<html>
<head>
<title>
HIGH_CARD_PARFOR - Estimate High Card Statistics in Parallel
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
HIGH_CARD_PARFOR <br>
Estimate High Card Statistics in Parallel
</h1>
<hr>
<p>
<b>HIGH_CARD_PARFOR</b>
is a MATLAB directory 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>
The rules for this game are as follows. You are given a deck of DECK_SIZE cards.
</p>
<p>
Your goal is to select the high card. For convenience, we can assume
the cards are a permutation of the integers from 1 to DECK_SIZE, but in
fact the user mustn't see such values or else it's obvious which is the
largest card. (For a truly difficult problem, we'd have to work harder
to disguise the range of values and the likely distribution!)
</p>
<p>
Your choice is made under the following rules: You may turn over
one card at a time. When a card is turned over, you may declare that to be
your choice, or else turn over another card. If you have not chosen a card
by the end, then your choice is the final card.
</p>
<p>
If you have no idea what to do, and simply decide in advance to pick
a card "at random", that is, for example, you decide to pick the 15th card
before having seen any cards, then your probability of winning is 1/DECK_SIZE.
</p>
<p>
The question is, can you do better than that?
</p>
<p>
A good strategy is as follows: always look at the first SKIP_NUM cards without
choosing them. Then choose the very next card you encounter that is larger
than the cards you skipped.
</p>
<p>
Now the question is, is there an optimal value of SKIP_NUM for a given DECK_SIZE?
One way to find an approximate answer is to choose DECK_SIZE, and then, for
each value of SKIP_NUM, play 1000 games, and keep track of how often you are right.
</p>
<p>
This program demonstrates how such a computation can be done in parallel
using the PARFOR command.
</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/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_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_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/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>
<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 = "high_card_fun.m">high_card_fun.m</a>,
the function which performs the computations.
</li>
<li>
<a href = "high_card_display.m">high_card_display.m</a>,
displays the statistics once they are computed.
</li>
<li>
<a href = "high_card.png">high_card.png</a>,
is a plot of the statistics for a game with 100 cards, estimated
from 1,000 trials for each value of SKIP_NUM.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>HIGH_CARD_POOL</b> executes the function locally and interactively.
<ul>
<li>
<a href = "high_card_pool.m">high_card_pool.m</a>
a script which uses the MATLABPOOL command to run the function
locally and interactively.
</li>
<li>
<a href = "high_card_pool_output.txt">high_card_pool_output.txt</a>
the output file.
</li>
</ul>
<p>
<p>
<b>HIGH_CARD_BATCH</b> executes the function locally and noninteractively.
<ul>
<li>
<a href = "high_card_script.m">high_card_script.m</a>
a script which calls the function, necessary for the BATCH command.
</li>
<li>
<a href = "high_card_batch_local.m">high_card_batch_local.m</a>
a script which uses the BATCH command to run the function indirectly
and locally.
</li>
<li>
<a href = "high_card_batch_local_output.txt">high_card_batch_local_output.txt</a>
the output file.
</li>
</ul>
<p>
<p>
<b>HIGH_CARD_FSU</b> executes the function on the FSU HPC cluster, noninteractively.
<ul>
<li>
<a href = "high_card_fsu.m">high_card_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 23 May 2012.
</i>
<!-- John Burkardt -->
</body>
</html>