How to get indices of unique elements in matrix in separate arrays

1.I have a 1D array eg. A=[2,5,7,8,3,9.....]. Elements have been extracted from a 2d matrix eg

M=  [1  5   2  17
         2  2  8    9
         3  4  7    5
          ..............]

2. Now, I need to find the indices of each element of A in Matrix M. Like,

A[1]= [1,3; 2,1; 2,2]
A[2]= [1,2;3,4]
A[3]= [3,3]
A[4]= [3,4].... so and so...

What is the nest way to do?

Answer 1

[Jan]

I would prefer one of the above suggestions, but for completeness a dull (but unexpectedly faster) loop:

M = [1  5  2  17; ...
     2  2  8   9; ...
     3  4  7   5];
A = [2,5,7,8,3,9];
R = cell(1, max(A));
for iA = A
  [r, c] = find(M == iA);
  R{iA}  = [r, c];
end

A small speed comparison:

M = randi([1, 100], 100, 100);
A = randperm(100, 80);
tic;
for kk = 1:100
  [R,C] = arrayfun(@(n)find(M==n),A,'Uni',0);
  Z = cellfun(@(r,c)[r(:),c(:)],R,C,'Uni',0);
end
toc;

tic;
for kk = 1:100
  [tf, idx] = ismember(M, A);
  used_subset = idx(tf);
  linear_idx = (1:numel(idx)).';
  indices = accumarray( used_subset, linear_idx(tf), [], @(C) {C}, {});
  r = size(M,1);
  locations = cellfun(@(LI) [mod(LI-1, r)+1, floor((LI-1)/r)+1], ...
                      indices, 'Uniform', 0);
end
toc;

tic;
for kk = 1:100
  R = cell(1, max(A));
  for iA = A
    [r, c] = find(M == iA);
    R{iA}  = [r, c];
  end
end
toc;

tic;
for kk = 1:100
  locations = regionprops(M, 'PixelList');
  locations = {locations(A)};
end
toc;

 % Matlab R2016b/64, Win7, Core2Duo
 Elapsed time is 0.700541 seconds.   % arrayfun/cellfun
 Elapsed time is 0.789638 seconds.   % accumarray
 Elapsed time is 0.455393 seconds.   % dull loop/find
 ... Could someone please post the results with regionprops of the IPT?

Oh, the dull loop runs fastert than it looks like.

Answer 2

[Stephen23]

>> [R,C] = arrayfun(@(n)find(M==n),A,'Uni',0);
>> Z = cellfun(@(r,c)[r(:),c(:)],R,C,'Uni',0);
>> Z{:}
ans =
     2     1
     2     2
     1     3
ans =
     1     2
     3     4
ans =
     3     3
ans =
     2     3
ans =
     3     1
ans =
     2     4

Answer 3

[Guillaume]

Another option, if you have the image processing toolbox, and assuming all the values in A and M are strictly positive integers:

locations = regionprops(M, 'PixelList');
locations = {locations(A).PixelList}

Note that rows and columns are swapped because mathworks can't settle on just one coordinate system.

Answer 4

[Walter Roberson]

[tf, idx] = ismember(M, A);
used_subset = idx(tf);
linear_idx = (1:numel(idx)).';
indices = accumarray( used_subset, linear_idx(tf), [], @(C) {C}, {});
r = size(M,1);
locations = cellfun(@(LI) [mod(LI-1, r)+1, floor((LI-1)/r)+1], indices, 'Uniform', 0);

Note: this might have difficulty if there were elements in A that were not originally in M.