bw2calc.least_squares
=====================

.. py:module:: bw2calc.least_squares


Classes
-------

.. autoapisummary::

   bw2calc.least_squares.LeastSquaresLCA


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

.. py:class:: LeastSquaresLCA(demand, method=None, weighting=None, normalization=None, database_filepath=None, log_config=None, presamples=None, seed=None, override_presamples_seed=False)

   Bases: :py:obj:`bw2calc.lca.LCA`

   .. autoapi-inheritance-diagram:: bw2calc.least_squares.LeastSquaresLCA
      :parts: 1
      :private-bases:


   Solve overdetermined technosphere matrix with more products than activities using least-squares approximation.

   See also:

   * `Multioutput processes in LCA <http://chris.mutel.org/multioutput.html>`_
   * `LSMR in SciPy <http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.lsmr.html#scipy.sparse.linalg.lsmr>`_
   * `Another least-squares algorithm in SciPy <http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.lsqr.html#scipy.sparse.linalg.lsqr>`_


   Create a new LCA calculation.

   :param \* *demand*: The demand or functional unit. Needs to be a dictionary to indicate amounts, e.g. ``{("my database", "my process"): 2.5}``.
   :type \* *demand*: dict
   :param \* *method*: LCIA Method tuple, e.g. ``("My", "great", "LCIA", "method")``. Can be omitted if only interested in calculating the life cycle inventory.
   :type \* *method*: tuple, optional

   :returns: A new LCA object


   .. py:method:: decompose_technosphere()
      :abstractmethod:


      Factorize the technosphere matrix into lower and upper triangular matrices, :math:`A=LU`. Does not solve the linear system :math:`Ax=B`.

      Doesn't return anything, but creates ``self.solver``.

      .. warning:: Incorrect results could occur if a technosphere matrix was factorized, and then a new technosphere matrix was constructed, as ``self.solver`` would still be the factorized older technosphere matrix. You are responsible for deleting ``self.solver`` when doing these types of advanced calculations.





   .. py:method:: solve_linear_system(solver=lsmr)

      Master solution function for linear system :math:`Ax=B`.

          To most numerical analysts, matrix inversion is a sin.

          -- Nicolas Higham, Accuracy and Stability of Numerical Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2002, p. 260.

      We use `UMFpack <http://www.cise.ufl.edu/research/sparse/umfpack/>`_, which is a very fast solver for sparse matrices.

      If the technosphere matrix has already been factorized, then the decomposed technosphere (``self.solver``) is reused. Otherwise the calculation is redone completely.