0
$\begingroup$

I want to try to make a list of lists of variable length in the following way

varNames = Table[Subscript[x, i], {i, 1, dim}]
varRange = Table[{varNames[[i]], 1, maxRange}, {i, 1, Length[varNames]}]

Flatten[ Table[varNames, varRange], dim -1]

Here, the variables dim and maxRange are arbitrary, and I will be setting them depending on the situation.

This does not work, because

a) The Table function gives the error

Non-list iterator varRange at position 2 does not evaluate to a real numeric value.

b) The would-be iterator needs to lose it's last set of brackets, i.e.

{{x1, 1, 4}, {x2, 1, 4}, {x3, 1, 4}}

needs to be

{x1, 1, 4}, {x2, 1, 4}, {x3, 1, 4}

Ideally, for dim=3 and maxRange=4, I want to get something like

varNames = {x1, x2, x3} 
varRange = {{x1, 1, 4}, {x2, 1, 4}, {x3, 1, 4}}

and the instruction would be to create a list of lists in the following way

Flatten[Table[{x1, x2, x3}, {x1, 1, 4}, {x2, 1, 4}, {x3, 1, 4} ], 2]

Is there a way to fix this or a simpler way to do what I want?

$\endgroup$
  • $\begingroup$ Your last line generates a list of numbers {{1, 1, 1}, {1, 1, 2}, {1, 1, 3}, {1, 1, 4}, {1, 2, 1}, {1, 2, 2}, {1,2, 3}, {1, 2, 4}...., i.e. Tuples[Range[4], 3]. Is that what you intend? Or are you looking for a list of variable names? $\endgroup$ – MelaGo Jul 10 at 18:29
  • $\begingroup$ Yes, this is what I intend. I'm actually trying to avoid using Tuples[ ] because I am dealing with a large length (order 100 and above) list and Tuples causes the kernel to quit. I find that using Table[] this way avoids crashing Mathematica. $\endgroup$ – nonreligious Jul 10 at 18:34
  • 1
    $\begingroup$ 4^100 elements is more than the number of particles in the observable universe; are you sure this is the list you want to create? $\endgroup$ – lirtosiast Jul 10 at 19:00
  • $\begingroup$ Sorry, maybe I mis-wrote what I meant but it would be more 100^4, or 100^6. $\endgroup$ – nonreligious Jul 10 at 19:01
1
$\begingroup$

I found what I think might be a solution to this, in an answer to another question, here.

dim = 4;
varNames = Table[Subscript[x, i], {i, 1, dim}]
varRange = Table[{varNames[[i]], 1, 100}, {i, 1, Length[varNames]}]
a = Flatten[Table[varRange[[All, 1]], ##] & @@ varRange, dim - 1]

This makes use of the slot sequence ## which hurts my head to think about.

Still takes a while, and I can't monitor what's going inside the iteration to create the table. And still takes up a lot of memory.

Can this be improved upon?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.