Matlab: avoid for loops to find the maximum among values with same labels

Question

I need to find the maximum among values with same labels, in matlab, and I am trying to avoid using for loops.

Specifically, I have an array L of labels and

Answer 1

This is a standard job for accumarray.

Three cases need to be considered, with increasing generality:

• Integer labels.
• Integer labels, specify fill value.
• Remove gaps; or non-integer labels. General case.

Integer labels

You can just use

S = accumarray(L(:), V(:), [], @max).';

In your example, this gives

>> L = [1 1 1 2 2 2 3 3 3 4 4 4 1 2 3 7];
>> V = [5 4 3 2 1 2 3 4 5 6 7 8 9 8 7 6];
>> S = accumarray(L(:), V(:), [], @max).'
S =
     9     8     7     8

Integer labels, specify fill value

If there are gaps between integers in L, the above will give a 0 result for the non-existing labels. If you want to change that fill value (for example to NaN), use a fifth input argument in acccumarray:

S = accumarray(L(:), V(:), [], @max, NaN).';

Example:

>> L = [1 1 1 2 2 2 3 3 3 4 4 4 1 2 3 7]; %// last element changed
>> V = [5 4 3 2 1 2 3 4 5 6 7 8 9 8 7 6]; %// same as in your example
>> S = accumarray(L(:), V(:), [], @max, NaN).'
S =
     9     8     7     8   NaN   NaN     6

Remove gaps; or non-integer labels. General case

When the gaps between integer labels are large, using a fill value may be inefficient. In that case you may want to get only the meaningful values in S, without fill values, i.e.skip non-existing labels. Also, it may be the case that L doesn't necessarily contain integers.

These two issues are solved by applying unique to the labels before using accumarray:

[~, ~, Li] = unique(L); %// transform L into consecutive integers
S = accumarray(Li(:), V(:), [], @max, NaN).';

Example:

>> L = [1.5 1.5 1.5 2 2 2 3 3 3 4 4 4 1 2 3 7.8]; %// note: non-integer values
>> V = [5   4   3   2 1 2 3 4 5 6 7 8 9 8 7 6  ]; %// same as in your example
>> [~, ~, Li] = unique(L); %// transform L into consecutive integers
>> S = accumarray(Li(:), V(:), [], @max, NaN).'
S =
     9     5     8     7     8     6

Answer 2

helper=[L.', V.'];
helper=sortrows(helper,-2);
[~,idx,~]=unique(helper(:,1));
S=helper(idx,2);

What I do is: I join the two arrays as columns. Then I sort them regarding second column with biggest element first. Then I get the idx of the unique Values in L before I return the corresponding Values from V.

The solution from Luis Mendo is faster. But as far as I see his solution doesn't work if there is a zero,negative value or a noninteger inside L:

Luis solution: Elapsed time is 0.722189 seconds.
My solution: Elapsed time is 2.575943 seconds.

I used:

L= ceil(rand(1,500)*10);
V= ceil(rand(1,500)*250);

and ran the code 10000 times.