Columnwise removal of first ones from binary matrix. MATLAB

Question

I have some binary matrix. I want to remove all first ones from each column, but keep one if this value is alone in column. I have some code, which produces correct result, but it looks ugly- I should iterate through all columns.

Could You give me a piece of advice how to improve my code?

Non-vectorised code:

% Dummy matrix for SE
M = 10^3;
N = 10^2;
ExampleMatrix = (rand(M,N)>0.9);
ExampleMatrix1=ExampleMatrix;
% Iterate columns
for iColumn = 1:size(ExampleMatrix,2)
    idx = find(ExampleMatrix(:,iColumn)); % all nonzeroes elements
    if numel(idx) > 1
        % remove all ones except first
        ExampleMatrix(idx(1),iColumn) = 0;
    end
end

Answer 1

I think this does what you want:

ind_col = find(sum(ExampleMatrix, 1)>1); % index of relevant columns
[~, ind_row] = max(ExampleMatrix(:,ind_col), [], 1); % index of first max of each column
ExampleMatrix(ind_row + (ind_col-1)*size(ExampleMatrix,1)) = 0; % linear indexing

The code uses:

• the fact that the second output of max gives the index of the first maximum value. In this case max is applied along the first dimension, to find the first maximum of each column;
• linear indexing.