88 lines
2.8 KiB
Python
88 lines
2.8 KiB
Python
# This file is part of Bertini 2.
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#
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# python/pybertini/endgame/__init__.py is free software: you can redistribute it and/or modify
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# it under the terms of the GNU General Public License as published by
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# the Free Software Foundation, either version 3 of the License, or
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# (at your option) any later version.
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#
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# python/pybertini/endgame/__init__.py is distributed in the hope that it will be useful,
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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# GNU General Public License for more details.
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#
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# You should have received a copy of the GNU General Public License
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# along with python/pybertini/endgame/__init__.py. If not, see <http://www.gnu.org/licenses/>.
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#
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# Copyright(C) 2018 by Bertini2 Development Team
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#
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# See <http://www.gnu.org/licenses/> for a copy of the license,
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# as well as COPYING. Bertini2 is provided with permitted
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# additional terms in the b2/licenses/ directory.
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# individual authors of this file include:
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#
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# silviana amethyst
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# UWEC
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# Spring 2018
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#
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"""
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Endgame-specific things -- endgames, configs
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***********************************************
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Endgames allow the computation of singular endpoints.
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Flavors
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=========
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There are two basic flavors of endgame implemented:
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1. Power Series, commonly written PS or PSEG
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2. Cauchy
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Both estimate the cycle number and use it to compute a root at a time which is never tracked to. PSEG uses Hermite interpolation and extrapolation, and Cauchy uses loops around the target time coupled with the `Cauchy integral formula <https://en.wikipedia.org/wiki/Cauchy%27s_integral_formula>`_. Both continue until two successive approximations of the root match to a given tolerance (:py:attr:`pybertini.endgame.config.Endgame.final_tolerance`).
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The implementations of the endgames go with a particular tracker, hence there are six provided endgame types. Choose the one that goes with your selected tracker type. Adaptive Multiple Precision is a good choice.
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Implementation reference
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=========================
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AMP Endgames
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-------------
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* :class:`~pybertini.endgame.AMPCauchyEG`
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* :class:`~pybertini.endgame.AMPPSEG`
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Fixed Double Precision Endgames
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---------------------------------
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* :class:`~pybertini.endgame.FixedDoublePSEG`
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* :class:`~pybertini.endgame.FixedDoublePSEG`
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Fixed Multiple Precision Endgames
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-------------------------------------
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* :class:`~pybertini.endgame.FixedMultiplePSEG`
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* :class:`~pybertini.endgame.FixedMultiplePSEG`
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"""
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import pybertini._pybertini.endgame
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from pybertini._pybertini.endgame import *
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__all__ = ['AMPCauchyEG',
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'AMPPSEG',
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'FixedDoubleCauchyEG',
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'FixedDoublePSEG',
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'FixedMultipleCauchyEG',
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'FixedMultiplePSEG',
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'__doc__',
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'__loader__',
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'__name__',
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'__package__',
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'__spec__',
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'config',
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'observers']
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