Predictors package

Module Predictors

This module contains all the predictor types that are provided by pyHarm. The module is organized around an abstract class ABCPredictor and a FactoryPredictor that is in charge of creating the objects. All predictor object must comply with the ABCPredictor abstract class. The section below presents the different classes that are available in this module.

ABCPredictor

The ABCPredictor class is an abstract class defining the essential components of any nonlinear solver. One abstract method is defined :

Methods	Use
bifurcation_detect	Returns a flag if a bifurcation is encountered. Switches the direction of prediction if a turning point is encountered
getPointerToSolution	Returns the last accepted point from the SystemSolution list
norm_dir	Normalises the prediction direction depending on the required normalisation policy
predict	Abstract method : Returns the predicted point

The parameters associated with the predictors are the following :

Parameter	Use	Default
norm	Type of normalisation to apply; “norm1” to normalise the prediction vector to one, “om” to normalise the vector such that the angular frequency component is 1 [str]	✓ : “norm1”
bifurcation_detect	Uses the detection of bifurcation function [bool]	✓ : True
verbose	Displays messages when a bifurcation is encountered and gives its type	✓ : True

Examples of creating an ABCPredictor and adding it into an input dictionary:

To be created, an ABCPredictor subclass needs its abstract method to be defined :

class FakePred(ABCPredictor): # inherits from abstract class
    factory_keyword="fakepred" # mandatory to define
    def predict(self, sollist:list[SystemSolution], ds:float, k_imposed=None) -> tuple[np.ndarray,SystemSolution,float]:
        # code the way to get the predicted point,
        # the last SystemSolution point that is linked to the prediction
        # and the direction of the prediction that has been used depending if the angular frequency increases or decreases
        return xpred,lstpt,self.sign_ds

INP = {
    "analysis":{
        "FRF":{
            "study":"frf",
            ...,
            "predictor":"fakepred", # call the criterion using factory_keyword.
            "predictor_options":{"norm":"om", "bifurcation_detection":False, "verbose":False},
            ...,
        },
        ...,
    },
    "plugin":[FakePred], # add to the factory using plugin
    ...,
}

FactoryPredictor

This file contains the dictionary of all the predictors that are available as well as the function generatePredictor that creates the predictor object.

PredictorPreviousSolution previous

Predicts the next point using the same displacement as the last converged point, and makes a step onto the angular frequency only.

PredictorTangent tangent

Uses the Jacobian at last converged point to compute the tangent of the Jacobian based on a QR decomposition (see [1]).

PredictorSecant secant

Inherits from the tangent predictor to make the first point prediction. Otherwise, uses the two last converged points to compute the secant line and predict the next point based on the required step size.

References

[1] E. Allgower and K. Georg, *Numerical Continuation Methods – An Introduction. Soc. Ind Appl Math. 2003.

API links

pyHarm.Predictors