MATLAB: Parallel Matrix row operation

Question

Hi, I have a function which project a matrix to the matrix space with row sum equal to 1 and constrained by a sparsity structure. Here is the code

function [out]  =  Proj_DoubleStochasticM_reloc(Y)
global sparsity 
Y = full(Y);
ii = [];
jj = [];
ss = [];
for i=1:length(sparsity)  
    ii = [ii;ones(size(sparsity{i}))*i];
    jj = [jj;sparsity{i}];
    ss = [ss Y(i,sparsity{i}) - (sum(Y(i,sparsity{i}))-1)/length(sparsity{i})];
end
[n,m] = size(Y);
out = sparse(ii, jj', ss', n,m);

So basically, the input is sparse. After I transform it to full, then a do a for loop on each row. The operation in each row is

Y(i,sparsity{i}) - (sum(Y(i,sparsity{i}))-1)/length(sparsity{i})

e.g

input = [1 2 3 4 5]

sparisty = [1 2]

then output is [1-(1+2-1)/2, 2-1-(1+2-1)/2, 0, 0, 0]

I was wondering whether there are any parallel approaches to do it, or direct methods on sparse matrix. Currently the most expensive line is last one, and full(), namely, transform sparsity; second is the for loop.

Thank you very much:)

Answer 1

function out =  Proj_DoubleStochasticM_reloc(Y,sparsity)
    [m,n]=size(Y);
    
    [I,J]=deal(sparsity);
    for k=1:length(sparsity)
        I{k}(:)=k;
    end
    
    I=cell2mat(I); J=cell2mat(J);
    
    bw=sparse(I,J,true,m,n);
    
    Y=Y.*bw;
    out=Y-bw.*(sum(Y,2)-1)./sum(bw,2); %EDITED
end