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<channel>
	<title>Dr. Frank Celler</title>
	<atom:link href="http://www.dr-celler.de/feed/" rel="self" type="application/rss+xml" />
	<link>http://www.dr-celler.de</link>
	<description>Mein privater Blog</description>
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		<title>NoSQL matters</title>
		<link>http://www.dr-celler.de/2011/11/08/nosql-matters/</link>
		<comments>http://www.dr-celler.de/2011/11/08/nosql-matters/#comments</comments>
		<pubDate>Tue, 08 Nov 2011 10:56:20 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Blog]]></category>

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		<description><![CDATA[The NoSQL conference in 2012 will take place in Cologne, Germany. See www.nosql-matters.org.]]></description>
			<content:encoded><![CDATA[<p>The NoSQL conference in 2012 will take place in Cologne, Germany. See <a title="Benchmarking SSD with MongoDB and CouchDB, Part 1" href="http://www.nosql-matters.org/">www.nosql-matters.org</a>.</p>
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		<title>Benchmarking SSD with MongoDB and CouchDB, Part 2</title>
		<link>http://www.dr-celler.de/2011/09/29/benchmarking-ssd-with-mongodb-and-couchdb-part-2/</link>
		<comments>http://www.dr-celler.de/2011/09/29/benchmarking-ssd-with-mongodb-and-couchdb-part-2/#comments</comments>
		<pubDate>Thu, 29 Sep 2011 20:44:15 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Blog]]></category>
		<category><![CDATA[CouchDB]]></category>
		<category><![CDATA[Datenbanken]]></category>
		<category><![CDATA[Ext3]]></category>
		<category><![CDATA[Ext4]]></category>
		<category><![CDATA[Linux]]></category>
		<category><![CDATA[MongoDB]]></category>
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		<guid isPermaLink="false">http://www.dr-celler.de/?p=200</guid>
		<description><![CDATA[In Part 1 I started to investigate the performance impact of SSD on MongoDB and CouchDB. However, I got sidetracked because of the strange behavior of Mac OS X. The Mac is lying about msync. You have to force a &#8230; <a href="http://www.dr-celler.de/2011/09/29/benchmarking-ssd-with-mongodb-and-couchdb-part-2/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>In <a title="Part 1" href="http://www.triagens.de/frank-celler/2011/09/benchmarking-ssd-with-mongodb-and-couchdb/" target="_blank">Part 1</a> I started to investigate the performance impact of SSD on MongoDB and CouchDB. However, I got sidetracked because of the strange behavior of Mac OS X. The Mac is lying about msync. You have to force a synchronization by explicitly calling fnctl with F_FULLSYNC for the underlying file descriptor. So, I decided to do some more experiments with block sizes, file systems, operation systems, connection types and SSD.</p>
<p>The two combatants for today are</p>

<a href='http://www.dr-celler.de/2011/09/29/benchmarking-ssd-with-mongodb-and-couchdb-part-2/adata/' title='adata'><img width="150" height="150" src="http://www.dr-celler.de/wp-content/uploads/2011/09/adata-150x150.jpg" class="attachment-thumbnail" alt="adata" title="adata" /></a>
<a href='http://www.dr-celler.de/2011/09/29/benchmarking-ssd-with-mongodb-and-couchdb-part-2/ocz/' title='ocz'><img width="150" height="150" src="http://www.dr-celler.de/wp-content/uploads/2011/09/ocz-150x150.jpg" class="attachment-thumbnail" alt="ocz" title="ocz" /></a>

<h2>Test Setup</h2>
<p>Recall that the test programs creates a sparse file, fills this file block by block, and does an msync at every block. For the first tests I&#8217;m using a AMD Phenom II X6 1055T, OpenSuSE 11.4. Simply using dd gives for the ADATA</p>
<pre>&gt; dd if=/dev/zero of=/ssd/test1 bs=512 count=10000000
10000000+0 Datensätze ein
10000000+0 Datensätze aus
5120000000 Bytes (5,1 GB) kopiert, 39,5451 s, 129 MB/s</pre>
<p>and for the OCZ</p>
<pre>&gt; dd if=/dev/zero of=/ssd/test1 bs=512 count=10000000
10000000+0 Datensätze ein
10000000+0 Datensätze aus
5120000000 Bytes (5,1 GB) kopiert, 21,7511 s, 235 MB/s</pre>
<h2>Blocksize</h2>
<p>The first test uses different block sizes. Keep in mind that the page size is 4096.</p>
<div id="attachment_1084" class="wp-caption aligncenter" style="width: 591px"><a title="http://www.triagens.de/wp-content/uploads/2011/09/bench1.png" href="http://www.triagens.de/wp-content/uploads/2011/09/bench1.png" target="_blank"><img class="size-full wp-image-1084 " title="bench1" src="http://www.triagens.de/wp-content/uploads/2011/09/bench1.png" alt="" width="581" height="494" /></a><p class="wp-caption-text">(click on diagram to enlarge)</p></div>
<p>The ADATA is much faster than the OCZ when using a small block size. With larger block sizes it wins because of its higher bandwidth.</p>
<h2>File Systems</h2>
<p>I&#8217;ve used the OCZ directly connected to the SATA on the mortherboard to test various file systems: EXT4, EXT3, EXT2, Reiser, XFS, VFAT, BTRFS. The results are as follows</p>
<div id="attachment_1085" class="wp-caption aligncenter" style="width: 636px"><a href="http://www.triagens.de/wp-content/uploads/2011/09/bench2.png" target="_blank"><img class="size-full wp-image-1085 " title="bench2" src="http://www.triagens.de/wp-content/uploads/2011/09/bench2.png" alt="" width="626" height="265" /></a><p class="wp-caption-text">(click on diagram to enlarge)</p></div>
<p>The tests used the <a href="https://github.com/fceller/couchdb-benchmarks" target="_blank">msync-bench</a> test with block sizes of 1024, 4096, and 65536.</p>
<h2>Next Steps</h2>
<p>The same tests have to redone using a hard disk. First tests indicate, that a SSD is 10 to 100 times faster in this setup. I hope the FireWire connector for the Mac arrives soon, so that I can tests the different operating systems and connection types (SATA, eSATA, FW, USB). I still have to figure out, what are good tests for MongoDB and CouchDB.</p>
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		<title>Benchmarking SSD with MongoDB and CouchDB, Part 1</title>
		<link>http://www.dr-celler.de/2011/09/26/bechmarking-ssd-with-mongodb-and-couchdb-part-1/</link>
		<comments>http://www.dr-celler.de/2011/09/26/bechmarking-ssd-with-mongodb-and-couchdb-part-1/#comments</comments>
		<pubDate>Mon, 26 Sep 2011 13:21:01 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Blog]]></category>
		<category><![CDATA[CouchDB]]></category>
		<category><![CDATA[Datenbanken]]></category>
		<category><![CDATA[Linux]]></category>
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		<category><![CDATA[linux]]></category>
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		<category><![CDATA[mongodb]]></category>
		<category><![CDATA[ssd]]></category>

		<guid isPermaLink="false">http://www.dr-celler.de/?p=192</guid>
		<description><![CDATA[Doing benchmarks is always complicate because it is most of the time totally unclear what one wants to measure and what will be measured. There is article describing this dilemma, see Benchmarks-You-are-Doing-it-Wrong. The CouchDB – The Definite guide contains a &#8230; <a href="http://www.dr-celler.de/2011/09/26/bechmarking-ssd-with-mongodb-and-couchdb-part-1/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p>Doing benchmarks is always complicate because it is most of the time totally unclear what one wants to measure and what will be measured. There is article describing this dilemma, see<a href="http://jan.prima.de/%7Ejan/plok/archives/175-Benchmarks-You-are-Doing-it-Wrong.html"> Benchmarks-You-are-Doing-it-Wrong</a>. The CouchDB – The Definite guide contains a longer version of this, see <a href="http://guide.couchdb.org/draft/performance.html">High Performance</a>. I assume that this is also one of the reasons why MongoDB does not officially publish benchmarks, see <a href="http://www.mongodb.org/display/DOCS/Benchmarks">Benchmarks</a>. Kristina Chodorow, Software Engineer at 10gen, published a nice, unofficial benchmark at <a href="http://www.snailinaturtleneck.com/blog/2009/06/29/couchdb-vs-mongodb-benchmark/">snailinaturtleneck</a>.</p>
<p>As SSD are getting cheaper and cheaper I wanted to investigate what impact SSD have on the performance of MongoDB and CouchDB. Let me stress that this is not a real life example, it is not exhaustive test. It is not a complete test suit measuring the performance of a document store. I did that test out of interest for the implication of SSD on the NoSQL movement. There are also more complete benchmarks of SSD, but as <a href="http://blog.zorinaq.com/?e=40">zorinaq</a> points out most of them are also flawed.</p>
<p>They very first question is “what do we actually measure?”. In order to answer that we need some baselines. CouchDB is using a REST/HTTP interface, so I am going to measure the throughput of this interface. Just requesting the version information should give a good indication. The next step would be to reproduce the claims in <a href="http://guide.couchdb.org/draft/performance.html">High Performance</a>. Basically I’m interested in the “reliable” setup, where each and every change is written back to disk. This should show the biggest difference in performance between hard disks and SSD. Again you might ask “what is the point?”. It is clear that only very few application require that level of reliability, but I do not want to measure how good CouchDB or MongoDB are handling main memory. That would be a completely different test setup. Presumable, you would want to setup some sort of 2 server replication and feed realistic request with a certain create/read/update/delete ratio, because that is what most web applications look like. Or you want append only tests with few reads and no replication because you are using that database as store for log-files. Or you want an update-centric setup, because you are storing ticks for shares. Or, or, or … There are quite a lot of very different scenarios and presumably MongoDB and CouchDB will behave differently in all these situations.</p>
<p>The article <a href="http://guide.couchdb.org/draft/performance.html">High Performance</a> suggest that there is a difference between Linux and Mac OS X in the way syncs are handled. Therefore the following hardware was used in the tests:</p>
<ul>
<li>iMac 2010 running Mac OS X 11 (Core i3)</li>
<li>Dell Optiplex 980 running OpenSuSE 11.4 (Core i7)</li>
<li><a href="http://www.ocztechnology.com/ocz-vertex-3-max-iops-sata-iii-2-5-ssd.html">OCZ Vertex 3 Max IOPS</a></li>
</ul>
<p>I first wanted to establish a few cornerstones.</p>
<ol>
<li>What is the disk / ssd throughput?</li>
<li>What is the throughput of msync?</li>
<li>What is the throughput of fsync?</li>
<li>What is the protocol overhead?</li>
</ol>
<h2>Disk Throughput of the Harddisk</h2>
<p>Using DD to copy a 1 GByte file with random data gave</p>
<p>MAC / Hard Disk</p>
<blockquote><p>&gt; dd if=random of=test<br />
2048000+0 records in<br />
2048000+0 records out<br />
1048576000 bytes transferred in 8.753879 secs (119784157 bytes/sec)</p></blockquote>
<p>Linux / Hard Disk</p>
<blockquote><p>&gt; dd if=random of=test<br />
2048000+0 Datensätze ein<br />
2048000+0 Datensätze aus<br />
1048576000 Bytes (1,0 GB) kopiert, 10,0028 s, 105 MB/s</p></blockquote>
<p>The write performance between Linux and Mac OS X seems to be comparable.</p>
<h2>Memory Mapped Files</h2>
<p>Because of the hints given by CouchDB concerning MacOS and Linux, I’ve tried to understand what the difference between Linux and Mac OS X concerning memory mapped files is. I wrote a program to create (append-only) memory mapped files, which can be found on <a href="https://github.com/fceller/couchdb-benchmarks" target="_blank">github</a>. The program repeatedly appends blocks of 674 bytes. After each append msync was called.</p>
<h3>Mac</h3>
<p>The throughput under Mac OS is</p>
<blockquote>
<pre>&gt; msync-bench "/tmp/test1" 674 10000
insert time: 2.277690 sec for 10000 documents (4390.413094 docs / sec, 0.000228 secs / doc)
2959138.425334 bytes / sec, 2.822054 mbyte / sec</pre>
</blockquote>
<p>Each memory page of size 4096 is written 6 times, because msync is called after 674 bytes.</p>
<p>To get a baseline for the overhead introduced by my programm I’ve switched off the msync &#8211; only one msync at the end.</p>
<blockquote>
<pre>&gt; msync-bench "/tmp/test1" 674 10000
insert time: 0.081228 sec for 10000 documents (123110.257547 docs / sec, 0.000008 secs / doc)
82976313.586448 bytes / sec, 79.132379 mbyte / sec</pre>
</blockquote>
<p>So msync is indeed doing something.</p>
<h3>Linux</h3>
<p>Under Linux the behavior is very different</p>
<blockquote>
<pre>&gt; msync-bench /tmp/test1 674 1000
insert time: 26.022067 sec for 1000 documents (38.428923 docs / sec, 0.026022 secs / doc)
25901.093868 bytes / sec, 0.024701 mbyte / sec</pre>
</blockquote>
<p>In order to investigated further I used a larger object of size 4096</p>
<blockquote>
<pre>&gt; msync-bench /tmp/test1 4096 1000
insert time: 25.632864 sec for 1000 documents (39.012418 docs / sec, 0.025633 secs / doc)
159794.863344 bytes / sec, 0.152392 mbyte / sec</pre>
</blockquote>
<p>The throughput seems to be independent from the size. The number of msync is what counts.</p>
<p>The baseline without msync (resp. only one msync at the end) is</p>
<blockquote>
<pre>&gt; msync-bench /tmp/test1 674 10000
insert time: 0.044011 sec for 1000 documents (22721.592329 docs / sec, 0.000044 secs / doc)
15314353.229874 bytes / sec, 14.604905 mbyte / sec</pre>
</blockquote>
<h2>Using FDATASYNC</h2>
<p>Instead of msync I also tried to fsync a file. Basically same setup as before. Open a file, append a block of 674 bytes and fdatasync the file descriptor.</p>
<h3>Mac</h3>
<p>Under Mac OS I get</p>
<blockquote>
<pre>&gt; fsync-bench /tmp/test2 674 10000
insert time: 34.173727 sec for 10000 documents (292.622458 docs / sec, 0.003417 secs / doc)
197227.536815 bytes / sec, 0.188091 mbyte / sec</pre>
</blockquote>
<p>Using fdatasync is much slower (10 times) than msync. Again to get a base without fdatasync</p>
<blockquote>
<pre>&gt; fsync-bench /tmp/test2 674 10000
insert time: 0.412287 sec for 10000 documents (24254.948616 docs / sec, 0.000041 secs / doc)
16347835.367111 bytes / sec, 15.590511 mbyte / sec</pre>
</blockquote>
<h3>Linux</h3>
<p>The same under Linux</p>
<blockquote>
<pre>&gt; fsync-bench /tmp/test2 674 10000
insert time: 11.934775 sec for 1000 documents (83.788760 docs / sec, 0.011935 secs / doc)
56473.624346 bytes / sec, 0.053857 mbyte / sec</pre>
</blockquote>
<p>and the baseline</p>
<blockquote>
<pre>&gt; fsync-bench /tmp/test2 674 10000
insert time: 0.046587 sec for 1000 documents (21465.215618 docs / sec, 0.000047 secs / doc)
14467555.326593 bytes / sec, 13.797336 mbyte / sec</pre>
</blockquote>
<h2>The MSYNC Mac Mystery</h2>
<table width="258" border="0" cellspacing="0" cellpadding="0">
<colgroup>
<col width="98" />
<col span="2" width="80" /> </colgroup>
<tbody>
<tr>
<td width="98" height="20"></td>
<td width="80"><strong>MAC</strong></td>
<td width="80"><strong>LINUX</strong></td>
</tr>
<tr>
<td height="20">msync</td>
<td align="right">4 390</td>
<td>38</td>
</tr>
<tr>
<td height="20">msync base</td>
<td align="right">123 110</td>
<td align="right">22 721</td>
</tr>
<tr>
<td height="20">fdatasync</td>
<td align="right">292</td>
<td align="right">83</td>
</tr>
<tr>
<td height="20">fdatasync base</td>
<td align="right">24 255</td>
<td align="right">21 465</td>
</tr>
</tbody>
</table>
<p>So, either memory mapped files are much better under Mac OS X than under Linux, Mac OS X is somehow lying about msync, I am missing some magic madvice flags, or one needs a different filesystem. I&#8217;m using EXT4 under Linux. Strangely, fdatasync base (writing the file and then fdatasync at the end) is equally fast on both machines.</p>
<p>Any suggestions about what is going on are welcome. Why is msync under Linux 100 times slower? With only one final msync the Linux version is still six times as slower.</p>
<h2>Next Steps</h2>
<p>I&#8217;ve ordered a OCZ Vertex 3 MAX IOPS. It will be fun to see if and how this changes the figures. I still have to figure out how to connect the SSD to my Mac. Maybe I&#8217;ll try Firewire first before resorting to more drastic measures. After that we are ready to test MongoDB &amp; CouchDB on this SSD.</p>
<p>To be continued &#8230;</p>
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		<title>Sankt Petersburg</title>
		<link>http://www.dr-celler.de/2003/07/20/145/</link>
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		<pubDate>Sat, 19 Jul 2003 22:00:18 +0000</pubDate>
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		<description><![CDATA[Bed &#38; Breakfast in St. Petersburg]]></description>
			<content:encoded><![CDATA[<p><a href="http://www.randhouse.ru/" target="_blank">Bed &amp; Breakfast in St. Petersburg</a></p>
<p><a href="http://www.dr-celler.de/wp-content/uploads/2003/07/0491.jpg"><img class="size-medium wp-image-152 alignnone" title="049" src="http://www.dr-celler.de/wp-content/uploads/2003/07/0491-300x225.jpg" alt="" width="300" height="225" /></a></p>
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		<title>Weimar</title>
		<link>http://www.dr-celler.de/2000/09/25/weimar/</link>
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		<pubDate>Sun, 24 Sep 2000 22:00:18 +0000</pubDate>
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		<description><![CDATA[Landidyll, ländliche Lebensfreude]]></description>
			<content:encoded><![CDATA[<p><a href="http://www.landidyll.de/" target="_blank">Landidyll</a>, ländliche Lebensfreude</p>
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		<title>Calculating the order of an invertible matrix</title>
		<link>http://www.dr-celler.de/1997/12/31/calculating-the-order-of-an-invertible-matrix/</link>
		<comments>http://www.dr-celler.de/1997/12/31/calculating-the-order-of-an-invertible-matrix/#comments</comments>
		<pubDate>Tue, 30 Dec 1997 23:00:57 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Matrixgruppen]]></category>
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		<description><![CDATA[Frank Celler and C. R. Leedham-Green in L. Finkelstein and B. Kantor, editors, Groups and Computation II, volume 28 of Amer. Math. Soc DIMACS Series, 1997, pages 55-60 Abstract: In the first part of this note we present an algorithm &#8230; <a href="http://www.dr-celler.de/1997/12/31/calculating-the-order-of-an-invertible-matrix/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p><strong>Frank Celler and C. R. Leedham-Green</strong><br />
in L. Finkelstein and B. Kantor, editors, Groups and Computation II, volume 28 of Amer. Math. Soc DIMACS Series, 1997, pages 55-60</p>
<p>Abstract: In the first part of this note we present an algorithm for computing the order of an invertible matrix over a finite field and analyse its complexity. In the second part we compare this algorithm to the so-called spinning algorithm and give variations of the main algorithm to find the projective order and the p&#8217;-part, and to decide whether a given prime occurs in the order.</p>
<p>Preprint: <a href="/wp-content/uploads/2011/09/order.dvi.gz" target="_blank">DVI file</a>, <a href="/wp-content/uploads/2011/09/order.ps.gz" target="_blank">PostScript file</a>, or <a href="/wp-content/uploads/2011/09/order.pdf" target="_blank">PDF</a></p>
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		<title>Konstruktive Erkennungsalgorithmen klassischer Gruppen in GAP</title>
		<link>http://www.dr-celler.de/1997/12/31/konstruktive-erkennungsalgorithmen-klassischer-gruppen-in-gap/</link>
		<comments>http://www.dr-celler.de/1997/12/31/konstruktive-erkennungsalgorithmen-klassischer-gruppen-in-gap/#comments</comments>
		<pubDate>Tue, 30 Dec 1997 23:00:37 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Matrixgruppen]]></category>
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		<description><![CDATA[Frank Celler Phd. Thesis, RWTH Aachen In German: DVI file, PostScript file, or PDF]]></description>
			<content:encoded><![CDATA[<p><strong>Frank Celler</strong><br />
Phd. Thesis, RWTH Aachen</p>
<p>In German: <a href="/wp-content/uploads/2011/09/phd.dvi.gz" target="_blank">DVI file</a>, <a href="/wp-content/uploads/2011/09/phd.ps.gz" target="_blank">PostScript file</a>, or <a href="/wp-content/uploads/2011/09/phd.pdf" target="_blank">PDF</a></p>
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		<title>A non-constructive recognition algorithm for the special linear and other classical groups</title>
		<link>http://www.dr-celler.de/1997/12/31/a-non-constructive-recognition-algorithm-for-the-special-linear-and-other-classical-groups/</link>
		<comments>http://www.dr-celler.de/1997/12/31/a-non-constructive-recognition-algorithm-for-the-special-linear-and-other-classical-groups/#comments</comments>
		<pubDate>Tue, 30 Dec 1997 23:00:07 +0000</pubDate>
		<dc:creator>admin</dc:creator>
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		<description><![CDATA[Frank Celler and C. R. Leedham-Green, in L. Finkelstein and B. Kantor, editors, Groups and Computation II, volume 28 of Amer. Math. Soc DIMACS Series, 1997, pages 61-67 Abstract: In the first part of this note we present a Monte &#8230; <a href="http://www.dr-celler.de/1997/12/31/a-non-constructive-recognition-algorithm-for-the-special-linear-and-other-classical-groups/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p><strong>Frank Celler and C. R. Leedham-Green,</strong><br />
in L. Finkelstein and B. Kantor, editors, Groups and Computation II, volume 28 of Amer. Math. Soc DIMACS Series, 1997, pages 61-67</p>
<p>Abstract: In the first part of this note we present a Monte Carlo algorithm that decides if a given set of matrices generates a group containing the special linear group. In the second part we give timings and extend the algorithm to the other classical groups.</p>
<p>Preprint: <a href="/wp-content/uploads/2011/09/ncrec.dvi.gz" target="_blank">DVI file</a>, <a href="http://www.dr-celler.de/wp-content/uploads/2011/09/ncrec.ps.gz" target="_blank">PostScript file</a>, or <a href="/wp-content/uploads/2011/09/ncrec.pdf" target="_blank">PDF</a></p>
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		<title>A constructive recognition algorithm for the special linear group</title>
		<link>http://www.dr-celler.de/1995/12/31/a-constructive-recognition-algorithm-for-the-special-linear-group/</link>
		<comments>http://www.dr-celler.de/1995/12/31/a-constructive-recognition-algorithm-for-the-special-linear-group/#comments</comments>
		<pubDate>Sat, 30 Dec 1995 23:00:14 +0000</pubDate>
		<dc:creator>admin</dc:creator>
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		<description><![CDATA[Frank Celler and C. R. Leedham-Green Proceedings of the ATLAS Conference 1995 Abstract: In the first part of this note we present an algorithm to recognise constructively the special linear group. In the second part we give timings and examples. &#8230; <a href="http://www.dr-celler.de/1995/12/31/a-constructive-recognition-algorithm-for-the-special-linear-group/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p><strong>Frank Celler and C. R. Leedham-Green</strong><br />
Proceedings of the ATLAS Conference 1995</p>
<p>Abstract: In the first part of this note we present an algorithm to recognise constructively the special linear group. In the second part we give timings and examples.</p>
<p>Preprint: <a href="/wp-content/uploads/2011/09/crec.dvi.gz" target="_blank">DVI file</a>, <a href="/wp-content/uploads/2011/09/crec.ps.gz" target="_blank">PostScript file,</a> or <a href="/wp-content/uploads/2011/09/crec.pdf" target="_blank">PDF</a></p>
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		<title>Generating Random Elements of a Finite Group</title>
		<link>http://www.dr-celler.de/1995/12/31/generating-random-elements-of-a-finite-group/</link>
		<comments>http://www.dr-celler.de/1995/12/31/generating-random-elements-of-a-finite-group/#comments</comments>
		<pubDate>Sat, 30 Dec 1995 23:00:14 +0000</pubDate>
		<dc:creator>admin</dc:creator>
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		<description><![CDATA[Frank Celler, Charles R. Leedham-Green, Scott H. Murray, Alice C. Niemeyer, and E. A. O&#8217;Brien Comm. Algebra, 23:4931-4948, 1995 Abstract: We present a practical algorithm to construct random elements of a matrix group. We analyse its theoretical behaviour and prove &#8230; <a href="http://www.dr-celler.de/1995/12/31/generating-random-elements-of-a-finite-group/">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p><strong></strong><strong>Frank Celler, Charles R. Leedham-Green, Scott H. Murray, Alice C. Niemeyer, and E. A. O&#8217;Brien</strong><br />
Comm. Algebra, 23:4931-4948, 1995</p>
<p>Abstract: We present a <em>practical</em> algorithm to construct random elements of a matrix group. We analyse its theoretical behaviour and prove that asymptotically it produces uniformly distributed sequences of elements. We discuss tests to assess its effectiveness and use these to decide when its results are acceptable.</p>
<p>Preprint: <a href="http://www.dr-celler.de/wp-content/uploads/2011/09/random.dvi.gz" target="_blank">DVI file</a>, <a href="http://www.dr-celler.de/wp-content/uploads/2011/09/random.ps.gz" target="_blank">PostScript file</a>, or <a href="/wp-content/uploads/2011/09/random.pdf" target="_blank">PDF</a></p>
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