> The task is to go from (as an example)
>
> X: 0 5 6 26
> Y: 10 _10 80 100
>
> to, say:
>
> U: 0 5 10 15 20 25 30 NB. Equidistant mesh.
> V: 10 _10 84 90 94 99 104 NB. Linear interpolation and extrapolation when
> needed.
> NB. The numbers with U>5 are rounded here for
> readability.
> NB. If U=26 were, by chance, in the mesh,
> NB. the value would be (exactly) 100.
>
> (This is not what the data look like in reality, but as an example it
> could suffice.)
I came up with this:
interpolate =. 4 : 0
u =. x
'x y' =. y
v =. (#u) # 0
ux =. x I. u
for_uj. u do.
l =. uj_index { ux
if. l = 0 do. l =. 1 end.
if. l = #x do. l =. l - 1 end.
xl =. l { x
xlm =. (l - 1) { x
yl =. l { y
ylm =. (l - 1) { y
vv =. (xl - xlm) %~ (yl*(uj - xlm)) + ylm*(xl - uj)
v =. vv uj_index } v
end.
v
)
then
x =. 0 5 6 26
y =. 10 _10 80 100
xy =. x,:y
u =. 0 5 10 15 20 25 30
+v =. u interpolate xy
results in the wanted
10 _10 84 89 94 99 104
.
It does what I need, though the code is probably not nice. I would assume a J
programmer would probably avoid the ifs, and perhaps the whole loop
altogether. If anybody can comment, please do.
(The code actually does not rely on the u-mesh to be equidistant, after all.)
Thanks!
Ruda
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