Source code for

# Copyright (C) 2013-2020 Martin Sandve Aln├Žs and Michal Habera
# This file is part of FFCx.(
# SPDX-License-Identifier:    LGPL-3.0-or-later
"""Main algorithm for building the integral intermediate representation."""

import collections
import itertools
import logging
import typing

import numpy as np

import ufl
from import compute_argument_factorization
from import build_scalar_graph
from import (analyse_modified_terminal,
from import visualise_graph
from import UniqueTableReferenceT, build_optimized_tables
from ufl.algorithms.balancing import balance_modifiers
from ufl.checks import is_cellwise_constant
from ufl.classes import QuadratureWeight

logger = logging.getLogger("ffcx")

class ModifiedArgumentDataT(typing.NamedTuple):
    ma_index: int
    tabledata: UniqueTableReferenceT

class BlockDataT(typing.NamedTuple):
    ttypes: typing.Tuple[str, ...]  # list of table types for each block rank
    factor_indices_comp_indices: typing.List[typing.Tuple[int, int]]  # list of tuples (factor index, component index)
    all_factors_piecewise: bool  # True if all factors for this block are piecewise
    unames: typing.Tuple[str, ...]  # list of unique FE table names for each block rank
    restrictions: typing.Tuple[str, ...]  # restriction "+" | "-" | None for each block rank
    transposed: bool  # block is the transpose of another
    is_uniform: bool
    ma_data: typing.Tuple[ModifiedArgumentDataT, ...]  # used in "full", "safe" and "partial"
    is_permuted: bool  # Do quad points on facets need to be permuted?

[docs]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 options for consumption in code generation ir["options"] = p # Shared unique tables for all quadrature loops ir["unique_tables"] = {} ir["unique_table_types"] = {} ir["integrand"] = {} 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_table_reference = build_optimized_tables( quadrature_rule, cell, integral_type, entitytype, initial_terminals.values(), ir["unique_tables"], use_sum_factorization=p["sum_factorization"], rtol=p["table_rtol"], atol=p["table_atol"] ) # Fetch unique tables for this quadrature rule table_types = { v.ttype for v in mt_table_reference.values()} tables = { v.values for v in mt_table_reference.values()} S_targets = [i for i, v in S.nodes.items() if v.get('target', False)] num_components = np.int32( if 'zeros' in table_types.values(): # If there are any 'zero' tables, replace symbolically and rebuild graph for i, mt in initial_terminals.items(): # Set modified terminals with zero tables to zero tr = mt_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) # Recreate expression with correct ufl_shape expressions = [None, ] * num_components for target in S_targets: for comp in S.nodes[target]["component"]: assert expressions[comp] is None expressions[comp] = S.nodes[target]["expression"] expression = ufl.as_tensor(np.reshape(expressions, expression.ufl_shape)) # 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_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_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( 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 name in unames: if tables[name].shape[0] > 1: block_is_permuted = True ma_data = [] for i, ma in enumerate(ma_indices): ma_data.append(ModifiedArgumentDataT(ma, trs[i])) block_is_transposed = False # FIXME: Handle transposes for these block types block_unames = unames blockdata = BlockDataT(ttypes, fi_ci, all_factors_piecewise, block_unames, block_restrictions, block_is_transposed, block_is_uniform, tuple(ma_data), 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': if tr.has_tensor_factorisation: for t in tr.tensor_factors: active_table_names.add( else: active_table_names.add( # 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: if mad.tabledata.has_tensor_factorisation: for t in mad.tabledata.tensor_factors: active_table_names.add( else: active_table_names.add( active_tables = {} active_table_types = {} for name in active_table_names: # Drop tables not referenced from modified terminals if table_types[name] not in ("zeros", "ones"): active_tables[name] = tables[name] active_table_types[name] = table_types[name] # Add tables and types for this quadrature rule to global tables dict ir["unique_tables"].update(active_tables) ir["unique_table_types"].update(active_table_types) # 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
def analyse_dependencies(F, mt_unique_table_reference): # Sets 'status' of all nodes to either: 'inactive', 'piecewise' or 'varying' # Children of 'target' nodes are either 'piecewise' or 'varying'. # All other nodes are 'inactive'. # Varying nodes are identified by their tables ('tr'). All their parent # nodes are also set to 'varying' - any remaining active nodes are 'piecewise'. # Set targets, and dependencies to 'active' targets = [i for i, v in F.nodes.items() if v.get('target')] for i, v in F.nodes.items(): v['status'] = 'inactive' while targets: s = targets.pop() F.nodes[s]['status'] = 'active' for j in F.out_edges[s]: if F.nodes[j]['status'] == 'inactive': targets.append(j) # Build piecewise/varying markers for factorized_vertices varying_ttypes = ("varying", "quadrature", "uniform") varying_indices = [] for i, v in F.nodes.items(): if v.get('mt') is None: continue tr = v.get('tr') if tr is not None: ttype = tr.ttype # Check if table computations have revealed values varying over points if ttype in varying_ttypes: varying_indices.append(i) else: if ttype not in ("fixed", "piecewise", "ones", "zeros"): raise RuntimeError("Invalid ttype %s" % (ttype, )) elif not is_cellwise_constant(v['expression']): raise RuntimeError("Error " + str(tr)) # Keeping this check to be on the safe side, # not sure which cases this will cover (if any) # varying_indices.append(i) # Set all parents of active varying nodes to 'varying' while varying_indices: s = varying_indices.pop() if F.nodes[s]['status'] == 'active': F.nodes[s]['status'] = 'varying' for j in F.in_edges[s]: varying_indices.append(j) # Any remaining active nodes must be 'piecewise' for i, v in F.nodes.items(): if v['status'] == 'active': v['status'] = 'piecewise' 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)