Creating permutations of vectors using basic matlab commands such as loops.

In the problem I have to take a vector x = [x1,x2,x3,x4] ,where 0 <= xi <= m, and m is an inputted integer.

For example if m = 1,

I would need to create vectors

[0,0,0,0]

[1,0,0,0]

[0,1,0,0]

[0,0,1,0]

[0,0,0,1]

[1,1,0,0]

all the way to [1,1,1,1]

[Daniel M]

Do you have a specific question? What have you tried so far? Also, here is a cheeky way of getting your result:

M = dec2bin(0:15)-'0'; % where 15 is length(x)^2-1

[cody madsen]

lets say that m = 4 so i would need all permutations of x = [x1,x2,x3,x4] where 0 <= xi <= 4. so I would need all permutations of [0,0,0,0],[1,0,0,0],[1,1,0,0],[1,1,1,0],[1,1,1,1],[2,0,0,0],[2,1,0,0] all the way to [4,4,4,4]

And I dont even know where to begin so I havent tried anything yet.

also i think i have to use a for-loop structure because i will have to use each of these permutations later in the second part of the problem.

Answer 1

[Daniel M]

You can do it in two lines of code by using ndgrid, and putting the four outputs column-wise into a matrix. That would be the most efficient way. If you're required to use loops, that is lame.

[a,b,c,d] = ndgrid(0:4);
M = [d(:) c(:) b(:) a(:)];

[cody madsen]

it is a basic matlab course so we havent learned many specialized commands. but i have to store each vector seperately so that I can look at each one individually and manipulate it using another loop.

[Daniel M]

I highly doubt you're required to store each vector separately. That would be 625 variables. And how are you supposed to utilize 625 variables in a subsequent loop, with 625 different names? As opposed to using one variable, M above, and looping over the rows of it.

[cody madsen]

for example I would have T(x) = [x1,x2,x3,x4] and use a loop

something like

count = 0

for k= 1: (total number of vectors)

while T(k) ~= [0,0,0,0]

T(k) = (some manipulations)

count = count + 1

end

end

there is obviously more to it than that but that is as example of how I would be using the vectors later in the program

[Daniel M]

Right, but all the vectors would be stored as rows in the matrix T. We're saying the same thing. As for your algorithm, start by calculating how many iterations you'll need, given N number of elements and M number of spots. E.g. you already know for N = 5 (from 0:4) and M = 4 the number of rows of T is 625. But how is that calculated?

Then start very simply using only M = 2 and N = 2, and see if you can code that properly.