Memory efficient vectorization of a for loop

Hello all,

I have the following piece of code which generate a nxnxm logical matrix A at the end. A matrix contains a lot of zeros. Each nxn matrix contains n 1s and remaining 0s.

clc;
clear; close all;

n = 3;
M = 2*n;
No_of_switches_in_each_column = [2,3,3,2,2];

tic
Ns = sum(No_of_switches_in_each_column);
All_possible_switching_states = 2^Ns;

I = eye(6);
Qi = [1,3,5,2,4,6];
Map_s2c =  I(Qi',:);
Map_c2s =  I(:,Qi);

TT_4allpossible_switch_states = dec2bin(0:All_possible_switching_states-1); % Truth table for Ns switches
Sw = cell(1,Ns);  % Cell to store state (bar or cross) matricess of Ns No of switches.
A = false([6 6 All_possible_switching_states]);
%//********************************************************************//
for i = 1:All_possible_switching_states
    comb_i = TT_4allpossible_switch_states(i,:);
    for n = 1:Ns
        if(strcmp(comb_i(n),'0'))
            Sw{n} = [1 0; 0 1];
        else 
            Sw{n} = [0 1; 1 0];
        end
    end
    S1 = Sw{1}; S2 = Sw{2}; S3 = Sw{3};
    S4 = Sw{4}; S5 = Sw{5}; S6 = Sw{6};
    S7 = Sw{7}; S8 = Sw{8}; S9 = Sw{9};
    S10 = Sw{10}; S11 = Sw{11}; 
    S12 = Sw{12}; 
     
    C1 = logical([1   zeros(1,5);...
         zeros(2,1) S1 zeros(2,3);...
         zeros(2,3)   S2 zeros(2,1);...
         zeros(1,5) 1]);
  
   C2 = logical([S3   zeros(2,4);...
         zeros(2) S4 zeros(2);...
         zeros(2,4) S5]);
     
   C3 = logical([S6   zeros(2,4);...
         zeros(2) S7 zeros(2);...
         zeros(2,4) S8]);
     
   C4 = logical([S9   zeros(2,4);...
          zeros(1,2) 1 zeros(1,3);...
          zeros(1,3) 1 zeros(1,2);...
         zeros(2,4) S10]);     
   
   C5 = logical([1   zeros(1,5);...
         zeros(2,1) S11 zeros(2,3);...
         zeros(2,3)   S12 zeros(2,1);...
         zeros(1,5) 1]);

    A(:,:,i) = logical(C1*C2*Map_s2c*C3*Map_c2s*C4*C5);
end

I want an efficient implementation of the above code in terms of memory (it fails for larger arrays - array exceeds maximum array size preference) and computations.

It would be desirable to not use for loop and cell arrays.

Thanks

[darova]

What about sparse matrix?

[Haider Ali]

@darova, yes I have looked at sparse matrix. But only 2D sparse matrices are supported.

I was thinking of first removing the for loop and then go for sparse matrix.

Answer 1

[darova]

Store values manually like sparse

    % preallocation?
irow = [];
icol = [];
iplane = [];
for i = 1:...
    % do stuff
    val = logical(C1*C2*Map_s2c*C3*Map_c2s*C4*C5);
    if sum(val(:))
        [ii,jj] = find(val);
        irow = [irow; ii];
        icol = [icol; jj];
        iplane = [iplane; i+ii*0];
    end
end