How do I use the existence of an array member as an 'If' condition?

Question

I have an oddly shaped array (it is 100 by 100 by {1 or 3}, with the 1 or 3 being essentially random). I want to run a 'Do' loop on the first 2 dimensions of the array, but I only want to do the thing in the loop when I am at a member with three members in the last dimension. Is there a way to do this? I tried playing with things like If[Array[[i]][[j]][[3]]!=Null,t,f], but to no avail. At the end of the day, what I want is a way to write the following in Mathematica's language:

• If Array[[i]][[j]][[3]] exists, then do expr

Looking forward to any solutions/advice/ideas.

Answer 1

Clear[f, fakef]
fakeData = Array[Range[RandomChoice[{1, 3}]] &, {10, 10}];
fakef = If[1 == Length[#], #, {Last[#]}] &;
Map[fakef, fakeData, {2}]

Answer 2

Since your question mentions a Do loop over your matrix, (not a Table or Map), I'll first assume you're not building a new matrix, you don't care at all about your single-element data, but you actually really care about the positions of the 3-element-stuff within your structure as well as the 3-element-stuff.

If you don't care about the positions and you're just looking to make a new matrix with your 3-element stuff modified, then as Alan says you can just Map your function at level {2} over your data with a conditional.

---

First I'll make some stuff;

stuff =  Table[  
  If[RandomReal[{0, 1}] < .01, {a[i, j], b[i, j], c[i, j]}, d], {i, 
     1, 100}, {j, 1, 100}];

If you really care about the positions in your matrix, i.e. you want to do something to the 3-element stuff, and you need to know where it came from, but you don't need to make a new matrix:

locationsOfLength3 = 
  Select[Position[stuff, x_ /; Length[x] === 3], Length[#] === 2 &];

Do[ somethingWithStuff[ stuff[[p[[1]], p[[2]]]] , p ], 
   {p,locationsOfLength3}]

Note: I'm passing the location to my function as well as what was in stuff at that location. If you don't need the location, and don't need a matrix, you can ignore that bit.

---

If you need a matrix, but your function somethingWithStuff also needs to know where in your matrix the 3-element-stuff came from, you can do it with MapIndexed:

 newMatrix=MapIndexed[  If[Length[#] === 1, #, 
          somethingWithStuff[#, #2]] &, stuff, {2}];