# Sum: every nth column and groups/blocks of columns

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Dom on 24 Aug 2022
Edited: Dyuman Joshi on 24 Aug 2022
Hi:
Is there any way to improve this code?
Thanks
Dominic
%
% Flows between sectors of countries
% 3 countries with 4 sectors
% Row and column headings are the same C1S1 C1S2 ......C4S3 C4S4
%
c=3; % no. of countries
s=4; % no. of sectors
X=magic(c*s); % 12
%
% add every 4th (sth) column of a matrix: 1,5,9 ... 4,8,12
% - result 12x4 (sum by sector)
%
S=sum(X(:,1:s:end),2); % 1:4:end
for k=2:s % 2:4
SS=sum(X(:,(k):s:end),2);
S=horzcat(S,SS);
end
%
% add columns in blocks of 4: 1-4, 5-8, 9-12 - result 12x3 (sum by country)
%
C=sum(X(:,[1:s]),2); % [1:4]
x=(s+1):s:(c*s); % 5:4:12
y=(2*s):s:(c*s); % 8:4:12
for k=[x;y]
CC=sum(X(:,[k(1):k(2)]),2);
C=horzcat(C,CC);
end

Bruno Luong on 24 Aug 2022
Edited: Bruno Luong on 24 Aug 2022
c=3; % no. of countries
s=4; % no. of sectors
X=magic(c*s); % 12
XX = reshape(X,size(X,1),s,[]);
S = sum(XX,3)
S = 12×4
420 18 21 411 51 381 378 60 87 345 342 96 312 126 129 303 276 162 165 267 195 237 234 204 231 201 198 240 168 270 273 159 132 306 309 123 339 93 90 348
C = squeeze(sum(XX,2))
C = 12×3
290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290
Dom on 24 Aug 2022
Thanks Bruno. I am sure it is.

Fangjun Jiang on 24 Aug 2022
x=magic(12);
y=reshape(x,12,4,[]);
z=squeeze(sum(y,2))
z = 12×3
290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290
Dom on 24 Aug 2022
Thank you Jiang, very elegant. Any comments on the first part?
Thanks again for taking the time.

Dyuman Joshi on 24 Aug 2022
Edited: Dyuman Joshi on 24 Aug 2022
%comment lines removed
c=3; % no. of countries
s=4; % no. of sectors
X=magic(c*s); % 12
Vectorized solution
S1=reshape(sum(reshape(X,[],c),2),[],s)
S1 = 12×4
420 18 21 411 51 381 378 60 87 345 342 96 312 126 129 303 276 162 165 267 195 237 234 204 231 201 198 240 168 270 273 159 132 306 309 123 339 93 90 348
C1=reshape(sum(reshape(X',s,[])),[],c)
C1 = 12×3
290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290
Dom on 24 Aug 2022
Thanks Dyuman. I have looked at all three contributions. @Bruno Luong and @Fangjun Jiang add another dimension. I am stuck in old loop and 2x2 thinking. All the answers work so I wonder why I can't accept all of them. Thanks.