       shuffling 10^8 numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg53276] shuffling 10^8 numbers
• From: George Szpiro <george at netvision.net.il>
• Date: Tue, 4 Jan 2005 03:12:52 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello:

Daniel's suggestion is exactly what I was looking for. but there is a
problem:

When I do the shuffle from the integers that are stored in the file GG.doc,
the time needed to do the shuffle increases by the SQUARE of the input size.
For 10,000 integers it took 3.3 seconds, for 100,000 integers it took 314
seconds. So it would be impossible to do it for 10^8 numbers.

Any suggestion?

Why did Daniel's shuffle only take 900 seconds for 10^8 real numbers (see
below).

Also: can I time intermediate progress, e.g., after every 1000 shuffles?

Thanks,
George

Clear[SSS,aa];
SSS=100000;

SetAttributes[shuffleSet, HoldFirst];
shuffleSet[LL_] := Module[{n=SSS, rand},
Do[
rand = Random[Integer, {j,n}];
LL[[{j,rand}]] = LL[[{rand,j}]],
{j,n}];
]

Timing[shuffleSet[aa]]

<<Utilities`CleanSlate`

OpenWrite["c:ShuffledGG.doc"];
Put[OutputForm[aa],"c:ShuffledGG.doc"]
Close["c:ShuffledGG.doc"];

Null
{314.292 Second,Null}

>
> My prior reply I point out that the memory requirements for generating a
> permutation and keeping both list and shuffled list can be close to the
> maximum allowable, if the list consists of machine reals. I should also
> point out that a purely in-place shuffle can manage 10^8 machine reals.
> Below code will do this. It is slow because we do not want to copy the
> original list, and hence lose the ability to use Compile.
>
> SetAttributes[shuffleSet, HoldFirst];
> shuffleSet[ll_] := Module[{n=Length[ll], rand},
>   Do[
>     rand = Random[Integer, {j,n}];
>     ll[[{j,rand}]] = ll[[{rand,j}]],
>     {j, n}];
>   ]
>
> len = 10^8;
> ll = Table[Random[],{len}];
>
> Timing[shuffleSet[ll]]
> Out= {904. Second, Null}
>
> A drawback is that there may be a copy of the original list lying around
> even though we did the shuffling in place. Use of
>
> <<Utilities`CleanSlate`
>
> in the AddOns:ExtraPackages directory might help to prevent this.
>
>
> Daniel Lichtblau
> Wolfram Research
>
>
>
>
>

```

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