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#!/usr/bin/env python
# This file is part of the pyMOR project (http://www.pymor.org).
# Copyright Holders: Rene Milk, Stephan Rave, Felix Schindler
# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
from __future__ import print_function
from __future__ import division
import numpy as np
from pymor.grids.interfaces import AffineGridInterface
from pymor.grids.referenceelements import line
class OnedGrid(AffineGridInterface):
'''One-dimensional |Grid| on an interval.
Parameters
----------
domain
Tuple `(left, right)` containing the left and right boundary of the domain.
num_intervals
The number of codim-0 entities.
'''
dim = 1
dim_outer = 1
reference_element = line
def __init__(self, domain=(0, 1), num_intervals=4, identify_left_right=False):
self.reference_element = line
self._domain = np.array(domain)
self._num_intervals = num_intervals
self._sizes = [num_intervals, num_intervals] if identify_left_right else [num_intervals, num_intervals + 1]
self._width = np.abs(self._domain[1] - self._domain[0]) / self._num_intervals
self.__subentities = np.vstack((np.arange(self._num_intervals, dtype=np.int32),
np.arange(self._num_intervals, dtype=np.int32) + 1))
if identify_left_right:
self.__subentities[-1, -1] = 0
self.__A = np.ones(self._num_intervals, dtype=np.int32)[:, np.newaxis, np.newaxis] * self._width
self.__B = (self._domain[0] + self._width * (np.arange(self._num_intervals, dtype=np.int32)))[:, np.newaxis]
def __str__(self):
return ('OnedGrid, domain [{xmin},{xmax}]'
+ ', {elements} elements'
+ ', {vertices} vertices'
).format(xmin=self._domain[0],
xmax=self._domain[1],
elements=self.size(0),
vertices=self.size(1))
def size(self, codim=0):
assert 0 <= codim <= 1, 'codim has to be between 0 and {}!'.format(self.dim)
return self._sizes[codim]
def subentities(self, codim, subentity_codim):
assert 0 <= codim <= 1, 'Invalid codimension'
assert codim <= subentity_codim <= self.dim, 'Invalid subentity codimension'
if codim == 0:
if subentity_codim == 0:
return np.arange(self.size(0), dtype='int32')[:, np.newaxis]
else:
return self.__subentities.T
else:
return super(OnedGrid, self).subentities(codim, subentity_codim)
def embeddings(self, codim):
if codim == 0:
return self.__A, self.__B
else:
return super(OnedGrid, self).embeddings(codim)
@staticmethod
def test_instances():
'''Used for unit testing.'''
return [OnedGrid(domain=np.array((-2, 2)), num_intervals=10),
OnedGrid(domain=np.array((-2, -4)), num_intervals=100),
OnedGrid(domain=np.array((-2, -4)), num_intervals=100, identify_left_right=True),
OnedGrid(domain=np.array((3, 2)), num_intervals=10),
OnedGrid(domain=np.array((3, 2)), num_intervals=10, identify_left_right=True),
OnedGrid(domain=np.array((1, 2)), num_intervals=10000)]
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