MATLAB: How to construct a cell array from another cell array

cell arrayindexingpermutation

I have a cell array with a variable number of cells and a variable number of elements within each cell. For instance, it could by V{1}{1}=1 2 3 4, V{1}{2}=3 4 1 0,V{1}{3}=3 5 -1 -9, and V{2}{1}=-1 -2 9, V{2}{2}= 0 9 6, i.e., the cell 1 has 3 vectors of length 4 elements and the cell 2 has 2 vectors of length 3. I want to construct another cell array such that it has all combinations of these vectors, here I could have 6 combinations (3*2=6). The new cell array has to be of length 6 cells (number of possible combinations), and each cell has a possible combinations, for example A{1}={1 2 3 4 and -1 -2 9} and A{2}={1 2 3 4 and 0 9 6} . Note that I will get these vectors from a matlab code so I do not know them in advance.

Best Answer

This fits the description from your comment under your question. It horizontally concatenates all combinations of the row vectors stored in V{1} and V{2}.

% Demo data
V{1}{1} = 1:4; % vec1 1x4
V{1}{2} = 2:5; % vec2 1x4
V{1}{3} = 3:6; % vec3 1x4
V{2}{1} = 1:3; % vec4 1x3
V{2}{2} = 2:4; % vec5 1x3
[v1idx, v2idx] = ndgrid(1:numel(V{1}), 1:numel(V{2})); 
D = cellfun(@(a,b)horzcat(a,b),{V{1}{v1idx(:)}}, {V{2}{v2idx(:)}}, 'UniformOutput', false)
% D = {[vec1,vec4], [vec2,vec4], [vec3,vec4], [vec1,vec5], [vec2,vec5], [vec3,vec5]}

Version 2: when number of sub-cells in V is variable.

cellCount = num2cell(1:numel(V)); 
nCellIdx = cellfun(@(x)1:numel(x), V, 'UniformOutput', false);
cellGrid = cell(size(nCellIdx)); 
[cellGrid{:}] = ndgrid(nCellIdx{:}); 
matGrid = cell2mat(cellfun(@(x)x(:),cellGrid,'UniformOutput',false)); % Each row is the index for 1 cell
D = cell(1,size(matGrid,1)); 
for i = 1:size(matGrid,1)
    D{i} = cellfun(@(ci,sci)V{ci}(sci),cellCount, num2cell(matGrid(i,:)));
end

D(i) contains the sub-cell indices listed in matGrid(i,:).

Related Solutions

MATLAB: How to pick up all combination of numbers from multiple vectors

Don't store your vectors separately. Instead, learn to use tools like cell arrays, which make things hugely more efficient.

V = {[1 2 3],[4 5 6 7],[8 9 10 11 12]};

Next, how do you use a cell array for this purpose? You pass the elements into ndgrid, using what is called acomma separated list. (Or meshgrid.) That is what you get when you type V{:}, a comma separated list. It allows you to pass in each element of the cell array into a function as if each element of the cell array was an argument of the function.

For example, if we did this:

[G1,G2,G3] = ndgrid(V{:});

Hmm. That creates three different arrays, that do contain all combinations of the elements of those vectors if you look carefully. But here we don't want to split the results into n different named arrays. We want a cell array as output. So now, try this:

C = cell(1,numel(V));
[C{:}] = ndgrid(V{:})
C =
  1×3 cell array
    {3×4×5 double}    {3×4×5 double}    {3×4×5 double}

Better. We have captured the output from ndgrid back into a cell array. But what we probably wanted was one flat array, with three columns, and here, 60 rows. We could convert each of those arrays into a column vector easily enough.

C = cellfun(@(X) reshape(X,[],1),C,'UniformOutput',false)
C =
  1×3 cell array
    {60×1 double}    {60×1 double}    {60×1 double}

And, now finally, just convert C into a flat array, using a tool like horzcat. (square brackets will suffice. That is...

C = horzcat(C{:})
C =
     1     4     8
     2     4     8
     3     4     8
     1     5     8
     2     5     8
     3     5     8
     1     6     8
     2     6     8
     3     6     8
     1     7     8
     2     7     8
     3     7     8
     1     4     9
     2     4     9
     3     4     9
     1     5     9
     
     ...
         
     2     7    12
     3     7    12

As you should see, nothing I did was dependent on the size of the arrays, the length of the vectors, the number of different vectors. That was all driven by the one initial cell array as I created it. Learn to use MATLAB, as it was designed to be used.

MATLAB: How can i find the position of a number in a cell consisting of arrays/matrices with different sizes

Here is one way:

C = {[1 6 7 9],  [1 6 7 9], [1 6 7 9];
     [8], [8], [2 6 7 9]};
 [ii,jj] = find(cell2mat(cellfun(@(x) any(ismember(x,2)),C,'UniformOutput',false)))

If you have more than one cell location with a 2 in it, ii will have all the row coordinates, and jj will have all the column coordinates.

There is a lot buried in that one line of code, including some assumptions about how you want this to generalize.

Best Answer

Related Solutions

MATLAB: How to pick up all combination of numbers from multiple vectors

MATLAB: How can i find the position of a number in a cell consisting of arrays/matrices with different sizes

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