Source code for elastica.boundary_conditions

__doc__ = """ Built-in boundary condition implementationss """
__all__ = [
    "ConstraintBase",
    "FreeBC",
    "OneEndFixedBC",
    "GeneralConstraint",
    "FixedConstraint",
    "HelicalBucklingBC",
]

import warnings
from typing import Optional, Type, Union

import numpy as np

from abc import ABC, abstractmethod

import numba
from numba import njit

from elastica._linalg import _batch_matvec, _batch_matrix_transpose
from elastica._rotations import _get_rotation_matrix
from elastica.rod import RodBase
from elastica.rigidbody import RigidBodyBase
from elastica.typing import SystemType


[docs]class ConstraintBase(ABC): """Base class for constraint and displacement boundary condition implementation. Notes ----- Constraint class must inherit BaseConstraint class. Attributes ---------- system : RodBase or RigidBodyBase node_indices : None or numpy.ndarray element_indices : None or numpy.ndarray """ _system: Union[Type[RodBase], Type[RigidBodyBase]] _constrained_position_idx: np.ndarray _constrained_director_idx: np.ndarray def __init__(self, *args, **kwargs): """Initialize boundary condition""" try: self._system = kwargs["_system"] self._constrained_position_idx = np.array( kwargs.get("constrained_position_idx", []), dtype=int ) self._constrained_director_idx = np.array( kwargs.get("constrained_director_idx", []), dtype=int ) except KeyError: raise KeyError( "Please use simulator.constrain(...).using(...) syntax to establish constraint." ) @property def system(self) -> Union[Type[RodBase], Type[RigidBodyBase]]: """get system (rod or rigid body) reference""" return self._system @property def constrained_position_idx(self) -> Optional[np.ndarray]: """get position-indices passed to "using" """ # TODO: This should be immutable somehow return self._constrained_position_idx @property def constrained_director_idx(self) -> Optional[np.ndarray]: """get director-indices passed to "using" """ # TODO: This should be immutable somehow return self._constrained_director_idx
[docs] @abstractmethod def constrain_values( self, rod: Union[Type[RodBase], Type[RigidBodyBase]], time: float ) -> None: # TODO: In the future, we can remove rod and use self.system """ Constrain values (position and/or directors) of a rod object. Parameters ---------- rod : Union[Type[RodBase], Type[RigidBodyBase]] Rod or rigid-body object. time : float The time of simulation. """ pass
[docs] @abstractmethod def constrain_rates( self, rod: Union[Type[RodBase], Type[RigidBodyBase]], time: float ) -> None: # TODO: In the future, we can remove rod and use self.system """ Constrain rates (velocity and/or omega) of a rod object. Parameters ---------- rod : Union[Type[RodBase], Type[RigidBodyBase]] Rod or rigid-body object. time : float The time of simulation. """ pass
[docs]class FreeBC(ConstraintBase): """ Boundary condition template. """ def __init__(self, **kwargs): super().__init__(**kwargs) def constrain_values( self, rod: Union[Type[RodBase], Type[RigidBodyBase]], time: float ) -> None: """In FreeBC, this routine simply passes.""" pass def constrain_rates( self, rod: Union[Type[RodBase], Type[RigidBodyBase]], time: float ) -> None: """In FreeBC, this routine simply passes.""" pass
[docs]class FreeRod(FreeBC): # Please clear this part beyond version 0.3.0 """Deprecated 0.2.1: Same implementation as FreeBC""" warnings.warn( "FreeRod is deprecated and renamed to FreeBC. The deprecated name will be removed in the future.", DeprecationWarning, )
[docs]class OneEndFixedBC(ConstraintBase): """ This boundary condition class fixes one end of the rod. Currently, this boundary condition fixes position and directors at the first node and first element of the rod. `Example case (timoshenko) <https://github.com/GazzolaLab/PyElastica/blob/master/examples/TimoshenkoBeamCase/timoshenko.py>`_ Examples -------- How to fix one ends of the rod: >>> simulator.constrain(rod).using( ... OneEndFixedBC, ... constrained_position_idx=(0,), ... constrained_director_idx=(0,) ... ) """
[docs] def __init__(self, fixed_position, fixed_directors, **kwargs): """ Initialization of the constraint. Any parameter passed to 'using' will be available in kwargs. Parameters ---------- constrained_position_idx : tuple Tuple of position-indices that will be constrained constrained_director_idx : tuple Tuple of director-indices that will be constrained """ super().__init__(**kwargs) self.fixed_position_collection = np.array(fixed_position) self.fixed_directors_collection = np.array(fixed_directors)
def constrain_values( self, rod: Union[Type[RodBase], Type[RigidBodyBase]], time: float ) -> None: # rod.position_collection[..., 0] = self.fixed_position # rod.director_collection[..., 0] = self.fixed_directors self.compute_constrain_values( rod.position_collection, self.fixed_position_collection, rod.director_collection, self.fixed_directors_collection, ) def constrain_rates( self, rod: Union[Type[RodBase], Type[RigidBodyBase]], time: float ) -> None: # rod.velocity_collection[..., 0] = 0.0 # rod.omega_collection[..., 0] = 0.0 self.compute_constrain_rates( rod.velocity_collection, rod.omega_collection, ) @staticmethod @njit(cache=True) def compute_constrain_values( position_collection, fixed_position_collection, director_collection, fixed_directors_collection, ): """ Computes constrain values in numba njit decorator Parameters ---------- position_collection : numpy.ndarray 2D (dim, blocksize) array containing data with `float` type. fixed_position : numpy.ndarray 2D (dim, 1) array containing data with 'float' type. director_collection : numpy.ndarray 3D (dim, dim, blocksize) array containing data with `float` type. fixed_directors : numpy.ndarray 3D (dim, dim, 1) array containing data with 'float' type. Returns ------- """ position_collection[..., 0] = fixed_position_collection director_collection[..., 0] = fixed_directors_collection @staticmethod @njit(cache=True) def compute_constrain_rates(velocity_collection, omega_collection): """ Compute contrain rates in numba njit decorator Parameters ---------- velocity_collection : numpy.ndarray 2D (dim, blocksize) array containing data with `float` type. omega_collection : numpy.ndarray 2D (dim, blocksize) array containing data with `float` type. Returns ------- """ velocity_collection[..., 0] = 0.0 omega_collection[..., 0] = 0.0
[docs]class OneEndFixedRod(OneEndFixedBC): # Please clear this part beyond version 0.3.0 """Deprecated 0.2.1: Same implementation as OneEndFixedBC""" warnings.warn( "OneEndFixedRod is deprecated and renamed to OneEndFixedBC. The deprecated name will be removed in the future.", DeprecationWarning, )
[docs]class GeneralConstraint(ConstraintBase): """ This boundary condition class allows the specified node/link to have a configurable constraint. Index can be passed to fix either or both the position or the director. Constraining position is equivalent to setting 0 translational DOF. Constraining director is equivalent to setting 0 rotational DOF. Examples -------- How to fix all translational and rotational dof except allowing twisting around the z-axis in an inertial frame: >>> simulator.constrain(rod).using( ... GeneralConstraint, ... constrained_position_idx=(0,), ... constrained_director_idx=(0,), ... translational_constraint_selector=np.array([True, True, True]), ... rotational_constraint_selector=np.array([True, True, False]), ... ) How to allow the end of the rod to move in the XY plane and allow all rotational dof: >>> simulator.constrain(rod).using( ... GeneralConstraint, ... constrained_position_idx=(-1,), ... translational_constraint_selector=np.array([True, True, False]), ... ) """
[docs] def __init__( self, *fixed_data, translational_constraint_selector: Optional[np.ndarray] = None, rotational_constraint_selector: Optional[np.array] = None, **kwargs, ): """ Initialization of the constraint. Any parameter passed to 'using' will be available in kwargs. Parameters ---------- constrained_position_idx : tuple Tuple of position-indices that will be constrained constrained_director_idx : tuple Tuple of director-indices that will be constrained translational_constraint_selector: Optional[np.ndarray] np.array of type bool indicating which translational degrees of freedom (dof) to constrain. If entry is True, the corresponding dof will be constrained. If None, we constrain all dofs. rotational_constraint_selector: Optional[np.ndarray] np.array of type bool indicating which translational degrees of freedom (dof) to constrain. If entry is True, the corresponding dof will be constrained. """ super().__init__(**kwargs) pos, dir = [], [] for data in fixed_data: if isinstance(data, np.ndarray) and data.shape == (3,): pos.append(data) elif isinstance(data, np.ndarray) and data.shape == ( 3, 3, ): dir.append(data) else: # TODO: This part is prone to error. break if len(pos) > 0: # transpose from (blocksize, dim) to (dim, blocksize) self.fixed_positions = np.array(pos).transpose((1, 0)) if len(dir) > 0: # transpose from (blocksize, dim, dim) to (dim, dim, blocksize) self.fixed_directors = np.array(dir).transpose((1, 2, 0)) if translational_constraint_selector is None: translational_constraint_selector = np.array([True, True, True]) if rotational_constraint_selector is None: rotational_constraint_selector = np.array([True, True, True]) # properly validate the user-provided constraint selectors assert ( type(translational_constraint_selector) == np.ndarray and translational_constraint_selector.dtype == bool and translational_constraint_selector.shape == (3,) ), "Translational constraint selector must be a 1D boolean array of length 3." assert ( type(rotational_constraint_selector) == np.ndarray and rotational_constraint_selector.dtype == bool and rotational_constraint_selector.shape == (3,) ), "Rotational constraint selector must be a 1D boolean array of length 3." # cast booleans to int self.translational_constraint_selector = ( translational_constraint_selector.astype(int) ) self.rotational_constraint_selector = rotational_constraint_selector.astype(int)
def constrain_values(self, system: SystemType, time: float) -> None: if self.constrained_position_idx.size: self.nb_constrain_translational_values( system.position_collection, self.fixed_positions, self.constrained_position_idx, self.translational_constraint_selector, ) def constrain_rates(self, system: SystemType, time: float) -> None: if self.constrained_position_idx.size: self.nb_constrain_translational_rates( system.velocity_collection, self.constrained_position_idx, self.translational_constraint_selector, ) if self.constrained_director_idx.size: self.nb_constrain_rotational_rates( system.director_collection, system.omega_collection, self.constrained_director_idx, self.rotational_constraint_selector, ) @staticmethod @njit(cache=True) def nb_constrain_translational_values( position_collection, fixed_position_collection, indices, constraint_selector ) -> None: """ Computes constrain values in numba njit decorator Parameters ---------- position_collection : numpy.ndarray 2D (dim, blocksize) array containing data with `float` type. fixed_position_collection : numpy.ndarray 2D (dim, blocksize) array containing data with `float` type. indices : numpy.ndarray 1D array containing the index of constraining nodes constraint_selector: numpy.ndarray 1D array of type int and size (3,) indicating which translational Degrees of Freedom (DoF) to constrain. Entries are integers in {0, 1} (e.g. a binary values of either 0 or 1). If entry is 1, the concerning DoF will be constrained, otherwise it will be free for translation. Selector shall be specified in the inertial frame """ block_size = indices.size for i in range(block_size): k = indices[i] # First term: add the old position values using the inverse constraint selector (e.g. DoF) # Second term: add the fixed position values using the constraint selector (e.g. constraint dimensions) position_collection[..., k] = ( 1 - constraint_selector ) * position_collection[ ..., k ] + constraint_selector * fixed_position_collection[ ..., i ] @staticmethod @njit(cache=True) def nb_constrain_translational_rates( velocity_collection, indices, constraint_selector ) -> None: """ Compute constrain rates in numba njit decorator Parameters ---------- velocity_collection : numpy.ndarray 2D (dim, blocksize) array containing data with `float` type. indices : numpy.ndarray 1D array containing the index of constraining nodes constraint_selector: numpy.ndarray 1D array of type int and size (3,) indicating which translational Degrees of Freedom (DoF) to constrain. Entries are integers in {0, 1} (e.g. a binary values of either 0 or 1). If entry is 1, the concerning DoF will be constrained, otherwise it will be free for translation. Selector shall be specified in the inertial frame """ block_size = indices.size for i in range(block_size): k = indices[i] # set the dofs to 0 where the constraint_selector mask is active velocity_collection[..., k] = ( 1 - constraint_selector ) * velocity_collection[..., k] @staticmethod @njit(cache=True) def nb_constrain_rotational_rates( director_collection, omega_collection, indices, constraint_selector ) -> None: """ Compute constrain rates in numba njit decorator Parameters ---------- director_collection : numpy.ndarray 2D (dim, blocksize) array containing data with `float` type. omega_collection : numpy.ndarray 2D (dim, blocksize) array containing data with `float` type. indices : numpy.ndarray 1D array containing the index of constraining nodes constraint_selector: numpy.ndarray 1D array of type int and size (3,) indicating which rotational Degrees of Freedom (DoF) to constrain. Entries are integers in {0, 1} (e.g. a binary values of either 0 or 1). If an entry is 1, the rotation around the respective axis will be constrained, otherwise the system can freely rotate around the axis. The selector shall be specified in the lab frame """ directors = director_collection[..., indices] # rotate angular velocities to lab frame omega_collection_lab_frame = _batch_matvec( _batch_matrix_transpose(directors), omega_collection[..., indices] ) # apply constraint selector to angular velocities in lab frame omega_collection_not_constrained = ( 1 - np.expand_dims(constraint_selector, 1) ) * omega_collection_lab_frame # rotate angular velocities vector back to local frame and apply to omega_collection omega_collection[..., indices] = _batch_matvec( directors, omega_collection_not_constrained )
[docs]class FixedConstraint(GeneralConstraint): """ This boundary condition class fixes the specified node or orientations. Index can be passed to fix either or both the position or the director. Constraining position is equivalent to setting 0 translational DOF. Constraining director is equivalent to setting 0 rotational DOF. Examples -------- How to fix two ends of the rod: >>> simulator.constrain(rod).using( ... FixedConstraint, ... constrained_position_idx=(0,-1), ... constrained_director_idx=(0,-1) ... ) How to pin the middle of the rod (10th node), without constraining the rotational DOF. >>> simulator.constrain(rod).using( ... FixedConstraint, ... constrained_position_idx=(10) ... ) See Also -------- GeneralConstraint: Generalized constraint with configurable DOF. """
[docs] def __init__(self, *args, **kwargs): """ Initialization of the constraint. Any parameter passed to 'using' will be available in kwargs. Parameters ---------- constrained_position_idx : tuple Tuple of position-indices that will be constrained constrained_director_idx : tuple Tuple of director-indices that will be constrained """ super().__init__( *args, translational_constraint_selector=np.array([True, True, True]), rotational_constraint_selector=np.array([True, True, True]), **kwargs, )
def constrain_values( self, rod: Union[Type[RodBase], Type[RigidBodyBase]], time: float ) -> None: if self.constrained_position_idx.size: self.nb_constrain_translational_values( rod.position_collection, self.fixed_positions, self.constrained_position_idx, ) if self.constrained_director_idx.size: self.nb_constraint_rotational_values( rod.director_collection, self.fixed_directors, self.constrained_director_idx, ) def constrain_rates( self, rod: Union[Type[RodBase], Type[RigidBodyBase]], time: float ) -> None: if self.constrained_position_idx.size: self.nb_constrain_translational_rates( rod.velocity_collection, self.constrained_position_idx, ) if self.constrained_director_idx.size: self.nb_constrain_rotational_rates( rod.omega_collection, self.constrained_director_idx, ) @staticmethod @njit(cache=True) def nb_constraint_rotational_values( director_collection, fixed_director_collection, indices ) -> None: """ Computes constrain values in numba njit decorator Parameters ---------- director_collection : numpy.ndarray 3D (dim, dim, blocksize) array containing data with `float` type. fixed_director_collection : numpy.ndarray 3D (dim, dim, blocksize) array containing data with `float` type. indices : numpy.ndarray 1D array containing the index of constraining nodes """ block_size = indices.size for i in range(block_size): k = indices[i] director_collection[..., k] = fixed_director_collection[..., i] @staticmethod @njit(cache=True) def nb_constrain_translational_values( position_collection, fixed_position_collection, indices ) -> None: """ Computes constrain values in numba njit decorator Parameters ---------- position_collection : numpy.ndarray 2D (dim, blocksize) array containing data with `float` type. fixed_position_collection : numpy.ndarray 2D (dim, blocksize) array containing data with `float` type. indices : numpy.ndarray 1D array containing the index of constraining nodes """ block_size = indices.size for i in range(block_size): k = indices[i] position_collection[..., k] = fixed_position_collection[..., i] @staticmethod @njit(cache=True) def nb_constrain_translational_rates(velocity_collection, indices) -> None: """ Compute constrain rates in numba njit decorator Parameters ---------- velocity_collection : numpy.ndarray 2D (dim, blocksize) array containing data with `float` type. indices : numpy.ndarray 1D array containing the index of constraining nodes """ block_size = indices.size for i in range(block_size): k = indices[i] velocity_collection[0, k] = 0.0 velocity_collection[1, k] = 0.0 velocity_collection[2, k] = 0.0 @staticmethod @njit(cache=True) def nb_constrain_rotational_rates(omega_collection, indices) -> None: """ Compute constrain rates in numba njit decorator Parameters ---------- omega_collection : numpy.ndarray 2D (dim, blocksize) array containing data with `float` type. indices : numpy.ndarray 1D array containing the index of constraining nodes """ block_size = indices.size for i in range(block_size): k = indices[i] omega_collection[0, k] = 0.0 omega_collection[1, k] = 0.0 omega_collection[2, k] = 0.0
[docs]class HelicalBucklingBC(ConstraintBase): """ This is the boundary condition class for Helical Buckling case in Gazzola et. al. RSoS (2018). The applied boundary condition is twist and slack on to the first and last nodes and elements of the rod. `Example case (helical buckling) <https://github.com/GazzolaLab/PyElastica/blob/master/examples/HelicalBucklingCase/helicalbuckling.py>`_ Attributes ---------- twisting_time: float Time to complete twist. final_start_position: numpy.ndarray 2D (dim, 1) array containing data with 'float' type. Position of first node of rod after twist completed. final_end_position: numpy.ndarray 2D (dim, 1) array containing data with 'float' type. Position of last node of rod after twist completed. ang_vel: numpy.ndarray 2D (dim, 1) array containing data with 'float' type. Angular velocity of rod during twisting time. shrink_vel: numpy.ndarray 2D (dim, 1) array containing data with 'float' type. Shrink velocity of rod during twisting time. final_start_directors: numpy.ndarray 3D (dim, dim, 1) array containing data with 'float' type. Directors of first element of rod after twist completed. final_end_directors: numpy.ndarray 3D (dim, dim, 1) array containing data with 'float' type. Directors of last element of rod after twist completed. """
[docs] def __init__( self, position_start: np.ndarray, position_end: np.ndarray, director_start: np.ndarray, director_end: np.ndarray, twisting_time: float, slack: float, number_of_rotations: float, **kwargs, ): """ Helical Buckling initializer Parameters ---------- position_start : numpy.ndarray 2D (dim, 1) array containing data with 'float' type. Initial position of first node. position_end : numpy.ndarray 2D (dim, 1) array containing data with 'float' type. Initial position of last node. director_start : numpy.ndarray 3D (dim, dim, blocksize) array containing data with 'float' type. Initial director of first element. director_end : numpy.ndarray 3D (dim, dim, blocksize) array containing data with 'float' type. Initial director of last element. twisting_time : float Time to complete twist. slack : float Slack applied to rod. number_of_rotations : float Number of rotations applied to rod. """ super().__init__(**kwargs) self.twisting_time = twisting_time angel_vel_scalar = ( 2.0 * number_of_rotations * np.pi / self.twisting_time ) / 2.0 shrink_vel_scalar = slack / (self.twisting_time * 2.0) direction = (position_end - position_start) / np.linalg.norm( position_end - position_start ) self.final_start_position = position_start + slack / 2.0 * direction self.final_end_position = position_end - slack / 2.0 * direction self.ang_vel = angel_vel_scalar * direction self.shrink_vel = shrink_vel_scalar * direction theta = number_of_rotations * np.pi self.final_start_directors = ( _get_rotation_matrix(theta, direction.reshape(3, 1)).reshape(3, 3) @ director_start ) # rotation_matrix wants vectors 3,1 self.final_end_directors = ( _get_rotation_matrix(-theta, direction.reshape(3, 1)).reshape(3, 3) @ director_end ) # rotation_matrix wants vectors 3,1
def constrain_values( self, rod: Union[Type[RodBase], Type[RigidBodyBase]], time: float ) -> None: if time > self.twisting_time: rod.position_collection[..., 0] = self.final_start_position rod.position_collection[..., -1] = self.final_end_position rod.director_collection[..., 0] = self.final_start_directors rod.director_collection[..., -1] = self.final_end_directors def constrain_rates( self, rod: Union[Type[RodBase], Type[RigidBodyBase]], time: float ) -> None: if time > self.twisting_time: rod.velocity_collection[..., 0] = 0.0 rod.omega_collection[..., 0] = 0.0 rod.velocity_collection[..., -1] = 0.0 rod.omega_collection[..., -1] = 0.0 else: rod.velocity_collection[..., 0] = self.shrink_vel rod.omega_collection[..., 0] = self.ang_vel rod.velocity_collection[..., -1] = -self.shrink_vel rod.omega_collection[..., -1] = -self.ang_vel