🎮 pybertini.endgame¶
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Notes¶
Auto-generated docs¶
Endgame-specific things – endgames, configs¶
Endgames allow the computation of singular endpoints.
Flavors¶
There are two basic flavors of endgame implemented:
- Power Series, commonly written PS or PSEG
- 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. Both continue until two successive approximations of the root match to a given tolerance (pybertini.endgame.config.Endgame.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¶
Fixed Double Precision Endgames¶
Fixed Multiple Precision Endgames¶
-
class
pybertini.endgame.
AMPCauchyEG
((object)arg1, (AMPTracker)arg2) → None¶ Bases:
Boost.Python.instance
The adaptive precision implementation of the Cauchy endgame
__init__( (object)arg1, (AMPTracker)arg2, (CauchyConfig)arg3) -> None
__init__( (object)arg1, (AMPTracker)arg2, (Endgame)arg3) -> None
__init__( (object)arg1, (AMPTracker)arg2, (Security)arg3) -> None
-
add_observer
((object)arg1, (object)arg2) → None¶
-
cycle_number
((AMPCauchyEG)arg1) → int :¶ Get the cycle number as currently computed
-
final_approximation
((AMPCauchyEG)arg1) → VectorXmp :¶ Get the current approximation of the root, in the ambient numeric type for the tracker being used
-
get_endgame_settings
((AMPCauchyEG)arg1) → Endgame :¶ Get the current non-specific endgame settings
-
get_security_settings
((AMPCauchyEG)arg1) → Security :¶ Get the ‘security’ settings for the endgame (path truncation near infinity)
-
get_system
((AMPCauchyEG)arg1) → System :¶ Get the tracked system. This is a reference to the internal system.
-
get_tracker
((AMPCauchyEG)arg1) → AMPTracker :¶ Get the tracker used in this endgame. This is the same tracker as you feed the endgame object when you make it. This is a reference variable
-
remove_observer
((object)arg1, (object)arg2) → None¶
-
run
((AMPCauchyEG)arg1, (Complex)start_time, (VectorXmp)start_point) → SuccessCode :¶ Run the endgame, from start point and start time, to t=0. Expects complex numeric type matching that of the tracker being used.
- run( (AMPCauchyEG)arg1, (Complex)start_time, (VectorXmp)start_point, (Complex)target_time) -> SuccessCode :
- Run the endgame, from start point and start time, to your choice of target time t. Expects complex numeric type matching that of the tracker being used.
-
set_endgame_settings
((AMPCauchyEG)arg1, (Endgame)arg2) → None :¶ Set the values of non-specific endgame settings
-
set_security_settings
((AMPCauchyEG)arg1, (Security)arg2) → None :¶ Set the values of security-level settings
-
-
class
pybertini.endgame.
AMPPSEG
((object)arg1, (AMPTracker)arg2) → None¶ Bases:
Boost.Python.instance
The adaptive precision implementation of the power series endgame.
__init__( (object)arg1, (AMPTracker)arg2, (PowerSeriesConfig)arg3) -> None
__init__( (object)arg1, (AMPTracker)arg2, (Endgame)arg3) -> None
__init__( (object)arg1, (AMPTracker)arg2, (Security)arg3) -> None
-
add_observer
((object)arg1, (object)arg2) → None¶
-
cycle_number
((AMPPSEG)arg1) → int :¶ Get the cycle number as currently computed
-
final_approximation
((AMPPSEG)arg1) → VectorXmp :¶ Get the current approximation of the root, in the ambient numeric type for the tracker being used
-
get_endgame_settings
((AMPPSEG)arg1) → Endgame :¶ Get the current non-specific endgame settings
-
get_security_settings
((AMPPSEG)arg1) → Security :¶ Get the ‘security’ settings for the endgame (path truncation near infinity)
-
get_system
((AMPPSEG)arg1) → System :¶ Get the tracked system. This is a reference to the internal system.
-
get_tracker
((AMPPSEG)arg1) → AMPTracker :¶ Get the tracker used in this endgame. This is the same tracker as you feed the endgame object when you make it. This is a reference variable
-
remove_observer
((object)arg1, (object)arg2) → None¶
-
run
((AMPPSEG)arg1, (Complex)start_time, (VectorXmp)start_point) → SuccessCode :¶ Run the endgame, from start point and start time, to t=0. Expects complex numeric type matching that of the tracker being used.
- run( (AMPPSEG)arg1, (Complex)start_time, (VectorXmp)start_point, (Complex)target_time) -> SuccessCode :
- Run the endgame, from start point and start time, to your choice of target time t. Expects complex numeric type matching that of the tracker being used.
-
set_endgame_settings
((AMPPSEG)arg1, (Endgame)arg2) → None :¶ Set the values of non-specific endgame settings
-
set_security_settings
((AMPPSEG)arg1, (Security)arg2) → None :¶ Set the values of security-level settings
-
-
class
pybertini.endgame.
FixedDoubleCauchyEG
((object)arg1, (DoublePrecisionTracker)arg2) → None¶ Bases:
Boost.Python.instance
The fixed double precision implementation of the Cauchy endgame
__init__( (object)arg1, (DoublePrecisionTracker)arg2, (CauchyConfig)arg3) -> None
__init__( (object)arg1, (DoublePrecisionTracker)arg2, (Endgame)arg3) -> None
__init__( (object)arg1, (DoublePrecisionTracker)arg2, (Security)arg3) -> None
-
add_observer
((object)arg1, (object)arg2) → None¶
-
cycle_number
((FixedDoubleCauchyEG)arg1) → int :¶ Get the cycle number as currently computed
-
final_approximation
((FixedDoubleCauchyEG)arg1) → VectorXd :¶ Get the current approximation of the root, in the ambient numeric type for the tracker being used
-
get_endgame_settings
((FixedDoubleCauchyEG)arg1) → Endgame :¶ Get the current non-specific endgame settings
-
get_security_settings
((FixedDoubleCauchyEG)arg1) → Security :¶ Get the ‘security’ settings for the endgame (path truncation near infinity)
-
get_system
((FixedDoubleCauchyEG)arg1) → System :¶ Get the tracked system. This is a reference to the internal system.
-
get_tracker
((FixedDoubleCauchyEG)arg1) → DoublePrecisionTracker :¶ Get the tracker used in this endgame. This is the same tracker as you feed the endgame object when you make it. This is a reference variable
-
remove_observer
((object)arg1, (object)arg2) → None¶
-
run
((FixedDoubleCauchyEG)arg1, (complex)start_time, (VectorXd)start_point) → SuccessCode :¶ Run the endgame, from start point and start time, to t=0. Expects complex numeric type matching that of the tracker being used.
- run( (FixedDoubleCauchyEG)arg1, (complex)start_time, (VectorXd)start_point, (complex)target_time) -> SuccessCode :
- Run the endgame, from start point and start time, to your choice of target time t. Expects complex numeric type matching that of the tracker being used.
-
set_endgame_settings
((FixedDoubleCauchyEG)arg1, (Endgame)arg2) → None :¶ Set the values of non-specific endgame settings
-
set_security_settings
((FixedDoubleCauchyEG)arg1, (Security)arg2) → None :¶ Set the values of security-level settings
-
-
class
pybertini.endgame.
FixedDoublePSEG
((object)arg1, (DoublePrecisionTracker)arg2) → None¶ Bases:
Boost.Python.instance
The double-precision implementation of the power series endgame
__init__( (object)arg1, (DoublePrecisionTracker)arg2, (PowerSeriesConfig)arg3) -> None
__init__( (object)arg1, (DoublePrecisionTracker)arg2, (Endgame)arg3) -> None
__init__( (object)arg1, (DoublePrecisionTracker)arg2, (Security)arg3) -> None
-
add_observer
((object)arg1, (object)arg2) → None¶
-
cycle_number
((FixedDoublePSEG)arg1) → int :¶ Get the cycle number as currently computed
-
final_approximation
((FixedDoublePSEG)arg1) → VectorXd :¶ Get the current approximation of the root, in the ambient numeric type for the tracker being used
-
get_endgame_settings
((FixedDoublePSEG)arg1) → Endgame :¶ Get the current non-specific endgame settings
-
get_security_settings
((FixedDoublePSEG)arg1) → Security :¶ Get the ‘security’ settings for the endgame (path truncation near infinity)
-
get_system
((FixedDoublePSEG)arg1) → System :¶ Get the tracked system. This is a reference to the internal system.
-
get_tracker
((FixedDoublePSEG)arg1) → DoublePrecisionTracker :¶ Get the tracker used in this endgame. This is the same tracker as you feed the endgame object when you make it. This is a reference variable
-
remove_observer
((object)arg1, (object)arg2) → None¶
-
run
((FixedDoublePSEG)arg1, (complex)start_time, (VectorXd)start_point) → SuccessCode :¶ Run the endgame, from start point and start time, to t=0. Expects complex numeric type matching that of the tracker being used.
- run( (FixedDoublePSEG)arg1, (complex)start_time, (VectorXd)start_point, (complex)target_time) -> SuccessCode :
- Run the endgame, from start point and start time, to your choice of target time t. Expects complex numeric type matching that of the tracker being used.
-
set_endgame_settings
((FixedDoublePSEG)arg1, (Endgame)arg2) → None :¶ Set the values of non-specific endgame settings
-
set_security_settings
((FixedDoublePSEG)arg1, (Security)arg2) → None :¶ Set the values of security-level settings
-
-
class
pybertini.endgame.
FixedMultipleCauchyEG
((object)arg1, (MultiplePrecisionTracker)arg2) → None¶ Bases:
Boost.Python.instance
The fixed multiple precision implementation of the Cauchy endgame
__init__( (object)arg1, (MultiplePrecisionTracker)arg2, (CauchyConfig)arg3) -> None
__init__( (object)arg1, (MultiplePrecisionTracker)arg2, (Endgame)arg3) -> None
__init__( (object)arg1, (MultiplePrecisionTracker)arg2, (Security)arg3) -> None
-
add_observer
((object)arg1, (object)arg2) → None¶
-
cycle_number
((FixedMultipleCauchyEG)arg1) → int :¶ Get the cycle number as currently computed
-
final_approximation
((FixedMultipleCauchyEG)arg1) → VectorXmp :¶ Get the current approximation of the root, in the ambient numeric type for the tracker being used
-
get_endgame_settings
((FixedMultipleCauchyEG)arg1) → Endgame :¶ Get the current non-specific endgame settings
-
get_security_settings
((FixedMultipleCauchyEG)arg1) → Security :¶ Get the ‘security’ settings for the endgame (path truncation near infinity)
-
get_system
((FixedMultipleCauchyEG)arg1) → System :¶ Get the tracked system. This is a reference to the internal system.
-
get_tracker
((FixedMultipleCauchyEG)arg1) → MultiplePrecisionTracker :¶ Get the tracker used in this endgame. This is the same tracker as you feed the endgame object when you make it. This is a reference variable
-
remove_observer
((object)arg1, (object)arg2) → None¶
-
run
((FixedMultipleCauchyEG)arg1, (Complex)start_time, (VectorXmp)start_point) → SuccessCode :¶ Run the endgame, from start point and start time, to t=0. Expects complex numeric type matching that of the tracker being used.
- run( (FixedMultipleCauchyEG)arg1, (Complex)start_time, (VectorXmp)start_point, (Complex)target_time) -> SuccessCode :
- Run the endgame, from start point and start time, to your choice of target time t. Expects complex numeric type matching that of the tracker being used.
-
set_endgame_settings
((FixedMultipleCauchyEG)arg1, (Endgame)arg2) → None :¶ Set the values of non-specific endgame settings
-
set_security_settings
((FixedMultipleCauchyEG)arg1, (Security)arg2) → None :¶ Set the values of security-level settings
-
-
class
pybertini.endgame.
FixedMultiplePSEG
((object)arg1, (MultiplePrecisionTracker)arg2) → None¶ Bases:
Boost.Python.instance
The fixed but arbitrary precision implementation of the power series endgame
__init__( (object)arg1, (MultiplePrecisionTracker)arg2, (PowerSeriesConfig)arg3) -> None
__init__( (object)arg1, (MultiplePrecisionTracker)arg2, (Endgame)arg3) -> None
__init__( (object)arg1, (MultiplePrecisionTracker)arg2, (Security)arg3) -> None
-
add_observer
((object)arg1, (object)arg2) → None¶
-
cycle_number
((FixedMultiplePSEG)arg1) → int :¶ Get the cycle number as currently computed
-
final_approximation
((FixedMultiplePSEG)arg1) → VectorXmp :¶ Get the current approximation of the root, in the ambient numeric type for the tracker being used
-
get_endgame_settings
((FixedMultiplePSEG)arg1) → Endgame :¶ Get the current non-specific endgame settings
-
get_security_settings
((FixedMultiplePSEG)arg1) → Security :¶ Get the ‘security’ settings for the endgame (path truncation near infinity)
-
get_system
((FixedMultiplePSEG)arg1) → System :¶ Get the tracked system. This is a reference to the internal system.
-
get_tracker
((FixedMultiplePSEG)arg1) → MultiplePrecisionTracker :¶ Get the tracker used in this endgame. This is the same tracker as you feed the endgame object when you make it. This is a reference variable
-
remove_observer
((object)arg1, (object)arg2) → None¶
-
run
((FixedMultiplePSEG)arg1, (Complex)start_time, (VectorXmp)start_point) → SuccessCode :¶ Run the endgame, from start point and start time, to t=0. Expects complex numeric type matching that of the tracker being used.
- run( (FixedMultiplePSEG)arg1, (Complex)start_time, (VectorXmp)start_point, (Complex)target_time) -> SuccessCode :
- Run the endgame, from start point and start time, to your choice of target time t. Expects complex numeric type matching that of the tracker being used.
-
set_endgame_settings
((FixedMultiplePSEG)arg1, (Endgame)arg2) → None :¶ Set the values of non-specific endgame settings
-
set_security_settings
((FixedMultiplePSEG)arg1, (Security)arg2) → None :¶ Set the values of security-level settings
-
🎮 pybertini.endgame.config¶
Configs for endgames
-
class
pybertini.endgame.config.
CauchyConfig
((object)arg1) → None¶ Bases:
Boost.Python.instance
Settings specific to the Cauchy endgame for computing singular endpoints
-
cycle_cutoff_time
¶
-
fail_safe_maximum_cycle_number
¶ max number of loops before giving up.
-
maximum_cauchy_ratio
¶
-
minimum_for_c_over_k_stabilization
¶
-
num_needed_for_stabilization
¶ When running stabilization testing for the cycle number when entering the endgame, this is the number of consecutive points for which the test must pass.
-
ratio_cutoff_time
¶
-
-
class
pybertini.endgame.config.
Endgame
((object)arg1) → None¶ Bases:
Boost.Python.instance
Generic endgame settings. Number of sample points, etc. Note that some of its configs are rational numbers
-
final_tolerance
¶ The tolerance to which to track the path, using the endgame. Endgames require two consecutive estimates to be this close to each other under the relative infinity norm. Default value is 1e-11.
-
max_num_newton_iterations
¶ the maximum number of newton iterations to be taken during sample point sharpening. Increasing this can help speed convergence, at the risk of path jumping.
-
min_track_time
¶ The minimum distance from the target time to track to. Decreasing this may help failing runs succeed, or maybe not, because you are, after all, tracking toward a singularity.
-
num_sample_points
¶ The number of points to use for extrapolant calculation. In the Power Series Endgame, the is the number of geometrically spaces points on the path. For Cauchy, this is the number of points on each circle tracked around the target time value.
-
sample_factor
¶ The factor by which to space the geometrically spaced `distance’ between sample points, or sample circles for Cauchy.
-
sample_point_refinement_factor
¶ Extra amount of tolerance for refining before computing the final approximation, during endgame.
-
-
class
pybertini.endgame.config.
PowerSeriesConfig
((object)arg1) → None¶ Bases:
Boost.Python.instance
Settings specific to the power series endgame for computing singular endpoints
-
cycle_number_amplification
¶ The maximum number allowable iterations during endgames, for points used to approximate the final solution.
-
max_cycle_number
¶ The maximum cycle number to consider, when calculating the cycle number which best fits the path being tracked.
-
-
class
pybertini.endgame.config.
Security
((object)arg1) → None¶ Bases:
Boost.Python.instance
Security settings for endgames. Control things like truncation because estimated root is near infinity
-
level
¶ Turns on or off truncation of paths going to infinity during the endgame. 0 is off, 1 is on.
-
max_norm
¶ If on, the norm at which to truncate a path.
-