pyHarm.Analysis.FRF_NonLinear
=============================

.. py:module:: pyHarm.Analysis.FRF_NonLinear


Classes
-------

.. autoapisummary::

   pyHarm.Analysis.FRF_NonLinear.FRF_NonLinear


Module Contents
---------------

.. py:class:: FRF_NonLinear(inputData: dict, System: pyHarm.Systems.ABCSystem.ABCSystem, logger: Optional[logging.Logger] = None, key: str = '', **kwargs)

   Bases: :py:obj:`pyHarm.Analysis.ABCAnalysis.ABCAnalysis`


   Nonlinear forced response analysis.

   Predicts a starting point using the predictor and then solves the residual equations from the starting point.

   .. attribute:: flag_print

      if True, prints a message after each Solve method.

      :type: bool

   .. attribute:: flag_purge

      if True, the jacobian values are purged from the solutions stored in the solution list.

      :type: bool

   .. attribute:: analysis_options

      input dictionary completed with the default values if keywords are missing.

      :type: dict

   .. attribute:: ds

      initial prediction step size.

      :type: float

   .. attribute:: SolList

      list of SystemSolution stored after each Solve method.

      :type: list[SystemSolution]

   .. attribute:: system

      ABCSystem associated with the analysis.

      :type: ABCSystem

   .. attribute:: adaptstep

      ABCStepSizeRule associated with the analysis.

      :type: ABCStepSizeRule

   .. attribute:: predictor

      ABCPredictor associated with the analysis.

      :type: ABCPredictor

   .. attribute:: corrector

      ABCCorrector associated with the analysis.

      :type: ABCCorrector

   .. attribute:: stopper

      ABCStopCriterion associated with the analysis.

      :type: ABCStopCriterion

   .. attribute:: solver

      ABCNLSolver associated with the analysis.

      :type: ABCNLSolver

   .. attribute:: corrector_init

      instance of no-continuation corrector for initial solution.

      :type: ABCCorrector

   .. attribute:: reductor

      ABCChainedReductor associated with the analysis.

      :type: ABCChainedReductor


   .. py:attribute:: factory_keyword
      :type:  str
      :value: 'frf'


      keyword that is used to call the creation of this class in the system factory.

      :type: str


   .. py:attribute:: name
      :value: 'Nonlinear FRF'



   .. py:attribute:: default

      default dictionary for the analysis.

      :type: dict


   .. py:attribute:: key
      :value: ''



   .. py:attribute:: analysis_options


   .. py:attribute:: flag_print


   .. py:attribute:: flag_purge


   .. py:attribute:: logger
      :type:  logging.Logger


   .. py:attribute:: ds


   .. py:attribute:: SolList
      :value: []



   .. py:attribute:: system


   .. py:attribute:: adaptstep


   .. py:attribute:: predictor


   .. py:attribute:: corrector


   .. py:attribute:: stopper


   .. py:attribute:: solver


   .. py:attribute:: corrector_init


   .. py:attribute:: reductor


   .. py:method:: initialise(x0=None, **kwargs)

      First Solve on the initial guess.

      :param x0: if None x0 is the linear solution at initial angular frequency, if "null" x0 is null vector, otherwise x0 is initialised using the provided array.
      :type x0: None|str|np.ndarray



   .. py:method:: _get_x0(x0)


   .. py:method:: CompleteSolution(sol: pyHarm.Solver.SystemSolution)

      Completes a SystemSolution informations that just went out of the Solve method.

      :param sol: solution to the system.
      :type sol: SystemSolution



   .. py:method:: globalResidual(solx: numpy.ndarray, sol: pyHarm.Solver.SystemSolution)

      Computes the residual of the whole system without the reducers.

      :param solx: displacement vector for which residual is computed.
      :type solx: np.ndarray
      :param sol: actual SystemSolution being solved.
      :type sol: SystemSolution



   .. py:method:: globalJacobian(solx: numpy.ndarray, sol: pyHarm.Solver.SystemSolution)

      Computes the jacobians of the whole system without the reducers.

      :param solx: displacement vector for which residual is computed.
      :type solx: np.ndarray
      :param sol: actual SystemSolution being solved.
      :type sol: SystemSolution



   .. py:method:: globalJacobianwRed(solq: numpy.ndarray, sol: pyHarm.Solver.SystemSolution)

      Computes the reduced jacobians of the whole system.

      :param solq: reduced displacement vector for which residual is computed.
      :type solq: np.ndarray
      :param sol: actual SystemSolution being solved.
      :type sol: SystemSolution



   .. py:method:: globalResidualwRed(solq: numpy.ndarray, sol: pyHarm.Solver.SystemSolution)

      Computes the reduced residuals of the whole system.

      :param solq: reduced displacement vector for which residual is computed.
      :type solq: np.ndarray
      :param sol: actual SystemSolution being solved.
      :type sol: SystemSolution



   .. py:method:: _update_reductor(xpred_full, last_solution_pointer=None)

      Updates the reducers

      :param xpred_full: full starting displacement vector.
      :type xpred_full: np.ndarray
      :param last_solution_pointer: SystemSolution from which the prediction has been generated.
      :type last_solution_pointer: SystemSolution

      :returns: reduced starting displacement vector.
                J_red (np.ndarray): reduced jacobian matrix.
                output_expl_dofs (pd.DataFrame): DataFrame of the dofs after applying the reduction layers.
      :rtype: xpred_red (np.ndarray)



   .. py:method:: makeStep(**kwargs)

      Makes a step of solving : get a step size, generate a predicted point, solve the nonlinear system, save the solution.



   .. py:method:: Solve(x0=None, **kwargs)

      Makes the whole analysis using continuation techniques until the stopping criterion is validated

      :param x0: if None x0 is the linear solution at initial angular frequency, if "null" x0 is null vector, otherwise x0 is initialised using the provided array.
      :type x0: None|str|np.ndarray



   .. py:method:: purge_jacobians()

      Purge the Jacobians of Solutions that are no longer used.



   .. py:method:: export(export_path: str, prefix: str, **kwargs) -> None

      export resutlts in csv files



   .. py:method:: _init_log()


   .. py:method:: _end_log()


   .. py:method:: _export_log()