Re: message 50001?

• To: mathgroup at smc.vnet.net
• Subject: [mg50042] Re: [mg50001] message 50001?
• From: Tomas Garza <tgarza01 at prodigy.net.mx>
• Date: Thu, 12 Aug 2004 05:44:31 -0400 (EDT)
• References: <200408110952.FAA04080@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```As you know, For loops are a no-no in Mathematica. I suggest the following -
and I'm aware there will be dozens of more elegant and straightforward
solutions in this MathGroup.
First construct an example. I use an array of random numbers drawn from a
binomial distribution, and then take their frequencies. This is a list of
{x, y} pairs with a peak somewhere. I assume you have loaded the Statistics
package beforehand.

In[1]:=
dist = BinomialDistribution[10, 0.5];

In[2]:=
aList = RandomArray[dist, 100];

In[3]:=
s = Reverse /@ Frequencies[aList]
Out[3]=
{{2, 3}, {3, 14}, {4, 20}, {5, 22}, {6, 20}, {7, 13}, {8, 7}, {9, 1}}

The peak in this example is 22 and corresponds to the index 5. Locate the
maximum within the y-values, determine its position in the list, and use
this position to find the corresponding x-value:

In[4]:=
t = Transpose[s]
Out[4]=
{{2, 3, 4, 5, 6, 7, 8, 9}, {3, 14, 20, 22, 20, 13, 7, 1}}

In[5]:=
t[[1,Position[t[[2]], x_ /; x == Max[t[[2]]]][[1,1]]]]
Out[5]=
5

This may be extended to more general situations where, for example, the peak
is attained at several x-values.

Tomas Garza
Mexico City
----- Original Message -----
From: "1.156" <rob at pio-vere.com>
To: mathgroup at smc.vnet.net
Subject: [mg50042] [mg50001] message 50001?

> Mathematica wizards, I've managed to cripple together code to do something
that
> I feel must be doable more easily and/or faster.
>
> S is a list of reals containing a signal with a prominent peak in
> amplitude. I simply want to find the index of the peak (x, the number of
> entries into the list where the peak occurs). Here's what I did.
>
>
> For[i = 1, S[[i]] ? max[S], i++, x = i];
>
> Can some suggest a better way, especially one not using a For loop?
>
> Thanks, Rob
>
>

```

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