Matlab 3d-matrix

Question

I have to create a very big 3D matrix (such as: 500000x60x60). Is there any way to do this in matlab?

When I try

omega = zeros(500000,60,60,'single');

I get an out-of-memory error.

The sparse function is no option since it is only meant for 2D matrices. So is there any alternative to that for higher dimensional matrices?

Answer 1

Matlab only has support for sparse matrices (2D). For 3D tensors/arrays, you'll have to use a workaround. I can think of two:

1. linear indexing
2. cell arrays

Linear indexing

You can create a sparse vector like so:

A = spalloc(500000*60*60, 1, 100); 

where the last entry (100) refers to the amount of non-zeros eventually to be assigned to A. If you know this amount beforehand it makes memory usage for A more efficient. If you don't know it beforehand just use some number close to it, it'll still work, but A can consume more memory in the end than it strictly needs to.

Then you can refer to elements as if it is a 3D array like so:

A(sub2ind(size(A), i,j,k)) 

where i, j and k are the indices to the 1st, 2nd and 3rd dimension, respectively.

Cell arrays

Create each 2D page in the 3D tensor/array as a cell array:

a = cellfun(@(x) spalloc(500000, 60, 100), cell(60,1), 'UniformOutput', false);

The same story goes for this last entry into spalloc. Then concatenate in 3D like so:

A = cat(3, a{:});

then you can refer to individual elements like so:

A{i,j,k}

where i, j and k are the indices to the 1st, 2nd and 3rd dimension, respectively.

Answer 2

Since your matrix is sparse, try to use ndsparse (N-dimensional sparse arrays FEX)