execution.
</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/prime_plot/prime_plot.html">
PRIME_PLOT</a>
a MATLAB program which
displays a box plot of the prime and composite numbers.
</p>
<p>
<a href = "../../m_src/prime_serial/prime_serial.html">
PRIME_SERIAL</a>,
a MATLAB program which
counts the number of primes between 1 and N,
intended as a starting point for the creation of a parallel version.
</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/quad_spmd/quad_spmd.html">
QUAD_SPMD</a>,
a MATLAB program which
estimates an integral using quadrature;
running in parallel using MATLAB's "SPMD" feature.
</p>
<p>
<a href = "../../m_src/quad_tasks/quad_tasks.html">
QUAD_TASKS</a>,
a MATLAB program which
estimates an integral using quadrature;
running in parallel using MATLAB's "TASK" feature.
</p>
<p>
<a href = "../../m_src/random_walk_2d_avoid_tasks/random_walk_2d_avoid_tasks.html">
RANDOM_WALK_2D_AVOID_TASKS</a>,
a MATLAB program which
computes many self avoiding random walks in 2D by creating a job which
defines each walk as a task, and then computes these independently
using MATLAB's Parallel Computing Toolbox task computing capability.
</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/subset_sum_tasks/subset_sum_tasks.html">
SUBSET_SUM_TASKS</a>,
a MATLAB program which
solves a subset sum problem by exhaustive search,
subdividing the search range among separate tasks.
</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">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "prime_fun.m">prime_fun.m</a>
the function which performs the computations.
</li>
<li>
<a href = "prime_pool.m">prime_pool.m</a>
a script which uses the MATLABPOOL command to run the function locally and
interactively.
</li>
<li>
<a href = "prime_script.m">prime_script.m</a>
a script which calls the function, necessary for the BATCH command.
</li>
<li>
<a href = "prime_batch_local.m">prime_batch_local.m</a>
a script which uses the BATCH command to run the function indirectly
and locally.
</li>
<li>
<a href = "prime_batch_ithaca.m">prime_batch_ithaca.m</a>
a script which uses the BATCH command to run the
function indirectly on the Ithaca cluster.
</li>
<li>
<a href = "prime_fsu.m">prime_fsu.m</a>
a script which uses the fsuClusterMatlab command to run the function
indirectly on the FSU HPC 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 01 June 2010.
</i>
<!-- John Burkardt -->
</body>
</html>