folivo/PINA
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Documentation for v0.1 version (#199)

Browse Source 
* Adding Equations, solving typos
* improve _code.rst
* the team rst and restuctore index.rst
* fixing errors

---------

Co-authored-by: Dario Coscia <dariocoscia@dhcp-015.eduroam.sissa.it>
This commit is contained in:
Dario Coscia
2023-11-08 14:39:00 +01:00
committed by Nicola Demo
parent 3f9305d475
commit 8b7b61b3bd
144 changed files with 2741 additions and 1766 deletions
Download Patch File Download Diff File Expand all files Collapse all files

79
pina/geometry/simplex.py
View File

@@ -13,17 +13,21 @@ class SimplexDomain(Location):
:param simplex_matrix: A matrix of LabelTensor objects representing
a vertex of the simplex (a tensor), and the coordinates of the
point (a list of labels).
:type simplex_matrix: list[LabelTensor]
:param sample_surface: A variable for choosing sample strategies. If
`sample_surface=True` only samples on the Simplex surface
frontier are taken. If `sample_surface=False`, no such criteria
``sample_surface=True`` only samples on the Simplex surface
frontier are taken. If ``sample_surface=False``, no such criteria
is followed.
:type sample_surface: bool
.. warning::
Sampling for dimensions greater or equal to 10 could result
in a shrinking of the simplex, which degrades the quality
of the samples. For dimensions higher than 10, other algorithms
for sampling should be used.
:Example:
>>> spatial_domain = SimplexDomain(
[
@@ -48,12 +52,14 @@ class SimplexDomain(Location):
matrix_labels = simplex_matrix[0].labels
if not all(vertex.labels == matrix_labels for vertex in simplex_matrix):
raise ValueError(f"Labels don't match.")
# check consistency dimensions
dim_simplex = len(matrix_labels)
if len(simplex_matrix) != dim_simplex + 1:
raise ValueError("An n-dimensional simplex is composed by n + 1 tensors of dimension n.")
raise ValueError(
"An n-dimensional simplex is composed by n + 1 tensors of dimension n."
)
# creating vertices matrix
self._vertices_matrix = LabelTensor.vstack(simplex_matrix)
@@ -86,8 +92,10 @@ class SimplexDomain(Location):
for i, coord in enumerate(self.variables):
sorted_vertices = sorted(vertices, key=lambda vertex: vertex[i])
# respective coord bounded by the lowest and highest values
span_dict[coord] = [float(sorted_vertices[0][i]),
float(sorted_vertices[-1][i])]
span_dict[coord] = [
float(sorted_vertices[0][i]),
float(sorted_vertices[-1][i])
]
return CartesianDomain(span_dict)
@@ -96,31 +104,32 @@ class SimplexDomain(Location):
Check if a point is inside the simplex.
Uses the algorithm described involving barycentric coordinates:
https://en.wikipedia.org/wiki/Barycentric_coordinate_system.
.. 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 simplex, default False.
of the simplex, default ``False``.
:type check_border: bool
:return: Returning True if the point is inside, False otherwise.
:return: Returning ``True`` if the point is inside, ``False`` otherwise.
:rtype: bool
.. 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.
"""
if not all(label in self.variables for label in point.labels):
raise ValueError(
"Point labels different from constructor"
f" dictionary labels. Got {point.labels},"
f" expected {self.variables}."
)
raise ValueError("Point labels different from constructor"
f" dictionary labels. Got {point.labels},"
f" expected {self.variables}.")
point_shift = point - self._vertices_matrix[-1]
point_shift = point_shift.tensor.reshape(-1, 1)
# compute barycentric coordinates
lambda_ = torch.linalg.solve(self._vectors_shifted * 1.0, point_shift * 1.0)
lambda_ = torch.linalg.solve(self._vectors_shifted * 1.0,
point_shift * 1.0)
lambda_1 = 1.0 - torch.sum(lambda_)
lambdas = torch.vstack([lambda_, lambda_1])
@@ -128,16 +137,15 @@ class SimplexDomain(Location):
if not check_border:
return all(torch.gt(lambdas, 0.0)) and all(torch.lt(lambdas, 1.0))
return all(torch.ge(lambdas, 0)) and (
any(torch.eq(lambdas, 0)) or any(torch.eq(lambdas, 1))
)
return all(torch.ge(lambdas, 0)) and (any(torch.eq(lambdas, 0))
or any(torch.eq(lambdas, 1)))
def _sample_interior_randomly(self, n, variables):
"""
Randomly sample points inside a simplex of arbitrary
dimension, without the boundary.
:param int n: Number of points to sample in the shape.
:param variables: pinn variable to be sampled, defaults to 'all'.
:param variables: pinn variable to be sampled, defaults to ``all``.
:type variables: str or list[str], optional
:return: Returns tensor of n sampled points.
:rtype: torch.Tensor
@@ -155,9 +163,9 @@ class SimplexDomain(Location):
sampled_points = []
while len(sampled_points) < n:
sampled_point = self._cartesian_bound.sample(
n=1, mode="random", variables=variables
)
sampled_point = self._cartesian_bound.sample(n=1,
mode="random",
variables=variables)
if self.is_inside(sampled_point, self._sample_surface):
sampled_points.append(sampled_point)
@@ -188,7 +196,9 @@ class SimplexDomain(Location):
# extract number of vertices
number_of_vertices = self._vertices_matrix.shape[0]
# extract idx lambda to set to zero randomly
idx_lambda = torch.randint(low=0, high=number_of_vertices, size=(1,))
idx_lambda = torch.randint(low=0,
high=number_of_vertices,
size=(1, ))
# build lambda vector
# 1. sampling [1, 2)
lambdas = torch.rand((number_of_vertices, 1))
@@ -203,13 +213,14 @@ class SimplexDomain(Location):
def sample(self, n, mode="random", variables="all"):
"""
Sample n points from Simplex domain.
: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: pinn variable to be sampled, defaults to 'all'.
:type variables: str or list[str], optional
:return: Returns LabelTensor of n sampled points
:rtype: LabelTensor(tensor)
: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
.. warning::
When ``sample_surface = True`` in the initialization, all
the variables are sampled, despite passing different once
@@ -225,4 +236,4 @@ class SimplexDomain(Location):
else:
raise NotImplementedError(f"mode={mode} is not implemented.")
return LabelTensor(sample_pts, labels=self.variables)
return LabelTensor(sample_pts, labels=self.variables)