Identify the positions of a marker in sublists

Question

I have a list of lists from which I would like to pick out the positions of the number 1 and then print out these positions for each sublist.

I am having some trouble collecting what I am printing into a list / matrix / array though. Below is my list of lists and the commands by which I find the positions of the 1's and print them out. Thanks.

ZeroCrossings = {{0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 1,
   0, 0, 1, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1,
   0}, {0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0}, {0, 0, 0, 1, 0, 0, 
  0, 0, 1, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0}}

Do[Print[Flatten[Transpose[Position[ZeroCrossings[[t]], 1]]]], {t, 1,Length[ZeroCrossings]}]

{3,9}

{4,5,8,12,13}

{4,12,13}

{4,8,11,13}

{4,9,12,13}

{5,6,11}

Answer 1

Primarily you just need to use Table instead of Do and Print. Also you can simplify the code:

Table[Flatten @ Position[t, 1], {t, ZeroCrossings}]

{{3, 9}, {4, 5, 8, 12, 13}, {4, 12, 13}, {4, 8, 11, 13}, {4, 9, 12, 13}, {5, 6, 11}}

See Case #2 of: Alternatives to procedural loops and iterating over lists in Mathematica

It may be simpler to use Map:

Flatten @ Position[#, 1] & /@ ZeroCrossings

This is probably a bit advanced for you right now but you could also use:

GatherBy[Position[ZeroCrossings, 1], First][[All, All, 2]]

Or if you are using Mathematica 10:

GroupBy[Position[ZeroCrossings, 1], First -> Last] // Values

Answer 2

Another approach:

ZeroCrossings = {{0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0,
     1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 
    0, 1, 1, 0}, {0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0}, {0, 0, 0,
     1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 
    1, 0, 0, 0}};

Map[Last, GatherBy[Position[ZeroCrossings, 1], First], {-2}]

{{3, 9}, {4, 5, 8, 12, 13}, {4, 12, 13}, {4, 8, 11, 13}, {4, 9, 12,
13}, {5, 6, 11}}

Answer 3

You can also use PositionIndex in Version 10

(PositionIndex /@ ZeroCrossings)[[All, 2]]

Gives:

{{3, 9}, {4, 5, 8, 12, 13}, {4, 12, 13}, {4, 8, 11, 13}, {4, 9, 12, 13}, {5, 6, 11}}

Answer 4

zeroCrossings = {{0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0,
     1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 
    0, 1, 1, 0}, {0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0}, {0, 0, 0,
     1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 
    1, 0, 0, 0}};

Using SequencePosition:

SequencePosition[#, {1}] & /@ zeroCrossings /. {a_, a_} :> a

Using MapIndexed:

MapIndexed[If[#1 == 1, First@#2, Nothing] &, #] & /@ zeroCrossings

{{3, 9}, {4, 5, 8, 12, 13}, {4, 12, 13}, {4, 8, 11, 13}, {4, 9, 12,
13}, {5, 6, 11}}

Answer 5

SparseArray[ZeroCrossings] @ "AdjacencyLists"

{{3, 9}, {4, 5, 8, 12, 13}, {4, 12, 13}, {4, 8, 11, 13}, 
 {4, 9, 12,  13}, {5, 6, 11}}