How to obtain the original matrix after performing symrcm or symamd in MATLAB?

I use the Cuthill-McKee algorithm. After finding the desired vector, I need to restore the original matrix. I found the answer here https://www.mathworks.com/matlabcentral/answers/94946-how-do-i-obtain-the-original-mapping-after-performing-symrcm-in-matlab-7-1-r14sp3 but for my images I get "Index exceeds matrix dimensions". Is there any other way to do this? (Preferably without the availability of the original matrix)

symV %original matrix

k1 = symrcm(symV)

matrix_after_cm = symV(k1,k1);

spy(first_after_cm)

Answer 1

[Fabio Freschi]

Can you share the symV original matrix?

[Kadyr Sherfedinov]

fullFileName = '/Users/user/Desktop/binary2.png';
  rgbImage = imread(fullFileName);
  binaryImage = ~im2bw(rgbImage, 0.5);%converting to binary image
  v = triu(binaryImage);%getting upper triangular matrix
  n = tril(binaryImage);%getting lower triangular matrix
 
  symV = (v+v') - eye(size(v,1)).*diag(v)%diagonal reflection of the upper triangular matrix (obtaining a symmetric matrix)
  symN = (n+n') - eye(size(n,1)).*diag(n)%diagonal reflection of the lower triangular matrix (obtaining a symmetric matrix)
  
  k1 = symrcm(symV)
  first_after_cm = symV(k1,k1);
  spy(first_after_cm)

[Fabio Freschi]

I run your code, then I run

[~,q] = sort(k1);
AfromB = first_after_cm(q,q);  % Elapsed time is 0.002503 seconds.
norm(AfromB-symV)  % ans = 0

without any problem. Note that your matrix is really sparse, so you can benefit handling it as sparse matrix. Can you try this

symV = sparse(symV);

before symrcm? It is not as smart as directly assembling the matrix as sparse, but it should work.

Answer 2

[Fabio Freschi]

Try this:

% matrix dimensions
N = 5;

% create symmetric matrix
A = rand(N);
A = A+A.';

% symrcm sorting
p = symrcm(A);

% sorted matrix
B = A(p,p);

% inverse sorting
[~,q] = sort(p)

% re-create A matrix
AfromB = B(q,q);

% chech
norm(A-AfromB);

% ans =
% 
%      0

[Kadyr Sherfedinov]

This works for matrix of dimension 5. I'm using real image(converted to binary and symmetry) with 1172x1172 size. And i get "Requested 1373584x1373584 (14057.3GB) array exceeds maximum array size preference. Creation of arrays greater than this limit may take a long time and cause MATLAB to become unresponsive." exception in this line of code

AfromB = B(q,q);