pyHarm.KinematicConditions.ABCKinematic
=======================================

.. py:module:: pyHarm.KinematicConditions.ABCKinematic


Classes
-------

.. autoapisummary::

   pyHarm.KinematicConditions.ABCKinematic.ABCKinematic


Functions
---------

.. autoapisummary::

   pyHarm.KinematicConditions.ABCKinematic.ConstructorPslavemaster


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

.. py:function:: ConstructorPslavemaster(nsub, subs, nodes, sub_expl_dofs)

   Function that creates the selection matrices for the slave dofs and the master dofs.

   :param nsub: number of substructures that are connected with the kinematic condition.
   :type nsub: int
   :param subs: list containing the name of the sbstructures connected with the kinematic condition.
   :type subs: list[str]
   :param nodes: list of nodes list that are connected with the kinematic condition.
   :type nodes: list[list[int]]
   :param sub_expl_dofs: explicit dofs DataFrame.
   :type sub_expl_dofs: pd.DataFrame

   :returns: selection matrix for the slave dofs.
             np.ndarray: selection matrix for the master dofs.
   :rtype: np.ndarray


.. py:class:: ABCKinematic(nh: int, nti: int, name: str, data: dict, CS: pyHarm.CoordinateSystem.CoordinateSystem)

   Bases: :py:obj:`abc.ABC`


   This is the abstract class ruling the kinematic conditions class. The kinematic conditions are responsible to impose kinematic on dofs of the system and transfer the residuals.

   :param nh: number of harmonics.
   :type nh: int
   :param nti: number of time steps.
   :type nti: int
   :param name: name given to the kinematic condition.
   :type name: str
   :param data: dictionary containing all the definition information of the kinematic condition.
   :type data: dict
   :param CS: local or global coordinate system the kinematic condition is defined on.
   :type CS: CoordinateSystem

   .. attribute:: nh

      number of harmonics.

      :type: int

   .. attribute:: nti

      number of time steps.

      :type: int

   .. attribute:: D

      Dynamic operators containing inverse discrete Fourier transform and discrete Fourier transform.

      :type: dict[np.ndarray,np.ndarray]

   .. attribute:: nabla

      Derivation operator.

      :type: np.ndarray

   .. attribute:: indices

      index of the dofs that the kinematic conditions needs.

      :type: np.ndarray

   .. attribute:: Pdir

      a slice of first dimension is a transformation matrix to a direction in local coordinate system.

      :type: np.ndarray

   .. attribute:: Pslave

      selection array that selects the slave dofs of the kinematic condition.

      :type: np.ndarray

   .. attribute:: Pmaster

      selection array that selects the master dofs of the kinematic condition.

      :type: np.ndarray

   .. attribute:: subs

      list containing the name of the substructures that are involved.

      :type: list[str]

   .. attribute:: nbSub

      number of substructure involved.

      :type: int

   .. attribute:: nodes

      list of list of nodes the kinematic conditions act on.

      :type: list[list]

   .. attribute:: nbdofi

      number of nodes involved per substructure.

      :type: int


   .. py:property:: factory_keyword
      :abstractmethod:



   .. py:method:: __init_flags__()


   .. py:method:: __init_harmonic_operators__(nh, nti)


   .. py:method:: __init_data__(name, data, CS)


   .. py:method:: __str__()


   .. py:method:: __repr__()


   .. py:method:: __post_init__(*args)


   .. py:method:: __flag_update__(*args)


   .. py:method:: generateIndices(expl_dofs: pandas.DataFrame)

      From the explicit dof DataFrame, generates the index of dofs concerned by the kinematic condition.

      :param expl_dofs: explicit dof DataFrame from the studied system.
      :type expl_dofs: pd.DataFrame

      .. attribute:: indices

         index of the dofs that the kinematic conditions needs.

         :type: np.ndarray

      .. attribute:: Pdir

         a slice of first dimension is a transformation matrix to a direction in local coordinate system.

         :type: np.ndarray

      .. attribute:: Pslave

         selection array that selects the slave dofs of the kinematic condition.

         :type: np.ndarray

      .. attribute:: Pmaster

         selection array that selects the master dofs of the kinematic condition.

         :type: np.ndarray



   .. py:method:: _generateMatrices(sub_expl_dofs)


   .. py:method:: adim(lc, wc)
      :abstractmethod:


      Using adim parameters, modifies the kinematic conditions accordingly.

      :param lc: characteristic length.
      :type lc: float
      :param wc: characteristic angular frequency.
      :type wc: float



   .. py:method:: complete_x(x, om)
      :abstractmethod:


      Returns a vector x_add of same size of x that completes the vector of displacement x = x + x_add.

      :param x: displacement vector.
      :type x: np.ndarray
      :param om: angular frequency.
      :type om: float



   .. py:method:: complete_R(R, x)
      :abstractmethod:


      Returns a vector R_add of same size of R that completes the vector of residual R = R + R_add

      :param R: residual vector.
      :type R: np.ndarray
      :param x: displacement vector.
      :type x: np.ndarray



   .. py:method:: complete_J(Jx, Jom, x)
      :abstractmethod:


      Returns a vector Jx_add and Jom_add of same size of Jx and Jom that completes the Jacobian

      :param Jx: jacobian matrix with respect to displacement.
      :type Jx: np.ndarray
      :param Jom: jacobian matrix with respect to angular frequency.
      :type Jom: np.ndarray
      :param x: displacement vector.
      :type x: np.ndarray