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https://github.com/thummeto/differentiableeigen.jl

The current implementation of `LinearAlgebra.eigen` does not support sensitivities. DifferentiableEigen.jl offers an `eigen` function that is differentiable by every AD-framework with support for ChainRulesCore.jl or ForwardDiff.jl.
https://github.com/thummeto/differentiableeigen.jl

Last synced: 15 days ago
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Host: GitHub
URL: https://github.com/thummeto/differentiableeigen.jl
Owner: ThummeTo
License: mit
Created: 2023-02-07T10:44:16.000Z (almost 2 years ago)
Default Branch: main
Last Pushed: 2024-11-25T17:04:26.000Z (about 1 month ago)
Last Synced: 2024-11-25T18:19:22.026Z (30 days ago)
Language: Julia
Homepage:
Size: 32.2 KB
Stars: 30
Watchers: 2
Forks: 2
Open Issues: 3
Metadata Files:
- Readme: README.md
- License: LICENSE

Awesome Lists containing this project

README

        # DifferentiableEigen.jl

[![Run Tests](https://github.com/ThummeTo/DifferentiableEigen.jl/actions/workflows/Test.yml/badge.svg)](https://github.com/ThummeTo/DifferentiableEigen.jl/actions/workflows/Test.yml)

[![Coverage](https://codecov.io/gh/ThummeTo/DifferentiableEigen.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/ThummeTo/DifferentiableEigen.jl)

[![ColPrac: Contributor's Guide on Collaborative Practices for Community Packages](https://img.shields.io/badge/ColPrac-Contributor's%20Guide-blueviolet)](https://github.com/SciML/ColPrac)

## What is DifferentiableEigen.jl?

The current implementation of `LinearAlgebra.eigen` does not support sensitivities. 

This package adds a new function `eigen`, that wraps the original function, but returns an array of reals instead of complex numbers (this is necessary, because some AD-frameworks do not support complex numbers). 

This `eigen` function is differentiable by every AD-framework with support for *ChainRulesCore.jl* and *ForwardDiff.jl*.

## How can I use DifferentiableEigen.jl?

1\. Open a Julia-REPL, switch to package mode using `]`, activate your preferred environment.

2\. Install [*DifferentiableEigen.jl*](https://github.com/ThummeTo/DifferentiableEigen.jl):

```julia-repl

(@v1.6) pkg> add DifferentiableEigen

```

3\. If you want to check that everything works correctly, you can run the tests bundled with [*DifferentiableEigen.jl*](https://github.com/ThummeTo/DifferentiableEigen.jl):

```julia-repl

(@v1.6) pkg> test DifferentiableEigen

```

## How does it work? 

```julia

import DifferentiableEigen

import LinearAlgebra

import ForwardDiff

A = rand(3,3)   # Random matrix 3x3 

eigvals, eigvecs = LinearAlgebra.eigen(A)   # This is the default eigen-function in Julia. Note, that eigenvalues and -vectors are complex numbers.

jac = ForwardDiff.jacobian((A) -> LinearAlgebra.eigen(A)[1], A)   # That doesn't work!

eigvals, eigvecs = DifferentiableEigen.eigen(A)   # This is the differentiable eigen-function. Note, that eigenvalues and -vectors are not complex numbers, but real arrays!  

jac = ForwardDiff.jacobian((A) -> DifferentiableEigen.eigen(A)[1], A)   # That does work! eigenvalue- and eigenvector-sensitvities

```

## Acknowledgement

This package was motivated by this [discourse thread](https://discourse.julialang.org/t/native-eigenvals-for-differentiable-programming/27126). 

For now, there is no other (known) ready to use solution for differentiable eigenvalues and -vectors. 

If this changes, please feel free to open a PR or discussion.

The sensitivity formulas are picked from:

Michael B. Giles. 2008. **An extended collection of matrix derivative results for forward and reverse mode algorithmic differentiation.** [PDF](https://people.maths.ox.ac.uk/gilesm/files/NA-08-01.pdf)

## How to cite? Related publications?

Tobias Thummerer and Lars Mikelsons. 2023. **Eigen-informed NeuralODEs: Dealing with stability and convergence issues of NeuralODEs.** ArXiv. [PDF](https://arxiv.org/abs/2302.10892)