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Nicola Demo
279
pina/domain/cartesian.py
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279
pina/domain/cartesian.py
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import torch
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from .domain_interface import DomainInterface
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from ..label_tensor import LabelTensor
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from ..utils import torch_lhs, chebyshev_roots
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class CartesianDomain(DomainInterface):
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"""PINA implementation of Hypercube domain."""
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def __init__(self, cartesian_dict):
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"""
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:param cartesian_dict: A dictionary with dict-key a string representing
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the input variables for the pinn, and dict-value a list with
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the domain extrema.
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:type cartesian_dict: dict
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:Example:
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>>> spatial_domain = CartesianDomain({'x': [0, 1], 'y': [0, 1]})
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"""
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self.fixed_ = {}
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self.range_ = {}
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for k, v in cartesian_dict.items():
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if isinstance(v, (int, float)):
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self.fixed_[k] = v
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elif isinstance(v, (list, tuple)) and len(v) == 2:
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self.range_[k] = v
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else:
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raise TypeError
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@property
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def variables(self):
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"""Spatial variables.
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:return: Spatial variables defined in ``__init__()``
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:rtype: list[str]
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"""
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return sorted(list(self.fixed_.keys()) + list(self.range_.keys()))
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def update(self, new_domain):
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"""Adding new dimensions on the ``CartesianDomain``
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:param CartesianDomain new_domain: A new ``CartesianDomain`` object to merge
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:Example:
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>>> spatial_domain = CartesianDomain({'x': [0, 1], 'y': [0, 1]})
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>>> spatial_domain.variables
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['x', 'y']
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>>> spatial_domain_2 = CartesianDomain({'z': [3, 4], 'w': [0, 1]})
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>>> spatial_domain.update(spatial_domain_2)
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>>> spatial_domain.variables
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['x', 'y', 'z', 'w']
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"""
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self.fixed_.update(new_domain.fixed_)
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self.range_.update(new_domain.range_)
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def _sample_range(self, n, mode, bounds):
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"""Rescale the samples to the correct bounds
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:param n: Number of points to sample, see Note below
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for reference.
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:type n: int
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:param mode: Mode for sampling, defaults to ``random``.
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Available modes include: random sampling, ``random``;
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latin hypercube sampling, ``latin`` or ``lh``;
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chebyshev sampling, ``chebyshev``; grid sampling ``grid``.
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:type mode: str
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:param bounds: Bounds to rescale the samples.
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:type bounds: torch.Tensor
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:return: Rescaled sample points.
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:rtype: torch.Tensor
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"""
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dim = bounds.shape[0]
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if mode in ["chebyshev", "grid"] and dim != 1:
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raise RuntimeError("Something wrong in Span...")
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if mode == "random":
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pts = torch.rand(size=(n, dim))
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elif mode == "chebyshev":
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pts = chebyshev_roots(n).mul(0.5).add(0.5).reshape(-1, 1)
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elif mode == "grid":
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pts = torch.linspace(0, 1, n).reshape(-1, 1)
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# elif mode == 'lh' or mode == 'latin':
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elif mode in ["lh", "latin"]:
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pts = torch_lhs(n, dim)
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pts *= bounds[:, 1] - bounds[:, 0]
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pts += bounds[:, 0]
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return pts
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def sample(self, n, mode="random", variables="all"):
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"""Sample routine.
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:param n: Number of points to sample, see Note below
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for reference.
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:type n: int
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:param mode: Mode for sampling, defaults to ``random``.
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Available modes include: random sampling, ``random``;
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latin hypercube sampling, ``latin`` or ``lh``;
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chebyshev sampling, ``chebyshev``; grid sampling ``grid``.
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:type mode: str
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:param variables: pinn variable to be sampled, defaults to ``all``.
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:type variables: str | list[str]
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:return: Returns ``LabelTensor`` of n sampled points.
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:rtype: LabelTensor
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.. note::
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The total number of points sampled in case of multiple variables
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is not ``n``, and it depends on the chosen ``mode``. If ``mode`` is
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'grid' or ``chebyshev``, the points are sampled independentely
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across the variables and the results crossed together, i.e. the
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final number of points is ``n`` to the power of the number of
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variables. If 'mode' is 'random', ``lh`` or ``latin``, the variables
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are sampled all together, and the final number of points
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.. warning::
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The extrema values of Span are always sampled only for ``grid`` mode.
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:Example:
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>>> spatial_domain = Span({'x': [0, 1], 'y': [0, 1]})
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>>> spatial_domain.sample(n=4, mode='random')
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tensor([[0.0108, 0.7643],
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[0.4477, 0.8015],
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[0.2063, 0.8087],
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[0.8735, 0.6349]])
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>>> spatial_domain.sample(n=4, mode='grid')
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tensor([[0.0000, 0.0000],
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[0.3333, 0.0000],
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[0.6667, 0.0000],
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[1.0000, 0.0000],
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[0.0000, 0.3333],
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[0.3333, 0.3333],
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[0.6667, 0.3333],
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[1.0000, 0.3333],
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[0.0000, 0.6667],
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[0.3333, 0.6667],
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[0.6667, 0.6667],
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[1.0000, 0.6667],
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[0.0000, 1.0000],
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[0.3333, 1.0000],
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[0.6667, 1.0000],
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[1.0000, 1.0000]])
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"""
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def _1d_sampler(n, mode, variables):
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"""Sample independentely the variables and cross the results"""
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tmp = []
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for variable in variables:
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if variable in self.range_.keys():
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bound = torch.tensor([self.range_[variable]])
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pts_variable = self._sample_range(n, mode, bound)
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pts_variable = pts_variable.as_subclass(LabelTensor)
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pts_variable.labels = [variable]
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tmp.append(pts_variable)
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result = tmp[0]
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for i in tmp[1:]:
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result = result.append(i, mode="cross")
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for variable in variables:
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if variable in self.fixed_.keys():
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value = self.fixed_[variable]
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pts_variable = torch.tensor([[value]]).repeat(
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result.shape[0], 1
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)
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pts_variable = pts_variable.as_subclass(LabelTensor)
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pts_variable.labels = [variable]
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result = result.append(pts_variable, mode="std")
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return result
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def _Nd_sampler(n, mode, variables):
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"""Sample all the variables together
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:param n: Number of points to sample.
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:type n: int
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:param mode: Mode for sampling, defaults to ``random``.
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Available modes include: random sampling, ``random``;
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latin hypercube sampling, ``latin`` or ``lh``;
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chebyshev sampling, ``chebyshev``; grid sampling ``grid``.
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:type mode: str.
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:param variables: pinn variable to be sampled, defaults to ``all``.
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:type variables: str or list[str].
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:return: Sample points.
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:rtype: list[torch.Tensor]
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"""
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pairs = [(k, v) for k, v in self.range_.items() if k in variables]
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keys, values = map(list, zip(*pairs))
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bounds = torch.tensor(values)
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result = self._sample_range(n, mode, bounds)
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result = result.as_subclass(LabelTensor)
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result.labels = keys
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for variable in variables:
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if variable in self.fixed_.keys():
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value = self.fixed_[variable]
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pts_variable = torch.tensor([[value]]).repeat(
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result.shape[0], 1
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)
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pts_variable = pts_variable.as_subclass(LabelTensor)
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pts_variable.labels = [variable]
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result = result.append(pts_variable, mode="std")
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return result
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def _single_points_sample(n, variables):
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"""Sample a single point in one dimension.
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:param n: Number of points to sample.
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:type n: int
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:param variables: Variables to sample from.
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:type variables: list[str]
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:return: Sample points.
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:rtype: list[torch.Tensor]
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"""
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tmp = []
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for variable in variables:
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if variable in self.fixed_.keys():
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value = self.fixed_[variable]
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pts_variable = torch.tensor([[value]]).repeat(n, 1)
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pts_variable = pts_variable.as_subclass(LabelTensor)
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pts_variable.labels = [variable]
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tmp.append(pts_variable)
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result = tmp[0]
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for i in tmp[1:]:
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result = result.append(i, mode="std")
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return result
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if variables == "all":
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variables = self.variables
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elif isinstance(variables, (list, tuple)):
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variables = sorted(variables)
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if self.fixed_ and (not self.range_):
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return _single_points_sample(n, variables)
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if mode in ["grid", "chebyshev"]:
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return _1d_sampler(n, mode, variables).extract(variables)
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elif mode in ["random", "lh", "latin"]:
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return _Nd_sampler(n, mode, variables).extract(variables)
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else:
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raise ValueError(f"mode={mode} is not valid.")
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def is_inside(self, point, check_border=False):
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"""Check if a point is inside the ellipsoid.
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:param point: Point to be checked
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:type point: LabelTensor
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:param check_border: Check if the point is also on the frontier
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of the hypercube, default ``False``.
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:type check_border: bool
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:return: Returning ``True`` if the point is inside, ``False`` otherwise.
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:rtype: bool
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"""
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is_inside = []
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# check fixed variables
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for variable, value in self.fixed_.items():
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if variable in point.labels:
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is_inside.append(point.extract([variable]) == value)
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# check not fixed variables
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for variable, bound in self.range_.items():
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if variable in point.labels:
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if check_border:
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check = bound[0] <= point.extract([variable]) <= bound[1]
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else:
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check = bound[0] < point.extract([variable]) < bound[1]
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is_inside.append(check)
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return all(is_inside)
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