RootedTrees

A collection of functionality around rooted trees to generate order conditions for Runge-Kutta methods in Julia for differential equations and scientific machine learning (SciML)

https://github.com/sciml/rootedtrees.jl

Science Score: 67.0%

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Keywords

differential-equations hacktoberfest julia rooted-trees runge-kutta scientific-machine-learning sciml

Keywords from Contributors

matrix-exponential ode bridge primitives arrays base composibility interface julialang exponential

Last synced: 6 months ago · JSON representation ·

Repository

A collection of functionality around rooted trees to generate order conditions for Runge-Kutta methods in Julia for differential equations and scientific machine learning (SciML)

Basic Info

Host: GitHub
Owner: SciML
License: mit
Language: Julia
Default Branch: main
Homepage: https://sciml.github.io/RootedTrees.jl
Size: 1.59 MB

Statistics

Stars: 37
Watchers: 3
Forks: 17
Open Issues: 13
Releases: 62

Topics

differential-equations hacktoberfest julia rooted-trees runge-kutta scientific-machine-learning sciml

Created almost 7 years ago · Last pushed 7 months ago

Metadata Files

Readme Contributing License Citation Zenodo

RootedTrees

A collection of functionality around rooted trees to generate order conditions for Runge-Kutta methods in Julia. This package also provides basic functionality for BSeries.jl.

API Documentation

The API of RootedTrees.jl is documented in the following. Additional information on each function is available in their docstrings and in the online documentation.

Construction

RootedTrees are represented using level sequences, i.e., AbstractVectors containing the distances of the nodes from the root, see

Beyer, Terry, and Sandra Mitchell Hedetniemi. "Constant time generation of rooted trees". SIAM Journal on Computing 9.4 (1980): 706-712. DOI: 10.1137/0209055

RootedTrees can be constructed from their level sequence using julia julia> t = rootedtree([1, 2, 3, 2]) RootedTree{Int64}: [1, 2, 3, 2] In the notation of Butcher (Numerical Methods for ODEs, 2016), this tree can be written as [[τ] τ] or (τ ∘ τ) ∘ (τ ∘ τ), where ∘ is the non-associative Butcher product of RootedTrees, which is also implemented.

To get the representation of a RootedTree introduced by Butcher, use butcher_representation: ```julia julia> t = rootedtree([1, 2, 3, 4, 3, 3, 2, 2, 2, 2, 2]) RootedTree{Int64}: [1, 2, 3, 4, 3, 3, 2, 2, 2, 2, 2]

julia> butcher_representation(t) "[[[τ]τ²]τ⁵]" ```

There are also some simple plot recipes for Plots.jl. Thus, you can visualize a rooted tree t using plot(t) when using Plots.

Additionally, there is an un-exported function RootedTrees.latexify that can generate LaTeX code for a rooted tree t based on the LaTeX package forest. The relevant code that needs to be included in the preamble can be obtained from the docstring of RootedTrees.latexify (type ? and RootedTrees.latexify in the Julia REPL). The same format is used when you are using Latexify and their function latexify, see Latexify.jl.

Iteration over `RootedTree`s

A RootedTreeIterator(order::Integer) can be used to iterate efficiently over all RootedTrees of a given order.

Be careful that the iterator is stateful for efficiency reasons, so you might need to use copy appropriately, e.g., ```julia julia> map(identity, RootedTreeIterator(4)) 4-element Array{RootedTrees.RootedTree{Int64,Array{Int64,1}},1}: RootedTree{Int64}: [1, 2, 2, 2] RootedTree{Int64}: [1, 2, 2, 2] RootedTree{Int64}: [1, 2, 2, 2] RootedTree{Int64}: [1, 2, 2, 2]

julia> map(copy, RootedTreeIterator(4)) 4-element Array{RootedTrees.RootedTree{Int64,Array{Int64,1}},1}: RootedTree{Int64}: [1, 2, 3, 4] RootedTree{Int64}: [1, 2, 3, 3] RootedTree{Int64}: [1, 2, 3, 2] RootedTree{Int64}: [1, 2, 2, 2] ```

Functions on Trees

The usual functions on RootedTrees are implemented, cf. Butcher (Numerical Methods for ODEs, 2016). - order(t::RootedTree): The order of a RootedTree, i.e., the length of its level sequence. - σ(t::RootedTree) or symmetry(t): The symmetry σ of a rooted tree, i.e., the order of the group of automorphisms on a particular labelling (of the vertices) of t. - γ(t::RootedTree) or density(t): The density γ(t) of a rooted tree, i.e., the product over all vertices of t of the order of the subtree rooted at that vertex. - α(t::RootedTree): The number of monotonic labelings of t not equivalent under the symmetry group. - β(t::RootedTree): The total number of labelings of t not equivalent under the symmetry group.

Additionally, functions on trees connected to Runge-Kutta methods are implemented. - elementary_weight(t, A, b, c): Compute the elementary weight Φ(t) of t::RootedTree for the Butcher coefficients A, b, c of a Runge-Kutta method. - derivative_weight(t, A, b, c): Compute the derivative weight (ΦᵢD)(t) of t for the Butcher coefficients A, b, c of a Runge-Kutta method. - residual_order_condition(t, A, b, c): The residual of the order condition (Φ(t) - 1/γ(t)) / σ(t) with elementary weight Φ(t), density γ(t), and symmetry σ(t) of the rooted tree t for the Runge-Kutta method with Butcher coefficients A, b, c.

Brief Changelog

v2.16: The LaTeX printing of rooted trees changed to allow representing colored rooted trees. Please update your LaTeX preamble as described in the docstring of RootedTrees.latexify.
v2.0: Rooted trees are considered up to isomorphisms introduced by shifting each coefficient of their level sequence by the same number.

Referencing

If you use RootedTrees.jl for your research, please cite the paper bibtex @article{ketcheson2023computing, title={Computing with {B}-series}, author={Ketcheson, David I and Ranocha, Hendrik}, journal={ACM Transactions on Mathematical Software}, volume={49}, number={2}, year={2023}, month={06}, doi={10.1145/3573384}, eprint={2111.11680}, eprinttype={arXiv}, eprintclass={math.NA} } In addition, you can also refer to RootedTrees.jl directly as bibtex @misc{ranocha2019rootedtrees, title={{RootedTrees.jl}: {A} collection of functionality around rooted trees to generate order conditions for {R}unge-{K}utta methods in {J}ulia for differential equations and scientific machine learning ({SciM}L)}, author={Ranocha, Hendrik and contributors}, year={2019}, month={05}, howpublished={\url{https://github.com/SciML/RootedTrees.jl}}, doi={10.5281/zenodo.5534590} }

Owner

Name: SciML Open Source Scientific Machine Learning
Login: SciML
Kind: organization
Email: contact@chrisrackauckas.com

Website: https://sciml.ai
Twitter: SciML_Org
Repositories: 170
Profile: https://github.com/SciML

Open source software for scientific machine learning

Citation (CITATION.bib)

@article{ketcheson2023computing,
  title={Computing with {B}-series},
  author={Ketcheson, David I and Ranocha, Hendrik},
  journal={ACM Transactions on Mathematical Software},
  volume={49},
  number={2},
  year={2023},
  month={06},
  doi={10.1145/3573384},
  eprint={2111.11680},
  eprinttype={arXiv},
  eprintclass={math.NA}
}

@misc{ranocha2019rootedtrees,
  title={{RootedTrees.jl}: {A} collection of functionality around rooted trees
         to generate order conditions for {R}unge-{K}utta methods in {J}ulia
         for differential equations and scientific machine learning ({SciM}L)},
  author={Ranocha, Hendrik and contributors},
  year={2019},
  month={05},
  howpublished={\url{https://github.com/SciML/RootedTrees.jl}},
  doi={10.5281/zenodo.5534590}
}

GitHub Events

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Delete event: 2
Issue comment event: 4
Push event: 22
Pull request review event: 5
Pull request review comment event: 7
Pull request event: 13
Fork event: 5
Create event: 2

Last Year

Delete event: 2
Issue comment event: 4
Push event: 22
Pull request review event: 5
Pull request review comment event: 7
Pull request event: 13
Fork event: 5
Create event: 2

Committers

Last synced: 8 months ago

All Time

Total Commits: 278
Total Committers: 12
Avg Commits per committer: 23.167
Development Distribution Score (DDS): 0.306

Past Year

Commits: 38
Committers: 7
Avg Commits per committer: 5.429
Development Distribution Score (DDS): 0.447

Top Committers

Name	Email	Commits
Hendrik Ranocha	m**l@r**e	193
dependabot[bot]	4****]	49
Christopher Rackauckas	C**t@C**m	11
github-actions[bot]	4****]	7
Yingbo Ma	m**5@g**m	5
Anant Thazhemadam	4****m	5
Philipp	1****f	2
Chris de Graaf	me@c****v	2
maja.k.gwozdz@gmail.com	m**z@g**m	1
Qingyu Qu	5****Y	1
Julia TagBot	5****t	1
Arno Strouwen	a**n@t**e	1

Committer Domains (Top 20 + Academic)

telenet.be: 1 cdg.dev: 1 chrisrackauckas.com: 1 ranocha.de: 1

Issues and Pull Requests

Last synced: 6 months ago

All Time

Total issues: 16
Total pull requests: 163
Average time to close issues: 29 days
Average time to close pull requests: 4 days
Total issue authors: 3
Total pull request authors: 11
Average comments per issue: 4.69
Average comments per pull request: 0.16
Merged pull requests: 150
Bot issues: 0
Bot pull requests: 60

Past Year

Issues: 0
Pull requests: 9
Average time to close issues: N/A
Average time to close pull requests: 2 days
Issue authors: 0
Pull request authors: 5
Average comments per issue: 0
Average comments per pull request: 0.0
Merged pull requests: 2
Bot issues: 0
Bot pull requests: 1

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Top Authors

Issue Authors

ranocha (14)
ketch (1)
thazhemadam (1)
JuliaTagBot (1)

Pull Request Authors

ranocha (87)
dependabot[bot] (71)
ChrisRackauckas (7)
github-actions[bot] (7)
thazhemadam (7)
pw0lf (3)
ArnoStrouwen (3)
btranmath (2)
christopher-dG (2)
YingboMa (2)
ErikQQY (1)

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Issue Labels

enhancement (9) bug (1)

Pull Request Labels

dependencies (71) enhancement (1) bug (1) github_actions (1)

Packages

Total packages: 1
Total downloads:
- julia 67 total

Total dependent packages: 2
Total dependent repositories: 0
Total versions: 62

juliahub.com: RootedTrees

A collection of functionality around rooted trees to generate order conditions for Runge-Kutta methods in Julia for differential equations and scientific machine learning (SciML)

Homepage: https://sciml.github.io/RootedTrees.jl
Documentation: https://docs.juliahub.com/General/RootedTrees/stable/
License: MIT
Latest release: 2.23.1
published over 1 year ago

Versions: 62
Dependent Packages: 2
Dependent Repositories: 0
Downloads: 67 Total

Rankings

Stargazers count: 18.8%

Average: 20.6%

Forks count: 22.3%

Last synced: 7 months ago

Dependencies

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RootedTrees

Science Score: 67.0%

Keywords

Keywords from Contributors

Repository

Basic Info

Statistics

Topics

Metadata Files

README.md

RootedTrees

API Documentation

Construction

Iteration over RootedTrees

Functions on Trees

Brief Changelog

Referencing

Owner

Citation (CITATION.bib)

GitHub Events

Total

Last Year

Committers

All Time

Past Year

Top Committers

Committer Domains (Top 20 + Academic)

Issues and Pull Requests

All Time

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Issue Labels

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Packages

juliahub.com: RootedTrees

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Dependencies

Iteration over `RootedTree`s