Automation of for loops and array dimesion

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Sandeep Parameshwara
Sandeep Parameshwara el 22 de En. de 2020
Comentada: Guillaume el 24 de En. de 2020
Hello members, I need some help.
rho_grid=[-1,0,1];
Nrho=length(rho_grid);
for i=Nrho:-1:1
rho1=rho_grid(i);
for j=Nrho:-1:1
rho2=rho_grid(j);
[U,S,V]= svd(pro(rho1,rho2));
[Uvals(:,:,j,i),Svals(:,:,j,i),Vvals(:,:,j,i)]= svd(pro(rho1,rho2)); % I need this later for plotting
Ti= inv(sqrt(S))*U'*Rq(rho1,rho2);
T = Rp(rho1,rho2)*V*inv(sqrt(S));
systrans(:,:,j,i)= ss2ss(sys.Data(:,:,j,i),Ti);
end
end
1) I have 2 'for' loops now to determine value of parameters 'rho1' and 'rho2'. In my case, this parameters will increase to very large number. If I have rho1,....,rho10 , I dont want to create all extra for loops manually. Is there any way that I can automate it? Please note that rho_grid = [-1,0,1] is same for all parameters. Similarly,
2) The dimension of 'systrans' will also change. If I add 1 extra for loop to this I have to change from my current systrans(:,:,j,i) to
systrans(:,:,k,j,i)
which I want to avoid and automate.
3) Last question, I want plot values stored in 'Svals' over parameter range. When I had only one parameter 'rho1' I did this:
plot(rho_grid,reshape(Svals(i,i,:),[1,length(rho_grid)]));
which gave me 2D plot. for 2 parameters case, I want to get a 3D plot and see the variation of entries of Svals over rho1 and rho2. How can I do that? I have attached Uvals,Svals and Vvals in .mat file
  5 comentarios
Guillaume
Guillaume el 23 de En. de 2020
I wouldn't use a recursion, it can all be done with a single loop. One last question, what's the size of the matrix returned by pro (or what's the size of U, S, V)? I'm assuming that it's independent of the number of rhos but if it does depend what's the formula.
It's required in order to preallocate, U_vals, S_sals, V_vals and systrans
Sandeep Parameshwara
Sandeep Parameshwara el 23 de En. de 2020
Hi Mr. Guillaume, you are right. pro is just a double matrix of size 8*8 in above case. Even though I increase number of parameters, it will be 2D matrix. I wrote Uvals(:,:,j,i) etc to store the values for each value of rho as you can see from my code.

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Guillaume
Guillaume el 24 de En. de 2020
Assumption: the matrices returned by pro, Rq, Rp, and ss2ss are all the same size (size defined by pro_outsize below
I've not changed your equations. As mentioned before inv is not recommended.
Untested code. I may have made a mistake but the princiiple should be correct:
num_rhos = 10; %number of rho variables
rho_grid = [-1 0 1];
pro_outsize = [8 8]; %size of matrices returned by pro, Rq, Rp and ss2ss
%create all permutation of picking num_rhos elements out of rho_grid. There's numel(rho_grid) ^ num_rhos permutations
rhoperms = cell(1, num_rhos);
[rhoperms{:}] = ndgrid(rho_grid);
rhoperms = reshape(cat(num_rhos + 1, rhoperms{:}), [], num_rhos); %each row of rows is a unique permutation. Height of the matrix is numel(rho_grid) ^ num_rhos
%preallocation of results as 3D matrices. Can be reshape to ND matrices at the end
U_vals = zeros([pro_outsize, size(rhoperms, 1)]);
S_vals = U_vals;
V_vals = U_vals;
systrans = U_vals;
%reshape sys.Data into 3D matrix for easier indexing later on
sysdata = reshape(sys.Data, size(sys.Data, 1), size(sys.Data, 2), []);
%loop over each unique combination
for ridx = 1:size(rhoperms, 1)
rhos = num2cell(rhoperms(ridx, :));
[U_vals(:, :, ridx), S_vals(:, :, ridx), V_vals(:, :, ridx)] = svd(pro(rhos{:}));
Ti = inv(sqrt(S_vals(:, :, ridx))) * U_vals(:, :, ridx)' * Rq(rhos{:}); %probably, shouldn't use inv
T = Rp(rhos{:}) * V_vals(:, :, ridx) * inv(sqrt(S_vals(:, :, ridx)));
systrans(:, :, ridx) = ss2ss(sysdata(:, :, ridx), Ti);
end
%Optionally: reshape into N-D matrices, where N = num_rhos + 2
newshape = [pro_outsize, repelem(numel(rho_grid), num_rhos)];
U_vals = reshape(U_vals, newshape);
S_vals = reshape(S_vals, newshape);
V_vals = reshape(V_vals, newshape);
systrans = reshape(systrans, newshape);
The code use the expansion of cell arrays into comma-separated lists to build the inputs of pro, Rq, and Rp.
  3 comentarios
Sandeep Parameshwara
Sandeep Parameshwara el 24 de En. de 2020
I reshaped it using reshape(systrans,[3 3]), it works. How should I make sure that the reshaped sequence is as intended? Sorry for repeated questions.
Guillaume
Guillaume el 24 de En. de 2020
I'm not sure I completely follow, since the rhos are the same in any dimension, wouldn't (:, :, 1, 3) and (:, :, 3, 1) be the same?
You can reorder the dimensions with permute, so after the reshape, you can do:
systrans = permute(systrans, [1 2, num_rhos+2:-1:2]);
I think! It's always difficult to think in >3D. But again, I'm not sure it makes a difference.

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