List combinations and count how many it appears

Question

JL 2019-8-9

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/475547-list-combinations-and-count-how-many-it-appears

评论： JL 2019-8-10

I have 2 matrices, W and Y. Using both as references, I want to list the different combinations and count how many times it appears from Y. Only count Y if the correponsing W value is >0.

W =[ 25
     0
     0
    28
     0
     0
    25
     0
     0
    25
     0
     0
    15
    14
     0
     0
    25
     0
     0];
 
Y =[ 1     2     0     0
     1     3     2     0
     1     4     3     2
     1     3     0     0
     1     2     3     0
     1     4     3     0
     1     4     0     0
     1     3     4     0
     1     2     3     4
     2     3     0     0
     2     1     3     0
     2     1     4     3
     2     1     4     0
     2     3     4     0
     2     1     3     4
     2     3     1     4
     3     4     0     0
     3     1     4     0
     3     2     1     4];
 
Zlist =
[12;
13;
14;
23;
24;
34;]

Add 2 1 to 1 2; 3 1 to 1 3; 4 1 to 1 4; 3 2 to 2 3; 4 3 to 3 4 and 4 2 to 24

Also, for Y with more > 2 numbers in the row like [2 1 4], it will have a combinations of 2 1, 1 4, 2 4 while [2 3 4] has 2 3, 3 4 and 2 4.

Zlistcount =
[2;
1;
2;
2;
2;
2;]

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JL 2019-8-9

Also, if we've counted how many 1 2 are there in Y, would we be able to tell which rows and columns they are located? For example, for 1 2, we know in W, they are situated at W(1,1) and W(13,1)

dpb 2019-8-9

Re-edit the posting so can copy and paste into command window and execute w/o editing the columns...as is is not readable

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Answer 1

Andrei Bobrov 2019-8-9

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https://ww2.mathworks.cn/matlabcentral/answers/475547-list-combinations-and-count-how-many-it-appears#answer_387032

编辑：Andrei Bobrov 2019-8-9

YY = Y(W~=0,:);
n = sum(YY>0,2);
k = factorial(n)./factorial(n-2)/2;
ie = cumsum(k);
ib = ie - k + 1;
zc = zeros(ie(end),2);
for ii = 1:numel(ib)
    zc(ib(ii):ie(ii),:) = sort(nchoosek(YY(ii,YY(ii,:)>0),2),2); 
end
[i1,i2,v] = find(accumarray(zc,1));
Zlistcount = [i1,i2,v];

and without loop (as in Dpb's answer):

YY = Y(W~=0,:);
zc = sort(cell2mat(arrayfun(@(x)nchoosek(YY(x,YY(x,:)>0),2),...
                                    (1:size(YY,1))','un',0)),2);
[i1,i2,v] = find(accumarray(zc,1));
Zlistcount = [i1,i2,v];

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JL 2019-8-10

Thanks Andrei and Dpb

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Answer 2

dpb 2019-8-9

1
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https://ww2.mathworks.cn/matlabcentral/answers/475547-list-combinations-and-count-how-many-it-appears#answer_387016

编辑：dpb 2019-8-9

y=Y(W~=0,:);
z=unique(sort(cell2mat(arrayfun(@(i) nchoosek(y(i,y(i,:)~=0),2),1:size(y,1),'uni',0).'),2),'rows');
nZ=arrayfun(@(i) sum(sum(ismember(y,z(i,:)),2)==2),1:size(z,1)).';

There's no other need for W once you've cleaned out the superfluous Y.

I suspect, but haven't thought about it at all, that a clever application of accumarray might also be a solution...