COPYRIGHTS

cppDE: Third-Party Copyright Notices
=====================================

cppDE itself is distributed under the MIT License; see the top-level
LICENSE / LICENSE.md.  Portions of the C++ implementation in
`inst/include/cppde/` are derived from the third-party projects listed
below and remain subject to the respective upstream licenses.  Their
original copyright notices and license texts are reproduced verbatim.


--------------------------------------------------------------------
1. SUNDIALS / CVODE(S)
--------------------------------------------------------------------

Scope of derivation
-------------------
The Nordsieck multistep stepper (BDF/NDF and Adams-Moulton variants)
in

  inst/include/cppde/cppde_multistepper.hpp
  inst/include/cppde/cppde_multistepper_controller.hpp
  inst/include/cppde/cppde_newton.hpp

is a port of the BDF/Adams algorithms, step-size and order control,
predictor/corrector pipeline, error-weight machinery, NDF kappa
modification, and Newton iteration from SUNDIALS/CVODE(S) (file
`cvode.c` and related sources).  Routine names referenced in inline
comments (cvSetAdams, cvAdjustParams, cvNlsFunctional, cvDlsSetup,
cvSensUpdateNorm, cvHin, …) point to their CVODE(S) origins.  The
sensitivity-aware staggered Newton path follows the CVODES
CV_STAGGERED convention.

Project: SUNDIALS  (https://computing.llnl.gov/projects/sundials)
Upstream license file: SUNDIALS LICENSE (BSD-3-Clause).

Original copyright notice
-------------------------
Copyright (c) 2002-2024, Lawrence Livermore National Security and
Southern Methodist University.
All rights reserved.

See the top-level LICENSE and NOTICE files in the SUNDIALS source
distribution for details.

License text (BSD 3-Clause "New" or "Revised" License)
------------------------------------------------------
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:

1. Redistributions of source code must retain the above copyright
   notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright
   notice, this list of conditions and the following disclaimer in
   the documentation and/or other materials provided with the
   distribution.

3. Neither the name of the copyright holder nor the names of its
   contributors may be used to endorse or promote products derived
   from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

The cvode() R-side wrapper (`R/cvode.R`) and the generated CVODE glue
in `inst/python/codegen_cvode.py` link against an unmodified system
SUNDIALS installation; that linkage is governed by the same BSD-3
license but does not vendor any SUNDIALS source.


--------------------------------------------------------------------
2. Boost.Numeric.Odeint
--------------------------------------------------------------------

Scope of derivation
-------------------
The Rosenbrock4 stepper architecture (stage matrix, dense output,
controller protocol) in

  inst/include/cppde/cppde_rosenbrock4.hpp
  inst/include/cppde/cppde_stage_matrix.hpp
  inst/include/cppde/cppde_onestep_controller.hpp
  inst/include/cppde/cppde_onestep_dense_output.hpp
  inst/include/cppde/cppde_odeint_compat.hpp

is derived from `boost::numeric::odeint::rosenbrock4` and its
surrounding stepper-protocol infrastructure.

Project: Boost.Numeric.Odeint
        (https://www.boost.org/doc/libs/release/libs/numeric/odeint/)

Original copyright notice
-------------------------
Copyright 2009-2015 Karsten Ahnert
Copyright 2009-2015 Mario Mulansky
Copyright 2011-2013 Christoph Koke

License text (Boost Software License, Version 1.0)
--------------------------------------------------
Permission is hereby granted, free of charge, to any person or
organization obtaining a copy of the software and accompanying
documentation covered by this license (the "Software") to use,
reproduce, display, distribute, execute, and transmit the Software,
and to prepare derivative works of the Software, and to permit
third-parties to whom the Software is furnished to do so, all subject
to the following:

The copyright notices in the Software and this entire statement,
including the above license grant, this restriction and the following
disclaimer, must be included in all copies of the Software, in whole
or in part, and all derivative works of the Software, unless such
copies or derivative works are solely in the form of machine-
executable object code generated by a source language processor.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-
INFRINGEMENT. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR ANYONE
DISTRIBUTING THE SOFTWARE BE LIABLE FOR ANY DAMAGES OR OTHER
LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT
OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.


--------------------------------------------------------------------
3. Tsitouras 5(4) coefficients
--------------------------------------------------------------------

`inst/include/cppde/cppde_tsit5.hpp` implements the 7-stage explicit
Runge-Kutta pair of Tsitouras (2011).  The numerical Butcher
coefficients are taken from the published paper; the implementation
itself is original.

Reference:
  Tsitouras, Ch. (2011). "Runge-Kutta pairs of order 5(4) satisfying
  only the first column simplifying assumption."  Computers &
  Mathematics with Applications, 62(2), 770-775.

Mathematical formulae and tableaux are not subject to copyright; this
entry is provided as scientific attribution, not a license obligation.


--------------------------------------------------------------------
4. SUNDIALS / SuiteSparse-KLU at runtime
--------------------------------------------------------------------

The `cvode()` backend and the sparse-Jacobian path of `cppODE()` link
against unmodified system installations of SUNDIALS (BSD-3-Clause)
and SuiteSparse-KLU (LGPL-2.1+).  No source from these libraries is
vendored in this package; their licenses govern the libraries
themselves at the user's installation site.