f

#### listing all subsets of a given set

```Hi All,

Is there a function in MATLAB that produces all subsets of a given
set?

Or alternatively, what is an efficient way to list all subsets in
MATLAB?

The original set is a vector of indices (integers).

(context: I need this for some model-selection experiments in
regression analysis.)
```
 0
mahani (4)
9/4/2004 8:47:27 PM
comp.soft-sys.matlab 211266 articles. 19 followers. lunamoonmoon (258) is leader.

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```I wrote a simple recursive function that does the job with the
following performance compared to "perms" in MATLAB:

Number Number
of of time time
elements repetitions perms my-function
------------------------------------------
% 4 1000 0.2 0.23
% 5 1000 0.36 0.491
% 6 1000 0.851 1.022
% 7 1000 7.291 2.013
% 8 100 6.119 0.41
% 9 10 7.041 0.09

(Of course, for n>4 the two are not directly comparable: 2^5=32
5!=120)

If there are faster algorithms please let me know.

reza

reza mahani wrote:
>
>
> Hi All,
>
> Is there a function in MATLAB that produces all subsets of a given
> set?
>
> Or alternatively, what is an efficient way to list all subsets in
> MATLAB?
>
> The original set is a vector of indices (integers).
>
> (context: I need this for some model-selection experiments in
> regression analysis.)
```
 0
mahani (4)
9/5/2004 2:17:23 AM
```reza:
<SNIP favorably compares his/her algo to ML's <perms> and
asks for even better ways of doing it...

well, could you show CSSM your code?
us
```
 0
us1 (8052)
9/5/2004 2:23:17 AM
```function S = AllSubsets(V)
% 9/4/04: [Reza Mahani]

% Lists all subsets of a set given by the vector V of length
n.

% Assumption: No "nan" in V.

% I use a "recursive" algorithm, AllSubsets call itself on
one-element-smaller subsets.

% CALL: S = AllSubsets(V)

[m n] = size(V);

if m>n, n=m; V=V'; end % makes V a row vector

S = nan*zeros(2^n,n); % initialization

%

i0 = 1;

%

if max(m,n)==1

S(i0,:) = V;

return

end

if n==2

S(i0:i0+2,:) = [V ; V(1) nan ; nan V(2)];

return

end

for i=1:(n-1)

S1 = AllSubsets(V(i+1:n));

S(i0:i0+2^(n-i)-1,i:n) = [ones(2^(n-i),1)*V(i) , S1];

i0 = i0 + 2^(n-i);

end

S(i0,n) = V(n);

return
```
 0
mahani (4)
9/5/2004 2:33:59 AM
```I just found out how stupid was my question. The following line gives
the result:

---------------------------------------

function SI = AllSubsets2(n)

SI = dec2bin(0:2^n-1,n);

---------------------------------------

Yes, just one line. However, my previous code was not very bad, see
how the two are compared:

n repetitions first second
3.0000 100.0000 0.0100 0.0100
4.0000 100.0000 0.0200 0.0200
5.0000 100.0000 0.0500 0.0100
6.0000 100.0000 0.1010 0.0200
7.0000 100.0000 0.2010 0.0400
8.0000 100.0000 0.4110 0.0600
```
 0
mahani (4)
9/5/2004 8:22:16 PM

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