from abc import ABCMeta, abstractproperty
from itertools import chain, product
import numpy
import gem
from gem.utils import cached_property
[docs]class AbstractPointSet(metaclass=ABCMeta):
"""A way of specifying a known set of points, perhaps with some
(tensor) structure.
Points, when stored, have shape point_set_shape + (point_dimension,)
where point_set_shape is () for scalar, (N,) for N element vector,
(N, M) for N x M matrix etc.
"""
@abstractproperty
def points(self):
"""A flattened numpy array of points or ``UnknownPointsArray``
object with shape (# of points, point dimension)."""
@property
def dimension(self):
"""Point dimension."""
_, dim = self.points.shape
return dim
@abstractproperty
def indices(self):
"""GEM indices with matching shape and extent to the structure of the
point set."""
@abstractproperty
def expression(self):
"""GEM expression describing the points, with free indices
``self.indices`` and shape (point dimension,)."""
[docs]class PointSingleton(AbstractPointSet):
"""A point set representing a single point.
These have a ``gem.Literal`` expression and no indices."""
def __init__(self, point):
"""Build a PointSingleton from a single point.
:arg point: A single point of shape (D,) where D is the dimension of
the point."""
point = numpy.asarray(point)
# 1 point ought to be a 1D array - see docstring above and points method
assert len(point.shape) == 1
self.point = point
[docs] @cached_property
def points(self):
# Make sure we conform to the expected (# of points, point dimension)
# shape
return self.point.reshape(1, -1)
indices = ()
[docs] @cached_property
def expression(self):
return gem.Literal(self.point)
[docs]class UnknownPointsArray():
"""A placeholder for a set of unknown points with appropriate length
and size but without indexable values. For use with
:class:`AbstractPointSet`s whose points are not known at compile
time."""
def __init__(self, shape):
"""
:arg shape: The shape of the unknown set of N points of shape
(N, D) where D is the dimension of each point.
"""
assert len(shape) == 2
self.shape = shape
def __len__(self):
return self.shape[0]
[docs]class UnknownPointSet(AbstractPointSet):
"""A point set representing a vector of points with unknown
locations but known ``gem.Variable`` expression.
The ``.points`` property is an `UnknownPointsArray` object with
shape (N, D) where N is the number of points and D is their
dimension.
The ``.expression`` property is a derived `gem.partial_indexed` with
shape (D,) and free indices for the points N."""
def __init__(self, points_expr):
"""Build a PointSingleton from a gem expression for a single point.
:arg points_expr: A ``gem.Variable`` expression representing a
vector of N points in D dimensions. Should have shape (N, D)
and no free indices. For runtime tabulation the variable
name should begin with \'rt_:\'."""
assert isinstance(points_expr, gem.Variable)
assert points_expr.free_indices == ()
assert len(points_expr.shape) == 2
self._points_expr = points_expr
[docs] @cached_property
def points(self):
return UnknownPointsArray(self._points_expr.shape)
[docs] @cached_property
def indices(self):
N, _ = self._points_expr.shape
return (gem.Index(extent=N),)
[docs] @cached_property
def expression(self):
return gem.partial_indexed(self._points_expr, self.indices)
[docs]class PointSet(AbstractPointSet):
"""A basic point set with no internal structure representing a vector of
points."""
def __init__(self, points):
"""Build a PointSet from a vector of points
:arg points: A vector of N points of shape (N, D) where D is the
dimension of each point."""
points = numpy.asarray(points)
assert len(points.shape) == 2
self.points = points
[docs] @cached_property
def points(self):
pass # set at initialisation
[docs] @cached_property
def indices(self):
return (gem.Index(extent=len(self.points)),)
[docs] @cached_property
def expression(self):
return gem.partial_indexed(gem.Literal(self.points), self.indices)
[docs] def almost_equal(self, other, tolerance=1e-12):
"""Approximate numerical equality of point sets"""
return type(self) is type(other) and \
self.points.shape == other.points.shape and \
numpy.allclose(self.points, other.points, rtol=0, atol=tolerance)
[docs]class GaussLegendrePointSet(PointSet):
"""Gauss-Legendre quadrature points on the interval.
This facilitates implementing discontinuous spectral elements.
"""
def __init__(self, points):
super(GaussLegendrePointSet, self).__init__(points)
assert self.points.shape[1] == 1
[docs]class GaussLobattoLegendrePointSet(PointSet):
"""Gauss-Lobatto-Legendre quadrature points on the interval.
This facilitates implementing continuous spectral elements.
"""
def __init__(self, points):
super(GaussLobattoLegendrePointSet, self).__init__(points)
assert self.points.shape[1] == 1
[docs]class TensorPointSet(AbstractPointSet):
def __init__(self, factors):
self.factors = tuple(factors)
[docs] @cached_property
def points(self):
return numpy.array([list(chain(*pt_tuple))
for pt_tuple in product(*[ps.points
for ps in self.factors])])
[docs] @cached_property
def indices(self):
return tuple(chain(*[ps.indices for ps in self.factors]))
[docs] @cached_property
def expression(self):
result = []
for point_set in self.factors:
for i in range(point_set.dimension):
result.append(gem.Indexed(point_set.expression, (i,)))
return gem.ListTensor(result)
[docs] def almost_equal(self, other, tolerance=1e-12):
"""Approximate numerical equality of point sets"""
return type(self) is type(other) and \
len(self.factors) == len(other.factors) and \
all(s.almost_equal(o, tolerance=tolerance)
for s, o in zip(self.factors, other.factors))
