Module evd

Low level implementation of the eigenvalue decomposition of a square diagonalizable matrix.

The eigenvalue decomposition of a square matrix $M$ of shape $(n, n)$ is a decomposition into two components $U$, $S$:

• $U$ has shape $(n, n)$ and is invertible,
• $S$ has shape $(n, n)$ and is a diagonal matrix,
• and finally:

$$M = U S U^{-1}.$$

If $M$ is Hermitian, then $U$ can be made unitary ($U^{-1} = U^H$), and $S$ is real valued.

Structs

• EvdParams
• HermitianEvdParams
  Hermitian eigendecomposition tuning parameters.

Enums

• ComputeVectors
  Indicates whether the eigenvectors are fully computed, partially computed, or skipped.

Functions

• compute_evd_complex
  Computes the eigenvalue decomposition of a square complex matrix.
• compute_evd_complex_custom_epsilon
  See compute_evd_complex.
• compute_evd_real
  Computes the eigenvalue decomposition of a square real matrix.
• compute_evd_real_custom_epsilon
  See compute_evd_real.
• compute_evd_req
  Computes the size and alignment of required workspace for performing an eigenvalue decomposition. The eigenvectors may be optionally computed.
• compute_hermitian_evd
  Computes the eigenvalue decomposition of a square Hermitian matrix. Only the lower triangular half of the matrix is accessed.
• compute_hermitian_evd_custom_epsilon
  See compute_hermitian_evd.
• compute_hermitian_evd_req
  Computes the size and alignment of required workspace for performing a Hermitian eigenvalue decomposition. The eigenvectors may be optionally computed.
• compute_hermitian_pseudoinverse
  Computes the pseudo inverse of a decomposed square Hermitian matrix.
  s represents the diagonal of the matrix $S$, and must have size equal to the dimension of the matrix.
  u represents the eigenvectors.
  The result is stored into pinv.
• compute_hermitian_pseudoinverse_custom_epsilon
  See compute_hermitian_pseudoinverse.
• compute_hermitian_pseudoinverse_req
  Computes the size and alignment of required workspace for performing a decomposed Hermitian matrix pseudoi inverse