-
Notifications
You must be signed in to change notification settings - Fork 54
/
collatz_parfor.html
339 lines (293 loc) · 9.48 KB
/
collatz_parfor.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
<html>
<head>
<title>
COLLATZ_PARFOR - A Parallel MATLAB Function Using PARFOR
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
COLLATZ_PARFOR <br> A Parallel MATLAB Function Using PARFOR
</h1>
<hr>
<p>
<b>COLLATZ_PARFOR</b>
is a directory which
illustrates how a MATLAB function using the PARFOR statement
can be run in parallel.
</p>
<p>
A Collatz sequence starting at the integer I computes the next term
by halving the number if it is even, or tripling and adding 1 if it is odd.
The sequence stops when the value 1 is reached.
</p>
<p>
The number of steps required to reach 1 varies greatly. No formula
has been determined, and in fact, it hasn't actually been proved that
the value of 1 will always be reached.
</p>
<p>
An interesting question, suitable for parallel execution, is to ask for
the length of the longest Collatz sequence between 1 and N.
</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 VT 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">
Usage:
</h3>
<p>
The basic calculation is done by <b>collatz_fun</b> and has the form:
<blockquote>
<i>j_max</i> = <b>collatz_fun</b> ( <i>n</i> )
</blockquote>
where
<ul>
<li>
<i>n</i> is the largest integer to check.
</li>
<li>
<i>j_max</i> is the longest sequence encountered.
</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>COLLATZ_PARFOR</b> is available in
<a href = "../../m_src/collatz_parfor/collatz_parfor.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/collatz/collatz.html">
COLLATZ</a>,
a MATLAB library which
computes and analyzes the Collatz
sequence (or "hailstone" sequence or "3n+1 sequence");
</p>
<p>
<a href = "../../m_src/collatz_recursive/collatz_recursive.html">
COLLATZ_RECURSIVE</a>,
a MATLAB library which
demonstrates recursive programming by considering the simple Collatz 3n+1 problem.
</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>,
MATLAB 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_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>
<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>
<li>
Michael Quinn,<br>
Parallel Programming in C with MPI and OpenMP,<br>
McGraw-Hill, 2004,<br>
ISBN13: 978-0071232654,<br>
LC: QA76.73.C15.Q55.
</li>
<li>
Eric Weisstein,<br>
"The Collatz Problem",<br>
CRC Concise Encyclopedia of Mathematics,<br>
CRC Press, 2002,<br>
Second edition,<br>
ISBN: 1584883472,<br>
LC: QA5.W45.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "collatz_fun.m">collatz_fun.m</a>
the function which performs the computations.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>COLLATZ_POOL</b> executes the function locally and interactively.
<ul>
<li>
<a href = "collatz_pool.m">collatz_pool.m</a>
a script which uses the MATLABPOOL command to run the function locally and
interactively.
</li>
<li>
<a href = "collatz_pool_output.txt">collatz_pool_output.txt</a>
the output file.
</li>
</ul>
</p>
<p>
<b>COLLATZ_BATCH</b> executes the function locally and noninteractively.
<ul>
<li>
<a href = "collatz_script.m">collatz_script.m</a>
a script which calls the function, necessary for the BATCH command.
</li>
<li>
<a href = "collatz_batch_local.m">collatz_batch_local.m</a>
a script which uses the BATCH command to run the function indirectly
and locally.
</li>
<li>
<a href = "collatz_batch_local_output.txt">collatz_batch_local_output.txt</a>
the output file.
</li>
</ul>
<p>
<p>
<b>COLLATZ_BATCH_ITHACA</b> executes the function remotely on the Virginia
Tech Ithaca cluster.
<ul>
<li>
<a href = "collatz_batch_ithaca.m">collatz_batch_ithaca.m</a>
a script which uses the BATCH command to run the function indirectly
and remotely, on the Virginia Tech Ithaca cluster.
</li>
</ul>
</p>
<p>
<b>COLLATZ_FSU</b> executes the function on the FSU HPC cluster.
<ul>
<li>
<a href = "collatz_fsu.m">collatz_fsu.m</a>
a script which uses the fsuClusterMatlab command to run the function
indirectly on the FSU HPC cluster.
</li>
</ul>
</p>
<hr>
<i>
Last modified on 23 May 2012.
</i>
<!-- John Burkardt -->
</body>
</html>