I want to divide one vector to two vectors that complement each other .. How can I obtain all possible combinations of these 2 vectors ?

I want to divide this vector [7 3 3 3 3 3 2 1 1 2] into 2 vectors that complement each other, for example: divide it to : A = [4 2 1 2 1 1 1 1 1 0] and B = [3 1 2 1 2 2 1 0 0 2] .. How can I obtain the all combinations of these 2 vectors ?

Answer 1

[James Tursa]

You could use the FEX submission ALLCOMB by Jos for this. E.g.,

x = your original vector of non-negative integers
c = cellfun(@(y)0:y,num2cell(x),'uni',false);
A = allcomb(c{:});
B = bsxfun(@minus,x,A);

The rows of A and B contain all of the possibilities. The usual caveat applies here ... if you have too many numbers with values that are too high this will blow up your memory and you will need to solve your problem a different way.

ALLCOMB can be found here:

https://www.mathworks.com/matlabcentral/fileexchange/10064-allcomb-varargin-

[Walter Roberson]

Install https://www.mathworks.com/matlabcentral/fileexchange/10064-allcomb-varargin-

[Mahmoud Ahmed]

I use this code instead of using ALLCOMB

x = [8 3 3 3 3 3 2 1 1 1] %Vector
c = cellfun(@(y)0:y,num2cell(x),'uni',false);
A = cell(1,10);
[A{:}] = ndgrid(c{:});
A = reshape(cat(10 + 1, A{:}), [], 10);
B = bsxfun(@minus,x,A);

[Walter Roberson]

I would suggest changing to

A = reshape( cat(length(A) + 1, A{:}), [], length(A));

[Mahmoud Ahmed]

Ok .. Done :) I have another problem: There is variable in the workspace that I want to see its values, but matlab said: Cannot display summaries of variables with more than 524288 elements. What can I do ?

[Walter Roberson]

You could get a job with Mathworks and help them to change that limit of 2^19 elements.

Or you could call max() and min() and whatever on the arrays when you want to know the summary statistics, and you could disp() portions of it. Or you could assign a sub-portion of the large array to a variable and then look at the new variable in the workspace browser.