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# preallocating sparse 4d matrix

Asked by Michael on 7 Mar 2013

Hi

I've got some code that preallocates some matrix L = zeros(50,50,50,50); and then iterates along the first two dimensions (for i = 1:50, for j = 1:50...) to populate L. At the end of my code I reshape L into a 2500x2500 matrix, and this is it in usable form.

I want to increase the dimensions from 50 to 100, but it's hitting a memory bottleneck when preallocating, and I can't use spalloc to generate a 4d matrix. Rather than re-writing all my loops, can anyone think of another way to get around this? The end result (a sparse 10000x10000 matrix) should be easy to create, but I can't make it sparse until it's 2d, which is after my calculations.

Thanks for any help Mike

Walter Roberson on 7 Mar 2013
```L = zeros(50,50,50,50, 'uint8');
```

Though if you want negatives, you will want 'int8' instead of 'uint8' :)

Michael on 7 Mar 2013

this method is working, although it doesn't seem I can generate a sparse matrix with int8 inputs, and this is now creating memory problems further down the line where I need to calculate L'*L.

Walter Roberson on 7 Mar 2013

Ah yes, sparse is restricted to double or uint8 (or logical, I think).

You could encode the negatives into uint8, e.g., 254 for -2 (which would be the two's complement to make it easier to track.) Doing the translation later might prove to be time consuming. It might be faster to record indices into a lookup table, and do something like

```usedidx = find(L);
[idx1, idx2] = idx2subs([N*N, N*N], usedidx);
sparse(idx1, idx2, LookupTable(L(usedidx)), ...)  %recheck arg order!
```

Notice I did an implicit reshape there by way of the first argument to idx2subs()

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Answer by James Tursa on 7 Mar 2013

For multi-dimensional sparse arrays, see this FEX submission by Matt J:

http://www.mathworks.com/matlabcentral/fileexchange/29832-n-dimensional-sparse-arrays

MATLAB only supports double and logical sparse arrays. For int8 sparse arrays, you will have to wait until I release my int8sp class in a month or two (basic code is mostly complete, but not fully tested yet).

Answer by Teja Muppirala on 7 Mar 2013

You can't make a sparse array with more than 2 dimensions, but you could make a 100x100 cell array that is filled with 100x100 sparse matrices. And then you can work on each cell separately, and then go back and shape it into a 10000x10000 afterwards.

```L = repmat({sparse(100,100)} ,100,100);
```
```for i = 1:100
for j = 1:100
L{i}{j} = ...
end
end
```