about finding maximum of submatrix at specific locations within a bigger matrix

Hello, I am looking to find the maximum value of a given size submatrix at multiple locations of a bigger matrix without using any loops. For a toy example, A = [1,2,3,4 5;6,7,8, 9,10] is my original matrix and I would like to get the max of the submatrix [2,3,4;7,8,9] which happens to be 8.

Using sepblockfun does not work.

Thank you in advance.

Answer 1

[Image Analyst]

That's not a matrix. Matrices need to be rectangular. You can't start the first row in column 2 of A and the second row in the column 1 of A like you did with 2,3,4 in row 1 and 6,7,8 in the second row.

But if you define a submatrix using rows and columns that are valid you can do

A = [1,2,3,4 5;6,7,8, 9,10] 

A = 2×5

1 2 3 4 5 6 7 8 9 10

submatrix = A(:, 2:4) 

submatrix = 2×3

2 3 4 7 8 9

% Find the max of the submatrix
maxValue = max(submatrix(:))

maxValue = 9

If you really want that jagged, non-rectangular region, you'll have to define a binary mask saying what elements you want included or not included:

mask = logical([0, 1, 1, 1, 0; 1, 1, 1, 0, 0]) % Create non-rectangular mask

mask = 2×5 logical array
   0   1   1   1   0
   1   1   1   0   0

maskedValues = A(mask) % Get a 1-D list of values in the irregularly-shaped mask.

maskedValues = 6×1

6 2 7 3 8 4

maxValue = max(maskedValues)

maxValue = 8

[MAM09]

Hello, thanks for the response. About the submatrix, I made a typo in my original question. Sorry about that. You rightly pointed out that I meant [2,3,4;7,8,9]. I realized the question I asked is also a bit incomplete and so updated my question too. I would like to do this for submatrices of the same size at multiple locations within a very big matrix. Is that doable without a loop?

[Image Analyst]

Probably not unless you want to make a function for it and call the function however many times you need to. How many max's do you need to get? Millions? If you have only a few hundred thousand or less submatrices, then a loop will be fine. You can do a loop with hundreds of millions of iterations in only a fraction of a second so it's not the looping itself that is slowing things down. It's what's happening inside the loop that take the time. Use a loop with no worries.

[MAM09]

Okay, thanks. The number of submatrices is about several hundred thousands. So, it is taking about 30 seconds with a loop.

[Image Analyst]

Let's just look at the loop alone, ignoring anything done inside it:

tic
for k = 1 : 500000
    ; % Do nothing but iterate
end
toc

Elapsed time is 0.000283 seconds.

OK so 283 microseconds. So the iteration itself is not the bottleneck. But if your matrices locations are going to be wandering all over the place, I don't see any reasonable alternative to doing it in a loop.