Math Matlab

Question

I need to create a very large three-dimensional matrix (e.g. 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.

A rare function is not an option, since it is intended only for 2D matrices. So, is there an alternative to this for more dimensional matrices?

Answer 1

Matlab only supports sparse matrices (2D). For 3D tensors / arrays you will have to use a workaround. I can think of two:

• linear indexing
• cell arrays

Linear indexing

You can create a sparse vector as follows:

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

where the last entry ( 100 ) refers to the number of nonzero elements that should ultimately be tied to A If you know this amount in advance, this makes memory usage for A more efficient. If you don’t know this beforehand, just use some number next to it, it will work anyway, but A may consume more memory at the end than necessary.

Then you can refer to the elements as if it were a three-dimensional array:

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

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

Array Cells

Create each 2D page in a 3D tensor / array as an array of cells:

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

The same applies to this last entry in spalloc . Then combine in 3D like this:

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

then you can refer to individual elements as follows:

 A{i,j,k} 

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

Answer 2

Since your matrix is ​​sparse, try using ndsparse (N-dimensional sparse FEX arrays)