CODEWITHSUNDEEP
loopsfor-loopgnuplot
Socob
Socob

Reputation: 1284

Gnuplot: Nested “plot” iteration (“plot for”) with dependent loop indices

I have recently attempted to concisely draw several graphs in a plot using gnuplot and the plot for ... syntax. In this case, I needed nested loops because I wanted to pass something like the following index combinations (simplified here) to the plot expression:

So i loops from 0 to some upper limit N and for each iteration of i, j loops from 0 to i (so i <= j). I tried doing this with the following:

# f(i, j, x) = ...
N = 5
plot for [i=0:N] for [j=0:i] f(i, j, x) title sprintf('j = %d', j)

but this only gives five iterations with j = 0 every time (as shown by the title). So it seems that gnuplot only evaluates the for expressions once, fixing i = 0 at the beginning and not re-evaluating to keep up with changing i values. Something like this has already been hinted at in this answer (“in the plot for ... structure the second index cannot depend on the first one.”).

Is there a simple way to do what I want in gnuplot (i.e. use the combinations of indices given above with some kind of loop)? There is the do for { ... } structure since gnuplot 4.6, but that requires individual statements in its body, so it can’t be used to assemble a single plot statement. I suppose one could use multiplot to get around this, but I’d like to avoid multiplot if possible because it makes things more complicated than seems necessary.

Upvotes: 3

Views: 659

Answers (1)

Miguel
Miguel

Reputation: 7627

I took your problem personally. For your specific problem you can use a mathematical trick. Remap your indices (i,j) to a single index k, such that

(0,0) -> (0)
(1,0) -> (1)
(1,1) -> (2)
(2,0) -> (3)
...

It can be shown that the relation between i and j and k is

k = i*(i+1)/2 + j

which can be inverted with a bit of algebra

i(k)=floor((sqrt(1+8.*k)-1.)/2.)
j(k)=k-i(k)*(i(k)+1)/2

Now, you can use a single index k in your loop

N = 5
kmax = N*(N+1)/2 + N
plot for [k=0:kmax] f(i(k), j(k), x) title sprintf('j = %d', j(k))

Upvotes: 1

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