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utils.eig

utils.eig​

Wraps jnp.linalg.eig in a jit-compatible, differentiable manner.

The custom vjp allows gradients with resepct to the eigenvectors, unlike the standard jax implementation of eig. We use an expression for the gradient given in [2019 Boeddeker] along with a regularization scheme used in [2021 Colburn]. The method effectively applies a Lorentzian broadening to a term containing the inverse difference of eigenvalues.

[2019 Boeddeker] https://arxiv.org/abs/1701.00392 [2021 Coluburn] https://www.nature.com/articles/s42005-021-00568-6

Args:​

  • matrix: The matrix for which eigenvalues and eigenvectors are sought.
  • eps: Parameter which determines the degree of broadening.

Returns:​

  • None: The eigenvalues and eigenvectors.