"Index in position 2 exceeds array bounds. Index must not exceed 401" Error. Can someone explain to me why here an error appears?

x_exact = randn(size(A,1),L+1); u_exact = randn(size(B,2),L+1);

for k = 1:L

x_exact(:,k+1) = A*x_exact(:,k) + B*u_exact(:,k);

y_exact(:,k) = C*x_exact(:,k);

end

[Dyuman Joshi]

In which line does the error occur?

What are the sizes of variables x_exact, u_exact, A, B and C and what is the value of L?

[Edfred]

In the line: x_exact(:,k+1) = A*x_exact(:,k) + B*u_exact(:,k);

Answer 1

[albara]

The error "Index in position 2 exceeds array bounds. Index must not exceed 401" occurs because the size of the x_exact array is not sufficient to store all the values being assigned to it in the loop. Specifically, the loop runs L times, with k taking values from 1 to L. In the second line of the loop, the code tries to assign values to x_exact(:,k+1), which means that on the last iteration of the loop, k takes the value L and x_exact(:,L+1) is accessed. However, x_exact has only L+1 columns, so the index L+1 exceeds the array bounds and causes an error.

To fix this error, you need to increase the size of the x_exact array to have at least L+1 columns. One way to do this is to initialize x_exact with zeros instead of randn and specify the size to be size(A,1),L+1 before the loop:

scss

x_exact = zeros(size(A,1),L+1);

u_exact = randn(size(B,2),L+1);

for k = 1:L

x_exact(:,k+1) = A*x_exact(:,k) + B*u_exact(:,k);

y_exact(:,k) = C*x_exact(:,k);

end

This will ensure that x_exact has the correct size to store all the values being assigned to it in the loop, and the error should be resolved.

Important: There may be some mistakes in this answer Experts can tell if there are any mistakes

[Edfred]

Thank you very much for your detailed answer :)

Does that mean that if I intialize x_exact with randn and the same dimensions as mentioned it does not work and that I can run it just with zeros as initialization?

[albara]

You're welcome!

If you initialize x_exact with randn and the same dimensions as mentioned, the code will run without errors as long as L is not too large, because the size of x_exact will be sufficient to store all the values being assigned to it in the loop. However, the initial values in x_exact will be random and may not satisfy any initial conditions or constraints that the system may have. Therefore, it is often better to initialize x_exact with a known or desired initial state, such as all zeros or some other value that is appropriate for the specific system being simulated.

In this case, initializing x_exact with zeros is a good choice because it ensures that the initial state is known and satisfies any initial conditions or constraints. Additionally, it has the same size as u_exact and makes it easier to combine x_exact and u_exact into a single matrix for later analysis, if desired.

Answer 2

[VBBV]

I guess, L may be a vector or array which keeps changing in your program. Try the below

x_exact = randn(size(A,1),length(L)+1);          
u_exact = randn(size(B,2),length(L)+1);
% 
for k = 1:length(L)
          %-->> 
    x_exact(:,k+1) = A*x_exact(:,k) + B*u_exact(:,k);
    y_exact(:,k) = C*x_exact(:,k);
end