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<html>
<head>
<title>
QUAD_SPMD - SPMD (Single Program/Multiple Data) Quadrature
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
QUAD_SPMD <br> SPMD (Single Program/Multiple Data) Quadrature
</h1>
<hr>
<p>
<b>QUAD_SPMD</b>
is a MATLAB program which
uses the <b>SPMD</b> (single program, multiple data) command to estimate
an integral using quadrature.
</p>
<p>
The <b>SPMD</b> command allows a programmer to set up parallel computations
that require more user control than the simple <b>parfor</b> command.
In particular, users familiar with MPI will see many features that are
similar to that parallel programming model, including the ability to
send and receive messages. (Messages will NOT be exhibited in this
simple example, however!)
</p>
<p>
The algorithm carried out estimates the integral of a function f(x)
from 0 to 1 by the trapezoidal rule:
<pre>
Integral ( a <= x <= b ) f(x) dx = ( b - a ) / ( 2 * ( n - 1 ) )
* ( f(x1) + 2*f(x2) + 2*f(x3) + ... + 2*f(xn-2) + 2*f(xn-1) + f(xn) )
</pre>
where xi is the i-th point equally spaced between a and b, with the
endpoints included.
</p>
<p>
It's clear that this calculation can be done in parallel, and in fact,
simply by defining appropriate values of ai and bi, we can have
parallel process i carry out the trapezoidal rule over [ai,bi] and
sum the results to get the answer.
</p>
<p>
This example demonstrates how MATLAB's SPMD facility can be used to
implement this parallel calculation. No attempt is made to compare
the timings of the parallel code to a sequential calculation. The point
here is simply the mechanics of setting up an SPMD calculation, and
showing what you can expect.
</p>
<p>
Several points are worth mentioning:
<ul>
<li>
Parallel sections of the code begin with the <b>spmd</b> statement,
and end with an <b>end</b> statement. The computations in these
blocks occur on the MATLAB workers. The client sits idly and "watches".
</li>
<li>
The <b>matlabpool</b> parameter of the <b>batch</b> command defines a number of workers.
Each <b>spmd</b> block brings these workers into activity.
Each worker has access to the variable <b>numlabs</b>, which
contains the number of workers. Each worker has a unique value
of the variable <b>labindex</b>, between 1 and <b>numlabs</b>.
</li>
<li>
Any variable defined by the client is "visible" to the workers and
can be used on the right hand side of equations within the <b>spmd</b> blocks.
</li>
<li>
Any variable defined by the workers is a "composite" variable. If a variable
called <b>X</b> is defined by the workers, then each worker has its own
value, and the set of values is accessible by the client, using the worker's
index. Thus <b>X{1}</b> is the value of <b>X</b> computed by worker 1.
</li>
<li>
A program can have several <b>spmd</b> blocks. If the program completes
an <b>spmd</b> block, carries out some commands in the client program,
and then enters another <b>spmd</b> block, then all the variables defined
during the previous <b>spmd</b> block still exist. The data that was
on worker 1 is still there, for instance. It is simply as though
each worker was "paused" while the client did some work.
</li>
<li>
Workers cannot directly see each other's variables. Communication from
one worker to another can be done through the client. However, a limited
number of special operators are available, that can be used within
<b>spmd</b> blocks, which combine variables. In particular, the command
<b>gplus</b> sums the values of a variable that exists on all the workers,
and returns to each worker the value of that sum.
</li>
</ul>
</p>
<p>
The function has the form:
<blockquote>
function value = quad_fun ( n )
</blockquote>
where
<ul>
<li>
n, is the number of points to use;
</li>
<li>
value, is the estimated integral.
</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>QUAD_SPMD</b> is available in
<a href = "../../m_src/quad_spmd/quad_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>,
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 = "../../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_spmd/prime_spmd.html">
PRIME_SPMD</a>,
a MATLAB program which
counts the number of primes between 1 and N;
running in parallel using MATLAB's "SPMD" 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/quad_serial/quad_serial.html">
QUAD_SERIAL</a>,
a MATLAB program which
approximates an integral using a quadrature rule,
and is intended as a starting point for parallelization exercises.
</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>
<ul>
<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>
</ul>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "quad_fun.m">quad_fun.m</a>,
a MATLAB function which returns an estimate for an integral,
using a given number of points.
</li>
<li>
<a href = "quad_pool.m">quad_pool.m</a>
a script which uses the MATLABPOOL command to run the function locally and
interactively.
</li>
<li>
<a href = "quad_script.m">quad_script.m</a>,
a MATLAB script file which simply invokes the function with
N = 10000 points.
</li>
<li>
<a href = "quad_batch_local.m">quad_batch_local.m</a>,
a batch command to run the job indirectly on the local system,
plus a few more commands
to monitor its progress, print the diary, and destroy the job at the end.
</li>
<li>
<a href = "quad_batch_ithaca.m">quad_batch_ithaca.m</a>,
a batch command to run the job indirectly on the Ithaca cluster,
plus a few more commands
to monitor its progress, print the diary, and destroy the job at the end.
</li>
<li>
<a href = "quad_fsu.m">quad_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 04 February 2010.
</i>
<!-- John Burkardt -->
</body>
</html>