{"id":281,"date":"2022-06-07T05:27:20","date_gmt":"2022-06-07T09:27:20","guid":{"rendered":"https:\/\/blogs.mathworks.com\/matlab\/?p=281"},"modified":"2022-06-07T05:36:34","modified_gmt":"2022-06-07T09:36:34","slug":"6-3-7-8-5-1-2-4-9-10-or-a-story-of-surprise-about-randomness","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/matlab\/2022\/06\/07\/6-3-7-8-5-1-2-4-9-10-or-a-story-of-surprise-about-randomness\/","title":{"rendered":"[6 3 7 8 5 1 2 4 9 10] – or “A Story of Surprise About Randomness”"},"content":{"rendered":"
Back in late March, Tom Rhys Marshall discovered something about MATLAB\u2019s handling of random numbers that he found both surprising and concerning! <\/span><\/div>
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The <\/span>randperm<\/span> function generates a random permutation of integers so <\/span>randperm(10)<\/span> <\/span>will return all integers from 1 to 10 in some random order. In a fresh MATLAB session that 'random' order is always the same<\/span><\/div>
randperm(10)<\/span><\/span><\/div>
ans = <\/span>1\u00d710<\/span><\/div><\/div>
6 3 7 8 5 1 2 4 9 10\r\n<\/div>
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As noted by Tom and others, the world is split into two types of people: those who think this is fine and commonly-known, and those who have no idea this was true and are very surprised and worried.<\/span><\/div>
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What if I told you....random numbers on a computer aren't random!<\/span><\/div>
For legal reasons, I'm told I can't use well known memes on this blog but you probably know the one I have in mind right? Anyway, the thing about random numbers in software like MATLAB, Python or R is that they are not random. They are completely deterministic. By design, however, the numbers returned by these '<\/span>pseudo<\/span> random number' algorithms have the same statistics as genuinely random numbers so, <\/span>provided we are careful<\/span>, we can go ahead with our M<\/span>onte-Carlo simulations and so on as if everything really was random.<\/span><\/div>
Let me say that again. <\/span>All 'random' number generators used in most modern programming languages and simulation platforms are completely deterministic<\/span>. If you are going to do anything serious using random numbers then this is a lesson you have to learn sooner or later. <\/span><\/div>
For quite a while now, the default algorithm used by MATLAB's random number generators has been one called <\/span>Mersenne Twister<\/span><\/a>. MathWorks' implementation of this, in common with many other implementations, will give you a different set of random numbers according to the 'seed' you set. The seed is an integer and is set using the <\/span>rng()<\/span> <\/span>function. When you start MATLAB, t<\/span>he seed is set to 0 by default.<\/span><\/div>
rng(0)<\/span><\/span><\/div><\/div>
randperm(10)<\/span><\/span><\/div>
ans = <\/span>1\u00d710<\/span><\/div><\/div>
6 3 7 8 5 1 2 4 9 10\r\n<\/div>
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A different seed gives a different result<\/span><\/div>
rng(1)<\/span><\/span><\/div><\/div>
randperm(10)<\/span><\/span><\/div>
ans = <\/span>1\u00d710<\/span><\/div><\/div>
3 6 5 7 4 8 9 1 10 2\r\n<\/div>
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Some people seem to believe that you have to do something fancy to the seed to get numbers that are somehow 'more random' but this isn't the case. <\/span>You can use any integer and you'll be fine for most common, simple uses of random numbers (It gets more complicated when dealing with parallel simulations!<\/span> <\/span>See the relevant references at the end of the post).<\/span><\/div>
A design choice: What should the seed be at start-up?<\/span><\/div>
If you follow the replies to Tom's<\/span>twitter thread<\/span><\/a> you'll see some people pointing out that some other systems do not behave as MATLAB does. The default generator in Python, for example, will give you (probably) a different set of random numbers every time you start it. This isn't because these systems are somehow more random than MATLAB, it\u2019s because they've chosen a different way of setting the seed. <\/span><\/div>
A common method of setting the seed at startup is to make use of the system time. The idea is that you use the current time to generate an integer and you use this as the seed. Voila! Every time you start up your system, you get a different seed and hence a different set of random numbers.<\/span><\/div>
You can do this in MATLAB too if you want by using <\/span>rng(\"shuffle\")<\/span><\/div>
rng(<\/span>\"shuffle\"<\/span>) <\/span>% Use the system clock to set the seed<\/span><\/span><\/div><\/div>
randperm(10)<\/span><\/span><\/div>
ans = <\/span>1\u00d710<\/span><\/div><\/div>
7 4 5 6 1 3 9 2 10 8\r\n<\/div>
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Now it could be argued (and many did on that twitter thread!) that this is somehow better than MATLAB's way of always using the same seed at start-up. Arguments for thinking this is a good idea include:<\/span><\/div>