# How to calculate derivative by Lagrange interpolation
**URL:** https://discourse.julialang.org/t/how-to-calculate-derivative-by-lagrange-interpolation/74905
**Category:** Modelling & Simulations
**Tags:** question, package, diffeq
**Created:** [January 20, 2022, 4:59am UTC](https://discourse.julialang.org/t/how-to-calculate-derivative-by-lagrange-interpolation/74905 "2022-01-20T04:59:15Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@manoj.centura](https://discourse.julialang.org/u/manoj.centura)
#### Post date: [January 20, 2022, 4:59am UTC](https://discourse.julialang.org/t/how-to-calculate-derivative-by-lagrange-interpolation/74905/1 "2022-01-20T04:59:15Z")
hi All,
is there a pkg to calculate derivative at untabulated points using langrange interpolation?
Thanks
M
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### Author:  [@dlakelan](https://discourse.julialang.org/u/dlakelan)
#### Post date: [January 20, 2022, 5:01am UTC](https://discourse.julialang.org/t/how-to-calculate-derivative-by-lagrange-interpolation/74905/2 "2022-01-20T05:01:18Z")
does it have to be lagrange interpolation? That’s not necessarily a stable method, for example there’s Runge’s phenomenon. [Runge's phenomenon - Wikipedia](https://en.wikipedia.org/wiki/Runge%27s_phenomenon)
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### Author:  [@goerch](https://discourse.julialang.org/u/goerch)
#### Post date: [January 20, 2022, 5:55am UTC](https://discourse.julialang.org/t/how-to-calculate-derivative-by-lagrange-interpolation/74905/3 "2022-01-20T05:55:13Z")
> [@manoj.centura](#):
>
> is there a pkg to calculate derivative at untabulated points using langrange interpolation?
I’d suspect the combination of [Polynomials.jl](https://juliamath.github.io/Polynomials.jl/stable/) and [SpecialPolynomials.jl](https://docs.juliahub.com/SpecialPolynomials/LrhA0/0.2.7/) could help.
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### Author:  [@tobydriscoll](https://discourse.julialang.org/u/tobydriscoll)
#### Post date: [January 20, 2022, 8:33pm UTC](https://discourse.julialang.org/t/how-to-calculate-derivative-by-lagrange-interpolation/74905/4 "2022-01-20T20:33:41Z")
I’m not sure what you mean by “untabulated,” but [ApproxFun](https://github.com/JuliaApproximation/ApproxFun.jl) may be of help. Especially look at the documentation FAQ about values on predefined grids.
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### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [January 20, 2022, 8:56pm UTC](https://discourse.julialang.org/t/how-to-calculate-derivative-by-lagrange-interpolation/74905/5 "2022-01-20T20:56:30Z")
> [@manoj.centura](#):
>
> is there a pkg to calculate derivative at untabulated points using langrange interpolation?
The numerically stable version of Lagrange interpolation is barycentric interpolation, which is implemented here: [GitHub - dawbarton/BarycentricInterpolation.jl: A Julia implementation of Barycentric interpolation and differentiation formulae](https://github.com/dawbarton/BarycentricInterpolation.jl) …always use this rather than Lagrange.
Beware that if you choose the interpolation points unwisely (e.g. equally spaced or randomly) then at high polynomial degrees you are likely to hit [Runge phenomena](https://en.wikipedia.org/wiki/Runge%27s_phenomenon) with _any_ polynomial interpolation method. The main ways around this is to (a) choose the points well, e.g. at Chebyshev nodes or (b) least-square fit to a lower-degree polynomial (e.g. fit to a degree-10 polynomial with 100 points). [GitHub - JuliaMath/FastChebInterp.jl: fast multidimensional Chebyshev interpolation and regression in Julia](https://github.com/stevengj/FastChebInterp.jl) can do both of those things for you, and there are other packages as well (e.g. ApproxFun can do it, but is really oriented towards other tasks than interpolating data).
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### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [April 4, 2022, 4:11pm UTC](https://discourse.julialang.org/t/how-to-calculate-derivative-by-lagrange-interpolation/74905/6 "2022-04-04T16:11:42Z")
[https://github.com/PumasAI/DataInterpolations.jl](https://github.com/PumasAI/DataInterpolations.jl)
It has an implementation of the Lagrange interpolation in Barycentric form (IIRC) and it specializes the derivative calculation as well.
[https://github.com/PumasAI/DataInterpolations.jl/blob/master/src/derivatives.jl#L55](https://github.com/PumasAI/DataInterpolations.jl/blob/master/src/derivatives.jl#L55)