How to create N-tuples in Matlab?

Question

Pontus Vikstål 2018-9-29

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https://ww2.mathworks.cn/matlabcentral/answers/421376-how-to-create-n-tuples-in-matlab

回答： Steven Lord 2024-1-5

采纳的回答： Bruno Luong

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))

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Answer 1

Bruno Luong 2018-9-29

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

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Andrew Dabrowski 2021-9-30

What does the "-'0'" do?

Walter Roberson 2021-9-30

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A = dec2bin(0:2^3-1)
A = 8×3 char array
    '000'
    '001'
    '010'
    '011'
    '100'
    '101'
    '110'
    '111'

dec2bin() outputs characters.

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

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.

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Answer 2

Steven Lord 2024-1-5

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

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Answer 3

Stephan Reichelt 2024-1-5

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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

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John D'Errico 2024-1-5

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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

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