README.md

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.