Pycaputo

---------------------------------

Features
^^^^^^^^

* Implement an implicit L1 method in :class:`pycaputo.fode.caputo.L1`.
* Store an :class:`~numpy.ndarray` for the orders so that they are not recomputed
at each time step in :class:`~pycaputo.stepping.FractionalDifferentialEquationMethod`.
Several functions using :func:`~pycaputo.utils.cached_on_first_arg`, e.g.
``gamma1p`` are also cached.
* Rework the hierarchy for the product integration methods and update their
names. They are now available in :mod:`pycaputo.fode.caputo` only and called
directly ``ForwardEuler`` (before it was ``CaputoForwardEulerMethod``).
* Promote events to :mod:`pycaputo.events`. Specific methods can then inherit
from there to return additional information, as required.
* Add some dataclass helpers, e.g. :func:`~pycaputo.utils.dc_stringify`. All
numerical methods store their parameters in a dataclass, so these are used
all over.

Fixes
^^^^^

* Add more extensive tests for the Mittag-Leffler function.
* Add a ``py.typed`` file for upstream projects.
* Updated and fixed Lorenz example with
:class:`~pycaputo.fode.caputo.WeightedEuler` (:ghpr:`19`).
* Use :func:`numpy.einsum` to compute weights for faster evaluation.

Maintenance
^^^^^^^^^^^

* Use ``ruff format`` for our formatting needs.
* Switch to a ``src`` based layout.

----------------------------------

Features
^^^^^^^^

* Released on PyPI!

----------------------------------

Features
^^^^^^^^

* Add support for adaptive time stepping (:ghpr:`32`). This functionality is
very nice and there isn't much literature on the matter so it will likely
need substantial improvements in the future. For the moment, the work of
[Jannelli2020]_ is implement and seems to work reasonably well.

Fixes
^^^^^

* Make all methods use a vector of orders ``alpha`` when solving systems to be
more future proof.

----------------------------------

Dependency changes
^^^^^^^^^^^^^^^^^^

* Bumped minimum Python version to 3.9 (to match latest Numpy).

Features
^^^^^^^^

* Added an example with the fractional Lorenz system (:ghpr:`13`).
* Add a guess for the number of corrector iterations
for :class:`~pycaputo.fode.caputo.PECE` from [Garrappa2010]_.
* Added a modified PECE method from [Garrappa2010]_ in the form of
:class:`~pycaputo.fode.caputo.ModifiedPECE`.
* Implement :class:`~pycaputo.quadrature.riemann_liouville.Simpson`, a
standard 3rd order method.
* Implement :class:`~pycaputo.quadrature.riemann_liouville.CubicHermite`, a
standard 4th order method.
* Implement differentiation methods for the Riemann-Liouville derivatives based
on the Caputo derivative in
:class:`~pycaputo.differentiation.riemann_liouville.RiemannLiouvilleFromCaputoMethod`.
* Support different fractional orders for FODE systems in
:class:`~pycaputo.fode.caputo.ForwardEuler`,
:class:`~pycaputo.fode.caputo.WeightedEuler` and others.
* Add approximation for the Lipschitz constant (:ghpr:`18`).
* Add a (rather slow) wrapper to compute a fractional gradient (:ghpr:`35`).

Fixes
^^^^^

* Fix :class:`~pycaputo.quadrature.riemann_liouville.Trapezoidal` on
uniform grids (:ghissue:`3`).
* Fix Jacobian construction for :class:`~pycaputo.fode.caputo.WeightedEuler`
which gave incorrect results for systems of equations (:ghissue:`11`).
* Add dark variants of plots to the documentation for nicer results.
* Promoto history management to :mod:`pycaputo.history`.

------------------------------

This is the initial release of the project and has some basic functionality
implemented already.

* Evaluate Caputo derivatives of arbitrary real orders; several numerical methods
are implemented (L1, L2, spectral) in :ref:`sec-differentiation`.
* Evaluate Riemann-Liouville integrals of arbitrary real orders; several numerical
methods are implemented (rectangular, trapezoidal, spectral) in
:ref:`sec-quadrature`.
* Solve single-term fractional ordinary differential equations; several numerical
methods are implemented (forward and backward Euler, PECE) in
:ref:`sec-fode`.

The library is not stable in any way. Performance work will likely require
changes to some interfaces.