eigd 1.0.0

Tools for eigenvector derivatives

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.