Reverse lookup in MATLAB cell array of indices

Question

I have hit a brick wall trying to solve this:

Given a 5x1 cell array of vectors of indices to an array of n elements I need to find the reverse mapping.

What I have is the relation "In group 2, there are elements 15, 16, 17,...." What I want to have is "Element 15 is member of group 2,4,5."

This is the structure of my cell array

myCellArray  = 

[1x228 double]
[1x79  double]
[1x136 double]
[1x93  double]
[1x81  double]

This is part of the contents of my index vector

myCellArray{2}(1:5) =

    15    16    17    18    19

What I want is a cell array of n cells containing the indices of group membership for each element.

help?

Answer 1

You can do this with a combination of cellfun and arrayfun. First create a cell array:

>> mycellarray = { [1 2], [4 5], [3 4], [1 2 3 4 5] };

To get the elements of the cell array that contain a particular number (say 1) you can use cellfun:

>> find( cellfun(@(s)ismember(1, s), mycellarray) )
ans =
    1   4

Which tells you that 1 is in the 1st and 4th elements of mycellarray. Now you can just map this over the list of all possible indexes using arrayfun. The arrays that are produced might be of different length, so we need to set 'UniformOutput' to false.

>> n = 5;
>> result = arrayfun(@(i)find(cellfun(@(s)ismember(i,s), mycellarray)), 1:n, ...
                     'UniformOutput', false);

The elements are the index vectors that you want --

>> result{1}
ans =
     1     4    # since 1 is in the 1st and 4th array
>> result{3}
ans =
     3     4    # since 3 is in the 3rd and 4th array