# Interpolations WeightedIndex trouble

**URL:** <https://discourse.julialang.org/t/interpolations-weightedindex-trouble/45547>\
**Category:** General Usage\
**Tags:** question, interpolations\
**Created:** [August 26, 2020, 3:40am UTC](https://discourse.julialang.org/t/interpolations-weightedindex-trouble/45547 "2020-08-26T03:40:42Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![tbeason](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tbeason/32/15898_2.png) [@tbeason](https://discourse.julialang.org/u/tbeason)\
**Post date:** [August 26, 2020, 3:40am UTC](https://discourse.julialang.org/t/interpolations-weightedindex-trouble/45547/1 "2020-08-26T03:40:42Z")

</div>

Have a bit of an advanced Interpolations.jl question here… I guess I just don’t understand how to use the `weightedindices` or its output.

Based on the docs, I assumed that I pass it the point to which I would want to interpolate, and then I can just use the output to interpolate rather than using the interpolation object itself. It seems that isn’t quite how it works?

```julia
julia> using Interpolations

julia> y = sort(rand(15))
15-element Array{Float64,1}:
 0.047341383036748175
 0.05128111599355356
 0.10902355783965456
 0.16089341732308426
 0.3088983112692745
 0.5533832682360411
 0.5771335063852496
 0.6641445249519693
 0.6662254205787557
 0.7066663941780806
 0.758685974796028
 0.7757959797477969
 0.8656767947261979
 0.9239102725958703
 0.9757619516714087

julia> x = collect(1:10.0)
10-element Array{Float64,1}:
  1.0
  2.0
  3.0
  4.0
  5.0
  6.0
  7.0
  8.0
  9.0
 10.0

julia> F = sin.(x.*y')
10×15 Array{Float64,2}:
 0.0473237 0.0512586 0.108808 0.1602 0.304009 0.525569 0.545624 0.616386 0.618023 0.649302 0.687968 0.700285 0.761534 0.797964 0.828129
 0.0945414 0.102383 0.216323 0.316262 0.57924 0.894256 0.914499 0.970739 0.97173 0.987628 0.998573 0.999816 0.987138 0.961874 0.928395
 0.141547 0.153237 0.32127 0.464155 0.79964 0.996011 0.987131 0.91242 0.909847 0.852941 0.761442 0.72718 0.518044 0.361487 0.21267
 0.188236 0.203689 0.422402 0.600058 0.944344 0.800458 0.739992 0.466221 0.458842 0.309747 0.106646 0.0383993 -0.315624 -0.526134 -0.689975
 0.234503 0.253605 0.518519 0.720461 0.999654 0.365971 0.253141 -0.178174 -0.188402 -0.381797 -0.606648 -0.672356 -0.927172 -0.995694 -0.986184
 0.280244 0.302855 0.608478 0.822254 0.960335 -0.177757 -0.315713 -0.746825 -0.755069 -0.890483 -0.987184 -0.998341 -0.886222 -0.674084 -0.41561
 0.325357 0.351308 0.691212 0.902808 0.83011 -0.668426 -0.782295 -0.997992 -0.998809 -0.972683 -0.826231 -0.753003 -0.221593 0.183147 0.520254
 0.369742 0.398838 0.765738 0.960041 0.621304 -0.959571 -0.99546 -0.824902 -0.815378 -0.589027 -0.212075 -0.0767419 0.598982 0.894851 0.998854
 0.413298 0.445319 0.831172 0.992475 0.353685 -0.964286 -0.886156 -0.301137 -0.283226 0.0767367 0.518408 0.643436 0.998023 0.895514 0.599535
 0.455927 0.490629 0.886736 0.999273 0.0525853 -0.681165 -0.489791 0.350645 0.370056 0.705748 0.964535 0.995393 0.694705 0.18461 -0.32673

julia> itp = LinearInterpolation((x,y),F,extrapolation_bc=Line())
10×15 extrapolate(interpolate((::Array{Float64,1},::Array{Float64,1}), ::Array{Float64,2}, Gridded(Linear())), Line()) with element type Float64:
 0.0473237 0.0512586 0.108808 0.1602 0.304009 0.525569 0.545624 0.616386 0.618023 0.649302 0.687968 0.700285 0.761534 0.797964 0.828129
 0.0945414 0.102383 0.216323 0.316262 0.57924 0.894256 0.914499 0.970739 0.97173 0.987628 0.998573 0.999816 0.987138 0.961874 0.928395
 0.141547 0.153237 0.32127 0.464155 0.79964 0.996011 0.987131 0.91242 0.909847 0.852941 0.761442 0.72718 0.518044 0.361487 0.21267
 0.188236 0.203689 0.422402 0.600058 0.944344 0.800458 0.739992 0.466221 0.458842 0.309747 0.106646 0.0383993 -0.315624 -0.526134 -0.689975
 0.234503 0.253605 0.518519 0.720461 0.999654 0.365971 0.253141 -0.178174 -0.188402 -0.381797 -0.606648 -0.672356 -0.927172 -0.995694 -0.986184
 0.280244 0.302855 0.608478 0.822254 0.960335 -0.177757 -0.315713 -0.746825 -0.755069 -0.890483 -0.987184 -0.998341 -0.886222 -0.674084 -0.41561
 0.325357 0.351308 0.691212 0.902808 0.83011 -0.668426 -0.782295 -0.997992 -0.998809 -0.972683 -0.826231 -0.753003 -0.221593 0.183147 0.520254
 0.369742 0.398838 0.765738 0.960041 0.621304 -0.959571 -0.99546 -0.824902 -0.815378 -0.589027 -0.212075 -0.0767419 0.598982 0.894851 0.998854
 0.413298 0.445319 0.831172 0.992475 0.353685 -0.964286 -0.886156 -0.301137 -0.283226 0.0767367 0.518408 0.643436 0.998023 0.895514 0.599535
 0.455927 0.490629 0.886736 0.999273 0.0525853 -0.681165 -0.489791 0.350645 0.370056 0.705748 0.964535 0.995393 0.694705 0.18461 -0.32673

julia> wi = Interpolations.weightedindexes((Interpolations.value_weights,), Interpolations.itpinfo(itp)...,(5.0,0.5))
(Interpolations.WeightedAdjIndex{2,Float64}(4, (0.0, 1.0)), Interpolations.WeightedAdjIndex{2,Float64}(1, (1.5, -0.5)))

julia> F[wi...]
0.2249513239238678

julia> itp(5,0.5)
0.5043358836315593

```

---

<div class="post-metadata">

**Author:** ![tim.holy](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tim.holy/32/52_2.png) [@tim.holy](https://discourse.julialang.org/u/tim.holy)\
**Post date:** [August 26, 2020, 2:26pm UTC](https://discourse.julialang.org/t/interpolations-weightedindex-trouble/45547/2 "2020-08-26T14:26:26Z")

</div>

WeightedIndexes refer to the integral indices of the underlying array, not the spatial location.

---

<div class="post-metadata">

**Author:** ![tbeason](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tbeason/32/15898_2.png) [@tbeason](https://discourse.julialang.org/u/tbeason)\
**Post date:** [August 26, 2020, 3:49pm UTC](https://discourse.julialang.org/t/interpolations-weightedindex-trouble/45547/3 "2020-08-26T15:49:30Z")

</div>

Ok I can see that now from the result. Presumably there is an intermediate function that Interpolations.jl uses to go from the actual point (in this case `(5,0.5)`), down to the indices. Could you point me in that direction? I am looking through where I think it should be and I do not see anything.

[https://github.com/JuliaMath/Interpolations.jl/blob/master/src/gridded/indexing.jl](https://github.com/JuliaMath/Interpolations.jl/blob/master/src/gridded/indexing.jl)

---

<div class="post-metadata">

**Author:** ![tbeason](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tbeason/32/15898_2.png) [@tbeason](https://discourse.julialang.org/u/tbeason)\
**Post date:** [August 26, 2020, 11:42pm UTC](https://discourse.julialang.org/t/interpolations-weightedindex-trouble/45547/4 "2020-08-26T23:42:17Z")

</div>

Figured it out I think! Not sure if this would always be true or not because my example uses one of the convenience constructors, but this piece in the call to `weightedindexes`

```julia
Interpolations.itpinfo(itp)

```

should be

```julia
Interpolations.itpinfo(itp.itp)

```

Ouput

```julia
julia> wi = Interpolations.weightedindexes((Interpolations.value_weights,), Interpolations.itpinfo(itp.itp)...,(5,0.5))
(Interpolations.WeightedAdjIndex{2,Float64}(4, (0.0, 1.0)), Interpolations.WeightedAdjIndex{2,Float64}(5, (0.21834990953368805, 0.781650090466312)))

julia> F[wi...]
0.5043358836315593 # now same as itp(5,0.5)

```

I should, and this builds on what Tim was saying (and already _did_ say in the Dev Docs), that this specific way only works for Linear interpolation. Otherwise the weights should be used to index the interpolant coefficients.

---

<div class="post-metadata">

**Author:** ![tbeason](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tbeason/32/15898_2.png) [@tbeason](https://discourse.julialang.org/u/tbeason)\
**Post date:** [August 27, 2020, 12:47am UTC](https://discourse.julialang.org/t/interpolations-weightedindex-trouble/45547/5 "2020-08-27T00:47:46Z")

</div>

Just a further warning on this. The extrapolation that takes place by doing this is linear but not the same as the `Line()` boundary condition given by the package.