import numpy
from functools import partial, singledispatch
import os
import tempfile
import abc
import FIAT
import ufl
import finat.ufl
from ufl.algorithms import extract_arguments, extract_coefficients, replace
from ufl.algorithms.signature import compute_expression_signature
from ufl.domain import as_domain, extract_unique_domain
from pyop2 import op2
from pyop2.caching import memory_and_disk_cache
from tsfc.finatinterface import create_element, as_fiat_cell
from tsfc import compile_expression_dual_evaluation
from tsfc.ufl_utils import extract_firedrake_constants
import gem
import finat
import firedrake
from firedrake import tsfc_interface, utils, functionspaceimpl
from firedrake.ufl_expr import Argument, action, adjoint
from firedrake.mesh import MissingPointsBehaviour, VertexOnlyMeshMissingPointsError
from firedrake.petsc import PETSc
from firedrake.halo import _get_mtype as get_dat_mpi_type
from mpi4py import MPI
from pyadjoint import stop_annotating, no_annotations
__all__ = (
"interpolate",
"Interpolator",
"Interpolate",
"DofNotDefinedError",
"CrossMeshInterpolator",
"SameMeshInterpolator",
)
[docs]
class Interpolate(ufl.Interpolate):
def __init__(self, expr, v,
subset=None,
access=op2.WRITE,
allow_missing_dofs=False,
default_missing_val=None):
"""Symbolic representation of the interpolation operator.
Parameters
----------
expr : ufl.core.expr.Expr or ufl.BaseForm
The UFL expression to interpolate.
v : firedrake.functionspaceimpl.WithGeometryBase or firedrake.ufl_expr.Coargument
The function space to interpolate into or the coargument defined
on the dual of the function space to interpolate into.
subset : pyop2.types.set.Subset
An optional subset to apply the interpolation over.
Cannot, at present, be used when interpolating across meshes unless
the target mesh is a :func:`.VertexOnlyMesh`.
access : pyop2.types.access.Access
The pyop2 access descriptor for combining updates to shared
DoFs. Possible values include ``WRITE`` and ``INC``. Only ``WRITE`` is
supported at present when interpolating across meshes. See note in
:func:`.interpolate` if changing this from default.
allow_missing_dofs : bool
For interpolation across meshes: allow degrees of freedom (aka DoFs/nodes)
in the target mesh that cannot be defined on the source mesh.
For example, where nodes are point evaluations, points in the target mesh
that are not in the source mesh. When ``False`` this raises a ``ValueError``
should this occur. When ``True`` the corresponding values are either
(a) unchanged if some ``output`` is given to the :meth:`interpolate` method
or (b) set to zero.
Can be overwritten with the ``default_missing_val`` kwarg of :meth:`interpolate`.
This does not affect transpose interpolation. Ignored if interpolating within
the same mesh or onto a :func:`.VertexOnlyMesh` (the behaviour of a
:func:`.VertexOnlyMesh` in this scenario is, at present, set when it is created).
default_missing_val : float
For interpolation across meshes: the optional value to assign to DoFs
in the target mesh that are outside the source mesh. If this is not set
then the values are either (a) unchanged if some ``output`` is given to
the :meth:`interpolate` method or (b) set to zero.
Ignored if interpolating within the same mesh or onto a :func:`.VertexOnlyMesh`.
"""
# Check function space
if isinstance(v, functionspaceimpl.WithGeometry):
v = Argument(v.dual(), 0)
# Get the primal space (V** = V)
vv = v if not isinstance(v, ufl.Form) else v.arguments()[0]
self._function_space = vv.function_space().dual()
super().__init__(expr, v)
# -- Interpolate data (e.g. `subset` or `access`) -- #
self.interp_data = {"subset": subset,
"access": access,
"allow_missing_dofs": allow_missing_dofs,
"default_missing_val": default_missing_val}
[docs]
def function_space(self):
return self._function_space
def _ufl_expr_reconstruct_(self, expr, v=None, **interp_data):
interp_data = interp_data or self.interp_data.copy()
return ufl.Interpolate._ufl_expr_reconstruct_(self, expr, v=v, **interp_data)
# Current behaviour of interpolation in Firedrake:
# - v.interpolate(expr),
# interpolate(expr, v),
# Interpolator(expr, v).interpolate(),
# v = interpolate(expr, V) and
# Interpolator(expr, V).interpolate(v)
# - Works with UFL expressions which contain no UFL Arguments. The
# expression can contain functions (UFL Coefficients) from other
# function spaces which will be interpolated into V.
# - Either operates on a function v in V (UFL Coefficient) or outputs a
# function in V.
# - Maths: v = A(expr) where A : W_0 x ... x W_n-1 -> V
# - NOTE: this will seem to work on assembled 1-forms (cofunctions) but
# is mathematical nonsense due to the absence of UFL Cofunctions in
# Firedrake. See
# https://github.com/firedrakeproject/firedrake/issues/3017
# - B = Interpolator(expr_1_argument, V)
# - creates the linear interpolation operator B : W -> V where the UFL
# Argument is linear in the expression and is in W. The UFL Argument must
# be number 0 (i.e. TestFunction(W) rather than TrialFunction(W)).
# - The rest of the expression, including any functions (UFL
# Coefficients), are already interpolated into V and are encorporated
# in the operator.
# - NOTE: Nonlinear Arguments are currently allowed in the expression and
# shouldn't be. See
# https://github.com/firedrakeproject/firedrake/issues/3018
# - w = B.interpolate(v)
# - v is a function in V (NOT an expression).
# - w is a function in W.
# - Maths: v = Bw
# - v_star = B.interpolate(w_star, transpose = True)
# - w_star is a cofunction in W^* (such as an assembled 1-form).
# - v_star is a cofunction in V^*.
# - Maths: v^* = B^* w^*
[docs]
@PETSc.Log.EventDecorator()
def interpolate(
expr,
V,
subset=None,
access=op2.WRITE,
allow_missing_dofs=False,
default_missing_val=None,
ad_block_tag=None
):
"""Interpolate an expression onto a new function in V.
:arg expr: a UFL expression.
:arg V: the :class:`.FunctionSpace` to interpolate into (or else
an existing :class:`.Function`).
:kwarg subset: An optional :class:`pyop2.types.set.Subset` to apply the
interpolation over. Cannot, at present, be used when interpolating
across meshes unless the target mesh is a :func:`.VertexOnlyMesh`.
:kwarg access: The pyop2 access descriptor for combining updates to shared
DoFs. Possible values include ``WRITE`` and ``INC``. Only ``WRITE`` is
supported at present when interpolating across meshes unless the target
mesh is a :func:`.VertexOnlyMesh`. See note below.
:kwarg allow_missing_dofs: For interpolation across meshes: allow
degrees of freedom (aka DoFs/nodes) in the target mesh that cannot be
defined on the source mesh. For example, where nodes are point
evaluations, points in the target mesh that are not in the source mesh.
When ``False`` this raises a ``ValueError`` should this occur. When
``True`` the corresponding values are either (a) unchanged if
some ``output`` is given to the :meth:`interpolate` method or (b) set
to zero. In either case, if ``default_missing_val`` is specified, that
value is used. This does not affect transpose interpolation. Ignored if
interpolating within the same mesh or onto a :func:`.VertexOnlyMesh`
(the behaviour of a :func:`.VertexOnlyMesh` in this scenario is, at
present, set when it is created).
:kwarg default_missing_val: For interpolation across meshes: the optional
value to assign to DoFs in the target mesh that are outside the source
mesh. If this is not set then the values are either (a) unchanged if
some ``output`` is given to the :meth:`interpolate` method or (b) set
to zero. Ignored if interpolating within the same mesh or onto a
:func:`.VertexOnlyMesh`.
:kwarg ad_block_tag: An optional string for tagging the resulting assemble block on the Pyadjoint tape.
:returns: a new :class:`.Function` in the space ``V`` (or ``V`` if
it was a Function).
.. note::
If you use an access descriptor other than ``WRITE``, the
behaviour of interpolation is changes if interpolating into a
function space, or an existing function. If the former, then
the newly allocated function will be initialised with
appropriate values (e.g. for MIN access, it will be initialised
with MAX_FLOAT). On the other hand, if you provide a function,
then it is assumed that its values should take part in the
reduction (hence using MIN will compute the MIN between the
existing values and any new values).
.. note::
If you find interpolating the same expression again and again
(for example in a time loop) you may find you get better
performance by using an :class:`Interpolator` instead.
"""
return Interpolator(
expr, V, subset=subset, access=access, allow_missing_dofs=allow_missing_dofs
).interpolate(default_missing_val=default_missing_val, ad_block_tag=ad_block_tag)
[docs]
class Interpolator(abc.ABC):
"""A reusable interpolation object.
:arg expr: The expression to interpolate.
:arg V: The :class:`.FunctionSpace` or :class:`.Function` to
interpolate into.
:kwarg subset: An optional :class:`pyop2.types.set.Subset` to apply the
interpolation over. Cannot, at present, be used when interpolating
across meshes unless the target mesh is a :func:`.VertexOnlyMesh`.
:kwarg freeze_expr: Set to True to prevent the expression being
re-evaluated on each call. Cannot, at present, be used when
interpolating across meshes unless the target mesh is a
:func:`.VertexOnlyMesh`.
:kwarg access: The pyop2 access descriptor for combining updates to shared
DoFs. Possible values include ``WRITE`` and ``INC``. Only ``WRITE`` is
supported at present when interpolating across meshes. See note in
:func:`.interpolate` if changing this from default.
:kwarg bcs: An optional list of boundary conditions to zero-out in the
output function space. Interpolator rows or columns which are
associated with boundary condition nodes are zeroed out when this is
specified.
:kwarg allow_missing_dofs: For interpolation across meshes: allow
degrees of freedom (aka DoFs/nodes) in the target mesh that cannot be
defined on the source mesh. For example, where nodes are point
evaluations, points in the target mesh that are not in the source mesh.
When ``False`` this raises a ``ValueError`` should this occur. When
``True`` the corresponding values are either (a) unchanged if
some ``output`` is given to the :meth:`interpolate` method or (b) set
to zero. Can be overwritten with the ``default_missing_val`` kwarg
of :meth:`interpolate`. This does not affect transpose interpolation.
Ignored if interpolating within the same mesh or onto a
:func:`.VertexOnlyMesh` (the behaviour of a :func:`.VertexOnlyMesh` in
this scenario is, at present, set when it is created).
This object can be used to carry out the same interpolation
multiple times (for example in a timestepping loop).
.. note::
The :class:`Interpolator` holds a reference to the provided
arguments (such that they won't be collected until the
:class:`Interpolator` is also collected).
"""
def __new__(cls, expr, V, **kwargs):
target_mesh = as_domain(V)
source_mesh = extract_unique_domain(expr) or target_mesh
if target_mesh is source_mesh or all(isinstance(m.topology, firedrake.mesh.MeshTopology) for m in [target_mesh, source_mesh]) and target_mesh.submesh_ancesters[-1] is source_mesh.submesh_ancesters[-1]:
return object.__new__(SameMeshInterpolator)
else:
if isinstance(target_mesh.topology, firedrake.mesh.VertexOnlyMeshTopology):
return object.__new__(SameMeshInterpolator)
else:
return object.__new__(CrossMeshInterpolator)
def __init__(
self,
expr,
V,
subset=None,
freeze_expr=False,
access=op2.WRITE,
bcs=None,
allow_missing_dofs=False,
):
self.expr = expr
self.V = V
self.subset = subset
self.freeze_expr = freeze_expr
self.access = access
self.bcs = bcs
self._allow_missing_dofs = allow_missing_dofs
self.callable = None
# Cope with the different convention of `Interpolate` and `Interpolator`:
# -> Interpolate(Argument(V1, 1), Argument(V2.dual(), 0))
# -> Interpolator(Argument(V1, 0), V2)
expr_args = extract_arguments(expr)
if expr_args and expr_args[0].number() == 0:
v, = expr_args
expr = replace(expr, {v: Argument(v.function_space(),
number=1,
part=v.part())})
self.expr_renumbered = expr
def _interpolate_future(self, *function, transpose=False, default_missing_val=None):
"""Define the :class:`Interpolate` object corresponding to the interpolation operation of interest.
Parameters
----------
*function: firedrake.function.Function or firedrake.cofunction.Cofunction
If the expression being interpolated contains an argument,
then the function value to interpolate.
transpose: bool
Set to true to apply the transpose (adjoint) of the
interpolation operator.
default_missing_val: bool
For interpolation across meshes: the
optional value to assign to DoFs in the target mesh that are
outside the source mesh. If this is not set then the values are
either (a) unchanged if some ``output`` is specified to the
:meth:`interpolate` method or (b) set to zero. This does not affect
transpose interpolation. Ignored if interpolating within the same
mesh or onto a :func:`.VertexOnlyMesh`.
Returns
-------
firedrake.interpolation.Interpolate or ufl.action.Action or ufl.adjoint.Adjoint
The symbolic object representing the interpolation operation.
Notes
-----
This method is the default future behaviour of interpolation. In a future release, the
``Interpolator.interpolate`` method will be replaced by this method.
"""
V = self.V
if isinstance(V, firedrake.Function):
V = V.function_space()
interp = Interpolate(self.expr_renumbered, V,
subset=self.subset,
access=self.access,
allow_missing_dofs=self._allow_missing_dofs,
default_missing_val=default_missing_val)
if transpose:
interp = adjoint(interp)
if function:
f, = function
# Passing in a function is equivalent to taking the action.
interp = action(interp, f)
# Return the `ufl.Interpolate` object
return interp
[docs]
@PETSc.Log.EventDecorator()
def interpolate(self, *function, output=None, transpose=False, default_missing_val=None,
ad_block_tag=None):
"""Compute the interpolation by assembling the appropriate :class:`Interpolate` object.
Parameters
----------
*function: firedrake.function.Function or firedrake.cofunction.Cofunction
If the expression being interpolated contains an argument,
then the function value to interpolate.
output: firedrake.function.Function or firedrake.cofunction.Cofunction
A function to contain the output.
transpose: bool
Set to true to apply the transpose (adjoint) of the
interpolation operator.
default_missing_val: bool
For interpolation across meshes: the
optional value to assign to DoFs in the target mesh that are
outside the source mesh. If this is not set then the values are
either (a) unchanged if some ``output`` is specified to the
:meth:`interpolate` method or (b) set to zero. This does not affect
transpose interpolation. Ignored if interpolating within the same
mesh or onto a :func:`.VertexOnlyMesh`.
ad_block_tag: str
An optional string for tagging the resulting assemble block on the Pyadjoint tape.
Returns
-------
firedrake.function.Function or firedrake.cofunction.Cofunction
The resulting interpolated function.
"""
import warnings
from firedrake.assemble import assemble
warnings.warn("""The use of `interpolate` to perform the numerical interpolation is deprecated.
This feature will be removed very shortly.
Instead, import `interpolate` from the `firedrake.__future__` module to update
the interpolation's behaviour to return the symbolic `ufl.Interpolate` object associated
with this interpolation.
You can then assemble the resulting object to get the interpolated quantity
of interest. For example,
```
from firedrake.__future__ import interpolate
...
assemble(interpolate(expr, V))
```
Alternatively, you can also perform other symbolic operations on the interpolation operator, such as taking
the derivative, and then assemble the resulting form.
""", FutureWarning)
# Get the Interpolate object
interp = self._interpolate_future(*function, transpose=transpose,
default_missing_val=default_missing_val)
if isinstance(self.V, firedrake.Function) and not output:
# V can be the Function to interpolate into (e.g. see `Function.interpolate``).
output = self.V
# Assemble the `ufl.Interpolate` object, which will then call `Interpolator._interpolate`
# to perform the interpolation. Having this structure ensures consistency between
# `Interpolator` and `Interp`. This mechanism handles annotation since performing interpolation will drop an
# `AssembleBlock` on the tape.
return assemble(interp, tensor=output, ad_block_tag=ad_block_tag)
@abc.abstractmethod
def _interpolate(self, *args, **kwargs):
"""
Compute the interpolation operation of interest.
.. note::
This method is called when an :class:`Interpolate` object is being assembled.
For instance, calling ``Interpolator.interpolate`` results in defining an :class:`Interpolate`
object and assembling it, which in turn calls this method.
"""
pass
[docs]
class DofNotDefinedError(Exception):
r"""Raised when attempting to interpolate across function spaces where the
target function space contains degrees of freedom (i.e. nodes) which cannot
be defined in the source function space. This typically occurs when the
target mesh covers a larger domain than the source mesh.
Attributes
----------
src_mesh : :func:`.Mesh`
The source mesh.
dest_mesh : :func:`.Mesh`
The destination mesh.
"""
def __init__(self, src_mesh, dest_mesh):
self.src_mesh = src_mesh
self.dest_mesh = dest_mesh
def __str__(self):
return (
f"The given target function space on domain {repr(self.dest_mesh)} "
"contains degrees of freedom which cannot cannot be defined in the "
f"source function space on domain {repr(self.src_mesh)}. "
"This may be because the target mesh covers a larger domain than the "
"source mesh. To disable this error, set allow_missing_dofs=True."
)
[docs]
class CrossMeshInterpolator(Interpolator):
"""
Interpolate a function from one mesh and function space to another.
For arguments, see :class:`.Interpolator`.
"""
@no_annotations
def __init__(
self,
expr,
V,
subset=None,
freeze_expr=False,
access=op2.WRITE,
bcs=None,
allow_missing_dofs=False,
):
if subset:
raise NotImplementedError("subset not implemented")
if freeze_expr:
# Probably just need to pass freeze_expr to the various
# interpolators for this to work.
raise NotImplementedError("freeze_expr not implemented")
if access != op2.WRITE:
raise NotImplementedError("access other than op2.WRITE not implemented")
if bcs:
raise NotImplementedError("bcs not implemented")
if V.ufl_element().mapping() != "identity":
# Identity mapping between reference cell and physical coordinates
# implies point evaluation nodes. A more general version would
# require finding the global coordinates of all quadrature points
# of the target function space in the source mesh.
raise NotImplementedError(
"Can only interpolate into spaces with point evaluation nodes."
)
super().__init__(expr, V, subset, freeze_expr, access, bcs, allow_missing_dofs)
self.arguments = extract_arguments(expr)
self.nargs = len(self.arguments)
if self._allow_missing_dofs:
missing_points_behaviour = MissingPointsBehaviour.IGNORE
else:
missing_points_behaviour = MissingPointsBehaviour.ERROR
# setup
V_dest = V
src_mesh = extract_unique_domain(expr)
dest_mesh = as_domain(V_dest)
src_mesh_gdim = src_mesh.geometric_dimension()
dest_mesh_gdim = dest_mesh.geometric_dimension()
if src_mesh_gdim != dest_mesh_gdim:
raise ValueError(
"geometric dimensions of source and destination meshes must match"
)
self.src_mesh = src_mesh
self.dest_mesh = dest_mesh
if numpy.any(
numpy.asarray(src_mesh.coordinates.function_space().ufl_element().degree())
> 1
):
# Need to implement vertex-only mesh immersion in high order meshes
# for this to work.
raise NotImplementedError(
"Cannot yet interpolate from high order meshes to other meshes."
)
self.sub_interpolators = []
# Create a VOM at the nodes of V_dest in src_mesh. We don't include halo
# node coordinates because interpolation doesn't usually include halos.
# NOTE: it is very important to set redundant=False, otherwise the
# input ordering VOM will only contain the points on rank 0!
# QUESTION: Should any of the below have annotation turned off?
ufl_scalar_element = V_dest.ufl_element()
if ufl_scalar_element.num_sub_elements and not isinstance(
ufl_scalar_element, finat.ufl.TensorProductElement
):
if all(
ufl_scalar_element.sub_elements[0] == e
for e in ufl_scalar_element.sub_elements
):
# For a VectorElement or TensorElement the correct
# VectorFunctionSpace equivalent is built from the scalar
# sub-element.
ufl_scalar_element = ufl_scalar_element.sub_elements[0]
if ufl_scalar_element.reference_value_shape != ():
raise NotImplementedError(
"Can't yet cross-mesh interpolate onto function spaces made from VectorElements or TensorElements made from sub elements with value shape other than ()."
)
elif type(ufl_scalar_element) is finat.ufl.MixedElement:
# Build and save an interpolator for each sub-element
# separately for MixedFunctionSpaces. NOTE: since we can't have
# expressions for MixedFunctionSpaces we know that the input
# argument ``expr`` must be a Function. V_dest can be a Function
# or a FunctionSpace, and subfunctions works for both.
if self.nargs == 1:
# Arguments don't have a subfunctions property so I have to
# make them myself. NOTE: this will not be correct when we
# start allowing interpolators created from an expression
# with arguments, as opposed to just being the argument.
expr_subfunctions = [
firedrake.TestFunction(V_src_sub_func)
for V_src_sub_func in self.expr.function_space().subfunctions
]
elif self.nargs > 1:
raise NotImplementedError(
"Can't yet create an interpolator from an expression with multiple arguments."
)
else:
expr_subfunctions = self.expr.subfunctions
if len(expr_subfunctions) != len(V_dest.subfunctions):
raise NotImplementedError(
"Can't interpolate from a non-mixed function space into a mixed function space."
)
for input_sub_func, target_sub_func in zip(
expr_subfunctions, V_dest.subfunctions
):
sub_interpolator = type(self)(
input_sub_func,
target_sub_func,
subset=subset,
freeze_expr=freeze_expr,
access=access,
bcs=bcs,
allow_missing_dofs=allow_missing_dofs,
)
self.sub_interpolators.append(sub_interpolator)
return
else:
raise NotImplementedError(
f"Unhandled cross-mesh interpolation ufl element type: {repr(ufl_scalar_element)}"
)
from firedrake.assemble import assemble
V_dest_vec = firedrake.VectorFunctionSpace(dest_mesh, ufl_scalar_element)
f_dest_node_coords = Interpolate(dest_mesh.coordinates, V_dest_vec)
f_dest_node_coords = assemble(f_dest_node_coords)
dest_node_coords = f_dest_node_coords.dat.data_ro.reshape(-1, dest_mesh_gdim)
try:
self.vom_dest_node_coords_in_src_mesh = firedrake.VertexOnlyMesh(
src_mesh,
dest_node_coords,
redundant=False,
missing_points_behaviour=missing_points_behaviour,
)
except VertexOnlyMeshMissingPointsError:
raise DofNotDefinedError(src_mesh, dest_mesh)
# vom_dest_node_coords_in_src_mesh uses the parallel decomposition of
# the global node coordinates of V_dest in the SOURCE mesh (src_mesh).
# I first point evaluate my expression at these locations, giving a
# P0DG function on the VOM. As described in the manual, this is an
# interpolation operation.
shape = V_dest.ufl_function_space().value_shape
if len(shape) == 0:
fs_type = firedrake.FunctionSpace
elif len(shape) == 1:
fs_type = firedrake.VectorFunctionSpace
else:
fs_type = partial(firedrake.TensorFunctionSpace, shape=shape)
P0DG_vom = fs_type(self.vom_dest_node_coords_in_src_mesh, "DG", 0)
self.point_eval_interpolate = Interpolate(self.expr_renumbered, P0DG_vom)
# The parallel decomposition of the nodes of V_dest in the DESTINATION
# mesh (dest_mesh) is retrieved using the input_ordering attribute of the
# VOM. This again is an interpolation operation, which, under the hood
# is a PETSc SF reduce.
P0DG_vom_i_o = fs_type(
self.vom_dest_node_coords_in_src_mesh.input_ordering, "DG", 0
)
self.to_input_ordering_interpolate = Interpolate(
firedrake.TrialFunction(P0DG_vom), P0DG_vom_i_o
)
# The P0DG function outputted by the above interpolation has the
# correct parallel decomposition for the nodes of V_dest in dest_mesh so
# we can safely assign the dat values. This is all done in the actual
# interpolation method below.
@PETSc.Log.EventDecorator()
def _interpolate(
self,
*function,
output=None,
transpose=False,
default_missing_val=None,
**kwargs,
):
"""Compute the interpolation.
For arguments, see :class:`.Interpolator`.
"""
from firedrake.assemble import assemble
if transpose and not self.nargs:
raise ValueError(
"Can currently only apply transpose interpolation with arguments."
)
if self.nargs != len(function):
raise ValueError(
"Passed %d Functions to interpolate, expected %d"
% (len(function), self.nargs)
)
if self.nargs:
(f_src,) = function
if not hasattr(f_src, "dat"):
raise ValueError(
"The expression had arguments: we therefore need to be given a Function (not an expression) to interpolate!"
)
else:
f_src = self.expr
if transpose:
try:
V_dest = self.expr.function_space().dual()
except AttributeError:
if self.nargs:
V_dest = self.arguments[0].function_space().dual()
else:
coeffs = extract_coefficients(self.expr)
if len(coeffs):
V_dest = coeffs[0].function_space().dual()
else:
raise ValueError(
"Can't transpose interpolate an expression with no coefficients or arguments."
)
else:
if isinstance(self.V, (firedrake.Function, firedrake.Cofunction)):
V_dest = self.V.function_space()
else:
V_dest = self.V
if output:
if output.function_space() != V_dest:
raise ValueError("Given output has the wrong function space!")
else:
if isinstance(self.V, (firedrake.Function, firedrake.Cofunction)):
output = self.V
else:
output = firedrake.Function(V_dest)
if len(self.sub_interpolators):
# MixedFunctionSpace case
for sub_interpolator, f_src_sub_func, output_sub_func in zip(
self.sub_interpolators, f_src.subfunctions, output.subfunctions
):
if f_src is self.expr:
# f_src is already contained in self.point_eval_interpolate,
# so the sub_interpolators are already prepared to interpolate
# without needing to be given a Function
assert not self.nargs
interp = sub_interpolator._interpolate_future(transpose=transpose, **kwargs)
assemble(interp, tensor=output_sub_func)
else:
interp = sub_interpolator._interpolate_future(transpose=transpose, **kwargs)
assemble(action(interp, f_src_sub_func), tensor=output_sub_func)
return output
if not transpose:
if f_src is self.expr:
# f_src is already contained in self.point_eval_interpolate
assert not self.nargs
f_src_at_dest_node_coords_src_mesh_decomp = (
assemble(self.point_eval_interpolate)
)
else:
f_src_at_dest_node_coords_src_mesh_decomp = (
assemble(action(self.point_eval_interpolate, f_src))
)
f_src_at_dest_node_coords_dest_mesh_decomp = firedrake.Function(
self.to_input_ordering_interpolate.function_space()
)
# We have to create the Function before interpolating so we can
# set default missing values (if requested).
if default_missing_val is not None:
f_src_at_dest_node_coords_dest_mesh_decomp.dat.data_wo[
:
] = default_missing_val
elif self._allow_missing_dofs:
# If we have allowed missing points we know we might end up
# with points in the target mesh that are not in the source
# mesh. However, since we haven't specified a default missing
# value we expect the interpolation to leave these points
# unchanged. By setting the dat values to NaN we can later
# identify these points and skip over them when assigning to
# the output function.
f_src_at_dest_node_coords_dest_mesh_decomp.dat.data_wo[:] = numpy.nan
interp = action(self.to_input_ordering_interpolate, f_src_at_dest_node_coords_src_mesh_decomp)
assemble(interp, tensor=f_src_at_dest_node_coords_dest_mesh_decomp)
# we can now confidently assign this to a function on V_dest
if self._allow_missing_dofs and default_missing_val is None:
indices = numpy.where(
~numpy.isnan(f_src_at_dest_node_coords_dest_mesh_decomp.dat.data_ro)
)[0]
output.dat.data_wo[
indices
] = f_src_at_dest_node_coords_dest_mesh_decomp.dat.data_ro[indices]
else:
output.dat.data_wo[
:
] = f_src_at_dest_node_coords_dest_mesh_decomp.dat.data_ro[:]
else:
# adjoint/transpose interpolation
# f_src is a cofunction on V_dest.dual as originally specified when
# creating the interpolator. Our first adjoint operation is to
# assign the dat values to a P0DG cofunction on our input ordering
# VOM. This has the parallel decomposition V_dest on our orinally
# specified dest_mesh. We can therefore safely create a P0DG
# cofunction on the input-ordering VOM (which has this parallel
# decomposition and ordering) and assign the dat values.
f_src_at_dest_node_coords_dest_mesh_decomp = firedrake.Cofunction(
self.to_input_ordering_interpolate.function_space().dual()
)
f_src_at_dest_node_coords_dest_mesh_decomp.dat.data_wo[
:
] = f_src.dat.data_ro[:]
# The rest of the transpose interpolation is merely the composition
# of the transpose interpolators in the reverse direction. NOTE: I
# don't have to worry about skipping over missing points here
# because I'm going from the input ordering VOM to the original VOM
# and all points from the input ordering VOM are in the original.
interp = action(adjoint(self.to_input_ordering_interpolate), f_src_at_dest_node_coords_dest_mesh_decomp)
f_src_at_src_node_coords = assemble(interp)
# NOTE: if I wanted the default missing value to be applied to
# transpose interpolation I would have to do it here. However,
# this would require me to implement default missing values for
# transpose interpolation from a point evaluation interpolator
# which I haven't done. I wonder if it is necessary - perhaps the
# adjoint operator always sets all the values of the resulting
# cofunction? My initial attempt to insert setting the dat values
# prior to performing the multTranspose operation in
# SameMeshInterpolator.interpolate did not effect the result. For
# now, I say in the docstring that it only applies to forward
# interpolation.
interp = action(adjoint(self.point_eval_interpolate), f_src_at_src_node_coords)
assemble(interp, tensor=output)
return output
[docs]
class SameMeshInterpolator(Interpolator):
"""
An interpolator for interpolation within the same mesh or onto a validly-
defined :func:`.VertexOnlyMesh`.
For arguments, see :class:`.Interpolator`.
"""
@no_annotations
def __init__(self, expr, V, subset=None, freeze_expr=False, access=op2.WRITE, bcs=None, **kwargs):
super().__init__(expr, V, subset, freeze_expr, access, bcs)
try:
self.callable, arguments = make_interpolator(expr, V, subset, access, bcs=bcs)
except FIAT.hdiv_trace.TraceError:
raise NotImplementedError("Can't interpolate onto traces sorry")
self.arguments = arguments
self.nargs = len(arguments)
@PETSc.Log.EventDecorator()
def _interpolate(self, *function, output=None, transpose=False, **kwargs):
"""Compute the interpolation.
For arguments, see :class:`.Interpolator`.
"""
if transpose and not self.nargs:
raise ValueError("Can currently only apply transpose interpolation with arguments.")
if self.nargs != len(function):
raise ValueError("Passed %d Functions to interpolate, expected %d"
% (len(function), self.nargs))
try:
assembled_interpolator = self.frozen_assembled_interpolator
copy_required = True
except AttributeError:
assembled_interpolator = self.callable()
copy_required = False # Return the original
if self.freeze_expr:
if self.nargs:
# Interpolation operator
self.frozen_assembled_interpolator = assembled_interpolator
else:
# Interpolation action
self.frozen_assembled_interpolator = assembled_interpolator.copy()
if self.nargs:
function, = function
if not hasattr(function, "dat"):
raise ValueError("The expression had arguments: we therefore need to be given a Function (not an expression) to interpolate!")
if transpose:
mul = assembled_interpolator.handle.multTranspose
V = self.arguments[0].function_space()
else:
mul = assembled_interpolator.handle.mult
V = self.V
result = output or firedrake.Function(V)
with function.dat.vec_ro as x, result.dat.vec_wo as out:
mul(x, out)
return result
else:
if output:
output.assign(assembled_interpolator)
return output
if isinstance(self.V, firedrake.Function):
if copy_required:
self.V.assign(assembled_interpolator)
return self.V
else:
if copy_required:
return assembled_interpolator.copy()
else:
return assembled_interpolator
@PETSc.Log.EventDecorator()
def make_interpolator(expr, V, subset, access, bcs=None):
assert isinstance(expr, ufl.classes.Expr)
arguments = extract_arguments(expr)
target_mesh = as_domain(V)
if len(arguments) == 0:
source_mesh = extract_unique_domain(expr) or target_mesh
vom_onto_other_vom = (
isinstance(target_mesh.topology, firedrake.mesh.VertexOnlyMeshTopology)
and isinstance(source_mesh.topology, firedrake.mesh.VertexOnlyMeshTopology)
and target_mesh is not source_mesh
)
if isinstance(V, firedrake.Function):
f = V
V = f.function_space()
else:
f = firedrake.Function(V)
if access in {firedrake.MIN, firedrake.MAX}:
finfo = numpy.finfo(f.dat.dtype)
if access == firedrake.MIN:
val = firedrake.Constant(finfo.max)
else:
val = firedrake.Constant(finfo.min)
f.assign(val)
tensor = f.dat
elif len(arguments) == 1:
if isinstance(V, firedrake.Function):
raise ValueError("Cannot interpolate an expression with an argument into a Function")
argfs = arguments[0].function_space()
source_mesh = argfs.mesh()
argfs_map = argfs.cell_node_map()
vom_onto_other_vom = (
isinstance(target_mesh.topology, firedrake.mesh.VertexOnlyMeshTopology)
and isinstance(source_mesh.topology, firedrake.mesh.VertexOnlyMeshTopology)
and target_mesh is not source_mesh
)
if isinstance(target_mesh.topology, firedrake.mesh.VertexOnlyMeshTopology) and target_mesh is not source_mesh and not vom_onto_other_vom:
if not isinstance(target_mesh.topology, firedrake.mesh.VertexOnlyMeshTopology):
raise NotImplementedError("Can only interpolate onto a Vertex Only Mesh")
if target_mesh.geometric_dimension() != source_mesh.geometric_dimension():
raise ValueError("Cannot interpolate onto a mesh of a different geometric dimension")
if not hasattr(target_mesh, "_parent_mesh") or target_mesh._parent_mesh is not source_mesh:
raise ValueError("Can only interpolate across meshes where the source mesh is the parent of the target")
if argfs_map:
# Since the par_loop is over the target mesh cells we need to
# compose a map that takes us from target mesh cells to the
# function space nodes on the source mesh. NOTE: argfs_map is
# allowed to be None when interpolating from a Real space, even
# in the trans-mesh case.
if source_mesh.extruded:
# ExtrudedSet cannot be a map target so we need to build
# this ourselves
argfs_map = vom_cell_parent_node_map_extruded(target_mesh, argfs_map)
else:
argfs_map = compose_map_and_cache(target_mesh.cell_parent_cell_map, argfs_map)
elif vom_onto_other_vom:
argfs_map = argfs.cell_node_map()
else:
argfs_map = argfs.entity_node_map(target_mesh.topology, "cell", None, None)
if vom_onto_other_vom:
# We make our own linear operator for this case using PETSc SFs
tensor = None
else:
sparsity = op2.Sparsity((V.dof_dset, argfs.dof_dset),
[(V.cell_node_map(), argfs_map, None)], # non-mixed
name="%s_%s_sparsity" % (V.name, argfs.name),
nest=False,
block_sparse=True)
tensor = op2.Mat(sparsity)
f = tensor
else:
raise ValueError("Cannot interpolate an expression with %d arguments" % len(arguments))
if vom_onto_other_vom:
# To interpolate between vertex-only meshes we use a PETSc SF
wrapper = VomOntoVomWrapper(V, source_mesh, target_mesh, expr, arguments)
# NOTE: get_dat_mpi_type ensures we get the correct MPI type for the
# data, including the correct data size and dimensional information
# (so for vector function spaces in 2 dimensions we might need a
# concatenation of 2 MPI.DOUBLE types when we are in real mode)
if tensor is not None:
# Callable will do interpolation into our pre-supplied function f
# when it is called.
assert f.dat is tensor
wrapper.mpi_type, _ = get_dat_mpi_type(f.dat)
assert not len(arguments)
def callable():
wrapper.forward_operation(f.dat)
return f
else:
assert len(arguments) == 1
assert tensor is None
# we know we will be outputting either a function or a cofunction,
# both of which will use a dat as a data carrier. At present, the
# data type does not depend on function space dimension, so we can
# safely use the argument function space. NOTE: If this changes
# after cofunctions are fully implemented, this will need to be
# reconsidered.
temp_source_func = firedrake.Function(argfs)
wrapper.mpi_type, _ = get_dat_mpi_type(temp_source_func.dat)
# Leave wrapper inside a callable so we can access the handle
# property (which is pretending to be a petsc mat)
def callable():
return wrapper
return callable, arguments
else:
# Make sure we have an expression of the right length i.e. a value for
# each component in the value shape of each function space
loops = []
if numpy.prod(expr.ufl_shape, dtype=int) != V.value_size:
raise RuntimeError('Expression of length %d required, got length %d'
% (V.value_size, numpy.prod(expr.ufl_shape, dtype=int)))
if len(V) > 1:
raise NotImplementedError(
"UFL expressions for mixed functions are not yet supported.")
loops.extend(_interpolator(V, tensor, expr, subset, arguments, access, bcs=bcs))
if bcs and len(arguments) == 0:
loops.extend(partial(bc.apply, f) for bc in bcs)
def callable(loops, f):
for l in loops:
l()
return f
return partial(callable, loops, f), arguments
@utils.known_pyop2_safe
def _interpolator(V, tensor, expr, subset, arguments, access, bcs=None):
try:
expr = ufl.as_ufl(expr)
except ValueError:
raise ValueError("Expecting to interpolate a UFL expression")
try:
to_element = create_element(V.ufl_element())
except KeyError:
# FInAT only elements
raise NotImplementedError("Don't know how to create FIAT element for %s" % V.ufl_element())
if access is op2.READ:
raise ValueError("Can't have READ access for output function")
if len(expr.ufl_shape) != len(V.value_shape):
raise RuntimeError('Rank mismatch: Expression rank %d, FunctionSpace rank %d'
% (len(expr.ufl_shape), len(V.value_shape)))
if expr.ufl_shape != V.value_shape:
raise RuntimeError('Shape mismatch: Expression shape %r, FunctionSpace shape %r'
% (expr.ufl_shape, V.value_shape))
# NOTE: The par_loop is always over the target mesh cells.
target_mesh = as_domain(V)
source_mesh = extract_unique_domain(expr) or target_mesh
if isinstance(target_mesh.topology, firedrake.mesh.VertexOnlyMeshTopology):
if target_mesh is not source_mesh:
if not isinstance(target_mesh.topology, firedrake.mesh.VertexOnlyMeshTopology):
raise NotImplementedError("Can only interpolate onto a Vertex Only Mesh")
if target_mesh.geometric_dimension() != source_mesh.geometric_dimension():
raise ValueError("Cannot interpolate onto a mesh of a different geometric dimension")
if not hasattr(target_mesh, "_parent_mesh") or target_mesh._parent_mesh is not source_mesh:
raise ValueError("Can only interpolate across meshes where the source mesh is the parent of the target")
# For trans-mesh interpolation we use a FInAT QuadratureElement as the
# (base) target element with runtime point set expressions as their
# quadrature rule point set and weights from their dual basis.
# NOTE: This setup is useful for thinking about future design - in the
# future this `rebuild` function can be absorbed into FInAT as a
# transformer that eats an element and gives you an equivalent (which
# may or may not be a QuadratureElement) that lets you do run time
# tabulation. Alternatively (and this all depends on future design
# decision about FInAT how dual evaluation should work) the
# to_element's dual basis (which look rather like quadrature rules) can
# have their pointset(s) directly replaced with run-time tabulated
# equivalent(s) (i.e. finat.point_set.UnknownPointSet(s))
rt_var_name = 'rt_X'
to_element = rebuild(to_element, expr, rt_var_name)
cell_set = target_mesh.cell_set
if subset is not None:
assert subset.superset == cell_set
cell_set = subset
parameters = {}
parameters['scalar_type'] = utils.ScalarType
# We need to pass both the ufl element and the finat element
# because the finat elements might not have the right mapping
# (e.g. L2 Piola, or tensor element with symmetries)
# FIXME: for the runtime unknown point set (for cross-mesh
# interpolation) we have to pass the finat element we construct
# here. Ideally we would only pass the UFL element through.
kernel = compile_expression(cell_set.comm, expr, to_element, V.ufl_element(),
domain=source_mesh, parameters=parameters,
log=PETSc.Log.isActive())
ast = kernel.ast
oriented = kernel.oriented
needs_cell_sizes = kernel.needs_cell_sizes
coefficient_numbers = kernel.coefficient_numbers
needs_external_coords = kernel.needs_external_coords
name = kernel.name
kernel = op2.Kernel(ast, name, requires_zeroed_output_arguments=True,
flop_count=kernel.flop_count, events=(kernel.event,))
parloop_args = [kernel, cell_set]
coefficients = tsfc_interface.extract_numbered_coefficients(expr, coefficient_numbers)
if needs_external_coords:
coefficients = [source_mesh.coordinates] + coefficients
if isinstance(target_mesh.topology, firedrake.mesh.VertexOnlyMeshTopology):
if target_mesh is not source_mesh:
# NOTE: TSFC will sometimes drop run-time arguments in generated
# kernels if they are deemed not-necessary.
# FIXME: Checking for argument name in the inner kernel to decide
# whether to add an extra coefficient is a stopgap until
# compile_expression_dual_evaluation
# (a) outputs a coefficient map to indicate argument ordering in
# parloops as `compile_form` does and
# (b) allows the dual evaluation related coefficients to be supplied to
# them rather than having to be added post-hoc (likely by
# replacing `to_element` with a CoFunction/CoArgument as the
# target `dual` which would contain `dual` related
# coefficient(s))
if rt_var_name in [arg.name for arg in kernel.code[name].args]:
# Add the coordinates of the target mesh quadrature points in the
# source mesh's reference cell as an extra argument for the inner
# loop. (With a vertex only mesh this is a single point for each
# vertex cell.)
coefficients.append(target_mesh.reference_coordinates)
if tensor in set((c.dat for c in coefficients)):
output = tensor
tensor = op2.Dat(tensor.dataset)
if access is not op2.WRITE:
copyin = (partial(output.copy, tensor), )
else:
copyin = ()
copyout = (partial(tensor.copy, output), )
else:
copyin = ()
copyout = ()
if isinstance(tensor, op2.Global):
parloop_args.append(tensor(access))
elif isinstance(tensor, op2.Dat):
parloop_args.append(tensor(access, V.cell_node_map()))
else:
assert access == op2.WRITE # Other access descriptors not done for Matrices.
rows_map = V.cell_node_map()
Vcol = arguments[0].function_space()
if isinstance(target_mesh.topology, firedrake.mesh.VertexOnlyMeshTopology):
columns_map = Vcol.cell_node_map()
if target_mesh is not source_mesh:
# Since the par_loop is over the target mesh cells we need to
# compose a map that takes us from target mesh cells to the
# function space nodes on the source mesh.
if source_mesh.extruded:
# ExtrudedSet cannot be a map target so we need to build
# this ourselves
columns_map = vom_cell_parent_node_map_extruded(target_mesh, columns_map)
else:
columns_map = compose_map_and_cache(target_mesh.cell_parent_cell_map,
columns_map)
else:
columns_map = Vcol.entity_node_map(target_mesh.topology, "cell", None, None)
lgmaps = None
if bcs:
bc_rows = [bc for bc in bcs if bc.function_space() == V]
bc_cols = [bc for bc in bcs if bc.function_space() == Vcol]
lgmaps = [(V.local_to_global_map(bc_rows), Vcol.local_to_global_map(bc_cols))]
parloop_args.append(tensor(op2.WRITE, (rows_map, columns_map), lgmaps=lgmaps))
if oriented:
co = target_mesh.cell_orientations()
parloop_args.append(co.dat(op2.READ, co.cell_node_map()))
if needs_cell_sizes:
cs = target_mesh.cell_sizes
parloop_args.append(cs.dat(op2.READ, cs.cell_node_map()))
for coefficient in coefficients:
if isinstance(target_mesh.topology, firedrake.mesh.VertexOnlyMeshTopology):
coeff_mesh = extract_unique_domain(coefficient)
if coeff_mesh is target_mesh or not coeff_mesh:
# NOTE: coeff_mesh is None is allowed e.g. when interpolating from
# a Real space
m_ = coefficient.cell_node_map()
elif coeff_mesh is source_mesh:
if coefficient.cell_node_map():
# Since the par_loop is over the target mesh cells we need to
# compose a map that takes us from target mesh cells to the
# function space nodes on the source mesh.
if source_mesh.extruded:
# ExtrudedSet cannot be a map target so we need to build
# this ourselves
m_ = vom_cell_parent_node_map_extruded(target_mesh, coefficient.cell_node_map())
else:
m_ = compose_map_and_cache(target_mesh.cell_parent_cell_map, coefficient.cell_node_map())
else:
# m_ is allowed to be None when interpolating from a Real space,
# even in the trans-mesh case.
m_ = coefficient.cell_node_map()
else:
raise ValueError("Have coefficient with unexpected mesh")
else:
m_ = coefficient.function_space().entity_node_map(target_mesh.topology, "cell", None, None)
parloop_args.append(coefficient.dat(op2.READ, m_))
for const in extract_firedrake_constants(expr):
parloop_args.append(const.dat(op2.READ))
parloop = op2.ParLoop(*parloop_args)
parloop_compute_callable = parloop.compute
if isinstance(tensor, op2.Mat):
return parloop_compute_callable, tensor.assemble
else:
return copyin + (parloop_compute_callable, ) + copyout
try:
_expr_cachedir = os.environ["FIREDRAKE_TSFC_KERNEL_CACHE_DIR"]
except KeyError:
_expr_cachedir = os.path.join(tempfile.gettempdir(),
f"firedrake-tsfc-expression-kernel-cache-uid{os.getuid()}")
def _compile_expression_key(comm, expr, to_element, ufl_element, domain, parameters, log):
"""Generate a cache key suitable for :func:`tsfc.compile_expression_dual_evaluation`."""
key = hash_expr(expr), hash(ufl_element), utils.tuplify(parameters), log
return key
@memory_and_disk_cache(
hashkey=_compile_expression_key,
cachedir=tsfc_interface._cachedir
)
@PETSc.Log.EventDecorator()
def compile_expression(comm, *args, **kwargs):
return compile_expression_dual_evaluation(*args, **kwargs)
@singledispatch
def rebuild(element, expr, rt_var_name):
raise NotImplementedError(f"Cross mesh interpolation not implemented for a {element} element.")
@rebuild.register(finat.fiat_elements.ScalarFiatElement)
def rebuild_dg(element, expr, rt_var_name):
# To tabulate on the given element (which is on a different mesh to the
# expression) we must do so at runtime. We therefore create a quadrature
# element with runtime points to evaluate for each point in the element's
# dual basis. This exists on the same reference cell as the input element
# and we can interpolate onto it before mapping the result back onto the
# target space.
expr_tdim = extract_unique_domain(expr).topological_dimension()
# Need point evaluations and matching weights from dual basis.
# This could use FIAT's dual basis as below:
# num_points = sum(len(dual.get_point_dict()) for dual in element.fiat_equivalent.dual_basis())
# weights = []
# for dual in element.fiat_equivalent.dual_basis():
# pts = dual.get_point_dict().keys()
# for p in pts:
# for w, _ in dual.get_point_dict()[p]:
# weights.append(w)
# assert len(weights) == num_points
# but for now we just fix the values to what we know works:
if element.degree != 0 or not isinstance(element.cell, FIAT.reference_element.Point):
raise NotImplementedError("Cross mesh interpolation only implemented for P0DG on vertex cells.")
num_points = 1
weights = [1.]*num_points
# gem.Variable name starting with rt_ forces TSFC runtime tabulation
assert rt_var_name.startswith("rt_")
runtime_points_expr = gem.Variable(rt_var_name, (num_points, expr_tdim))
rule_pointset = finat.point_set.UnknownPointSet(runtime_points_expr)
try:
expr_fiat_cell = as_fiat_cell(expr.ufl_element().cell)
except AttributeError:
# expression must be pure function of spatial coordinates so
# domain has correct ufl cell
expr_fiat_cell = as_fiat_cell(extract_unique_domain(expr).ufl_cell())
rule = finat.quadrature.QuadratureRule(rule_pointset, weights=weights)
return finat.QuadratureElement(expr_fiat_cell, rule)
@rebuild.register(finat.TensorFiniteElement)
def rebuild_te(element, expr, rt_var_name):
return finat.TensorFiniteElement(rebuild(element.base_element,
expr, rt_var_name),
element._shape,
transpose=element._transpose)
def compose_map_and_cache(map1, map2):
"""
Retrieve a :class:`pyop2.ComposedMap` map from the cache of map1
using map2 as the cache key. The composed map maps from the iterset
of map1 to the toset of map2. Makes :class:`pyop2.ComposedMap` and
caches the result on map1 if the composed map is not found.
:arg map1: The map with the desired iterset from which the result is
retrieved or cached
:arg map2: The map with the desired toset
:returns: The composed map
"""
cache_key = hash((map2, "composed"))
try:
cmap = map1._cache[cache_key]
except KeyError:
# Real function space case separately
cmap = None if map2 is None else op2.ComposedMap(map2, map1)
map1._cache[cache_key] = cmap
return cmap
def vom_cell_parent_node_map_extruded(vertex_only_mesh, extruded_cell_node_map):
"""Build a map from the cells of a vertex only mesh to the nodes of the
nodes on the source mesh where the source mesh is extruded.
Parameters
----------
vertex_only_mesh : :class:`mesh.MeshGeometry`
The ``mesh.VertexOnlyMesh`` whose cells we iterate over.
extruded_cell_node_map : :class:`pyop2.Map`
The cell node map of the function space on the extruded mesh within
which the ``mesh.VertexOnlyMesh`` is immersed.
Returns
-------
:class:`pyop2.Map`
The map from the cells of the vertex only mesh to the nodes of the
source mesh's cell node map. The map iterset is the
``vertex_only_mesh.cell_set`` and the map toset is the
``extruded_cell_node_map.toset``.
Notes
-----
For an extruded mesh the cell node map is a map from a
:class:`pyop2.ExtrudedSet` (the cells of the extruded mesh) to a
:class:`pyop2.Set` (the nodes of the extruded mesh).
Take for example
``mx = ExtrudedMesh(UnitIntervalMesh(2), 3)`` with
``mx.layers = 4``
which looks like
.. code-block:: text
-------------------layer 4-------------------
| parent_cell_num = 2 | parent_cell_num = 5 |
| | |
| extrusion_height = 2 | extrusion_height = 2 |
-------------------layer 3-------------------
| parent_cell_num = 1 | parent_cell_num = 4 |
| | |
| extrusion_height = 1 | extrusion_height = 1 |
-------------------layer 2-------------------
| parent_cell_num = 0 | parent_cell_num = 3 |
| | |
| extrusion_height = 0 | extrusion_height = 0 |
-------------------layer 1-------------------
base_cell_num = 0 base_cell_num = 1
If we declare ``FunctionSpace(mx, "CG", 2)`` then the node numbering (i.e.
Degree of Freedom/DoF numbering) is
.. code-block:: text
6 ---------13----------20---------27---------34
| | |
5 12 19 26 33
| | |
4 ---------11----------18---------25---------32
| | |
3 10 17 24 31
| | |
2 ---------9-----------16---------23---------30
| | |
1 8 15 22 29
| | |
0 ---------7-----------14---------21---------28
base_cell_num = 0 base_cell_num = 1
Cell node map values for an extruded mesh are indexed by the base cell
number (rows) and the degree of freedom (DoF) index (columns). So
``extruded_cell_node_map.values[0] = [14, 15, 16, 0, 1, 2, 7, 8, 9]``
are all the DoF/node numbers for the ``base_cell_num = 0``.
Similarly
``extruded_cell_node_map.values[1] = [28, 29, 30, 21, 22, 23, 14, 15, 16]``
contain all 9 of the DoFs for ``base_cell_num = 1``.
To get the DoFs/nodes for the rest of the cells we need to include the
``extruded_cell_node_map.offset``, which tells us how far each cell's
DoFs/nodes are translated up from the first layer to the second, and
multiply these by the the given ``extrusion_height``. So in our example
``extruded_cell_node_map.offset = [2, 2, 2, 2, 2, 2, 2, 2, 2]`` (we index
this with the DoF/node index - it's an array because each DoF/node in the
extruded mesh cell, in principal, can be offset upwards by a different
amount).
For ``base_cell_num = 0`` with ``extrusion_height = 1``
(``parent_cell_num = 1``) we add ``1*2 = 2`` to each of the DoFs/nodes in
``extruded_cell_node_map.values[0]`` to get
``extruded_cell_node_map.values[0] + 1 * extruded_cell_node_map.offset[0] =
[16, 17, 18, 2, 3, 4, 9, 10, 11]`` where ``0`` is the DoF/node index.
For each cell (vertex) of a vertex only mesh immersed in a parent
extruded mesh, we can can get the corresponding ``base_cell_num`` and
``extrusion_height`` of the parent extruded mesh. Armed with this
information we use the above to work out the corresponding DoFs/nodes on
the parent extruded mesh.
"""
if not isinstance(vertex_only_mesh.topology, firedrake.mesh.VertexOnlyMeshTopology):
raise TypeError("The input mesh must be a VertexOnlyMesh")
cnm = extruded_cell_node_map
vmx = vertex_only_mesh
dofs_per_target_cell = cnm.arity
base_cells = vmx.cell_parent_base_cell_list
heights = vmx.cell_parent_extrusion_height_list
assert cnm.values_with_halo.shape[1] == dofs_per_target_cell
assert len(cnm.offset) == dofs_per_target_cell
target_cell_parent_node_list = [
cnm.values_with_halo[base_cell, :] + height * cnm.offset[:]
for base_cell, height in zip(base_cells, heights)
]
return op2.Map(
vmx.cell_set, cnm.toset, dofs_per_target_cell, target_cell_parent_node_list
)
class GlobalWrapper(object):
"""Wrapper object that fakes a Global to behave like a Function."""
def __init__(self, glob):
self.dat = glob
self.cell_node_map = lambda *arguments: None
self.ufl_domain = lambda: None
def hash_expr(expr):
"""Return a numbering-invariant hash of a UFL expression.
:arg expr: A UFL expression.
:returns: A numbering-invariant hash for the expression.
"""
domain_numbering = {d: i for i, d in enumerate(ufl.domain.extract_domains(expr))}
coefficient_numbering = {c: i for i, c in enumerate(extract_coefficients(expr))}
constant_numbering = {c: i for i, c in enumerate(extract_firedrake_constants(expr))}
return compute_expression_signature(
expr, {**domain_numbering, **coefficient_numbering, **constant_numbering}
)
class VomOntoVomWrapper(object):
"""Utility class for interpolating from one ``VertexOnlyMesh`` to it's
intput ordering ``VertexOnlyMesh``, or vice versa.
Parameters
----------
V : `.FunctionSpace`
The P0DG function space (which may be vector or tensor valued) on the
source vertex-only mesh.
source_vom : `.VertexOnlyMesh`
The vertex-only mesh we interpolate from.
target_vom : `.VertexOnlyMesh`
The vertex-only mesh we interpolate to.
expr : `ufl.Expr`
The expression to interpolate. If ``arguments`` is not empty, those
arguments must be present within it.
arguments : list of `ufl.Argument`
The arguments in the expression. These are not extracted from expr here
since, where we use this, we already have them.
"""
def __init__(self, V, source_vom, target_vom, expr, arguments):
reduce = False
if source_vom.input_ordering is target_vom:
reduce = True
original_vom = source_vom
elif target_vom.input_ordering is source_vom:
original_vom = target_vom
else:
raise ValueError(
"The target vom and source vom must be linked by input ordering!"
)
self.V = V
self.source_vom = source_vom
self.expr = expr
self.arguments = arguments
self.reduce = reduce
# note that interpolation doesn't include halo cells
self.handle = VomOntoVomDummyMat(
original_vom.input_ordering_without_halos_sf, reduce, V, source_vom, expr, arguments
)
@property
def mpi_type(self):
"""
The MPI type to use for the PETSc SF.
Should correspond to the underlying data type of the PETSc Vec.
"""
return self.handle.mpi_type
@mpi_type.setter
def mpi_type(self, val):
self.handle.mpi_type = val
def forward_operation(self, target_dat):
coeff = self.handle.expr_as_coeff()
with coeff.dat.vec_ro as coeff_vec, target_dat.vec_wo as target_vec:
self.handle.mult(coeff_vec, target_vec)
class VomOntoVomDummyMat(object):
"""Dummy object to stand in for a PETSc ``Mat`` when we are interpolating
between vertex-only meshes.
Parameters
----------
sf: PETSc.sf
The PETSc Star Forest (SF) to use for the operation
forward_reduce : bool
If ``True``, the action of the operator (accessed via the `mult`
method) is to perform a SF reduce from the source vec to the target
vec, whilst the adjoint action (accessed via the `multTranspose`
method) is to perform a SF broadcast from the source vec to the target
vec. If ``False``, the opposite is true.
V : `.FunctionSpace`
The P0DG function space (which may be vector or tensor valued) on the
source vertex-only mesh.
source_vom : `.VertexOnlyMesh`
The vertex-only mesh we interpolate from.
expr : `ufl.Expr`
The expression to interpolate. If ``arguments`` is not empty, those
arguments must be present within it.
arguments : list of `ufl.Argument`
The arguments in the expression.
"""
def __init__(self, sf, forward_reduce, V, source_vom, expr, arguments):
self.sf = sf
self.forward_reduce = forward_reduce
self.V = V
self.source_vom = source_vom
self.expr = expr
self.arguments = arguments
@property
def mpi_type(self):
"""
The MPI type to use for the PETSc SF.
Should correspond to the underlying data type of the PETSc Vec.
"""
return self._mpi_type
@mpi_type.setter
def mpi_type(self, val):
self._mpi_type = val
def expr_as_coeff(self, source_vec=None):
"""
Return a coefficient that corresponds to the expression used at
construction, where the expression has been interpolated into the P0DG
function space on the source vertex-only mesh.
Will fail if there are no arguments.
"""
# Since we always output a coefficient when we don't have arguments in
# the expression, we should evaluate the expression on the source mesh
# so its dat can be sent to the target mesh.
with stop_annotating():
element = self.V.ufl_element() # Could be vector/tensor valued
P0DG = firedrake.FunctionSpace(self.source_vom, element)
# if we have any arguments in the expression we need to replace
# them with equivalent coefficients now
coeff_expr = self.expr
if len(self.arguments):
if len(self.arguments) > 1:
raise NotImplementedError(
"Can only interpolate expressions with one argument!"
)
if source_vec is None:
raise ValueError("Need to provide a source dat for the argument!")
arg = self.arguments[0]
arg_coeff = firedrake.Function(arg.function_space())
arg_coeff.dat.data_wo[:] = source_vec.getArray().reshape(
arg_coeff.dat.data_wo.shape
)
coeff_expr = ufl.replace(self.expr, {arg: arg_coeff})
coeff = firedrake.Function(P0DG).interpolate(coeff_expr)
return coeff
def reduce(self, source_vec, target_vec):
source_arr = source_vec.getArray()
target_arr = target_vec.getArray()
self.sf.reduceBegin(
self.mpi_type,
source_arr,
target_arr,
MPI.REPLACE,
)
self.sf.reduceEnd(
self.mpi_type,
source_arr,
target_arr,
MPI.REPLACE,
)
def broadcast(self, source_vec, target_vec):
source_arr = source_vec.getArray()
target_arr = target_vec.getArray()
self.sf.bcastBegin(
self.mpi_type,
source_arr,
target_arr,
MPI.REPLACE,
)
self.sf.bcastEnd(
self.mpi_type,
source_arr,
target_arr,
MPI.REPLACE,
)
def mult(self, source_vec, target_vec):
# need to evaluate expression before doing mult
coeff = self.expr_as_coeff(source_vec)
with coeff.dat.vec_ro as coeff_vec:
if self.forward_reduce:
self.reduce(coeff_vec, target_vec)
else:
self.broadcast(coeff_vec, target_vec)
def multTranspose(self, source_vec, target_vec):
# can only do transpose if our expression exclusively contains a
# single argument, making the application of the adjoint operator
# straightforward (haven't worked out how to do this otherwise!)
if not len(self.arguments) == 1:
raise NotImplementedError(
"Can only apply transpose to expressions with one argument!"
)
if self.arguments[0] is not self.expr:
raise NotImplementedError(
"Can only apply transpose to expressions consisting of a single argument at the moment."
)
if self.forward_reduce:
self.broadcast(source_vec, target_vec)
else:
# We need to ensure the target vec is zeroed for SF Reduce to
# represent multTranspose in case the interpolation matrix is not
# square (in which case it will have columns which are zero). This
# happens when we interpolate from an input-ordering vertex-only
# mesh to an immersed vertex-only mesh where the input ordering
# contains points that are not in the immersed mesh. The resulting
# interpolation matrix will have columns of zeros for the points
# that are not in the immersed mesh. The adjoint interpolation
# matrix will then have rows of zeros for those points.
target_vec.zeroEntries()
self.reduce(source_vec, target_vec)
