在MATLAB中生成所有可能的配置

Question

I have a 2D matrix A , which contains only binary values:

A = [0 0
     0 1
     1 0
     1 1];

I want to create a function which generates all possible configurations of the values in A . In this case, the word configuration corresponds to any possible combination of values within a row of the data (ie, pairs of columns, triplets, etc). For example, in the simple case of the data provided above, i want the function to return:

B = [ A(:,1)==1, ...
      A(:,2)==1, ...
      A(:,1)==0 & A(:,2)==0, ...
      A(:,1)==0 & A(:,2)==1, ...
      A(:,1)==1 & A(:,2)==0, ...
      A(:,1)==1 & A(:,2)==1];

B =

     0     0     1     0     0     0
     0     1     0     1     0     0
     1     0     0     0     1     0
     1     1     0     0     0     1

However, i would like the function to be able to handle matrices of any size. In the case of a 3-column matrix, the resulting number of configurations is much larger:

A = [ 0 0 0
      0 0 1
      0 1 0
      0 1 1
      1 0 0
      1 0 1
      1 1 0
      1 1 1]

B = [A(:,1)==1, ...
     A(:,2)==1, ...
     A(:,3)==1, ...
     A(:,1)==0 & A(:,2)==0, ...
     A(:,1)==0 & A(:,2)==1, ...
     A(:,1)==0 & A(:,3)==0, ...
     A(:,1)==0 & A(:,3)==1, ...
     A(:,1)==1 & A(:,2)==0, ...
     A(:,1)==1 & A(:,2)==1, ...
     A(:,1)==1 & A(:,3)==0, ...
     A(:,1)==1 & A(:,3)==1, ...
     A(:,2)==0 & A(:,3)==0, ...
     A(:,2)==0 & A(:,3)==1, ...
     A(:,2)==1 & A(:,3)==0, ...
     A(:,2)==1 & A(:,3)==1, ...
     A(:,1)==0 & A(:,2)==0 & A(:,3)==0, ...
     A(:,1)==0 & A(:,2)==0 & A(:,3)==1, ...
     A(:,1)==0 & A(:,2)==1 & A(:,3)==0, ...
     A(:,1)==0 & A(:,2)==1 & A(:,3)==1, ...
     A(:,1)==1 & A(:,2)==0 & A(:,3)==0, ...
     A(:,1)==1 & A(:,2)==0 & A(:,3)==1, ...
     A(:,1)==1 & A(:,2)==1 & A(:,3)==0, ...
     A(:,1)==1 & A(:,2)==1 & A(:,3)==1]

This seems like a pretty challenging problem, so i'm wondering if the SO community has any ideas!

I use this [ugly] function currently. It relies on the the allcomb function from the MATLAB file exchange:

function [B] = allconfigs(A)

% some information about A
N = size(A,1);  
D = size(A,2);

% set up storage
B = A==1;

% iterate over levels of dimensionality (pairs, triplets, etc)
%   I==1 can be ignored, as it is equal to A.
%   I==(D-1) can be ignored, as it is an identity matrix of size N

for I = 2:(D-1)

%   get all possible values given dimensionality I
    possiblevalues  = cell(1,I);
    for j = 1:I
        possiblevalues{j} = [0 1];
    end
    possiblevalues = allcomb(possiblevalues{:});
    npossible = size(possiblevalues,1);

%   get all possible combinations of dimensions
    combinations = combnk(1:D,I);
    ncombs = size(combinations,1);

%   check if the data under each dimension combination matches each value possibility
    for J = 1:ncombs
        dimensions = A(:,combinations(J,:));

        for K = 1:npossible
            matches = dimensions == repmat(possiblevalues(K,:),[N,1]);
            matches = all(matches==1,2);

            B = cat(2,B,matches);
        end
    end
end

% if I is the full set of data, the matches are an identity matrix.
B = cat(2,B,eye(N));
return

That function returns the correct results (though note that the columns it produces are not in the same order that i typed out). Its just so darn ugly. Does anyone know of something more elegant?

Answer 1

I still got a problem understanding the pattern which you generate for B, nevertheless there are probably only one or two lines missing. My idea to simplify is, to encode the combinations in [1,0,nan] where nan stands for don't care. For example A(:,1)==1 & A(:,2)==0 would be represented as [1,0,nan]

This code builds up all combinations you want in B. As I did not fully understand the pattern, it generates all possible combinations:

c=size(A,2);
p={[0,1,nan]};
%1=colum is 1
%0=colum is 0
%nan= don't care
all_rows=allcomb(p{ones(c,1)});
%TODO filter out unwanted rows

Now it's simple, compare each row in all_rows with each colum of your input. Its true if both are equal or the reference is nan (don't care)

B=true(size(A,1),size(all_rows,1));
for ix=1:size(all_rows,1)
    B(:,ix)=all(bsxfun(@(a,b)isnan(a)|eq(a,b),all_rows(ix,:),A),2);
end