293 lines
11 KiB
Python
293 lines
11 KiB
Python
import torch
|
|
|
|
from .location import Location
|
|
from ..label_tensor import LabelTensor
|
|
from ..utils import check_consistency
|
|
|
|
|
|
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()))
|
|
|
|
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
|
|
|
|
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 variables == "all":
|
|
variables = self.variables
|
|
elif isinstance(variables, (list, tuple)):
|
|
variables = sorted(variables)
|
|
|
|
if self.fixed_ and (not self.range_):
|
|
return _single_points_sample(n, variables).extract(variables)
|
|
|
|
if variables == "all":
|
|
variables = self.variables
|
|
|
|
if mode in ["random"]:
|
|
return _Nd_sampler(n, mode, variables).extract(variables)
|
|
else:
|
|
raise NotImplementedError(f"mode={mode} is not implemented.")
|