# [ACCEPTED]-What's the best way to iterate through columns of a matrix?-enumeration

Score: 10

The MATLAB "for" statement actually loops 8 over the columns of whatever's supplied 7 - normally, this just results in a sequence 6 of scalars since the vector passed into 5 for (as in your example above) is a row 4 vector. This means that you can rewrite 3 the above code like this:

``````function result = map_column(m, func)
result = [];
for m_col = m
result = horzcat(result, func(m_col));
end
``````

If func does not 2 return a column vector, then you can add 1 something like

``````f = func(m_col);
result = horzcat(result, f(:));
``````

to force it into a column.

Score: 3

Note that horizcat 10 exacts a substantial performance penalty 9 for large matrices. It makes the code be 8 O(N^2) instead of O(N). For a 100x10,000 7 matrix, your implementation takes 2.6s on 6 my machine, the horizcat one takes 64.5s. For 5 a 100x5000 matrix, the horizcat implementation 4 takes 15.7s.

If you wanted, you could generalize 3 your function a little and make it be able 2 to iterate over the final dimension or even 1 over arbitrary dimensions (not just columns).

Score: 2

Maybe you could always transform the matrix 3 with the ' operator and then transform the 2 result back.

``````smoothed = smooth(input', 9)';
``````

That at least works with the 1 fft function.

Score: 2

A way to cause an implicit loop across the 10 columns of a matrix is to use cellfun. That 9 is, you must first convert the matrix to 8 a cell array, each cell will hold one column. Then 7 call cellfun. For example:

``````A = randn(10,5);
``````

See that here 6 I've computed the standard deviation for 5 each column.

``````cellfun(@std,mat2cell(A,size(A,1),ones(1,size(A,2))))

ans =
0.78681       1.1473      0.89789      0.66635       1.3482
``````

Of course, many functions in 4 MATLAB are already set up to work on rows 3 or columns of an array as the user indicates. This 2 is true of std of course, but this is a 1 convenient way to test that `cellfun` worked successfully.

``````std(A,[],1)

ans =
0.78681       1.1473      0.89789      0.66635       1.3482
``````
Score: 1

Don't forget to preallocate the result matrix 4 if you are dealing with large matrices. Otherwise 3 your CPU will spend lots of cycles repeatedly 2 re-allocating the matrix every time it adds 1 a new row/column.

Score: 0

If this is a common use-case for your function, it 9 would perhaps be a good idea to make the 8 function iterate through the columns automatically 7 if the input is not a vector.

This doesn't 6 exactly solve your problem but it would 5 simplify the functions' usage. In that case, the 4 output should be a matrix, too.

You can also 3 transform the matrix to one long column 2 by using `m(:,:) = m(:)`. However, it depends on your function 1 if this would make sense.

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