:py:mod:`bempp.api.linalg`
==========================

.. py:module:: bempp.api.linalg

.. autoapi-nested-parse::

   Linear solvers.

   Documentation of the functionality of this module and examples
   can be found at https://bempp.com/handbook/api/solvers.html



Submodules
----------
.. toctree::
   :titlesonly:
   :maxdepth: 1

   direct_solvers/index.rst
   iterative_solvers/index.rst


Package Contents
----------------


Functions
~~~~~~~~~

.. autoapisummary::

   bempp.api.linalg.gmres
   bempp.api.linalg.cg
   bempp.api.linalg.lu



.. py:function:: gmres(A, b, tol=1e-05, restart=None, maxiter=None, use_strong_form=False, return_residuals=False, return_iteration_count=False)

   Perform GMRES solve via interface to scipy.

   This function behaves like the scipy.sparse.linalg.gmres function. But
   instead of a linear operator and a vector b it takes a boundary operator
   and a grid function or a blocked operator and a list of grid functions.
   The result is returned as a grid function or as a list of grid functions
   in the correct spaces.



.. py:function:: cg(A, b, tol=1e-05, maxiter=None, use_strong_form=False, return_residuals=False, return_iteration_count=False)

   Perform CG solve via interface to scipy.

   This function behaves like the scipy.sparse.linalg.cg function. But
   instead of a linear operator and a vector b it takes a boundary operator
   and a grid function. The result is returned as a grid function in the
   correct space.



.. py:function:: lu(A, b, lu_factor=None)

   Perform an LU solve.

   This function takes an operator and a grid function,
   converts the operator into a dense matrix and solves
   the system via LU decomposition. The result is again
   returned as a grid function.

   Parameters
   ----------
   A : bempp.api.BoundaryOperator
        The left-hand side boundary operator
   b : bempp.api.GridFunction
        The right-hand side grid function
   lu_decomp : tuple
        Optionally pass the tuple (lu, piv)
        obtained by the scipy method scipy.linalg.lu_factor