def mark_facets(mesh: df.Mesh, ffun: df.MeshFunction):
"""
Mark mesh according to facet function
"""
for facet in df.facets(mesh):
if ffun[facet] == 2**64 - 1:
ffun[facet] = 0
mesh.domains().set_marker((facet.index(), ffun[facet]), 2)
def test_convert_diffpack(self):
from dolfin import Mesh, MPI, MeshFunction
if MPI.num_processes() != 1:
return
fname = os.path.join("data", "diffpack_tet")
dfname = fname+".xml"
# Read triangle file and convert to a dolfin xml mesh file
meshconvert.diffpack2xml(fname+".grid", dfname)
# Read in dolfin mesh and check number of cells and vertices
mesh = Mesh(dfname)
self.assertEqual(mesh.num_vertices(), 27)
self.assertEqual(mesh.num_cells(), 48)
self.assertEqual(mesh.domains().markers(3).size(), 48)
self.assertEqual(mesh.domains().markers(2).size(), 16)
mf_basename = dfname.replace(".xml", "_marker_%d.xml")
for marker, num in [(3, 9), (6, 9), (7, 3), (8, 1)]:
mf_name = mf_basename % marker
mf = MeshFunction("uint", mesh, mf_name)
self.assertEqual(sum(mf.array()==marker), num)
os.unlink(mf_name)
# Clean up
os.unlink(dfname)
def test_convert_diffpack_2d(self):
from dolfin import Mesh, MPI, MeshFunction
fname = os.path.join(os.path.dirname(__file__), "data", "diffpack_tri")
dfname = fname + ".xml"
# Read triangle file and convert to a dolfin xml mesh file
meshconvert.diffpack2xml(fname + ".grid", dfname)
# Read in dolfin mesh and check number of cells and vertices
mesh = Mesh(dfname)
self.assertEqual(mesh.num_vertices(), 41)
self.assertEqual(mesh.num_cells(), 64)
self.assertEqual(len(mesh.domains().markers(2)), 64)
mf_basename = dfname.replace(".xml", "_marker_%d.xml")
for marker, num in [(1, 10), (2, 5), (3, 5)]:
mf_name = mf_basename % marker
mf = MeshFunction("size_t", mesh, mf_name)
self.assertEqual(sum(mf.array() == marker), num)
os.unlink(mf_name)
# Clean up
os.unlink(dfname)
def test_convert_diffpack(self):
from dolfin import Mesh, MPI, MeshFunction, mpi_comm_world
if MPI.size(mpi_comm_world()) != 1:
return
fname = os.path.join("data", "diffpack_tet")
dfname = fname + ".xml"
# Read triangle file and convert to a dolfin xml mesh file
meshconvert.diffpack2xml(fname + ".grid", dfname)
# Read in dolfin mesh and check number of cells and vertices
mesh = Mesh(dfname)
self.assertEqual(mesh.num_vertices(), 27)
self.assertEqual(mesh.num_cells(), 48)
self.assertEqual(len(mesh.domains().markers(3)), 48)
self.assertEqual(len(mesh.domains().markers(2)), 16)
mf_basename = dfname.replace(".xml", "_marker_%d.xml")
for marker, num in [(3, 9), (6, 9), (7, 3), (8, 1)]:
mf_name = mf_basename % marker
mf = MeshFunction("size_t", mesh, mf_name)
self.assertEqual(sum(mf.array() == marker), num)
os.unlink(mf_name)
# Clean up
os.unlink(dfname)
def test_convert_diffpack_2d(self):
from dolfin import Mesh, MPI, MeshFunction, mpi_comm_world
fname = os.path.join(os.path.dirname(__file__), "data", "diffpack_tri")
dfname = fname+".xml"
# Read triangle file and convert to a dolfin xml mesh file
meshconvert.diffpack2xml(fname+".grid", dfname)
# Read in dolfin mesh and check number of cells and vertices
mesh = Mesh(dfname)
self.assertEqual(mesh.num_vertices(), 41)
self.assertEqual(mesh.num_cells(), 64)
self.assertEqual(len(mesh.domains().markers(2)), 64)
mf_basename = dfname.replace(".xml", "_marker_%d.xml")
for marker, num in [(1,10), (2,5), (3,5)]:
mf_name = mf_basename % marker
mf = MeshFunction("size_t", mesh, mf_name)
self.assertEqual(sum(mf.array()==marker), num)
os.unlink(mf_name)
# Clean up
os.unlink(dfname)
def import_from_gmsh(fname):
"Convert from gmsh to dolfin"
# read with meshio
msh = meshio.read(fname)
# create a DOLFIN mesh (assuming 2d)
gdim, tdim = 2, 2
mm = Mesh()
editor = MeshEditor()
editor.open(mm, "triangle", gdim, tdim)
npt = msh.points.shape[0]
nc = msh.get_cells_type("triangle").shape[0]
editor.init_vertices_global(npt, npt)
editor.init_cells_global(nc, nc)
for i, p in enumerate(msh.points):
editor.add_vertex(i, p[:2])
for i, c in enumerate(msh.get_cells_type("triangle")):
editor.add_cell(i, c)
editor.close()
# domains
md = mm.domains()
md.init(tdim)
markers = {}
if 'gmsh:physical' not in msh.cell_data_dict:
# no markers at all
return mm, markers
phy = msh.cell_data_dict['gmsh:physical']
if 'triangle' in phy:
for eid, val in enumerate(phy['triangle']):
md.set_marker((eid, val), 2)
if 'line' in phy:
mm.init(0, 1)
p2e = mm.topology()(0, 1)
for l, k in zip(msh.get_cells_type("line"), phy['line']):
e = set(p2e(l[0])).intersection(p2e(l[1])).pop()
md.set_marker((e, k), 1)
if 'vertex' in phy:
for eid, val in zip(msh.get_cells_type("vertex"), phy['vertex']):
md.set_marker((eid[0], val), 0)
# names
markers = tuple(
{n: v.item()
for n, (v, d) in msh.field_data.items() if d == dim}
for dim in range(tdim + 1))
return mm, markers
def mark_biv_mesh(
mesh: df.Mesh,
ffun: Optional[df.MeshFunction] = None,
markers: Optional[Dict[str, int]] = None,
tol: float = 0.01,
values: Dict[str, int] = {
"lv": 0,
"septum": 1,
"rv": 2
},
) -> df.MeshFunction:
from .ldrb import scalar_laplacians
scalars = scalar_laplacians(mesh=mesh, ffun=ffun, markers=markers)
for cell in df.cells(mesh):
lv = scalars["lv"](cell.midpoint())
rv = scalars["rv"](cell.midpoint())
epi = scalars["epi"](cell.midpoint())
print(cell.index(), "lv = {}, rv = {}".format(lv, rv))
if (lv > tol or epi > 1 - tol) and rv < tol:
print("LV")
value = values["lv"]
if lv < tol and rv > lv:
value = values["rv"]
elif (rv > tol or epi > 1 - tol) and lv < tol:
print("RV")
value = values["rv"]
else:
print("SEPTUM")
value = values["septum"]
mesh.domains().set_marker((cell.index(), value), 3)
sfun = df.MeshFunction("size_t", mesh, 3, mesh.domains())
return sfun
def write_fenics_file(dim, ofilename):
ofile = File(ofilename + '.xml')
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, dim, dim)
editor.init_vertices(nodes.shape[1])
editor.init_cells(len(cell_map))
for i in range(nodes.shape[1]):
if dim == 2:
editor.add_vertex(i, nodes[0, i], nodes[1, i])
else:
editor.add_vertex(i, nodes[0, i], nodes[1, i], nodes[2, i])
for i in range(1, len(cell_map)+1):
if dim == 2:
editor.add_cell(i-1, cell_map[i][0]-1, cell_map[i][1]-1, cell_map[i][2]-1)
else:
editor.add_cell(i-1, cell_map[i][0]-1, cell_map[i][1]-1, cell_map[i][2]-1, cell_map[i][3]-1)
mesh.order()
mvc = mesh.domains().markers(dim-1)
for zone, cells in boundary_cells.iteritems():
for cell, nds in cells.iteritems():
dolfin_cell = Cell(mesh, cell-1)
nodes_of_cell = dolfin_cell.entities(0)
#print cell
#print nodes_of_cell
nodes_of_face = nds - 1
#print nodes_of_face
for jj, ff in enumerate(facets(dolfin_cell)):
facet_nodes = ff.entities(0)
#print facet_nodes
if all(map(lambda x: x in nodes_of_face, facet_nodes)):
local_index = jj
break
mvc.set_value(cell-1, local_index, zone)
ofile << mesh
from dolfin import plot
plot(mesh, interactive=True)
print 'Finished writing FEniCS mesh\n'
def _copy(self, deepcopy):
new_mesh = Mesh(self.mesh)
new_markerfunctions = {}
for dim, fun in ((0, "vfun"), (1, "ffun"), (2, "cfun")):
f_old = get_attribute(self, fun)
if f_old is None:
continue
f = MeshFunction("size_t", new_mesh, dim, new_mesh.domains())
f.set_values(f_old.array())
new_markerfunctions[fun] = f
markerfunctions = MarkerFunctions2D(**new_markerfunctions)
new_microstructure = {}
for field in ("f0", "s0", "n0"):
v0_old = get_attribute(self, field)
if v0_old is None:
continue
v0 = map_vector_field(v0_old, new_mesh)
new_microstructure[field] = v0
microstructure = Microstructure(**new_microstructure)
new_crl_basis = {}
for basis in ("c0", "r0", "l0"):
v0_old = get_attribute(self, basis)
if v0_old is None:
continue
v0 = map_vector_field(v0_old, new_mesh)
new_crl_basis[basis] = v0
crl_basis = CRLBasis(**new_crl_basis)
return dict(
mesh=new_mesh,
markers=self.markers,
markerfunctions=markerfunctions,
microstructure=microstructure,
crl_basis=crl_basis,
)
def test_convert_triangle(self): # Disabled because it fails, see FIXME below
# test no. 1
from dolfin import Mesh, MPI
if MPI.num_processes() != 1:
return
fname = os.path.join("data", "triangle")
dfname = fname+".xml"
# Read triangle file and convert to a dolfin xml mesh file
meshconvert.triangle2xml(fname, dfname)
# Read in dolfin mesh and check number of cells and vertices
mesh = Mesh(dfname)
self.assertEqual(mesh.num_vertices(), 96)
self.assertEqual(mesh.num_cells(), 159)
# Clean up
os.unlink(dfname)
# test no. 2
from dolfin import MPI, Mesh, MeshFunction, \
edges, Edge, faces, Face, \
SubsetIterator, facets, CellFunction
if MPI.num_processes() != 1:
return
fname = os.path.join("data", "test_Triangle_3")
dfname = fname+".xml"
dfname0 = fname+".attr0.xml"
# Read triangle file and convert to a dolfin xml mesh file
meshconvert.triangle2xml(fname, dfname)
# Read in dolfin mesh and check number of cells and vertices
mesh = Mesh(dfname)
mesh.init()
mfun = MeshFunction('double', mesh, dfname0)
self.assertEqual(mesh.num_vertices(), 58)
self.assertEqual(mesh.num_cells(), 58)
# Create a size_t CellFunction and assign the values based on the
# converted Meshfunction
cf = CellFunction("size_t", mesh)
cf.array()[mfun.array()==10.0] = 0
cf.array()[mfun.array()==-10.0] = 1
# Meassure total area of cells with 1 and 2 marker
add = lambda x, y : x+y
area0 = reduce(add, (Face(mesh, cell.index()).area() \
for cell in SubsetIterator(cf, 0)), 0.0)
area1 = reduce(add, (Face(mesh, cell.index()).area() \
for cell in SubsetIterator(cf, 1)), 0.0)
total_area = reduce(add, (face.area() for face in faces(mesh)), 0.0)
# Check that all cells in the two domains are either above or below y=0
self.assertTrue(all(cell.midpoint().y()<0 for cell in SubsetIterator(cf, 0)))
self.assertTrue(all(cell.midpoint().y()>0 for cell in SubsetIterator(cf, 1)))
# Check that the areas add up
self.assertAlmostEqual(area0+area1, total_area)
# Measure the edge length of the two edge domains
edge_markers = mesh.domains().facet_domains()
self.assertTrue(edge_markers is not None)
length0 = reduce(add, (Edge(mesh, e.index()).length() \
for e in SubsetIterator(edge_markers, 0)), 0.0)
length1 = reduce(add, (Edge(mesh, e.index()).length() \
for e in SubsetIterator(edge_markers, 1)), 0.0)
# Total length of all edges and total length of boundary edges
total_length = reduce(add, (e.length() for e in edges(mesh)), 0.0)
boundary_length = reduce(add, (Edge(mesh, f.index()).length() \
for f in facets(mesh) if f.exterior()), 0.0)
# Check that the edges add up
self.assertAlmostEqual(length0+length1, total_length)
self.assertAlmostEqual(length1, boundary_length)
# Clean up
os.unlink(dfname)
os.unlink(dfname0)
def load_geometry_from_h5(
h5name,
h5group="",
fendo=None,
fepi=None,
include_sheets=True,
comm=mpi_comm_world,
):
"""Load geometry and other mesh data from
a h5file to an object.
If the file contains muliple fiber fields
you can spefify the angles, and if the file
contais sheets and cross-sheets this can also
be included
:param str h5name: Name of the h5file
:param str h5group: The group within the file
:param int fendo: Helix fiber angle (endocardium) (if available)
:param int fepi: Helix fiber angle (epicardium) (if available)
:param bool include_sheets: Include sheets and cross-sheets
:returns: An object with geometry data
:rtype: object
"""
# Set default groups
ggroup = "{}/geometry".format(h5group)
mgroup = "{}/mesh".format(ggroup)
lgroup = "{}/local basis functions".format(h5group)
fgroup = "{}/microstructure".format(h5group)
if not os.path.isfile(h5name):
raise IOError("File {} does not exist".format(h5name))
# Check that the given file contains
# the geometry in the given h5group
if not check_h5group(h5name, mgroup, delete=False, comm=comm):
msg = ("Error!\nGroup: '{}' does not exist in file:"
"\n{}").format(mgroup, h5name)
with h5py.File(h5name) as h:
keys = h.keys()
msg += "\nPossible values for the h5group are {}".format(keys)
raise IOError(msg)
# Dummy class to store attributes in
class Geometry(object):
pass
geo = Geometry()
with HDF5File(comm, h5name, "r") as h5file:
# Load mesh
mesh = Mesh(comm)
h5file.read(mesh, mgroup, False)
geo.mesh = mesh
# Get mesh functions
meshfunctions = ["vfun", "efun", "ffun", "cfun"]\
if mesh.topology().dim() == 3 else ["vfun", "ffun", "cfun"]
for dim, attr in enumerate(meshfunctions):
dgroup = "{}/mesh/meshfunction_{}".format(ggroup, dim)
mf = MeshFunction("size_t", mesh, dim, mesh.domains())
if h5file.has_dataset(dgroup):
h5file.read(mf, dgroup)
setattr(geo, attr, mf)
load_local_basis(h5file, lgroup, mesh, geo)
load_microstructure(h5file, fgroup, mesh, geo, include_sheets)
# Load the boundary markers
markers = load_markers(h5file, mesh, ggroup, dgroup)
geo.markers = markers
origmeshgroup = "{}/original_geometry".format(h5group)
if h5file.has_dataset(origmeshgroup):
original_mesh = Mesh(comm)
h5file.read(original_mesh, origmeshgroup, True)
setattr(geo, "original_geometry", original_mesh)
for attr in meshfunctions:
if not hasattr(geo, attr):
setattr(geo, attr, None)
for attr in (["f0", "s0", "n0", "r0", "c0", "l0"]):
if not hasattr(geo, attr):
setattr(geo, attr, None)
return geo
def test_convert_triangle(
self): # Disabled because it fails, see FIXME below
# test no. 1
from dolfin import Mesh, MPI
fname = os.path.join(os.path.dirname(__file__), "data", "triangle")
dfname = fname + ".xml"
# Read triangle file and convert to a dolfin xml mesh file
meshconvert.triangle2xml(fname, dfname)
# Read in dolfin mesh and check number of cells and vertices
mesh = Mesh(dfname)
self.assertEqual(mesh.num_vertices(), 96)
self.assertEqual(mesh.num_cells(), 159)
# Clean up
os.unlink(dfname)
# test no. 2
from dolfin import MPI, Mesh, MeshFunction, \
edges, Edge, faces, Face, \
SubsetIterator, facets
fname = os.path.join(os.path.dirname(__file__), "data",
"test_Triangle_3")
dfname = fname + ".xml"
dfname0 = fname + ".attr0.xml"
# Read triangle file and convert to a dolfin xml mesh file
meshconvert.triangle2xml(fname, dfname)
# Read in dolfin mesh and check number of cells and vertices
mesh = Mesh(dfname)
mesh.init()
mfun = MeshFunction('double', mesh, dfname0)
self.assertEqual(mesh.num_vertices(), 58)
self.assertEqual(mesh.num_cells(), 58)
# Create a size_t MeshFunction and assign the values based on the
# converted Meshfunction
cf = MeshFunction("size_t", mesh, mesh.topology().dim())
cf.array()[mfun.array() == 10.0] = 0
cf.array()[mfun.array() == -10.0] = 1
# Meassure total area of cells with 1 and 2 marker
add = lambda x, y: x + y
area0 = reduce(add, (Face(mesh, cell.index()).area() \
for cell in SubsetIterator(cf, 0)), 0.0)
area1 = reduce(add, (Face(mesh, cell.index()).area() \
for cell in SubsetIterator(cf, 1)), 0.0)
total_area = reduce(add, (face.area() for face in faces(mesh)), 0.0)
# Check that all cells in the two domains are either above or below y=0
self.assertTrue(
all(cell.midpoint().y() < 0 for cell in SubsetIterator(cf, 0)))
self.assertTrue(
all(cell.midpoint().y() > 0 for cell in SubsetIterator(cf, 1)))
# Check that the areas add up
self.assertAlmostEqual(area0 + area1, total_area)
# Measure the edge length of the two edge domains
#edge_markers = mesh.domains().facet_domains()
edge_markers = mesh.domains().markers(mesh.topology().dim() - 1)
self.assertTrue(edge_markers is not None)
#length0 = reduce(add, (Edge(mesh, e.index()).length() \
# for e in SubsetIterator(edge_markers, 0)), 0.0)
length0, length1 = 0.0, 0.0
for item in list(edge_markers.items()):
if item[1] == 0:
e = Edge(mesh, int(item[0]))
length0 += Edge(mesh, int(item[0])).length()
elif item[1] == 1:
length1 += Edge(mesh, int(item[0])).length()
# Total length of all edges and total length of boundary edges
total_length = reduce(add, (e.length() for e in edges(mesh)), 0.0)
boundary_length = reduce(add, (Edge(mesh, f.index()).length() \
for f in facets(mesh) if f.exterior()), 0.0)
# Check that the edges add up
self.assertAlmostEqual(length0 + length1, total_length)
self.assertAlmostEqual(length1, boundary_length)
# Clean up
os.unlink(dfname)
os.unlink(dfname0)
def scalar_laplacians(
mesh: df.Mesh,
markers: Optional[Dict[str, int]] = None,
ffun: Optional[MeshFunction] = None,
use_krylov_solver: bool = False,
krylov_solver_atol: Optional[float] = None,
krylov_solver_rtol: Optional[float] = None,
krylov_solver_max_its: Optional[int] = None,
verbose: bool = False,
strict: bool = False,
) -> Dict[str, df.Function]:
"""
Calculate the laplacians
Arguments
---------
mesh : dolfin.Mesh
A dolfin mesh
markers : dict (optional)
A dictionary with the markers for the
different bondaries defined in the facet function
or within the mesh itself.
The follwing markers must be provided:
'base', 'lv', 'epi, 'rv' (optional).
If the markers are not provided the following default
vales will be used: base = 10, rv = 20, lv = 30, epi = 40.
fiber_space : str
A string on the form {familiy}_{degree} which
determines for what space the fibers should be calculated for.
use_krylov_solver: bool
If True use Krylov solver, by default False
krylov_solver_atol: float (optional)
If a Krylov solver is used, this option specifies a
convergence criterion in terms of the absolute
residual. Default: 1e-15.
krylov_solver_rtol: float (optional)
If a Krylov solver is used, this option specifies a
convergence criterion in terms of the relative
residual. Default: 1e-10.
krylov_solver_max_its: int (optional)
If a Krylov solver is used, this option specifies the
maximum number of iterations to perform. Default: 10000.
verbose: bool
If true, print more info, by default False
strict: bool
If true raise RuntimeError if solutions does not sum to 1.0
"""
if not isinstance(mesh, df.Mesh):
raise TypeError("Expected a dolfin.Mesh as the mesh argument.")
# Init connectivities
mesh.init(2)
if ffun is None:
ffun = df.MeshFunction("size_t", mesh, 2, mesh.domains())
# Boundary markers, solutions and cases
cases, boundaries, markers = find_cases_and_boundaries(ffun, markers)
markers_str = "\n".join(
["{}: {}".format(k, v) for k, v in markers.items()])
df.info(("Compute scalar laplacian solutions with the markers: \n"
"{}").format(markers_str, ), )
check_boundaries_are_marked(
mesh=mesh,
ffun=ffun,
markers=markers,
boundaries=boundaries,
)
# Compte the apex to base solutons
num_vertices = mesh.num_vertices()
num_cells = mesh.num_cells()
if mesh.mpi_comm().size > 1:
num_vertices = mesh.mpi_comm().allreduce(num_vertices)
num_cells = mesh.mpi_comm().allreduce(num_cells)
df.info(" Num vertices: {0}".format(num_vertices))
df.info(" Num cells: {0}".format(num_cells))
if "mv" in cases and "av" in cases:
# Use Doste approach
pass
# Else use the Bayer approach
return bayer(
cases=cases,
mesh=mesh,
markers=markers,
ffun=ffun,
verbose=verbose,
use_krylov_solver=use_krylov_solver,
strict=strict,
krylov_solver_atol=krylov_solver_atol,
krylov_solver_rtol=krylov_solver_rtol,
krylov_solver_max_its=krylov_solver_max_its,
)
def dolfin_ldrb(
mesh: df.Mesh,
fiber_space: str = "CG_1",
ffun: Optional[df.MeshFunction] = None,
markers: Optional[Dict[str, int]] = None,
log_level: int = logging.INFO,
use_krylov_solver: bool = False,
krylov_solver_atol: Optional[float] = None,
krylov_solver_rtol: Optional[float] = None,
krylov_solver_max_its: Optional[int] = None,
strict: bool = False,
save_markers: bool = False,
alpha_endo_lv: float = 40,
alpha_epi_lv: float = -50,
alpha_endo_rv: Optional[float] = None,
alpha_epi_rv: Optional[float] = None,
alpha_endo_sept: Optional[float] = None,
alpha_epi_sept: Optional[float] = None,
beta_endo_lv: float = -65,
beta_epi_lv: float = 25,
beta_endo_rv: Optional[float] = None,
beta_epi_rv: Optional[float] = None,
beta_endo_sept: Optional[float] = None,
beta_epi_sept: Optional[float] = None,
):
r"""
Create fiber, cross fibers and sheet directions
Arguments
---------
mesh : dolfin.Mesh
The mesh
fiber_space : str
A string on the form {familiy}_{degree} which
determines for what space the fibers should be calculated for.
If not provdied, then a first order Lagrange space will be used,
i.e Lagrange_1.
ffun : dolfin.MeshFunctionSizet (optional)
A facet function containing markers for the boundaries.
If not provided, the markers stored within the mesh will
be used.
markers : dict (optional)
A dictionary with the markers for the
different bondaries defined in the facet function
or within the mesh itself.
The follwing markers must be provided:
'base', 'lv', 'epi, 'rv' (optional).
If the markers are not provided the following default
vales will be used: base = 10, rv = 20, lv = 30, epi = 40
log_level : int
How much to print. DEBUG=10, INFO=20, WARNING=30.
Default: INFO
use_krylov_solver: bool
If True use Krylov solver, by default False
krylov_solver_atol: float (optional)
If a Krylov solver is used, this option specifies a
convergence criterion in terms of the absolute
residual. Default: 1e-15.
krylov_solver_rtol: float (optional)
If a Krylov solver is used, this option specifies a
convergence criterion in terms of the relative
residual. Default: 1e-10.
krylov_solver_max_its: int (optional)
If a Krylov solver is used, this option specifies the
maximum number of iterations to perform. Default: 10000.
strict: bool
If true raise RuntimeError if solutions does not sum to 1.0
save_markers: bool
If true save markings of the geometry. This is nice if you
want to see that the LV, RV and Septum are marked correctly.
angles : kwargs
Keyword arguments with the fiber and sheet angles.
It is possible to set different angles on the LV,
RV and septum, however it either the RV or septum
angles are not provided, then the angles on the LV
will be used. The default values are taken from the
original paper, namely
.. math::
\alpha_{\text{endo}} &= 40 \\
\alpha_{\text{epi}} &= -50 \\
\beta_{\text{endo}} &= -65 \\
\beta_{\text{epi}} &= 25
The following keyword arguments are possible:
alpha_endo_lv : scalar
Fiber angle at the LV endocardium.
alpha_epi_lv : scalar
Fiber angle at the LV epicardium.
beta_endo_lv : scalar
Sheet angle at the LV endocardium.
beta_epi_lv : scalar
Sheet angle at the LV epicardium.
alpha_endo_rv : scalar
Fiber angle at the RV endocardium.
alpha_epi_rv : scalar
Fiber angle at the RV epicardium.
beta_endo_rv : scalar
Sheet angle at the RV endocardium.
beta_epi_rv : scalar
Sheet angle at the RV epicardium.
alpha_endo_sept : scalar
Fiber angle at the septum endocardium.
alpha_epi_sept : scalar
Fiber angle at the septum epicardium.
beta_endo_sept : scalar
Sheet angle at the septum endocardium.
beta_epi_sept : scalar
Sheet angle at the septum epicardium.
"""
df.set_log_level(log_level)
if not isinstance(mesh, df.Mesh):
raise TypeError("Expected a dolfin.Mesh as the mesh argument.")
if ffun is None:
ffun = df.MeshFunction("size_t", mesh, 2, mesh.domains())
# Solve the Laplace-Dirichlet problem
verbose = log_level < logging.INFO
data = laplace(
mesh=mesh,
fiber_space=fiber_space,
markers=markers,
ffun=ffun,
use_krylov_solver=use_krylov_solver,
krylov_solver_atol=krylov_solver_atol,
krylov_solver_rtol=krylov_solver_rtol,
krylov_solver_max_its=krylov_solver_max_its,
verbose=verbose,
strict=strict,
)
dofs = dofs_from_function_space(mesh, fiber_space)
marker_scalar = np.zeros_like(data["lv_scalar"])
system = compute_fiber_sheet_system(
dofs=dofs,
marker_scalar=marker_scalar,
alpha_endo_lv=alpha_endo_lv,
alpha_epi_lv=alpha_epi_lv,
alpha_endo_rv=alpha_endo_rv,
alpha_epi_rv=alpha_epi_rv,
alpha_endo_sept=alpha_endo_sept,
alpha_epi_sept=alpha_epi_sept,
beta_endo_lv=beta_endo_lv,
beta_epi_lv=beta_epi_lv,
beta_endo_rv=beta_endo_rv,
beta_epi_rv=beta_epi_rv,
beta_endo_sept=beta_endo_sept,
beta_epi_sept=beta_epi_sept,
**data,
) # type:ignore
if save_markers:
Vv = utils.space_from_string(fiber_space, mesh, dim=1)
markers_fun = df.Function(Vv)
markers_fun.vector().set_local(marker_scalar)
markers_fun.vector().apply("insert")
df.File("markers.pvd") << markers_fun
df.set_log_level(log_level)
return fiber_system_to_dolfin(system, mesh, fiber_space)
def dolfin_ldrb(
mesh: df.Mesh,
fiber_space: str = "CG_1",
ffun: Optional[df.MeshFunction] = None,
markers: Optional[Dict[str, int]] = None,
log_level: int = logging.INFO,
use_krylov_solver: bool = False,
strict: bool = False,
**angles: Optional[float],
):
r"""
Create fiber, cross fibers and sheet directions
Arguments
---------
mesh : dolfin.Mesh
The mesh
fiber_space : str
A string on the form {familiy}_{degree} which
determines for what space the fibers should be calculated for.
If not provdied, then a first order Lagrange space will be used,
i.e Lagrange_1.
ffun : dolfin.MeshFunctionSizet (optional)
A facet function containing markers for the boundaries.
If not provided, the markers stored within the mesh will
be used.
markers : dict (optional)
A dictionary with the markers for the
different bondaries defined in the facet function
or within the mesh itself.
The follwing markers must be provided:
'base', 'lv', 'epi, 'rv' (optional).
If the markers are not provided the following default
vales will be used: base = 10, rv = 20, lv = 30, epi = 40
log_level : int
How much to print. DEBUG=10, INFO=20, WARNING=30.
Default: INFO
use_krylov_solver: bool
If True use Krylov solver, by default False
strict: bool
If true raise RuntimeError if solutions does not sum to 1.0
angles : kwargs
Keyword arguments with the fiber and sheet angles.
It is possible to set different angles on the LV,
RV and septum, however it either the RV or septum
angles are not provided, then the angles on the LV
will be used. The default values are taken from the
original paper, namely
.. math::
\alpha_{\text{endo}} &= 40 \\
\alpha_{\text{epi}} &= -50 \\
\beta_{\text{endo}} &= -65 \\
\beta_{\text{epi}} &= 25
The following keyword arguments are possible:
alpha_endo_lv : scalar
Fiber angle at the LV endocardium.
alpha_epi_lv : scalar
Fiber angle at the LV epicardium.
beta_endo_lv : scalar
Sheet angle at the LV endocardium.
beta_epi_lv : scalar
Sheet angle at the LV epicardium.
alpha_endo_rv : scalar
Fiber angle at the RV endocardium.
alpha_epi_rv : scalar
Fiber angle at the RV epicardium.
beta_endo_rv : scalar
Sheet angle at the RV endocardium.
beta_epi_rv : scalar
Sheet angle at the RV epicardium.
alpha_endo_sept : scalar
Fiber angle at the septum endocardium.
alpha_epi_sept : scalar
Fiber angle at the septum epicardium.
beta_endo_sept : scalar
Sheet angle at the septum endocardium.
beta_epi_sept : scalar
Sheet angle at the septum epicardium.
"""
df.set_log_level(log_level)
if not isinstance(mesh, df.Mesh):
raise TypeError("Expected a dolfin.Mesh as the mesh argument.")
if ffun is None:
ffun = df.MeshFunction("size_t", mesh, 2, mesh.domains())
# Solve the Laplace-Dirichlet problem
verbose = log_level < logging.INFO
data = laplace(
mesh=mesh,
fiber_space=fiber_space,
markers=markers,
ffun=ffun,
use_krylov_solver=use_krylov_solver,
verbose=verbose,
strict=strict,
)
dofs = dofs_from_function_space(mesh, fiber_space)
system = compute_fiber_sheet_system(dofs=dofs, **data,
**angles) # type:ignore
df.set_log_level(log_level)
return fiber_system_to_dolfin(system, mesh, fiber_space)