Generate combinations with scaleable code

I have a tight piece of code which generates a 16x4 matrix which essentially is 16 vectors with 4 elements each and i want all the combinations where the vector elements are -1 or 1

[a1,a2,a3,a4] = ndgrid([1 -1],[1 -1],[1 -1],[1 -1]);

a_all_combos = [a1(:),a2(:),a3(:),a4(:)]

clear a1 a2 a3 a4

The code yields the following output:

1 1 1 1

-1 1 1 1

1 -1 1 1

-1 -1 1 1

1 1 -1 1

-1 1 -1 1

1 -1 -1 1

-1 -1 -1 1

1 1 1 -1

-1 1 1 -1

1 -1 1 -1

-1 -1 1 -1

1 1 -1 -1

-1 1 -1 -1

1 -1 -1 -1

-1 -1 -1 -1

However, this code does not scale-up nicely if I want nine-element vectors, yielding a x9 matrix.

Would welcome any suggestions on how to do this concisely.

Answer 1

[the cyclist]

There happens to be a quite obfuscated way to do this:

n = 9;
a_all_combos = 2*(dec2bin(0:2^n-1) - '0') - 1

a_all_combos = 512×9

-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 1

[Howard Wilton]

Thanks very much. Neat!