r"""This module implements parallel loops reading and writing
:class:`.Function`\s. This provides a mechanism for implementing
non-finite element operations such as slope limiters."""
import collections
from ufl.indexed import Indexed
from ufl.domain import join_domains
from pyop2 import op2, READ, WRITE, RW, INC, MIN, MAX
import loopy
from loopy.version import LOOPY_USE_LANGUAGE_VERSION_2018_2 # noqa: F401
from firedrake.parameters import target
from firedrake import constant
from firedrake.ufl_expr import extract_domains
from firedrake.petsc import PETSc
from cachetools import LRUCache
kernel_cache = LRUCache(maxsize=128)
__all__ = ['par_loop', 'direct', 'READ', 'WRITE', 'RW', 'INC', 'MIN', 'MAX']
class _DirectLoop(object):
r"""A singleton object which can be used in a :func:`par_loop` in place
of the measure in order to indicate that the loop is a direct loop
over degrees of freedom."""
def integral_type(self):
return "direct"
def __repr__(self):
return "direct"
direct = _DirectLoop()
r"""A singleton object which can be used in a :func:`par_loop` in place
of the measure in order to indicate that the loop is a direct loop
over degrees of freedom."""
def indirect_measure(mesh, measure):
return mesh.measure_set(measure.integral_type(),
measure.subdomain_id())
_maps = {
'cell': {
'nodes': lambda x: x.cell_node_map(),
'itspace': indirect_measure
},
'interior_facet': {
'nodes': lambda x: x.interior_facet_node_map(),
'itspace': indirect_measure
},
'exterior_facet': {
'nodes': lambda x: x.exterior_facet_node_map(),
'itspace': indirect_measure
},
'direct': {
'nodes': lambda x: None,
'itspace': lambda mesh, measure: mesh
}
}
r"""Map a measure to the correct maps."""
def _form_loopy_kernel(kernel_domains, instructions, measure, args, **kwargs):
kargs = []
for var, (func, intent) in args.items():
is_input = intent in [INC, READ, RW, MAX, MIN]
is_output = intent in [INC, RW, WRITE, MAX, MIN]
if isinstance(func, constant.Constant):
if intent is not READ:
raise RuntimeError("Only READ access is allowed to Constant")
# Constants modelled as Globals, so no need for double
# indirection
ndof = func.dat.cdim
kargs.append(loopy.GlobalArg(var, dtype=func.dat.dtype, shape=(ndof,), is_input=is_input, is_output=is_output))
else:
# Do we have a component of a mixed function?
if isinstance(func, Indexed):
c, i = func.ufl_operands
idx = i._indices[0]._value
ndof = c.function_space()[idx].finat_element.space_dimension()
cdim = c.dat[idx].cdim
dtype = c.dat[idx].dtype
else:
if func.function_space().ufl_element().family() == "Real":
ndof = func.function_space().dim() # == 1
kargs.append(loopy.GlobalArg(var, dtype=func.dat.dtype, shape=(ndof,), is_input=is_input, is_output=is_output))
continue
else:
if len(func.function_space()) > 1:
raise NotImplementedError("Must index mixed function in par_loop.")
ndof = func.function_space().finat_element.space_dimension()
cdim = func.dat.cdim
dtype = func.dat.dtype
if measure.integral_type() == 'interior_facet':
ndof *= 2
# FIXME: shape for facets [2][ndof]?
kargs.append(loopy.GlobalArg(var, dtype=dtype, shape=(ndof, cdim), is_input=is_input, is_output=is_output))
kernel_domains = kernel_domains.replace(var+".dofs", str(ndof))
if kernel_domains == "":
kernel_domains = "[] -> {[]}"
try:
key = (kernel_domains, tuple(instructions), tuple(map(tuple, kwargs.items())))
# Add shape, dtype and intent to the cache key
for func, intent in args.values():
if isinstance(func, Indexed):
for dat in func.ufl_operands[0].dat.split:
key += (dat.shape, dat.dtype, intent)
else:
key += (func.dat.shape, func.dat.dtype, intent)
return kernel_cache[key]
except KeyError:
kargs.append(...)
knl = loopy.make_function(kernel_domains, instructions, kargs, name="par_loop_kernel", target=target,
seq_dependencies=True, silenced_warnings=["summing_if_branches_ops"])
knl = op2.Kernel(knl, "par_loop_kernel", **kwargs)
return kernel_cache.setdefault(key, knl)
[docs]
@PETSc.Log.EventDecorator()
def par_loop(kernel, measure, args, kernel_kwargs=None, **kwargs):
r"""A :func:`par_loop` is a user-defined operation which reads and
writes :class:`.Function`\s by looping over the mesh cells or facets
and accessing the degrees of freedom on adjacent entities.
:arg kernel: A 2-tuple of (domains, instructions) to create
a loopy kernel . The domains and instructions should be specified
in loopy kernel syntax. See the `loopy tutorial
<https://documen.tician.de/loopy/tutorial.html>`_ for details.
:arg measure: is a UFL :class:`~ufl.measure.Measure` which determines the
manner in which the iteration over the mesh is to occur.
Alternatively, you can pass :data:`direct` to designate a direct loop.
:arg args: is a dictionary mapping variable names in the kernel to
:class:`.Function`\s or components of mixed :class:`.Function`\s and
indicates how these :class:`.Function`\s are to be accessed.
:arg kernel_kwargs: keyword arguments to be passed to the
``pyop2.Kernel`` constructor
:arg kwargs: additional keyword arguments are passed to the underlying
``pyop2.par_loop``
:kwarg iterate: Optionally specify which region of an
:class:`pyop2.types.set.ExtrudedSet` to iterate over.
Valid values are the following objects from pyop2:
- ``ON_BOTTOM``: iterate over the bottom layer of cells.
- ``ON_TOP`` iterate over the top layer of cells.
- ``ALL`` iterate over all cells (the default if unspecified)
- ``ON_INTERIOR_FACETS`` iterate over all the layers
except the top layer, accessing data two adjacent (in
the extruded direction) cells at a time.
**Example**
Assume that `A` is a :class:`.Function` in CG1 and `B` is a
:class:`.Function` in DG0. Then the following code sets each DoF in
`A` to the maximum value that `B` attains in the cells adjacent to
that DoF::
A.assign(numpy.finfo(0.).min)
domain = '{[i]: 0 <= i < A.dofs}'
instructions = '''
for i
A[i] = max(A[i], B[0])
end
'''
par_loop((domain, instructions), dx, {'A' : (A, RW), 'B': (B, READ)})
**Argument definitions**
Each item in the `args` dictionary maps a string to a tuple
containing a :class:`.Function` or :class:`.Constant` and an
argument intent. The string is the c language variable name by
which this function will be accessed in the kernel. The argument
intent indicates how the kernel will access this variable:
`READ`
The variable will be read but not written to.
`WRITE`
The variable will be written to but not read. If multiple kernel
invocations write to the same DoF, then the order of these writes
is undefined.
`RW`
The variable will be both read and written to. If multiple kernel
invocations access the same DoF, then the order of these accesses
is undefined, but it is guaranteed that no race will occur.
`INC`
The variable will be added into using +=. As before, the order in
which the kernel invocations increment the variable is undefined,
but there is a guarantee that no races will occur.
.. note::
Only `READ` intents are valid for :class:`.Constant`
coefficients, and an error will be raised in other cases.
**The measure**
The measure determines the mesh entities over which the iteration
will occur, and the size of the kernel stencil. The iteration will
occur over the same mesh entities as if the measure had been used
to define an integral, and the stencil will likewise be the same
as the integral case. That is to say, if the measure is a volume
measure, the kernel will be called once per cell and the DoFs
accessible to the kernel will be those associated with the cell,
its facets, edges and vertices. If the measure is a facet measure
then the iteration will occur over the corresponding class of
facets and the accessible DoFs will be those on the cell(s)
adjacent to the facet, and on the facets, edges and vertices
adjacent to those facets.
For volume measures the DoFs are guaranteed to be in the FInAT
local DoFs order. For facet measures, the DoFs will be in sorted
first by the cell to which they are adjacent. Within each cell,
they will be in FInAT order. Note that if a continuous
:class:`.Function` is accessed via an internal facet measure, the
DoFs on the interface between the two facets will be accessible
twice: once via each cell. The orientation of the cell(s) relative
to the current facet is currently arbitrary.
A direct loop over nodes without any indirections can be specified
by passing :data:`direct` as the measure. In this case, all of the
arguments must be :class:`.Function`\s in the same
:class:`.FunctionSpace`.
**The kernel code**
Indirect free variables referencing :class:`.Function`\s are all
of type `double*`. For spaces with rank greater than zero (Vector
or TensorElement), the data are laid out XYZ... XYZ... XYZ....
With the vector/tensor component moving fastest.
In loopy syntax, these may be addressed using 2D indexing::
A[i, j]
Where ``i`` runs over nodes, and ``j`` runs over components.
In a direct :func:`par_loop`, the variables will all be of type
`double*` with the single index being the vector component.
:class:`.Constant`\s are always of type `double*`, both for
indirect and direct :func:`par_loop` calls.
"""
# catch deprecated C-string parloops
if isinstance(kernel, str):
raise TypeError("C-string kernels are no longer supported by Firedrake parloops")
if "is_loopy_kernel" in kwargs:
if kwargs.pop("is_loopy_kernel"):
import warnings
warnings.warn(
"is_loopy_kernel does not need to be specified", FutureWarning)
else:
raise ValueError(
"Support for C-string kernels has been dropped, firedrake.parloop "
"will only work with loopy parloops.")
if kernel_kwargs is None:
kernel_kwargs = {}
_map = _maps[measure.integral_type()]
# Ensure that the dict args passed in are consistently ordered
# (sorted by the string key).
sorted_args = collections.OrderedDict()
for k in sorted(args.keys()):
sorted_args[k] = args[k]
args = sorted_args
if measure is direct:
mesh = None
for (func, intent) in args.values():
if isinstance(func, Indexed):
c, i = func.ufl_operands
idx = i._indices[0]._value
if mesh and c.node_set[idx] is not mesh:
raise ValueError("Cannot mix sets in direct loop.")
mesh = c.node_set[idx]
else:
try:
if mesh and func.node_set is not mesh:
raise ValueError("Cannot mix sets in direct loop.")
mesh = func.node_set
except AttributeError:
# Argument was a Global.
pass
if not mesh:
raise TypeError("No Functions passed to direct par_loop")
else:
domains = []
for func, _ in args.values():
domains.extend(extract_domains(func))
domains = join_domains(domains)
# Assume only one domain
domain, = domains
mesh = domain
kernel_domains, instructions = kernel
op2args = [_form_loopy_kernel(kernel_domains, instructions, measure, args, **kernel_kwargs)]
op2args.append(_map['itspace'](mesh, measure))
def mkarg(f, intent):
if isinstance(f, Indexed):
c, i = f.ufl_operands
idx = i._indices[0]._value
m = _map['nodes'](c)
return c.dat[idx](intent, m.split[idx] if m else None)
return f.dat(intent, _map['nodes'](f))
op2args += [mkarg(func, intent) for (func, intent) in args.values()]
return op2.parloop(*op2args, **kwargs)
