How to create N-tuples in Matlab?

What would be the easiest way to create a list of n-tuples in Matlab?

For example, if I want to generate all possible 3-tuples of 0 and 1: I'd want to generate the following set of tuples:

((0,0,0),(0,0,1),(0,1,0),(0,1,1),(1,0,0),(1,0,1),(1,1,0),(1,1,1))

Answer 1

[Bruno Luong]

dec2bin(0:2^3-1)-'0'

[Andrew Dabrowski]

What does the "-'0'" do?

[Walter Roberson]

A = dec2bin(0:2^3-1)

A = 8×3 char array
    '000'
    '001'
    '010'
    '011'
    '100'
    '101'
    '110'
    '111'

dec2bin() outputs characters.

double(A)

ans = 8×3

48 48 48 48 48 49 48 49 48 48 49 49 49 48 48 49 48 49 49 49 48 49 49 49

Those characters have internal codes 48 ('0') or 49 ('1')

B = '0'

B = '0'

double(B)

ans = 48

The character code for '0' is 48

A - B

ans = 8×3

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

subtract the character code for '0' from the character codes for the bits to get relative offsets compared to '0' . Characters that were '0', upon having '0' subtracted, give a result of (numeric) 0 . Characters that were '1', upon having '1' subtracted, give a result of (numeric) 1 because the internal code for the character '1' is (numeric) 1 greater than the internal code for the character '0'

So subtracting '0 converts between characters '0' and '1' to numeric 0 and 1.

Answer 2

[Steven Lord]

If you're using release R2023a or later of MATLAB you could use the combinations function to do this.

v = [0 1];
c = combinations(v, v, v)

c = 8×3 table
    v    v_1    v_2
    _    ___    ___

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

If you need the result as a numeric array rather than a table array:

c = combinations(v, v, v).Variables

c = 8×3

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

Answer 3

[Stephan Reichelt]

There is another quite simple implementation of this problem:

% define the values
v = [0, 1]

v = 1×2

0 1

% generate all combinations of length 3 with repetitions
C = combvec(v,v,v)'

C = 8×3

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

[John D'Errico]

Note that combvec is not found in MATLAB, unless you have the neural net toolbox.

which combvec -all

/MATLAB/toolbox/nnet/nnet/nndatafun/combvec.m

help combvec

 COMBVEC Create all combinations of vectors.
 
   combvec(A1,A2,...) takes any number of inputs A, where each Ai has
   Ni columns, and return a matrix of (N1*N2*...) column vectors, where
   the columns consist of all combinations found by combining one column
   vector from each Ai.
 
   For instance, here the four combinations of two 2-column matrices are
   found.
   
     a1 = [1 2 3; 4 5 6];
     a2 = [7 8; 9 10];
     a3 = combvec(a1,a2)

    Documentation for combvec
       doc combvec