Looping through to find max value without using max() - matlab

Question

I'm trying to iterate in MATLAB (not allowed to use in built functions) to find the maximum value of each row in a certain matrix. I've been able to find the max value of the whole matrix but am unsure about isolating the row and finding the max value (once again without using max()).
My loop currently looks like this:
for i = 1:size(A, 1)
for j = 1:size(A, 2)
if A(i, j) > matrix_max
matrix_max = A(i, j);
row = i;
column = j;
end
end
end

Answer 1

You need a vector of results, not a single value. Note you could initialise this to zero. Don't initialise to zero unless you know you only have positive values. Instead, initialise to -inf using -inf*ones(...), as all values are greater than negative infinity. Or (see the bottom code block) initialise to the first column of A.
% Set up results vector, same number of rows as A, start at negative infinity
rows_max = -inf*ones(size(A,1),1);
% Set up similar to track column number. No need to track row number as doing each row!
col_nums = zeros(size(A,1),1);
% Loop through. i and j = sqrt(-1) by default in MATLAB, use ii and jj instead
for ii = 1:size(A,1)
for jj = 1:size(A,2)
if A(ii,jj) > rows_max(ii)
rows_max(ii) = A(ii,jj);
col_nums(ii) = jj;
end
end
end
Note that if vectorisation doesn't violate your "no built-ins" rule (it should be fine, it's making the most of the MATLAB language), then you can remove the outer (row) loop
rows_max = -inf*ones(size(A,1),1);
col_nums = zeros(size(A,1),1);
for jj = 1:size(A,2)
% Get rows where current column is larger than current max stored in row_max
idx = A(:,jj) > rows_max;
% Store new max values
rows_max(idx) = A(idx,jj);
% Store new column indices
col_nums(idx) = jj;
end
Even better, you can cut your loop short by 1, and initialise to the first column of A.
rows_max = A(:,1); % Set current max to the first column
col_nums = ones(size(A,1),1); % ditto
% Loop from 2nd column now that we've already used the first column
for jj = 2:size(A,2)
idx = A(:,jj) > rows_max;
rows_max(idx) = A(idx,jj);
col_nums(idx) = jj;
end

Answer 2

You can modified it likes the following to get each max for each row:
% initialize
matrix_max = zeros(size(A,1),1);
columns = zeros(size(A,1),1);
% find max
for i = 1:size(A, 1)
matrix_max(i) = A(i,1);
columns(i) = 1;
for j = 2:size(A, 2)
if A(i, j) > matrix_max(i)
matrix_max(i) = A(i, j);
columns(i) = j;
end
end
end