Conditional sum on particular column of a matrix

Dear all, I am trying to sum first 5 elements of column 1 of matrix m x n one after the other. Eg. say 1 2 3 4 5 6 then I want result as 1 3 6 10 15 21. After than I want to repeat the process again for m rows. Please help me with this. Regards, Suri

[Stephen23]

You write that you want "to sum first 5 elements", and then give an example with six elements. Do you want five or six elements? Or a general solution?

It is also not clear how the size of the matrix m*n relates to the number of rows that you are trying to sum: is m equal to five, or is m a multiple of five? Or is this relationship unknown?

[Surendra Kumar Singupalli]

Hi Stephen,thanks for your message. Let me explain: I have a 1000 x 4 matrix. My aim is to add as you did below for every 5 elements per column (4 in total)up to 1000 elements. So for example matrix A; assume the sum window is 3 (not 5 as in my case) then it should look like this (column 1): 1 3 6 4 9 15 Am I clear this time? Thanks.

Answer 1

[Stephen23]

You can use cumsum for this:

>> A = bsxfun(@plus,(1:6).',[0,2,5,10])
A =
     1     3     6    11
     2     4     7    12
     3     5     8    13
     4     6     9    14
     5     7    10    15
     6     8    11    16
>> cumsum(A,1)
ans =
     1     3     6    11
     3     7    13    23
     6    12    21    36
    10    18    30    50
    15    25    40    65
    21    33    51    81

[Surendra Kumar Singupalli]

Thanks. I will check if it works with the condition that I want to do the summation in blocks of 5 elements.

[Stephen23]

The trick is to use reshape to create a new array with one more dimension than you currently have, use cumsum on the columns of this, and then reshape back in the shape of the original array. First we create some fake data:

>> A = bsxfun(@plus,(1:6).',[0,2,5,10])
A =
     1     3     6    11
     2     4     7    12
     3     5     8    13
     4     6     9    14
     5     7    10    15
     6     8    11    16

Then we reshape to get a new array with only as many rows/elements as you want to sum over:

>> N = 3 % pick how many elements per block
>> B = reshape(A,N,size(A,2),[])
B(:,:,1) =
     1     4     3     6
     2     5     4     7
     3     6     5     8
B(:,:,2) =
     6     9    11    14
     7    10    12    15
     8    11    13    16

Get the cummulative sum:

>> C = cumsum(B)
C(:,:,1) =
     1     4     3     6
     3     9     7    13
     6    15    12    21
C(:,:,2) =
     6     9    11    14
    13    19    23    29
    21    30    36    45

And finally reshape for the final output:

>> D = reshape(C,size(A))
D =
     1     3     6    11
     3     7    13    23
     6    12    21    36
     4     6     9    14
     9    13    19    29
    15    21    30    45

Note this method only works if the number of rows is a multiple of the elements per block.

[Surendra Kumar Singupalli]

Thanks Stephen. I followed this solution and it works for me. However, as you mentioned, if I have a dataset which is not multiple of variable N as above; it misses some of the day. Do we have a solution based on conditional loop may be?

[Stephen23]

Vectorized code would be neater and faster than trying to solve this in a loop. The simplest way would be to follow these steps:

1. check if the number of rows is a multiple
2. use an if conditional
3. add one single zero to the last required row (the other rows will get filled automatically)
4. perform the method that we defined above.
5. trim the extra rows.