| Re: Randomize array order [message #55003 is a reply to message #55001] |
Fri, 27 July 2007 05:03   |
Allan Whiteford
Messages: 117
Registered: June 2006
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Senior Member |
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Conor wrote:
> Hi everyone!
>
> Anyone know an efficient way to randomize an array (I have a
> sorted array that I want unsorted). Initially, I tried something like
> this:
>
> array = findgen(1000000)
> unsort = array[sort(randomu(seed,1000000))]
>
> It works, but sorting on a million elements is rather slow. Anyone
> know a faster way?
>
Slightly different point and probably a bit academic:
If you have a million elements then you have 1000000! (i.e. one million
factorial) different ways to re-order the data. However, your seed is a
4 byte integer which can only take 2^32 different values.
Some messing about suggests that:
1000000! =~ 10^5568636
which means there are ~ 10^5568636 different ways to re-arrange your
elements as opposed to the 4 x 10^9 values your seed can take.
Thus, using any of the algorithms suggested you're only going to sample
10^-5568625 %
of the possible values. This is a really small number. It means that no
matter how hard you try and how many times you do things you'll never be
able to access anything but a tiny number of the possibilities without
doing multiple shufflings - I think it's something like 618737
sub-shufflings (i.e. 5568636 / 9) but that could be wrong. However, that
requires producing 618737 seeds per major-shuffle (and you can't use a
generator based on a 4 byte seed to produce these seeds).
But, since you're only going to be running the code 1000-10,000 times
(which is much smaller than 4e9) I guess everything will be ok. I don't
know if anyone has studied possible correlations of results as a
function of the very small number of seeds (compared to the data),
whatever random number generator is used and the shuffling method.
Presumably they have and presumably everything is ok. Does anyone know?
Thanks,
Allan
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