how to accelate the 'for loop' command' It's not end processing !!

clear all, close all, clc
%import data from excel sheet I have attached

x = x.'; %just x variable

n =5000;                   % number of rows
m =2726;                   % number of columns
index1 = 1:n;
index2 = n:n+m-1;

X = []; Xprime=[];

for ir = 1:size(x,1)
   
    % Hankel blocks ()
    c = x(ir,index1).'; r = x(ir,index2);
    H = hankel(c,r).';
    c = x(ir,index1+1).'; r = x(ir,index2+1);
    UH= hankel(c,r).';
    
     X=[X,H]; Xprime=[Xprime,UH];
end

%% DMD of x
dt = 1;
t=[0:1:7725];
r = 16 ;
[U, S, V] = svd(X, 'econ');
r = min(r, size(U,2));

U_r = U(:, 1:r); % truncate to rank-r
S_r = S(1:r, 1:r);
V_r = V(:, 1:r);

Atilde = U_r' * Xprime * V_r / S_r; % low-rank dynamics
[W_r, D] = eig(Atilde);
Phi = Xprime * V_r / S_r * W_r;     % DMD modes
%PhiP = U_r * V_r;                   % Projected DMD modes

lambda = diag(D); % discrete-time eigenvalues
omega = log(lambda)/dt; % continuous-time eigenvalues

% Compute DMD mode amplitudes b
x1 = X(:, 2);
b = Phi\x1;   % equal to b = pinv(Phi)*x1


% DMD reconstruction
time_dynamics = zeros(r, length(t));
for iter = 1:length(t)
    time_dynamics(:,iter) = (b.*exp(omega*t(iter)));
end
Xdmd = Phi * time_dynamics;

 


% DMD reconstruction 
rr = length(lambda) ;
T = size(X,2) ;
time_dmd = zeros(T-1,rr);
for iter = 1:T-1
    for p = 1:rr
        time_dmd(iter,p) = b(p)*(exp(omega(p)*t(iter)));
        Xdm(:,iter,p) = real(Phi(:,p)*(b(p).*exp(omega(p)*t(iter))));
    end
end
   
X_dmd = sum(Xdm,3) ;

[DGM]

What is the size of x?

[Ahmed Gharieb naga]

1x7726

Answer 1

[DGM]

Again, you're trying to construct large (~1.7 GB) arrays by growing them (in the reconstruction part). That will take an impractically long time (at least an hour or so). Like the other answer I gave, the loops are unnecessary anyway, so the whole issue can be avoided. Even on my dumpster computer with minimal ram, the loopless replacement section takes about 5 seconds.

As to whether the rest of the code works, I don't know. That's all over my head. I just tried to make sure my edits didn't change the results.

n = 5000;                   % number of rows
m = 2726;                   % number of columns

x = rand(1,n+m);

index1 = 1:n;
index2 = n:n+m-1;

% preallocate
szx = size(x,1);
X = zeros(m,n*szx);
Xprime = zeros(m,n*szx);

tic
for ir = 1:szx
    % Hankel blocks ()
    c = x(ir,index1).'; 
    r = x(ir,index2);
    H = hankel(c,r).';
    c = x(ir,index1+1).';
    r = x(ir,index2+1); 
    UH = hankel(c,r).';
    
    cols = n*(ir-1)+1:n*ir;
    X(:,cols) = H; 
    Xprime(:,cols) = UH;
end
toc

% preallocating would have been more important if x had more than one row
% if x never has more than one row, then the entire loop is unnecessary

%% DMD of x
dt = 1;
t = 0:1:7725;
r = 16 ;
[U, S, V] = svd(X, 'econ');
%%
r = min(r, size(U,2));
U_r = U(:, 1:r); % truncate to rank-r
S_r = S(1:r, 1:r);
V_r = V(:, 1:r);
Atilde = U_r' * Xprime * V_r / S_r; % low-rank dynamics
[W_r, D] = eig(Atilde);
Phi = Xprime * V_r / S_r * W_r;     % DMD modes
%PhiP = U_r * V_r;                   % Projected DMD modes

lambda = diag(D); % discrete-time eigenvalues
omega = log(lambda)/dt; % continuous-time eigenvalues

% Compute DMD mode amplitudes b
x1 = X(:, 2);
b = Phi\x1;   % equal to b = pinv(Phi)*x1

% DMD reconstruction 
time_dmd = b.'.*exp(omega.'.*reshape(t(1:size(X,2)-1),[],1));
Xdm = permute(Phi,[3 2 1]).*time_dmd;
Xdm = real(permute(Xdm,[3 1 2]));
X_dmd = sum(Xdm,3);