How can i find out all indices of nonzero elements in a sets of matrices?

I have 19 sparse matrices which are 30000 * 30000 big. Each matrix is slightly different from another. How can i use [row, col] = find() function to get row and col vectors, which contain all position of nonzero element?

For example, A = [1 0; 0 0], B = [ 0 1; 0 0], C = [ 0 0 ; 1 0], D = [ 0 1; 1 0]

row = [ 1 1 2], col = [1 2 1]

Answer 1

[Aman]

Hi Jiahong,

Assuming that you want to have unique pairs of row and column, the following code should work:

% Create a cell array of example sparse matrices
A = sparse([1 0; 0 0]);
B = sparse([0 1; 0 0]);
C = sparse([0 0; 1 0]);
D = sparse([0 1; 1 0]);
matrices = {A, B, C, D};

% Initialize empty row and column vectors
row = [];
col = [];

% Loop over each matrix in the cell array
for i = 1:numel(matrices)
    % Use find to get the row and column indices of all nonzero elements
    [r, c, ~] = find(matrices{i});
    % Append the row and column indices to the overall row and column vectors
    row = [row; r];
    col = [col; c];
end

% Remove duplicate pairs from row and col
[row_col, idx] = unique([row, col], 'rows');
row = row_col(:,1);
col = row_col(:,2);

% Display the row and column vectors
row
col

If you want all pairs of row and column, use the following code:

% Create a cell array of example sparse matrices
A = sparse([1 0; 0 0]);
B = sparse([0 1; 0 0]);
C = sparse([0 0; 1 0]);
D = sparse([0 1; 1 0]);
matrices = {A, B, C, D};

% Initialize empty row and column vectors
row = [];
col = [];

% Loop over each matrix in the cell array
for i = 1:numel(matrices)
    % Use find to get the row and column indices of all nonzero elements
    [r, c, ~] = find(matrices{i});
    % Append the row and column indices to the overall row and column vectors
    row = [row; r];
    col = [col; c];
end

% Display the row and column vectors
row
col

Hope this helps!

[Jiahong Zou]

Hi Aman, thx for the answer. There are actually about 180000 nonzero elements in each matrix. I'm afraid it will run out of memory before removing duplicate pairs. Is there a more memory-saving way?

Answer 2

[Jiahong Zou]

Well this would work but is there a way not to repeat 19 times for 19 matrices?

[row, col] = find(A ~= 0 | B ~= 0 | C ~= 0 | D ~= 0)