qmat.mathutils
==============

.. py:module:: qmat.mathutils

.. autoapi-nested-parse::

   Base module for math utility functions



Functions
---------

.. autoapisummary::

   qmat.mathutils.numericalOrder
   qmat.mathutils.lduFactorization
   qmat.mathutils.getExtrapolationMatrix


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

.. py:function:: numericalOrder(nSteps, err)

   Compute numerical order from two vectors containing the error and the number of time-steps.

   :Parameters: * **nSteps** (*np.1darray or list*) -- Different number of steps to compute the error.
                * **err** (*np.1darray*) -- Diffenrent error values associated to the number of steps.

   :returns: * **beta** (*float*) -- Order coefficient computed through linear regression.
             * **rmse** (*float*) -- The root mean square error of the linear regression.


.. py:function:: lduFactorization(A: numpy.ndarray)

   Perform LDU factorization on a square matrix A.

   :Parameters: **A** (*np.2darray*) -- The square matrix to factorize (n x n).

   :returns: * **L** (*np.2darray*) -- Lower triangular matrix with ones on the diagonal.
             * **D** (*np.2darray*) -- Diagonal matrix.
             * **U** (*np.2darray*) -- Upper triangular matrix with ones on the diagonal.


.. py:function:: getExtrapolationMatrix(nodes, times, pOrder=None)

   Generate a polynomial based extrapolation matrix,
   base on polynomial regression of a function represented
   on given nodes.

   :Parameters: * **nodes** (*np.1darray like, shape (M,)*) -- The nodes where function values are known.
                * **times** (*np.1darray like, shape (N,)*) -- The times where to extrapolate the polynomial.
                * **pOrder** (*int*) -- Order of the polynomial regression on the node values
                  (default = len(nodes)-1).

   :returns: **P** -- Extrapolation matrix, that can be used on any node values.
   :rtype: np.2darray, shape (N, M)