qmat
====

.. py:module:: qmat

.. autoapi-nested-parse::

   **Main sub-packages** 📦

   - :class:`qcoeff` : to generate the :math:`Q`-coefficients (Butcher tables)
   - :class:`qdelta` : to generate :math:`Q_\Delta` approximations for :math:`Q` matrices

   **Secondary sub-packages** 🍭

   - :class:`solvers` : implementations of time-integration solvers that make use of `qmat`-generated coefficients
   - :class:`playgrounds`: **non-tested but documented** codes with experiments or small applications with `qmat`

   **Utility modules** ⚙️

   - :class:`lagrange` : Barycentric polynomial approximations (integral, interpolation, derivative)
   - :class:`nodes` : generation of multiple types of quadrature nodes
   - :class:`mathutils` : utility functions for math operations
   - :class:`utils` : utility functions for the whole package

   .. rubric:: Examples

   >>> from qmat import genQCoeffs, genQDeltaCoeffs
   >>>
   >>> # Coefficients of a specific collocation method
   >>> nodes, weights, Q = genQCoeffs(
   >>>     "Collocation", nNodes=4, nodeType="LEGENDRE", quadType="RADAU-RIGHT")
   >>>
   >>> # QDelta matrix from Implicit-Euler based SDC
   >>> QDelta = genQDeltaCoeffs("IE", nodes=nodes)
   >>>
   >>> # Butcher table of the classical explicit RK4 method
   >>> c, b, A = genQCoeffs("ERK4")

   >>> from qmat import Q_GENERATORS, QDELTA_GENERATORS
   >>> print(Q_GENERATORS)         # list all available generator classes for Q coefficients
   >>> print(QDELTA_GENERATORS)    # list all available generator classes for QDelta approximations



Submodules
----------

.. toctree::
   :maxdepth: 1

   /api/qmat/lagrange/index
   /api/qmat/mathutils/index
   /api/qmat/nodes/index
   /api/qmat/playgrounds/index
   /api/qmat/qcoeff/index
   /api/qmat/qdelta/index
   /api/qmat/solvers/index
   /api/qmat/utils/index