import torch
from .location import Location
from ..label_tensor import LabelTensor
from ..utils import check_consistency
[docs]
class EllipsoidDomain(Location):
"""PINA implementation of Ellipsoid domain."""
def __init__(self, ellipsoid_dict, sample_surface=False):
"""PINA implementation of Ellipsoid domain.
:param ellipsoid_dict: A dictionary with dict-key a string representing
the input variables for the pinn, and dict-value a list with
the domain extrema.
:type ellipsoid_dict: dict
:param sample_surface: A variable for choosing sample strategies. If
``sample_surface=True`` only samples on the ellipsoid surface
frontier are taken. If ``sample_surface=False`` only samples on
the ellipsoid interior are taken, defaults to ``False``.
:type sample_surface: bool
.. warning::
Sampling for dimensions greater or equal to 10 could result
in a shrinking of the ellipsoid, which degrades the quality
of the samples. For dimensions higher than 10, other algorithms
for sampling should be used, such as: Dezert, Jean, and Christian
Musso. "An efficient method for generating points uniformly
distributed in hyperellipsoids." Proceedings of the Workshop on
Estimation, Tracking and Fusion: A Tribute to Yaakov Bar-Shalom.
Vol. 7. No. 8. 2001.
:Example:
>>> spatial_domain = Ellipsoid({'x':[-1, 1], 'y':[-1,1]})
"""
self.fixed_ = {}
self.range_ = {}
self._centers = None
self._axis = None
# checking consistency
check_consistency(sample_surface, bool)
self._sample_surface = sample_surface
for k, v in ellipsoid_dict.items():
if isinstance(v, (int, float)):
self.fixed_[k] = v
elif isinstance(v, (list, tuple)) and len(v) == 2:
self.range_[k] = v
else:
raise TypeError
# perform operation only for not fixed variables (if any)
if self.range_:
# convert dict vals to torch [dim, 2] matrix
list_dict_vals = list(self.range_.values())
tmp = torch.tensor(list_dict_vals, dtype=torch.float)
# get the ellipsoid center
normal_basis = torch.eye(len(list_dict_vals))
centers = torch.diag(normal_basis * tmp.mean(axis=1))
# get the ellipsoid axis
ellipsoid_axis = (tmp - centers.reshape(-1, 1))[:, -1]
# save elipsoid axis and centers as dict
self._centers = dict(zip(self.range_.keys(), centers.tolist()))
self._axis = dict(zip(self.range_.keys(), ellipsoid_axis.tolist()))
@property
def variables(self):
"""Spatial variables.
:return: Spatial variables defined in '__init__()'
:rtype: list[str]
"""
return sorted(list(self.fixed_.keys()) + list(self.range_.keys()))
[docs]
def is_inside(self, point, check_border=False):
"""Check if a point is inside the ellipsoid domain.
.. note::
When ``sample_surface`` in the ``__init()__``
is set to ``True``, then the method only checks
points on the surface, and not inside the domain.
:param point: Point to be checked.
:type point: LabelTensor
:param check_border: Check if the point is also on the frontier
of the ellipsoid, default ``False``.
:type check_border: bool
:return: Returning True if the point is inside, ``False`` otherwise.
:rtype: bool
"""
# small check that point is labeltensor
check_consistency(point, LabelTensor)
# get axis ellipse as tensors
list_dict_vals = list(self._axis.values())
tmp = torch.tensor(list_dict_vals, dtype=torch.float)
ax_sq = LabelTensor(tmp.reshape(1, -1) ** 2, self.variables)
# get centers ellipse as tensors
list_dict_vals = list(self._centers.values())
tmp = torch.tensor(list_dict_vals, dtype=torch.float)
centers = LabelTensor(tmp.reshape(1, -1), self.variables)
if not all([i in ax_sq.labels for i in point.labels]):
raise ValueError(
"point labels different from constructor"
f" dictionary labels. Got {point.labels},"
f" expected {ax_sq.labels}."
)
# point square + shift center
point_sq = (point - centers).pow(2)
point_sq.labels = point.labels
# calculate ellispoid equation
eqn = torch.sum(point_sq.extract(ax_sq.labels) / ax_sq) - 1.0
# if we have sampled only the surface, we check that the
# point is inside the surface border only
if self._sample_surface:
return torch.allclose(eqn, torch.zeros_like(eqn))
# otherwise we check the ellipse
if check_border:
return bool(eqn <= 0)
return bool(eqn < 0)
def _sample_range(self, n, mode, variables):
"""Rescale the samples to the correct bounds.
:param n: Number of points to sample in the ellipsoid.
:type n: int
:param mode: Mode for sampling, defaults to ``random``.
Available modes include: random sampling, ``random``.
:type mode: str, optional
:param variables: Variables to be rescaled in the samples.
:type variables: torch.Tensor
:return: Rescaled sample points.
:rtype: torch.Tensor
"""
# =============== For Developers ================ #
#
# The sampling startegy used is fairly simple.
# For all `mode`s first we sample from the unit
# sphere and then we scale and shift according
# to self._axis.values() and self._centers.values().
#
# =============================================== #
# get dimension
dim = len(variables)
# get values center
pairs_center = [
(k, v) for k, v in self._centers.items() if k in variables
]
_, values_center = map(list, zip(*pairs_center))
values_center = torch.tensor(values_center)
# get values axis
pairs_axis = [(k, v) for k, v in self._axis.items() if k in variables]
_, values_axis = map(list, zip(*pairs_axis))
values_axis = torch.tensor(values_axis)
# Sample in the unit sphere
if mode == "random":
# 1. Sample n points from the surface of a unit sphere
# 2. Scale each dimension using torch.rand()
# (a random number between 0-1) so that it lies within
# the sphere, only if self._sample_surface=False
# 3. Multiply with self._axis.values() to make it ellipsoid
# 4. Shift the mean of the ellipse by adding self._centers.values()
# step 1.
pts = torch.randn(size=(n, dim))
pts = pts / torch.linalg.norm(pts, axis=-1).view((n, 1))
if not self._sample_surface: # step 2.
scale = torch.rand((n, 1))
pts = pts * scale
# step 3. and 4.
pts *= values_axis
pts += values_center
return pts
[docs]
def sample(self, n, mode="random", variables="all"):
"""Sample routine.
:param int n: Number of points to sample in the shape.
:param str mode: Mode for sampling, defaults to ``random``. Available modes include: ``random``.
:param variables: Variables to be sampled, defaults to ``all``.
:type variables: str | list[str]
:return: Returns ``LabelTensor`` of n sampled points.
:rtype: LabelTensor
:Example:
>>> elips = Ellipsoid({'x':[1, 0], 'y':1})
>>> elips.sample(n=6)
tensor([[0.4872, 1.0000],
[0.2977, 1.0000],
[0.0422, 1.0000],
[0.6431, 1.0000],
[0.7272, 1.0000],
[0.8326, 1.0000]])
"""
def _Nd_sampler(n, mode, variables):
"""Sample all the variables together
:param n: Number of points to sample.
:type n: int
:param mode: Mode for sampling, defaults to ``random``.
Available modes include: random sampling, ``random``;
latin hypercube sampling, 'latin' or 'lh';
chebyshev sampling, 'chebyshev'; grid sampling 'grid'.
:type mode: str, optional.
:param variables: pinn variable to be sampled, defaults to ``all``.
:type variables: str or list[str], optional.
:return: Sample points.
:rtype: list[torch.Tensor]
"""
pairs = [(k, v) for k, v in self.range_.items() if k in variables]
keys, _ = map(list, zip(*pairs))
result = self._sample_range(n, mode, keys)
result = result.as_subclass(LabelTensor)
result.labels = keys
for variable in variables:
if variable in self.fixed_.keys():
value = self.fixed_[variable]
pts_variable = torch.tensor([[value]]).repeat(
result.shape[0], 1
)
pts_variable = pts_variable.as_subclass(LabelTensor)
pts_variable.labels = [variable]
result = result.append(pts_variable, mode="std")
return result
def _single_points_sample(n, variables):
"""Sample a single point in one dimension.
:param n: Number of points to sample.
:type n: int
:param variables: Variables to sample from.
:type variables: list[str]
:return: Sample points.
:rtype: list[torch.Tensor]
"""
tmp = []
for variable in variables:
if variable in self.fixed_.keys():
value = self.fixed_[variable]
pts_variable = torch.tensor([[value]]).repeat(n, 1)
pts_variable = pts_variable.as_subclass(LabelTensor)
pts_variable.labels = [variable]
tmp.append(pts_variable)
result = tmp[0]
for i in tmp[1:]:
result = result.append(i, mode="std")
return result
if self.fixed_ and (not self.range_):
return _single_points_sample(n, variables)
if variables == "all":
variables = self.variables
if mode in ["random"]:
return _Nd_sampler(n, mode, variables)
else:
raise NotImplementedError(f"mode={mode} is not implemented.")
