How to return the row vector containing the highest values from a matrix?

Hi, I can't seem to find a solution to this but it's a pretty simple problem. Say I have a matrix:

M = [10 9 11 7 8; 
     10 9 8  7 6; 
      9 6 7  8 5]

What I want to do is to somehow extract the row vector which holds the largest sequence. I have tried the max() function but it just doesn't retain the individual rows. It is important that it returns a specific row vector from M.

The rows won't always necessarily be sequential like this, so I cannot just use the row that sums to the largest value either.

Thanks

[James Tursa]

Please define "largest sequence" for us. What is the exact criteria you want for this? What would be returned for your example above?

[Lewis]

Ah, the example isn't so good actually, but the largest sequence in that example would be

 [10 9 11 7 8]

A better example might be:

 M = [13 9   8 7 6; 
      13 12 11 9 8;  
      13 11  5 3 2]

Where I would want to return the following vector:

 [13 12 11 9 8]

because if we were to sort all elements of each vector, then this one would contain the highest, the second highest, the third highest, etc.

Answer 1

[Image Analyst]

Try this:

M = [13 9   8 7 6;
     13 12 11 9 8;
     13 11  5 3 2]
% Find the maxima in each column independently.
columnMaxima = max(M, [], 1)
% Now sort in decending order.
columnMaxima = sort(columnMaxima, 'Descend')

[Lewis]

This works! Thanks again

[Lewis]

Actually I have just come across an issue with this.

I had the following matrix:

 M = [2 6 4 3 5; 6 4 3 2 5]

This is something that will happen occasionally - the two vectors will contain the same values. In this case, the max(M, [], 1) returns the following, which is obviously incorrect:

 ans = [6 6 4 3 5]

Is there some way of working around this and just returning the first vector?

I would guess it would be something like the following (not tested):

[m_rows, ~] = size(M);
if m_rows == 2
    firstrow = sortrows(M(1, :), 'descend');
    secondrow = sortrows(M(2, :), 'descend');
    if firstrow == secondrow
          best_row = firstrow
    else
          % your code
    end
end

But I'm not sure if there is a more straightforward way to do it, especially in the case that there are any number of repeating rows so that it isn't hardcoded to deal with just 2 repeating rows..

[Image Analyst]

Not sure what you want in the case of the same number being in multiple columns. Do you just want to run it through unique() to sort it and throw out duplicates all in one shot?

[Lewis]

If possible then just taking the first row should be fine... I'd quite like to keep an index of which row from M it came from.

The same issue also occurs in the following example:

 M = [9 6 7 5 8; 6 7 5 8 4];
columnMaxima = max(M, [], 1);
columnMaxima = sort(columnMaxima, 'Descend')
columnMaxima = [9 7 7 8 8]

[Image Analyst]

The second, optional output of max supplies the index from which the max value came from. Use it.

[Lewis]

Thank you for the help - seems to be working perfectly now.

Answer 2

[dpb]

Sort first by row (already done here in these examples), then by column, retaining the sort index. Then (I think, altho didn't prove concluseively) the row will be minimum of the sum of those indices (fewest permutations to arrange).

>> [~,ix]=sort(M,1);
>> [~,ix]=min(sum(ix,2))
>> M(ix,:)
ans =
  13    12    11     9     8
>>

[Lewis]

Thanks for the suggestion