I want to implement all possible 2*2 or 3*3 or n*n matrices by using 0 or/and 1 as their elements.

I want to implement all possible 2*2 or 3*3 or n*n matrices by using 0 or/and 1 as their elements.

Answer 1

[Jan]

n = 3;
M = rem(uint8(floor((0:2^(n*n)-1) .* pow2(0:-1:1-n^2).')), 2);
M = reshape(M, n, n, []);
M(:, :, 1)

ans = 3×3

0 0 0 0 0 0 0 0 0

M(:, :, 2)

ans = 3×3

1 0 0 0 0 0 0 0 0

M(:, :, 512)

ans = 3×3

1 1 1 1 1 1 1 1 1

This is growing extremely fast. After n=7 2^(n*n) leave the range of accurate integer values. For n=6 you need 550 GB RAM. Unfortunately I do not find a way to create this array directly as UINT8 in pure Matlab. Otherwise 69 GB RAM would be sufficient for n=6.

For standard computers, the function is bearable for n=1 to 5 only. It does not seem to be worth to write a C-Mex function for this job.

[Deepak Kumar Sahoo]

Thanks a lot.

[Bruno Luong]

"Unfortunately I do not find a way to create this array directly as UINT8 in pure Matlab"

What about (16 bits char intermediate however)

n = 3;
M = reshape((uint8(dec2bin(uint64(0):2^(n^2)-1))-uint8('0'))',n,n,[])

[Jan]

Almost, @Bruno Luong, if dec2bin() would create the array a little bit smarter (R2021b):

% s = char(ones(numel(d),numBits)*48);

Intermediately a double array is created before it is converted to char. What a pity.

Worth to send an enhancement request to MathWorks.

Did you take a look into the code to extract the bits of the uint64 values in dec2bin?

It would be smart, if we can use bitget with implicit expanding and replying uint8 instead of doubles:

bitget((0:2^(n*n)-1).', 1:n, 'uint8')  % Not working!!!

[Bruno Luong]

No I did not look at the code dec2bin.

After taking a look fromm your attention, yeah the implementation seems not particularly cheap in term of memory and speed.

Answer 2

[Benjamin Thompson]

Looks like 16 combinations of 4 values for the 2x2, and 2^9 combinations of 9 values for the 3x3. Try using dec2bin and reshape in a for loop, and post code and specific questions if you run into problems.