warp.fem.linalg.tridiagonal_symmetric_eigenvalues_qr#

warp.fem.linalg.tridiagonal_symmetric_eigenvalues_qr = <Function tridiagonal_symmetric_eigenvalues_qr(D: typing.Any, L: typing.Any, Q: typing.Any, tol: typing.Any)>#

Computes the eigenvalues and eigen vectors of a symmetric tridiagonal matrix using the Symmetric tridiagonal QR algorithm with implicit Wilkinson shift

Parameters:

  • D (Any) – Main diagonal of the matrix

  • L (Any) – Lower diagonal of the matrix, indexed such that L[i] = A[i+1, i]

  • Q (Any) – Initialization for the eigenvectors, useful if a pre-transformation has been applied, otherwise may be identity

  • tol (Any) – Tolerance for the diagonalization residual (Linf norm of off-diagonal over diagonal terms)

Returns a tuple (D: vector of eigenvalues, P: matrix with one eigenvector per row) such that A = P^T D P

Ref: Arbenz P, Numerical Methods for Solving Large Scale Eigenvalue Problems, Chapter 4 (QR algorithm, Mar 13, 2018)