CubicSpline errors with SingularException for repeated time point

[Ickaser]

Describe the bug 🐞

CubicSpline interpolations error with a LinearAlgebra.SingularException when a time point is repeated.

Expected behavior

Perhaps a fallback to some default behavior, but probably a more descriptive error stating that time points are repeated, like happens if the time points are not sorted. I am not sure what a cubic spline's behavior "should" be for a repeated time point, so probably an error is best.

Minimal Reproducible Example 👇

This fails:

using DataInterpolations
u = [1.0, 2.0, 3.0]
t = [1.0, 1.0, 2.0]
CubicSpline(u, t)

This works:

u = [1.0, 2.0, 3.0]
t = [1.0, 1.0+eps(Float64), 2.0]
CubicSpline(u, t)

This also fails:

u = [1.0, 2.0, 3.0]
t = [1.0, 1.0+eps(Float64)/2, 2.0]
CubicSpline(u, t)

Error & Stacktrace ⚠️

ERROR: LinearAlgebra.SingularException(1)
Stacktrace:
  [1] checknonsingular
    @ C:\Program Files\julia-1.11.1\share\julia\stdlib\v1.11\LinearAlgebra\src\factorization.jl:69 [inlined]
  [2] _check_lu_success
    @ C:\Program Files\julia-1.11.1\share\julia\stdlib\v1.11\LinearAlgebra\src\lu.jl:84 [inlined]
  [3] _lu_tridiag!
    @ C:\Program Files\julia-1.11.1\share\julia\stdlib\v1.11\LinearAlgebra\src\lu.jl:652 [inlined]
  [4] lu!(A::LinearAlgebra.Tridiagonal{Float64, Vector{…}}, pivot::LinearAlgebra.RowMaximum; check::Bool, allowsingular::Bool)
    @ LinearAlgebra C:\Program Files\julia-1.11.1\share\julia\stdlib\v1.11\LinearAlgebra\src\lu.jl:578
  [5] lu! (repeats 2 times)
    @ C:\Program Files\julia-1.11.1\share\julia\stdlib\v1.11\LinearAlgebra\src\lu.jl:569 [inlined]
  [6] _lu
    @ C:\Program Files\julia-1.11.1\share\julia\stdlib\v1.11\LinearAlgebra\src\lu.jl:347 [inlined]
  [7] lu
    @ C:\Program Files\julia-1.11.1\share\julia\stdlib\v1.11\LinearAlgebra\src\lu.jl:341 [inlined]
  [8] \(A::LinearAlgebra.Tridiagonal{Float64, Vector{Float64}}, B::Vector{Float64})
    @ LinearAlgebra C:\Program Files\julia-1.11.1\share\julia\stdlib\v1.11\LinearAlgebra\src\generic.jl:1132
  [9] CubicSpline(u::StepRangeLen{…}, t::Vector{…}; extrapolation::DataInterpolations.ExtrapolationType.T, extrapolation_left::DataInterpolations.ExtrapolationType.T, extrapolation_right::DataInterpolations.ExtrapolationType.T, cache_parameters::Bool, assume_linear_t::Float64)
    @ DataInterpolations C:\Users\iwheeler\.julia\packages\DataInterpolations\6jW9q\src\interpolation_caches.jl:649
 [10] CubicSpline(u::StepRangeLen{Float64, Base.TwicePrecision{…}, Base.TwicePrecision{…}, Int64}, t::Vector{Float64})
    @ DataInterpolations C:\Users\iwheeler\.julia\packages\DataInterpolations\6jW9q\src\interpolation_caches.jl:625
 [11] top-level scope
    @ REPL[32]:1

For reference, out-of-order time points

u = [1.0, 2.0, 3.0]
t = [1.0, 1.0-eps(Float64), 2.0]
CubicSpline(u, t)

yield the following stacktrace:

ERROR: ArgumentError: The second argument (`t`), which is used for the interpolation domain, is not sorted.
It looks like the arguments `u` and `t` were inversed, make sure you used the arguments in the correct order.
Stacktrace:
 [1] munge_data(u::StepRangeLen{…}, t::Vector{…}; check_sorted::Vector{…}, sorted_arg_name::Tuple{…})
   @ DataInterpolations C:\Users\iwheeler\.julia\packages\DataInterpolations\6jW9q\src\interpolation_utils.jl:109
 [2] munge_data
   @ C:\Users\iwheeler\.julia\packages\DataInterpolations\6jW9q\src\interpolation_utils.jl:94 [inlined]
 [3] CubicSpline(u::StepRangeLen{…}, t::Vector{…}; extrapolation::DataInterpolations.ExtrapolationType.T, extrapolation_left::DataInterpolations.ExtrapolationType.T, extrapolation_right::DataInterpolations.ExtrapolationType.T, cache_parameters::Bool, assume_linear_t::Float64)
   @ DataInterpolations C:\Users\iwheeler\.julia\packages\DataInterpolations\6jW9q\src\interpolation_caches.jl:633
 [4] CubicSpline(u::StepRangeLen{Float64, Base.TwicePrecision{…}, Base.TwicePrecision{…}, Int64}, t::Vector{Float64})
   @ DataInterpolations C:\Users\iwheeler\.julia\packages\DataInterpolations\6jW9q\src\interpolation_caches.jl:625
 [5] top-level scope
   @ REPL[34]:1

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

[82cc6244] DataInterpolations v8.6.1