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I am very new to Mathematica (first time!) and I'm already having troubles with arrays. I basically have a 4D tensor, that is a matrix (call it M) which has for each entry another matrix. I want to select the elements of the nested matrices that are bigger than zero, but Select[M, # > 0 &] doesn't work. I suspect it is because I do not respect the dimensions. I am kind of lost. Thanks in advance

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  • $\begingroup$ Can you post M here? $\endgroup$ – J. M. will be back soon May 15 '13 at 14:20
  • $\begingroup$ Do you want the result as a simple list or something more structured (nested lists) ? $\endgroup$ – andre314 May 15 '13 at 14:25
  • $\begingroup$ @J.M., i cannot post the whole thing because each entry is an integral of two function multiplied together. $\endgroup$ – user24273 May 15 '13 at 14:37
  • $\begingroup$ @andre, i need to make a matrix out of it $\endgroup$ – user24273 May 15 '13 at 14:38
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    $\begingroup$ here is how it looks like, where the s and s' are the functions that i integrate. ex = Array[s[#1, #2] s'[#3, #4] &, {4, 4, 4, 4}, {1, 0, 1, 0}] $\endgroup$ – user24273 May 15 '13 at 14:41
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m = RandomInteger[{1, 42}, {3, 3, 3, 3}];

Cases will extract every element equal to 42 here. (There won't always be any for the random nature.)

Cases[m, i_Integer /; i == 42, Infinity]

With Position you can identify where these elements are.

Position[m, i_Integer /; i == 42, Infinity]

Select selects sublists (row of matrices in this case) with some property, whether for example they containt a matrix with 42.

Select[m, MemberQ[Flatten[#], 42] &]
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  • $\begingroup$ You can replace levelspec Infinity with {4} for the nature of your input. $\endgroup$ – BoLe May 15 '13 at 14:33
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    $\begingroup$ "(There won't always be any for the random nature.)" - for reproducibility, look up SeedRandom[]. $\endgroup$ – J. M. will be back soon May 15 '13 at 14:37
  • $\begingroup$ @J.M. BlockRandom[...] for example, I know that. Chances are with that many elements there will be at least one 42. :) $\endgroup$ – BoLe May 15 '13 at 14:42
  • $\begingroup$ yes!!! It worked! I think its just because its the first time i use this program and i dont know how and where to use the right functions. Thanks a lot guys. $\endgroup$ – user24273 May 15 '13 at 14:48
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    $\begingroup$ @user, if you're searching for a specific number, then this also works: Cases[m, 42, Infinity] (similarly with Position[]). $\endgroup$ – J. M. will be back soon May 15 '13 at 15:13
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If you goal is a matrix of the origial dimensions retaining only the selectred values you could do something like this:

  Map[ If[# > 0, #, Null] & , m , {-1}]
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