qmat.qcoeff.collocation
=======================

.. py:module:: qmat.qcoeff.collocation

.. autoapi-nested-parse::

   Submodule to generate Q matrices based on Collocation

   .. rubric:: Examples

   >>> from qmat.qcoeff.collocation import Collocation
   >>> coll = Collocation(nNodes=4, nodeType="LEGENDRE", quadType="RADAU-RIGHT")
   >>> nodes, weights, Q = coll.genCoeffs()
   >>> S = coll.S



Classes
-------

.. autoapisummary::

   qmat.qcoeff.collocation.Collocation


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

.. py:class:: Collocation(nNodes, nodeType, quadType, tLeft=0, tRight=1)


   .. autoapi-inheritance-diagram:: qmat.qcoeff.collocation.Collocation
      :parts: 1


   Base class to generate :math:`Q`-coefficients for a Collocation method.

   :Parameters: * **nNodes** (*int*) -- Number of collocation nodes.
                * **nodeType** (*str*) -- Type of node distributions, see :class:`qmat.nodes` for possible choices.
                * **quadType** (*str*) -- Quadrature type, see :class:`qmat.nodes` for possible choices.
                * **tLeft** (*float, optional*) -- Left boundary for the nodes. The default is 0.
                * **tRight** (*float, optional*) -- Right boundary for the nodes. The default is 1.


   .. py:attribute:: aliases
      :value: ['coll']



   .. py:attribute:: DEFAULT_PARAMS

      Defaults parameters for getInstance


   .. py:attribute:: approx


   .. py:property:: nodes
      :type: numpy.ndarray


      Nodes :math:`\tau` (:math:`c` coefficients in Butcher table)


   .. py:property:: Q
      :type: numpy.ndarray


      :math:`Q` coefficients (:math:`A` Butcher table)


   .. py:property:: weights
      :type: numpy.ndarray


      Weights :math:`\omega` (:math:`b` coefficients in Butcher table)


   .. py:property:: S
      :type: numpy.ndarray


      Quadrature matrix in node to node (N2N)


   .. py:property:: hCoeffs
      :type: numpy.ndarray


      :math:`h` interpolation coefficients for the right boundary


   .. py:property:: order
      :type: int


      Global convergence order of the method