generating a subset of specific of unique 3 groups out of 84

Hi all, I've the following indices: indices = nchoosek ([1:9], 3)

indices =

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

where each row of the above 84 rows gives a specific value as shown: C1=reshape(C_IA,size(indices,1) ,[])

C1 =

26.5871 - 0.0000i
25.3748 + 0.0000i
29.1875 - 0.0000i
27.8822 - 0.0000i
27.9279 - 0.0000i
29.8068 - 0.0000i
20.1088 + 0.0000i
28.9700 + 0.0000i
31.4866 - 0.0000i
30.7709 - 0.0000i
29.1391 - 0.0000i
29.5271 - 0.0000i
28.7390 - 0.0000i
32.2309 - 0.0000i
26.0994 - 0.0000i
31.6562 - 0.0000i
27.2213 + 0.0000i
19.1752 + 0.0000i
29.0539 + 0.0000i
31.9886 + 0.0000i
28.7934 + 0.0000i
26.9325 + 0.0000i
30.8589 + 0.0000i
26.5858 + 0.0000i
27.5174 + 0.0000i
31.3600 + 0.0000i
29.4643 - 0.0000i
28.1896 - 0.0000i
20.4114 + 0.0000i
25.9653 - 0.0000i
29.2150 - 0.0000i
29.3785 + 0.0000i
25.1405 - 0.0000i
25.2144 - 0.0000i
19.9587 - 0.0000i
27.7516 + 0.0000i
27.5817 + 0.0000i
30.9471 - 0.0000i
21.9452 + 0.0000i
25.7818 - 0.0000i
27.0898 - 0.0000i
25.6516 + 0.0000i
27.9703 - 0.0000i
29.8913 - 0.0000i
28.7567 + 0.0000i
26.5974 - 0.0000i
27.8911 + 0.0000i
28.2247 + 0.0000i
30.4570 - 0.0000i
32.3383 - 0.0000i
23.6659 - 0.0000i
26.0332 - 0.0000i
24.4511 - 0.0000i
31.6553 - 0.0000i
28.5011 + 0.0000i
28.2660 - 0.0000i
25.6020 - 0.0000i
30.5952 + 0.0000i
23.9412 + 0.0000i
18.3079 - 0.0000i
27.3033 + 0.0000i
29.0838 + 0.0000i
29.8749 - 0.0000i
28.0912 + 0.0000i
19.2981 + 0.0000i
23.3627 - 0.0000i
29.4325 - 0.0000i
31.1372 - 0.0000i
22.5496 - 0.0000i
27.3350 - 0.0000i
28.2363 + 0.0000i
34.0017 + 0.0000i
28.1177 - 0.0000i
32.8989 + 0.0000i
28.2460 - 0.0000i
26.2227 - 0.0000i
24.6639 - 0.0000i
25.9026 + 0.0000i
30.5478 - 0.0000i
25.5483 - 0.0000i
29.4994 - 0.0000i
31.3045 + 0.0000i
31.9083 - 0.0000i
32.6127 - 0.0000i

I would like to generate 3 different group of numbers in one time (where each row represent a number) so that all the three groups has unique (not repeated) numbers. i.e. If the 1st generated group was : 1 2 3 (which has a value of 26.5871 then the 2nd group must be any three numbers from 1 to 9 except 1 2 3 (let's say 2nd generated group was: 4 5 6 which has a value of 19.2981 ) then the 3rd generated group must be any number from 1 to 9 except all previously selected numbers (any 3 numbers except 1,2,3,4,5,6) hence we have 3rd group is: 7 8 9 which has a value of 32.6127 so, the expected result of my example is : 26.5871 19.2981 32.6127

I need to do this for all different cases (and not for only the above case), i.e to generate all possible ways of dividing up the numbers from 1 to 9 into three groups with three numbers in each group. The total number of these is 9!/3!/3!/3! = 1680 different result. (the above Example gives only one result out of those 1680 result that i need)

another 2nd example for clarity, if one combination out of the 1680 combinations was: 7 8 9 4 5 6 1 2 3 then i expect to get C1(84,:) and C1(65,:) and C1(1,:)

any help?

P.S. I've already got the 1680 rows combinations but don't know how to map those to my 84 result of C1

Answer 1

[Roger Stafford]

Suppose [i1,i2,i3,i4,i5,i6,i7,i8,i9] is one of your combinations. Then you can reference the corresponding three values in C1 using the three indices k1, k2, and k3 in the following:

 n = 9;
 k1 = n*(n-1)*(n-2)/6-(n-i1)*(n-1-i1)*(n-2-i1)/6-(n-i2)*(n-1-i2)/2-(n-i3);
 k2 = n*(n-1)*(n-2)/6-(n-i4)*(n-1-i4)*(n-2-i4)/6-(n-i5)*(n-1-i5)/2-(n-i6);
 k3 = n*(n-1)*(n-2)/6-(n-i7)*(n-1-i7)*(n-2-i7)/6-(n-i8)*(n-1-i8)/2-(n-i9);

and get

 C1(k1), C1(k2), C1(k3)

(This formula is in fact valid for any n, not just n = 9.)

Answer 2

[Andrei Bobrov]

C1 = real(C1);
ii = nchoosek ([1:9], 3);

[~,groups1] = sort(randi(100,10,9),2); % example
[l,i1] = ismember(sort(reshape(groups1',3,[])',2),ii,'rows');
out = reshape(C1(i1(l)),3,[]).';

[Hisham]

I'm not sure if you got me right, but I want to get 1680 result (all different combinations) and not a random group example

Answer 3

[Jos (10584)]

The following generates three arrays with 3 columns and 1680 rows each. Each row corresponds to a unique combination of numbers. Every number from 1 to 9 is present only once among the same rows of Group1, Group2 and Group3:

tf1 = permpos(3,9) ;
tf2 = permpos(3,6) ;
sz1 = size(tf1,1) ; sz2 = size(tf2,1) ;
sz = sz1 * sz2 ; % total size (should be 1680)
tf1 = kron(tf1,ones(sz2,1)).' ; % expand
tf2 = repmat(tf2,sz1,1).' ;
tf2 = 3 - tf2 ;
tf1(tf1==0) = tf2 ; % now tf1 hold group number
% convert to numbers 1:9
x = repmat([1 2 3],sz,1).' ;
tf1 = -tf1 ;
tf1(tf1==-1) = x ;
tf1(tf1==-2) = x+3 ;
tf1(tf1==-3) = x+6 ;
% each row of t1 holds the unique order of numbers

% split (if really needed)
Group1 = tf1(1:3,:).' ;
Group2 = tf1(4:6,:).' ;
Group3 = tf1(7:9,:).' ;

Now you can convert (select?) from C using these indices.

PERMPOS can be downloaded here: http://www.mathworks.com/matlabcentral/fileexchange/11216-permpos

[Hisham]

Thanks alot for the code, but my problem is that I don't know how to select from C to get 1680 results. I already have the following code which generate 1680 indices:

 C1 = nchoosek([1:K],sel_user);
     C1 = [C1,zeros(size(C1,1),6)];  %6 should be 2
  x = 1:9; %should be from 1:3
  for p = 1:size(C1,1)
    t = true(1,9); %9 should be 3
    t(C1(p,1:3)) = false(1,3);
    C1(p,4:9) = x(t); %should be from 2:3
  end
  C2 = nchoosek(1:6,3); %
  C2 = [C2,zeros(size(C2,1),3)];
  x = 1:6; %from 1:2
  for q = 1:size(C2,1)
    t = true(1,6); t(C2(q,1:3)) = false(1,3);
    C2(q,4:6) = x(t);
  end
  A = zeros(size(C1,1)*size(C2,1),9);
  k = 0;
  for p = 1:size(C1,1)
    x = C1(p,1:3);
    y = C1(p,4:9);
    for q = 1:size(C2,1)
      k = k + 1;
      A(k,:) = [x,y(C2(q,:))];
    end
  end

the matrix A is the 1680 combinations but I want to map the matrix A into my C1 matrix in order to get 1680 result (out from C1)

[Jos (10584)]

Create the 84 indices and find the location of the three groups using ismember:

indices84 = nchoosek ([1:9], 3)

[~, Cind1] = ismember(Group1, indices84,'rows') ;
[~, Cind2] = ismember(Group2, indices84,'rows') ;
[~, Cind3] = ismember(Group3, indices84,'rows') ;

AllC = [C(Cind1) C(Cind2) C(Cind3)] ;

Answer 4

[Hisham]

 for clarity, if one combination out of the 1680 combinations was: 7 8 9 4 5 6 1 2 3 then i expect to get C1(84,:) and C1(65,:) and C1(1,:)

any help?

P.S. I've already got the 1680 rows combinations but don't know how to map those to my 84 result of C1