def build_mapping(self, S3, V3):
"""
S3 is the vector function space of the 2d mesh
V3 is the vector function space of the corresponding 3d mesh
"""
vert_to_dof2 = df.vertex_to_dof_map(S3)
dof_to_vert2 = df.dof_to_vertex_map(S3)
vert_to_dof3 = df.vertex_to_dof_map(V3)
dof_to_vert3 = df.dof_to_vertex_map(V3)
map_2d_to_3d = np.zeros(V3.dim(), dtype=np.int32)
n2d = S3.dim()
for i in range(n2d):
map_2d_to_3d[i] = vert_to_dof3[dof_to_vert2[i]]
map_2d_to_3d[i + n2d] = vert_to_dof3[dof_to_vert2[i] + n2d]
self.map_2d_to_3d = map_2d_to_3d
# print map_2d_to_3d
n3d = V3.dim()
map_3d_to_2d = np.zeros(V3.dim(), dtype=np.int32)
for i in range(V3.dim()):
map_3d_to_2d[i] = vert_to_dof2[dof_to_vert3[i] % n2d]
self.map_3d_to_2d = map_3d_to_2d
def data_reordering(V):
'''Reshaping/reordering data read from files'''
# HDF5/VTK store 3d vectors and 3d tensor so we need to chop the data
# also reorder as in 2017.2.0 only(?) vertex values are dumped
if V.ufl_element().value_shape() == ():
dof2v = dof_to_vertex_map(V)
reorder = lambda a: a[dof2v]
return reorder
Vi = V.sub(0).collapse()
dof2v = dof_to_vertex_map(Vi)
gdim = V.mesh().geometry().dim()
# WARNING: below there are assumption on component ordering
# Vector
if len(V.ufl_element().value_shape()) == 1:
# Ellim Z for vectors in 2d
keep = [0, 1] if gdim == 2 else range(gdim)
reorder = lambda a, keep=keep, dof2f=dof2v: (np.column_stack(
[row[dof2v] for row in (a[:, keep]).T]).flatten())
return reorder
# And tensor
if len(V.ufl_element().value_shape()) == 2:
# Ellim Z
keep = [0, 1, 3, 4] if gdim == 2 else range(gdim**2)
reorder = lambda a, keep=keep, dof2f=dof2v: (np.column_stack(
[row[dof2v] for row in (a[:, keep]).T]).flatten())
return reorder
def _assemble(self, dtype, device):
if self._mode.lower() == 'manualinterpolation':
Vf, Vc = self._physics['fom'].V, self._physics['rom'].V
free_dofs = self._physics['fom'].free_dofs
coords = Vf.mesh().coordinates()
dvmap = df.dof_to_vertex_map(Vf)
points = np.zeros((Vf.dim(), self._physics['fom'].tdim))
for i, mapped_dof in enumerate(dvmap):
points[i, :] = coords[mapped_dof, :]
if self._only_free_dofs:
points = points[free_dofs, :]
W = AssembleBasisFunctionMatrix(Vc, points, ReturnType='scipy')
self._W = Convert_ScipySparse_PyTorchSparse(W.T,
dtype=dtype,
device=device)
# ugly fix: cast to dense tensor
self._W = self._W.to_dense()
else:
raise ValueError('Interpolation mode unknown')
def transfer_vertex_function(mesh_fine, mesh_foo_coarse, output=VertexFunction):
'''
Assuming that mesh_fine is created by meshing around the mesh underlying
mesh_foo_coarse this function interpolates the data from mesh_foo_coarse
'''
assert isinstance(mesh_fine, EmbeddedMesh)
mesh_fine = mesh_fine.mesh # FIXME: remove when EmbeddedMesh <: Mesh
assert mesh_fine.topology().dim() == 1 and mesh_fine.geometry().dim() > 1
mesh = mesh_foo_coarse.mesh()
assert mesh.topology().dim() == 1 and mesh.geometry().dim() > 1
# The strategy here is to interpolate into a CG1 function on mesh_fine
# and then turn it to vertex function. NOTE: consider CG1 as function
# for it is easier to get e.g. DG0 (midpoint values) out of it
Vf = FunctionSpace(mesh_fine, 'CG', 1)
assert mesh_foo_coarse.cpp_value_type() == 'double'
assert mesh_foo_coarse.dim() == 0
mesh_coarse = mesh_foo_coarse.mesh()
Vc = FunctionSpace(mesh, 'CG', 1)
fc = Function(Vc)
# Fill the data
fc.vector().set_local(mesh_foo_coarse.array()[dof_to_vertex_map(Vc)])
fc.vector().apply('insert')
ff = interpolate(fc, Vf)
if output == Function: return ff
# Combe back to vertex function
vertex_foo = VertexFunction('double', mesh_fine, 0.0)
vertex_foo.set_values(ff.vector().array()[vertex_to_dof_map(Vf)])
return vertex_foo
def __init__(self, V, geo, name, f):
self.V = V
# get dofs lying in subdomain
dofmap = V.dofmap()
tup = geo.physicaldomain(name)
sub = geo.subdomains
mesh = geo.mesh
subdofs = set()
for i, cell in enumerate(dolfin.cells(mesh)):
if sub[cell] in tup:
celldofs = dofmap.cell_dofs(i)
subdofs.update(celldofs)
subdofs = np.array(list(subdofs), dtype="intc")
d2v = dolfin.dof_to_vertex_map(V)
co = mesh.coordinates()
# create function with desired values
# could also be implemented with Expression.eval_cell like pwconst
bc_f = dolfin.Function(V)
for dof in subdofs:
x = co[d2v[dof]]
bc_f.vector()[dof] = f(x)
self.bc_f = bc_f
self.dof_set = subdofs
def test_invariance():
"""Asserts invariance of cost functional w.r.t. translation and rotation"""
centers, J = _get_macadam()
n = 1
problem = PiecewiseEllipse(centers, J.copy(), n)
alpha = problem.alpha.copy()
c0 = problem.cost_min(alpha)
alpha += 1.23
c1 = problem.cost_min(alpha)
assert abs(c0 - c1) < 1.0e-12 * c0
d2v = dof_to_vertex_map(problem.V)
v2d = vertex_to_dof_map(problem.V)
alpha = problem.alpha.copy()
alpha = alpha.reshape(2, -1).T
coords = alpha[v2d]
# rotate
theta = 0.35 * numpy.pi
sin = numpy.sin(theta)
cos = numpy.cos(theta)
R = numpy.array([[cos, -sin], [sin, cos]])
rcoords = numpy.dot(R, coords.T)
# map back to alpha)
alpha = numpy.concatenate(rcoords[:, d2v])
c2 = problem.cost_min(alpha)
assert abs(c0 - c2) < 1.0e-12 * c0
return
def img2funvec(img: np.array) -> np.array:
"""Takes a 2D array and returns an array suited to assign to piecewise
linear approximation on a triangle grid.
Each pixel corresponds to one vertex of a triangle mesh.
Args:
img (np.array): The input array of shape (m, n).
Returns:
np.array: A vector of shape (m * n,).
"""
m, n = img.shape
# Create mesh and function space.
mesh = UnitSquareMesh(m - 1, n - 1)
xm = mesh.coordinates().reshape((-1, 2))
# Create function space.
V = create_function_space(mesh, 'default')
# Evaluate function at vertices.
hx, hy = 1 / (m - 1), 1 / (n - 1)
x = np.array(np.round(xm[:, 0] / hx), dtype=int)
y = np.array(np.round(xm[:, 1] / hy), dtype=int)
fv = img[x, y]
# Map pixel values to vertices.
d2v = dof_to_vertex_map(V)
return fv[d2v]
def imgseq2funvec(img: np.array) -> np.array:
"""Takes a 3D array and returns an array suited to assign to piecewise
linear approximation on a triangle grid.
Each pixel corresponds to one vertex of a triangle mesh.
Args:
img (np.array): The input array.
Returns:
np.array: A vector.
"""
# Create mesh.
[m, n, o] = img.shape
mesh = UnitCubeMesh(m-1, n-1, o-1)
mc = mesh.coordinates().reshape((-1, 3))
# Evaluate function at vertices.
hx, hy, hz = 1./(m-1), 1./(n-1), 1./(o-1)
x = np.array(np.round(mc[:, 0]/hx), dtype=int)
y = np.array(np.round(mc[:, 1]/hy), dtype=int)
z = np.array(np.round(mc[:, 2]/hz), dtype=int)
fv = img[x, y, z]
# Create function space.
V = FunctionSpace(mesh, 'CG', 1)
# Map pixel values to vertices.
d2v = dof_to_vertex_map(V)
return fv[d2v]
def p1_trace(fenics_space):
"""
Return the P1 trace operator.
This function returns a pair (space, trace_matrix),
where space is a BEM++ space object and trace_matrix is the corresponding
matrix that maps the coefficients of a FEniCS function to its boundary
trace coefficients in the corresponding BEM++ space.
"""
import dolfin #pylint: disable=import-error
from bempp.api.fenics_interface.coupling import fenics_space_info
from bempp.api import function_space, grid_from_element_data
import numpy as np
family, degree = fenics_space_info(fenics_space)
if not (family == 'Lagrange' and degree == 1):
raise ValueError("fenics_space must be a p1 Lagrange space")
mesh = fenics_space.mesh()
boundary_mesh = dolfin.BoundaryMesh(mesh, "exterior", False)
bm_nodes = boundary_mesh.entity_map(0).array().astype(np.int64)
bm_coords = boundary_mesh.coordinates()
bm_cells = boundary_mesh.cells()
bempp_boundary_grid = grid_from_element_data(bm_coords.transpose(),
bm_cells.transpose())
# First get trace space
space = function_space(bempp_boundary_grid, "P", 1)
# Now compute the mapping from FEniCS dofs to BEM++ dofs.
# First the BEM++ dofs from the boundary vertices
from scipy.sparse import coo_matrix
bempp_dofs_from_b_vertices = p1_dof_to_vertex_matrix(space).transpose()
# Now FEniCS vertices to boundary dofs
b_vertices_from_vertices = coo_matrix(
(np.ones(len(bm_nodes)), (np.arange(len(bm_nodes)), bm_nodes)),
shape=(len(bm_nodes), mesh.num_vertices()),
dtype='float64').tocsc()
# Finally FEniCS dofs to vertices.
vertices_from_fenics_dofs = coo_matrix(
(np.ones(mesh.num_vertices()), (dolfin.dof_to_vertex_map(fenics_space),
np.arange(mesh.num_vertices()))),
shape=(mesh.num_vertices(), mesh.num_vertices()),
dtype='float64').tocsc()
# Get trace matrix by multiplication
trace_matrix = bempp_dofs_from_b_vertices * \
b_vertices_from_vertices * vertices_from_fenics_dofs
# Now return everything
return space, trace_matrix
def p1_trace(fenics_space):
"""
Return the P1 trace operator.
This function returns a pair (space, trace_matrix),
where space is a Bempp space object and trace_matrix is the corresponding
matrix that maps the coefficients of a FEniCS function to its boundary
trace coefficients in the corresponding Bempp space.
"""
import dolfin
import bempp.api
from scipy.sparse import coo_matrix
import numpy as np
family, degree = fenics_space_info(fenics_space)
if not (family == "Lagrange" and degree == 1):
raise ValueError("fenics_space must be a p1 Lagrange space")
mesh = fenics_space.mesh()
boundary_mesh = dolfin.BoundaryMesh(mesh, "exterior", False)
bm_nodes = boundary_mesh.entity_map(0).array().astype(np.int64)
bm_coords = boundary_mesh.coordinates()
bm_cells = boundary_mesh.cells()
bempp_boundary_grid = bempp.api.Grid(bm_coords.transpose(),
bm_cells.transpose())
# First get trace space
space = bempp.api.function_space(bempp_boundary_grid, "P", 1)
# Now FEniCS vertices to boundary dofs
b_vertices_from_vertices = coo_matrix(
(np.ones(len(bm_nodes)), (np.arange(len(bm_nodes)), bm_nodes)),
shape=(len(bm_nodes), mesh.num_vertices()),
dtype="float64",
).tocsc()
# Finally FEniCS dofs to vertices.
vertices_from_fenics_dofs = coo_matrix(
(
np.ones(mesh.num_vertices()),
(dolfin.dof_to_vertex_map(fenics_space),
np.arange(mesh.num_vertices())),
),
shape=(mesh.num_vertices(), mesh.num_vertices()),
dtype="float64",
).tocsc()
# Get trace matrix by multiplication
trace_matrix = b_vertices_from_vertices @ vertices_from_fenics_dofs
# Now return everything
return space, trace_matrix
def to_P1_function(f):
'''Vertex function -> P1'''
assert f.dim() == 0, f.dim()
V = df.FunctionSpace(f.mesh(), 'CG', 1)
g = df.Function(V)
g_values = g.vector().get_local()
g_values[:] = f.array()[df.dof_to_vertex_map(V)]
g.vector().set_local(g_values)
return g
def vertices(self):
"""
Returns the vertices of the surface of the object
This information might be useful for calculating the current density
into the object surface
"""
coords = self.V.mesh().coordinates()
d2v = df.dof_to_vertex_map(self.V)
vertex_indices = list(set(d2v[self.dofs]))
return coords[vertex_indices]
def p1_trace(fenics_space):
import dolfin
from .coupling import fenics_space_info
from bempp import function_space, grid_from_element_data
import numpy as np
family, degree = fenics_space_info(fenics_space)
if not (family == 'Lagrange' and degree == 1):
raise ValueError("fenics_space must be a p1 Lagrange space")
mesh = fenics_space.mesh()
bm = dolfin.BoundaryMesh(mesh, "exterior", False)
bm_nodes = bm.entity_map(0).array().astype(np.int64)
bm_coords = bm.coordinates()
bm_cells = bm.cells()
bempp_boundary_grid = grid_from_element_data(bm_coords.transpose(),
bm_cells.transpose())
# First get trace space
space = function_space(bempp_boundary_grid, "P", 1)
# Now compute the mapping from BEM++ dofs to FEniCS dofs
# First the BEM++ dofs to the boundary vertices
from ._lagrange_coupling import p1_vertex_map
from scipy.sparse import coo_matrix
vertex_to_dof_map = p1_vertex_map(space)
vertex_indices = np.arange(space.global_dof_count)
data = np.ones(space.global_dof_count)
bempp_dofs_from_b_vertices = coo_matrix(
(data, (vertex_to_dof_map, vertex_indices)), dtype='float64').tocsr()
# Now the boundary vertices to all the vertices
b_vertices_from_vertices = coo_matrix(
(np.ones(len(bm_nodes)), (np.arange(len(bm_nodes)), bm_nodes)),
shape=(len(bm_nodes), mesh.num_vertices()),
dtype='float64').tocsr()
# Finally the vertices to FEniCS dofs
vertices_from_fenics_dofs = coo_matrix(
(np.ones(mesh.num_vertices()), (dolfin.dof_to_vertex_map(fenics_space),
np.arange(mesh.num_vertices()))),
shape=(mesh.num_vertices(), mesh.num_vertices()),
dtype='float64').tocsr()
# Get trace matrix by multiplication
trace_matrix = bempp_dofs_from_b_vertices * b_vertices_from_vertices * vertices_from_fenics_dofs
# Now return everything
return (space, trace_matrix)
def submesh_dof_to_vertex(Vsubmesh, species_index, index=None):
num_species = Vsubmesh.num_sub_spaces()
if num_species == 0: num_species = 1
num_dofs = int(len(Vsubmesh.dofmap().dofs()) / num_species)
if index == None:
index = range(num_dofs)
mapping = d.dof_to_vertex_map(Vsubmesh)
mapping = mapping[range(species_index, len(mapping),
num_species)] / num_species
mapping = [int(x) for x in mapping]
return [mapping[x] for x in index]
def plot_deltas_2D(vertex_vector, mesh_path, save_dir):
mesh = Mesh()
with XDMFFile(mesh_path) as f:
f.read(mesh)
V = FunctionSpace(mesh, 'CG', 1)
value = Function(V)
value.vector()[:] = vertex_vector[dof_to_vertex_map(V)]
delta_S = project(value.dx(0), V)
delta_file = XDMFFile(save_dir)
delta_file.write_checkpoint(delta_S, 'delta_S', 0, XDMFFile.Encoding.HDF5,
True)
delta_v = project(value.dx(1), V)
delta_file.write_checkpoint(delta_v, 'delta_v', 0, XDMFFile.Encoding.HDF5,
True)
def normalise_dofmap(self):
"""
Overwrite own field values with normalised ones.
"""
dofmap = df.vertex_to_dof_map(self.functionspace)
reordered = self.f.vector().array()[
dofmap] # [x1, y1, z1, ..., xn, yn, zn]
vectors = reordered.reshape(
(3, -1)) # [[x1, y1, z1], ..., [xn, yn, zn]]
lengths = np.sqrt(np.add.reduce(vectors * vectors, axis=1))
normalised = np.dot(vectors.T, np.diag(1 / lengths)).T.ravel()
vertexmap = df.dof_to_vertex_map(self.functionspace)
normalised_original_order = normalised[vertexmap]
self.from_array(normalised_original_order)
def vertex_to_DG0_foo(data):
'''
Convert vertex function to DG0 function on the same mesh
'''
mesh = data.mesh()
# Build CG
P1 = FunctionSpace(mesh, 'CG', 1)
f = Function(P1)
f.vector().set_local(
np.array(data.array()[dof_to_vertex_map(P1)], dtype=float))
f.vector().apply('insert')
# Then gen midpoint value by interpolation
DG0 = FunctionSpace(mesh, 'DG', 0)
f = interpolate(f, DG0)
return f
def p1_trace(fenics_space):
import dolfin
from .coupling import fenics_space_info
from bempp import function_space,grid_from_element_data
import numpy as np
family,degree = fenics_space_info(fenics_space)
if not (family=='Lagrange' and degree == 1):
raise ValueError("fenics_space must be a p1 Lagrange space")
mesh = fenics_space.mesh()
bm = dolfin.BoundaryMesh(mesh,"exterior",False)
bm_nodes = bm.entity_map(0).array().astype(np.int64)
bm_coords = bm.coordinates()
bm_cells = bm.cells()
bempp_boundary_grid = grid_from_element_data(bm_coords.transpose(),bm_cells.transpose())
# First get trace space
space = function_space(bempp_boundary_grid,"P",1)
# Now compute the mapping from BEM++ dofs to FEniCS dofs
# First the BEM++ dofs to the boundary vertices
from ._lagrange_coupling import p1_vertex_map
from scipy.sparse import coo_matrix
vertex_to_dof_map = p1_vertex_map(space)
vertex_indices = np.arange(space.global_dof_count)
data = np.ones(space.global_dof_count)
bempp_dofs_from_b_vertices = coo_matrix((data,(vertex_to_dof_map,vertex_indices)),dtype='float64').tocsr()
# Now the boundary vertices to all the vertices
b_vertices_from_vertices = coo_matrix((
np.ones(len(bm_nodes)),(np.arange(len(bm_nodes)),bm_nodes)),
shape=(len(bm_nodes),mesh.num_vertices()),dtype='float64').tocsr()
# Finally the vertices to FEniCS dofs
vertices_from_fenics_dofs = coo_matrix((
np.ones(mesh.num_vertices()),(dolfin.dof_to_vertex_map(fenics_space),np.arange(mesh.num_vertices()))),
shape=(mesh.num_vertices(),mesh.num_vertices()),dtype='float64').tocsr()
# Get trace matrix by multiplication
trace_matrix = bempp_dofs_from_b_vertices*b_vertices_from_vertices*vertices_from_fenics_dofs
# Now return everything
return (space,trace_matrix)
def read_function_group(self, key):
group = self.file[key]
if key in self.scalar_groups:
space = dolfin.FunctionSpace(self.mesh, 'CG', 1)
elif key in self.vector_groups:
space = dolfin.VectorFunctionSpace(self.mesh, 'CG', 1)
index_map = dolfin.dof_to_vertex_map(space)
functions = []
ii = 0
key = f'{ii}'
while key in group:
dset = group[key]
functions.append(dolfin.Function(space, name='u'))
functions[-1].vector().set_local(dset[:][index_map])
ii += 1
key = f'{ii}'
return functions
def time_deriv(img: np.array) -> Function:
# Evaluate function at vertices.
mc = mesh.coordinates().reshape((-1, 3))
hx, hy, hz = 1./(t-2), 1./(m-1), 1./(n-1)
x = np.array(mc[:, 0]/hx, dtype=int)
y = np.array(mc[:, 1]/hy, dtype=int)
z = np.array(mc[:, 2]/hz, dtype=int)
# Map pixel values to vertices.
d2v = dof_to_vertex_map(V)
# Compute derivative wrt. time.
imgt = img[1:] - img[0:-1]
ftv = imgt[x, y, z]
# Create function.
ft = Function(V)
ft.vector()[:] = ftv[d2v]
return ft
def retrieve_ensemble(bip,
dir_name,
f_name,
ensbl_sz,
max_iter,
img_out=False,
whiten=False):
f = df.HDF5File(bip.pde.mpi_comm, os.path.join(dir_name, f_name), "r")
ensbl_f = df.Function(bip.prior.V)
num_ensbls = max_iter * ensbl_sz
eldeg = bip.prior.V.ufl_element().degree()
if img_out:
gdim = bip.prior.V.mesh().geometry().dim()
imsz = bip.meshsz if hasattr(bip, 'meshsz') else (np.floor(
(bip.prior.V.dim() / eldeg**2)**(1. /
gdim)).astype('int'), ) * gdim
# out_shape=(num_ensbls,np.int((bip.prior.V.dim()/bip.prior.V.ufl_element().degree()**2)/imsz**(gdim-1)))+(imsz,)*(gdim-1)
out_shape = (num_ensbls, ) + imsz
else:
out_shape = (num_ensbls, bip.mesh.num_vertices())
out = np.zeros(out_shape)
prog = np.ceil(num_ensbls * (.1 + np.arange(0, 1, .1)))
V_P1 = df.FunctionSpace(adif.mesh, 'Lagrange', 1)
d2v = df.dof_to_vertex_map(V_P1)
for n in range(max_iter):
for j in range(ensbl_sz):
f.read(ensbl_f, 'iter{0}_ensbl{1}'.format(n + ('Y' not in TRAIN),
j))
s = n * ensbl_sz + j
ensbl_v = ensbl_f.vector()
if whiten: ensbl_v = bip.prior.u2v(ensbl_v)
if img_out:
out[s] = bip.vec2img(ensbl_v) # convert to images
else:
out[s] = ensbl_f.compute_vertex_values(
bip.mesh)[d2v] if eldeg > 1 else ensbl_v.get_local(
) # convert to P1 space (keep dof order) if necessary
if s + 1 in prog:
print('{0:.0f}% ensembles have been retrieved.'.format(
np.float(s + 1) / num_ensbls * 100))
f.close()
return out
def dolfin_function2BoxField(dolfin_function, dolfin_mesh,
division=None, uniform_mesh=True):
"""
Turn a DOLFIN P1 finite element field over a structured mesh into
a BoxField object. (Mostly for ease of plotting with scitools.)
Standard DOLFIN numbering numbers the nodes along the x[0] axis,
then x[1] axis, and so on.
If the DOLFIN function employs elements of degree > 1, one should
project or interpolate the field onto a field with elements of
degree=1.
"""
if dolfin_function.ufl_element().degree() != 1:
raise TypeError("""\
The dolfin_function2BoxField function works with degree=1 elements
only. The DOLFIN function (dolfin_function) has finite elements of type
%s
i.e., the degree=%d != 1. Project or interpolate this function
onto a space of P1 elements, i.e.,
V2 = FunctionSpace(mesh, 'CG', 1)
u2 = project(u, V2)
# or
u2 = interpolate(u, V2)
""" % (str(dolfin_function.ufl_element()), dolfin_function.ufl_element().degree()))
if dolfin.__version__[:3] == "1.0":
nodal_values = dolfin_function.vector().array().copy()
else:
#map = dolfin_function.function_space().dofmap().vertex_to_dof_map(dolfin_mesh)
d2v = dolfin.dof_to_vertex_map(dolfin_function.function_space())
nodal_values = dolfin_function.vector().array().copy()
nodal_values[d2v] = dolfin_function.vector().array().copy()
if uniform_mesh:
grid = dolfin_mesh2UniformBoxGrid(dolfin_mesh, division)
else:
grid = dolfin_mesh2BoxGrid(dolfin_mesh, division)
if nodal_values.size > grid.npoints:
# vector field, treat each component separately
ncomponents = int(nodal_values.size/grid.npoints)
try:
nodal_values.shape = (ncomponents, grid.npoints)
except ValueError as e:
raise ValueError('Vector field (nodal_values) has length %d, there are %d grid points, and this does not match with %d components' % (nodal_values.size, grid.npoints, ncomponents))
vector_field = [_rank12rankd_mesh(nodal_values[i,:].copy(),
grid.shape) \
for i in range(ncomponents)]
nodal_values = array(vector_field)
bf = BoxField(grid, name=dolfin_function.name(),
vector=ncomponents, values=nodal_values)
else:
try:
nodal_values = _rank12rankd_mesh(nodal_values, grid.shape)
except ValueError as e:
raise ValueError('DOLFIN function has vector of size %s while the provided mesh has %d points and shape %s' % (nodal_values.size, grid.npoints, grid.shape))
bf = BoxField(grid, name=dolfin_function.name(),
vector=0, values=nodal_values)
return bf
def solve_tr_dir__const_rheo(mesh_name, hol_cyl, deg_choice, T_in_expr,
T_inf_expr, HTC, T_old_v, k_mesh, cp_mesh,
rho_mesh, k_mesh_old, cp_mesh_old, rho_mesh_old,
dt, time_v, theta, bool_plot, bool_solv,
savings_do, logger_f):
'''
mesh_name: a proper XML file.
bool_plot: plots if bool_plot = 1.
Solves a direct, steady-state heat conduction problem, and
returns A_np, b_np, D_np, T_np, bool_ex, bool_in.
A_np: stiffness matrix, ordered by vertices.
b_np: integrated volumetric heat sources and surface heat fluxes, ordered by vertices.
The surface heat fluxes come from the solution to the direct problem;
hence, these terms will not be there in a real IHCP.
D_np: integrated Laplacian of T, ordered by vertices.
Option 2.
The Laplacian of q is properly assembled from D_np.
If do.dx(domain = hol_cyl) -> do.Measure('ds')[boundary_faces] and
do.Measure('ds')[boundary_faces] -> something representative of Gamma,
I would get option 1.
T_np: solution to the direct heat conduction problem, ordered by vertices.
bool_ex: boolean array declaring which vertices lie on the outer boundary.
bool_in: boolean array indicating which vertices lie on the inner boundary.
T_sol: solution to the direct heat conduction problem.
deg_choice: degree in FunctionSpace.
hol_cyl: mesh.
'''
#comm1 = MPI.COMM_WORLD
#current proc
#rank1 = comm1.Get_rank()
V = do.FunctionSpace(hol_cyl, 'CG', deg_choice)
if 'hollow' in mesh_name and 'cyl' in mesh_name:
from hollow_cyl_inv_mesh import geo_fun as geo_fun_hollow_cyl
geo_params_d = geo_fun_hollow_cyl()[1]
#x_c is a scalar here
#y_c is a scalar here
elif 'four' in mesh_name and 'cyl' in mesh_name:
from four_hole_cyl_inv_mesh import geo_fun as geo_fun_four_hole_cyl
geo_params_d = geo_fun_four_hole_cyl()[1]
#x_c is an array here
#y_c is an array here
x_c_l = [geo_params_d['x_0_{}'.format(itera)] for itera in xrange(4)]
y_c_l = [geo_params_d['y_0_{}'.format(itera)] for itera in xrange(4)]
elif 'one_hole_cir' in mesh_name:
from one_hole_cir_adj_mesh import geo_fun as geo_fun_one_hole_cir
geo_params_d = geo_fun_one_hole_cir()[1]
#x_c is an array here
#y_c is an array here
x_c_l = [geo_params_d['x_0']]
y_c_l = [geo_params_d['y_0']]
elif 'reinh_cir' in mesh_name:
from reinh_cir_adj_mesh import geo_fun as geo_fun_one_hole_cir
geo_params_d = geo_fun_one_hole_cir()[1]
#x_c is an array here
#y_c is an array here
x_c_l = [geo_params_d['x_0']]
y_c_l = [geo_params_d['y_0']]
elif 'small_circle' in mesh_name:
from four_hole_small_cir_adj_mesh import geo_fun as geo_fun_four_hole_cir
geo_params_d = geo_fun_four_hole_cir()[1]
#x_c is an array here
#y_c is an array here
x_c_l = [geo_params_d['x_0_{}'.format(itera)] for itera in xrange(4)]
y_c_l = [geo_params_d['y_0_{}'.format(itera)] for itera in xrange(4)]
#center of the cylinder base
x_c = geo_params_d['x_0']
y_c = geo_params_d['y_0']
R_in = geo_params_d['R_in']
R_ex = geo_params_d['R_ex']
#define variational problem
T = do.TrialFunction(V)
g = do.Function(V)
v = do.TestFunction(V)
T_old = do.Function(V)
T_inf = do.Function(V)
#scalar
T_old.vector()[:] = T_old_v
T_inf.vector()[:] = T_inf_expr
#solution
T_sol = do.Function(V)
#scalar
T_sol.vector()[:] = T_old_v
# Create boundary markers
mark_all = 3
mark_in = 4
mark_ex = 5
#x_c is an array here
#y_c is an array here
g_in = g_in_mesh(mesh_name, x_c_l, y_c_l, R_in)
g_ex = g_ex_mesh(mesh_name, x_c, y_c, R_ex)
in_boundary = do.AutoSubDomain(g_in)
ex_boundary = do.AutoSubDomain(g_ex)
#normal
unitNormal = do.FacetNormal(hol_cyl)
boundary_faces = do.MeshFunction('size_t', hol_cyl,
hol_cyl.topology().dim() - 1)
boundary_faces.set_all(mark_all)
in_boundary.mark(boundary_faces, mark_in)
ex_boundary.mark(boundary_faces, mark_ex)
bc_in = do.DirichletBC(V, T_in_expr, boundary_faces, mark_in)
#bc_ex = do.DirichletBC(V, T_ex_expr, boundary_faces, mark_ex)
bcs = [bc_in]
#k = do.Function(V) #W/m/K
#k.vector()[:] = k_mesh
#A0 = k * do.dot(do.grad(T), do.grad(v)) * do.dx(domain = hol_cyl)
A = dt / 2. * k_mesh * do.dot(do.grad(T), do.grad(v)) * do.dx(domain = hol_cyl) + \
rho_mesh * cp_mesh * T * v * do.dx(domain = hol_cyl)
A_full = A + dt / 2. * HTC * T * v * do.ds(
mark_ex, domain=hol_cyl, subdomain_data=boundary_faces)
L = -dt / 2. * k_mesh_old * do.dot(do.grad(T_old), do.grad(v)) * \
do.dx(domain = hol_cyl) + \
rho_mesh_old * cp_mesh_old * T_old * v * do.dx(domain = hol_cyl) - \
dt / 2. * HTC * (T_old) * v * do.ds(mark_ex,
domain = hol_cyl,
subdomain_data = boundary_faces) + \
dt * HTC * T_inf * v * do.ds(mark_ex,
domain = hol_cyl,
subdomain_data = boundary_faces)
#numpy version of A, T, and (L + int_fluxT)
#A_np__not_v2d = do.assemble(A).array() #before applying BCs - needs v2d
#L_np__not_v2d = do.assemble(L).array() #before applying BCs - needs v2d
#Laplacian of T, without any -1/k int_S q*n*v dS
'''
Approximated integral of the Laplacian of T.
Option 2.
The Laplacian of q is properly assembled from D_np.
If do.dx(domain = hol_cyl) -> do.Measure('ds')[boundary_faces] and
do.Measure('ds')[boundary_faces] -> something representative of Gamma,
I would get option 1.
'''
#D_np__not_v2d = do.assemble(-do.dot(do.grad(T), do.grad(v)) * do.dx(domain = hol_cyl) +
# do.dot(unitNormal, do.grad(T)) * v *
# do.Measure('ds')[boundary_faces]).array()
#print np.max(D_np__not_v2d)#, np.max(A_np__not_v2d)
#logger_f.warning('shape of D_np = {}, {}'.format(D_np__not_v2d.shape[0],
#D_np__not_v2d.shape[1]))
#nonzero_entries = []
#for row in D_np__not_v2d:
# nonzero_entries += [len(np.where(abs(row) > 1e-16)[0])]
#logger_f.warning('max, min, and mean of nonzero_entries = {}, {}, {}'.format(
# max(nonzero_entries), min(nonzero_entries), np.mean(nonzero_entries)))
#solver parameters
#linear solvers from
#list_linear_solver_methods()
#preconditioners from
#do.list_krylov_solver_preconditioners()
solver = do.KrylovSolver('gmres', 'ilu')
do.info(solver.parameters, True) #prints default values
solver.parameters['relative_tolerance'] = 1e-16
solver.parameters['maximum_iterations'] = 20000000
solver.parameters['monitor_convergence'] = True #on the screen
#http://fenicsproject.org/qa/1124/is-there-a-way-to-set-the-inital-guess-in-the-krylov-solver
'''solver.parameters['nonzero_initial_guess'] = True'''
solver.parameters['absolute_tolerance'] = 1e-15
#uses whatever in q_v as my initial condition
#the next lines are used for CHECK 3 only
#A_sys, b_sys = do.assemble_system(A, L, bcs)
do.File(
os.path.join(savings_do, '{}__markers.pvd'.format(
mesh_name.split('.')[0]))) << boundary_faces
if bool_plot:
do.plot(boundary_faces, '3D mesh', title='boundary markers')
#storage
T_sol_d = {}
g_d = {}
if bool_solv == 1:
xdmf_DHCP_T = do.File(os.path.join(savings_do, 'DHCP', 'T.pvd'))
xdmf_DHCP_q = do.File(os.path.join(savings_do, 'DHCP', 'q.pvd'))
for count_t_i, t_i in enumerate(time_v[1:]):
#T_in_expr.ts = t_i
#T_ex_expr.ts = t_i
#storage
T_sol_d[count_t_i] = do.Function(V)
T_sol_d[count_t_i].vector()[:] = T_sol.vector().array()
do.solve(A_full == L, T_sol, bcs)
'''
TO BE UPDATED:
rheology is not updated
'''
#updates L
T_old.assign(T_sol)
T_sol.rename('DHCP_T', 'temperature from DHCP')
#write solution to file
#paraview format
xdmf_DHCP_T << (T_sol, t_i)
#plot solution
if bool_plot:
do.plot(T_sol, title='T') #, interactive = True)
logger_f.warning('len(T) = {}'.format(len(T_sol.vector().array())))
print 'T: count_t = {}, min(T_DHCP) = {}'.format(
count_t_i, min(T_sol_d[count_t_i].vector().array()))
print 'T: count_t = {}, max(T_DHCP) = {}'.format(
count_t_i, max(T_sol_d[count_t_i].vector().array())), '\n'
#save flux - required for solving IHCP
#same result if do.ds(mark_ex, subdomain_data = boundary_faces)
#instead of do.Measure('ds')[boundary_faces]
#Langtangen, p. 37:
#either do.dot(do.nabla_grad(T), unitNormal)
#or do.dot(unitNormal, do.grad(T))
#int_fluxT = do.assemble(-k * do.dot(unitNormal, do.grad(T_sol)) * v *
# do.Measure('ds')[boundary_faces])
fluxT = do.project(
-k_mesh * do.grad(T_sol),
do.VectorFunctionSpace(hol_cyl, 'CG', deg_choice, dim=2))
if bool_plot:
do.plot(fluxT,
title='flux at iteration = {}'.format(count_t_i))
fluxT.rename('DHCP_flux', 'flux from DHCP')
xdmf_DHCP_q << (fluxT, t_i)
print 'DHCP: iteration = {}'.format(count_t_i)
####################################################
#full solution
#T_sol_full = do.Vector()
#T_sol.vector().gather(T_sol_full, np.array(range(V.dim()), 'intc'))
####################################################
count_t_i += 1
#copy previous lines
#storage
T_sol_d[count_t_i] = do.Function(V)
T_sol_d[count_t_i].vector()[:] = T_sol.vector().array()
for count_t_i, t_i in enumerate(time_v):
#storage
g_d[count_t_i] = do.Function(V)
g_d[count_t_i].vector()[:] = g.vector().array()
gdim = hol_cyl.geometry().dim()
dofmap = V.dofmap()
dofs = dofmap.dofs()
#Get coordinates as len(dofs) x gdim array
dofs_x = V.tabulate_dof_coordinates().reshape((-1, gdim))
#booleans corresponding to the outer boundary -> ints since they are sent to root = 0
bool_ex = 1. * np.array([g_ex(dof_x) for dof_x in dofs_x])
#booleans corresponding to the inner boundary -> ints since they are sent to root = 0
bool_in = 1. * np.array([g_in(dof_x) for dof_x in dofs_x])
T_np_ex = []
T_np_in = []
for i_coor, coor in enumerate(dofs_x):
if g_ex(coor):
T_np_ex += [T_sol.vector().array()[i_coor]]
if g_in(coor):
T_np_in += [T_sol.vector().array()[i_coor]]
print 'CHECK: mean(T) on the outer boundary = ', np.mean(np.array(T_np_ex))
print 'CHECK: mean(T) on the inner boundary = ', np.mean(np.array(T_np_in))
print 'CHECK: mean(HTC) = ', np.mean(do.project(HTC, V).vector().array())
#v2d = do.vertex_to_dof_map(V) #orders by hol_cyl.coordinates()
if deg_choice == 1:
print 'len(dof_to_vertex_map) = ', len(do.dof_to_vertex_map(V))
print 'min(dofs) = ', min(dofs), ', max(dofs) = ', max(dofs)
print 'len(bool ex) = ', len(bool_ex)
print 'len(bool in) = ', len(bool_in)
print 'bool ex[:10] = ', repr(bool_ex[:10])
print 'type(T) = ', type(T_sol.vector().array())
#first global results, then local results
return A, L, g_d, \
V, v, k_mesh, \
mark_in, mark_ex, \
boundary_faces, bool_ex, \
R_in, R_ex, T_sol_d, deg_choice, hol_cyl, \
unitNormal, dofs_x
def long_run_compare(self):
mesh = UnitIntervalMesh(5)
# FIXME: We need to make this run in paralell.
if MPI.size(mesh.mpi_comm()) > 1:
return
Model = Tentusscher_2004_mcell
tstop = 10
ind_V = 0
dt_ref = 0.1
time_ref = np.linspace(0, tstop, int(tstop / dt_ref) + 1)
dir_path = os.path.dirname(__file__)
Vm_reference = np.fromfile(os.path.join(dir_path, "Vm_reference.npy"))
params = Model.default_parameters()
time = Constant(0.0)
stim = Expression("(time >= stim_start) && (time < stim_start + stim_duration)"\
" ? stim_amplitude : 0.0 ", time=time, stim_amplitude=52.0, \
stim_start=1.0, stim_duration=1.0, degree=1)
# Initiate solver, with model and Scheme
if dolfin_adjoint:
adj_reset()
solver = self._setup_solver(Model, Scheme, mesh, time, stim, params)
solver._pi_solver.parameters["newton_solver"][
"relative_tolerance"] = 1e-8
solver._pi_solver.parameters["newton_solver"][
"maximum_iterations"] = 30
solver._pi_solver.parameters["newton_solver"]["report"] = False
scheme = solver._scheme
(vs_, vs) = solver.solution_fields()
vs.assign(vs_)
dof_to_vertex_map_values = dof_to_vertex_map(vs.function_space())
scheme.t().assign(0.0)
vs_array = np.zeros(mesh.num_vertices()*\
vs.function_space().dofmap().num_entity_dofs(0))
vs_array[dof_to_vertex_map_values] = vs.vector().get_local()
output = [vs_array[ind_V]]
time_output = [0.0]
dt = dt_org
# Time step
next_dt = max(min(tstop - float(scheme.t()), dt), 0.0)
t0 = 0.0
while next_dt > 0.0:
# Step solver
solver.step((t0, t0 + next_dt))
vs_.assign(vs)
# Collect plt output data
vs_array[dof_to_vertex_map_values] = vs.vector().get_local()
output.append(vs_array[ind_V])
time_output.append(float(scheme.t()))
# Next time step
t0 += next_dt
next_dt = max(min(tstop - float(scheme.t()), dt), 0.0)
# Compare solution from CellML run using opencell
assert_almost_equal(output[-1], Vm_reference[-1], abs_tol)
output = np.array(output)
time_output = np.array(time_output)
output = np.interp(time_ref, time_output, output)
value = np.sqrt(np.sum(
((Vm_reference - output) / Vm_reference)**2)) / len(Vm_reference)
assert_almost_equal(value, 0.0, rel_tol)
def fun(mesh3d, npoints):
'''A random curve starting close to (-1, -1, -1) and continueing inside'''
import networkx as nx
import random
edge_f = df.MeshFunction('size_t', mesh3d, 1, 0)
mesh3d.init(1, 0)
# Init the graph
G = nx.Graph()
edge_indices = {
tuple(sorted(e.entities(0).tolist())): e_index
for e_index, e in enumerate(df.edges(mesh3d))
}
G.add_edges_from(iter(edge_indices.keys()))
# Let's find boundary vertices
V = df.FunctionSpace(mesh3d, 'CG', 1)
bdry = df.CompiledSubDomain(
'near(std::max(std::max(std::abs(x[0]), std::abs(x[1])), std::abs(x[2])), 1, tol)',
tol=TOL)
bc = df.DirichletBC(V, df.Constant(0), bdry, 'pointwise')
bc_vertices = set(
df.dof_to_vertex_map(V)[list(bc.get_boundary_values().keys())])
# Start at the boundary at (-1, -1, 1)
X = mesh3d.coordinates()
start = np.argmin(np.sum((X - np.array([-1, -1, -1]))**2, axis=1))
# All vertices
vertices = list(range(mesh3d.num_vertices()))
first = None
while npoints:
# Pick the next vertex, inside
while True:
stop = random.choice(vertices)
if start != stop and stop not in bc_vertices: break
# The path is a shortest path between vertices
path = nx.shortest_path(G, source=start, target=stop)
# Here it can happen that the path will have surface points
if first is None:
# So we walk back (guaranteed to be in) until we hit the surface
clean_path = []
for p in reversed(path):
clean_path.append(p)
if p in bc_vertices:
print('Shifted start to', X[p])
first = p
break
path = clean_path
start = first
# Start in, must end in and stay in
else:
if set(path) & bc_vertices: continue
for v0, v1 in zip(path[:-1], path[1:]):
edge = (v0, v1) if v0 < v1 else (v1, v0)
edge_f[edge_indices[edge]] = 1
start = stop
npoints -= 1
# df.File('x.pvd') << edge_f
return edge_f, X[first]
def initialize_variables(self):
r"""
Initialize the model variables to default values. The variables
defined here are:
Various things :
* ``self.element`` -- the finite-element
* ``self.top_dim`` -- the topological dimension
* ``self.dofmap`` -- :class:`~dolfin.cpp.fem.DofMap` for converting between vertex to nodal indicies
* ``self.h`` -- Cell diameter formed by calling :func:`~dolfin.functions.specialfunctions.CellDiameter` with ``self.mesh``
Grid velocity vector :math:`\mathbf{u}_i = [u\ v\ w]^{\intercal}`:
* ``self.U_mag`` -- velocity vector magnitude
* ``self.U3`` -- velocity vector
* ``self.u`` -- :math:`x`-component of velocity vector
* ``self.v`` -- :math:`y`-component of velocity vector
* ``self.w`` -- :math:`z`-component of velocity vector
Grid acceleration vector :math:`\mathbf{a}_i = [a_x\ a_y\ a_z]^{\intercal}`:
* ``self.a_mag`` -- acceleration vector magnitude
* ``self.a3`` -- acceleration vector
* ``self.a_x`` -- :math:`x`-component of acceleration vector
* ``self.a_y`` -- :math:`y`-component of acceleration vector
* ``self.a_z`` -- :math:`z`-component of acceleration vector
Grid internal force vector :math:`\mathbf{f}_i^{\mathrm{int}} = [f_x^{\mathrm{int}}\ f_y^{\mathrm{int}}\ f_z^{\mathrm{int}}]^{\intercal}`:
* ``self.f_int_mag`` -- internal force vector magnitude
* ``self.f_int`` -- internal force vector
* ``self.f_int_x`` -- :math:`x`-component of internal force vector
* ``self.f_int_y`` -- :math:`y`-component of internal force vector
* ``self.f_int_z`` -- :math:`z`-component of internal force vector
Grid mass :math:`m_i`:
* ``self.m`` -- mass :math:`m_i`
* ``self.m0`` -- inital mass :math:`m_i^0`
"""
s = "::: initializing grid variables :::"
print_text(s, cls=self.this)
# the finite-element used :
self.element = self.Q.element()
# topological dimension :
self.top_dim = self.element.geometric_dimension()
# map from verticies to nodes :
self.dofmap = self.Q.dofmap()
# for finding vertices sitting on boundary :
self.d2v = dl.dof_to_vertex_map(self.Q)
# list of arrays of vertices and bcs set by self.set_boundary_conditions() :
self.bc_vrt = None
self.bc_val = None
# cell diameter :
self.h = dl.project(dl.CellDiameter(self.mesh), self.Q)
# cell volume :
self.Ve = dl.project(dl.CellVolume(self.mesh), self.Q)
# grid velocity :
self.U_mag = dl.Function(self.Q, name='U_mag')
self.U3 = dl.Function(self.Q3, name='U3')
u, v, w = self.U3.split()
u.rename('u', '')
v.rename('v', '')
w.rename('w', '')
self.u = u
self.v = v
self.w = w
# grid acceleration :
self.a_mag = dl.Function(self.Q, name='a_mag')
self.a3 = dl.Function(self.Q3, name='a3')
a_x, a_y, a_z = self.a3.split()
a_x.rename('a_x', '')
a_y.rename('a_y', '')
a_z.rename('a_z', '')
self.a_x = a_x
self.a_y = a_y
self.a_z = a_z
# grid internal force vector :
self.f_int_mag = dl.Function(self.Q, name='f_int_mag')
self.f_int = dl.Function(self.Q3, name='f_int')
f_int_x, f_int_y, f_int_z = self.f_int.split()
f_int_x.rename('f_int_x', '')
f_int_y.rename('f_int_y', '')
f_int_z.rename('f_int_z', '')
self.f_int_x = f_int_x
self.f_int_y = f_int_y
self.f_int_z = f_int_z
# grid mass :
self.m = dl.Function(self.Q, name='m')
self.m0 = dl.Function(self.Q, name='m0')
# function assigners speed assigning up :
self.assu = dl.FunctionAssigner(self.u.function_space(), self.Q)
self.assv = dl.FunctionAssigner(self.v.function_space(), self.Q)
self.assw = dl.FunctionAssigner(self.w.function_space(), self.Q)
self.assa_x = dl.FunctionAssigner(self.a_x.function_space(), self.Q)
self.assa_y = dl.FunctionAssigner(self.a_y.function_space(), self.Q)
self.assa_z = dl.FunctionAssigner(self.a_z.function_space(), self.Q)
self.assf_int_x = dl.FunctionAssigner(self.f_int_x.function_space(),
self.Q)
self.assf_int_y = dl.FunctionAssigner(self.f_int_y.function_space(),
self.Q)
self.assf_int_z = dl.FunctionAssigner(self.f_int_z.function_space(),
self.Q)
self.assm = dl.FunctionAssigner(self.m.function_space(), self.Q)
# save the number of degrees of freedom :
self.dofs = self.m.vector().size()
def scalar_laplacians(mesh):
"""
Calculate the laplacians needed by fiberrule algorithms
Arguments
---------
mesh : dolfin.Mesh
A dolfin mesh with marked boundaries:
base = 10, rv = 20, lv = 30, epi = 40
The base is assumed placed at x=0
"""
if not isinstance(mesh, d.Mesh):
raise TypeError("Expected a dolfin.Mesh as the mesh argument.")
# Init connectivities
mesh.init(2)
facet_markers = d.MeshFunction("size_t", mesh, 2, mesh.domains())
# Boundary markers, solutions and cases
markers = dict(base=10, rv=20, lv=30, epi=40, apex=50)
# Solver parameters
solver_param=dict(solver_parameters=dict(
preconditioner="ml_amg" if d.has_krylov_solver_preconditioner("ml_amg") \
else "default", linear_solver="gmres"))
cases = ["rv", "lv", "epi"]
boundaries = cases + ["base"]
# Check that all boundary faces are marked
num_boundary_facets = d.BoundaryMesh(mesh, "exterior").num_cells()
if num_boundary_facets != sum(np.sum(\
facet_markers.array()==markers[boundary])\
for boundary in boundaries):
d.error("Not all boundary faces are marked correctly. Make sure all "\
"boundary facets are marked as: base = 10, rv = 20, lv = 30, "\
"epi = 40.")
# Coords and cells
coords = mesh.coordinates()
cells_info = mesh.cells()
# Find apex by solving a laplacian with base solution = 0
# Create Base variational problem
V = d.FunctionSpace(mesh, "CG", 1)
u = d.TrialFunction(V)
v = d.TestFunction(V)
a = d.dot(d.grad(u), d.grad(v)) * d.dx
L = v * d.Constant(1) * d.dx
DBC_10 = d.DirichletBC(V, 1, facet_markers, markers["base"], "topological")
# Create solutions
solutions = dict(
(what, d.Function(V)) for what in markers if what != "base")
d.solve(a == L,
solutions["apex"],
DBC_10,
solver_parameters={"linear_solver": "gmres"})
apex_values = solutions["apex"].vector().array()
apex_values[d.dof_to_vertex_map(V)] = solutions["apex"].vector().array()
ind_apex_max = apex_values.argmax()
apex_coord = coords[ind_apex_max, :]
# Update rhs
L = v * d.Constant(0) * d.dx
d.info(" Apex coord: ({0}, {1}, {2})".format(*apex_coord))
d.info(" Num coords: {0}".format(len(coords)))
d.info(" Num cells: {0}".format(len(cells_info)))
# Calculate volume
volume = 0.0
for cell in d.cells(mesh):
volume += cell.volume()
d.info(" Volume: {0}".format(volume))
d.info("")
# Cases
# =====
#
# 1) base: 1, apex: 0
# 2) lv: 1, rv, epi: 0
# 3) rv: 1, lv, epi: 0
# 4) epi: 1, rv, lv: 0
class ApexDomain(d.SubDomain):
def inside(self, x, on_boundary):
return d.near(x[0], apex_coord[0]) and d.near(x[1], apex_coord[1]) and \
d.near(x[2], apex_coord[2])
apex_domain = ApexDomain()
# Case 1:
Poisson = 1
DBC_11 = d.DirichletBC(V, 0, apex_domain, "pointwise")
# Using Poisson
if Poisson:
d.solve(a == L,
solutions["apex"], [DBC_10, DBC_11],
solver_parameters={"linear_solver": "gmres"})
# Using Eikonal equation
else:
Le = v * d.Constant(1) * d.dx
d.solve(a == Le,
solutions["apex"],
DBC_11,
solver_parameters={"linear_solver": "gmres"})
# Create Eikonal problem
eps = d.Constant(mesh.hmax() / 25)
y = solutions["apex"]
F = d.sqrt(d.inner(d.grad(y), d.grad(y)))*v*d.dx - \
d.Constant(1)*v*d.dx + eps*d.inner(d.grad(y), d.grad(v))*d.dx
d.solve(F == 0,
y,
DBC_11,
solver_parameters={
"linear_solver": "lu",
"newton_solver": {
"relative_tolerance": 1e-5
}
})
# Check that solution of the three last cases all sum to 1.
sol = solutions["apex"].vector().copy()
sol[:] = 0.0
# Iterate over the three different cases
for case in cases:
# Solve linear system
bcs = [d.DirichletBC(V, 1 if what == case else 0, \
facet_markers, markers[what], "topological") \
for what in cases]
def dolfin_fiberrules(
mesh,
fiber_space=None,
fiber_rotation_epi=50, # 50
fiber_rotation_endo=40, # 40
sheet_rotation_epi=65, # 65
sheet_rotation_endo=25, # 25
alpha_noise=0.0,
beta_noise=0.0):
"""
Create fiber, cross fibers and sheet directions
Arguments
---------
mesh : dolfin.Mesh
A dolfin mesh with marked boundaries:
base = 10, rv = 20, lv = 30, epi = 40
The base is assumed placed at x=0
fiber_space : dolfin.FunctionSpace (optional)
Determines for what space the fibers should be calculated for.
fiber_rotation_epi : float (optional)
Fiber rotation angle on the endocardial surfaces.
fiber_rotation_endo : float (optional)
Fiber rotation angle on the epicardial surfaces.
sheet_rotation_epi : float (optional)
Sheet rotation angle on the endocardial surfaces.
sheet_rotation_endo : float (optional)
Sheet rotation angle on the epicardial surfaces.
"""
#import cpp
if not isinstance(mesh, d.Mesh):
raise TypeError("Expected a dolfin.Mesh as the mesh argument.")
# Default fiber space is P1
fiber_space = fiber_space or d.FunctionSpace(mesh, "P", 1)
# Create scalar laplacian solutions
d.info("Calculating scalar fields")
scalar_solutions = scalar_laplacians(mesh)
# Create gradients
d.info("\nCalculating gradients")
data = project_gradients(mesh, fiber_space, scalar_solutions)
# Assign the fiber and sheet rotations
data.fiber_rotation_epi = fiber_rotation_epi
data.fiber_rotation_endo = fiber_rotation_endo
data.sheet_rotation_epi = sheet_rotation_epi
data.sheet_rotation_endo = sheet_rotation_endo
#Gaussian field with correlation length l
#p , l = np.inf, 2
#number of terms in expansion
#k = 10
#kernel = Matern(p = p,l = l) #0,1Exponential covariance kernel
#kle = KLE(mesh, kernel, verbose = True)
#kle.compute_eigendecomposition(k = k)#20 by default
#Generate realizations
#noise = kle.realizations()
#x = np.zeros(len(noise))
#noise = np.array(x)
#noise[0:len(noise)/2] = 30
##print y
#print "noise array", noise
#V = d.FunctionSpace(mesh, "CG", 1)
#random_field =d.Function(V)
#random_f = np.zeros((mesh.num_vertices()),dtype =float)
#random_f = noise
#random_field.vector()[:] = random_f[d.dof_to_vertex_map(V)]
#d.plot(random_field, mesh, interactive =True)
##random_f = noise
#x = np.zeros(len(noise))
#y = np.array(x)
#y[0:len(noise)/2] = 30
##print y
#print "noise array", y
# Check noise
if np.isscalar(alpha_noise):
alpha_noise = np.zeros(mesh.num_vertices(), dtype=float)
if np.isscalar(beta_noise):
beta_noise = np.zeros(mesh.num_vertices(), dtype=float)
# Call the fiber sheet generation
cpp.computeFiberSheetSystem(data,
alpha_noise[d.dof_to_vertex_map(fiber_space)],
beta_noise[d.dof_to_vertex_map(fiber_space)])
#cpp.computeFiberSheetSystem(data,noise)
# Create output Functions
Vv = d.VectorFunctionSpace(mesh, fiber_space.ufl_element().family(), \
fiber_space.ufl_element().degree())
V = fiber_space
fiber_sheet_tensor = data.fiber_sheet_tensor
fiber_components = []
scalar_size = fiber_sheet_tensor.size / 9
indices = np.zeros(scalar_size * 3, dtype="L")
indices[0::3] = np.arange(scalar_size, dtype="L") * 9 # x
indices[1::3] = np.arange(scalar_size, dtype="L") * 9 + 3 # y
indices[2::3] = np.arange(scalar_size, dtype="L") * 9 + 6 # z
for ind, name in enumerate(["f0", "n0", "s0"]):
component = d.Function(Vv, name=name)
# Sort the fibers and sheets in dolfin degrees of freedom (dofs)
component.vector()[:] = fiber_sheet_tensor[indices]
fiber_components.append(component)
indices += 1
# Make sheet the last component
fiber_components = [fiber_components[0]] + fiber_components[-1:0:-1]
return fiber_components
fig,axes = plt.subplots(nrows=1, ncols=2, sharex=True, sharey=True, figsize=(12,6), facecolor='white')
plt.ion()
# plt.show(block=True)
n_dif = 100
dif = np.zeros((n_dif,2))
loaded=np.load(file=os.path.join(folder,algs[alg_no]+'_ensbl'+str(ensbl_sz)+'_training_XY.npz'))
prng=np.random.RandomState(2020)
sel4eval = prng.choice(num_samp,size=n_dif,replace=False)
X=loaded['X'][sel4eval]; Y=loaded['Y'][sel4eval]
sel4print = prng.choice(n_dif,size=10,replace=False)
prog=np.ceil(n_dif*(.1+np.arange(0,1,.1)))
u_f = df.Function(adif.prior.V)
eldeg = adif.prior.V.ufl_element().degree()
if eldeg>1:
V_P1 = df.FunctionSpace(adif.mesh,'Lagrange',1)
d2v = df.dof_to_vertex_map(V_P1)
u_f1 = df.Function(V_P1)
else:
u_f1 = u_f
for n in range(n_dif):
u=X[n]
# calculate gradient
t_start=timeit.default_timer()
u_f1.vector().set_local(u); u_v = u_f1.vector() # u already in dof order
if eldeg>1:
u_f.interpolate(u_f1)
u_v = u_f.vector()
# u_f = img2fun(u, adif.prior.V); u_v = u_f.vector() # for u in vertex order
ll_xact,dll_xact = adif.get_geom(u_v,[0,1])[:2]
t_used[0] += timeit.default_timer()-t_start
# emulate gradient
# closest_point_vectorized() took 157871 microseconds
# nquery= 100000 , dt_closest_SM= 0.2701895236968994
# and
# closest_point_vectorized() took 1249172 microseconds
# nquery= 1000000 , dt_closest_SM= 3.3071250915527344
# EVALUATE FUNCTION AT POINT
mesh = circle_mesh(np.array([0.0, 0.0]), 1.0, 1e-2)
V = dl.FunctionSpace(mesh, 'CG', 1)
# check that I'm using the dof to vertex mapping right
mesh_coords = mesh.coordinates()
dof_coords = V.tabulate_dof_coordinates()
dof2vertex = dl.dof_to_vertex_map(V)
vertex2dof = dl.vertex_to_dof_map(V)
u = dl.Function(V)
u.vector()[:] = dof_coords[:, 0]**2 + 2 * dof_coords[:, 1]**2
u.set_allow_extrapolation(True)
uu = u.vector()[vertex2dof]
# uu = u.vector()[dof2vertex]
uu_true = np.zeros(V.dim())
for ii in range(V.dim()):
uu_true[ii] = u(mesh_coords[ii, :])
err_uu = np.linalg.norm(uu - uu_true)
print('err_uu=', err_uu)
def dolfin_function2BoxField(dolfin_function,
dolfin_mesh,
division=None,
uniform_mesh=True):
"""
Turn a DOLFIN P1 finite element field over a structured mesh into
a BoxField object. (Mostly for ease of plotting with scitools.)
Standard DOLFIN numbering numbers the nodes along the x[0] axis,
then x[1] axis, and so on.
If the DOLFIN function employs elements of degree > 1, one should
project or interpolate the field onto a field with elements of
degree=1.
"""
if dolfin_function.ufl_element().degree() != 1:
raise TypeError("""\
The dolfin_function2BoxField function works with degree=1 elements
only. The DOLFIN function (dolfin_function) has finite elements of type
%s
i.e., the degree=%d != 1. Project or interpolate this function
onto a space of P1 elements, i.e.,
V2 = FunctionSpace(mesh, 'CG', 1)
u2 = project(u, V2)
# or
u2 = interpolate(u, V2)
""" % (str(dolfin_function.ufl_element()),
dolfin_function.ufl_element().degree()))
if dolfin.__version__[:3] == "1.0":
nodal_values = dolfin_function.vector().array().copy()
else:
#map = dolfin_function.function_space().dofmap().vertex_to_dof_map(dolfin_mesh)
d2v = dolfin.dof_to_vertex_map(dolfin_function.function_space())
nodal_values = dolfin_function.vector().array().copy()
nodal_values[d2v] = dolfin_function.vector().array().copy()
if uniform_mesh:
grid = dolfin_mesh2UniformBoxGrid(dolfin_mesh, division)
else:
grid = dolfin_mesh2BoxGrid(dolfin_mesh, division)
if nodal_values.size > grid.npoints:
# vector field, treat each component separately
ncomponents = int(nodal_values.size / grid.npoints)
try:
nodal_values.shape = (ncomponents, grid.npoints)
except ValueError as e:
raise ValueError(
'Vector field (nodal_values) has length %d, there are %d grid points, and this does not match with %d components'
% (nodal_values.size, grid.npoints, ncomponents))
vector_field = [_rank12rankd_mesh(nodal_values[i,:].copy(),
grid.shape) \
for i in range(ncomponents)]
nodal_values = array(vector_field)
bf = BoxField(grid,
name=dolfin_function.name(),
vector=ncomponents,
values=nodal_values)
else:
try:
nodal_values = _rank12rankd_mesh(nodal_values, grid.shape)
except ValueError as e:
raise ValueError(
'DOLFIN function has vector of size %s while the provided mesh has %d points and shape %s'
% (nodal_values.size, grid.npoints, grid.shape))
bf = BoxField(grid,
name=dolfin_function.name(),
vector=0,
values=nodal_values)
return bf
def geom(unknown_lat,bip_lat,bip,autoencoder,geom_ord=[0],whitened=False,**kwargs):
loglik=None; gradlik=None; metact=None; rtmetact=None; eigs=None
# un-whiten if necessary
if whitened=='latent':
unknown_lat=bip_lat.prior.v2u(unknown_lat)
eldeg = bip.prior.V.ufl_element().degree()
if 'Conv' in type(autoencoder).__name__:
u_latin=bip_lat.vec2img(unknown_lat)
width=tuple(np.mod(i,2) for i in u_latin.shape)
u_latin=chop(u_latin,width)[None,:,:,None] if autoencoder.activations['latent'] is None else u_latin.flatten()[None,:]
unknown=bip.img2vec(pad(np.squeeze(autoencoder.decode(u_latin)),width), bip.prior.V if eldeg>1 else None)
else:
u_latin=unknown_lat.get_local()[None,:]
# unknown=df.Function(V).vector()
# unknown.set_local(autoencoder.decode(u_latin).flatten())
u_decoded=autoencoder.decode(u_latin).flatten()
unknown=bip.prior.gen_vector(u_decoded) if eldeg==1 else vinPn(u_decoded, bip.prior.V)
emul_geom=kwargs.pop('emul_geom',None)
full_geom=kwargs.pop('full_geom',None)
try:
if len(kwargs)==0:
loglik,gradlik,metact_,rtmetact_ = emul_geom(unknown,geom_ord,whitened=='emulated',inP1=True)
else:
loglik,gradlik,metact_,eigs_ = emul_geom(unknown,geom_ord,whitened=='emulated',inP1=True,**kwargs)
except:
try:
if len(kwargs)==0:
loglik,gradlik,metact_,rtmetact_ = full_geom(unknown,geom_ord,whitened=='original')
else:
loglik,gradlik,metact_,eigs_ = full_geom(unknown,geom_ord,whitened=='original',**kwargs)
except:
raise RuntimeError('No geometry in the original space available!')
if any(s>=1 for s in geom_ord):
if whitened=='latent':
gradlik = bip.prior.C_act(gradlik,.5)
# jac=autoencoder.jacobian(u_latin,'decode')
if 'Conv' in type(autoencoder).__name__:
jac=autoencoder.jacobian(u_latin,'decode')
jac=pad(jac,width*2 if autoencoder.activations['latent'] is None else width+(0,))
jac=jac.reshape((np.prod(jac.shape[:2]),np.prod(jac.shape[2:])))
jac=jac[np.ix_(df.dof_to_vertex_map(bip.prior.V), df.dof_to_vertex_map(bip_lat.prior.V))]
gradlik_=jac.T.dot(gradlik.get_local())
gradlik_ = autoencoder.jacvec(u_latin,gradlik.get_local()[None,:])
gradlik=bip_lat.prior.gen_vector(gradlik_)
# print('time consumed:{}'.format(timeit.default_timer()-t_start))
if any(s>=1.5 for s in geom_ord):
def _get_metact_misfit(u_actedon):
if type(u_actedon) is df.Vector:
u_actedon=u_actedon.get_local()
tmp=df.Vector(unknown); tmp.zero()
jac.reduce(tmp,u_actedon)
v=df.Vector(unknown_lat)
v.set_local(jac.dot(metact_(tmp)))
return v
def _get_rtmetact_misfit(u_actedon):
if type(u_actedon) is not df.Vector:
u_=df.Vector(unknown)
u_.set_local(u_actedon)
u_actedon=u_
v=df.Vector(unknown_lat)
v.set_local(jac.dot(rtmetact_(u_actedon)))
return v
metact = _get_metact_misfit
rtmetact = _get_rtmetact_misfit
if any(s>1 for s in geom_ord) and len(kwargs)!=0:
if bip_lat is None: raise ValueError('No latent inverse problem defined!')
# compute eigen-decomposition using randomized algorithms
if whitened=='latent':
# generalized eigen-decomposition (_C^(1/2) F _C^(1/2), M), i.e. _C^(1/2) F _C^(1/2) = M V D V', V' M V = I
def invM(a):
a=bip_lat.prior.gen_vector(a)
invMa=bip_lat.prior.gen_vector()
bip_lat.prior.Msolver.solve(invMa,a)
return invMa
eigs = geigen_RA(metact, lambda u: bip_lat.prior.M*u, invM, dim=bip_lat.prior.V.dim(),**kwargs)
else:
# generalized eigen-decomposition (F, _C^(-1)), i.e. F = _C^(-1) U D U^(-1), U' _C^(-1) U = I, V = _C^(-1/2) U
eigs = geigen_RA(metact,lambda u: bip_lat.prior.C_act(u,-1),lambda u: bip_lat.prior.C_act(u),dim=bip_lat.prior.V.dim(),**kwargs)
if any(s>1.5 for s in geom_ord):
# adjust the gradient
# update low-rank approximate Gaussian posterior
bip_lat.post_Ga = Gaussian_apx_posterior(bip_lat.prior,eigs=eigs)
# Hu = bip_lat.prior.gen_vector()
# bip_lat.post_Ga.Hlr.mult(unknown, Hu)
# gradlik.axpy(1.0,Hu)
if len(kwargs)==0:
return loglik,gradlik,metact,rtmetact
else:
return loglik,gradlik,metact,eigs