tlm_adjoint.eigendecomposition

Module Contents

tlm_adjoint.eigendecomposition.eigendecompose(space, A_action, *, B_action=None, arg_space_type='primal', action_space_type=None, N_eigenvalues=None, solver_type=None, problem_type=None, which=None, tolerance=1e-12, pre_callback=None, post_callback=None)

Interface with SLEPc via slepc4py, for the matrix free solution of eigenproblems

\[A v = \lambda v,\]

or generalized eigenproblems

\[A v = \lambda B v.\]

Originally developed by loosely following the slepc4py 3.6.0 demo demo/ex3.py. slepc4py 3.6.0 license information follows:

=========================
LICENSE: SLEPc for Python
=========================

:Author:  Lisandro Dalcin
:Contact: dalcinl@gmail.com


Copyright (c) 2015, Lisandro Dalcin.
All rights reserved.

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modification, are permitted provided that the following conditions
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* Redistributions of source code must retain the above copyright
  notice, this list of conditions and the following disclaimer.

* Redistributions in binary form must reproduce the above copyright
  notice, this list of conditions and the following disclaimer in the
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"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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Parameters:

  • space – The space for each eigenvector.

  • A_action – A callable. Accepts a single variable argument, and returns a variable containing the result after left multiplication of the input by \(A\).

  • B_action – A callable. Accepts a single variable argument, and returns a variable containing the result after left multiplication of the input by \(B\).

  • arg_space_type – The space type of eigenvectors. ‘primal’, ‘dual’, ‘conjugate’, or ‘conjugate_dual’.

  • action_space_type – The space type of the result of multiplication by \(A\) or \(B\). ‘primal’, ‘dual’, ‘conjugate’, or ‘conjugate_dual’. Defaults to the space type conjugate dual to arg_space_type.

  • N_eigenvalues – An int, the number of eigenvalues to attempt to compute. Defaults to the dimension of space.

  • problem_type – The eigenproblem type – see slepc4py.SLEPc.EPS.ProblemType. Defaults to slepc4py.SLEPc.EPS.ProblemType.GNHEP if B_action is supplied, or slepc4py.SLEPc.EPS.ProblemType.NHEP otherwise.

  • which – Which eigenvalues to attempt to compute – see slepc4py.SLEPc.EPS.Which. Defaults to slepc4py.SLEPc.EPS.Which.LARGEST_MAGNITUDE.

  • tolerance – Convergence tolerance. By default the convergence criterion is defined using slepc4py.SLEPc.EPS.Conv.REL.

  • pre_callback – A callable accepting a single slepc4py.SLEPc.EPS argument. Used for detailed manual configuration. Called after all other configuration options are set, but before the slepc4py.SLEPc.EPS.setUp method is called.

  • post_callback – A callable accepting a single slepc4py.SLEPc.EPS argument. Called after the slepc4py.SLEPc.EPS.solve method has been called.

Returns:

A tuple (lam, V). lam is a numpy.ndarray containing eigenvalues. For non-Hermitian algorithms and a real build of PETSc, V is a tuple (V_r, V_i), where V_r and V_i are each a tuple of variables containing respectively the real and complex parts of corresponding eigenvectors. Otherwise V is a tuple of variables containing corresponding eigenvectors.