Re: For Loop and Array related

• To: mathgroup at smc.vnet.net
• Subject: [mg58015] Re: For Loop and Array related
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Thu, 16 Jun 2005 06:43:50 -0400 (EDT)
• Organization: The University of Western Australia
• References: <d8oucl\$t6q\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <d8oucl\$t6q\$1 at smc.vnet.net>,
"mchangun at gmail.com" <mchangun at gmail.com> wrote:

> I have an array with 100 elements, all set to zero initially.  Then I
> want to randomly choose one element and increase its value by one, and
> repeat this 16000 times. Here is my code:
>
> Lattice = Table[0, {n, 100}];
> For[i = 1, i = 16000, i++, Lattice[[Random[Integer, {1, 100}]]]++]
>
> So now if I add all the elements in the list Lattice together, I should
> get 16000 (I use Total[Lattice] to get the sum of the list).  But this
> doesn't happen, and strangely, each time I run this, the sum of the
> list is different!  What am I doing wrong?

A syntax error (use of == vs. =) and a subtlety. Here is the modified
code:

Lattice = Table[0, {n, 100}];

SeedRandom[1];

Module[{t}, For[i = 1, i <= 16000, i++,
t = Random[Integer, {1, 100}]; Lattice[[t]]++]];

Lattice

I've included SeedRandom[1]; so that we get a "repeatable" random
sequence.

Note the use of the local variable t. If you write

Lattice[[Random[Integer, {1, 100}]]]++

then, essentially, you are evaluating

Lattice[[Random[Integer, {1, 100}]]] =
Lattice[[Random[Integer, {1, 100}]]] + 1

which involves two _different_ random numbers.

> Also I'm aware that a lot of Mathematica newbies try and write code
> like it were C++ and I think i've fallen into this trap as well.  So is
> there a different (more Mathematica) way which I can implement the
> above?

First compute a list of 16000 numbers:

SeedRandom[1]; t = Table[Random[Integer, {1, 100}], {16000}];

Here are three ways to compute Lattice:

[1] Count[t, #]& /@ Range[100]

[2] << "Statistics`";

BinCounts[t, {0, 100}]

[3] Length /@ Split[Sort[t]]

These 3 codes give the same result as above.

The last code will not work with short lists because it does not return
any zero counts.

Cheers,
Paul

--
Paul Abbott                                      Phone: +61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)
AUSTRALIA                               http://physics.uwa.edu.au/~paul
http://InternationalMathematicaSymposium.org/IMS2005/

```

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