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Re: <Null> while building lists

On 9/3/10 at 6:09 AM, alexxx.magni at (Alessandro) wrote:

>Hi group, I'm sure I'll bang me on my head as soon as I will Press
><Post Message>, but it's since yesterday that I'm struggling with

>I fast defined this awkward function, to collect the {index,value}
>of the maxima of a list of reals (a Fourier transform):

>maxima[f_] := Block[{old = f[[1]], m = {}},
>For[i = 2, i < Length[f]/2, i++,
>If[f[[i]] > old && f[[i + 1]] < f[[i]],
>AppendTo[m, {i, f[[i]]}]];
>old = f[[i]]

>Problem is, what I get is e.g. this:
>>maxima[f] {{14 Null, 10.8853 Null}, {21 Null, 3.34261 Null}, {28
>>Null, 1.47219 Null}}

>I'm sure I do not have spaces anywhere (it happened something
>similar due to this error, time ago), so what's wrong?

For your code to work as intended, you need to terminate the
For[...] portion with a semicolon.

As written, the last thing your code evaluates is the output
from For (which will be a Null) times the array you built m
which is not what you want.

As an aside, code that uses For and AppendTo like this is not
fast in Mathematica. If the data list isn't too large, then this
may not matter. But if you are using Fourier to compute the FFT
of a large data set, this code is going to be painfully slow.

Here is an example of something that will work much faster for
large data sets

In[1]:= data =
   6 Cos[2 x] + 3 Cos[5 x] /.
    x -> Rescale[Range[256] // N, {1, 256}, {0, 2 Pi}];

In[2]:= Most@
   ArrayRules@SparseArray[Chop[Abs@Fourier[data][[;; 128]], 10]] /.
  HoldPattern[{a_} -> b_] :> {a, b}

Out[2]= {{3, 48.31196595883446}, {6, 23.95982793367838}}

Note, this is an example. To generalize this approach, I would
want to change the hard coded value 10 to something computed
from the data or the FFT of the data.

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