Source code for pymor.grids.constructions

# This file is part of the pyMOR project (http://www.pymor.org).
# Copyright 2013-2019 pyMOR developers and contributors. All rights reserved.
# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)

import numpy as np

from pymor.tools.floatcmp import float_cmp
from pymor.tools.relations import inverse_relation
from pymor.grids.rect import RectGrid
from pymor.grids.tria import TriaGrid


[docs]def flatten_grid(grid): """This method is used by our visualizers to render n-dimensional grids which cannot be embedded into R^n by duplicating vertices which would have to be mapped to multiple points at once (think of grids on rectangular domains with identified edges). Parameters ---------- grid The |Grid| to flatten. Returns ------- subentities The `subentities(0, grid.dim)` relation for the flattened grid. coordinates The coordinates of the codim-`grid.dim` entities. entity_map Maps the indices of the codim-`grid.dim` entities of the flattened grid to the indices of the corresponding entities in the original grid. """ # special handling of known flat grids if isinstance(grid, (RectGrid, TriaGrid)) and not grid.identify_left_right and not grid.identify_bottom_top: subentities = grid.subentities(0, grid.dim) coordinates = grid.centers(grid.dim) entity_map = np.arange(grid.size(grid.dim), dtype=np.int32) return subentities, coordinates, entity_map # first we determine which vertices are mapped to different coordinates when using the # embeddings of their codim-0 superentities dim = grid.dim global_coordinates = grid.embeddings(dim)[1] subentities = grid.subentities(0, dim) super_entities = grid.superentities(dim, 0) superentity_indices = grid.superentity_indices(dim, 0) A, B = grid.embeddings(0) ref_el_coordinates = grid.reference_element.subentity_embedding(dim)[1] local_coordinates = np.einsum('eij,vj->evi', A, ref_el_coordinates) + B[:, np.newaxis, :] critical_vertices = np.unique(subentities[np.logical_not(np.all(float_cmp(global_coordinates[subentities], local_coordinates), axis=2))]) del A del B # when there are critical vertices, we have to create additional vertices if len(critical_vertices) > 0: subentities = subentities.copy() supe = super_entities[critical_vertices] supi = superentity_indices[critical_vertices] coord = local_coordinates[supe, supi] new_points = np.ones_like(supe, dtype=np.int32) * -1 new_points[:, 0] = critical_vertices num_points = grid.size(dim) entity_map = np.empty((0,), dtype=np.int32) for i in range(new_points.shape[1]): for j in range(i): new_points[:, i] = np.where(supe[:, i] == -1, new_points[:, i], np.where(np.all(float_cmp(coord[:, i], coord[:, j]), axis=1), new_points[:, j], new_points[:, i])) new_point_inds = np.where(np.logical_and(new_points[:, i] == -1, supe[:, i] != -1))[0] new_points[new_point_inds, i] = np.arange(num_points, num_points + len(new_point_inds)) num_points += len(new_point_inds) entity_map = np.hstack((entity_map, critical_vertices[new_point_inds])) entity_map = np.hstack((np.arange(grid.size(dim), dtype=np.int32), entity_map)) # handle -1 entries in supe/supi correctly ... ci = np.where(critical_vertices == subentities[-1, -1])[0] if len(ci) > 0: assert len(ci) == 1 ci = ci[0] i = np.where(supe[ci] == (grid.size(0) - 1))[0] if len(i) > 0: assert len(i) == 1 i = i[0] new_points[supe == -1] = new_points[ci, i] else: new_points[supe == -1] = subentities[-1, -1] else: new_points[supe == -1] = subentities[-1, -1] subentities[supe, supi] = new_points super_entities, superentity_indices = inverse_relation(subentities, size_rhs=num_points, with_indices=True) coordinates = local_coordinates[super_entities[:, 0], superentity_indices[:, 0]] else: coordinates = global_coordinates entity_map = np.arange(grid.size(dim), dtype=np.int32) return subentities, coordinates, entity_map