MATLAB: How to speed up making large matrices, and reduce memory usage

making matrixmatrixmemoryspeed uptruncating

How can I speed up making a large matrix, and also cut down memory usage?
I need to make a matrix which turns out to be in the order of 2,000 by 30,000 ish.
I can run it, but it'd be great to be able to speed it up, and also reduce memory use.
At the moment my code is as below, there length of C is 1800.
Creating Aineq is my final aim!
Aineq=[ones(length(C))]; %size of matrix to represent size one of the decision variables Q or G
Aineq1=[tril(Aineq),-tril(Aineq),tril(Aineq),-tril(Aineq),Aineq*0,Aineq*0,Aineq*0,zeros((length(C)),length(F))]; %1 matrix for first DV, then the next DV
Aineq2=[-tril(Aineq),tril(Aineq),-tril(Aineq),tril(Aineq),Aineq*0,Aineq*0,Aineq*0,zeros((length(C)),length(F))]; %2
Aineq3=[eye(length(C)),eye(length(C)),Aineq*0,Aineq*0,Aineq*0,Aineq*0,Aineq*0,zeros((length(C)),length(F))]; %3
Aineq4=[tril(Aineq,-1)*-1,tril(Aineq),tril(Aineq,-1)*-1,tril(Aineq,-1),Aineq*0,Aineq*0,Aineq*0,zeros((length(C)),length(F))]; %4
Aineq5=[Aineq*0,Aineq*0,Aineq*0,eye(length(C)),Aineq*0,Aineq*0,Aineq*0,zeros((length(C)),length(F))]; %5
Aineq6=[Aineq*0,Aineq*0,tril(Aineq,-1)*-1,tril(Aineq,-1),tril(Aineq,-1),tril(Aineq,-1)*-1,tril(Aineq,-1)*-1,zeros((length(C)),length(F))]; %6
Aineq7=[Aineq*0,Aineq*0,tril(Aineq)*-1,tril(Aineq),tril(Aineq),tril(Aineq)*-1,tril(Aineq)*-1,zeros((length(C)),length(F))]; %7
Aineq8=[Aineq*0,Aineq*0,tril(Aineq,-1),tril(Aineq,-1)*-1,tril(Aineq,-1)*-1,tril(Aineq,-1),tril(Aineq,-1),zeros((length(C)),length(F))]; %8
Aineq9=[Aineq*0,Aineq*0,tril(Aineq),tril(Aineq)*-1,tril(Aineq)*-1,tril(Aineq),tril(Aineq),zeros((length(C)),length(F))];%9
Aineq10=[Aineq*0,Aineq*0,eye(length(C)),Aineq*0,Aineq*0,Aineq*0,Aineq*0,zeros((length(C)),length(F))]; %10
Aineq11=[Aineq*0,Aineq*0,Aineq*0,eye(length(C)),Aineq*0,Aineq*0,Aineq*0,zeros((length(C)),length(F))]; %11
Aineq12=[Aineq*0,Aineq*0,Aineq*0,Aineq*0,Aineq*0,eye(length(C)),Aineq*0,zeros((length(C)),length(F))]; %12
Aineq13=[Aineq*0,Aineq*0,Aineq*0,Aineq*0,eye(length(C)),Aineq*0,Aineq*0,zeros((length(C)),length(F))]; %13
Aineq14=[Aineq*0,Aineq*0,Aineq*0,Aineq*0,Aineq*0,Aineq*0,eye(length(C)),zeros((length(C)),length(F))]; %14  
Aineq15=[Aineq*0,Aineq*0,Aineq*0,Aineq*0,Aineq*0,Aineq*0,eye(length(C))*-1,zeros((length(C)),length(F))]; %15
clear Aineq
% Aineq=[Aineq1;Aineq2;Aineq3;Aineq4;Aineq5;Aineq6;Aineq7;Aineq8;Aineq9;Aineq10;Aineq11;Aineq12;Aineq13;Aineq14;Aineq15];
Aineq=[Aineq1]; clear Aineq1
Aineq=[Aineq;Aineq2]; clear Aineq2
Aineq=[Aineq;Aineq3]; clear Aineq3
Aineq=[Aineq;Aineq4]; clear Aineq4
Aineq=[Aineq;Aineq5]; clear Aineq5
Aineq=[Aineq;Aineq6]; clear Aineq6
Aineq=[Aineq;Aineq7]; clear Aineq7
Aineq=[Aineq;Aineq8]; clear Aineq8 
Aineq=[Aineq;Aineq9]; clear Aineq9
Aineq=[Aineq;Aineq10]; clear Aineq10
Aineq=[Aineq;Aineq11]; clear Aineq11
Aineq=[Aineq;Aineq12]; clear Aineq12
Aineq=[Aineq;Aineq13]; clear Aineq13
Aineq=[Aineq;Aineq14]; clear Aineq14
Aineq=[Aineq;Aineq15]; clear Aineq15

Best Answer

This looks like a very sparse matrix, right? Then I would first figure out how to assign the blocks of Aineq from its components, something like this:
blksz = [3,13]; % or whatever they become
nBlks = 15;
Aineq = zeros(blksz*nBlks);
for i1 = 1:nBlks
  for i2 = 1:nBlks
    % Some logics here for selecting which block to fill Aineq with
    Aineq((1:blksz(1))+blksz*(i1-1),(1:blksz(2))+blksz(2)*(i2-1)) = CurrBlk;
  end
end
Once you've figured that one out, you should look at what components of every block is non-zero and start to build sparse blocks, and then concatenate them instead, that would be much more memmory efficient. Then the last step (or preferably the firts, but I find it easier to move to sparse representations of comlex matrices step-by-step), is to calculate vectors with the row and column-indices and the corresponding matrix element and then simply concatenate those into three arrays i_rows, i_cols, val and then call sparse:
Asparse = sparse(i_rows,i_cols,vals,nRows,nCols);
HTH
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