{"id":166,"date":"2008-12-08T12:18:02","date_gmt":"2008-12-08T11:18:02","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=166"},"modified":"2008-12-08T12:18:29","modified_gmt":"2008-12-08T11:18:29","slug":"notes-on-mathematica-7-parallelize-on-ubuntu","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=166","title":{"rendered":"Notes on Mathematica 7 : Parallelize on Ubuntu"},"content":{"rendered":"

Mathematica 7 includes some very nice support for parallel computing and one of the easiest commands to use is Parallelize<\/strong>.\u00a0 If you have a multi-core computer (and most of them are these days) then, in some cases, you can get a speedup of a factor of 2 or more simply by wrapping your code with the Parallelize <\/strong>command.\u00a0 I’ll stress that it’s not always<\/strong> this easy but, when it is, it’s very nice.<\/p>\n

To start getting my head around the new command I looked at the following small piece of code which is included in the Mathematica 7 documentation.
\n
\ndata = Table[ PrimeQ[n! + 1], {n, 400, 550}];
\n<\/code>
\nThis code calculates numbers of the form n!+1 for n between 400 and 550 and tests to see if they are prime or not. Let’s see how long it takes on my dual core 2Ghz Dell XPS M1330:
\n
\ndata = Table[ PrimeQ[n! + 1], {n, 400, 550}]; \/\/ AbsoluteTiming<\/code><\/p>\n

Out[1]={14.092809, Null}<\/p>\n

We see from the above that it took just over 14 seconds before we apply any parallelism. Let’s see how much improvement we get by using the Parallelize command:
\n
\ndata = Parallelize[Table[ PrimeQ[n! + 1], {n, 400, 550}]]; \/\/ AbsoluteTiming
\nOut[2]= {21.124572, Null}
\n<\/code>
\nOh dear, something has gone drastically wrong! The parallel calculation is taking 7 seconds (or 50%) longer than the serial calculation. Before writing a bug report to Wolfram, I thought I would dig around a little to try and work out what was going on.<\/p>\n

First things first, let’s take a look at how hard Mathematica is pushing the processor in both cases.\u00a0 I can add a little CPU monitoring applet to my GNOME panel by right clicking on it and selecting add to Panel<\/strong>.\u00a0 From the resulting list I choose CPU Frequency Scaling Monitor.<\/strong><\/p>\n

When I initially did this, the applet informed me that my CPU was running at 800 Mhz – way below its maximum speed of 2Ghz.\u00a0 When I click on this applet I get a range of settings that could be applied to my CPU such as On demand, Performance <\/strong>and Powersave <\/strong>along with specific speed settings from 800Mhz to 2 Ghz. The one selected was on demand<\/strong>.<\/p>\n

Turning back to Mathematica I run the sequential code again<\/p>\n

data = Table[ PrimeQ[n! + 1], {n, 400, 550}]; \/\/ AbsoluteTiming
\nOut[3]={14.117028, Null}
\n<\/code><\/p>\n

According to the CPU Monitor, my computer was running at 2Ghz (its top speed) during the entire calculation. However, when I ran the Parallelize<\/strong> version, the processor speed remained at 800Mhz the whole time. So, the calculation may well have been running in parallel but each of the 2 cores was only running at 40% of top speed.\u00a0 The problem seems to lie with Mathematica’s interaction with the on demand<\/strong> setting of the processor manager.<\/p>\n

By clicking on the GNOME CPU monitor, I can fix the processor to run at 2Ghz at all times – no fancy processor management here – just the fastest speed my computer can manage.\u00a0 Let’s see what the results of the two versions of the code are when I do this.
\n
\ndata = Table[ PrimeQ[n! + 1], {n, 400, 550}]; \/\/ AbsoluteTiming<\/code><\/p>\n

Out[4]={14.062377, Null}<\/p>\n

data = Parallelize[Table[ PrimeQ[n! + 1], {n, 400, 550}]]; \/\/ AbsoluteTiming<\/p>\n

Out[5]={7.635570, Null}<\/p>\n

That’s more like it! The parallel version is almost twice as fast as the serial version – just as we would expect on a dual core system. So, the moral of the story is to ensure that you don’t have your system set to modify it’s processor speed on demand<\/strong> when trying to make use of the new Parallel features of Mathematica 7.<\/p>\n

For the record I am running GNOME 2.24.1 on Ubuntu 8.10 with Mathematica 7.<\/p>\n","protected":false},"excerpt":{"rendered":"

Mathematica 7 includes some very nice support for parallel computing and one of the easiest commands to use is Parallelize.\u00a0 If you have a multi-core computer (and most of them are these days) then, in some cases, you can get a speedup of a factor of 2 or more simply by wrapping your code with […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[4,8],"tags":[],"class_list":["post-166","post","type-post","status-publish","format-standard","hentry","category-math-software","category-mathematica"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3swhs-2G","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/166","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=166"}],"version-history":[{"count":7,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/166\/revisions"}],"predecessor-version":[{"id":435,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/166\/revisions\/435"}],"wp:attachment":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=166"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=166"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=166"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}