How do cumulatively add a matrix column based on a vector

Hello all, I have the following matrix,

t = 
  1.0000    7.0000         0         0
  2.0000    9.0000    0.6000    3.0000
  3.0000   11.0000   -0.5000   -0.5000
  4.0000   13.0000    0.6000    2.4000
  5.0000   14.0000   -0.7000   -2.5000
  6.0000   18.0000    0.7000    2.4000
  7.0000   19.0000   -0.2000    1.0000
  8.0000   20.0000         0    1.0000
  9.0000   22.0000    0.7000    2.1000
 10.0000   23.0000   -0.1000    1.4000
 11.0000   24.0000         0    1.4000
 12.0000   25.0000    0.2000    0.4000
 13.0000   26.0000         0    0.4000
 14.0000   28.0000    0.5000    0.5000
 15.0000   29.0000   -0.2000   -0.9000
 16.0000   30.0000    0.2000    0.5000
 17.0000   31.0000   -0.1000   -0.2000
 18.0000   32.0000    0.3000         0
 19.0000   33.0000   -0.3000   -2.1000
 20.0000   34.0000    0.2000   -0.7000
 21.0000   35.0000   -0.1000   -1.4000
 22.0000   39.0000         0   -1.4000
 23.0000   42.0000   -0.3000   -3.5000
 24.0000   44.0000    0.3000   -1.4000
 25.0000   45.0000   -0.2000   -2.8000

& a vector m, corresponding to column 1 of t, as

   m = [1 2 4 9 12 14 18];

So, I need to cumulatively add the values in column 3 of matrix t from

   0 (1+1 : 2-1), that is m(1)+1 : m(2)-1
   3 (2+1 : 4-1)
   5, 6, 7, 8 (4+1 : 9-1)
   10, 11 (9+1 : 12-1)
   13 (12+1 : 14-1)
   15, 16, 17 (14+1 : 18-1)
   19 to 25 (18+1 : end)

& put these in column 4. Right now it has incorrect values. The starting points should all be 0. column 3 (m(n)) = 0, meaning m(1) = 0; m(2) = 0, m(4) = 0, etc.

My method with loops produces a lot of overlap & doesn't quite work. Hope this is not too confusing.

Any suggestions? Thanks Damo Nair

[Stephen23]

@Damo Nair: your explanation is not clear. You have provided us with incorrect output data. More useful would be if you provide us with correct output data, then we have something to compare our code output against.

[Damo Nair]

Ok, sorry about that Stephen ... here is a better explanation (I hope) of the output I need ...

This is what col 4 would look like ...

0 (because m(1) = 1) 0 (because m(2) = 2) -0.5 (got it from col 3, result of cumsum) 0 (because m(3) = 4) -0.7 0 -0.2 -0.2 0 (m(4) = 9) -0.1 0 0 (m(5) = 12) 0 0 (m(6) = 14) -0.2 0 -0.1 0 (m(end) = 18) -0.3 -0.1 -0.2 -0.2 -0.5 -0.2 -0.4

So, what is happening is that for rows of m there is a reset to 0 & in between the indices of m there is a cumsum. I hope this is a bit clearer.

Thanks again. Damo Nair

[Matt J]

@Damo, I recommend that you edit your post with t displayed with the correct data (manually entered by you).

Answer 1

[Image Analyst]

Try this:

t = [...
  1.0000    7.0000         0         0
  2.0000    9.0000    0.6000    3.0000
  3.0000   11.0000   -0.5000   -0.5000
  4.0000   13.0000    0.6000    2.4000
  5.0000   14.0000   -0.7000   -2.5000
  6.0000   18.0000    0.7000    2.4000
  7.0000   19.0000   -0.2000    1.0000
  8.0000   20.0000         0    1.0000
  9.0000   22.0000    0.7000    2.1000
  10.0000   23.0000   -0.1000    1.4000
  11.0000   24.0000         0    1.4000
  12.0000   25.0000    0.2000    0.4000
  13.0000   26.0000         0    0.4000
  14.0000   28.0000    0.5000    0.5000
  15.0000   29.0000   -0.2000   -0.9000
  16.0000   30.0000    0.2000    0.5000
  17.0000   31.0000   -0.1000   -0.2000
  18.0000   32.0000    0.3000         0
  19.0000   33.0000   -0.3000   -2.1000
  20.0000   34.0000    0.2000   -0.7000
  21.0000   35.0000   -0.1000   -1.4000
  22.0000   39.0000         0   -1.4000
  23.0000   42.0000   -0.3000   -3.5000
  24.0000   44.0000    0.3000   -1.4000
  25.0000   45.0000   -0.2000   -2.8000];

% Extract column 1 of t.
column1 = t(:, 1);
% & a vector m, corresponding to column 1 of t, defined as
m = [1 2 4 9 12 14 18];
for k = 1 : length(m) - 1
  index1 = m(k) + 1;
  index2 = m(k + 1) - 1;
  theSum(k) = sum(column1(index1:index2));
  fprintf('Summing column1 from index %d to %d and getting %.1f.\n', index1, index2, theSum(k));
end

You get:

Summing column1 from index 2 to 1 and getting 0.0.
Summing column1 from index 3 to 3 and getting 3.0.
Summing column1 from index 5 to 8 and getting 26.0.
Summing column1 from index 10 to 11 and getting 21.0.
Summing column1 from index 13 to 13 and getting 13.0.
Summing column1 from index 15 to 17 and getting 48.0.

[Image Analyst]

So, (with your modifications), put this before the loop:

column3 = t(:, 3);

then, in the loop

theSum(k) = sum(column3(index1:index2)); % Sum column3
% Set column 4 of t to zero for this m value.
t(m(k), 4) = 0;

[Damo Nair]

Yes, thanks Image Analyst, I changed that to col 3 & sum to cumsum, added some end effects & it works now!

Have a good day. Damo.

Answer 2

[Damo Nair]

Thanks, Stephen, Matt & Image Analyst, very sorry for the clumsiness! Here at last is the correct t matrix ...

t =

    1.0000    7.0000         0         0
    2.0000    9.0000    0.6000         0
    3.0000   11.0000   -0.5000   -0.5000
    4.0000   13.0000    0.6000         0
    5.0000   14.0000   -0.7000   -0.7000
    6.0000   18.0000    0.7000         0
    7.0000   19.0000   -0.2000   -0.2000
    8.0000   20.0000         0   -0.2000
    9.0000   22.0000    0.7000         0
   10.0000   23.0000   -0.1000   -0.1000
   11.0000   24.0000         0         -0.1
   12.0000   25.0000    0.2000         0
   13.0000   26.0000         0         0
   14.0000   28.0000    0.5000         0
   15.0000   29.0000   -0.2000   -0.2000
   16.0000   30.0000    0.2000         0
   17.0000   31.0000   -0.1000   -0.1000
   18.0000   32.0000    0.3000         0
   19.0000   33.0000   -0.3000   -0.3000
   20.0000   34.0000    0.2000   -0.1000
   21.0000   35.0000   -0.1000   -0.2000
   22.0000   39.0000         0   -0.2000
   23.0000   42.0000   -0.3000   -0.5000
   24.0000   44.0000    0.3000   -0.2000

m = [1 2 4 9 12 14 18];

In col 4 I am resetting to 0 at the m values. In between the m indices I am trying to do a cumulative sum of column 3. I hope its a bit clearer this time.

Thanks, appreciate the help. Damo Nair