Sum: every nth column and groups/blocks of columns

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

Answer 1

[Bruno Luong]

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]

Thank you Bruno, even fewer lines of code! Appreciate your efforts on my behalf.

[Bruno Luong]

Not only fewer line of code. It probably the fatest as it avoid matrix transposition.

[Dom]

Thanks Bruno. I am sure it is.

Answer 2

[Fangjun Jiang]

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]

Thank you Jiang, very elegant. Any comments on the first part?

Thanks again for taking the time.

Answer 3

[Dyuman Joshi]

%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]

Thank you Dyuman, like Jiang very elegant indeed. Clearly I need to think differently.

Appreciate your taking the time.

[Dyuman Joshi]

I would suggest you to take a look at @Bruno Luong's answer as well, it's a bit simpler than mine.

I got to know about squeeze from the other 2 answers now only!

[Dom]

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.