import collections
import itertools
import numpy
import os
import ufl
import finat.ufl
from ufl.domain import extract_unique_domain
from itertools import chain
from pyop2.mpi import COMM_WORLD, internal_comm
from pyop2.utils import as_tuple
from pyadjoint import no_annotations
from firedrake.petsc import PETSc
from firedrake.utils import IntType
from .paraview_reordering import *
__all__ = ("VTKFile", )
VTK_INTERVAL = 3
VTK_TRIANGLE = 5
VTK_QUADRILATERAL = 9
VTK_TETRAHEDRON = 10
VTK_HEXAHEDRON = 12
VTK_WEDGE = 13
# Lagrange VTK cells:
VTK_LAGRANGE_CURVE = 68
VTK_LAGRANGE_TRIANGLE = 69
VTK_LAGRANGE_QUADRILATERAL = 70
VTK_LAGRANGE_TETRAHEDRON = 71
VTK_LAGRANGE_HEXAHEDRON = 72
VTK_LAGRANGE_WEDGE = 73
ufl_quad = ufl.TensorProductCell(ufl.Cell("interval"),
ufl.Cell("interval"))
ufl_wedge = ufl.TensorProductCell(ufl.Cell("triangle"),
ufl.Cell("interval"))
ufl_hex = ufl.TensorProductCell(ufl.Cell("quadrilateral"),
ufl.Cell("interval"))
cells = {
(ufl.Cell("interval"), False): VTK_INTERVAL,
(ufl.Cell("interval"), True): VTK_LAGRANGE_CURVE,
(ufl.Cell("triangle"), False): VTK_TRIANGLE,
(ufl.Cell("triangle"), True): VTK_LAGRANGE_TRIANGLE,
(ufl.Cell("quadrilateral"), False): VTK_QUADRILATERAL,
(ufl.Cell("quadrilateral"), True): VTK_LAGRANGE_QUADRILATERAL,
(ufl_quad, True): VTK_LAGRANGE_QUADRILATERAL,
(ufl_quad, False): VTK_QUADRILATERAL,
(ufl.Cell("tetrahedron"), False): VTK_TETRAHEDRON,
(ufl.Cell("tetrahedron"), True): VTK_LAGRANGE_TETRAHEDRON,
(ufl_wedge, False): VTK_WEDGE,
(ufl_wedge, True): VTK_LAGRANGE_WEDGE,
(ufl_hex, False): VTK_HEXAHEDRON,
(ufl_hex, True): VTK_LAGRANGE_HEXAHEDRON,
(ufl.Cell("hexahedron"), False): VTK_HEXAHEDRON,
(ufl.Cell("hexahedron"), True): VTK_LAGRANGE_HEXAHEDRON,
}
OFunction = collections.namedtuple("OFunction", ["array", "name", "function"])
def is_cg(V):
"""Is the provided space continuous?
:arg V: A FunctionSpace.
"""
nvertex = V.mesh().ufl_cell().num_vertices()
entity_dofs = V.finat_element.entity_dofs()
# If there are as many dofs on vertices as there are vertices,
# assume a continuous space.
try:
return sum(map(len, entity_dofs[0].values())) == nvertex
except KeyError:
return sum(map(len, entity_dofs[(0, 0)].values())) == nvertex
def is_dg(V):
"""Is the provided space fully discontinuous?
:arg V: A FunctionSpace.
"""
return V.finat_element.entity_dofs() == V.finat_element.entity_closure_dofs()
def is_linear(V):
"""Is the provided space linear?
:arg V: A FunctionSpace.
"""
nvertex = V.mesh().ufl_cell().num_vertices()
return V.finat_element.space_dimension() == nvertex
def get_sup_element(*elements, continuous=False, max_degree=None):
"""Given ufl elements and a continuity flag, return
a new ufl element that contains all elements.
:arg elements: ufl elements.
:continous: A flag indicating if all elements are continous.
:returns: A ufl element containing all elements.
"""
try:
cell, = set(e.cell for e in elements)
except ValueError:
raise ValueError("All cells must be identical")
degree = max(chain(*(as_tuple(e.degree()) for e in elements)))
if continuous:
family = "CG"
else:
if cell.cellname() in {"interval", "triangle", "tetrahedron"}:
family = "DG"
else:
family = "DQ"
return finat.ufl.FiniteElement(
family, cell=cell, degree=degree if max_degree is None else max_degree,
variant="equispaced")
@PETSc.Log.EventDecorator()
def get_topology(coordinates):
r"""Get the topology for VTU output.
:arg coordinates: The coordinates defining the mesh.
:returns: A tuple of ``(connectivity, offsets, types)``
:class:`OFunction`\s.
"""
V = coordinates.function_space()
nonLinear = not is_linear(V)
mesh = V.mesh().topology
cell = mesh.ufl_cell()
values = V.cell_node_map().values
value_shape = values.shape
basis_dim = value_shape[1]
offsetMap = V.cell_node_map().offset
perm = None
# Non-simplex cells and non-linear cells need reordering
# Connectivity of bottom cell in extruded mesh
if cells[cell, nonLinear] == VTK_QUADRILATERAL:
# Quad is
#
# 1--3 3--2
# | | -> | |
# 0--2 0--1
values = values[:, [0, 2, 3, 1]]
elif cells[cell, nonLinear] == VTK_WEDGE:
# Wedge is
#
# 5 5
# /|\ /|\
# / | \ / | \
# 1----3 3----4
# | 4 | -> | 2 |
# | /\ | | /\ |
# |/ \| |/ \|
# 0----2 0----1
values = values[:, [0, 2, 4, 1, 3, 5]]
elif cells[cell, nonLinear] == VTK_HEXAHEDRON:
# Hexahedron is
#
# 5----7 7----6
# /| /| /| /|
# 4----6 | -> 4----5 |
# | 1--|-3 | 3--|-2
# |/ |/ |/ |/
# 0----2 0----1
values = values[:, [0, 2, 3, 1, 4, 6, 7, 5]]
elif cells[cell, nonLinear] == VTK_LAGRANGE_TETRAHEDRON:
perm = vtk_lagrange_tet_reorder(V.ufl_element())
values = values[:, perm]
elif cells[cell, nonLinear] == VTK_LAGRANGE_HEXAHEDRON:
perm = vtk_lagrange_hex_reorder(V.ufl_element())
values = values[:, perm]
elif cells[cell, nonLinear] == VTK_LAGRANGE_CURVE:
perm = vtk_lagrange_interval_reorder(V.ufl_element())
values = values[:, perm]
elif cells[cell, nonLinear] == VTK_LAGRANGE_TRIANGLE:
perm = vtk_lagrange_triangle_reorder(V.ufl_element())
values = values[:, perm]
elif cells[cell, nonLinear] == VTK_LAGRANGE_QUADRILATERAL:
perm = vtk_lagrange_quad_reorder(V.ufl_element())
values = values[:, perm]
elif cells[cell, nonLinear] == VTK_LAGRANGE_WEDGE:
perm = vtk_lagrange_wedge_reorder(V.ufl_element())
values = values[:, perm]
elif cells.get((cell, nonLinear)) is None:
# Never reached, but let's be safe.
raise ValueError("Unhandled cell type %r" % cell)
# Repeat up the column
num_cells = mesh.cell_set.size
if not mesh.cell_set._extruded:
cell_layers = 1
offsets = 0
else:
if perm is not None:
offsetMap = offsetMap[perm]
if mesh.variable_layers:
layers = mesh.cell_set.layers_array[:num_cells, ...]
cell_layers = layers[:, 1] - layers[:, 0] - 1
def vrange(cell_layers):
return numpy.repeat(cell_layers - cell_layers.cumsum(),
cell_layers) + numpy.arange(cell_layers.sum())
offsets = numpy.outer(vrange(cell_layers), offsetMap).astype(IntType)
num_cells = cell_layers.sum()
else:
cell_layers = mesh.cell_set.layers - 1
offsets = numpy.outer(numpy.arange(cell_layers, dtype=IntType), offsetMap)
offsets = numpy.tile(offsets, (num_cells, 1))
num_cells *= cell_layers
connectivity = numpy.repeat(values, cell_layers, axis=0)
# Add offsets going up the column
con = connectivity + offsets
connectivity = con.flatten()
if not nonLinear:
offsets_into_con = numpy.arange(start=cell.num_vertices(),
stop=cell.num_vertices() * (num_cells + 1),
step=cell.num_vertices(),
dtype=IntType)
else:
offsets_into_con = numpy.arange(start=basis_dim,
stop=basis_dim * (num_cells + 1),
step=basis_dim,
dtype=IntType)
cell_types = numpy.full(num_cells, cells[cell, nonLinear], dtype="uint8")
return (OFunction(connectivity, "connectivity", None),
OFunction(offsets_into_con, "offsets", None),
OFunction(cell_types, "types", None))
def get_byte_order(dtype):
import sys
native = {"little": "LittleEndian", "big": "BigEndian"}[sys.byteorder]
return {"=": native,
"|": "LittleEndian",
"<": "LittleEndian",
">": "BigEndian"}[dtype.byteorder]
def prepare_ofunction(ofunction, real):
array, name, _ = ofunction
if array.dtype.kind == "c":
if real:
arrays = (array.real, )
names = (name, )
else:
arrays = (array.real, array.imag)
names = (name + " (real part)", name + " (imaginary part)")
else:
arrays = (array, )
names = (name,)
return arrays, names
def write_array(f, ofunction, real=False):
arrays, _ = prepare_ofunction(ofunction, real=real)
for array in arrays:
numpy.uint32(array.nbytes).tofile(f)
if get_byte_order(array.dtype) == "BigEndian":
array = array.byteswap()
array.tofile(f)
def write_array_descriptor(f, ofunction, offset=None, parallel=False, real=False):
arrays, names = prepare_ofunction(ofunction, real)
nbytes = 0
for array, name in zip(arrays, names):
shape = array.shape[1:]
ncmp = {0: "",
1: "3",
2: "9"}[len(shape)]
typ = {numpy.dtype("float32"): "Float32",
numpy.dtype("float64"): "Float64",
numpy.dtype("int32"): "Int32",
numpy.dtype("int64"): "Int64",
numpy.dtype("uint8"): "UInt8"}[array.dtype]
if parallel:
f.write(('<PDataArray Name="%s" type="%s" '
'NumberOfComponents="%s" />' % (name, typ, ncmp)).encode('ascii'))
else:
if offset is None:
raise ValueError("Must provide offset")
offset += nbytes
nbytes += (4 + array.nbytes) # 4 is for the array size (uint32)
f.write(('<DataArray Name="%s" type="%s" '
'NumberOfComponents="%s" '
'format="appended" '
'offset="%d" />\n' % (name, typ, ncmp, offset)).encode('ascii'))
return nbytes
def active_field_attributes(ofunctions):
# select first function of each rank present as "active field"
# and return the corresponding attributes for the (P)PointData element
s = ''
ranks = set()
for ofunction in ofunctions:
array, name, _ = ofunction
rank = len(array.shape[1:])
if rank in ranks:
continue
ranks.add(rank)
if rank == 0:
s += ' Scalars="%s"' % name
elif rank == 1:
s += ' Vectors="%s"' % name
elif rank == 2:
s += ' Tensors="%s"' % name
return s.encode('ascii')
def get_vtu_name(basename, rank, size):
if size == 1:
return "%s.vtu" % basename
else:
return "%s_%s.vtu" % (basename, rank)
def get_pvtu_name(basename):
return "%s.pvtu" % basename
def get_array(function):
shape = function.ufl_shape
# Despite not writing connectivity data in the halo, we need to
# write data arrays in the halo because the cell node map for
# owned cells can index into ghost data.
array = function.dat.data_ro_with_halos
if len(shape) == 0:
pass
elif len(shape) == 1:
# Vectors must be padded to three components
reshape = (-1, ) + shape
if shape != (3, ):
array = numpy.pad(array.reshape(reshape), ((0, 0), (0, 3 - shape[0])),
mode="constant")
elif len(shape) == 2:
# Tensors must be padded to 3x3.
reshape = (-1, ) + shape
if shape != (3, 3):
array = numpy.pad(array.reshape(reshape), ((0, 0), (0, 3 - shape[0]), (0, 3 - shape[1])),
mode="constant")
else:
raise ValueError("Can't write data with shape %s" % (shape, ))
return array
[docs]
class VTKFile(object):
_header = (b'<?xml version="1.0" ?>\n'
b'<VTKFile type="Collection" version="0.1" '
b'byte_order="LittleEndian">\n'
b'<Collection>\n')
_footer = (b'</Collection>\n'
b'</VTKFile>\n')
def __init__(self, filename, project_output=False, comm=None, mode="w",
target_degree=None, target_continuity=None, adaptive=False):
"""Create an object for outputting data for visualisation.
This produces output in VTU format, suitable for visualisation
with Paraview or other VTK-capable visualisation packages.
:arg filename: The name of the output file (must end in
``.pvd``).
:kwarg project_output: Should the output be projected to
a computed output space? Default is to use interpolation.
:kwarg comm: The MPI communicator to use.
:kwarg mode: "w" to overwrite any existing file, "a" to append to an existing file.
:kwarg target_degree: override the degree of the output space.
:kwarg target_continuity: override the continuity of the output space;
A UFL :class:`ufl.sobolevspace.SobolevSpace` object: `H1` for a
continuous output and `L2` for a discontinuous output.
:kwarg adaptive: allow different meshes at different exports if `True`.
.. note::
Visualisation is only possible for Lagrange fields (either
continuous or discontinuous). All other fields are first
either projected or interpolated to Lagrange elements
before storing for visualisation purposes.
"""
filename = os.path.abspath(filename)
basename, ext = os.path.splitext(filename)
if ext not in (".pvd", ):
raise ValueError("Only output to PVD is supported")
if mode not in ["w", "a"]:
raise ValueError("Mode must be 'a' or 'w'")
if mode == "a" and not os.path.isfile(filename):
mode = "w"
self.comm = comm or COMM_WORLD
self._comm = internal_comm(self.comm, self)
if self._comm.rank == 0 and mode == "w":
if not os.path.exists(basename):
os.makedirs(basename)
elif self._comm.rank == 0 and mode == "a":
if not os.path.exists(os.path.abspath(filename)):
raise ValueError("Need a file to restart from.")
self._comm.barrier()
self.filename = filename
self.basename = basename
# The vtu files will be in the subdirectory named same with the pvd file.
# Assuming the absolute path of the pvd file is "/path/to/foo.pvd", the vtu
# files will be in the subdirectory "foo" like this:
#
# /path/to/foo/foo_0.vtu
# /path/to/foo/foo_1.vtu
#
# The basename for this example is `/path/to/foo`, and the vtu_basename
# is `/path/to/foo/foo`.
self.vtu_basename = os.path.join(basename, os.path.basename(basename))
self.project = project_output
self.target_degree = target_degree
self.target_continuity = target_continuity
if target_degree is not None and target_degree < 0:
raise ValueError("Invalid target_degree")
if target_continuity is not None and target_continuity not in {ufl.H1, ufl.L2}:
raise ValueError("target_continuity must be either 'H1' or 'L2'.")
countstart = 0
if self._comm.rank == 0 and mode == "w":
with open(self.filename, "wb") as f:
f.write(self._header)
f.write(self._footer)
elif self._comm.rank == 0 and mode == "a":
import xml.etree.ElementTree as ElTree
tree = ElTree.parse(os.path.abspath(filename))
# Count how many the file already has
for parent in tree.iter():
for child in list(parent):
if child.tag != "DataSet":
continue
countstart += 1
if mode == "a":
# Need to communicate the count across all cores involved; default op is SUM
countstart = self._comm.allreduce(countstart)
self.counter = itertools.count(countstart)
self.timestep = itertools.count(countstart)
self._fnames = None
self._topology = None
self._adaptive = adaptive
@no_annotations
def _prepare_output(self, function, max_elem):
from firedrake import FunctionSpace, VectorFunctionSpace, \
TensorFunctionSpace, Function
name = function.name()
# Need to project/interpolate?
# If space is not the max element, we must do so.
if function.function_space().ufl_element() == max_elem:
return OFunction(array=get_array(function),
name=name, function=function)
# OK, let's go and do it.
# Build appropriate space for output function.
shape = function.ufl_shape
if len(shape) == 0:
V = FunctionSpace(extract_unique_domain(function), max_elem)
elif len(shape) == 1:
if numpy.prod(shape) > 3:
raise ValueError("Can't write vectors with more than 3 components")
V = VectorFunctionSpace(extract_unique_domain(function), max_elem,
dim=shape[0])
elif len(shape) == 2:
if numpy.prod(shape) > 9:
raise ValueError("Can't write tensors with more than 9 components")
V = TensorFunctionSpace(extract_unique_domain(function), max_elem,
shape=shape)
else:
raise ValueError("Unsupported shape %s" % (shape, ))
output = Function(V)
if self.project:
output.project(function)
else:
output.interpolate(function)
return OFunction(array=get_array(output), name=name, function=output)
def _write_vtu(self, *functions):
from firedrake.function import Function
# Check if the user has requested to write out a plain mesh
if len(functions) == 1 and isinstance(functions[0], ufl.Mesh):
from firedrake.functionspace import FunctionSpace
mesh = functions[0]
V = FunctionSpace(mesh, "CG", 1)
functions = [Function(V)]
for f in functions:
if not isinstance(f, Function):
raise ValueError("Can only output Functions or a single mesh, not %r" % type(f))
meshes = tuple(extract_unique_domain(f) for f in functions)
if not all(m == meshes[0] for m in meshes):
raise ValueError("All functions must be on same mesh")
mesh = meshes[0]
cell = mesh.topology.ufl_cell()
if (cell, True) not in cells and (cell, False) not in cells:
raise ValueError("Unhandled cell type %r" % cell)
if self._fnames is not None:
if tuple(f.name() for f in functions) != self._fnames:
raise ValueError("Writing different set of functions")
else:
self._fnames = tuple(f.name() for f in functions)
continuous = all(is_cg(f.function_space()) for f in functions) and \
is_cg(mesh.coordinates.function_space())
if self.target_continuity is not None:
continuous = self.target_continuity == ufl.H1
# Since Points define nodes for both the mesh and function, we must
# interpolate/project ALL involved elements onto a single larger
# finite element.
mesh_elem = mesh.coordinates.ufl_element()
max_elem = get_sup_element(mesh_elem, *(f.ufl_element()
for f in functions),
continuous=continuous,
max_degree=self.target_degree)
coordinates = self._prepare_output(mesh.coordinates, max_elem)
functions = tuple(self._prepare_output(f, max_elem)
for f in functions)
if self._topology is None or self._adaptive:
self._topology = get_topology(coordinates.function)
basename = f"{self.vtu_basename}_{next(self.counter)}"
vtu = self._write_single_vtu(basename, coordinates, *functions)
if self.comm.size > 1:
vtu = self._write_single_pvtu(basename, coordinates, *functions)
return vtu
def _write_single_vtu(self, basename,
coordinates,
*functions):
connectivity, offsets, types = self._topology
num_points = coordinates.array.shape[0]
num_cells = types.array.shape[0]
fname = get_vtu_name(basename, self.comm.rank, self.comm.size)
with open(fname, "wb") as f:
# Running offset for appended data
offset = 0
f.write(b'<?xml version="1.0" ?>\n')
f.write(b'<VTKFile type="UnstructuredGrid" version="2.2" '
b'byte_order="LittleEndian" '
b'header_type="UInt32">\n')
f.write(b'<UnstructuredGrid>\n')
f.write(('<Piece NumberOfPoints="%d" '
'NumberOfCells="%d">\n' % (num_points, num_cells)).encode('ascii'))
f.write(b'<Points>\n')
# Vertex coordinates
offset += write_array_descriptor(f, coordinates, offset=offset, real=True)
f.write(b'</Points>\n')
f.write(b'<Cells>\n')
offset += write_array_descriptor(f, connectivity, offset=offset)
offset += write_array_descriptor(f, offsets, offset=offset)
offset += write_array_descriptor(f, types, offset=offset)
f.write(b'</Cells>\n')
f.write(b'<PointData%s>\n' % active_field_attributes(functions))
for function in functions:
offset += write_array_descriptor(f, function, offset=offset)
f.write(b'</PointData>\n')
f.write(b'</Piece>\n')
f.write(b'</UnstructuredGrid>\n')
f.write(b'<AppendedData encoding="raw">\n')
# Appended data must start with "_", separating whitespace
# from data
f.write(b'_')
write_array(f, coordinates, real=True)
write_array(f, connectivity)
write_array(f, offsets)
write_array(f, types)
for function in functions:
write_array(f, function)
f.write(b'\n</AppendedData>\n')
f.write(b'</VTKFile>\n')
return fname
def _write_single_pvtu(self, basename,
coordinates,
*functions):
connectivity, offsets, types = self._topology
fname = get_pvtu_name(basename)
with open(fname, "wb") as f:
f.write(b'<?xml version="1.0" ?>\n')
f.write(b'<VTKFile type="PUnstructuredGrid" version="2.2" '
b'byte_order="LittleEndian">\n')
f.write(b'<PUnstructuredGrid>\n')
f.write(b'<PPoints>\n')
# Vertex coordinates
write_array_descriptor(f, coordinates, parallel=True, real=True)
f.write(b'</PPoints>\n')
f.write(b'<PCells>\n')
write_array_descriptor(f, connectivity, parallel=True)
write_array_descriptor(f, offsets, parallel=True)
write_array_descriptor(f, types, parallel=True)
f.write(b'</PCells>\n')
f.write(b'<PPointData%s>\n' % active_field_attributes(functions))
for function in functions:
write_array_descriptor(f, function, parallel=True)
f.write(b'</PPointData>\n')
size = self.comm.size
for rank in range(size):
# need a relative path so files can be moved around:
vtu_name = os.path.relpath(get_vtu_name(basename, rank, size),
os.path.dirname(self.vtu_basename))
f.write(('<Piece Source="%s" />\n' % vtu_name).encode('ascii'))
f.write(b'</PUnstructuredGrid>\n')
f.write(b'</VTKFile>\n')
return fname
[docs]
@PETSc.Log.EventDecorator()
def write(self, *functions, **kwargs):
"""Write functions to this :class:`VTKFile`.
:arg functions: list of functions to write.
:kwarg time: optional timestep value.
You may save more than one function to the same file.
However, all calls to :meth:`write` must use the same set of
functions.
"""
time = kwargs.get("time", None)
vtu = self._write_vtu(*functions)
if time is None:
time = next(self.timestep)
# Write into collection as relative path, so we can move
# things around.
vtu = os.path.relpath(vtu, os.path.dirname(self.basename))
if self.comm.rank == 0:
with open(self.filename, "r+b") as f:
# Seek backwards from end to beginning of footer
f.seek(-len(self._footer), 2)
# Write new dataset name
f.write(('<DataSet timestep="%s" '
'file="%s" />\n' % (time, vtu)).encode('ascii'))
# And add footer again, so that the file is valid
f.write(self._footer)
