How can I form a matrix of all possible values of three variables?

I have three variables (bgt, Trigger, alpha), and each one of it could take any value from the set of three values {0.1, 0.5, 0.9} . How can I form a matrix of size 27 by 3 that contains all the possible combinations? And then for the following Script, I want MATLAB to run each row of this newly formed matrix( 27 different runs in total) and save the results (Check % Save The Results Section ). Eventually, I want to pick any three rows easily and plot Mavg against its length (Three curves on the same plot. Nine plots in total)

Thanks!

Start_time = tic();
N = 5000;
p = 0.2;

% The three Variables
bgt = 0.9* N;
Trigger = 0.9 * N;
alpha = 0.9;

init_attack = 8; % no. of nodes attacked initially 
mde = 0; %mode of attack
disturb = 350; % disturbance added to the loads
tol = 0.2; % tolerance parameter alpha C = L + a
iter = 1;
tmax = 120;

M_iter = zeros(iter, tmax);
for jj = 1:iter

    N = numnodes(G);% number of nodes(components)


    [G_dmg,attack,G_orig, needRemoveNode,LoadneedDist,M, tmax, lastIndex] = Load_initial(G,init_attack,mde,disturb,tol,Load, tmax); % initial attack (disruption)
    
    
    
    alreadyCalled = false; % Say that decision and implement have not been called yet.
    for tt = 3: tmax
        
        
        if any(needRemoveNode)|| ~any(needRemoveNode)
            
            [G_dmg,LoadneedDist,needRemoveNode,M, tmax, lastIndex] = Load_Stages(G_dmg,needRemoveNode,LoadneedDist,M, tmax, lastIndex); % a cascade of failure will be triggered

            
        end
        if  (M(tt) >= (Trigger)) && ~alreadyCalled % triggering level
            % Calling for the very first time if we get here.
            [G_dmg, Nodes_p, tmax] =  Loads_decision(G_dmg, tmax);
            [G_dmg, M, tmax, lastIndex] = Loads_implement(G_dmg, Nodes_p, M, tmax, lastIndex, p, bgt, alpha);
            alreadyCalled = true; % Set flag to indicate we've called it.
        elseif alreadyCalled
            % Once they've been called already, call them regardless of the "if" test.
            [G_dmg, Nodes_p, tmax] =  Loads_decision(G_dmg, tmax); %decide which nodes to recover first
            [G_dmg, M, tmax, lastIndex] = Loads_implement(G_dmg, Nodes_p, M, tmax, lastIndex, p, bgt, alpha); % implement recovery
        end
    end
    
    M_iter(jj,:)=M;
    S = std(M_iter);
    SE = S/sqrt(size(M_iter,1));
end

% Save The Results
% if Trigger == 0.1 * N
    save('M_iter.mat','M_iter');
    Mavg = mean(M_iter,1);
    save('Mavg.mat','Mavg');
    save('SE.mat','SE')
% elseif Trigger == 0.5 * N
%     save('M_iter2.mat','M_iter');
%     Mavg = mean(M_iter,1);
%     save('Mavg2.mat','Mavg');
%     save('SE2.mat','SE')
% elseif Trigger == 0.9 * N
%     save('M_iter3.mat','M_iter');
%     Mavg = mean(M_iter,1);
%     save('Mavg3.mat','Mavg');
%     save('SE3.mat','SE')
% end

% Plotting
figure(1)
% errorbar(1:length(Mavg),Mavg,SE);hold on
plot(1:length(Mavg),Mavg); hold on
legend({'Triggering Level = 10%', 'Triggering Level = 50%', 'Triggering Level = 90%'}, 'Location', 'NorthWest');
xlabel('Time')
ylabel('No. of Inactive Nodes')
toc(Start_time)

Answer 1

[DGM]

This is what I did off the top of my head

v = [0.1 0.5 0.9];
k = 3;
combs = unique(nchoosek(repmat(v,[1 k]),k),'rows')

combs = 27×3

0.1000 0.1000 0.1000 0.1000 0.1000 0.5000 0.1000 0.1000 0.9000 0.1000 0.5000 0.1000 0.1000 0.5000 0.5000 0.1000 0.5000 0.9000 0.1000 0.9000 0.1000 0.1000 0.9000 0.5000 0.1000 0.9000 0.9000 0.5000 0.1000 0.1000

This can also be done using ndgrid and some reshaping. It's a bit faster, but the readability isn't remotely comparable. For the same reason, it's not something I find easy to remember either.

v = [0.1 0.5 0.9];
k = 3;

c = cell(1,k);
vc = repmat({v},[1 k]);
[c{:}] = ndgrid(vc{:});
n = length(c);
combs = reshape(cat(n+1,c{:}),[],n)

combs = 27×3

0.1000 0.1000 0.1000 0.5000 0.1000 0.1000 0.9000 0.1000 0.1000 0.1000 0.5000 0.1000 0.5000 0.5000 0.1000 0.9000 0.5000 0.1000 0.1000 0.9000 0.1000 0.5000 0.9000 0.1000 0.9000 0.9000 0.1000 0.1000 0.1000 0.5000

[Waseem AL Aqqad]

Thank you so much.

How can I let my script goes through each row of this matrix? So, I want the variables bgt, Trigger, and alpha to take the three entries of the first row and then run whole script and save the results, and then the same variables take the entries of the second row and run the whole script and save the results, and continue in the same pattern for the 27 rows.

Thanks again

[DGM]

Something like this might be a start

combs = % however you decide to generate the combination array

for k = 1:size(combs,1)
    bgt = combs(k,1);
    Trigger = combs(k,2);
    alpha = combs(k,3);
    % do the loop to calculate Miter
end

How you handle output collection is up to you. You could either collect the outputs in an N-D array or you can dump them to mat-files individually. Since I don't know what size they are intended to be, I'm going to leave that decision up to you.

Say you want Miter to be N-D. You might do the assignment like so:

M_iter(jj,:,k) = M;

or maybe you want to write each 2-D output to a unique file instead...

save(sprintf('M_iter%03d.mat',k),'M_iter');

If you want to plot the data for all 27 parameter combinations, you're probably going to be better off deciding on a way to collect the outputs into an ND array. Making a readable plot might be another challenge.

[Waseem AL Aqqad]

Thank you so much. It's greatly appreciated.

To preallocate M_iter, I must do this (outside the two for loops) :

M_iter = zeros(iter, tmax, size(combs,1));

Instead of :

M_iter = zeros(iter, tmax);

Correct?