Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Unstable quadratic spline #353

Closed
marcobonici opened this issue Nov 9, 2024 · 9 comments · Fixed by #354
Closed

Unstable quadratic spline #353

marcobonici opened this issue Nov 9, 2024 · 9 comments · Fixed by #354
Labels
bug Something isn't working

Comments

@marcobonici
Copy link

Describe the bug 🐞

When using the quadratic spline on some smooth data, I get some oddly unstable behaviour which I do not get when using Linear, Cubic, or Akima interpolation.

image

scipy quadratic spline doesn't give the problems I am getting here.

Expected behavior

I would expect the interpolated function to be smooth.

Minimal Reproducible Example 👇

Here is the MWE, with the input data and the few lines of code used to interpolate.

using DataInterpolations
using Plots
x = [
    0.0010000000000000002,
    0.0017752321946474007,
    0.0024267002652361017,
    0.0033172416515725852,
    0.004534590584823373,
    0.006198677676141205,
    0.008473445223762798,
    0.011582998457310494,
    0.015833683905314526,
    0.021644269999465116,
    0.027500000000000004,
    0.035,
    0.045,
    0.05500000000000001,
    0.065,
    0.07500000000000001,
    0.08500000000000002,
    0.095,
    0.10500000000000001,
    0.11500000000000002,
    0.125,
    0.135,
    0.14500000000000002,
    0.15500000000000003,
    0.16500000000000004,
    0.17500000000000002,
    0.18500000000000003,
    0.19500000000000003,
    0.20500000000000004,
    0.21500000000000002,
    0.22500000000000003,
    0.23500000000000004,
    0.24500000000000002,
    0.255,
    0.265,
    0.275,
    0.28500000000000003,
    0.29500000000000004,
    0.30500000000000005,
    0.31500000000000006,
    0.32500000000000007,
    0.3350000000000001,
    0.3450000000000001,
    0.3550000000000001
]

y = [
    5190.637641981792,
    7054.516750766953,
    8483.359766937583,
    10242.377065660536,
    12311.64774616498,
    14597.662186600648,
    16874.673426455174,
    18741.458718393267,
    19601.555134229395,
    18791.388448976686,
    16849.721552634255,
    14119.969123708168,
    11401.438814333158,
    9872.291030242288,
    8897.45028292953,
    7939.589949465878,
    6921.696117540585,
    6045.454473119229,
    5442.664651823272,
    5065.775803272168,
    4790.269329831499,
    4525.179074496522,
    4254.760461650933,
    4009.1729908298153,
    3812.346818122069,
    3661.235920371446,
    3539.003374456872,
    3429.56319904424,
    3325.156402636274,
    3226.4245323568866,
    3138.3866304167577,
    3063.6389312516476,
    2999.2226261547366,
    2939.297113982252,
    2880.5669180920513,
    2824.330589926546,
    2772.657918361617,
    2726.2124622096726,
    2683.9727215170833,
    2644.1125465749265,
    2605.4010829283898,
    2568.214641677636,
    2532.46768215855,
    2498.262704089512
]
new_x = LinRange(x[1], x[end], 1000)
p = plot(x, y, label = "Data")
plot!(p, new_x, DataInterpolations.LinearInterpolation(y, x).(new_x), label = "Linear Interpolation")
plot!(p, new_x, DataInterpolations.QuadraticSpline(y, x).(new_x), label = "Quadratic Spline")
plot!(p, new_x, DataInterpolations.CubicSpline(y, x).(new_x), label = "Cubic Spline")
plot!(p, new_x, DataInterpolations.AkimaInterpolation(y, x).(new_x), label = "Akima Interpolation")
p

Error & Stacktrace ⚠️

There is no stack trace, the code is just giving a weird output.

Environment (please complete the following information):

  • Output of using Pkg; Pkg.status()
[47edcb42] ADTypes v1.9.0
  [c83c1981] AbstractCosmologicalEmulators v0.6.1
  [6e4b80f9] BenchmarkTools v1.5.0
  [a93c6f00] DataFrames v1.7.0
  [82cc6244] DataInterpolations v6.5.2
  [39dd38d3] Dierckx v0.5.3
  [ace19e24] Effort v0.2.0 `~/Desktop/work/CosmologicalEmulators/Effort.jl`
  [ef107171] EmulatorsTrainer v0.2.0 `~/Desktop/work/CosmologicalEmulators/EmulatorsTrainer.jl`
  [f6369f11] ForwardDiff v0.10.38
  [a98d9a8b] Interpolations v0.15.1
  [682c06a0] JSON v0.21.4
  [0f8b85d8] JSON3 v1.14.1
  [b964fa9f] LaTeXStrings v1.4.0
  [15e1cf62] NPZ v0.4.3
  [3bd65402] Optimisers v0.4.1
  [91a5bcdd] Plots v1.40.8
  [3f865c0f] ScatteredInterpolation v0.3.6
  [de6bee2f] SimpleChains v0.4.7
  [e88e6eb3] Zygote v0.6.72
  [37e2e46d] LinearAlgebra
  [9a3f8284] Random
  [10745b16] Statistics v1.10.0
  • Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
[47edcb42] ADTypes v1.9.0
  [c83c1981] AbstractCosmologicalEmulators v0.6.1
  [621f4979] AbstractFFTs v1.5.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.38
  [79e6a3ab] Adapt v4.1.1
  [66dad0bd] AliasTables v1.1.3
  [dce04be8] ArgCheck v2.3.0
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.17.0
  [4c555306] ArrayLayouts v1.10.4
  [a9b6321e] Atomix v0.1.0
  [13072b0f] AxisAlgorithms v1.1.0
  [6e4b80f9] BenchmarkTools v1.5.0
  [e2ed5e7c] Bijections v0.1.9
  [d1d4a3ce] BitFlags v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
  [082447d4] ChainRules v1.71.0
  [d360d2e6] ChainRulesCore v1.25.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [da1fd8a2] CodeTracking v1.3.6
  [944b1d66] CodecZlib v0.7.6
  [35d6a980] ColorSchemes v3.27.1
⌅ [3da002f7] ColorTypes v0.11.5
⌃ [c3611d14] ColorVectorSpace v0.10.0
⌃ [5ae59095] Colors v0.12.11
  [861a8166] Combinatorics v1.0.2
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [f0e56b4a] ConcurrentUtilities v2.4.2
  [187b0558] ConstructionBase v1.5.8
  [d38c429a] Contour v0.6.3
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [a93c6f00] DataFrames v1.7.0
  [82cc6244] DataInterpolations v6.5.2
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [8bb1440f] DelimitedFiles v1.9.1
  [39dd38d3] Dierckx v0.5.3
  [2b5f629d] DiffEqBase v6.158.3
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.6.22
  [8d63f2c5] DispatchDoctor v0.4.17
  [b4f34e82] Distances v0.10.12
  [31c24e10] Distributions v0.25.113
  [ffbed154] DocStringExtensions v0.9.3
  [5b8099bc] DomainSets v0.7.14
  [7c1d4256] DynamicPolynomials v0.6.0
  [ace19e24] Effort v0.2.0 `~/Desktop/work/CosmologicalEmulators/Effort.jl`
  [ef107171] EmulatorsTrainer v0.2.0 `~/Desktop/work/CosmologicalEmulators/EmulatorsTrainer.jl`
  [4e289a0a] EnumX v1.0.4
  [f151be2c] EnzymeCore v0.8.5
  [460bff9d] ExceptionUnwrapping v0.1.10
  [d4d017d3] ExponentialUtilities v1.26.1
  [e2ba6199] ExprTools v0.1.10
⌅ [6b7a57c9] Expronicon v0.8.5
  [c87230d0] FFMPEG v0.4.2
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [442a2c76] FastGaussQuadrature v1.0.2
  [29a986be] FastLapackInterface v2.0.4
  [a4df4552] FastPower v1.1.1
  [5789e2e9] FileIO v1.16.4
  [1a297f60] FillArrays v1.13.0
  [64ca27bc] FindFirstFunctions v1.4.1
  [6a86dc24] FiniteDiff v2.26.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v0.10.38
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
⌅ [d9f16b24] Functors v0.4.12
⌅ [0c68f7d7] GPUArrays v10.3.1
⌅ [46192b85] GPUArraysCore v0.1.6
  [28b8d3ca] GR v0.73.8
  [14197337] GenericLinearAlgebra v0.3.14
  [c145ed77] GenericSchur v0.5.4
  [86223c79] Graphs v1.12.0
  [42e2da0e] Grisu v1.0.2
  [19dc6840] HCubature v1.7.0
  [cd3eb016] HTTP v1.10.10
  [3e5b6fbb] HostCPUFeatures v0.1.17
  [0e44f5e4] Hwloc v3.3.0
  [34004b35] HypergeometricFunctions v0.3.24
  [7869d1d1] IRTools v0.4.14
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [842dd82b] InlineStrings v1.4.2
  [18e54dd8] IntegerMathUtils v0.1.2
  [de52edbc] Integrals v4.5.0
  [a98d9a8b] Interpolations v0.15.1
  [8197267c] IntervalSets v0.7.10
  [3587e190] InverseFunctions v0.1.17
  [41ab1584] InvertedIndices v1.3.0
  [92d709cd] IrrationalConstants v0.2.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.8
  [692b3bcd] JLLWrappers v1.6.1
  [682c06a0] JSON v0.21.4
  [0f8b85d8] JSON3 v1.14.1
  [aa1ae85d] JuliaInterpreter v0.9.36
  [ef3ab10e] KLU v0.6.0
  [63c18a36] KernelAbstractions v0.9.29
  [ba0b0d4f] Krylov v0.9.8
  [929cbde3] LLVM v9.1.3
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.5
  [73f95e8e] LatticeRules v0.0.1
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.2.1
  [3db4a2ba] LegendrePolynomials v0.4.5
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.3.0
  [7ed4a6bd] LinearSolve v2.36.2
  [2ab3a3ac] LogExpFunctions v0.3.28
  [e6f89c97] LoggingExtras v1.1.0
  [bdcacae8] LoopVectorization v0.12.171
  [6f1432cf] LoweredCodeUtils v3.0.5
  [b2108857] Lux v1.2.3
  [bb33d45b] LuxCore v1.1.0
  [82251201] LuxLib v1.3.7
  [7e8f7934] MLDataDevices v1.5.0
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.4
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.2
  [6fafb56a] Memoization v0.2.1
  [e1d29d7a] Missings v1.2.0
  [4886b29c] MonteCarloIntegration v0.2.0
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.7
  [d8a4904e] MutableArithmetics v1.5.2
  [d41bc354] NLSolversBase v7.8.3
  [872c559c] NNlib v0.9.24
  [15e1cf62] NPZ v0.4.3
  [77ba4419] NaNMath v1.0.2
  [b8a86587] NearestNeighbors v0.4.20
⌅ [8913a72c] NonlinearSolve v3.15.1
  [6fe1bfb0] OffsetArrays v1.14.1
  [4d8831e6] OpenSSL v1.4.3
  [3bd65402] Optimisers v0.4.1
  [bac558e1] OrderedCollections v1.6.3
  [1dea7af3] OrdinaryDiffEq v6.89.0
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.1.0
  [6ad6398a] OrdinaryDiffEqBDF v1.1.2
  [bbf590c4] OrdinaryDiffEqCore v1.10.0
  [50262376] OrdinaryDiffEqDefault v1.1.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.1.0
  [9286f039] OrdinaryDiffEqExplicitRK v1.1.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.1.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.2.1
  [5960d6e9] OrdinaryDiffEqFIRK v1.2.0
  [101fe9f7] OrdinaryDiffEqFeagin v1.1.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.1.1
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.1.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.1.0
  [521117fe] OrdinaryDiffEqLinear v1.1.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.2.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.2.1
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.2.2
  [c9986a66] OrdinaryDiffEqNordsieck v1.1.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.1.0
  [5b33eab2] OrdinaryDiffEqPRK v1.1.0
  [04162be5] OrdinaryDiffEqQPRK v1.1.0
  [af6ede74] OrdinaryDiffEqRKN v1.1.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.2.0
  [2d112036] OrdinaryDiffEqSDIRK v1.1.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.2.0
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.1.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.1.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.1.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.1.0
  [79d7bb75] OrdinaryDiffEqVerner v1.1.1
  [90014a1f] PDMats v0.11.31
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [b98c9c47] Pipe v1.3.0
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.3
  [91a5bcdd] Plots v1.40.8
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [f27b6e38] Polynomials v4.0.11
  [2dfb63ee] PooledArrays v1.4.3
  [d236fae5] PreallocationTools v0.4.24
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [08abe8d2] PrettyTables v2.4.0
  [27ebfcd6] Primes v0.5.6
  [43287f4e] PtrArrays v1.2.1
  [1fd47b50] QuadGK v2.11.1
  [8a4e6c94] QuasiMonteCarlo v0.3.3
  [c84ed2f1] Ratios v0.4.5
  [c1ae055f] RealDot v0.1.0
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [731186ca] RecursiveArrayTools v3.27.3
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.0
  [295af30f] Revise v3.6.2
  [79098fc4] Rmath v0.8.0
  [47965b36] RootedTrees v2.23.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
  [3f865c0f] ScatteredInterpolation v0.3.6
  [0bca4576] SciMLBase v2.59.1
  [19f34311] SciMLJacobianOperators v0.1.1
  [c0aeaf25] SciMLOperators v0.3.12
  [53ae85a6] SciMLStructures v1.5.0
  [6c6a2e73] Scratch v1.2.1
  [91c51154] SentinelArrays v1.4.7
  [efcf1570] Setfield v1.1.1
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
  [de6bee2f] SimpleChains v0.4.7
⌅ [727e6d20] SimpleNonlinearSolve v1.12.3
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [ed01d8cd] Sobol v1.5.0
  [a2af1166] SortingAlgorithms v1.2.1
  [9f842d2f] SparseConnectivityTracer v0.6.8
  [47a9eef4] SparseDiffTools v2.23.0
  [dc90abb0] SparseInverseSubset v0.1.2
  [0a514795] SparseMatrixColorings v0.4.9
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.4.0
  [860ef19b] StableRNGs v1.0.2
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.8
  [1e83bf80] StaticArraysCore v1.4.3
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.3
  [4c63d2b9] StatsFuns v1.3.2
  [7792a7ef] StrideArraysCore v0.5.7
  [892a3eda] StringManipulation v0.4.0
  [09ab397b] StructArrays v0.6.18
  [856f2bd8] StructTypes v1.11.0
  [2efcf032] SymbolicIndexingInterface v0.3.34
  [19f23fe9] SymbolicLimits v0.2.2
  [d1185830] SymbolicUtils v3.7.2
  [0c5d862f] Symbolics v6.18.3
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [62fd8b95] TensorCore v0.1.1
  [8ea1fca8] TermInterface v2.0.0
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.25
  [3bb67fe8] TranscodingStreams v0.11.3
  [d5829a12] TriangularSolve v0.2.1
  [781d530d] TruncatedStacktraces v1.4.0
  [bc48ee85] Tullio v0.3.7
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.21.0
  [45397f5d] UnitfulLatexify v1.6.4
  [a7c27f48] Unityper v0.1.6
  [013be700] UnsafeAtomics v0.2.1
  [d80eeb9a] UnsafeAtomicsLLVM v0.2.1
  [41fe7b60] Unzip v0.2.0
  [3d5dd08c] VectorizationBase v0.21.71
  [33b4df10] VectorizedRNG v0.2.25
  [19fa3120] VertexSafeGraphs v0.2.0
  [d49dbf32] WeightInitializers v1.0.4
  [efce3f68] WoodburyMatrices v1.0.0
  [a5390f91] ZipFile v0.10.1
  [e88e6eb3] Zygote v0.6.72
  [700de1a5] ZygoteRules v0.2.5
  [6e34b625] Bzip2_jll v1.0.8+2
  [83423d85] Cairo_jll v1.18.2+1
  [ee1fde0b] Dbus_jll v1.14.10+0
  [cd4c43a9] Dierckx_jll v0.1.0+0
  [2702e6a9] EpollShim_jll v0.0.20230411+0
  [2e619515] Expat_jll v2.6.2+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
  [a3f928ae] Fontconfig_jll v2.13.96+0
  [d7e528f0] FreeType2_jll v2.13.2+0
  [559328eb] FriBidi_jll v1.0.14+0
  [0656b61e] GLFW_jll v3.4.0+1
  [d2c73de3] GR_jll v0.73.8+0
  [78b55507] Gettext_jll v0.21.0+0
  [7746bdde] Glib_jll v2.80.5+0
  [3b182d85] Graphite2_jll v1.3.14+0
  [2e76f6c2] HarfBuzz_jll v8.3.1+0
  [e33a78d0] Hwloc_jll v2.11.2+1
  [1d5cc7b8] IntelOpenMP_jll v2024.2.1+0
  [aacddb02] JpegTurbo_jll v3.0.4+0
  [c1c5ebd0] LAME_jll v3.100.2+0
  [88015f11] LERC_jll v4.0.0+0
  [dad2f222] LLVMExtra_jll v0.0.34+0
  [1d63c593] LLVMOpenMP_jll v18.1.7+0
  [dd4b983a] LZO_jll v2.10.2+1
⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.11.0+0
  [7e76a0d4] Libglvnd_jll v1.6.0+0
  [7add5ba3] Libgpg_error_jll v1.50.0+0
  [94ce4f54] Libiconv_jll v1.17.0+1
  [4b2f31a3] Libmount_jll v2.40.1+0
  [89763e89] Libtiff_jll v4.7.0+0
  [38a345b3] Libuuid_jll v2.40.1+0
  [856f044c] MKL_jll v2024.2.0+0
  [e7412a2a] Ogg_jll v1.3.5+1
  [458c3c95] OpenSSL_jll v3.0.15+1
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.3+0
  [36c8627f] Pango_jll v1.54.1+0
  [30392449] Pixman_jll v0.43.4+0
  [c0090381] Qt6Base_jll v6.7.1+1
  [629bc702] Qt6Declarative_jll v6.7.1+2
  [ce943373] Qt6ShaderTools_jll v6.7.1+1
  [e99dba38] Qt6Wayland_jll v6.7.1+1
  [f50d1b31] Rmath_jll v0.5.1+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+1
  [2381bf8a] Wayland_protocols_jll v1.31.0+0
  [02c8fc9c] XML2_jll v2.13.4+0
  [aed1982a] XSLT_jll v1.1.41+0
  [ffd25f8a] XZ_jll v5.6.3+0
  [f67eecfb] Xorg_libICE_jll v1.1.1+0
  [c834827a] Xorg_libSM_jll v1.2.4+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.11+0
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.4+0
  [1082639a] Xorg_libXext_jll v1.3.6+0
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+0
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+0
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.0+0
  [3161d3a3] Zstd_jll v1.5.6+1
  [35ca27e7] eudev_jll v3.2.9+0
  [214eeab7] fzf_jll v0.53.0+0
  [1a1c6b14] gperf_jll v3.1.1+0
  [a4ae2306] libaom_jll v3.9.0+0
  [0ac62f75] libass_jll v0.15.2+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.3+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.44+0
  [f27f6e37] libvorbis_jll v1.3.7+2
  [009596ad] mtdev_jll v1.1.6+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
⌅ [1270edf5] x264_jll v2021.5.5+0
⌅ [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+1
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [9abbd945] Profile
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.0.5+1
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+2
  [05823500] OpenLibm_jll v0.8.1+2
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.8.0+1
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2
  • Output of versioninfo()
Julia Version 1.10.0
Commit 3120989f39b (2023-12-25 18:01 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 20 × 13th Gen Intel(R) Core(TM) i7-13700H
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, goldmont)
  Threads: 1 on 20 virtual cores
Environment:
  LD_GOLD = /home/marcobonici/miniconda3/bin/x86_64-conda-linux-gnu-ld.gold
@marcobonici marcobonici added the bug Something isn't working label Nov 9, 2024
@ChrisRackauckas
Copy link
Member

@SouthEndMusic you were the last one to look at the indexing of quadratic, seems like it could be off by one or something in one of the dispatches?

@SouthEndMusic
Copy link
Member

SouthEndMusic commented Nov 9, 2024

The quadratic spline interpolation does what it is supposed to: it's $C^1$ smooth and goes through the data points. This example shows that QuadraticSpline is not a always a good choice to interpolate between data points. It could be called an example of overfitting.

You could represent this data better with a QuadraticSpline than the shown plot, but then you would have to optimize for the (hyper)parameters.

@marcobonici
Copy link
Author

Hello, thank you for your answer!
A couple of follow-up questions:

  1. Is there any check that might be performed on the data, to "detect" a possible instability?
  2. Is there a reason why scipy.interp1d when using a quadratic spline does not fail on the same data?
  3. If it is not possible to do any kind of check, which is the best "default"? Maybe the Akima spline?
    Best,
    Marco

@SouthEndMusic
Copy link
Member

Hi Marco,

When it comes to detecting an instability: it depends on how you do define that. In general the best strategy is to choose the type of interpolation that has the properties that you want. AkimaInterpolation is popular. I haven't looked into the properties of that one thoroughly, but I know of PCHIPInterpolation that it never overshoots the data.

As to why scipy.interp1d does a better job: I had a quick look, and it seems like it does some more clever fitting. Might be worth looking into.

@SouthEndMusic
Copy link
Member

One of the weird things this interpolation type does is assume that the derivative in the first point is 0, throwing away a perfectly good degree of freedom.

@marcobonici
Copy link
Author

@SouthEndMusic , what do you mean with "this interpolation type"? The quadratic spline in general, the algorithm implemented here...?

@SouthEndMusic
Copy link
Member

SouthEndMusic commented Nov 10, 2024

@marcobonici the algorithm for QuadraticSpline in DataInterpolations assumes a derivative of $0$ at the first data point.

I hardcoded a degree 2 B-spline fit to your data, and it works well:

using DataInterpolations
using GLMakie

# Don't use x[end-1] in knot vector
# This is a choice, but something has to be done to make
# the number of degrees of freedom match the amount of data
k = zeros(length(x) + 3)
k[1:3] .= x[1]
k[(end-2):end] .= x[end]
k[4:(end-3)] .= x[2:(end-2)]

function B(t, i)
    return if t < k[i]
        zero(t)
    elseif t <= k[i+1]
        enum = (t - k[i])^2 
        denom = (k[i+2] - k[i]) * (k[i+1] - k[i])
        if (enum == 0 && denom == 0)
            i == 1 ? one(t) : zero(t)
        else
            enum/denom
        end
    elseif t <= k[i+2]
        (t - k[i]) * (k[i+2] - t) / ((k[i+2] - k[i]) * (k[i+2] - k[i+1])) +
        (k[i+3] - t) * (t - k[i+1]) / ((k[i+3] - k[i+1]) * (k[i+2] - k[i+1]))
    elseif t <= k[i+3]
        ((k[i+3] - t)^2) / ((k[i+3] - k[i+1]) * (k[i+3] - k[i+2]))
    else
        zero(t)
    end
end

# A * c = y
n = length(x)
A = zeros(n, n)
for j in 1:n
    for i in 1:n
        A[j,i] = B(x[j], i)
    end
end

c = A \ y

function itp(t)
    out = zero(t)
    for i in 1:n
        out += c[i] * B(t, i)
    end
    out
end

new_x = LinRange(x[1], x[end], 10000)

fig = Figure()
ax_bf = Axis(fig[1,1], title = "Basis functions")
scatter!(ax_bf, x, zero(x))

for i in 1:n
    lines!(ax_bf, new_x, B.(new_x, i))
end

ax_fit = Axis(fig[2,1], title = "Interpolation")
lines!(ax_fit, new_x, itp.(new_x))
scatter!(ax_fit, x,y, label = "Data")
fig

image

We should probably incorporate something like this in QuadraticSpline.

I don't know exactly what the current QuadraticSpline implementation does as it wasn't written by me, but curiously I got very similar oscillations to what you showed when I accidentally used the transpose of my matrix A instead of the matrix itself.

@SouthEndMusic
Copy link
Member

I have a POC of an improved lightweight implementation, I will open a PR when I find the time.

@marcobonici
Copy link
Author

Thank you very much! :)

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Labels
bug Something isn't working
Projects
None yet
Development

Successfully merging a pull request may close this issue.

3 participants