tempnet.parallel_expm
=====================

.. py:module:: tempnet.parallel_expm

.. autoapi-nested-parse::

   #
   # flow stability
   #
   # Copyright (C) 2021 Alexandre Bovet <alexandre.bovet@maths.ox.ac.uk>
   #
   # This program is free software; you can redistribute it and/or modify it under
   # the terms of the GNU Lesser General Public License as published by the Free
   # Software Foundation; either version 3 of the License, or (at your option) any
   # later version.
   #
   # This program is distributed in the hope that it will be useful, but WITHOUT
   # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
   # FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
   # details.
   #
   # You should have received a copy of the GNU Lesser General Public License
   # along with this program. If not, see <http://www.gnu.org/licenses/>.




Attributes
----------

.. autoapisummary::

   tempnet.parallel_expm.var_dict


Functions
---------

.. autoapisummary::

   tempnet.parallel_expm.compute_parallel_expm
   tempnet.parallel_expm.compute_subspace_expm_parallel


Module Contents
---------------

.. py:function:: compute_parallel_expm(A, nproc=1, thresh_ratio=None, normalize_rows=True, verbose=True)

   Computes the exponential matrix of A by computing each column separately
   exploiting the fact that the column i of expm(A) is expm_multiply(A,delta_i)
   where delta i is the vector with zeros everywhere except on i.
   This only works if A is equal to (minus) a Laplacian matrix


   :param A: Square csc sparse matrix representing (+ or -) a Laplacian.
             If A is not csc, it will be converted to csc format.
   :type A: scipy csc sparse matrix
   :param nproc: number of parallel processes. The default is 1.
   :type nproc: int, optional
   :param thresh_ratio: Threshold ratio used to trim negligible values in the resulting matrix.
                        For each columns `c`, values smaller than `max(c)/thresh_ratio` are set to
                        zero. Default is None.
   :type thresh_ratio: float, optional.
   :param normalize_rows: Whether rows of the resulting matrix are normalized to sum to 1.
   :type normalize_rows: bool, optional.

   :returns: scipy csr sparse matrix
   :rtype: expm(A).


.. py:function:: compute_subspace_expm_parallel(A, n_comp=None, comp_labels=None, verbose=False, nproc=1, thresh_ratio=None, normalize_rows=True)

   Compute the exponential matrix of `A` by applying expm on each connected
   subgraphs defined by A and recomposing it to return expm(A).
   Small subgraphs are computed in parallel, each using scipy expm,
   and large subgraphs are computed with compute_parallel_expm.

   :param A:
   :type A: scipy.sparse.csc_matrix

   nproc : int, optional
       number of parallel processes. The default is 1.
   thresh_ratio: float, optional.
       Threshold ratio used to trim negligible values in the resulting matrix.
       Values smaller than `max(expm(A))/thresh_ratio` are set to
       zero. Default is None.
   normalize_rows: bool, optional.
       Whether rows of the resulting matrix are normalized to sum to 1.


   :returns: * **expm(A)** (*scipy.sparse.csr_matrix*)
             * *matrix exponential of A*


.. py:data:: var_dict