Hessian calculations error in > 3-dimensional problems

[jurreht]

When the interpolated data is 4 dimensions or higher, calculating the Hessian gives an error.

Minimal working example:

using Interpolations

nsamples = 5
fn3 = interpolate(rand(nsamples, nsamples, nsamples), BSpline(Linear()))
@show Interpolations.hessian(fn3, 1, 1, 1)  # Works as expected

fn4 = interpolate(rand(nsamples, nsamples, nsamples, nsamples), BSpline(Linear()))
@show Interpolations.hessian(fn4, 1, 1, 1, 1)  # Error

Expected Results: Some 3x3 and some 4x4 matrix

Result:

Interpolations.hessian(fn3, 1, 1, 1) = [0.0 -0.35524799325078593 -0.08388587488866439; -0.35524799325078593 0.0 -0.2697169146789593; -0.08388587488866439 -0.2697169146789593 0.0]
ERROR: LoadError: MethodError: no method matching symmatrix(::NTuple{10,Float64})
Closest candidates are:
  symmatrix(!Matched::Tuple{Any}) at C:\Users\mail\.julia\packages\Interpolations\TuOdO\src\b-splines\indexing.jl:195
  symmatrix(!Matched::Tuple{L,Any}) where L at C:\Users\mail\.julia\packages\Interpolations\TuOdO\src\b-splines\indexing.jl:199
  symmatrix(!Matched::Tuple{Any,Any,Any}) at C:\Users\mail\.julia\packages\Interpolations\TuOdO\src\b-splines\indexing.jl:196
  ...
Stacktrace:
 [1] hessian(::Interpolations.BSplineInterpolation{Float64,4,Array{Float64,4},BSpline{Linear},NTuple{4,Base.OneTo{Int64}}}, ::Int64, ::Int64, ::Int64, ::Int64) at C:\Users\mail\.julia\packages\Interpolations\TuOdO\src\b-splines\indexing.jl:40
 [2] top-level scope at show.jl:613
 [3] include(::Module, ::String) at .\Base.jl:377
 [4] exec_options(::Base.JLOptions) at .\client.jl:288
 [5] _start() at .\client.jl:484
in expression starting at ...\testhessian.jl:8

versioninfo():

Julia Version 1.4.0
Commit b8e9a9ecc6 (2020-03-21 16:36 UTC)
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: Intel(R) Core(TM) i7-8550U CPU @ 1.80GHz
  WORD_SIZE: 64
  LIBM: libopenlibm

Package version: v0.12.9

[timholy]

symmatrix makes a packed symmetric matrix. Might be enough info for you to help fix this? See #365.