Module evd 

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

the eigenvalue decomposition of a square matrix $A$ 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:

$$A = U S U^{-1}$$

if $A$ is self-adjoint, then $U$ can be made unitary ($U^{-1} = U^H$), and $S$ is real valued

Modules

hessenberg

hessenberg decomposition

tridiag

self-adjoint tridiagonalization

Structs

EvdFromSchurParams

schur to eigendecomposition conversion parameters

EvdParams

eigendecomposition tuning parameters

SelfAdjointEvdParams

self-adjoint eigendecomposition tuning parameters

Enums

ComputeEigenvectors

whether the eigenvectors should be computed

EvdError

eigendecomposition error

Functions

evd_cplx

computes the matrix $A$’s eigendecomposition

evd_real

computes the matrix $A$’s eigendecomposition

evd_scratch

computes the size and alignment of the workspace required to compute a matrix’s eigendecomposition

pseudoinverse_from_self_adjoint_evd

computes a self-adjoint matrix’s pseudoinverse, given the eigendecomposition factors $S$ and $U$

pseudoinverse_from_self_adjoint_evd_scratch

computes the size and alignment of the workspace required to compute a self-adjoint matrix’s pseudoinverse, given the eigendecomposition

pseudoinverse_from_self_adjoint_evd_with_tolerance

computes a self-adjoint matrix’s pseudoinverse, given the eigendecomposition factors $S$ and $U$, and tolerance parameters for determining zero eigenvalues

self_adjoint_evd

computes the matrix $A$’s eigendecomposition, assuming it is self-adjoint

self_adjoint_evd_scratch

computes the size and alignment of the workspace required to compute a self-adjoint matrix’s eigendecomposition