semvec/pypi-packages huggingface dataset:
eigd 1.0.0
Tools for eigenvector derivatives
License: Apache License, Version 2.0

# eigd
## Tools for computing eigenvector derivatives

The `eigd` package uses the adjoint method to compute the total derivative of functions that depend on the eigenvalues and eigenvectors of a generalized eigenvalue problem. The eigenvalue problem takes the form

$$A(x) \phi_{i} = \lambda_{i} B(x) \phi_{i}$$ 

for $i = 1,\ldots,N$, where the matrices $A$ and $B$ are square and depend on design variables $x$ and $B$ is positive definite. The eigenvectors are $B$ orthonormal.

The eigenvectors and eigenvalues can then be used to compute a function of interest as

$$f(\lambda_{1}, \ldots, \lambda_{N}, \phi_{1}, \ldots, \phi_{N})$$

`eigd` takes the derivative of the function of interest with respect to the design variables using the adjoint method.

## Installation

* Clone this repository, then enter the folder in the command line terminal.
* Enter `pip install -e .` within the `eigd` folder.