How to calculate differences in matrix

I have matrix A as follows:

A = [
1  245
1  370
1  1555
1  1620
2  255
2  295
2  335
2  1375
2  1415
2  1575
2  1615
2  1655
3  250
3  415
3  520
3  565
3  1405
];

I want to create a new third column where it represent the difference between two successive arrays of the second column of matrix A. The process should be restarted whenever the unique ID (first column) changed. Also, in calculation of last array since ID is changing then the value should be calculated from absolute value of difference between last and first arrays.

    out = [
    1  245  125
  1  370  1185
  1  1555  65
  1  1620  1375
  2  255  40
  2  295  40
  2  335  1040
  2  1375  40
  2  1415  160
  2  1575  40
  2  1615  40
  2  1655  1400
  3  250  165
  3  415  105
  3  520  45
  3  565  840
  3  1405  1155
    ];

% abs(1620-245) = 1375

Answer 1

[the cyclist]

I think this does what you intend

A = [
1  245
1  370
1  1555
1  1620
2  255
2  295
2  335
2  1375
2  1415
2  1575
2  1615
2  1655
3  250
3  415
3  520
3  565
3  1405
];

out = [[A, [diff(A(:,2)); 0]]; [max(A(:,1))+1 0 0]];

indexToOutAbsVal = find(diff(out(:,1))~=0);

out(indexToOutAbsVal,3) = abs(A(indexToOutAbsVal,2) - A([1; indexToOutAbsVal(1:end-1)+1],2)); out(end,:) = [];

[Tiffan]

@the cyclist, I realized that your code is correct just for first ID (1). The same way for first ID that 1375 = 1620 - 245, for other IDs the last diff should be calculated:

$ e.g. for ID 2: 1655 - 255 = 1400
% e.g. for ID 3: 1405 - 250 = 1155

Result should be like:

1  245  125
1  370  1185
1  1555  65
1  1620  1375
2  255  40
2  295  40
2  335  1040
2  1375  40
2  1415  160
2  1575  40
2  1615  40
2  1655  1400
3  250  165
3  415  105
3  520  45
3  565  840
3  1405  1155

Can you please correct your code?

[the cyclist]

Sorry, I got the indexing wrong. I edited one line in my answer, and it works now.

Answer 2

[Akira Agata]

Another strait forward way to calculate this would be as follows:

 A = [
 1  245
 1  370
 1  1555
 1  1620
 2  255
 2  295
 2  335
 2  1375
 2  1415
 2  1575
 2  1615
 2  1655
 3  250
 3  415
 3  520
 3  565
 3  1405
 ];

 out = zeros(size(A,1),1);

 numGroup = max(A(:,1));

 for kk = 1:numGroup
    idx = A(:,1) == kk;
    a = A(idx,2);
    out(idx) = [a(2:end) - a(1:end-1); a(end) - a(1)];
 end

 out = [A, out];