Power Set

I just got MatLab and I have to preform some simulations. To do them correctly I need to have the program run over all subsets of a given set of options. What is the easiest way to do this? Is there a package that already exists to do this in Matlab?

Thanks for any help!

[Paulo Abelha]

You might want to use my funciton: https://uk.mathworks.com/matlabcentral/fileexchange/62752-powerset--s--

Answer 1

[Joseph]

function logical_indices = logical_indices_for_power_set(set_size)
%LOGICAL_INDICES_FOR_POWER_SET creates a cell array containing all possible
%combinations of logical indices to extract the members of a power set
%by indexing into the original set. This saves the memory overhead of
%storage of the set elements themselves, and instead only needs storage for
%the indices of the original set. 
%2^N cells of logical indices each of [1 x set_size].

%Converts the sequence of numbers from 0 to 2^set_size-1 to binary string
%representation. The characters of the string are turned into ascii
%characters. 48 is the ascii code for zero, so testing for equality will a 
%a matrix of logical indices, where the first row identifies all elements
%of the set.

logical_indices = mat2cell(double(dec2bin(0:2^set_size-1,set_size))==48,ones(2^set_size,1));

Answer 2

[Wayne King]

How many items are you trying to do this for? This can get computationally expensive very fast. But combnk might help you.

% the set
x = 1:4;
for nn = 1:4
% all the combinations taken nn items at a time
combnz{nn} = combnk(x,nn);
end

[Jacob]

Thanks, Wanye. I know that it gets computational expensive. The number of subsets is 2^N if I recall correctly. I have a computer that can handle a reasonable set, but my University has computers made for such simulations with only MathLab, Linux, and 64 GB RAM.

So, after I get the combnz file, I can write a loop that goes through it first by each column in the main area, and then inside each cell go by row until out of rows, then to the next column in the main area?

Do you think that is the easiest way to go about this?

What I plan to do with it is that each number represents a risky asset and I am determining which bundle of risky assets seems to have the highest payoff under different situations. So to do that I have to have my simulation compare all possible bundles.

[Wayne King]

Yes each cell array will contain the elements of your set taken k at a time with each row of the cell array corresponding to one of the elements of the power set. Check the reference page for combnk() about trying this if the set has more than 15 elements.

Answer 3

[holly chen]

function PSet = PowerSet(SetA)

% Generate Power Set

% take input like {1,3,'B'}
% convert to {'1','3','B'}
 SetB={};
 for i=1:length(SetA)
     if isnumeric(SetA{i})
       SetB= union(SetB,[num2str(SetA{i}),' ']);
     elseif ischar(SetA{i})
       SetB= union(SetB,[SetA{i},' ']);
     else
       error('Error input');
     end;
 end;

   Set= unique(SetB);    % It is a set, no repeat elements
   PSet = fPowerSet(Set);
   for i=1:length(PSet)
       PSet(i)=deblank(PSet(i)); %trimming
   end;
end

function PSet = fPowerSet(Set)

     if isempty(Set)   
        PSet={''};
        return; 
     else
        A = Set{1};
        P = fPowerSet(setdiff(Set, A));
        AP = {};
        for i =1: length(P)
            AP = union(AP, [A, P{i}]);

        end 
        PSet = union(P, AP);
        return;
     end ;
 end

testing case:

PowerSet({1,12,'A'})

ans: '' '1' '1 12' '1 12 A' '1 A' '12' '12 A' 'A'

Answer 4

[Paulo Abelha]

You might want to use my funciton: https://uk.mathworks.com/matlabcentral/fileexchange/62752-powerset--s--