xemd: third-party code, authors and licenses

xemd is distributed under the GNU General Public License, version 3
(License: GPL-3 in DESCRIPTION). Parts of its R code are adapted from the
software listed below, in alphabetical order. Each entry names the source
and its revision, the authors and the copyright notice that the source
states, its license, the files of xemd that contain the adapted code
(paths of the source package) and the dates on which xemd modified them.
The texts of the Apache License 2.0, the GNU General Public License
version 3, the GNU Library General Public License version 2 and the MIT
license are the standard licenses that R ships in the directory
share/licenses of its installation (R.home("share")); the package does not
install copies of them. Every MIT copyright notice is reproduced in full
below.



emd.m, distributed with CEEMDAN
-------------------------------

Adapted from emd.m by G. Rilling (last modification March 2007), as
distributed with CEEMDAN, revision af9a0f83, in R/extendExtrema.R
(modified for xemd on 2026-10-09) and R/interpolateSpline.R (modified for
xemd on 2026-10-06 and 2026-10-09).

MIT License

Copyright (c) 2020 Marcelo A. Colominas

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

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 AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.


emdr 1.2.3
----------

Adapted from emdr 1.2.3 (R), revision
a802208b98e506071bb4f3c7eea4d2e5ad0a16f7, R/memd.R, function
get.projections, by Pierre Masselot: the angles that turn each Hammersley
point into a unit direction, in R/buildDirections.R. Modified for xemd on
2026-10-11.
License: GPL-3, as declared in the DESCRIPTION of emdr 1.2.3.


ewtpy
-----

Adapted from ewtpy (Python), revision
f9ff38bc5cd7859eea58c5b29099f8a503792b63, by Vinícius Rezende Carvalho,
in R/buildFilterBank.R, R/segmentSpectrum.R and R/transformEWT.R. The
ewtpy functions name Jerome Gilles as author of the MATLAB code they
translate, together with Kathryn Heal for the detection of boundaries and
local maxima. Modified for xemd on 2026-10-11.

Copyright (c) 2019 Vinícius Carvalho & Eduardo Mazoni

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

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 AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.


fifpy
-----

Adapted from fifpy (Python), revision
26e51e7d45e551950dea8be37ece447fc4340296, in R/iterateFluctuationPeriodic.R,
R/iterateFluctuationZero.R, R/resampleFilter.R and R/selectHalfWidth.R.
The fifpy sources name Emanuele Papini as author of the Python version and
Antonio Cicone as author of the original MATLAB version. Modified for xemd
on 2026-10-11.

MIT License

Copyright (c) 2022 Emanuele Papini

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

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 AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.


gmsp 0.8.0
----------

Adapted from gmsp 0.8.0, commit 28e2ca2bf177358c039cf9384620216b0034dacb, by
Alejandro Verri Kozlowski: the regularization of the time grid
(lib/R/regularize.R) and the rationalization of the sampling interval
(lib/R/utils.R), in R/regularizeSeries.R and R/rationalizeStep.R.
Modified for xemd on 2026-10-11.

MIT License

Copyright (c) 2026 Alejandro Verri Kozlowski

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

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 AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.



LMD 1.2.1
---------

Adapted from LMD 1.2.1 (R), revision
ec11b721ec7b05f0137eeb67a619b28f62ef85a2, by Shubhra Prakash, in
R/buildLocalLevels.R and R/extractProduct.R. Modified for xemd on
2026-10-11.
License: Apache License (>= 2), as declared in the DESCRIPTION of LMD
1.2.1. The LMD sources carry no copyright notice and no NOTICE file. The
same DESCRIPTION states that LMD is based on the approach suggested by
Smith (2005) and on the Python library PyLMD.


pyewt
-----

Adapted from pyewt (Python), revision
9d60a340f34e92356ed4f7a6a8b7044f524455e3, by Jerome Gilles, in
R/synthesizeBands.R. Modified for xemd on 2026-10-11.

MIT License

Copyright (c) 2024 Jerome Gilles

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

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 AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.


pytvfemd 0.3.14
---------------

Adapted from pytvfemd 0.3.14 (Python), by Stefano Bianchi and Alessandro
Longo, in R/approximateSpline.R, R/decomposeTVFEMD.R, R/estimateCutoff.R,
R/extractTVFMode.R, R/measureBandwidth.R, R/placeKnots.R and
R/realignCutoff.R. Modified for xemd on 2026-10-11.
License: GPL-3, as declared in the METADATA of pytvfemd 0.3.14
("License: GPLv3.0"); its LICENSE file is the text of the GNU General Public
License version 3 in share/licenses of the R installation.

Copyright (C) 2022-  Stefano Bianchi, Alessandro Longo

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <https://www.gnu.org/licenses/>.


SynchWave 1.1.2
---------------

Adapted from SynchWave 1.1.2 (R and Fortran), revision
9ac80b2c3e60b417d0ee5567a66e8e64faa1a979, in R/evaluateMorlet.R,
R/reassignCWT.R and R/transformCWT.R (modified for xemd on 2026-10-06 and
2026-10-11), R/invertSST.R (modified for xemd on 2026-10-11) and
R/traceSSTRidge.R and R/extractSSTModes.R (modified for xemd on
2026-10-14). The SynchWave DESCRIPTION names the authors as "Matlab
original by Eugene Brevdo; R port by Dongik Jang, Hee-Seok Oh and Donghoh
Kim"; its Fortran source names Eugene Brevdo and Hau-Tieng Wu as original
authors of the Synchrosqueezing Toolbox, and Jianfeng Lu as original author
and Eugene Brevdo as maintainer of curve_ext. R/traceSSTRidge.R adapts
curve_ext, and R/extractSSTModes.R adapts curve_ext_multi, which calls
curve_ext once per curve.
License: LGPL (>= 2), as declared in the DESCRIPTION of SynchWave 1.1.2:
the GNU Library General Public License version 2 or any later version.
xemd distributes these six files under the GNU General Public License
version 3, as section 3 of the GNU Library General Public License version 2
permits.
