Maximum Values of Matrix Subrows

Hello,

What is a smart way (without loops) to find maximum values of matrix sub rows, with variable start and end subscripts. E.g., for a NxN matrix, I want to get a Nx1 vector of maximum values for each matrix sub row, with variable start and end subscripts.

Many thanks!

Answer 1

[David Goodmanson]

ADD, if I understand the question correctly, for matrix M this would be a = max(M,[ ],2) where the 2 is for max along rows instead of along columns.

[ADD]

David, The problem is that I want to find maximum values in subsets of rows. So for an NxN matrix M, I want max(M(i,a(i):b(i))), for i = 1,...,N, where i is the row and a(i) and b(i) are starting and ending cols that define the range within each row. I have a very large matrix and looking for a way to do this without doing a loop over i.

[David Goodmanson]

I see I didn't understand the question and it will be interesting to see if someone finds a way.

Answer 2

[David Goodmanson]

ADD, ok here is one way to do this. It does modify the matrix in order to get the answer, so in this script file M gets changed and I suppose in a function you need more memory for a copy, I'n not quite sure. There are probably better ways to do this, depending for one thing on how long the selected rows are compared to N, on average.

I don't know how big your matrix is but not counting creating the initial matrix, for a 20k x 20k matrix of doubles this took a little less than 7 sec. on my PC.

However, it only took 3 sec. to do the same thing with a for loop. The slow way is faster. Negative progress! Hopefully someone will weigh in with a more efficient method.

% find max of M(k,a:b) by row, for an NxN matrix M
% a is a vector of row indices
% b is a vector of row indices, a<=b

Q = zeros(N,N+1,'int8');        % includes helper column for b index
aa = sub2ind([N,N+1],1:N,a  );
bb = sub2ind([N,N+1],1:N,b+1);
Q(aa) = 1;
Q(bb) = -1;
Q = cumsum(Q,2);                % mark elements to save
Q = Q(:,1:end-1);               % take away helper column
M(~Q) = nan;                    % nans are ignored by max
rowmax_a_b = max(M,[ ],2);