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POIntersection of several sets of results corresponding to different events in matlab
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copied!<p>I have a matrix (5x10000) with the fifth line contains values between 1 and 50 corresponding to different events of an experiment. My goal is to find the columns of the matrix which are the same for different events. In other words, I want the columns results for all possible combinations of different events (subsets of {1,2, .., 50}) (For example: {1,3,7} and {7,1,3} are of course the same combination). It sounds like a problem of intersection of sets that each contains all possible outcomes for a given event. I hope also that the computation time is reasonable.</p> <p>example with a matrix (5x20):</p> <p>A =</p> <pre><code>20 4 4 74 20 20 3 1 1 4 3 3 3 7 4 1 20 3 3 74 36 1 1 11 36 36 3 3 3 1 3 3 3 9 4 3 36 4 3 11 77 1 1 15 77 77 1 3 3 1 1 1 1 10 3 2 77 4 1 15 9 4 4 40 9 9 2 4 4 4 2 2 2 40 1 4 9 3 2 40 3 4 2 6 7 3 4 5 2 7 4 2 7 6 7 2 5 5 1 3 </code></pre> <p>in this case we have seven different events from 1 to 7: line 5</p> <p>for example:</p> <p>the intersection of the results of events 3, 5 and 7 is the vector: [20 36 77 9]'</p> <p>the intersection of the results of events 1, 2, 4 and 7 is the vector: [3 3 1 2]'</p> <p>the intersection of the results of events 3 and 6 are the vectors: [20 36 77 9]' and [74 11 15 40]'</p> <p>So what I want is the common columns for a specified number of different events between 1 and 50. For example, how to get the columns common to 20 different events? The problem becomes more complicated for me when I think to find this result for all possible combinations of 20 events in the set {1,2,..., 50}.</p> <p>I want the common columns for all possible combination for a given number of different events, but I gave the number 20 just as an example on which to base one solution.</p> <p>I'll rephrase my question that to make it clearer:</p> <p>the following matrices are sub-matrix of A, each corresponding to a given event:</p> <p>A1= [3;3;1;2;1]</p> <p>A1 corresponds to results of the event 1</p> <p>A2= [4 1 3 1;1 3 3 3;1 3 1 2;4 4 2 4;2 2 2 2]</p> <p>A2 corresponds to results of the event 2</p> <p>A3= [20 20 74;36 36 11;77 77 15;9 9 40;3 3 3]</p> <p>A3 corresponds to results of the event 3</p> <p>A4= [4 3 3;1 3 3;1 1 1;4 2 2;4 4 4]</p> <p>A4 corresponds to results of the event 4</p> <p>A5= [1 20 3;3 36 4;3 77 4;4 9 3;5 5 5]</p> <p>A5 corresponds to results of the event 5</p> <p>A6= [74 7;11 9;15 10;40 40;6 ]6</p> <p>A6 corresponds to results of the event 6</p> <p>A7= [20 4 3 4 7;36 1 3 4;77 1 1 3;9 4 2 1;7 7 7 7]</p> <p>A7 corresponds to results of the event</p> <p>my goal is to find intersection along the columns of the matrix Ai (1:4,:) i = 1,2, ... 7</p> <p>in other words:</p> <p>intersection(Ai,Aj)(1:4,:) for i and j different</p> <p>intersection(Ai,Aj,Ak)(1:4,:) for i,j and k different</p> <p>intersection(Ai,Aj,Ak,Al)(1:4,:) for i,j,k and l different</p> <p>intersection(Ai,Aj,Ak,Al,Am)(1:4,:) for i,j,k,l and m different</p> <p>intersection(Ai,Aj,Ak,Al,Am,An)(1:4,:) for i,j,k,l,m and n different</p> <p>intersection(Ai,Aj,Ak,Al,Am,An,Ao)(1:4,:) for i,j,k,l,m,n and o different</p> <p>intersection(Ai,Aj,Ak,Al,Am,An,Ao,Ap)(1:4,:) for i,j,k,l,m,n,o and p different</p> <p>when I say "intersection (Ai, Aj)(1:4,:) for i and j different," I want the columns common to the matrix Ai(1:4,:) and Aj(1:4,:)</p> <p>the result for each intersection can be many column vectors, not necessarily one, depending on the columns of the matrix A.</p> <p>I hope that each result contains the vector column of the matrix Ai(1:4,:) followed by the corresponding values of events, such as: if [3 3 1 2]' is the intersection of A1, A2, A4 and A7, I want to get as a result the vector [3 3 1 2 1 2 4 7]'</p> <p>for example: intersection(A1,A2,A3,A4)(1:4,:): my goal is to avoid the following loop:</p> <pre><code>[n1 m1] = size(A1); [n2 m2] = size(A2); [n3 m3] = size(A3); [n4 m4] = size(A4); k=1; for i1=1:m1 for i2=1:m2 for i3=1:m3 for i4=1:m4 if A1(1:4,i1)==A2(1:4,i2) && A2(1:4,i2)==A3(1:4,i3) && A3(1:4,i3)==A4(1:4,i4) intersection1234(:,k) = [A1(1:4,i1);A1(5,i1);A2(5,i2);A3(5,i3);A4(5,i4)]; k=k+1; end end end end end </code></pre>

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