# Merge 3D matrices into one cell array without using a loop

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mashtine on 24 Jun 2015
Edited: Stephen on 25 Jun 2015
I have three 3D matrices (mxnxt) that I would like to merge into a single array of mxn with each array holding the corresponding data from the original matrices. Thus {1,1} of the new array will have a tx3 matrix containing the data.
For instance, A, B and C are 10x10x300 matrices. How do I make D to be a 10x10 array where {1,1} is a 300x3 matrix, without using a loop, but simple vector indexing.
Hope this makes sense!

Stephen on 24 Jun 2015
Edited: Stephen on 24 Jun 2015
Try this:
A = rand(10,10,300);
B = rand(10,10,300);
C = rand(10,10,300);
D = permute(cat(4,A,B,C),[3,4,1,2]); % join together, re-orient
V = ones(1,10);
D = squeeze(mat2cell(D,300,3,V,V)); % split into cell
And the output:
>> size(D)
ans =
10 10
>> size(D{1,1})
ans =
300 3
Stephen on 25 Jun 2015
There are basically three ways of dealing with Big Data:
1. Change the algorithm so that it is not necessary to hold all of the data in memory.
2. Use tools designed to operate on Big Data.
Do an [internet search engine] search for "MATLAB Big Data" and you will find lots of discussions on these topics. Well, mostly on the first two, but the third gets mentioned too!

Matt J on 25 Jun 2015
Edited: Matt J on 25 Jun 2015
There is no way to do it without for-loops. Note that mat2cell and friends are all mfiles that use loops internally.
The data organization you are pursuing is ill-advised. Instead of cell arrays, you should just cat() them into a 4D numeric array
D=cat(4,A,B,C);
Now to access a tx3 sub-array, you can do things like
squeeze(D(i,j,:,:))
It would have been much better and cleaner if you had instead made the original arrays tx1xmxn. That way, you could concatenate as
cat(2,A,B,C)
and your sub-arrays would be in more efficient memory-contiguous blocks and also more simply indexed as D(:,:,i,j). You can use permute() to achieve this, of course, but permute() is an expensive operation.