def compute_form_action(form, coefficient):
"""Compute the action of a form on a Coefficient.
This works simply by replacing the last Argument
with a Coefficient on the same function space (element).
The form returned will thus have one Argument less
and one additional Coefficient at the end if no
Coefficient has been provided.
"""
# TODO: Check whatever makes sense for coefficient
# Extract all arguments
arguments = form.arguments()
parts = [arg.part() for arg in arguments]
if set(parts) - {None}:
error("compute_form_action cannot handle parts.")
# Pick last argument (will be replaced)
u = arguments[-1]
fs = u.ufl_function_space()
if coefficient is None:
coefficient = Coefficient(fs)
elif coefficient.ufl_function_space() != fs:
debug("Computing action of form on a coefficient in a different function space.")
return replace(form, {u: coefficient})
def compute_form_action(form, coefficient):
"""Compute the action of a form on a Coefficient.
This works simply by replacing the last Argument
with a Coefficient on the same function space (element).
The form returned will thus have one Argument less
and one additional Coefficient at the end if no
Coefficient has been provided.
"""
# TODO: Check whatever makes sense for coefficient
# Extract all arguments
arguments = form.arguments()
parts = [arg.part() for arg in arguments]
if set(parts) - {None}:
error("compute_form_action cannot handle parts.")
# Pick last argument (will be replaced)
u = arguments[-1]
fs = u.ufl_function_space()
if coefficient is None:
coefficient = Coefficient(fs)
elif coefficient.ufl_function_space() != fs:
debug("Computing action of form on a coefficient in a different function space.")
return replace(form, {u: coefficient})
def compute_form_action(form, coefficient):
"""Compute the action of a form on a Coefficient.
This works simply by replacing the last Argument
with a Coefficient on the same function space (element).
The form returned will thus have one Argument less
and one additional Coefficient at the end if no
Coefficient has been provided.
"""
# TODO: Check whatever makes sense for coefficient
# Extract all arguments
arguments = extract_arguments(form)
# Pick last argument (will be replaced)
u = arguments[-1]
e = u.element()
if coefficient is None:
coefficient = Coefficient(e)
else:
#ufl_assert(coefficient.element() == e, \
if coefficient.element() != e:
debug("Computing action of form on a coefficient in a different element space.")
return replace(form, { u: coefficient })
def compute_form_action(form, coefficient):
"""Compute the action of a form on a Coefficient.
This works simply by replacing the last Argument
with a Coefficient on the same function space (element).
The form returned will thus have one Argument less
and one additional Coefficient at the end if no
Coefficient has been provided.
"""
# TODO: Check whatever makes sense for coefficient
# Extract all arguments
arguments = extract_arguments(form)
# Pick last argument (will be replaced)
u = arguments[-1]
e = u.element()
if coefficient is None:
coefficient = Coefficient(e)
else:
#ufl_assert(coefficient.element() == e, \
if coefficient.element() != e:
debug(
"Computing action of form on a coefficient in a different element space."
)
return replace(form, {u: coefficient})
def transform_integrands(form, transform, domain_type=None):
"""Apply transform(expression) to each integrand
expression in form, or to form if it is an Expr."""
if isinstance(form, Form):
newintegrals = []
for itg in form.integrals():
integrand = itg.integrand()
if domain_type is None or domain_type == itg.domain_type():
integrand = transform(integrand)
if not isinstance(integrand, Zero):
newitg = itg.reconstruct(integrand)
newintegrals.append(newitg)
if not newintegrals:
debug(
"No integrals left after transformation, returning empty form."
)
return Form(newintegrals)
elif isinstance(form, Integral):
integral = form
integrand = transform(integral.integrand())
new_integral = integral.reconstruct(integrand)
return new_integral
elif isinstance(form, Expr):
expr = form
return transform(expr)
else:
error("Expecting Form or Expr.")
def coefficient(self, o):
# Define dw/dw := d/ds [w + s v] = v
debug("In CoefficientAD.coefficient:")
debug("o = %s" % o)
debug("self._w = %s" % self._w)
debug("self._v = %s" % self._v)
# Find o among w
for (w, v) in izip(self._w, self._v):
if o == w:
return (w, v)
# If o is not among coefficient derivatives, return do/dw=0
oprimesum = Zero(o.shape())
oprimes = self._cd._data.get(o)
if oprimes is None:
if self._cd._data:
# TODO: Make it possible to silence this message in particular?
# It may be good to have for debugging...
warning("Assuming d{%s}/d{%s} = 0." % (o, self._w))
else:
# Make sure we have a tuple to match the self._v tuple
if not isinstance(oprimes, tuple):
oprimes = (oprimes,)
ufl_assert(len(oprimes) == len(self._v), "Got a tuple of arguments, "+\
"expecting a matching tuple of coefficient derivatives.")
# Compute do/dw_j = do/dw_h : v.
# Since we may actually have a tuple of oprimes and vs in a
# 'mixed' space, sum over them all to get the complete inner
# product. Using indices to define a non-compound inner product.
for (oprime, v) in izip(oprimes, self._v):
so, oi = as_scalar(oprime)
rv = len(v.shape())
oi1 = oi[:-rv]
oi2 = oi[-rv:]
prod = so*v[oi2]
if oi1:
oprimesum += as_tensor(prod, oi1)
else:
oprimesum += prod
# Example:
# (f : g) -> (dfdu : v) : g + ditto
# shape(f) == shape(g) == shape(dfdu : v)
# shape(dfdu) == shape(f) + shape(v)
return (o, oprimesum)
def is_multilinear(form):
"Check if form is multilinear in arguments."
# An attempt at implementing is_multilinear using extract_argument_dependencies.
# TODO: This has some false negatives for "multiple configurations". (Does it still? Needs testing!)
# TODO: FFC probably needs a variant of this which checks for some sorts of linearity
# in Coefficients as well, this should be a fairly simple extension of the current algorithm.
try:
for e in iter_expressions(form):
deps = extract_argument_dependencies(e)
nargs = [len(d) for d in deps]
if len(nargs) == 0:
debug("This form is a functional.")
if len(nargs) == 1:
debug("This form is linear in %d arguments." % nargs[0])
if len(nargs) > 1:
warning("This form has more than one argument "\
"'configuration', it has terms that are linear in %s "\
"arguments respectively." % str(nargs))
except NotMultiLinearException, msg:
warning("Form is not multilinear, the offending term is: %s" % msg)
return False
def coefficient(self, o):
# Define dw/dw := d/ds [w + s v] = v
debug("In CoefficientAD.coefficient:")
debug("o = %s" % o)
debug("self._w = %s" % self._w)
debug("self._v = %s" % self._v)
# Find o among w
for (w, v) in izip(self._w, self._v):
if o == w:
return (w, v)
# If o is not among coefficient derivatives, return do/dw=0
oprimesum = Zero(o.shape())
oprimes = self._cd._data.get(o)
if oprimes is None:
if self._cd._data:
# TODO: Make it possible to silence this message in particular?
# It may be good to have for debugging...
warning("Assuming d{%s}/d{%s} = 0." % (o, self._w))
else:
# Make sure we have a tuple to match the self._v tuple
if not isinstance(oprimes, tuple):
oprimes = (oprimes, )
ufl_assert(len(oprimes) == len(self._v), "Got a tuple of arguments, "+\
"expecting a matching tuple of coefficient derivatives.")
# Compute do/dw_j = do/dw_h : v.
# Since we may actually have a tuple of oprimes and vs in a
# 'mixed' space, sum over them all to get the complete inner
# product. Using indices to define a non-compound inner product.
for (oprime, v) in izip(oprimes, self._v):
so, oi = as_scalar(oprime)
rv = len(v.shape())
oi1 = oi[:-rv]
oi2 = oi[-rv:]
prod = so * v[oi2]
if oi1:
oprimesum += as_tensor(prod, oi1)
else:
oprimesum += prod
# Example:
# (f : g) -> (dfdu : v) : g + ditto
# shape(f) == shape(g) == shape(dfdu : v)
# shape(dfdu) == shape(f) + shape(v)
return (o, oprimesum)
def is_multilinear(form):
"Check if form is multilinear in arguments."
# An attempt at implementing is_multilinear using extract_argument_dependencies.
# TODO: This has some false negatives for "multiple configurations". (Does it still? Needs testing!)
# TODO: FFC probably needs a variant of this which checks for some sorts of linearity
# in Coefficients as well, this should be a fairly simple extension of the current algorithm.
try:
for e in iter_expressions(form):
deps = extract_argument_dependencies(e)
nargs = [len(d) for d in deps]
if len(nargs) == 0:
debug("This form is a functional.")
if len(nargs) == 1:
debug("This form is linear in %d arguments." % nargs[0])
if len(nargs) > 1:
warning("This form has more than one argument "\
"'configuration', it has terms that are linear in %s "\
"arguments respectively." % str(nargs))
except NotMultiLinearException, msg:
warning("Form is not multilinear, the offending term is: %s" % msg)
return False
def _debug_visit(self, o):
"Debugging hook, enable this by renaming to 'visit'."
r = Transformer.visit(self, o)
f, df = r
if not f is o:
debug("In ForwardAD.visit, didn't get back o:")
debug(" o: %s" % str(o))
debug(" f: %s" % str(f))
debug(" df: %s" % str(df))
fi_diff = set(f.free_indices()) ^ set(df.free_indices())
if fi_diff:
debug("In ForwardAD.visit, got free indices diff:")
debug(" o: %s" % str(o))
debug(" f: %s" % str(f))
debug(" df: %s" % str(df))
debug(" f.fi(): %s" % lstr(f.free_indices()))
debug(" df.fi(): %s" % lstr(df.free_indices()))
debug(" fi_diff: %s" % str(fi_diff))
return r
def build_uflacs_ir(cell, integral_type, entitytype,
integrands, tensor_shape,
coefficient_numbering,
quadrature_rules, parameters):
# The intermediate representation dict we're building and returning here
ir = {}
# Extract uflacs specific optimization and code generation parameters
p = parse_uflacs_optimization_parameters(parameters, integral_type)
# Pass on parameters for consumption in code generation
ir["params"] = p
# { ufl coefficient: count }
ir["coefficient_numbering"] = coefficient_numbering
# Shared unique tables for all quadrature loops
ir["unique_tables"] = {}
ir["unique_table_types"] = {}
# Shared piecewise expr_ir for all quadrature loops
ir["piecewise_ir"] = empty_expr_ir()
# { num_points: expr_ir for one integrand }
ir["varying_irs"] = {}
# Temporary data structures to build shared piecewise data
pe2i = {}
piecewise_modified_argument_indices = {}
# Whether we expect the quadrature weight to be applied or not
# (in some cases it's just set to 1 in ufl integral scaling)
tdim = cell.topological_dimension()
expect_weight = (
integral_type not in ("expression",) + point_integral_types
and (entitytype == "cell"
or (entitytype == "facet" and tdim > 1)
or (integral_type in custom_integral_types)
)
)
if integral_type == "expression":
# TODO: Figure out how to get non-integrand expressions in here, this is just a draft:
# Analyse all expressions in one list
assert isinstance(integrands, (tuple, list))
all_num_points = [None]
cases = [(None, integrands)]
else:
# Analyse each num_points/integrand separately
assert isinstance(integrands, dict)
all_num_points = sorted(integrands.keys())
cases = [(num_points, [integrands[num_points]])
for num_points in all_num_points]
ir["all_num_points"] = all_num_points
for num_points, expressions in cases:
# Rebalance order of nested terminal modifiers
expressions = [balance_modifiers(expr) for expr in expressions]
# Build initial scalar list-based graph representation
V, V_deps, V_targets = build_scalar_graph(expressions)
# Build terminal_data from V here before factorization.
# Then we can use it to derive table properties for all modified terminals,
# and then use that to rebuild the scalar graph more efficiently before
# argument factorization. We can build terminal_data again after factorization
# if that's necessary.
initial_terminal_indices = [i for i, v in enumerate(V)
if is_modified_terminal(v)]
initial_terminal_data = [analyse_modified_terminal(V[i])
for i in initial_terminal_indices]
unique_tables, unique_table_types, unique_table_num_dofs, mt_unique_table_reference = \
build_optimized_tables(num_points, quadrature_rules,
cell, integral_type, entitytype, initial_terminal_data,
ir["unique_tables"], p["enable_table_zero_compression"],
rtol=p["table_rtol"], atol=p["table_atol"])
# Replace some scalar modified terminals before reconstructing expressions
# (could possibly use replace() on target expressions instead)
z = as_ufl(0.0)
one = as_ufl(1.0)
for i, mt in zip(initial_terminal_indices, initial_terminal_data):
if isinstance(mt.terminal, QuadratureWeight):
# Replace quadrature weight with 1.0, will be added back later
V[i] = one
else:
# Set modified terminals with zero tables to zero
tr = mt_unique_table_reference.get(mt)
if tr is not None and tr.ttype == "zeros":
V[i] = z
# Propagate expression changes using dependency list
for i in range(len(V)):
deps = [V[j] for j in V_deps[i]]
if deps:
V[i] = V[i]._ufl_expr_reconstruct_(*deps)
# Rebuild scalar target expressions and graph
# (this may be overkill and possible to optimize
# away if it turns out to be costly)
expressions = [V[i] for i in V_targets]
# Rebuild scalar list-based graph representation
SV, SV_deps, SV_targets = build_scalar_graph(expressions)
assert all(i < len(SV) for i in SV_targets)
# Compute factorization of arguments
(argument_factorizations, modified_arguments,
FV, FV_deps, FV_targets) = \
compute_argument_factorization(SV, SV_deps, SV_targets, len(tensor_shape))
assert len(SV_targets) == len(argument_factorizations)
# TODO: Still expecting one target variable in code generation
assert len(argument_factorizations) == 1
argument_factorization, = argument_factorizations
# Store modified arguments in analysed form
for i in range(len(modified_arguments)):
modified_arguments[i] = analyse_modified_terminal(modified_arguments[i])
# Build set of modified_terminal indices into factorized_vertices
modified_terminal_indices = [i for i, v in enumerate(FV)
if is_modified_terminal(v)]
# Build set of modified terminal ufl expressions
modified_terminals = [analyse_modified_terminal(FV[i])
for i in modified_terminal_indices]
# Make it easy to get mt object from FV index
FV_mts = [None]*len(FV)
for i, mt in zip(modified_terminal_indices, modified_terminals):
FV_mts[i] = mt
# Mark active modified arguments
#active_modified_arguments = numpy.zeros(len(modified_arguments), dtype=int)
#for ma_indices in argument_factorization:
# for j in ma_indices:
# active_modified_arguments[j] = 1
# Dependency analysis
inv_FV_deps, FV_active, FV_piecewise, FV_varying = \
analyse_dependencies(FV, FV_deps, FV_targets,
modified_terminal_indices,
modified_terminals,
mt_unique_table_reference)
# Extend piecewise V with unique new FV_piecewise vertices
pir = ir["piecewise_ir"]
for i, v in enumerate(FV):
if FV_piecewise[i]:
j = pe2i.get(v)
if j is None:
j = len(pe2i)
pe2i[v] = j
pir["V"].append(v)
pir["V_active"].append(1)
mt = FV_mts[i]
if mt is not None:
pir["mt_tabledata"][mt] = mt_unique_table_reference.get(mt)
pir["V_mts"].append(mt)
# Extend piecewise modified_arguments list with unique new items
for mt in modified_arguments:
ma = piecewise_modified_argument_indices.get(mt)
if ma is None:
ma = len(pir["modified_arguments"])
pir["modified_arguments"].append(mt)
piecewise_modified_argument_indices[mt] = ma
# Loop over factorization terms
block_contributions = defaultdict(list)
for ma_indices, fi in sorted(argument_factorization.items()):
# Get a bunch of information about this term
rank = len(ma_indices)
trs = tuple(mt_unique_table_reference[modified_arguments[ai]] for ai in ma_indices)
unames = tuple(tr.name for tr in trs)
ttypes = tuple(tr.ttype for tr in trs)
assert not any(tt == "zeros" for tt in ttypes)
blockmap = tuple(tr.dofmap for tr in trs)
block_is_uniform = all(tr.is_uniform for tr in trs)
# Collect relevant restrictions to identify blocks
# correctly in interior facet integrals
block_restrictions = []
for i, ma in enumerate(ma_indices):
if trs[i].is_uniform:
r = None
else:
r = modified_arguments[ma].restriction
block_restrictions.append(r)
block_restrictions = tuple(block_restrictions)
# Store piecewise status for fi and translate
# index to piecewise scope if relevant
factor_is_piecewise = FV_piecewise[fi]
if factor_is_piecewise:
factor_index = pe2i[FV[fi]]
else:
factor_index = fi
# TODO: Add separate block modes for quadrature
# Both arguments in quadrature elements
"""
for iq
fw = f*w
#for i
# for j
# B[i,j] = fw*U[i]*V[j] = 0 if i != iq or j != iq
BQ[iq] = B[iq,iq] = fw
for (iq)
A[iq+offset0, iq+offset1] = BQ[iq]
"""
# One argument in quadrature element
"""
for iq
fw[iq] = f*w
#for i
# for j
# B[i,j] = fw*UQ[i]*V[j] = 0 if i != iq
for j
BQ[iq,j] = fw[iq]*V[iq,j]
for (iq) for (j)
A[iq+offset, j+offset] = BQ[iq,j]
"""
# Decide how to handle code generation for this block
if p["enable_preintegration"] and (factor_is_piecewise
and rank > 0 and "quadrature" not in ttypes):
# - Piecewise factor is an absolute prerequisite
# - Could work for rank 0 as well but currently doesn't
# - Haven't considered how quadrature elements work out
block_mode = "preintegrated"
elif p["enable_premultiplication"] and (rank > 0
and all(tt in piecewise_ttypes for tt in ttypes)):
# Integrate functional in quadloop, scale block after quadloop
block_mode = "premultiplied"
elif p["enable_sum_factorization"]:
if (rank == 2 and any(tt in piecewise_ttypes for tt in ttypes)):
# Partial computation in quadloop of f*u[i],
# compute (f*u[i])*v[i] outside quadloop,
# (or with u,v swapped)
block_mode = "partial"
else:
# Full runtime integration of f*u[i]*v[j],
# can still do partial computation in quadloop of f*u[i]
# but must compute (f*u[i])*v[i] as well inside quadloop.
# (or with u,v swapped)
block_mode = "full"
else:
# Use full runtime integration with nothing fancy going on
block_mode = "safe"
# Carry out decision
if block_mode == "preintegrated":
# Add to contributions:
# P = sum_q weight*u*v; preintegrated here
# B[...] = f * P[...]; generated after quadloop
# A[blockmap] += B[...]; generated after quadloop
cache = ir["piecewise_ir"]["preintegrated_blocks"]
block_is_transposed = False
pname = cache.get(unames)
# Reuse transpose to save memory
if p["enable_block_transpose_reuse"] and pname is None and len(unames) == 2:
pname = cache.get((unames[1], unames[0]))
if pname is not None:
# Cache hit on transpose
block_is_transposed = True
if pname is None:
# Cache miss, precompute block
weights = quadrature_rules[num_points][1]
if integral_type == "interior_facet":
ptable = integrate_block_interior_facets(weights, unames, ttypes,
unique_tables, unique_table_num_dofs)
else:
ptable = integrate_block(weights, unames, ttypes,
unique_tables, unique_table_num_dofs)
ptable = clamp_table_small_numbers(ptable, rtol=p["table_rtol"], atol=p["table_atol"])
pname = "PI%d" % (len(cache,))
cache[unames] = pname
unique_tables[pname] = ptable
unique_table_types[pname] = "preintegrated"
assert factor_is_piecewise
block_unames = (pname,)
blockdata = preintegrated_block_data_t(block_mode, ttypes,
factor_index, factor_is_piecewise,
block_unames, block_restrictions,
block_is_transposed, block_is_uniform,
pname)
block_is_piecewise = True
elif block_mode == "premultiplied":
# Add to contributions:
# P = u*v; computed here
# FI = sum_q weight * f; generated inside quadloop
# B[...] = FI * P[...]; generated after quadloop
# A[blockmap] += B[...]; generated after quadloop
cache = ir["piecewise_ir"]["premultiplied_blocks"]
block_is_transposed = False
pname = cache.get(unames)
# Reuse transpose to save memory
if p["enable_block_transpose_reuse"] and pname is None and len(unames) == 2:
pname = cache.get((unames[1], unames[0]))
if pname is not None:
# Cache hit on transpose
block_is_transposed = True
if pname is None:
# Cache miss, precompute block
if integral_type == "interior_facet":
ptable = multiply_block_interior_facets(0, unames, ttypes, unique_tables, unique_table_num_dofs)
else:
ptable = multiply_block(0, unames, ttypes, unique_tables, unique_table_num_dofs)
pname = "PM%d" % (len(cache,))
cache[unames] = pname
unique_tables[pname] = ptable
unique_table_types[pname] = "premultiplied"
block_unames = (pname,)
blockdata = premultiplied_block_data_t(block_mode, ttypes,
factor_index, factor_is_piecewise,
block_unames, block_restrictions,
block_is_transposed, block_is_uniform,
pname)
block_is_piecewise = False
elif block_mode == "scaled": # TODO: Add mode, block is piecewise but choose not to be premultiplied
# Add to contributions:
# FI = sum_q weight * f; generated inside quadloop
# B[...] = FI * u * v; generated after quadloop
# A[blockmap] += B[...]; generated after quadloop
raise NotImplementedError("scaled block mode not implemented.")
# (probably need mostly the same data as premultiplied, except no P table name or values)
block_is_piecewise = False
elif block_mode in ("partial", "full", "safe"):
# Translate indices to piecewise context if necessary
block_is_piecewise = factor_is_piecewise and not expect_weight
ma_data = []
for i, ma in enumerate(ma_indices):
if trs[i].is_piecewise:
ma_index = piecewise_modified_argument_indices[modified_arguments[ma]]
else:
block_is_piecewise = False
ma_index = ma
ma_data.append(ma_data_t(ma_index, trs[i]))
block_is_transposed = False # FIXME: Handle transposes for these block types
if block_mode == "partial":
# Add to contributions:
# P[i] = sum_q weight * f * u[i]; generated inside quadloop
# B[i,j] = P[i] * v[j]; generated after quadloop (where v is the piecewise ma)
# A[blockmap] += B[...]; generated after quadloop
# Find first piecewise index TODO: Is last better? just reverse range here
for i in range(rank):
if trs[i].is_piecewise:
piecewise_ma_index = i
break
assert rank == 2
not_piecewise_ma_index = 1 - piecewise_ma_index
block_unames = (unames[not_piecewise_ma_index],)
blockdata = partial_block_data_t(block_mode, ttypes,
factor_index, factor_is_piecewise,
block_unames, block_restrictions,
block_is_transposed,
tuple(ma_data), piecewise_ma_index)
elif block_mode in ("full", "safe"):
# Add to contributions:
# B[i] = sum_q weight * f * u[i] * v[j]; generated inside quadloop
# A[blockmap] += B[i]; generated after quadloop
block_unames = unames
blockdata = full_block_data_t(block_mode, ttypes,
factor_index, factor_is_piecewise,
block_unames, block_restrictions,
block_is_transposed,
tuple(ma_data))
else:
error("Invalid block_mode %s" % (block_mode,))
if block_is_piecewise:
# Insert in piecewise expr_ir
ir["piecewise_ir"]["block_contributions"][blockmap].append(blockdata)
else:
# Insert in varying expr_ir for this quadrature loop
block_contributions[blockmap].append(blockdata)
# Figure out which table names are referenced in unstructured partition
active_table_names = set()
for i, mt in zip(modified_terminal_indices, modified_terminals):
tr = mt_unique_table_reference.get(mt)
if tr is not None and FV_active[i]:
active_table_names.add(tr.name)
# Figure out which table names are referenced in blocks
for blockmap, contributions in chain(block_contributions.items(),
ir["piecewise_ir"]["block_contributions"].items()):
for blockdata in contributions:
if blockdata.block_mode in ("preintegrated", "premultiplied"):
active_table_names.add(blockdata.name)
elif blockdata.block_mode in ("partial", "full", "safe"):
for mad in blockdata.ma_data:
active_table_names.add(mad.tabledata.name)
# Record all table types before dropping tables
ir["unique_table_types"].update(unique_table_types)
# Drop tables not referenced from modified terminals
# and tables of zeros and ones
unused_ttypes = ("zeros", "ones", "quadrature")
keep_table_names = set()
for name in active_table_names:
ttype = ir["unique_table_types"][name]
if ttype not in unused_ttypes:
if name in unique_tables:
keep_table_names.add(name)
unique_tables = { name: unique_tables[name]
for name in keep_table_names }
# Add to global set of all tables
for name, table in unique_tables.items():
tbl = ir["unique_tables"].get(name)
if tbl is not None and not numpy.allclose(tbl, table, rtol=p["table_rtol"], atol=p["table_atol"]):
error("Table values mismatch with same name.")
ir["unique_tables"].update(unique_tables)
# Analyse active terminals to check what we'll need to generate code for
active_mts = []
for i, mt in zip(modified_terminal_indices, modified_terminals):
if FV_active[i]:
active_mts.append(mt)
# Figure out if we need to access CellCoordinate to
# avoid generating quadrature point table otherwise
if integral_type == "cell":
need_points = any(isinstance(mt.terminal, CellCoordinate)
for mt in active_mts)
elif integral_type in facet_integral_types:
need_points = any(isinstance(mt.terminal, FacetCoordinate)
for mt in active_mts)
elif integral_type in custom_integral_types:
need_points = True # TODO: Always?
else:
need_points = False
# Figure out if we need to access QuadratureWeight to
# avoid generating quadrature point table otherwise
#need_weights = any(isinstance(mt.terminal, QuadratureWeight)
# for mt in active_mts)
# Count blocks of each mode
block_modes = defaultdict(int)
for blockmap, contributions in block_contributions.items():
for blockdata in contributions:
block_modes[blockdata.block_mode] += 1
# Debug output
summary = "\n".join(" %d\t%s" % (count, mode)
for mode, count in sorted(block_modes.items()))
debug("Blocks of each mode: \n" + summary)
# If there are any blocks other than preintegrated we need weights
if expect_weight and any(mode != "preintegrated" for mode in block_modes):
need_weights = True
elif integral_type in custom_integral_types:
need_weights = True # TODO: Always?
else:
need_weights = False
# Build IR dict for the given expressions
expr_ir = {}
# (array) FV-index -> UFL subexpression
expr_ir["V"] = FV
# (array) V indices for each input expression component in flattened order
expr_ir["V_targets"] = FV_targets
### Result of factorization:
# (array) MA-index -> UFL expression of modified arguments
expr_ir["modified_arguments"] = modified_arguments
# (dict) tuple(MA-indices) -> FV-index of monomial factor
#expr_ir["argument_factorization"] = argument_factorization
expr_ir["block_contributions"] = block_contributions
### Modified terminals
# (array) list of FV-indices to modified terminals
#expr_ir["modified_terminal_indices"] = modified_terminal_indices
# Dependency structure of graph:
# (CRSArray) FV-index -> direct dependency FV-index list
#expr_ir["dependencies"] = FV_deps
# (CRSArray) FV-index -> direct dependee FV-index list
#expr_ir["inverse_dependencies"] = inv_FV_deps
# Metadata about each vertex
#expr_ir["active"] = FV_active # (array) FV-index -> bool
#expr_ir["V_piecewise"] = FV_piecewise # (array) FV-index -> bool
expr_ir["V_varying"] = FV_varying # (array) FV-index -> bool
expr_ir["V_mts"] = FV_mts
# Store mapping from modified terminal object to
# table data, this is used in integralgenerator
expr_ir["mt_tabledata"] = mt_unique_table_reference
# To emit quadrature rules only if needed
expr_ir["need_points"] = need_points
expr_ir["need_weights"] = need_weights
# Store final ir for this num_points
ir["varying_irs"][num_points] = expr_ir
return ir
def build_uflacs_ir(cell, integral_type, entitytype, integrands, tensor_shape,
coefficient_numbering, quadrature_rules, parameters):
# The intermediate representation dict we're building and returning here
ir = {}
# Extract uflacs specific optimization and code generation parameters
p = parse_uflacs_optimization_parameters(parameters, integral_type)
# Pass on parameters for consumption in code generation
ir["params"] = p
# { ufl coefficient: count }
ir["coefficient_numbering"] = coefficient_numbering
# Shared unique tables for all quadrature loops
ir["unique_tables"] = {}
ir["unique_table_types"] = {}
# Shared piecewise expr_ir for all quadrature loops
ir["piecewise_ir"] = empty_expr_ir()
# { num_points: expr_ir for one integrand }
ir["varying_irs"] = {}
# Temporary data structures to build shared piecewise data
pe2i = {}
piecewise_modified_argument_indices = {}
# Whether we expect the quadrature weight to be applied or not
# (in some cases it's just set to 1 in ufl integral scaling)
tdim = cell.topological_dimension()
expect_weight = (
integral_type not in ("expression", ) + point_integral_types
and (entitytype == "cell" or (entitytype == "facet" and tdim > 1) or
(integral_type in custom_integral_types)))
if integral_type == "expression":
# TODO: Figure out how to get non-integrand expressions in here, this is just a draft:
# Analyse all expressions in one list
assert isinstance(integrands, (tuple, list))
all_num_points = [None]
cases = [(None, integrands)]
else:
# Analyse each num_points/integrand separately
assert isinstance(integrands, dict)
all_num_points = sorted(integrands.keys())
cases = [(num_points, [integrands[num_points]])
for num_points in all_num_points]
ir["all_num_points"] = all_num_points
for num_points, expressions in cases:
# Rebalance order of nested terminal modifiers
expressions = [balance_modifiers(expr) for expr in expressions]
# Build initial scalar list-based graph representation
V, V_deps, V_targets = build_scalar_graph(expressions)
# Build terminal_data from V here before factorization.
# Then we can use it to derive table properties for all modified terminals,
# and then use that to rebuild the scalar graph more efficiently before
# argument factorization. We can build terminal_data again after factorization
# if that's necessary.
initial_terminal_indices = [
i for i, v in enumerate(V) if is_modified_terminal(v)
]
initial_terminal_data = [
analyse_modified_terminal(V[i]) for i in initial_terminal_indices
]
unique_tables, unique_table_types, unique_table_num_dofs, mt_unique_table_reference = \
build_optimized_tables(num_points, quadrature_rules,
cell, integral_type, entitytype, initial_terminal_data,
ir["unique_tables"], p["enable_table_zero_compression"],
rtol=p["table_rtol"], atol=p["table_atol"])
# Replace some scalar modified terminals before reconstructing expressions
# (could possibly use replace() on target expressions instead)
z = as_ufl(0.0)
one = as_ufl(1.0)
for i, mt in zip(initial_terminal_indices, initial_terminal_data):
if isinstance(mt.terminal, QuadratureWeight):
# Replace quadrature weight with 1.0, will be added back later
V[i] = one
else:
# Set modified terminals with zero tables to zero
tr = mt_unique_table_reference.get(mt)
if tr is not None and tr.ttype == "zeros":
V[i] = z
# Propagate expression changes using dependency list
for i in range(len(V)):
deps = [V[j] for j in V_deps[i]]
if deps:
V[i] = V[i]._ufl_expr_reconstruct_(*deps)
# Rebuild scalar target expressions and graph
# (this may be overkill and possible to optimize
# away if it turns out to be costly)
expressions = [V[i] for i in V_targets]
# Rebuild scalar list-based graph representation
SV, SV_deps, SV_targets = build_scalar_graph(expressions)
assert all(i < len(SV) for i in SV_targets)
# Compute factorization of arguments
(argument_factorizations, modified_arguments,
FV, FV_deps, FV_targets) = \
compute_argument_factorization(SV, SV_deps, SV_targets, len(tensor_shape))
assert len(SV_targets) == len(argument_factorizations)
# TODO: Still expecting one target variable in code generation
assert len(argument_factorizations) == 1
argument_factorization, = argument_factorizations
# Store modified arguments in analysed form
for i in range(len(modified_arguments)):
modified_arguments[i] = analyse_modified_terminal(
modified_arguments[i])
# Build set of modified_terminal indices into factorized_vertices
modified_terminal_indices = [
i for i, v in enumerate(FV) if is_modified_terminal(v)
]
# Build set of modified terminal ufl expressions
modified_terminals = [
analyse_modified_terminal(FV[i]) for i in modified_terminal_indices
]
# Make it easy to get mt object from FV index
FV_mts = [None] * len(FV)
for i, mt in zip(modified_terminal_indices, modified_terminals):
FV_mts[i] = mt
# Mark active modified arguments
#active_modified_arguments = numpy.zeros(len(modified_arguments), dtype=int)
#for ma_indices in argument_factorization:
# for j in ma_indices:
# active_modified_arguments[j] = 1
# Dependency analysis
inv_FV_deps, FV_active, FV_piecewise, FV_varying = \
analyse_dependencies(FV, FV_deps, FV_targets,
modified_terminal_indices,
modified_terminals,
mt_unique_table_reference)
# Extend piecewise V with unique new FV_piecewise vertices
pir = ir["piecewise_ir"]
for i, v in enumerate(FV):
if FV_piecewise[i]:
j = pe2i.get(v)
if j is None:
j = len(pe2i)
pe2i[v] = j
pir["V"].append(v)
pir["V_active"].append(1)
mt = FV_mts[i]
if mt is not None:
pir["mt_tabledata"][
mt] = mt_unique_table_reference.get(mt)
pir["V_mts"].append(mt)
# Extend piecewise modified_arguments list with unique new items
for mt in modified_arguments:
ma = piecewise_modified_argument_indices.get(mt)
if ma is None:
ma = len(pir["modified_arguments"])
pir["modified_arguments"].append(mt)
piecewise_modified_argument_indices[mt] = ma
# Loop over factorization terms
block_contributions = defaultdict(list)
for ma_indices, fi in sorted(argument_factorization.items()):
# Get a bunch of information about this term
rank = len(ma_indices)
trs = tuple(mt_unique_table_reference[modified_arguments[ai]]
for ai in ma_indices)
unames = tuple(tr.name for tr in trs)
ttypes = tuple(tr.ttype for tr in trs)
assert not any(tt == "zeros" for tt in ttypes)
blockmap = tuple(tr.dofmap for tr in trs)
block_is_uniform = all(tr.is_uniform for tr in trs)
# Collect relevant restrictions to identify blocks
# correctly in interior facet integrals
block_restrictions = []
for i, ma in enumerate(ma_indices):
if trs[i].is_uniform:
r = None
else:
r = modified_arguments[ma].restriction
block_restrictions.append(r)
block_restrictions = tuple(block_restrictions)
# Store piecewise status for fi and translate
# index to piecewise scope if relevant
factor_is_piecewise = FV_piecewise[fi]
if factor_is_piecewise:
factor_index = pe2i[FV[fi]]
else:
factor_index = fi
# TODO: Add separate block modes for quadrature
# Both arguments in quadrature elements
"""
for iq
fw = f*w
#for i
# for j
# B[i,j] = fw*U[i]*V[j] = 0 if i != iq or j != iq
BQ[iq] = B[iq,iq] = fw
for (iq)
A[iq+offset0, iq+offset1] = BQ[iq]
"""
# One argument in quadrature element
"""
for iq
fw[iq] = f*w
#for i
# for j
# B[i,j] = fw*UQ[i]*V[j] = 0 if i != iq
for j
BQ[iq,j] = fw[iq]*V[iq,j]
for (iq) for (j)
A[iq+offset, j+offset] = BQ[iq,j]
"""
# Decide how to handle code generation for this block
if p["enable_preintegration"] and (factor_is_piecewise and rank > 0
and "quadrature" not in ttypes):
# - Piecewise factor is an absolute prerequisite
# - Could work for rank 0 as well but currently doesn't
# - Haven't considered how quadrature elements work out
block_mode = "preintegrated"
elif p["enable_premultiplication"] and (rank > 0 and all(
tt in piecewise_ttypes for tt in ttypes)):
# Integrate functional in quadloop, scale block after quadloop
block_mode = "premultiplied"
elif p["enable_sum_factorization"]:
if (rank == 2
and any(tt in piecewise_ttypes for tt in ttypes)):
# Partial computation in quadloop of f*u[i],
# compute (f*u[i])*v[i] outside quadloop,
# (or with u,v swapped)
block_mode = "partial"
else:
# Full runtime integration of f*u[i]*v[j],
# can still do partial computation in quadloop of f*u[i]
# but must compute (f*u[i])*v[i] as well inside quadloop.
# (or with u,v swapped)
block_mode = "full"
else:
# Use full runtime integration with nothing fancy going on
block_mode = "safe"
# Carry out decision
if block_mode == "preintegrated":
# Add to contributions:
# P = sum_q weight*u*v; preintegrated here
# B[...] = f * P[...]; generated after quadloop
# A[blockmap] += B[...]; generated after quadloop
cache = ir["piecewise_ir"]["preintegrated_blocks"]
block_is_transposed = False
pname = cache.get(unames)
# Reuse transpose to save memory
if p["enable_block_transpose_reuse"] and pname is None and len(
unames) == 2:
pname = cache.get((unames[1], unames[0]))
if pname is not None:
# Cache hit on transpose
block_is_transposed = True
if pname is None:
# Cache miss, precompute block
weights = quadrature_rules[num_points][1]
if integral_type == "interior_facet":
ptable = integrate_block_interior_facets(
weights, unames, ttypes, unique_tables,
unique_table_num_dofs)
else:
ptable = integrate_block(weights, unames, ttypes,
unique_tables,
unique_table_num_dofs)
ptable = clamp_table_small_numbers(ptable,
rtol=p["table_rtol"],
atol=p["table_atol"])
pname = "PI%d" % (len(cache, ))
cache[unames] = pname
unique_tables[pname] = ptable
unique_table_types[pname] = "preintegrated"
assert factor_is_piecewise
block_unames = (pname, )
blockdata = preintegrated_block_data_t(
block_mode, ttypes, factor_index, factor_is_piecewise,
block_unames, block_restrictions, block_is_transposed,
block_is_uniform, pname)
block_is_piecewise = True
elif block_mode == "premultiplied":
# Add to contributions:
# P = u*v; computed here
# FI = sum_q weight * f; generated inside quadloop
# B[...] = FI * P[...]; generated after quadloop
# A[blockmap] += B[...]; generated after quadloop
cache = ir["piecewise_ir"]["premultiplied_blocks"]
block_is_transposed = False
pname = cache.get(unames)
# Reuse transpose to save memory
if p["enable_block_transpose_reuse"] and pname is None and len(
unames) == 2:
pname = cache.get((unames[1], unames[0]))
if pname is not None:
# Cache hit on transpose
block_is_transposed = True
if pname is None:
# Cache miss, precompute block
if integral_type == "interior_facet":
ptable = multiply_block_interior_facets(
0, unames, ttypes, unique_tables,
unique_table_num_dofs)
else:
ptable = multiply_block(0, unames, ttypes,
unique_tables,
unique_table_num_dofs)
pname = "PM%d" % (len(cache, ))
cache[unames] = pname
unique_tables[pname] = ptable
unique_table_types[pname] = "premultiplied"
block_unames = (pname, )
blockdata = premultiplied_block_data_t(
block_mode, ttypes, factor_index, factor_is_piecewise,
block_unames, block_restrictions, block_is_transposed,
block_is_uniform, pname)
block_is_piecewise = False
elif block_mode == "scaled": # TODO: Add mode, block is piecewise but choose not to be premultiplied
# Add to contributions:
# FI = sum_q weight * f; generated inside quadloop
# B[...] = FI * u * v; generated after quadloop
# A[blockmap] += B[...]; generated after quadloop
raise NotImplementedError("scaled block mode not implemented.")
# (probably need mostly the same data as premultiplied, except no P table name or values)
block_is_piecewise = False
elif block_mode in ("partial", "full", "safe"):
# Translate indices to piecewise context if necessary
block_is_piecewise = factor_is_piecewise and not expect_weight
ma_data = []
for i, ma in enumerate(ma_indices):
if trs[i].is_piecewise:
ma_index = piecewise_modified_argument_indices[
modified_arguments[ma]]
else:
block_is_piecewise = False
ma_index = ma
ma_data.append(ma_data_t(ma_index, trs[i]))
block_is_transposed = False # FIXME: Handle transposes for these block types
if block_mode == "partial":
# Add to contributions:
# P[i] = sum_q weight * f * u[i]; generated inside quadloop
# B[i,j] = P[i] * v[j]; generated after quadloop (where v is the piecewise ma)
# A[blockmap] += B[...]; generated after quadloop
# Find first piecewise index TODO: Is last better? just reverse range here
for i in range(rank):
if trs[i].is_piecewise:
piecewise_ma_index = i
break
assert rank == 2
not_piecewise_ma_index = 1 - piecewise_ma_index
block_unames = (unames[not_piecewise_ma_index], )
blockdata = partial_block_data_t(
block_mode, ttypes, factor_index, factor_is_piecewise,
block_unames, block_restrictions, block_is_transposed,
tuple(ma_data), piecewise_ma_index)
elif block_mode in ("full", "safe"):
# Add to contributions:
# B[i] = sum_q weight * f * u[i] * v[j]; generated inside quadloop
# A[blockmap] += B[i]; generated after quadloop
block_unames = unames
blockdata = full_block_data_t(
block_mode, ttypes, factor_index, factor_is_piecewise,
block_unames, block_restrictions, block_is_transposed,
tuple(ma_data))
else:
error("Invalid block_mode %s" % (block_mode, ))
if block_is_piecewise:
# Insert in piecewise expr_ir
ir["piecewise_ir"]["block_contributions"][blockmap].append(
blockdata)
else:
# Insert in varying expr_ir for this quadrature loop
block_contributions[blockmap].append(blockdata)
# Figure out which table names are referenced in unstructured partition
active_table_names = set()
for i, mt in zip(modified_terminal_indices, modified_terminals):
tr = mt_unique_table_reference.get(mt)
if tr is not None and FV_active[i]:
active_table_names.add(tr.name)
# Figure out which table names are referenced in blocks
for blockmap, contributions in chain(
block_contributions.items(),
ir["piecewise_ir"]["block_contributions"].items()):
for blockdata in contributions:
if blockdata.block_mode in ("preintegrated", "premultiplied"):
active_table_names.add(blockdata.name)
elif blockdata.block_mode in ("partial", "full", "safe"):
for mad in blockdata.ma_data:
active_table_names.add(mad.tabledata.name)
# Record all table types before dropping tables
ir["unique_table_types"].update(unique_table_types)
# Drop tables not referenced from modified terminals
# and tables of zeros and ones
unused_ttypes = ("zeros", "ones", "quadrature")
keep_table_names = set()
for name in active_table_names:
ttype = ir["unique_table_types"][name]
if ttype not in unused_ttypes:
if name in unique_tables:
keep_table_names.add(name)
unique_tables = {
name: unique_tables[name]
for name in keep_table_names
}
# Add to global set of all tables
for name, table in unique_tables.items():
tbl = ir["unique_tables"].get(name)
if tbl is not None and not numpy.allclose(
tbl, table, rtol=p["table_rtol"], atol=p["table_atol"]):
error("Table values mismatch with same name.")
ir["unique_tables"].update(unique_tables)
# Analyse active terminals to check what we'll need to generate code for
active_mts = []
for i, mt in zip(modified_terminal_indices, modified_terminals):
if FV_active[i]:
active_mts.append(mt)
# Figure out if we need to access CellCoordinate to
# avoid generating quadrature point table otherwise
if integral_type == "cell":
need_points = any(
isinstance(mt.terminal, CellCoordinate) for mt in active_mts)
elif integral_type in facet_integral_types:
need_points = any(
isinstance(mt.terminal, FacetCoordinate) for mt in active_mts)
elif integral_type in custom_integral_types:
need_points = True # TODO: Always?
else:
need_points = False
# Figure out if we need to access QuadratureWeight to
# avoid generating quadrature point table otherwise
#need_weights = any(isinstance(mt.terminal, QuadratureWeight)
# for mt in active_mts)
# Count blocks of each mode
block_modes = defaultdict(int)
for blockmap, contributions in block_contributions.items():
for blockdata in contributions:
block_modes[blockdata.block_mode] += 1
# Debug output
summary = "\n".join(" %d\t%s" % (count, mode)
for mode, count in sorted(block_modes.items()))
debug("Blocks of each mode: \n" + summary)
# If there are any blocks other than preintegrated we need weights
if expect_weight and any(mode != "preintegrated"
for mode in block_modes):
need_weights = True
elif integral_type in custom_integral_types:
need_weights = True # TODO: Always?
else:
need_weights = False
# Build IR dict for the given expressions
expr_ir = {}
# (array) FV-index -> UFL subexpression
expr_ir["V"] = FV
# (array) V indices for each input expression component in flattened order
expr_ir["V_targets"] = FV_targets
### Result of factorization:
# (array) MA-index -> UFL expression of modified arguments
expr_ir["modified_arguments"] = modified_arguments
# (dict) tuple(MA-indices) -> FV-index of monomial factor
#expr_ir["argument_factorization"] = argument_factorization
expr_ir["block_contributions"] = block_contributions
### Modified terminals
# (array) list of FV-indices to modified terminals
#expr_ir["modified_terminal_indices"] = modified_terminal_indices
# Dependency structure of graph:
# (CRSArray) FV-index -> direct dependency FV-index list
#expr_ir["dependencies"] = FV_deps
# (CRSArray) FV-index -> direct dependee FV-index list
#expr_ir["inverse_dependencies"] = inv_FV_deps
# Metadata about each vertex
#expr_ir["active"] = FV_active # (array) FV-index -> bool
#expr_ir["V_piecewise"] = FV_piecewise # (array) FV-index -> bool
expr_ir["V_varying"] = FV_varying # (array) FV-index -> bool
expr_ir["V_mts"] = FV_mts
# Store mapping from modified terminal object to
# table data, this is used in integralgenerator
expr_ir["mt_tabledata"] = mt_unique_table_reference
# To emit quadrature rules only if needed
expr_ir["need_points"] = need_points
expr_ir["need_weights"] = need_weights
# Store final ir for this num_points
ir["varying_irs"][num_points] = expr_ir
return ir
def _debug_visit(self, o):
"Debugging hook, enable this by renaming to 'visit'."
r = Transformer.visit(self, o)
f, df = r
if not f is o:
debug("In ForwardAD.visit, didn't get back o:")
debug(" o: %s" % str(o))
debug(" f: %s" % str(f))
debug(" df: %s" % str(df))
fi_diff = set(f.free_indices()) ^ set(df.free_indices())
if fi_diff:
debug("In ForwardAD.visit, got free indices diff:")
debug(" o: %s" % str(o))
debug(" f: %s" % str(f))
debug(" df: %s" % str(df))
debug(" f.fi(): %s" % lstr(f.free_indices()))
debug(" df.fi(): %s" % lstr(df.free_indices()))
debug(" fi_diff: %s" % str(fi_diff))
return r