Writing a matfile in a parloop

I have a very simple code that works pretty well when the size of the involved objects is manageable by the memory.

%%% Variables
% Z -> matrix of dimensions (r,T)
% V -> matrix of dimensions (r,r,T)
% nanY -> matrix of dimensions (n,T)
% y -> matrix of dimensions (n,T)

nanY = isnan(y);
y(nanY) = 0;

denom = sparse(zeros(n*r,n*r));
nom = sparse(zeros(n,r));
parfor t=1:T
    nanYt = sparse(diag(~nanY(:,t)))p;
    denom = denom + kron(Z(:,t+1)*Z(:,t+1)'+Vsmooth(:,:,t+1),nanYt);
    nom = nom + y(:,t)*Z(:,t+1)';
    
end

 vec = denom\nom(:);
 

In practical application, that bunch of code has to run with the parameter n taking values around 80k leading quickly to an unfeasible memory load. The solution I figured out relies on matfiles, at the expenses of paralellizionation and general performance. This is the version with which I am able to handle it for large n.

nanY = isnan(y);
y(nanY) = 0;

denom = zeros(n*r,n*r,T);
nom = zeros(n,r,T);

save var_cyc.mat denom nom y nanY -v7.3;
v = matfile('var_cyc.mat', 'Writable', true);

for t=1:T
    v.nanYt = sparse(diag(~v.nanY(:,t)))p;
    v.denom(:,:,T) = kron(Z(:,t+1)*Z(:,t+1)' + V(:,:,t+1),v.nanYt);
    v.nom(:,:,T) = v.y(:,t)*Z(:,t+1)';
end

 vec = sum(v.denom,3)\sum(v.nom(:),3);

Unfortunately this script cannot be paralellizable because conflicts generate when workers try to write on the matfile. I'm wondering if there is a way to recover the initial parallelization structure using matlab file to handle huge file without incurring in 'out of memory errors'.

Thanks.

Answer 1

[Jason Ross]

Have you looked into using tall arrays?

[Angelo Cuzzola]

Yes, but nom and denom are not exactly tall. They are 60kx60k matrices