🗡 C++-flavored gory-detail documentation

_pybertini

class bertini._pybertini.Exception((object)arg1, (str)arg2)

__init__((object)arg1, (str)arg2) → None

property message

None( (bertini._pybertini.Exception)arg1) -> str

class bertini._pybertini.boost_type_index

The class type_index holds implementation-specific information about a type, including the name of the type and means to compare two types for equality or collating order.

Raises an exception This class cannot be instantiated from Python

__init__()

Raises an exception This class cannot be instantiated from Python

hash_code((boost_type_index)self) → int :

Returns an unspecified value (here denoted by hash code) such that for all std::type_info objects referring to the same type, their hash code is the same.

name((boost_type_index)self) → str :

Returns an implementation defined null-terminated character string containing the name of the type. No guarantees are given; in particular, the returned string can be identical for several types and change between invocations of the same program.

pretty_name((boost_type_index)self) → str :

Human readible name.

bertini._pybertini.seed((int)seed_value) → None :

Initialize the pseudo-random number generator with the argument seed_value.

bertini._pybertini.sharedMemory((bool)value) → None :

Share the memory when converting from Eigen to Numpy.

sharedMemory() -> bool :

Status of the shared memory when converting from Eigen to Numpy. If True, the memory is shared when converting an Eigen::Matrix to a numpy.array. Otherwise, a deep copy of the Eigen::Matrix is performed.

class bertini._pybertini.std_type_index

The class type_index holds implementation-specific information about a type, including the name of the type and means to compare two types for equality or collating order.

Raises an exception This class cannot be instantiated from Python

__init__()

Raises an exception This class cannot be instantiated from Python

hash_code((std_type_index)self) → int :

Returns an unspecified value (here denoted by hash code) such that for all std::type_info objects referring to the same type, their hash code is the same.

name((std_type_index)self) → str :

Returns an implementation defined null-terminated character string containing the name of the type. No guarantees are given; in particular, the returned string can be identical for several types and change between invocations of the same program.

pretty_name((std_type_index)self) → str :

Human readible name.

_pybertini.function_tree

The symbolics for Bertini2. Operator overloads let you write arithmetic do form your system, after making variables, etc.

class bertini._pybertini.function_tree.AbstractNode

Raises an exception This class cannot be instantiated from Python

__init__()

Raises an exception This class cannot be instantiated from Python

degree((AbstractNode)self) → int :

compute the algebraic degree of node in a function tree, with respect to all variables. returns one integer. negative is non-algebraic.

degree( (AbstractNode)self, (bertini._pybertini.function_tree.symbol.Variable)var) -> int :

compute the algebraic degree of node in a function tree, with respect to a particular variable. returns one integer. negative is non-algebraic.

degree( (AbstractNode)self, (bertini._pybertini.container.VariableGroup)vars) -> int :

compute the algebraic degree of node in a function tree, with respect to a variable group. returns one integer. negative is non-algebraic.

differentiate((AbstractNode)self) → AbstractNode :

differentiate a node. is with respect to all variables. you get a Jacobian back, which represents derivatives wrt all variables simultaneously.

differentiate( (AbstractNode)arg1, (bertini._pybertini.function_tree.symbol.Variable)self) -> AbstractNode :

differentiate a node with respect to one variable. You get a regular old Node in a Function Tree back.

eval_d((AbstractNode)self) → complex :

evaluate in double precision. uses the values of variables already set in a preceding call to var.set_current_value()

eval_d( (AbstractNode)self, (bertini._pybertini.function_tree.symbol.Variable)var) -> complex :

evaluate the derivative of this node with respect to variable var in double precision. uses the values of variables already set in a preceding call to var.set_current_value()

eval_mp((AbstractNode)self) → bertini._pybertini.multiprec.Complex :

evaluate in multiple precision. uses the values of variables already set in a preceding call to var.set_current_value()

eval_mp( (AbstractNode)self, (bertini._pybertini.function_tree.symbol.Variable)var) -> bertini._pybertini.multiprec.Complex :

evaluate the derivative of this node with respect to variable var in multiple precision. uses the values of variables already set in a preceding call to var.set_current_value()

homogenize((AbstractNode)self, (bertini._pybertini.container.VariableGroup)vars, (bertini._pybertini.function_tree.symbol.Variable)homvar) → None :

Homogenize this function tree with respect to the variables in vars using the homogenizing variables homvar. Essentially, multiply all terms downward so they have the same degree, using homvar to make up the degree defficiency.

is_homogeneous((AbstractNode)self) → bool :

test if this Node is homogeneous with respect to all Variables.

is_homogeneous( (AbstractNode)self, (bertini._pybertini.function_tree.symbol.Variable)var) -> bool :

test if this Node is homogeneous with respect to Variable var.

is_homogeneous( (AbstractNode)self, (bertini._pybertini.container.VariableGroup)vars) -> bool :

test if this Node is homogeneous with respect to the Variables in vars.

is_polynomial((AbstractNode)self) → bool :

test if this Node is polynomial with respect to all Variables.

is_polynomial( (AbstractNode)self, (bertini._pybertini.function_tree.symbol.Variable)var) -> bool :

test if this Node is polynomial with respect to Variable var.

is_polynomial( (AbstractNode)self, (bertini._pybertini.container.VariableGroup)vars) -> bool :

test if this Node is polynomial with respect to Variables vars.

multidegree((AbstractNode)self, (bertini._pybertini.container.VariableGroup)vars) → bertini._pybertini.container.ListOfInt :

Compute an integer vector containing the degrees with respect to the variables in vars. Negative entries indicate non-polynomiality

precision((AbstractNode)self) → int

precision( (AbstractNode)self, (int)precision) -> None

reset((AbstractNode)self) → None :

reset (downward) the values of a function tree so that when the next eval_mp or eval_d is called, the tree re-computes

bertini._pybertini.function_tree.acos((AbstractNode)arg1) → AbstractNode :

the symbolic arccosine operator

bertini._pybertini.function_tree.asin((AbstractNode)arg1) → AbstractNode :

the symbolic arcsine operator

bertini._pybertini.function_tree.atan((AbstractNode)arg1) → AbstractNode :

the symbolic arctangent operator

bertini._pybertini.function_tree.cos((AbstractNode)arg1) → AbstractNode :

the symbolic cosine operator

bertini._pybertini.function_tree.exp((AbstractNode)arg1) → AbstractNode :

the symbolic exponential operator

bertini._pybertini.function_tree.log((AbstractNode)arg1) → AbstractNode :

the symbolic natural log operator

bertini._pybertini.function_tree.sin((AbstractNode)arg1) → AbstractNode :

the symbolic sine operator

bertini._pybertini.function_tree.tan((AbstractNode)arg1) → AbstractNode :

the symbolic tangent operator

_pybertini.tracking

Observers for trackers.

class bertini._pybertini.tracking.AMPTracker((object)arg1, (bertini._pybertini.system.System)arg2)

The adaptive multiple precision (AMP) tracker. Ambient numeric type is multiple-precision (mpfr_complex). Contruct one by feeding it a system – cannot be constructed without feeding it a system. Adjust its settings via configs and the setup function. Then, call method track_path.

__init__((object)arg1, (bertini._pybertini.system.System)arg2) → None

add_observer((object)self, (object)observer) → None :

Attach an observer to this observable object

current_point((AMPTracker)self) → numpy.ndarray :

what is the current point?

current_precision((AMPTracker)self) → int :

what is the current working precision?

current_time((AMPTracker)self) → bertini._pybertini.multiprec.Complex :

what is the current time?

get_newton((AMPTracker)self) → bertini._pybertini.tracking.config.NewtonConfig :

Get the tracker’s internal configuration for Newton correction

get_stepping((AMPTracker)self) → bertini._pybertini.tracking.config.SteppingConfig :

Get the tracker’s internal configuration for things that control stepping behaviour

get_system((AMPTracker)arg1) → bertini._pybertini.system.System :

Gets an internal reference to the tracked system.

infinite_truncation((AMPTracker)self, (bool)val) → None :

Decide whether the tracker should truncate infinite paths. See also infinite_truncation_tolerance

infinite_truncation( (AMPTracker)self) -> bool :

Get the bool for whether the tracker should truncate infinite paths. See also infinite_truncation_tolerance

infinite_truncation_tolerance((AMPTracker)self, (float)tol) → None :

Set the path truncation tolerance for infinite paths for the tracker

infinite_truncation_tolerance( (AMPTracker)self) -> float :

Get the path truncation tolerance for infinite paths for the tracker

num_total_steps_taken((AMPTracker)self) → int :

Ask how many steps have been taken so far, including failures

observers = ['Abstract', 'FirstPrecisionRecorder', 'GoryDetailLogger', '__doc__', '__loader__', '__name__', '__package__', '__spec__']

precision_preservation((AMPTracker)arg1, (bool)arg2) → None :

Turn on or off the preservation of precision. That is, if this is on (true), then the precision of the final point will be the precision of the start point. Generally, you want to let precision drift, methinks.

precision_setup((AMPTracker)arg1, (bertini._pybertini.tracking.config.AMPConfig)arg2) → None

predictor((AMPTracker)self) → Predictor :

Query the current predictor method used by the tracker.

predictor( (AMPTracker)self, (Predictor)predictor) -> None :

Set the predictor method used by the tracker.

refine((AMPTracker)self, (numpy.ndarray)result, (numpy.ndarray)start_point, (complex)time) → SuccessCode :

refine a point using this tracker, from start_point, at fixed time. returns a success code, computed refined point is in result.

refine( (AMPTracker)self, (numpy.ndarray)result, (numpy.ndarray)start_point, (bertini._pybertini.multiprec.Complex)time) -> SuccessCode :

refine a point using this tracker, from start_point, at fixed time. returns a success code, computed refined point is in result.

refine( (AMPTracker)self, (numpy.ndarray)result, (numpy.ndarray)start_point, (complex)time, (float)tolerance, (int)max_iterations) -> SuccessCode :

refine a point using this tracker, from start_point, at fixed time. returns a success code, computed refined point is in result.

refine( (AMPTracker)self, (numpy.ndarray)result, (numpy.ndarray)start_point, (bertini._pybertini.multiprec.Complex)time, (float)tolerance, (int)max_iterations) -> SuccessCode :

refine a point using this tracker, from start_point, at fixed time. returns a success code, computed refined point is in result.

reinitialize_initial_step_size((AMPTracker)self, (bool)val) → None :

Set whether the tracker should re-set the stepsize to the configured-initial stepsize when it starts tracking. Feed it a bool

remove_observer((object)self, (object)observer) → None :

Remove an observer to this observable object

set_newton((AMPTracker)self, (bertini._pybertini.tracking.config.NewtonConfig)config) → None :

Set the tracker’s internal configuration for Newton correction

set_stepping((AMPTracker)self, (bertini._pybertini.tracking.config.SteppingConfig)config) → None :

Set the tracker’s internal configuration for things that control stepping behaviour

set_stepsize((AMPTracker)self, (bertini._pybertini.multiprec.Float)stepsize) → None :

Set the stepsize for the tracker

setup((AMPTracker)arg1, (Predictor)predictor, (float)tolerance, (float)truncation, (bertini._pybertini.tracking.config.SteppingConfig)stepping, (bertini._pybertini.tracking.config.NewtonConfig)newton) → None :

Set values for the internal configuration of the tracker. tolerance and truncation are both real doubles. predictor is a valid value for predictor choice. stepping and newton are the config structs from bertini.tracking.config.

track_path((AMPTracker)self, (numpy.ndarray)result, (bertini._pybertini.multiprec.Complex)start_time, (bertini._pybertini.multiprec.Complex)end_time, (numpy.ndarray)start_point) → SuccessCode :

The main function of the tracker, once its set up. The first argument is the output. Feed it, in (result, start_time, end_time, start_point

tracking_tolerance((AMPTracker)self) → float :

Get. A step is labeled as a failure if newton correcting doesn’t yield a residual less than this tolerance. A real number, the smaller the slower tracking, generally speaking

tracking_tolerance( (AMPTracker)self, (float)tol) -> None :

Set the tracking tolerance for the tracker

class bertini._pybertini.tracking.DoublePrecisionTracker((object)arg1, (bertini._pybertini.system.System)arg2)

The double precision tracker. Tracks using only complex doubles. Ambient numeric type is double. Contruct one by feeding it a system – cannot be constructed without feeding it a system. Adjust its settings via configs and the setup function. Then, call method track_path.

__init__((object)arg1, (bertini._pybertini.system.System)arg2) → None

add_observer((object)self, (object)observer) → None :

Attach an observer to this observable object

current_point((DoublePrecisionTracker)self) → numpy.ndarray :

what is the current point?

current_precision((DoublePrecisionTracker)self) → int :

what is the current working precision?

current_time((DoublePrecisionTracker)self) → complex :

what is the current time?

get_newton((DoublePrecisionTracker)self) → bertini._pybertini.tracking.config.NewtonConfig :

Get the tracker’s internal configuration for Newton correction

get_stepping((DoublePrecisionTracker)self) → bertini._pybertini.tracking.config.SteppingConfig :

Get the tracker’s internal configuration for things that control stepping behaviour

get_system((DoublePrecisionTracker)arg1) → bertini._pybertini.system.System :

Gets an internal reference to the tracked system.

infinite_truncation((DoublePrecisionTracker)self, (bool)val) → None :

Decide whether the tracker should truncate infinite paths. See also infinite_truncation_tolerance

infinite_truncation( (DoublePrecisionTracker)self) -> bool :

Get the bool for whether the tracker should truncate infinite paths. See also infinite_truncation_tolerance

infinite_truncation_tolerance((DoublePrecisionTracker)self, (float)tol) → None :

Set the path truncation tolerance for infinite paths for the tracker

infinite_truncation_tolerance( (DoublePrecisionTracker)self) -> float :

Get the path truncation tolerance for infinite paths for the tracker

num_total_steps_taken((DoublePrecisionTracker)self) → int :

Ask how many steps have been taken so far, including failures

observers = ['Abstract', 'FirstPrecisionRecorder', 'GoryDetailLogger', '__doc__', '__loader__', '__name__', '__package__', '__spec__']

predictor((DoublePrecisionTracker)self) → Predictor :

Query the current predictor method used by the tracker.

predictor( (DoublePrecisionTracker)self, (Predictor)predictor) -> None :

Set the predictor method used by the tracker.

refine((DoublePrecisionTracker)self, (numpy.ndarray)result, (numpy.ndarray)start_point, (complex)time) → SuccessCode :

refine a point using this tracker, from start_point, at fixed time. returns a success code, computed refined point is in result.

refine( (DoublePrecisionTracker)self, (numpy.ndarray)result, (numpy.ndarray)start_point, (complex)time, (float)tolerance, (int)max_iterations) -> SuccessCode :

refine a point using this tracker, from start_point, at fixed time. returns a success code, computed refined point is in result.

reinitialize_initial_step_size((DoublePrecisionTracker)self, (bool)val) → None :

Set whether the tracker should re-set the stepsize to the configured-initial stepsize when it starts tracking. Feed it a bool

remove_observer((object)self, (object)observer) → None :

Remove an observer to this observable object

set_newton((DoublePrecisionTracker)self, (bertini._pybertini.tracking.config.NewtonConfig)config) → None :

Set the tracker’s internal configuration for Newton correction

set_stepping((DoublePrecisionTracker)self, (bertini._pybertini.tracking.config.SteppingConfig)config) → None :

Set the tracker’s internal configuration for things that control stepping behaviour

set_stepsize((DoublePrecisionTracker)self, (float)stepsize) → None :

Set the stepsize for the tracker

setup((DoublePrecisionTracker)arg1, (Predictor)predictor, (float)tolerance, (float)truncation, (bertini._pybertini.tracking.config.SteppingConfig)stepping, (bertini._pybertini.tracking.config.NewtonConfig)newton) → None :

Set values for the internal configuration of the tracker. tolerance and truncation are both real doubles. predictor is a valid value for predictor choice. stepping and newton are the config structs from bertini.tracking.config.

track_path((DoublePrecisionTracker)self, (numpy.ndarray)result, (complex)start_time, (complex)end_time, (numpy.ndarray)start_point) → SuccessCode :

The main function of the tracker, once its set up. The first argument is the output. Feed it, in (result, start_time, end_time, start_point

tracking_tolerance((DoublePrecisionTracker)self) → float :

Get. A step is labeled as a failure if newton correcting doesn’t yield a residual less than this tolerance. A real number, the smaller the slower tracking, generally speaking

tracking_tolerance( (DoublePrecisionTracker)self, (float)tol) -> None :

Set the tracking tolerance for the tracker

class bertini._pybertini.tracking.MultiplePrecisionTracker((object)arg1, (bertini._pybertini.system.System)arg2)

The fixed multiple precision tracker. Ambient numeric type is multiple-precision (mpfr_complex). Precision is the value of bertini.default_precision() at contruction. Errors if you try to feed it things not at that precision. Contruct one by feeding it a system – cannot be constructed without feeding it a system. Adjust its settings via configs and the setup function. Then, call method track_path.

__init__((object)arg1, (bertini._pybertini.system.System)arg2) → None

add_observer((object)self, (object)observer) → None :

Attach an observer to this observable object

current_point((MultiplePrecisionTracker)self) → numpy.ndarray :

what is the current point?

current_precision((MultiplePrecisionTracker)self) → int :

what is the current working precision?

current_time((MultiplePrecisionTracker)self) → bertini._pybertini.multiprec.Complex :

what is the current time?

get_newton((MultiplePrecisionTracker)self) → bertini._pybertini.tracking.config.NewtonConfig :

Get the tracker’s internal configuration for Newton correction

get_stepping((MultiplePrecisionTracker)self) → bertini._pybertini.tracking.config.SteppingConfig :

Get the tracker’s internal configuration for things that control stepping behaviour

get_system((MultiplePrecisionTracker)arg1) → bertini._pybertini.system.System :

Gets an internal reference to the tracked system.

infinite_truncation((MultiplePrecisionTracker)self, (bool)val) → None :

Decide whether the tracker should truncate infinite paths. See also infinite_truncation_tolerance

infinite_truncation( (MultiplePrecisionTracker)self) -> bool :

Get the bool for whether the tracker should truncate infinite paths. See also infinite_truncation_tolerance

infinite_truncation_tolerance((MultiplePrecisionTracker)self, (float)tol) → None :

Set the path truncation tolerance for infinite paths for the tracker

infinite_truncation_tolerance( (MultiplePrecisionTracker)self) -> float :

Get the path truncation tolerance for infinite paths for the tracker

num_total_steps_taken((MultiplePrecisionTracker)self) → int :

Ask how many steps have been taken so far, including failures

observers = ['Abstract', 'FirstPrecisionRecorder', 'GoryDetailLogger', '__doc__', '__loader__', '__name__', '__package__', '__spec__']

predictor((MultiplePrecisionTracker)self) → Predictor :

Query the current predictor method used by the tracker.

predictor( (MultiplePrecisionTracker)self, (Predictor)predictor) -> None :

Set the predictor method used by the tracker.

refine((MultiplePrecisionTracker)self, (numpy.ndarray)result, (numpy.ndarray)start_point, (bertini._pybertini.multiprec.Complex)time) → SuccessCode :

refine a point using this tracker, from start_point, at fixed time. returns a success code, computed refined point is in result.

refine( (MultiplePrecisionTracker)self, (numpy.ndarray)result, (numpy.ndarray)start_point, (bertini._pybertini.multiprec.Complex)time, (float)tolerance, (int)max_iterations) -> SuccessCode :

refine a point using this tracker, from start_point, at fixed time. returns a success code, computed refined point is in result.

reinitialize_initial_step_size((MultiplePrecisionTracker)self, (bool)val) → None :

Set whether the tracker should re-set the stepsize to the configured-initial stepsize when it starts tracking. Feed it a bool

remove_observer((object)self, (object)observer) → None :

Remove an observer to this observable object

set_newton((MultiplePrecisionTracker)self, (bertini._pybertini.tracking.config.NewtonConfig)config) → None :

Set the tracker’s internal configuration for Newton correction

set_stepping((MultiplePrecisionTracker)self, (bertini._pybertini.tracking.config.SteppingConfig)config) → None :

Set the tracker’s internal configuration for things that control stepping behaviour

set_stepsize((MultiplePrecisionTracker)self, (bertini._pybertini.multiprec.Float)stepsize) → None :

Set the stepsize for the tracker

setup((MultiplePrecisionTracker)arg1, (Predictor)predictor, (float)tolerance, (float)truncation, (bertini._pybertini.tracking.config.SteppingConfig)stepping, (bertini._pybertini.tracking.config.NewtonConfig)newton) → None :

Set values for the internal configuration of the tracker. tolerance and truncation are both real doubles. predictor is a valid value for predictor choice. stepping and newton are the config structs from bertini.tracking.config.

track_path((MultiplePrecisionTracker)self, (numpy.ndarray)result, (bertini._pybertini.multiprec.Complex)start_time, (bertini._pybertini.multiprec.Complex)end_time, (numpy.ndarray)start_point) → SuccessCode :

The main function of the tracker, once its set up. The first argument is the output. Feed it, in (result, start_time, end_time, start_point

tracking_tolerance((MultiplePrecisionTracker)self) → float :

Get. A step is labeled as a failure if newton correcting doesn’t yield a residual less than this tolerance. A real number, the smaller the slower tracking, generally speaking

tracking_tolerance( (MultiplePrecisionTracker)self, (float)tol) -> None :

Set the tracking tolerance for the tracker

class bertini._pybertini.tracking.Predictor

Constant = bertini._pybertini.tracking.Predictor.Constant

Euler = bertini._pybertini.tracking.Predictor.Euler

Heun = bertini._pybertini.tracking.Predictor.Heun

HeunEuler = bertini._pybertini.tracking.Predictor.HeunEuler

RK4 = bertini._pybertini.tracking.Predictor.RK4

RKCashKarp45 = bertini._pybertini.tracking.Predictor.RKCashKarp45

RKDormandPrince56 = bertini._pybertini.tracking.Predictor.RKDormandPrince56

RKF45 = bertini._pybertini.tracking.Predictor.RKF45

RKNorsett34 = bertini._pybertini.tracking.Predictor.RKNorsett34

RKVerner67 = bertini._pybertini.tracking.Predictor.RKVerner67

names = {'Constant': bertini._pybertini.tracking.Predictor.Constant, 'Euler': bertini._pybertini.tracking.Predictor.Euler, 'Heun': bertini._pybertini.tracking.Predictor.Heun, 'HeunEuler': bertini._pybertini.tracking.Predictor.HeunEuler, 'RK4': bertini._pybertini.tracking.Predictor.RK4, 'RKCashKarp45': bertini._pybertini.tracking.Predictor.RKCashKarp45, 'RKDormandPrince56': bertini._pybertini.tracking.Predictor.RKDormandPrince56, 'RKF45': bertini._pybertini.tracking.Predictor.RKF45, 'RKNorsett34': bertini._pybertini.tracking.Predictor.RKNorsett34, 'RKVerner67': bertini._pybertini.tracking.Predictor.RKVerner67}

values = {0: bertini._pybertini.tracking.Predictor.Constant, 1: bertini._pybertini.tracking.Predictor.Euler, 2: bertini._pybertini.tracking.Predictor.Heun, 3: bertini._pybertini.tracking.Predictor.RK4, 4: bertini._pybertini.tracking.Predictor.HeunEuler, 5: bertini._pybertini.tracking.Predictor.RKNorsett34, 6: bertini._pybertini.tracking.Predictor.RKF45, 7: bertini._pybertini.tracking.Predictor.RKCashKarp45, 8: bertini._pybertini.tracking.Predictor.RKDormandPrince56, 9: bertini._pybertini.tracking.Predictor.RKVerner67}

class bertini._pybertini.tracking.SuccessCode

CycleNumTooHigh = bertini._pybertini.tracking.SuccessCode.CycleNumTooHigh

ExternallyTerminated = bertini._pybertini.tracking.SuccessCode.ExternallyTerminated

FailedToConverge = bertini._pybertini.tracking.SuccessCode.FailedToConverge

Failure = bertini._pybertini.tracking.SuccessCode.Failure

GoingToInfinity = bertini._pybertini.tracking.SuccessCode.GoingToInfinity

HigherPrecisionNecessary = bertini._pybertini.tracking.SuccessCode.HigherPrecisionNecessary

MatrixSolveFailure = bertini._pybertini.tracking.SuccessCode.MatrixSolveFailure

MatrixSolveFailureFirstPartOfPrediction = bertini._pybertini.tracking.SuccessCode.MatrixSolveFailureFirstPartOfPrediction

MaxNumStepsTaken = bertini._pybertini.tracking.SuccessCode.MaxNumStepsTaken

MaxPrecisionReached = bertini._pybertini.tracking.SuccessCode.MaxPrecisionReached

MinStepSizeReached = bertini._pybertini.tracking.SuccessCode.MinStepSizeReached

MinTrackTimeReached = bertini._pybertini.tracking.SuccessCode.MinTrackTimeReached

ReduceStepSize = bertini._pybertini.tracking.SuccessCode.ReduceStepSize

SecurityMaxNormReached = bertini._pybertini.tracking.SuccessCode.SecurityMaxNormReached

SingularStartPoint = bertini._pybertini.tracking.SuccessCode.SingularStartPoint

Success = bertini._pybertini.tracking.SuccessCode.Success

names = {'CycleNumTooHigh': bertini._pybertini.tracking.SuccessCode.CycleNumTooHigh, 'ExternallyTerminated': bertini._pybertini.tracking.SuccessCode.ExternallyTerminated, 'FailedToConverge': bertini._pybertini.tracking.SuccessCode.FailedToConverge, 'Failure': bertini._pybertini.tracking.SuccessCode.Failure, 'GoingToInfinity': bertini._pybertini.tracking.SuccessCode.GoingToInfinity, 'HigherPrecisionNecessary': bertini._pybertini.tracking.SuccessCode.HigherPrecisionNecessary, 'MatrixSolveFailure': bertini._pybertini.tracking.SuccessCode.MatrixSolveFailure, 'MatrixSolveFailureFirstPartOfPrediction': bertini._pybertini.tracking.SuccessCode.MatrixSolveFailureFirstPartOfPrediction, 'MaxNumStepsTaken': bertini._pybertini.tracking.SuccessCode.MaxNumStepsTaken, 'MaxPrecisionReached': bertini._pybertini.tracking.SuccessCode.MaxPrecisionReached, 'MinStepSizeReached': bertini._pybertini.tracking.SuccessCode.MinStepSizeReached, 'MinTrackTimeReached': bertini._pybertini.tracking.SuccessCode.MinTrackTimeReached, 'ReduceStepSize': bertini._pybertini.tracking.SuccessCode.ReduceStepSize, 'SecurityMaxNormReached': bertini._pybertini.tracking.SuccessCode.SecurityMaxNormReached, 'SingularStartPoint': bertini._pybertini.tracking.SuccessCode.SingularStartPoint, 'Success': bertini._pybertini.tracking.SuccessCode.Success}

values = {0: bertini._pybertini.tracking.SuccessCode.Success, 1: bertini._pybertini.tracking.SuccessCode.HigherPrecisionNecessary, 2: bertini._pybertini.tracking.SuccessCode.ReduceStepSize, 3: bertini._pybertini.tracking.SuccessCode.GoingToInfinity, 4: bertini._pybertini.tracking.SuccessCode.FailedToConverge, 5: bertini._pybertini.tracking.SuccessCode.MatrixSolveFailure, 6: bertini._pybertini.tracking.SuccessCode.MatrixSolveFailureFirstPartOfPrediction, 7: bertini._pybertini.tracking.SuccessCode.MaxNumStepsTaken, 8: bertini._pybertini.tracking.SuccessCode.MaxPrecisionReached, 9: bertini._pybertini.tracking.SuccessCode.MinStepSizeReached, 10: bertini._pybertini.tracking.SuccessCode.Failure, 11: bertini._pybertini.tracking.SuccessCode.SingularStartPoint, 12: bertini._pybertini.tracking.SuccessCode.ExternallyTerminated, 13: bertini._pybertini.tracking.SuccessCode.MinTrackTimeReached, 14: bertini._pybertini.tracking.SuccessCode.SecurityMaxNormReached, 15: bertini._pybertini.tracking.SuccessCode.CycleNumTooHigh}

_pybertini.endgames

Endgames and associated types and functions. For tracking around singularities.

class bertini._pybertini.endgame.AMPCauchyEG((object)self, (bertini._pybertini.tracking.AMPTracker)tracker) → None :

The adaptive precision implementation of the Cauchy endgame

Default construct with default settings

__init__( (object)self, (bertini._pybertini.tracking.AMPTracker)tracker, (bertini._pybertini.endgame.config.CauchyConfig)cauchyconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.AMPTracker)tracker, (bertini._pybertini.endgame.config.Endgame)endgameconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.AMPTracker)tracker, (bertini._pybertini.endgame.config.Security)securityconfig) -> None

__init__((object)self, (bertini._pybertini.tracking.AMPTracker)tracker) → None :

Default construct with default settings

__init__( (object)self, (bertini._pybertini.tracking.AMPTracker)tracker, (bertini._pybertini.endgame.config.CauchyConfig)cauchyconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.AMPTracker)tracker, (bertini._pybertini.endgame.config.Endgame)endgameconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.AMPTracker)tracker, (bertini._pybertini.endgame.config.Security)securityconfig) -> None

add_observer((object)self, (object)observer) → None :

Attach an observer to this observable object

cycle_number((AMPCauchyEG)self) → int :

Get the cycle number as currently computed

final_approximation((AMPCauchyEG)self) → numpy.ndarray :

Get the current approximation of the root, in the ambient numeric type for the tracker being used

get_endgame_settings((AMPCauchyEG)self) → bertini._pybertini.endgame.config.Endgame :

Get the current non-specific endgame settings

get_security_settings((AMPCauchyEG)self) → bertini._pybertini.endgame.config.Security :

Get the ‘security’ settings for the endgame (path truncation near infinity)

get_system((AMPCauchyEG)self) → bertini._pybertini.system.System :

Get the tracked system. This is a reference to the internal system.

get_tracker((AMPCauchyEG)self) → bertini._pybertini.tracking.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)self, (object)observer) → None :

Remove an observer to this observable object

run((AMPCauchyEG)self, (bertini._pybertini.multiprec.Complex)start_time, (numpy.ndarray)start_point) → bertini._pybertini.tracking.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)self, (bertini._pybertini.multiprec.Complex)start_time, (numpy.ndarray)start_point, (bertini._pybertini.multiprec.Complex)target_time) -> bertini._pybertini.tracking.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)self, (bertini._pybertini.endgame.config.Endgame)settings) → None :

Set the values of non-specific endgame settings

set_security_settings((AMPCauchyEG)self, (bertini._pybertini.endgame.config.Security)settings) → None :

Set the values of security-level settings

class bertini._pybertini.endgame.AMPPSEG((object)self, (bertini._pybertini.tracking.AMPTracker)tracker) → None :

The adaptive precision implementation of the power series endgame.

Default construct with default settings

__init__( (object)self, (bertini._pybertini.tracking.AMPTracker)tracker, (bertini._pybertini.endgame.config.PowerSeriesConfig)powerseriesconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.AMPTracker)tracker, (bertini._pybertini.endgame.config.Endgame)endgameconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.AMPTracker)tracker, (bertini._pybertini.endgame.config.Security)securityconfig) -> None

__init__((object)self, (bertini._pybertini.tracking.AMPTracker)tracker) → None :

Default construct with default settings

__init__( (object)self, (bertini._pybertini.tracking.AMPTracker)tracker, (bertini._pybertini.endgame.config.PowerSeriesConfig)powerseriesconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.AMPTracker)tracker, (bertini._pybertini.endgame.config.Endgame)endgameconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.AMPTracker)tracker, (bertini._pybertini.endgame.config.Security)securityconfig) -> None

add_observer((object)self, (object)observer) → None :

Attach an observer to this observable object

cycle_number((AMPPSEG)self) → int :

Get the cycle number as currently computed

final_approximation((AMPPSEG)self) → numpy.ndarray :

Get the current approximation of the root, in the ambient numeric type for the tracker being used

get_endgame_settings((AMPPSEG)self) → bertini._pybertini.endgame.config.Endgame :

Get the current non-specific endgame settings

get_security_settings((AMPPSEG)self) → bertini._pybertini.endgame.config.Security :

Get the ‘security’ settings for the endgame (path truncation near infinity)

get_system((AMPPSEG)self) → bertini._pybertini.system.System :

Get the tracked system. This is a reference to the internal system.

get_tracker((AMPPSEG)self) → bertini._pybertini.tracking.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)self, (object)observer) → None :

Remove an observer to this observable object

run((AMPPSEG)self, (bertini._pybertini.multiprec.Complex)start_time, (numpy.ndarray)start_point) → bertini._pybertini.tracking.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)self, (bertini._pybertini.multiprec.Complex)start_time, (numpy.ndarray)start_point, (bertini._pybertini.multiprec.Complex)target_time) -> bertini._pybertini.tracking.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)self, (bertini._pybertini.endgame.config.Endgame)settings) → None :

Set the values of non-specific endgame settings

set_security_settings((AMPPSEG)self, (bertini._pybertini.endgame.config.Security)settings) → None :

Set the values of security-level settings

class bertini._pybertini.endgame.FixedDoubleCauchyEG((object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker) → None :

The fixed double precision implementation of the Cauchy endgame

Default construct with default settings

__init__( (object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker, (bertini._pybertini.endgame.config.CauchyConfig)cauchyconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Endgame)endgameconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Security)securityconfig) -> None

__init__((object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker) → None :

Default construct with default settings

__init__( (object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker, (bertini._pybertini.endgame.config.CauchyConfig)cauchyconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Endgame)endgameconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Security)securityconfig) -> None

add_observer((object)self, (object)observer) → None :

Attach an observer to this observable object

cycle_number((FixedDoubleCauchyEG)self) → int :

Get the cycle number as currently computed

final_approximation((FixedDoubleCauchyEG)self) → numpy.ndarray :

Get the current approximation of the root, in the ambient numeric type for the tracker being used

get_endgame_settings((FixedDoubleCauchyEG)self) → bertini._pybertini.endgame.config.Endgame :

Get the current non-specific endgame settings

get_security_settings((FixedDoubleCauchyEG)self) → bertini._pybertini.endgame.config.Security :

Get the ‘security’ settings for the endgame (path truncation near infinity)

get_system((FixedDoubleCauchyEG)self) → bertini._pybertini.system.System :

Get the tracked system. This is a reference to the internal system.

get_tracker((FixedDoubleCauchyEG)self) → bertini._pybertini.tracking.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)self, (object)observer) → None :

Remove an observer to this observable object

run((FixedDoubleCauchyEG)self, (complex)start_time, (numpy.ndarray)start_point) → bertini._pybertini.tracking.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)self, (complex)start_time, (numpy.ndarray)start_point, (complex)target_time) -> bertini._pybertini.tracking.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)self, (bertini._pybertini.endgame.config.Endgame)settings) → None :

Set the values of non-specific endgame settings

set_security_settings((FixedDoubleCauchyEG)self, (bertini._pybertini.endgame.config.Security)settings) → None :

Set the values of security-level settings

class bertini._pybertini.endgame.FixedDoublePSEG((object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker) → None :

The double-precision implementation of the power series endgame

Default construct with default settings

__init__( (object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker, (bertini._pybertini.endgame.config.PowerSeriesConfig)powerseriesconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Endgame)endgameconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Security)securityconfig) -> None

__init__((object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker) → None :

Default construct with default settings

__init__( (object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker, (bertini._pybertini.endgame.config.PowerSeriesConfig)powerseriesconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Endgame)endgameconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.DoublePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Security)securityconfig) -> None

add_observer((object)self, (object)observer) → None :

Attach an observer to this observable object

cycle_number((FixedDoublePSEG)self) → int :

Get the cycle number as currently computed

final_approximation((FixedDoublePSEG)self) → numpy.ndarray :

Get the current approximation of the root, in the ambient numeric type for the tracker being used

get_endgame_settings((FixedDoublePSEG)self) → bertini._pybertini.endgame.config.Endgame :

Get the current non-specific endgame settings

get_security_settings((FixedDoublePSEG)self) → bertini._pybertini.endgame.config.Security :

Get the ‘security’ settings for the endgame (path truncation near infinity)

get_system((FixedDoublePSEG)self) → bertini._pybertini.system.System :

Get the tracked system. This is a reference to the internal system.

get_tracker((FixedDoublePSEG)self) → bertini._pybertini.tracking.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)self, (object)observer) → None :

Remove an observer to this observable object

run((FixedDoublePSEG)self, (complex)start_time, (numpy.ndarray)start_point) → bertini._pybertini.tracking.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)self, (complex)start_time, (numpy.ndarray)start_point, (complex)target_time) -> bertini._pybertini.tracking.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)self, (bertini._pybertini.endgame.config.Endgame)settings) → None :

Set the values of non-specific endgame settings

set_security_settings((FixedDoublePSEG)self, (bertini._pybertini.endgame.config.Security)settings) → None :

Set the values of security-level settings

class bertini._pybertini.endgame.FixedMultipleCauchyEG((object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker) → None :

The fixed multiple precision implementation of the Cauchy endgame

Default construct with default settings

__init__( (object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker, (bertini._pybertini.endgame.config.CauchyConfig)cauchyconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Endgame)endgameconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Security)securityconfig) -> None

__init__((object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker) → None :

Default construct with default settings

__init__( (object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker, (bertini._pybertini.endgame.config.CauchyConfig)cauchyconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Endgame)endgameconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Security)securityconfig) -> None

add_observer((object)self, (object)observer) → None :

Attach an observer to this observable object

cycle_number((FixedMultipleCauchyEG)self) → int :

Get the cycle number as currently computed

final_approximation((FixedMultipleCauchyEG)self) → numpy.ndarray :

Get the current approximation of the root, in the ambient numeric type for the tracker being used

get_endgame_settings((FixedMultipleCauchyEG)self) → bertini._pybertini.endgame.config.Endgame :

Get the current non-specific endgame settings

get_security_settings((FixedMultipleCauchyEG)self) → bertini._pybertini.endgame.config.Security :

Get the ‘security’ settings for the endgame (path truncation near infinity)

get_system((FixedMultipleCauchyEG)self) → bertini._pybertini.system.System :

Get the tracked system. This is a reference to the internal system.

get_tracker((FixedMultipleCauchyEG)self) → bertini._pybertini.tracking.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)self, (object)observer) → None :

Remove an observer to this observable object

run((FixedMultipleCauchyEG)self, (bertini._pybertini.multiprec.Complex)start_time, (numpy.ndarray)start_point) → bertini._pybertini.tracking.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)self, (bertini._pybertini.multiprec.Complex)start_time, (numpy.ndarray)start_point, (bertini._pybertini.multiprec.Complex)target_time) -> bertini._pybertini.tracking.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)self, (bertini._pybertini.endgame.config.Endgame)settings) → None :

Set the values of non-specific endgame settings

set_security_settings((FixedMultipleCauchyEG)self, (bertini._pybertini.endgame.config.Security)settings) → None :

Set the values of security-level settings

class bertini._pybertini.endgame.FixedMultiplePSEG((object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker) → None :

The fixed but arbitrary precision implementation of the power series endgame

Default construct with default settings

__init__( (object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker, (bertini._pybertini.endgame.config.PowerSeriesConfig)powerseriesconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Endgame)endgameconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Security)securityconfig) -> None

__init__((object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker) → None :

Default construct with default settings

__init__( (object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker, (bertini._pybertini.endgame.config.PowerSeriesConfig)powerseriesconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Endgame)endgameconfig) -> None

__init__( (object)self, (bertini._pybertini.tracking.MultiplePrecisionTracker)tracker, (bertini._pybertini.endgame.config.Security)securityconfig) -> None

add_observer((object)self, (object)observer) → None :

Attach an observer to this observable object

cycle_number((FixedMultiplePSEG)self) → int :

Get the cycle number as currently computed

final_approximation((FixedMultiplePSEG)self) → numpy.ndarray :

Get the current approximation of the root, in the ambient numeric type for the tracker being used

get_endgame_settings((FixedMultiplePSEG)self) → bertini._pybertini.endgame.config.Endgame :

Get the current non-specific endgame settings

get_security_settings((FixedMultiplePSEG)self) → bertini._pybertini.endgame.config.Security :

Get the ‘security’ settings for the endgame (path truncation near infinity)

get_system((FixedMultiplePSEG)self) → bertini._pybertini.system.System :

Get the tracked system. This is a reference to the internal system.

get_tracker((FixedMultiplePSEG)self) → bertini._pybertini.tracking.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)self, (object)observer) → None :

Remove an observer to this observable object

run((FixedMultiplePSEG)self, (bertini._pybertini.multiprec.Complex)start_time, (numpy.ndarray)start_point) → bertini._pybertini.tracking.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)self, (bertini._pybertini.multiprec.Complex)start_time, (numpy.ndarray)start_point, (bertini._pybertini.multiprec.Complex)target_time) -> bertini._pybertini.tracking.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)self, (bertini._pybertini.endgame.config.Endgame)settings) → None :

Set the values of non-specific endgame settings

set_security_settings((FixedMultiplePSEG)self, (bertini._pybertini.endgame.config.Security)settings) → None :

Set the values of security-level settings