__doc__ = """ Built-in boundary condition implementationss """
import warnings
from typing import Optional
import numpy as np
from abc import ABC, abstractmethod
from numba import njit
from elastica._linalg import _batch_matvec, _batch_matrix_transpose
from elastica._rotations import _get_rotation_matrix
from elastica.typing import SystemType, RodType
[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: SystemType
_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) -> SystemType:
"""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, system: SystemType, 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
----------
system : SystemType
Rod or rigid-body object.
time : float
The time of simulation.
"""
pass
[docs] @abstractmethod
def constrain_rates(self, system: SystemType, 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
----------
system : SystemType
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, system: SystemType, time: float) -> None:
"""In FreeBC, this routine simply passes."""
pass
def constrain_rates(self, system: SystemType, 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, system: SystemType, time: float) -> None:
# system.position_collection[..., 0] = self.fixed_position
# system.director_collection[..., 0] = self.fixed_directors
self.compute_constrain_values(
system.position_collection,
self.fixed_position_collection,
system.director_collection,
self.fixed_directors_collection,
)
def constrain_rates(self, system: SystemType, time: float) -> None:
# system.velocity_collection[..., 0] = 0.0
# system.omega_collection[..., 0] = 0.0
self.compute_constrain_rates(
system.velocity_collection,
system.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(system).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, 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,
)
if self.constrained_director_idx.size:
self.nb_constraint_rotational_values(
system.director_collection,
self.fixed_directors,
self.constrained_director_idx,
)
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,
)
if self.constrained_director_idx.size:
self.nb_constrain_rotational_rates(
system.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: RodType, 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: RodType, 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
