nifty8.operator_spectrum module

operator_spectrum(A, k, hermitian, which='LM', tol=0, return_eigenvectors=False)

Find k eigenvalues and eigenvectors of the endomorphism A.

Parameters:

• A (LinearOperator) – Operator of which eigenvalues shall be computed.

• k (int) – The number of eigenvalues and eigenvectors desired. k must be smaller than N-1. It is not possible to compute all eigenvectors of a matrix.

• hermitian (bool) – Specifies whether A is hermitian or not.

• which (str, ['LM' | 'SM' | 'LR' | 'SR' | 'LI' | 'SI'], optional) –

  Which k eigenvectors and eigenvalues to find:

  ’LM’ : largest magnitude

  ’SM’ : smallest magnitude

  ’LR’ : largest real part

  ’SR’ : smallest real part

  ’LI’ : largest imaginary part

  ’SI’ : smallest imaginary part

• tol (float, optional) – Relative accuracy for eigenvalues (stopping criterion) The default value of 0 implies machine precision.

• return_eigenvectors (bool, optional) – Return eigenvectors (True) in addition to eigenvalues

Returns:

• w (ndarray) – Array of k eigenvalues.

• v (ndarray) – An array representing the k eigenvectors. The column v[:, i] is the eigenvector corresponding to the eigenvalue w[i].

Raises:

ArpackNoConvergence – When the requested convergence is not obtained. The currently converged eigenvalues and eigenvectors can be found as eigenvalues and eigenvectors attributes of the exception object.