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https://github.com/ritchieng/eigenvectors-from-eigenvalues
PyTorch implementation comparison of old and new method of determining eigenvectors from eigenvalues.
https://github.com/ritchieng/eigenvectors-from-eigenvalues
colab determining-eigenvectors eigenvalues eigenvectors pytorch
Last synced: about 1 month ago
JSON representation
PyTorch implementation comparison of old and new method of determining eigenvectors from eigenvalues.
- Host: GitHub
- URL: https://github.com/ritchieng/eigenvectors-from-eigenvalues
- Owner: ritchieng
- License: mit
- Created: 2019-11-15T07:27:38.000Z (about 5 years ago)
- Default Branch: master
- Last Pushed: 2021-11-03T04:02:34.000Z (about 3 years ago)
- Last Synced: 2024-10-23T08:52:37.257Z (about 2 months ago)
- Topics: colab, determining-eigenvectors, eigenvalues, eigenvectors, pytorch
- Language: Jupyter Notebook
- Homepage: https://www.researchgate.net/publication/337322294_Eigenvectors_from_Eigenvalues_CPU_and_GPU_Implementation
- Size: 42 KB
- Stars: 99
- Watchers: 6
- Forks: 10
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
- awesome-fluid-dynamics - ritchieng/eigenvectors-from-eigenvalues - This repository implements a calculation of eigenvectors from eigenvectors elegantly through PyTorch.  (Post-processing and Data Analysis / ML / Optical Flow)
README
# New Eigenvectors from Eigenvalues Calculation
This repository implements this [paper](https://arxiv.org/pdf/1908.03795.pdf) that allows us to calculate eigenvectors from eigenvalues elegantly through PyTorch that allows your code to run on your CPU, GPU, or TPU.
Easily run it on your browser through Google Colab or copy the function locally.
## Run Notebook on Google Colab
[](https://colab.research.google.com/github/ritchieng/eigenvectors-from-eigenvalues/blob/master/notebooks/comparison.ipynb)
## Core Equation: Lemma 2
**Lemma 2.** The norm squared of the elements of the eigenvectors are related to the eigenvalues and the submatrix eigenvalues.
```
Mathjax of Lemma 2
$$| v_{i, j} | ^ 2 \prod_{k=1; k \neq i}^{n} (\lambda_i (A) - \lambda_k (A)) = \prod_{k=1}^{n - 1} (\lambda_i (A) - \lambda_k (M_j))$$
```
## Authors and Abstract
Peter B. Denton, Stephen J. Parke, Terance Tao, and Xining Zhang
```
We present a new method of succinctly determining eigenvectors
from eigenvalues. Specifically, we relate the norm squared of the elements of
eigenvectors to the eigenvalues and the submatrix eigenvalues.
```
## Dependencies
- PyTorch 1.9.1 (can be most versions of PyTorch as I used very core basic PyTorch functions)
- Python 3.8 (doesn't matter much as I use basic operations)
## Code Repository Citation
- If you would like to give some credit to this code implementation, these are the relevant links.
- [](https://zenodo.org/badge/latestdoi/221868248)
- [Eigenvectors from Eigenvalues CPU and GPU Implementation](https://www.researchgate.net/publication/337322294_Eigenvectors_from_Eigenvalues_CPU_and_GPU_Implementation)
## License
MIT