QMat Package ************ .. raw:: html PyPI - Package PyPI - Download Last Commit CI pipeline Codecov `qmat` is a python package to generate matrix coefficients related to Collocation methods, Spectral Deferred Corrections (SDC), and more generally for Runge-Kutta methods. It allows to generate :math:`Q`-coefficients for multi-stages methods (equivalent to Butcher tables) : .. math:: Q\text{-coefficients : } \begin{array} {c|c} \tau & Q \\ \hline & w^\top \end{array} \quad \Leftrightarrow \quad \begin{array} {c|c} c & A \\ \hline & b^\top \end{array} \quad\text{(Butcher table)} and many different **lower-triangular** approximations of the :math:`Q` matrix, named :math:`Q_\Delta`, which are key elements for Spectral Deferred Correction (SDC), or more general Iterated Runge-Kutta Methods. It also contains **generic time-integration solvers** based on :math:`Q` and :math:`Q_\Delta` coefficients, that can be used for quick testing and experiments. .. raw:: html DOI This package can be installed using `pip` : .. code-block:: bash pip install qmat ... but you can also use `conda` or installation from sources, see the :doc:`Installation Instructions 💾` 📜 *If you are already familiar with those concepts, you can use this package like this :* .. code-block:: python from qmat import genQCoeffs, genQDeltaCoeffs # Coefficients or 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") *But if you are new to this, then welcome ! ... and please have a look at the* **step by step tutorials** *below* 😉 For any contribution, please checkout out (very cool) :doc:`Contribution Guidelines 🔑` and the current :doc:`Development Roadmap 🎯` Projects relying on `qmat` ========================== * `pySDC `_ : *Python implementation of the spectral deferred correction (SDC) approach and its flavors, esp. the multilevel extension MLSDC and PFASST.* * `SWEET `_ : *Shallow Water Equation Environment for Tests, Awesome! (C++).* Doc Contents ============ .. toctree:: :maxdepth: 1 installation notebooks contributing API reference Links ===== * Code repository: https://github.com/Parallel-in-Time/qmat * Issues Tracker : https://github.com/Parallel-in-Time/qmat/issues * Q&A : https://github.com/Parallel-in-Time/qmat/discussions/categories/q-a * Project Proposals : https://github.com/Parallel-in-Time/qmat/discussions/categories/project-proposals Developers ========== * `Thibaut Lunet `_ * `Thomas Saupe (né Baumann) `_