Sorting a vector with another vector of multiple maximums

Hi,

I have a function that I want to compute a queue "Qevents", which gets information from a set of points "P" (columns x and y) and sorts them by maximum y value. If there are other (same) maximum y values, I want to store the maximum y-value that has the largest corresponding x value. As the code is executed, points are deleted from the original data set so a new maximum can be examined. I have started writing out the code to this:

 % given a list of points P(n,2) representing x,y coordinates

 for i=1:length(P)
     indx = P==max(P(:,2));        % find index of maximum in set of points..

     if "multiple maximums"               % don't know the code for this line
        if indx(i,1)==1 && indx(i,2)==1   % checks for maximums in both columns 
            Qevents(i) = max(P(:,2));     % stores maximum y-value recursively
            P(i,:) = [];                  % and removes it from the list of points
        end
     else
        Qevents(i) = max(P(:,2))
        P(indx) = [];
     end
 end

I have no idea how to check for multiple maximums and use it in a loop properly. Any help would be appreciated. Thanks!

Ian

Answer 1

[kjetil87]

Im not a 100% sure if this is what you are asking for, but as for checking for multiple maximums you are actually already doing this.

Example:

%here test(:,2) has two max values.
test=[1,2;...
      2,3;...
      3,3];

indx=test(:,2)==max(test(:,2)) 

indx =

       0
       1
       1

index now holds true if test(:,2) is the maximum value. if there are more then 1 true element in indx , it means that there are several maxima so to test for this simply use :

if nnz(indx)>1

to check for the maximum x value (i assume this is test(:,1) ) you do the same exercise but use logical indexing to sort out the possible candidates:

 indxX=test(:,1)==max(test(indx,1));%i assume that x values cannot be equal

indxX now holds the index for the row containing maximum value of both x and y.

so Qevents(i)=test(indxX,2);

Another more readable solution would be to use sort and find.

test=[1,2;...
      3,3;...
      2,3];  % i now made sure that the x values are not sorted.

% sort the array with respect to x values.

 [~,idx]=sort(test(:,1));
 test=test(idx,1:2); % remember to also switch around the y values.

Then you can use find(..) to get the last maximum y value (since x is now sorted)

 indx=find(test(:,2)==max(test(:,2)),1,'last');

Note that index is now a scalar index and not a logical vector. But still the value you are looking for is:

test(indx,2);

Play around with the two methods see which one fits you best =)

[Ian Wood]

Thanks for your help! This is perfect and exactly what I needed. Sort is a very useful tool to do deal with multiple maximum values.

Answer 2

[Ian Wood]

With the help of kjetil87, I was able to write the appropriate code for this situation. It is shown here:

 [~,idx] = sort(P(:,1));    % sort x values in increasing order
 P = P(idx,1:2);            % sort y values corresponding to increasing x values

 for i=1:length(P)
    indx = find(P(:,2)==max(P(:,2)),1,'last'); % find index with maximum y
    Qevents(i,:) = P(indx,:);                  % store maximum y-value recursively
    P(indx,:) = [];                        % and remove it from the list of points
 end

Now the Qevents vector is properly stored with y-values in decreasing order corresponding to their x-value!

Ian

Edit: improved the code to not include unnecessary actions inside of the loop.