I want to sum specific elements in an a 2D matrix

I have a matrix like this

4  3 6 8 1 10 5 2 9
1 10 3 9 4  2 5 7 6
9  5 1 7 8 10 3 4 2

What i want to do is a 3x3 matrix that contains this

For cell (1,1) --- (4 + 8 + 5) - 4 (i.e. 4(the first element in the array) + 8(the fourth element in the array) + 5(the 7th element in the array) - 4(my initial cell))

For cell (1,2) --- (3 + 1 + 2) - 3 (i.e. 3(the second element in the array) + 1(the fifth element in the array) + 2(the 8th element in the array) - 3(my initial cell))

and so on... For cell (2,1) --- (1 + 9 + 5) - 1

It's like calculating the total of all the numbers where the indices are separated by 3

output =

13 3 19
14 11 8
10 12 12

[Azzi Abdelmalek]

Why the your output is 3x3? And why add the first element to subtract it?

[N.]

I added the first element to subtract it to not lose the sequence. and 3x3 the first 3 is the number of rows, the second 3 depends on the distance between the indices which means that if i want to add the elements every 4 indices on a bigger matrix then i will have a 3x4 matrix

Answer 1

[Star Strider]

A loop is the only way I can see to do this:

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

for k1 = 1:3
    for k2 = 1:3
        S(k1,k2) = sum(M(k1,3+k2:3:end),2);
    end
end
S

S =

      13     3    19
      14    11     8
      10    12    12

[dpb]

Can do it in only one loop, though...

>> for ic=1:3,S(:,ic)=sum(M(:,ic+3:3:end),2);,end
>> S
S =
  13     3    19
  14    11     8
  10    12    12
>>

accumarray ought to be able to be brought to bear, but it's Sunday afternoon... :)

[sasso samer]

what if i want to do the same thing but on all the numbers not the first 3 numbers only.

Answer 2

[Andrei Bobrov]

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

n = 3;
out = sum(reshape(a(:,n+1:end),n,n,[]),3);

[dpb]

Nicely done...