def get_ref_coors_general(field, coors, close_limit=0.1, get_cells_fun=None, cache=None, verbose=False):
"""
Get reference element coordinates and elements corresponding to given
physical coordinates.
Parameters
----------
field : Field instance
The field defining the approximation.
coors : array
The physical coordinates.
close_limit : float, optional
The maximum limit distance of a point from the closest
element allowed for extrapolation.
get_cells_fun : callable, optional
If given, a function with signature ``get_cells_fun(coors, cmesh,
**kwargs)`` returning cells and offsets that potentially contain points
with the coordinates `coors`. When not given,
:func:`get_potential_cells()` is used.
cache : Struct, optional
To speed up a sequence of evaluations, the field mesh and other data
can be cached. Optionally, the cache can also contain the reference
element coordinates as `cache.ref_coors`, `cache.cells` and
`cache.status`, if the evaluation occurs in the same coordinates
repeatedly. In that case the mesh related data are ignored.
verbose : bool
If False, reduce verbosity.
Returns
-------
ref_coors : array
The reference coordinates.
cells : array
The cell indices corresponding to the reference coordinates.
status : array
The status: 0 is success, 1 is extrapolation within `close_limit`, 2 is
extrapolation outside `close_limit`, 3 is failure, 4 is failure due to
non-convergence of the Newton iteration in tensor product cells. If
close_limit is 0, then status 5 indicates points outside of the field
domain that had no potential cells.
"""
ref_coors = get_default_attr(cache, "ref_coors", None)
if ref_coors is None:
extrapolate = close_limit > 0.0
get = get_potential_cells if get_cells_fun is None else get_cells_fun
ref_coors = nm.empty_like(coors)
cells = nm.empty((coors.shape[0],), dtype=nm.int32)
status = nm.empty((coors.shape[0],), dtype=nm.int32)
cmesh = get_default_attr(cache, "cmesh", None)
if cmesh is None:
tt = time.clock()
mesh = field.create_mesh(extra_nodes=False)
cmesh = mesh.cmesh
gels = create_geometry_elements()
cmesh.set_local_entities(gels)
cmesh.setup_entities()
if get_cells_fun is None:
centroids = cmesh.get_centroids(cmesh.tdim)
else:
centroids = None
output("cmesh setup: %f s" % (time.clock() - tt), verbose=verbose)
else:
centroids = cache.centroids
tt = time.clock()
potential_cells, offsets = get(coors, cmesh, centroids=centroids, extrapolate=extrapolate)
output("potential cells: %f s" % (time.clock() - tt), verbose=verbose)
ap = field.ap
ps = ap.interp.gel.interp.poly_spaces["v"]
mtx_i = ps.get_mtx_i()
ac = nm.ascontiguousarray
tt = time.clock()
crc.find_ref_coors(
ref_coors,
cells,
status,
ac(coors),
cmesh,
potential_cells,
offsets,
ps.geometry.coors,
ps.nodes,
mtx_i,
extrapolate,
close_limit,
1e-15,
100,
1e-8,
)
if extrapolate:
assert_(nm.all(status < 5))
output("ref. coordinates: %f s" % (time.clock() - tt), verbose=verbose)
else:
cells = cache.cells
status = cache.status
return ref_coors, cells, status
def get_ref_coors(field, coors, strategy='kdtree', close_limit=0.1, cache=None,
verbose=False):
"""
Get reference element coordinates and elements corresponding to given
physical coordinates.
Parameters
----------
field : Field instance
The field defining the approximation.
coors : array
The physical coordinates.
strategy : str, optional
The strategy for finding the elements that contain the
coordinates. Only 'kdtree' is supported for the moment.
close_limit : float, optional
The maximum limit distance of a point from the closest
element allowed for extrapolation.
cache : Struct, optional
To speed up a sequence of evaluations, the field mesh and other data
can be cached. Optionally, the cache can also contain the reference
element coordinates as `cache.ref_coors`, `cache.cells` and
`cache.status`, if the evaluation occurs in the same coordinates
repeatedly. In that case the mesh related data are ignored.
verbose : bool
If False, reduce verbosity.
Returns
-------
ref_coors : array
The reference coordinates.
cells : array
The cell indices corresponding to the reference coordinates.
status : array
The status: 0 is success, 1 is extrapolation within `close_limit`, 2 is
extrapolation outside `close_limit`, 3 is failure, 4 is failure due to
non-convergence of the Newton iteration in tensor product cells.
Notes
-----
Outline of the algorithm for finding xi such that X(xi) = P:
1. make inverse connectivity - for each vertex have cells it is in.
2. find the closest vertex V.
3. choose initial cell: i0 = first from cells incident to V.
4. while not P in C_i, change C_i towards P, check if P in new C_i.
"""
ref_coors = get_default_attr(cache, 'ref_coors', None)
if ref_coors is None:
ref_coors = nm.empty_like(coors)
cells = nm.empty((coors.shape[0],), dtype=nm.int32)
status = nm.empty((coors.shape[0],), dtype=nm.int32)
cmesh = get_default_attr(cache, 'cmesh', None)
if cmesh is None:
mesh = field.create_mesh(extra_nodes=False)
tt = time.clock()
mesh = field.create_mesh(extra_nodes=False)
cmesh = mesh.cmesh
gels = create_geometry_elements()
cmesh.set_local_entities(gels)
cmesh.setup_entities()
centroids = cmesh.get_centroids(cmesh.tdim)
if field.gel.name != '3_8':
normals0 = cmesh.get_facet_normals()
normals1 = None
else:
normals0 = cmesh.get_facet_normals(0)
normals1 = cmesh.get_facet_normals(1)
output('cmesh setup: %f s' % (time.clock()-tt), verbose=verbose)
else:
centroids = cache.centroids
normals0 = cache.normals0
normals1 = cache.normals1
kdtree = get_default_attr(cache, 'kdtree', None)
if kdtree is None:
from scipy.spatial import cKDTree as KDTree
tt = time.clock()
kdtree = KDTree(cmesh.coors)
output('kdtree: %f s' % (time.clock()-tt), verbose=verbose)
tt = time.clock()
ics = kdtree.query(coors)[1]
output('kdtree query: %f s' % (time.clock()-tt), verbose=verbose)
ics = nm.asarray(ics, dtype=nm.int32)
ap = field.ap
ps = ap.interp.gel.interp.poly_spaces['v']
mtx_i = ps.get_mtx_i()
ac = nm.ascontiguousarray
tt = time.clock()
find_ref_coors(ref_coors, cells, status, ac(coors), cmesh, centroids,
normals0, normals1, ics,
ps.geometry.coors, ps.nodes, mtx_i,
1, close_limit, 1e-15, 100, 1e-8)
output('ref. coordinates: %f s' % (time.clock()-tt), verbose=verbose)
else:
cells = cache.cells
status = cache.status
return ref_coors, cells, status