# Packages defining functional data types

**URL:** <https://discourse.julialang.org/t/packages-defining-functional-data-types/73539>\
**Category:** Statistics\
**Tags:** package, fda\
**Created:** [December 23, 2021, 6:23pm UTC](https://discourse.julialang.org/t/packages-defining-functional-data-types/73539 "2021-12-23T18:23:52Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![juliohm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/juliohm/32/215266_2.png) [@juliohm](https://discourse.julialang.org/u/juliohm)\
**Post date:** [December 23, 2021, 6:23pm UTC](https://discourse.julialang.org/t/packages-defining-functional-data-types/73539/1 "2021-12-23T18:23:52Z")

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Any package out there defining a function type with inner product? In functional data analysis we often define the inner product between two functions as

\langle f, g \rangle = \int\_a^b f(t)\bar{g(t)} dt

More formally, this defines the Hilbert space of functions in the interval [a,b].

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**Author:** ![PatrickXie17](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/patrickxie17/32/23412_2.png) [@PatrickXie17](https://discourse.julialang.org/u/PatrickXie17)\
**Post date:** [February 2, 2022, 8:34pm UTC](https://discourse.julialang.org/t/packages-defining-functional-data-types/73539/2 "2022-02-02T20:34:45Z")

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I used to write some simple implementations for functional data analysis mimicking what the R package `fda` does. To my knowledge, there is no Julia package dedicated for FDA, and my quick and dirty suggestion (and what I have been doing) is to evaluate the two functions at discrete points and approximate the inner product of two functions with vector inner product.

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**Author:** ![juliohm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/juliohm/32/215266_2.png) [@juliohm](https://discourse.julialang.org/u/juliohm)\
**Post date:** [February 2, 2022, 8:50pm UTC](https://discourse.julialang.org/t/packages-defining-functional-data-types/73539/3 "2022-02-02T20:50:41Z")

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ApproxFun.jl has useful definitions, it is just not exposed to end users yet:

[https://github.com/JuliaApproximation/ApproxFun.jl/issues/753](https://github.com/JuliaApproximation/ApproxFun.jl/issues/753)