ApproxFun

Julia package for function approximation

https://github.com/juliaapproximation/approxfun.jl

Science Score: 54.0%

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6 of 45 committers (13.3%) from academic institutions
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Scientific vocabulary similarity
Low similarity (11.4%) to scientific vocabulary

Keywords

approximation julia partial-differential-equations

Keywords from Contributors

pde graphics sde sciml differential-equations differentialequations stochastic-differential-equations matrix-exponential data-frame data-structures

Last synced: 6 months ago · JSON representation ·

Repository

Julia package for function approximation

Basic Info

Host: GitHub
Owner: JuliaApproximation
License: other
Language: Julia
Default Branch: master
Homepage: http://juliaapproximation.github.io/ApproxFun.jl/
Size: 113 MB

Statistics

Stars: 556
Watchers: 19
Forks: 70
Open Issues: 180
Releases: 59

Topics

approximation julia partial-differential-equations

Created over 12 years ago · Last pushed 10 months ago

Metadata Files

Readme Changelog License Citation

ApproxFun.jl

ApproxFun is a package for approximating functions. It is in a similar vein to the Matlab package Chebfun and the Mathematica package RHPackage.

The ApproxFun Documentation contains detailed information, or read on for a brief overview of the package. The documentation contains examples of usage, such as solving ordinary and partial differential equations.

The ApproxFun Examples repo contains many examples of using this package, in Jupyter notebooks and Julia scripts. Note that this is independently maintained, so it might not always be in sync with the latest version of ApproxFun. We recommend checking the examples in the documentation first, as these will always be compatible with the latest version of the package.

Introduction

Approximating Functions

Take your two favourite functions on an interval and create approximations to them as simply as:

julia using LinearAlgebra, SpecialFunctions, Plots, ApproxFun x = Fun(identity,0..10) f = sin(x^2) g = cos(x)

Evaluating f(.1) will return a high accuracy approximation to sin(0.01). All the algebraic manipulations of functions are supported and more. For example, we can add f and g^2 together and compute the roots and extrema:

```julia h = f + g^2 r = roots(h) rp = roots(h')

plot(h; label="f + g^2") scatter!(r, h.(r); label="roots") scatter!(rp, h.(rp); label="extrema") ```

Differentiation and integration

Notice from above that to find the extrema, we used ' overridden for the differentiate function. Several other Julia base functions are overridden for the purposes of calculus. We may check that the exponential is its own derivative, by evaluating the norm of the difference and checking that it is small:

julia f = Fun(exp, -1..1) norm(f-f') # 4.4391656415701095e-14

Similarly, cumsum defines an indefinite integration operator:

julia g = cumsum(f) g = g + f(-1) norm(f-g) # 3.4989733283850415e-15d

Algebraic and differential operations are also implemented where possible, and most of Julia's built-in functions (and special functions from SpecialFunctions.jl) are overridden to accept Funs:

julia x = Fun() f = erf(x) g = besselj(3,exp(f)) h = airyai(10asin(f)+2g)

Examples of Usage

Check the documentation for examples of usage.

References

J. L. Aurentz & R. M. Slevinsky (2019), On symmetrizing the ultraspherical spectral method for self-adjoint problems, arxiv:1903.08538

S. Olver & A. Townsend (2014), A practical framework for infinite-dimensional linear algebra, Proceedings of the 1st First Workshop for High Performance Technical Computing in Dynamic Languages, 57–62

A. Townsend & S. Olver (2014), The automatic solution of partial differential equations using a global spectral method, J. Comp. Phys., 299: 106–123

S. Olver & A. Townsend (2013), Fast inverse transform sampling in one and two dimensions, arXiv:1307.1223

S. Olver & A. Townsend (2013), A fast and well-conditioned spectral method, SIAM Review, 55:462–489

Owner

Name: JuliaApproximation
Login: JuliaApproximation
Kind: organization

Repositories: 42
Profile: https://github.com/JuliaApproximation

Citation (CITATION.bib)

@inproceedings{ApproxFun.jl-2014,
  year = {2014},
  publisher = {{IEEE}},
  author = {Sheehan Olver and Alex Townsend},
  title = {A practical framework for infinite-dimensional linear algebra},
  booktitle = {Proceedings of the 1st Workshop for High Performance Technical Computing in Dynamic Languages -- HPTCDL `14}
}

GitHub Events

Total

Create event: 4
Commit comment event: 2
Release event: 1
Issues event: 12
Watch event: 18
Delete event: 2
Issue comment event: 23
Push event: 14
Pull request event: 5

Last Year

Create event: 4
Commit comment event: 2
Release event: 1
Issues event: 12
Watch event: 18
Delete event: 2
Issue comment event: 23
Push event: 14
Pull request event: 5

Committers

Last synced: 9 months ago

All Time

Total Commits: 3,801
Total Committers: 45
Avg Commits per committer: 84.467
Development Distribution Score (DDS): 0.172

Past Year

Commits: 6
Committers: 3
Avg Commits per committer: 2.0
Development Distribution Score (DDS): 0.333

Top Committers

Name	Email	Commits
Sheehan Olver	s**r@m**m	3,147
Richard Mikael Slevinsky	R**y@m**k	275
Jishnu Bhattacharya	j**b@g**m	114
Sheehan Olver	d**y@g**m	57
John Wormell	j**l@g**m	42
Marcus	m**b@g**m	27
github-actions[bot]	4****]	25
Sheehan Olver	s**r@g**m	16
AT	t**d@m**k	16
goretkin	g**n@g**m	12
MasonProtter	m**r@g**m	7
PEIFENG WU	4****g	6
zz5016	z**6@i**k	5
Kirill Ignatiev	i****l	4
Lucas C Wilcox	l**s@s**m	3
Rodney Polkinghorne	t**d@g**m	3
Steven G. Johnson	s**j@m**u	3
Yichao Yu	y**2@g**m	3
cmarcotte	c**t@g**m	3
Ziyao Zhang	4****6	3
Christopher Rackauckas	a**s@c**m	2
Erik Schnetter	s**r@g**m	2
Lucas Aschenbach	3****h	2
femtocleaner[bot]	f****]	2
Wonseok Shin	w**7@g**m	2
spaette	1****e	1
michele	m**n@g**m	1
ksil	k****l	1
CompatHelper Julia	c**y@j**g	1
Pietro Vertechi	p**i@n**g	1
and 15 more...

Committer Domains (Top 20 + Academic)

mit.edu: 2 maths.ox.ac.uk: 2 simons-rock.edu: 1 macmillen.net: 1 student.otago.ac.nz: 1 johnmyleswhite.com: 1 cfcl.com: 1 imag.fr: 1 neuro.fchampalimaud.org: 1 julialang.org: 1 chrisrackauckas.com: 1 swirlee.com: 1 ic.ac.uk: 1 mac.com: 1

Issues and Pull Requests

Last synced: 6 months ago

All Time

Total issues: 74
Total pull requests: 109
Average time to close issues: over 1 year
Average time to close pull requests: 6 days
Total issue authors: 48
Total pull request authors: 6
Average comments per issue: 2.55
Average comments per pull request: 1.01
Merged pull requests: 103
Bot issues: 0
Bot pull requests: 11

Past Year

Issues: 10
Pull requests: 4
Average time to close issues: 4 days
Average time to close pull requests: 11 days
Issue authors: 9
Pull request authors: 2
Average comments per issue: 0.6
Average comments per pull request: 1.0
Merged pull requests: 4
Bot issues: 0
Bot pull requests: 2

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Top Authors

Issue Authors

dlfivefifty (4)
macd (4)
ay111 (3)
falematte (3)
jishnub (3)
andreasvarga (3)
benjione (3)
Jilhg (2)
GrigorySarnitsky (2)
MikaelSlevinsky (2)
Veenty (2)
nilsbecker (2)
AshtonSBradley (2)
weymouth (2)
alanedelman (2)

Pull Request Authors

jishnub (94)
github-actions[bot] (11)
LucasAschenbach (2)
dependabot[bot] (1)
dstahlke (1)
spaette (1)

Top Labels

Issue Labels

enhancement (2) feature (1)

Pull Request Labels

dependencies (1)

Packages

Total packages: 1
Total downloads:
- julia 80 total

Total dependent packages: 19
Total dependent repositories: 19
Total versions: 57

juliahub.com: ApproxFun

Julia package for function approximation

Homepage: http://juliaapproximation.github.io/ApproxFun.jl/
Documentation: https://docs.juliahub.com/General/ApproxFun/stable/
License: BSD-3-Clause
Latest release: 0.13.28
published about 1 year ago

Versions: 57
Dependent Packages: 19
Dependent Repositories: 19
Downloads: 80 Total

Rankings

Stargazers count: 1.3%

Forks count: 1.6%

Dependent repos count: 1.9%

Average: 2.2%

Dependent packages count: 4.0%

Last synced: 6 months ago

Dependencies

.github/workflows/CompatHelper.yml actions

julia-actions/setup-julia v1 composite

.github/workflows/DocPreviewCleanup.yml actions

actions/checkout v3 composite

.github/workflows/TagBot.yml actions

JuliaRegistries/TagBot v1 composite

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actions/cache v3 composite
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codecov/codecov-action v3 composite
fkirc/skip-duplicate-actions v5 composite
julia-actions/julia-buildpkg v1 composite
julia-actions/julia-processcoverage v1 composite
julia-actions/julia-runtest v1 composite
julia-actions/setup-julia v1 composite

.github/workflows/docs.yml actions

actions/cache v3 composite
actions/checkout v3 composite
julia-actions/setup-julia latest composite

ApproxFun

Science Score: 54.0%

Keywords

Keywords from Contributors

Repository

Basic Info

Statistics

Topics

Metadata Files

README.md

ApproxFun.jl

Introduction

Approximating Functions

Differentiation and integration

Examples of Usage

References

Owner

Citation (CITATION.bib)

GitHub Events

Total

Last Year

Committers

All Time

Past Year

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juliahub.com: ApproxFun

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