Source code for ufl.measure

"""The Measure class."""

# Copyright (C) 2008-2016 Martin Sandve Aln├Žs
#
# This file is part of UFL (https://www.fenicsproject.org)
#
# SPDX-License-Identifier:    LGPL-3.0-or-later
#
# Modified by Anders Logg 2008-2016
# Modified by Massimiliano Leoni, 2016.

import numbers
from itertools import chain

from ufl.checks import is_true_ufl_scalar
from ufl.constantvalue import as_ufl
from ufl.core.expr import Expr
from ufl.domain import AbstractDomain, as_domain, extract_domains
from ufl.protocols import id_or_none

# Export list for ufl.classes
__all_classes__ = ["Measure", "MeasureSum", "MeasureProduct"]


# TODO: Design a class IntegralType(name, shortname, codim, num_cells, ...)?
# TODO: Improve descriptions below:

# Enumeration of valid domain types
_integral_types = [
    # === Integration over full topological dimension:
    ("cell", "dx"),  # Over cells of a mesh
    # === Integration over topological dimension - 1:
    ("exterior_facet", "ds"),  # Over one-sided exterior facets of a mesh
    ("interior_facet", "dS"),  # Over two-sided facets between pairs of adjacent cells of a mesh
    # === Integration over topological dimension 0
    ("vertex", "dP"),  # Over vertices of a mesh
    # === Integration over custom domains
    ("custom", "dc"),  # Over custom user-defined domains (run-time quadrature points)
    ("cutcell", "dC"),  # Over a cell with some part cut away (run-time quadrature points)
    (
        "interface",
        "dI",
    ),  # Over a facet fragment overlapping with two or more cells (run-time quadrature points)
    (
        "overlap",
        "dO",
    ),  # Over a cell fragment overlapping with two or more cells (run-time quadrature points)
    # === Firedrake specifics:
    ("exterior_facet_bottom", "ds_b"),  # Over bottom facets on extruded mesh
    ("exterior_facet_top", "ds_t"),  # Over top facets on extruded mesh
    ("exterior_facet_vert", "ds_v"),  # Over side facets of an extruded mesh
    ("interior_facet_horiz", "dS_h"),  # Over horizontal facets of an extruded mesh
    ("interior_facet_vert", "dS_v"),  # Over vertical facets of an extruded mesh
]

integral_type_to_measure_name = {i: s for i, s in _integral_types}
measure_name_to_integral_type = {s: i for i, s in _integral_types}

custom_integral_types = ("custom", "cutcell", "interface", "overlap")
point_integral_types = ("vertex",)  # "point")
facet_integral_types = ("exterior_facet", "interior_facet")


[docs]def register_integral_type(integral_type, measure_name): """Register an integral type.""" global integral_type_to_measure_name, measure_name_to_integral_type if measure_name != integral_type_to_measure_name.get(integral_type, measure_name): raise ValueError("Integral type already added with different measure name!") if integral_type != measure_name_to_integral_type.get(measure_name, integral_type): raise ValueError("Measure name already used for another domain type!") integral_type_to_measure_name[integral_type] = measure_name measure_name_to_integral_type[measure_name] = integral_type
[docs]def as_integral_type(integral_type): """Map short name to long name and require a valid one.""" integral_type = integral_type.replace(" ", "_") integral_type = measure_name_to_integral_type.get(integral_type, integral_type) if integral_type not in integral_type_to_measure_name: raise ValueError("Invalid integral_type.") return integral_type
[docs]def integral_types(): """Return a tuple of all domain type strings.""" return tuple(sorted(integral_type_to_measure_name.keys()))
[docs]def measure_names(): """Return a tuple of all measure name strings.""" return tuple(sorted(measure_name_to_integral_type.keys()))
[docs]class Measure(object): """Representation of an integration measure. The Measure object holds information about integration properties to be transferred to a Form on multiplication with a scalar expression. """ __slots__ = ("_integral_type", "_domain", "_subdomain_id", "_metadata", "_subdomain_data") def __init__( self, integral_type, # "dx" etc domain=None, subdomain_id="everywhere", metadata=None, subdomain_data=None, ): """Initialise. Args: integral_type: one of "cell", etc, or short form "dx", etc domain: an AbstractDomain object (most often a Mesh) subdomain_id: either string "everywhere", a single subdomain id int, or tuple of ints metadata: dict, with additional compiler-specific parameters affecting how code is generated, including parameters for optimization or debugging of generated code subdomain_data: object representing data to interpret subdomain_id with """ # Map short name to long name and require a valid one self._integral_type = as_integral_type(integral_type) # Check that we either have a proper AbstractDomain or none if domain is not None: domain = as_domain(domain) if not isinstance(domain, AbstractDomain): raise ValueError("Invalid domain.") self._domain = domain # Store subdomain data self._subdomain_data = subdomain_data # FIXME: Cannot require this (yet) because we currently have # no way to implement ufl_id for dolfin SubDomain # if not (self._subdomain_data is None or hasattr(self._subdomain_data, "ufl_id")): # raise ValueError("Invalid domain data, missing ufl_id() implementation.") # Accept "everywhere", single subdomain, or multiple # subdomains if isinstance(subdomain_id, tuple): for did in subdomain_id: if not isinstance(did, numbers.Integral): raise ValueError(f"Invalid subdomain_id {did}.") else: if not (subdomain_id in ("everywhere",) or isinstance(subdomain_id, numbers.Integral)): raise ValueError(f"Invalid subdomain_id {subdomain_id}.") self._subdomain_id = subdomain_id # Validate compiler options are None or dict if metadata is not None and not isinstance(metadata, dict): raise ValueError("Invalid metadata.") self._metadata = metadata or {}
[docs] def integral_type(self): """Return the domain type. Valid domain types are "cell", "exterior_facet", "interior_facet", etc. """ return self._integral_type
[docs] def ufl_domain(self): """Return the domain associated with this measure. This may be None or a Domain object. """ return self._domain
[docs] def subdomain_id(self): """Return the domain id of this measure (integer).""" return self._subdomain_id
[docs] def metadata(self): """Return the integral metadata. This data is not interpreted by UFL. It is passed to the form compiler which can ignore it or use it to compile each integral of a form in a different way. """ return self._metadata
[docs] def reconstruct( self, integral_type=None, subdomain_id=None, domain=None, metadata=None, subdomain_data=None ): """Construct a new Measure object with some properties replaced with new values. Example: <dm = Measure instance> b = dm.reconstruct(subdomain_id=2) c = dm.reconstruct(metadata={ "quadrature_degree": 3 }) Used by the call operator, so this is equivalent: b = dm(2) c = dm(0, { "quadrature_degree": 3 }) """ if subdomain_id is None: subdomain_id = self.subdomain_id() if domain is None: domain = self.ufl_domain() if metadata is None: metadata = self.metadata() if subdomain_data is None: subdomain_data = self.subdomain_data() return Measure( self.integral_type(), domain=domain, subdomain_id=subdomain_id, metadata=metadata, subdomain_data=subdomain_data, )
[docs] def subdomain_data(self): """Return the integral subdomain_data. This data is not interpreted by UFL. Its intension is to give a context in which the domain id is interpreted. """ return self._subdomain_data
# Note: Must keep the order of the first two arguments here # (subdomain_id, metadata) for backwards compatibility, because # some tutorials write e.g. dx(0, {...}) to set metadata. def __call__( self, subdomain_id=None, metadata=None, domain=None, subdomain_data=None, degree=None, scheme=None, ): """Reconfigure measure with new domain specification or metadata.""" # Let syntax dx() mean integral over everywhere all_args = (subdomain_id, metadata, domain, subdomain_data, degree, scheme) if all(arg is None for arg in all_args): return self.reconstruct(subdomain_id="everywhere") # Let syntax dx(domain) or dx(domain, metadata) mean integral # over entire domain. To do this we need to hijack the first # argument: if subdomain_id is not None and ( isinstance(subdomain_id, AbstractDomain) or hasattr(subdomain_id, "ufl_domain") ): if domain is not None: raise ValueError( "Ambiguous: setting domain both as keyword argument and first argument." ) subdomain_id, domain = "everywhere", subdomain_id # If degree or scheme is set, inject into metadata. This is a # quick fix to enable the dx(..., degree=3) notation. # TODO: Make degree and scheme properties of integrals instead of adding to metadata. if (degree, scheme) != (None, None): metadata = {} if metadata is None else metadata.copy() if degree is not None: metadata["quadrature_degree"] = degree if scheme is not None: metadata["quadrature_rule"] = scheme # If we get any keywords, use them to reconstruct Measure. # Note that if only one argument is given, it is the # subdomain_id, e.g. dx(3) == dx(subdomain_id=3) return self.reconstruct( subdomain_id=subdomain_id, domain=domain, metadata=metadata, subdomain_data=subdomain_data, ) def __str__(self): """Format as a string.""" name = integral_type_to_measure_name[self._integral_type] args = [] if self._subdomain_id is not None: args.append("subdomain_id=%s" % (self._subdomain_id,)) if self._domain is not None: args.append("domain=%s" % (self._domain,)) if self._metadata: # Stored as {} if None args.append("metadata=%s" % (self._metadata,)) if self._subdomain_data is not None: args.append("subdomain_data=%s" % (self._subdomain_data,)) return "%s(%s)" % (name, ", ".join(args)) def __repr__(self): """Return a repr string for this Measure.""" args = [] args.append(repr(self._integral_type)) if self._subdomain_id is not None: args.append("subdomain_id=%s" % repr(self._subdomain_id)) if self._domain is not None: args.append("domain=%s" % repr(self._domain)) if self._metadata: # Stored as {} if None args.append("metadata=%s" % repr(self._metadata)) if self._subdomain_data is not None: args.append("subdomain_data=%s" % repr(self._subdomain_data)) r = "%s(%s)" % (type(self).__name__, ", ".join(args)) return r def __hash__(self): """Return a hash value for this Measure.""" metadata_hashdata = tuple(sorted((k, id(v)) for k, v in list(self._metadata.items()))) hashdata = ( self._integral_type, self._subdomain_id, hash(self._domain), metadata_hashdata, id_or_none(self._subdomain_data), ) return hash(hashdata) def __eq__(self, other): """Checks if two Measures are equal.""" sorted_metadata = sorted((k, id(v)) for k, v in list(self._metadata.items())) sorted_other_metadata = sorted((k, id(v)) for k, v in list(other._metadata.items())) return ( isinstance(other, Measure) and self._integral_type == other._integral_type and self._subdomain_id == other._subdomain_id and self._domain == other._domain and id_or_none(self._subdomain_data) == id_or_none(other._subdomain_data) and sorted_metadata == sorted_other_metadata ) def __add__(self, other): """Add two measures (self+other). Creates an intermediate object used for the notation expr * (dx(1) + dx(2)) := expr * dx(1) + expr * dx(2) """ if isinstance(other, Measure): # Let dx(1) + dx(2) equal dx((1,2)) return MeasureSum(self, other) else: # Can only add Measures return NotImplemented def __mul__(self, other): """Multiply two measures (self*other). Creates an intermediate object used for the notation expr * (dm1 * dm2) := expr * dm1 * dm2 This is work in progress and not functional. """ if isinstance(other, Measure): # Tensor product measure support return MeasureProduct(self, other) else: # Can't multiply Measure from the right with non-Measure type return NotImplemented def __rmul__(self, integrand): """Multiply a scalar expression with measure to construct a form with a single integral. This is to implement the notation form = integrand * self Integration properties are taken from this Measure object. """ # Avoid circular imports from ufl.form import Form from ufl.integral import Integral # Allow python literals: 1*dx and 1.0*dx if isinstance(integrand, (int, float)): integrand = as_ufl(integrand) # Let other types implement multiplication with Measure if # they want to (to support the dolfin-adjoint TimeMeasure) if not isinstance(integrand, Expr): return NotImplemented # Allow only scalar integrands if not is_true_ufl_scalar(integrand): raise ValueError( "Can only integrate scalar expressions. The integrand is a " f"tensor expression with value shape {integrand.ufl_shape} and " f"free indices with labels {integrand.ufl_free_indices}." ) # If we have a tuple of domain ids build the integrals one by # one and construct as a Form in one go. subdomain_id = self.subdomain_id() if isinstance(subdomain_id, tuple): return Form( list( chain( *( (integrand * self.reconstruct(subdomain_id=d)).integrals() for d in subdomain_id ) ) ) ) # Check that we have an integer subdomain or a string # ("everywhere" or "otherwise", any more?) if not isinstance( subdomain_id, ( str, numbers.Integral, ), ): raise ValueError("Expecting integer or string domain id.") # If we don't have an integration domain, try to find one in # integrand domain = self.ufl_domain() if domain is None: domains = extract_domains(integrand) if len(domains) == 1: (domain,) = domains elif len(domains) == 0: raise ValueError("This integral is missing an integration domain.") else: raise ValueError( "Multiple domains found, making the choice of integration domain ambiguous." ) # Otherwise create and return a one-integral form integral = Integral( integrand=integrand, integral_type=self.integral_type(), domain=domain, subdomain_id=subdomain_id, metadata=self.metadata(), subdomain_data=self.subdomain_data(), ) return Form([integral])
[docs]class MeasureSum(object): """Represents a sum of measures. This is a notational intermediate object to translate the notation f*(ds(1)+ds(3)) into f*ds(1) + f*ds(3) """ __slots__ = ("_measures",) def __init__(self, *measures): """Initialise.""" self._measures = measures def __rmul__(self, other): """Multiply.""" integrals = [other * m for m in self._measures] return sum(integrals) def __add__(self, other): """Add.""" if isinstance(other, Measure): return MeasureSum(*(self._measures + (other,))) elif isinstance(other, MeasureSum): return MeasureSum(*(self._measures + other._measures)) return NotImplemented def __str__(self): """Format as a string.""" return "{\n " + "\n + ".join(map(str, self._measures)) + "\n}"
[docs]class MeasureProduct(object): """Represents a product of measures. This is a notational intermediate object to handle the notation f*(dm1*dm2) This is work in progress and not functional. It needs support in other parts of ufl and the rest of the code generation chain. """ __slots__ = ("_measures",) def __init__(self, *measures): """Create MeasureProduct from given list of measures.""" self._measures = measures if len(self._measures) < 2: raise ValueError("Expecting at least two measures.") def __mul__(self, other): """Flatten multiplication of product measures. This is to ensure that (dm1*dm2)*dm3 is stored as a simple list (dm1,dm2,dm3) in a single MeasureProduct. """ if isinstance(other, Measure): measures = self.sub_measures() + [other] return MeasureProduct(*measures) else: return NotImplemented def __rmul__(self, integrand): """Multiply.""" # TODO: Implement MeasureProduct.__rmul__ to construct integral and form somehow. raise NotImplementedError()
[docs] def sub_measures(self): """Return submeasures.""" return self._measures