dubfi.linalg.dense
==================

.. py:module:: dubfi.linalg.dense

.. autoapi-nested-parse::

   Dense numpy array implementation of generic linear algebra types.

   .. codeauthor:: Valentin Bruch, DWD <valentin.bruch@dwd.de>
   .. versionadded:: 0.1.0 (initial release)



Classes
-------

.. autoapisummary::

   dubfi.linalg.dense.DenseMatrix
   dubfi.linalg.dense.LinParamVector
   dubfi.linalg.dense.DenseEnsLinPostRNoloc
   dubfi.linalg.dense.DenseEnsLinPostR
   dubfi.linalg.dense.DiagonalEnsLinPostR


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

.. py:class:: DenseMatrix(array)

   Bases: :py:obj:`dubfi.linalg.types.AbstractOperator`


   Operator represented by a dense matrix.


   .. py:property:: shape
      :type: tuple[int, Ellipsis]


      Shape of array (matrix) representation of self.


   .. py:property:: data
      :type: numpy.ndarray


      Numpy array (matrix) representation of self.


   .. py:method:: tonumpy()

      Numpy array (matrix) representation of self.



   .. py:method:: diagonal()

      Return copy of the diagonal of self.



   .. py:method:: __mul__(other)

      Multiply element-wise.



   .. py:method:: __imul__(other)

      Multiply element-wise in-place.



   .. py:method:: __add__(other)

      Add two linear operators.



   .. py:method:: __iadd__(other)

      Add two linear operators in-place.



   .. py:method:: __sub__(other)

      Subtract other operator.



   .. py:method:: __isub__(other)

      Subtract other operator in-place.



   .. py:method:: apply(vec)

      Apply operator on vector: self @ vec.



   .. py:method:: rapply(vec)

      Apply transpose operator on vector: self.T @ vec.



   .. py:method:: inv()

      Compute (multiplicative) inverse operator.



   .. py:method:: solve(vec)

      Solve linear equation self @ x = vec for x.



   .. py:method:: chain(other)

      Combine operators: self @ other.



   .. py:method:: trace()

      Compute trace of self.



   .. py:method:: trace_product(other)

      Compute trace of (self @ other).



   .. py:method:: logdet()

      Compute log(det(self)) assuming that self is a positive definite, real-symmetric matrix.



   .. py:method:: dot(other)

      Inner product along non-vector dimensions.



.. py:class:: LinParamVector(array)

   Bases: :py:obj:`dubfi.linalg.generic.ParametrizedVector`


   Linear parametrized simple dense vector.


   .. py:method:: __call__(s)

      Vector at given parameter array.



   .. py:method:: grad(s)

      Gradient w.r.t. parameters s.



   .. py:method:: hess(s)

      Hesse matrix w.r.t. parameters s.



.. py:class:: DenseEnsLinPostRNoloc(h_ensemble)

   Bases: :py:obj:`dubfi.linalg.generic.ParametrizedOperator`


   Dense operator constructed based on a flux ensemble without localization.


   .. py:method:: __call__(s)

      Operator at given parameter array.



   .. py:method:: grad(s)

      Gradient w.r.t. parameters s.



   .. py:method:: grad_vec(s, vec)

      Equivalent to self.grad(s) @ vec.



   .. py:method:: hess(s)

      Hesse matrix w.r.t. parameters s.



   .. py:method:: hess_vec(s, vec)

      Equivalent to self.hess(s) @ vec.



   .. py:method:: vec_hess_vec(s, left, right)

      Equivalent to left @ (self.hess(s) @ right).



.. py:class:: DenseEnsLinPostR(h_ensemble, loc, regularization = 0.0, bg_ens = None, bc_ens = None)

   Bases: :py:obj:`dubfi.linalg.generic.ParametrizedOperator`


   Dense operator constructed based on a flux ensemble with localization.

   Ensemble-based parametrized linear operator with localization.

   :param h_ensemble: shape (ensemble, state, observations) array representing
                      the observation operator in the different ensemble members.
   :type h_ensemble: np.ndarray
   :param loc: shape (observations, observations) array for suppressing
               correlations in the ensemble estimate
   :type loc: np.ndarray
   :param regularization: regularization term added to the diagonal of self.
   :type regularization: float | np.ndarray, optional
   :param bg_ens: ensemble of background concentrations, must be the same
                  ensemble as used for h_ensemble.
   :type bg_ens: np.ndarray, optional
   :param bc_ens: ensemble to estimate the boundary condition uncertainty,
                  must be an independent ensemble from bg_ens and h_ensemble.
   :type bc_ens: np.ndarray, optional


   .. py:method:: set_bg_ens(bg_ens)

      Set the background (or total concentration) meteorological ensemble.



   .. py:method:: set_bc_ens(bc_ens)

      Set boundary condition ensemble.



   .. py:method:: __call__(s)

      Compute operator at given parameter vector s.



   .. py:method:: grad(s)

      Gradient at given parameter vector s.



   .. py:method:: hess(s)

      Hesse matrix at given parameter vector s.



.. py:class:: DiagonalEnsLinPostR(h_ensemble, regularization = 0.0, bg_ens = None)

   Bases: :py:obj:`dubfi.linalg.generic.ParametrizedOperator`


   Diagonal operator constructed based on a flux ensemble.


   .. py:method:: set_bg_ens(bg_ens)

      Set the background (or total concentration) meteorological ensemble.



   .. py:method:: __call__(s)

      Compute operator at given parameter vector s.



   .. py:method:: grad(s)

      Gradient at given parameter vector s.



   .. py:method:: hess(s)

      Hesse matrix at given parameter vector s.