Correctors package

Module Corrector

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

ABCAnalysis

The ABCCorrector class is an abstract class defining the essential components of any corrector. Two abstract methods are defined :

Methods	Use
ClosureEquation	Abstract method : Returns the residual value of the closure equation based on displacement vector and a SystemSolution object
ClosureJacobian	Abstract method : Returns the jacobian values with respect to displacement and the angular frequency of the closure equation based on displacement vector and a SystemSolution object

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

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

class FakeCorrector(ABCCorrector): # inherits from abstract class
    factory_keyword="fakecorr" # mandatory to define
    def ClosureEquation(self, solx:np.ndarray,sol:SystemSolution,sollist:list[SystemSolution],**kwargs) -> np.ndarray:
        R_cont =  ... # compute the residual equation of the correction equation.
        return R_cont
    def ClosureJacobian(self, solx:np.ndarray,sol:SystemSolution,sollist:list[SystemSolution],**kwargs) -> tuple[np.ndarray,np.ndarray]:
        dRdx =  ... # compute the jacobian with respect to the displacement of the correction equation.
        dRdom =  ... # compute the jacobian with respect to the angular frequency of the correction equation.
        return dRdx, dRdom

INP = {
    "analysis":{
        "FRF":{
            "study":"frf",
            ...,
            "corrector":"fakecorr", # call the criterion using factory_keyword.
            ...,
        },
        ...,
    },
    "plugin":[FakeCorrector], # add to the factory using plugin
    ...,
}

FactoryCorrector

This file contains the dictionary of all the correctors that are available as well as the function generateCorrector that creates the corrector object based on the desired type of corrector.

Corrector_no_continuation nocontinuation

This corrector corresponds to a no-correction closure equation. The residual is expressed as follows :

\[R(x,\omega) = \omega - \omega_{start}\]

which forces the angular frequency to remain constant.

Corrector pseudo arc length pseudo_arc_length

This corrector forces the seeked solution to belong to an hyperplan perpendicular to the prediction direction. This corrector allows for treating turning points. The residual is expressed as follows :

\[R(x,\omega) = <(x_{start} - x_{previous});(x-x_{start})>\]

where \(<;>\) defines the classical scalar product.

Corrector arc length arc_length

This corrector forces the seeked solution to belong to an hypersphere of radius \(`ds`\), where \(`ds`\) is the length of the prediction vector. This corrector also allows for treating turning points. The residual is expressed as follows :

\[{\displaystyle R(x,\omega) = (x - x_{previous})^{2} + (\omega - \omega_{previous})^{2} + ds^{2}}\]

API links

pyHarm.Correctors