如何在特定条件下生成n个向量的所有可能组合

Question

From A = {[2 31 40],[11 17],[5 8]} , And by using this specific combination of the three vectors (add 100 for each element of a vector, without changing other elements):

  2   31  140         11  117         5  108
  2  131   40        111   17       105    8
102   31   40

I hope to be able to produce all possible combinations (matrix 12x7) between the different lines of these three matrices.

Answer 1

You can do this combining cellfun and bsxfun like this:

B = cellfun(@(n) bsxfun(@plus, n, 100*eye(numel(n))), A, 'UniformOutput', false)

B{:}
ans =
   102    31    40
     2   131    40
     2    31   140

ans =
   111    17
    11   117

ans =
   105     8
     5   108

If you have to have them in the order you had in the question, try flipud or fliplr . An alternative to bsxfun is repmat :

B = cellfun(@(n) 100*eye(numel(n))+repmat(n,numel(n),1), A, 'UniformOutput',false)

Answer 2

You keep asking questions very closely related, and getting answers for them, you should try to connect all the bits by yourself.

In this case, start with the excellent answer from Horchler, inject this result in the (just as excellent) answer from Luis Mendo to get all possible combinations (which you were given many times in your several questions), then build your final matrix.

In practice:

%% // initial data
A = {[2 31 40],[11 17],[5 8]} ;

%% // count a few things before we start
nBlock = numel(A) ;                 %// number of elements sub matrix in "A"
nElem  = cellfun( @numel , A ) ;    %// number of elements in each sub matrix of "A"
nLines = prod(nElem) ;              %// number of lines in the final matrix

%% // Horchler solution (to get all the sub-matrix you requested)
B = cellfun(@(n) bsxfun(@plus, n, 100*eye(numel(n))), A, 'UniformOutput', false) ;

%% // connect both solution
Lines = arrayfun( @linspace , ones(1,nBlock) , nElem , nElem , 'UniformOutput',false) ;

%% // Luis Mendo solution
% // https://stackoverflow.com/questions/21895335/generate-a-matrix-containing-all-combinations-of-elements-taken-from-n-vectors
nBlock = numel(Lines);               %// number of vectors
combs = cell(1,nBlock);              %// pre-define to generate comma-separated list
[combs{end:-1:1}] = ndgrid(Lines{end:-1:1}); %// the reverse order in these two
%// comma-separated lists is needed to produce the rows of the result matrix in lexicographical order 
combs = cat(nBlock+1, combs{:});     %// concat the n n-dim arrays along dimension n+1
combs = reshape(combs,[],nBlock);    %// reshape to obtain desired matrix

%% // Finalisation (can be optimized but it works as it is)
for ii=nLines:-1:1
    tmpLine = [] ;
    for jj=1:nBlock
        tmpLine = [ tmpLine B{1,jj}(combs(ii,jj),:) ] ; %// %#ok<AGROW>
    end
    C(ii,:) = tmpLine ;
end

gives you

>> C
C =
   102    31    40   111    17   105     8
   102    31    40   111    17     5   108
   102    31    40    11   117   105     8
   102    31    40    11   117     5   108
     2   131    40   111    17   105     8
     2   131    40   111    17     5   108
     2   131    40    11   117   105     8
     2   131    40    11   117     5   108
     2    31   140   111    17   105     8
     2    31   140   111    17     5   108
     2    31   140    11   117   105     8
     2    31   140    11   117     5   108