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Edit: My original question implicated D in the problem, but it seems unrelated, so I've removed that part of the question.

I am writing a function that uses functions involving subscripts and an open-ended Sum. It's unreasonably slow. Here's a minimal example (the real situation is much worse):

Sum[
  -2 Exp[-(xx - Subscript[x, k])^2/(V + Subscript[Vx, k]^2)] Subscript[n, k] (xx - Subscript[x, k])/(V + Subscript[Vx, k]^2)
, {k, nsp}] // AbsoluteTiming

enter image description here

Sum[
  -2 Exp[-(xx - subscript[x, k])^2/(V + subscript[Vx, k]^2)] subscript[n, k] (xx - subscript[x, k])/(V + subscript[Vx, k]^2)
, {k, nsp}] // AbsoluteTiming

enter image description here

Well, good thing I'm not using Superscript, because that's 10X worse:

Sum[
  -2 Exp[-(xx - Superscript[x, k])^2/(V + Superscript[Vx, k]^2)] Superscript[n, k] (xx - Superscript[x, k])/(V + Superscript[Vx, k]^2)
, {k, nsp}] // AbsoluteTiming

enter image description here

So, is there some way to tell Sum not to bother trying anything fancy? And what's with the 100-fold range of timing of otherwise identical code?

N.B.: these timings change on rerunning the same code due to some kind of caching

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8
  • $\begingroup$ This is not a speed-up from "without subscripts" but after using "without subscripts" just apply x_[j] -> Subscript[x, j]]. $\endgroup$
    – JimB
    Commented Jun 26, 2021 at 21:27
  • 2
    $\begingroup$ Use Format[x[j_]] := Subscript[x, j] and similar, then the indexed variables will display as subscripts in the output. $\endgroup$
    – Bob Hanlon
    Commented Jun 26, 2021 at 23:35
  • $\begingroup$ You could use Block to temporarily redefine Sum and Subscript with your own versions. These need only implement minimal functionality $\endgroup$
    – mikado
    Commented Jun 27, 2021 at 7:05
  • $\begingroup$ @JimB Yeah I thought of that, but applying that back-transformation eats up basically all of the time-savings. $\endgroup$
    – Chris K
    Commented Jun 27, 2021 at 15:30
  • 3
    $\begingroup$ Why not wrap Inactive around your sum, i.e., D[Inactive[Sum][...], ..]? $\endgroup$
    – Carl Woll
    Commented Jun 27, 2021 at 16:04

1 Answer 1

Reset to default
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Seems like the Sum option I was looking for is Method -> "Procedural":

Sum[
  -2 Exp[-(xx - Subscript[x, k])^2/(V + Subscript[Vx, k]^2)] Subscript[n, k] (xx - Subscript[x, k])/(V + Subscript[Vx, k]^2)
, {k, nsp}, Method -> "Procedural"] // AbsoluteTiming

enter image description here

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