warp.fem.linalg.tridiagonal_symmetric_eigenvalues_qr#

warp.fem.linalg.tridiagonal_symmetric_eigenvalues_qr(D: Any, L: Any, Q: Any, tol: Any)[source]#
  • Kernel

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

Parameters:

  • D – Main diagonal of the matrix

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

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

  • tol – Tolerance on off-diagonal terms, relative to their neighboring diagonal terms. Tolerances below the machine epsilon of the scalar type fall back to the tightest attainable criterion.

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)