How to split 4D matrix in equal parts?

Hi everyone!

I have here a doubt that consists in how can I split a 4D matrix (112x112x25x100) in equal parts and put it in 2D? This problem appeared because I will use the corrcoef function and it onluy accepts 2D input, so I need to transform this 4D matrix into 2D. And I want to split to avoid problems with the memory because this matrix is kinda big,

Hope you can help me!!

Thanks in advance,

Hugo

Answer 1

[Ameer Hamza]

You can access a 2D component of a 4D matrix by indexing like this

x = rand(112, 112, 25, 100);
y = x(:,:,1,1); % 3rd dimension can vary to 25 and fourth to 100

Alternatively you can create a 25x100 cell array

x = rand(112, 112, 25, 100);

y = mat2cell(x, size(x,1), size(x,2), ones(size(x,3),1), ones(size(x,4),1));
y = squeeze(y);

[Walter Roberson]

The squeeze() is probably not going to be useful there.

Note that in the mat2cell version, y is going to be a cell array, and you would have to loop over the elements, either with a for loop or by using cellfun()

[Iugo]

Thank you both!

But I really wanted to compress all the 4D matrix elements into a 2D matrix without changing the elements order... can I do it with reshape?

Thank you for your help!

Hugo

[Walter Roberson]

If the in-memory order is not going to change then reshape can sometimes work. What size of output do you need? I have a suspicion you are going to need permute() as well.

[Iugo]

I wanted to use a for loop to go through all the elements of my matrix and calculate the correlations by using the corrcoef(A), being A my 112x112x25x100, and this corrcoef only works with 2D input, so the output would've be 2D. But since this 4D matrix is kinda big, I needed to split this matrix also, to avoid so memory issues...

Thanks for your time Walter!

[Walter Roberson]

You cannot simultaneously split the matrix into smaller pieces but not change the order of the elements in memory. (Well, actually there is a fex contribution that might permit that.)

If memory size was not a problem then what dimensions would the 2d array have?

I am suspicious of what you want to correlate against what.

[Iugo]

I dont have a specific dimension for the 2D array...

I'm working with fMRI data, that is that 112x112x25x100 matrix, with the first 3 dimensions being x,y,z and the last one the time. I want to correlate the full time series of this matrix by using the corrcoef with just one input argument.

[Ameer Hamza]

But simply converting a 4D matrix to 2D without understanding of the problem does not seem useful. You can convert it into a 2D matrix but running.

x = rand(112, 112, 25, 100);
M = reshape(x, 112, []);

But I am not sure if corrcoef will give any meaningful result.

[Walter Roberson]

For correlating the time series use

M = reshape(permute(x, [4 1 2 3], size(x,4), []);

Now each row is one observation (time) and each column is a variable (pixel location).

The result would, in theory, be a square matrix in which each pixel is correlated against each other pixel.

However... you have 313600 pixels and the correlation matrix would require about 3/4 of a petabyte.

You could break the matrix up into smaller pieces, but even if you manage to assemble it in pieces, you still have the problem that as long as correlation of every pixel to every other pixel is your goal, then your final matrix is going to have to be that size. Your only chance for success is if that is not really your final goal and your actual goal does not need as much information to represent.

[Iugo]

Thank you so much Walter! I really appreciate your help!

Cheers,

Hugo