# This file is part of Bertini 2.
#
# python/bertini/endgame/__init__.py 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.
#
# python/bertini/endgame/__init__.py 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 python/bertini/endgame/__init__.py. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) Bertini2 Development Team
#
# See <http://www.gnu.org/licenses/> for a copy of the license,
# as well as COPYING. Bertini2 is provided with permitted
# additional terms in the b2/licenses/ directory.
# individual authors of this file include:
#
# silviana amethyst
# UWEC
# Spring 2018
#
"""
Endgame-specific things -- endgames, configs
***********************************************
Endgames allow the computation of singular endpoints.
Flavors
=========
There are two basic flavors of endgame implemented:
1. Power Series, commonly written PS or PSEG
2. Cauchy
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:`bertini.endgame.EndgameConfig.final_tolerance`).
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.
Implementation reference
=========================
AMP Endgames
-------------
* :class:`~bertini.endgame.AMPCauchyEndgame`
* :class:`~bertini.endgame.AMPPowerSeriesEndgame`
Fixed Double Precision Endgames
---------------------------------
* :class:`~bertini.endgame.FixedDoubleCauchyEndgame`
* :class:`~bertini.endgame.FixedDoublePowerSeriesEndgame`
Fixed Multiple Precision Endgames
-------------------------------------
* :class:`~bertini.endgame.FixedMultipleCauchyEndgame`
* :class:`~bertini.endgame.FixedMultiplePowerSeriesEndgame`
"""
import bertini._pybertini.endgame as _pybe
from bertini._pybertini.endgame import observers
from bertini._pybertini.endgame import (
CauchyConfig,
EndgameConfig,
PowerSeriesConfig,
SecurityConfig,
)
# configs gain update()/to_dict()/from_dict()/repr/eq
from ..config import _enhance_all
_enhance_all(_pybe)
class _EndgameBase:
"""Thin wrapper that stores the endgame boundary time at construction.
The C++ Run() re-precisions the stored boundary time to match whatever
precision the incoming point is at, so callers never need to manage that.
"""
def __init__(self, cpp_class, tracker, boundary_time):
object.__setattr__(self, '_eg', cpp_class(tracker))
self._eg.set_boundary_time(boundary_time)
def run(self, point):
return self._eg.run(point)
def __getattr__(self, name):
if name == '_eg':
raise AttributeError('_eg not initialized')
return getattr(self._eg, name)
[docs]
class AMPCauchyEndgame(_EndgameBase):
[docs]
def __init__(self, tracker, boundary_time):
super().__init__(_pybe.AMPCauchyEndgame, tracker, boundary_time)
[docs]
class AMPPowerSeriesEndgame(_EndgameBase):
[docs]
def __init__(self, tracker, boundary_time):
super().__init__(_pybe.AMPPowerSeriesEndgame, tracker, boundary_time)
[docs]
class FixedDoubleCauchyEndgame(_EndgameBase):
[docs]
def __init__(self, tracker, boundary_time):
super().__init__(_pybe.FixedDoubleCauchyEndgame, tracker, boundary_time)
[docs]
class FixedDoublePowerSeriesEndgame(_EndgameBase):
[docs]
def __init__(self, tracker, boundary_time):
super().__init__(_pybe.FixedDoublePowerSeriesEndgame, tracker, boundary_time)
[docs]
class FixedMultipleCauchyEndgame(_EndgameBase):
[docs]
def __init__(self, tracker, boundary_time):
super().__init__(_pybe.FixedMultipleCauchyEndgame, tracker, boundary_time)
[docs]
class FixedMultiplePowerSeriesEndgame(_EndgameBase):
[docs]
def __init__(self, tracker, boundary_time):
super().__init__(_pybe.FixedMultiplePowerSeriesEndgame, tracker, boundary_time)
__all__ = [
'AMPCauchyEndgame',
'AMPPowerSeriesEndgame',
'CauchyConfig',
'EndgameConfig',
'FixedDoubleCauchyEndgame',
'FixedDoublePowerSeriesEndgame',
'FixedMultipleCauchyEndgame',
'FixedMultiplePowerSeriesEndgame',
'PowerSeriesConfig',
'SecurityConfig',
'observers',
]