submatrix extraction based on a specific criterion

Hi everybody, I would like to extract a list of submatrix from an inital matrix, like so:

A=

    1 2 3
    2 1 2
    4 9 1
    5 2 4
    7 1 0
    8 4 8 
    9 4 1
   11 2 4

The 1st column is time in second. I would like to obtain all blocs in which the difference of time between the 1st one and the last one must not be greater than 3s. In this case, we will have:

Block 1:

      1 2 3
      2 1 2
      4 9 1

Block 2:

      5 2 4
      7 1 0
      8 4 8

Block 3:

      9 4 1
     11 2 4

Could you give me some idea to solve this problem?

Regards,

Winn

[Image Analyst]

What if it doesn't happen, like if

A=[...
    1 2 3
    2 1 2
    5 2 4
    7 1 0
    8 4 8 
    9 4 1
   11 2 4];

Would the first block be

    1 2 3
    2 1 2
    5 2 4

or

    1 2 3
    2 1 2

[Win co]

thanks for your very good remark. In fact, time difference must not be above 3s. So in your case, the right one is the second solution. I've edited my post following your remark.

Answer 1

[Image Analyst]

How about the brute force approach of a for loop?

clc;
clear 'blocks';
A=[...
    1 2 3
    2 1 2
    4 9 1
    5 2 4
    7 1 0
    8 4 8 
    9 4 1
   11 2 4]
blockStartingRow = 1;
counter = 1;
lastRow = size(A, 1);
for row = 2 : lastRow
  if A(row, 1) > A(blockStartingRow, 1) + 3
    % Start a block
    blocks{counter} = {A(blockStartingRow:(row-1),:)}
    counter = counter + 1;
    blockStartingRow = row; % Move start of block pointer.
  end
end
% Pick up last block if we need to
if blockStartingRow < lastRow
  blocks{counter} = {A(blockStartingRow:end,:)}
end
    
celldisp(blocks)

In the command window:

blocks{1}{1} =
     1     2     3
     2     1     2
     4     9     1
blocks{2}{1} =
     5     2     4
     7     1     0
     8     4     8
blocks{3}{1} =
     9     4     1
    11     2     4

If you don't know what a cell array is, read the FAQ.

[Win co]

My real matrix is in very high dimension: about 1 million rows x 20 columns. So I wouldn't like to use for loop if possible.

[Win co]

It works perfectly your code. Thank you very much for your help.

[Image Analyst]

Don't worry about loops. I did one billion , yes billion , loops in just over 2 seconds on my work computer, so a measly million iterations is just a fraction of a second. Even on my slow old home computer I'm clocking a million iterations at 3 milliseconds. If 3 milliseconds is too slow for you, then you'd better lay off the caffeine.