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AayushSabharwalChrisRackauckas
AayushSabharwal
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ChrisRackauckas
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feat: add NonlinearSolveHomotopyContinuation.jl (#523)
* feat: add `NonlinearSolveHomotopyContinuation.jl` * feat: add `solve` implementations * test: add tests for all roots solve * fix: fix jacobian implementation, add taylor implementation * fix: fix system evaluate and jacobian * fix: fix inplace system taylor * fix: fix homotopy and implement taylor * fix: fix jacobian building for systems * fix: fix single root solve implementation * build: add TaylorSeries as a dependency * fix: fix jacobian and taylor implementations * test: add tests for single roots, fix allroots tests * build: add compat entries * docs: add docstrings to NonlinearSolveHomotopyContinuation.jl * ci: add NonlinearSolveHomotopyContinuation.jl to CI * docs: add NonlinearSolveHomotopyContinuation to docs * build: fix LinearAlgebra compat * test: do not rely on singular roots for tests * test: sort roots in `allroots` test * refactor: format * test: do not rely on singular roots * Update homotopycontinuation.md * docs: add `NonlinearSolveHomotopyContinuation` to doc build * refactor: use TaylorDiff.jl instead of TaylorSeries.jl --------- Co-authored-by: Christopher Rackauckas <[email protected]>
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‎.github/workflows/CI_NonlinearSolveHomotopyContinuation.yml

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name: CI (NonlinearSolveHomotopyContinuation)
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on:
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pull_request:
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branches:
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- master
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paths:
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- "lib/NonlinearSolveHomotopyContinuation/**"
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- ".github/workflows/CI_NonlinearSolveHomotopyContinuation.yml"
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- "lib/NonlinearSolveBase/**"
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push:
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branches:
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- master
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concurrency:
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# Skip intermediate builds: always.
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# Cancel intermediate builds: only if it is a pull request build.
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group: ${{ github.workflow }}-${{ github.ref }}
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cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
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jobs:
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test:
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runs-on: ${{ matrix.os }}
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strategy:
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fail-fast: false
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matrix:
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version:
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- "1.10"
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- "1"
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os:
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- ubuntu-latest
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- macos-latest
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- windows-latest
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steps:
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- uses: actions/checkout@v4
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- uses: julia-actions/setup-julia@v2
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with:
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version: ${{ matrix.version }}
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- uses: actions/cache@v4
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env:
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cache-name: cache-artifacts
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with:
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path: ~/.julia/artifacts
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key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
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restore-keys: |
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${{ runner.os }}-test-${{ env.cache-name }}-
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${{ runner.os }}-test-
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${{ runner.os }}-
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- name: "Install Dependencies and Run Tests"
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run: |
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import Pkg
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Pkg.Registry.update()
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# Install packages present in subdirectories
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dev_pks = Pkg.PackageSpec[]
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for path in ("lib/NonlinearSolveBase",)
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push!(dev_pks, Pkg.PackageSpec(; path))
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end
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Pkg.develop(dev_pks)
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Pkg.instantiate()
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Pkg.test(; coverage="user")
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shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/NonlinearSolveHomotopyContinuation {0}
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- uses: julia-actions/julia-processcoverage@v1
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with:
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directories: lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/NonlinearSolveHomotopyContinuation/src
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- uses: codecov/codecov-action@v5
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with:
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file: lcov.info
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token: ${{ secrets.CODECOV_TOKEN }}
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verbose: true
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fail_ci_if_error: false
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downgrade:
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runs-on: ubuntu-latest
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strategy:
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fail-fast: false
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matrix:
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version:
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- "1.10"
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steps:
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- uses: actions/checkout@v4
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- uses: julia-actions/setup-julia@v2
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with:
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version: ${{ matrix.version }}
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- uses: julia-actions/julia-downgrade-compat@v1
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with:
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skip: NonlinearSolveBase, SciMLJacobianOperators
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- name: "Install Dependencies and Run Tests"
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run: |
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import Pkg
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Pkg.Registry.update()
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# Install packages present in subdirectories
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dev_pks = Pkg.PackageSpec[]
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for path in ("lib/NonlinearSolveBase",)
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push!(dev_pks, Pkg.PackageSpec(; path))
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end
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Pkg.develop(dev_pks)
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Pkg.instantiate()
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Pkg.test(; coverage="user")
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shell: julia --color=yes --code-coverage=user --depwarn=yes --project=lib/NonlinearSolveHomotopyContinuation {0}
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- uses: julia-actions/julia-processcoverage@v1
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with:
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directories: lib/NonlinearSolveBase/src,lib/NonlinearSolveBase/ext,lib/NonlinearSolveHomotopyContinuation/src
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- uses: codecov/codecov-action@v5
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with:
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file: lcov.info
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token: ${{ secrets.CODECOV_TOKEN }}
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verbose: true
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fail_ci_if_error: false

‎.github/workflows/Documentation.yml

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Pkg.Registry.update()
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# Install packages present in subdirectories
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dev_pks = Pkg.PackageSpec[]
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for path in ("lib/SciMLJacobianOperators", ".", "lib/SimpleNonlinearSolve", "lib/NonlinearSolveBase", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveFirstOrder", "lib/NonlinearSolveQuasiNewton", "lib/NonlinearSolveSpectralMethods")
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for path in ("lib/SciMLJacobianOperators", ".", "lib/SimpleNonlinearSolve", "lib/NonlinearSolveBase", "lib/BracketingNonlinearSolve", "lib/NonlinearSolveFirstOrder", "lib/NonlinearSolveQuasiNewton", "lib/NonlinearSolveSpectralMethods", "lib/NonlinearSolveHomotopyContinuation")
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push!(dev_pks, Pkg.PackageSpec(; path))
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end
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Pkg.develop(dev_pks)

‎docs/Project.toml

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@@ -15,6 +15,7 @@ LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
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NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
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NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
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NonlinearSolveFirstOrder = "5959db7a-ea39-4486-b5fe-2dd0bf03d60d"
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NonlinearSolveHomotopyContinuation = "2ac3b008-d579-4536-8c91-a1a5998c2f8b"
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NonlinearSolveQuasiNewton = "9a2c21bd-3a47-402d-9113-8faf9a0ee114"
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NonlinearSolveSpectralMethods = "26075421-4e9a-44e1-8bd1-420ed7ad02b2"
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OrdinaryDiffEqTsit5 = "b1df2697-797e-41e3-8120-5422d3b24e4a"

‎docs/make.jl

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using NonlinearSolveBase, SciMLBase, DiffEqBase
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using SimpleNonlinearSolve, BracketingNonlinearSolve
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using NonlinearSolveFirstOrder, NonlinearSolveQuasiNewton, NonlinearSolveSpectralMethods
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using NonlinearSolveHomotopyContinuation
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using SciMLJacobianOperators
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using NonlinearSolve, SteadyStateDiffEq
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NonlinearSolveBase, SciMLBase, DiffEqBase,
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SimpleNonlinearSolve, BracketingNonlinearSolve,
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NonlinearSolveFirstOrder, NonlinearSolveQuasiNewton, NonlinearSolveSpectralMethods,
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NonlinearSolveHomotopyContinuation,
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Sundials,
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SciMLJacobianOperators,
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NonlinearSolve, SteadyStateDiffEq

‎docs/pages.jl

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"api/petsc.md",
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"api/siamfanlequations.md",
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"api/speedmapping.md",
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"api/sundials.md"
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"api/sundials.md",
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"api/homotopycontinuation.md"
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],
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"Sub-Packages" => Any[
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"api/SciMLJacobianOperators.md",

‎docs/src/api/homotopycontinuation.md

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# HomotopyContinuation.jl
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NonlinearSolve wraps the homotopy continuation algorithm implemented in
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HomotopyContinuation.jl. This solver is not included by default and needs
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to be installed separately:
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```julia
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using Pkg
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Pkg.add("NonlinearSolveHomotopyContinuation")
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using NonlinearSolveHomotopyContinuation, NonlinearSolve
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```
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# Solver API
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```@docs
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NonlinearSolveHomotopyContinuation.HomotopyContinuationJL
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SciMLBase.HomotopyContinuationFunction
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```

‎lib/NonlinearSolveHomotopyContinuation/LICENSE

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MIT License
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Copyright (c) 2024 Aayush Sabharwal <[email protected]> and contributors
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.

‎lib/NonlinearSolveHomotopyContinuation/Project.toml

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name = "NonlinearSolveHomotopyContinuation"
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uuid = "2ac3b008-d579-4536-8c91-a1a5998c2f8b"
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authors = ["Aayush Sabharwal <[email protected]> and contributors"]
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version = "0.1.0"
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[deps]
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ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
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CommonSolve = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
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ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
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DifferentiationInterface = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
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DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
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HomotopyContinuation = "f213a82b-91d6-5c5d-acf7-10f1c761b327"
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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NonlinearSolveBase = "be0214bd-f91f-a760-ac4e-3421ce2b2da0"
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SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
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SymbolicIndexingInterface = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
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TaylorDiff = "b36ab563-344f-407b-a36a-4f200bebf99c"
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[compat]
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ADTypes = "1.11.0"
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Aqua = "0.8"
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CommonSolve = "0.2.4"
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ConcreteStructs = "0.2.3"
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DifferentiationInterface = "0.6.27"
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DocStringExtensions = "0.9.3"
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HomotopyContinuation = "2.12.0"
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LinearAlgebra = "1.10"
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NonlinearSolve = "4"
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NonlinearSolveBase = "1.3.3"
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SciMLBase = "2.71"
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SymbolicIndexingInterface = "0.3.36"
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TaylorDiff = "0.3.1"
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Test = "1.10"
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julia = "1.10"
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[extras]
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Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
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NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
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Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
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[targets]
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test = ["Aqua", "Test", "NonlinearSolve"]

‎lib/NonlinearSolveHomotopyContinuation/src/NonlinearSolveHomotopyContinuation.jl

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module NonlinearSolveHomotopyContinuation
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using SciMLBase: AbstractNonlinearProblem
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using SciMLBase
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using NonlinearSolveBase
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using SymbolicIndexingInterface
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using LinearAlgebra
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using ADTypes
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using TaylorDiff
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using DocStringExtensions
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import CommonSolve
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import HomotopyContinuation as HC
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import DifferentiationInterface as DI
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using ConcreteStructs: @concrete
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export HomotopyContinuationJL, HomotopyNonlinearFunction
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"""
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HomotopyContinuationJL{AllRoots}(; autodiff = true, kwargs...)
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HomotopyContinuationJL(; kwargs...) = HomotopyContinuationJL{false}(; kwargs...)
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This algorithm is an interface to `HomotopyContinuation.jl`. It is only valid for
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fully determined polynomial systems. The `AllRoots` type parameter can be `true` or
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`false` and controls whether the solver will find all roots of the polynomial
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or a single root close to the initial guess provided to the `NonlinearProblem`.
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The polynomial function must allow complex numbers to be provided as the state.
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If `AllRoots` is `true`, the initial guess in the `NonlinearProblem` is ignored.
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The function must be traceable using HomotopyContinuation.jl's symbolic variables.
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Note that higher degree polynomials and systems with multiple unknowns can increase
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solve time significantly.
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If `AllRoots` is `false`, a single path is traced during the homotopy. The traced path
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depends on the initial guess provided to the `NonlinearProblem` being solved. This method
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does not require that the polynomial function is traceable via HomotopyContinuation.jl's
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symbolic variables.
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HomotopyContinuation.jl requires the jacobian of the system. In case a jacobian function
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is provided, it will be used. Otherwise, the `autodiff` keyword argument controls the
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autodiff method used to compute the jacobian. A value of `true` refers to
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`AutoForwardDiff` and `false` refers to `AutoFiniteDiff`. Alternate algorithms can be
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specified using ADTypes.jl.
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HomotopyContinuation.jl requires the taylor series of the polynomial system for the single
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root method. This is automatically computed using TaylorSeries.jl.
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"""
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@concrete struct HomotopyContinuationJL{AllRoots} <:
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NonlinearSolveBase.AbstractNonlinearSolveAlgorithm
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autodiff
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kwargs
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end
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function HomotopyContinuationJL{AllRoots}(; autodiff = true, kwargs...) where {AllRoots}
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if autodiff isa Bool
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autodiff = autodiff ? AutoForwardDiff() : AutoFiniteDiff()
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end
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HomotopyContinuationJL{AllRoots}(autodiff, kwargs)
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end
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HomotopyContinuationJL(; kwargs...) = HomotopyContinuationJL{false}(; kwargs...)
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include("interface_types.jl")
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include("solve.jl")
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end

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