def getops(e):
"""Get a modifiable list of operands of e, optionally treating modified terminals as a unit."""
# TODO: Maybe use e._ufl_is_terminal_modifier_
if e._ufl_is_terminal_ or (skip_terminal_modifiers
and is_modified_terminal(e)):
return []
else:
return list(e.ufl_operands)
def replace_quadratureweight(expression):
"""Remove any QuadratureWeight terminals and replace with 1.0."""
r = []
for node in ufl.corealg.traversal.unique_pre_traversal(expression):
if is_modified_terminal(node) and isinstance(node, QuadratureWeight):
r.append(node)
replace_map = {q: 1.0 for q in r}
return ufl.algorithms.replace(expression, replace_map)
def _find_terminals_in_ufl_expression(e, etype):
"""Recursively search expression for terminals of type etype."""
r = []
for op in e.ufl_operands:
if is_modified_terminal(op) and isinstance(op, etype):
r.append(op)
else:
r += _find_terminals_in_ufl_expression(op, etype)
return r
def rebuild_with_scalar_subexpressions(G):
"""Build a new expression2index mapping where each subexpression is scalar valued.
Input:
- G.e2i
- G.V
- G.V_symbols
- G.total_unique_symbols
Output:
- NV - Array with reverse mapping from index to expression
- nvs - Tuple of ne2i indices corresponding to the last vertex of G.V
"""
# Compute symbols over graph and rebuild scalar expression
#
# New expression which represents usually an algebraic operation
# generates a new symbol
value_numberer = ValueNumberer(G)
# V_symbols maps an index of a node to a list of
# symbols which are present in that node
V_symbols = value_numberer.compute_symbols()
total_unique_symbols = value_numberer.symbol_count
# Array to store the scalar subexpression in for each symbol
W = numpy.empty(total_unique_symbols, dtype=object)
# Iterate over each graph node in order
for i, v in G.nodes.items():
expr = v['expression']
# Find symbols of v components
vs = V_symbols[i]
# Skip if there's nothing new here (should be the case for indexing types)
# New symbols are not given to indexing types, so W[symbol] already equals
# an expression, since it was assigned to the symbol in a previous loop
# cycle
if all(W[s] is not None for s in vs):
continue
if is_modified_terminal(expr):
sh = expr.ufl_shape
if sh:
# Store each terminal expression component. We may not
# actually need all of these later, but that will be
# optimized away.
# Note: symmetries will be dealt with in the value numbering.
ws = [expr[c] for c in ufl.permutation.compute_indices(sh)]
else:
# Store single modified terminal expression component
if len(vs) != 1:
raise RuntimeError(
"Expecting single symbol for scalar valued modified terminal."
)
ws = [expr]
# FIXME: Replace ws[:] with 0's if its table is empty
# Possible redesign: loop over modified terminals only first,
# then build tables for them, set W[s] = 0.0 for modified terminals with zero table,
# then loop over non-(modified terminal)s to reconstruct expression.
else:
# Find symbols of operands
sops = []
for j, vop in enumerate(expr.ufl_operands):
if isinstance(vop, ufl.classes.MultiIndex):
# TODO: Store MultiIndex in G.V and allocate a symbol to it for this to work
if not isinstance(expr, ufl.classes.IndexSum):
raise RuntimeError("Not expecting a %s." % type(expr))
sops.append(())
else:
# TODO: Build edge datastructure and use instead?
# k = G.E[i][j]
k = G.e2i[vop]
sops.append(V_symbols[k])
# Fetch reconstructed operand expressions
wops = [tuple(W[k] for k in so) for so in sops]
# Reconstruct scalar subexpressions of v
ws = reconstruct(expr, wops)
# Store all scalar subexpressions for v symbols
if len(vs) != len(ws):
raise RuntimeError("Expecting one symbol for each expression.")
# Store each new scalar subexpression in W at the index of its symbol
handled = set()
for s, w in zip(vs, ws):
if W[s] is None:
W[s] = w
handled.add(s)
else:
assert s in handled # Result of symmetry! - but I think this never gets reached anyway (CNR)
# Find symbols of final v from input graph
vs = V_symbols[-1]
scalar_expressions = W[vs]
return scalar_expressions
def compute_integral_ir(cell, integral_type, entitytype, integrands, argument_shape,
p, visualise):
# The intermediate representation dict we're building and returning
# here
ir = {}
# Pass on parameters for consumption in code generation
ir["params"] = p
# Shared unique tables for all quadrature loops
ir["unique_tables"] = {}
ir["unique_table_types"] = {}
ir["integrand"] = {}
ir["table_dofmaps"] = {}
for quadrature_rule, integrand in integrands.items():
expression = integrand
# Rebalance order of nested terminal modifiers
expression = balance_modifiers(expression)
# Remove QuadratureWeight terminals from expression and replace with 1.0
expression = replace_quadratureweight(expression)
# Build initial scalar list-based graph representation
S = build_scalar_graph(expression)
# 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_terminals = {i: analyse_modified_terminal(v['expression'])
for i, v in S.nodes.items()
if is_modified_terminal(v['expression'])}
mt_unique_table_reference = build_optimized_tables(
quadrature_rule,
cell,
integral_type,
entitytype,
initial_terminals.values(),
ir["unique_tables"],
rtol=p["table_rtol"],
atol=p["table_atol"])
unique_tables = {v.name: v.values for v in mt_unique_table_reference.values()}
unique_table_types = {v.name: v.ttype for v in mt_unique_table_reference.values()}
S_targets = [i for i, v in S.nodes.items() if v.get('target', False)]
if 'zeros' in unique_table_types.values() and len(S_targets) == 1:
# If there are any 'zero' tables, replace symbolically and rebuild graph
#
# TODO: Implement zero table elimination for non-scalar graphs
for i, mt in initial_terminals.items():
# Set modified terminals with zero tables to zero
tr = mt_unique_table_reference.get(mt)
if tr is not None and tr.ttype == "zeros":
S.nodes[i]['expression'] = ufl.as_ufl(0.0)
# Propagate expression changes using dependency list
for i, v in S.nodes.items():
deps = [S.nodes[j]['expression'] for j in S.out_edges[i]]
if deps:
v['expression'] = v['expression']._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)
expression = S.nodes[S_targets[0]]['expression']
# Rebuild scalar list-based graph representation
S = build_scalar_graph(expression)
# Output diagnostic graph as pdf
if visualise:
visualise_graph(S, 'S.pdf')
# Compute factorization of arguments
rank = len(argument_shape)
F = compute_argument_factorization(S, rank)
# Get the 'target' nodes that are factors of arguments, and insert in dict
FV_targets = [i for i, v in F.nodes.items() if v.get('target', False)]
argument_factorization = {}
for fi in FV_targets:
# Number of blocks using this factor must agree with number of components
# to which this factor contributes. I.e. there are more blocks iff there are more
# components
assert len(F.nodes[fi]['target']) == len(F.nodes[fi]['component'])
k = 0
for w in F.nodes[fi]['target']:
comp = F.nodes[fi]['component'][k]
argument_factorization[w] = argument_factorization.get(w, [])
# Store tuple of (factor index, component index)
argument_factorization[w].append((fi, comp))
k += 1
# Get list of indices in F which are the arguments (should be at start)
argkeys = set()
for w in argument_factorization:
argkeys = argkeys | set(w)
argkeys = list(argkeys)
# Build set of modified_terminals for each mt factorized vertex in F
# and attach tables, if appropriate
for i, v in F.nodes.items():
expr = v['expression']
if is_modified_terminal(expr):
mt = analyse_modified_terminal(expr)
F.nodes[i]['mt'] = mt
tr = mt_unique_table_reference.get(mt)
if tr is not None:
F.nodes[i]['tr'] = tr
# Attach 'status' to each node: 'inactive', 'piecewise' or 'varying'
analyse_dependencies(F, mt_unique_table_reference)
# Output diagnostic graph as pdf
if visualise:
visualise_graph(F, 'F.pdf')
# Loop over factorization terms
block_contributions = collections.defaultdict(list)
for ma_indices, fi_ci in sorted(argument_factorization.items()):
# Get a bunch of information about this term
assert rank == len(ma_indices)
trs = tuple(F.nodes[ai]['tr'] 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 = []
for tr in trs:
begin = tr.offset
num_dofs = tr.values.shape[3]
dofmap = tuple(begin + i * tr.block_size for i in range(num_dofs))
blockmap.append(dofmap)
blockmap = tuple(blockmap)
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, ai in enumerate(ma_indices):
if trs[i].is_uniform:
r = None
else:
r = F.nodes[ai]['mt'].restriction
block_restrictions.append(r)
block_restrictions = tuple(block_restrictions)
# Check if each *each* factor corresponding to this argument is piecewise
all_factors_piecewise = all(F.nodes[ifi[0]]["status"] == 'piecewise' for ifi in fi_ci)
block_is_permuted = False
for n in unames:
if unique_tables[n].shape[0] > 1:
block_is_permuted = True
ma_data = []
for i, ma in enumerate(ma_indices):
ma_data.append(ma_data_t(ma, trs[i]))
block_is_transposed = False # FIXME: Handle transposes for these block types
block_unames = unames
blockdata = block_data_t(ttypes, fi_ci,
all_factors_piecewise, block_unames,
block_restrictions, block_is_transposed,
block_is_uniform, None, tuple(ma_data), None, block_is_permuted)
# Insert in expr_ir for this quadrature loop
block_contributions[blockmap].append(blockdata)
# Figure out which table names are referenced
active_table_names = set()
for i, v in F.nodes.items():
tr = v.get('tr')
if tr is not None and F.nodes[i]['status'] != 'inactive':
active_table_names.add(tr.name)
# Figure out which table names are referenced in blocks
for blockmap, contributions in itertools.chain(
block_contributions.items()):
for blockdata in contributions:
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")
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"]):
raise RuntimeError("Table values mismatch with same name.")
ir["unique_tables"] = unique_tables
# Build IR dict for the given expressions
# Store final ir for this num_points
ir["integrand"][quadrature_rule] = {"factorization": F,
"modified_arguments": [F.nodes[i]['mt'] for i in argkeys],
"block_contributions": block_contributions}
restrictions = [i.restriction for i in initial_terminals.values()]
ir["needs_facet_permutations"] = "+" in restrictions and "-" in restrictions
return ir