def test_expressions(): x = gem.Variable("x", (3, 4)) y = gem.Variable("y", (4, )) i, j = gem.indices(2) xij = x[i, j] yj = y[j] assert xij == gem.Indexed(x, (i, j)) assert yj == gem.Indexed(y, (j, )) assert xij + yj == gem.Sum(xij, yj) assert xij * yj == gem.Product(xij, yj) assert xij - yj == gem.Sum(xij, gem.Product(gem.Literal(-1), yj)) assert xij / yj == gem.Division(xij, yj) assert xij + 1 == gem.Sum(xij, gem.Literal(1)) assert 1 + xij == gem.Sum(gem.Literal(1), xij) assert (xij + y).shape == (4, ) assert (x @ y).shape == (3, ) assert x.T.shape == (4, 3) with pytest.raises(ValueError): xij.T @ y with pytest.raises(ValueError): xij + "foo"
def compile_to_gem(expr, translator): """Compile a single pointwise expression to GEM. :arg expr: The expression to compile. :arg translator: a :class:`Translator` instance. :returns: A (lvalue, rvalue) pair of preprocessed GEM.""" if not isinstance(expr, Assign): raise ValueError( f"Don't know how to assign expression of type {type(expr)}") spaces = tuple(c.function_space() for c in expr.coefficients) if any( type(s.ufl_element()) is ufl.MixedElement for s in spaces if s is not None): raise ValueError("Not expecting a mixed space at this point, " "did you forget to index a function with .sub(...)?") if len(set(s.ufl_element() for s in spaces if s is not None)) != 1: raise ValueError("All coefficients must be defined on the same space") lvalue = expr.lvalue rvalue = expr.rvalue broadcast = all( isinstance(c, firedrake.Constant) for c in expr.rcoefficients) and rvalue.ufl_shape == () if not broadcast and lvalue.ufl_shape != rvalue.ufl_shape: try: rvalue = reshape(rvalue, lvalue.ufl_shape) except ValueError: raise ValueError( "Mismatching shapes between lvalue and rvalue in pointwise assignment" ) rvalue, = map_expr_dags(LowerCompoundAlgebra(), [rvalue]) try: lvalue, rvalue = map_expr_dags(translator, [lvalue, rvalue]) except (AssertionError, ValueError): raise ValueError("Mismatching shapes in pointwise assignment. " "For intrinsically vector-/tensor-valued spaces make " "sure you're not using shaped Constants or literals.") indices = gem.indices(len(lvalue.shape)) if not broadcast: if rvalue.shape != lvalue.shape: raise ValueError( "Mismatching shapes in pointwise assignment. " "For intrinsically vector-/tensor-valued spaces make " "sure you're not using shaped Constants or literals.") rvalue = gem.Indexed(rvalue, indices) lvalue = gem.Indexed(lvalue, indices) if isinstance(expr, IAdd): rvalue = gem.Sum(lvalue, rvalue) elif isinstance(expr, ISub): rvalue = gem.Sum(lvalue, gem.Product(gem.Literal(-1), rvalue)) elif isinstance(expr, IMul): rvalue = gem.Product(lvalue, rvalue) elif isinstance(expr, IDiv): rvalue = gem.Division(lvalue, rvalue) return preprocess_gem([lvalue, rvalue])
def test_refactorise(): f = gem.Variable('f', (3,)) u = gem.Variable('u', (3,)) v = gem.Variable('v', ()) i = gem.Index() f_i = gem.Indexed(f, (i,)) u_i = gem.Indexed(u, (i,)) def classify(atomics_set, expression): if expression in atomics_set: return ATOMIC for node in traversal([expression]): if node in atomics_set: return COMPOUND return OTHER classifier = partial(classify, {u_i, v}) # \sum_i 5*(2*u_i + -1*v)*(u_i + v*f) expr = gem.IndexSum( gem.Product( gem.Literal(5), gem.Product( gem.Sum(gem.Product(gem.Literal(2), u_i), gem.Product(gem.Literal(-1), v)), gem.Sum(u_i, gem.Product(v, f_i)) ) ), (i,) ) expected = [ Monomial((i,), (u_i, u_i), gem.Literal(10)), Monomial((i,), (u_i, v), gem.Product(gem.Literal(5), gem.Sum(gem.Product(f_i, gem.Literal(2)), gem.Literal(-1)))), Monomial((), (v, v), gem.Product(gem.Literal(5), gem.IndexSum(gem.Product(f_i, gem.Literal(-1)), (i,)))), ] actual, = collect_monomials([expr], classifier) assert expected == list(actual)
def translate_cell_edge_vectors(terminal, mt, ctx): # WARNING: Assumes straight edges! coords = CellVertices(terminal.ufl_domain()) ufl_expr = construct_modified_terminal(mt, coords) cell_vertices = ctx.translator(ufl_expr) e = gem.Index() c = gem.Index() expr = gem.ListTensor([ gem.Sum( gem.Indexed(cell_vertices, (u, c)), gem.Product(gem.Literal(-1), gem.Indexed(cell_vertices, (v, c)))) for _, (u, v) in sorted(ctx.fiat_cell.get_topology()[1].items()) ]) return gem.ComponentTensor(gem.Indexed(expr, (e, )), (e, c))
def dg_injection_kernel(Vf, Vc, ncell): from firedrake import Tensor, AssembledVector, TestFunction, TrialFunction from firedrake.slate.slac import compile_expression macro_builder = MacroKernelBuilder(ScalarType_c, ncell) f = ufl.Coefficient(Vf) macro_builder.set_coefficients([f]) macro_builder.set_coordinates(Vf.mesh()) Vfe = create_element(Vf.ufl_element()) macro_quadrature_rule = make_quadrature( Vfe.cell, estimate_total_polynomial_degree(ufl.inner(f, f))) index_cache = {} parameters = default_parameters() integration_dim, entity_ids = lower_integral_type(Vfe.cell, "cell") macro_cfg = dict(interface=macro_builder, ufl_cell=Vf.ufl_cell(), precision=parameters["precision"], integration_dim=integration_dim, entity_ids=entity_ids, index_cache=index_cache, quadrature_rule=macro_quadrature_rule) fexpr, = fem.compile_ufl(f, **macro_cfg) X = ufl.SpatialCoordinate(Vf.mesh()) C_a, = fem.compile_ufl(X, **macro_cfg) detJ = ufl_utils.preprocess_expression( abs(ufl.JacobianDeterminant(f.ufl_domain()))) macro_detJ, = fem.compile_ufl(detJ, **macro_cfg) Vce = create_element(Vc.ufl_element()) coarse_builder = firedrake_interface.KernelBuilder("cell", "otherwise", 0, ScalarType_c) coarse_builder.set_coordinates(Vc.mesh()) argument_multiindices = (Vce.get_indices(), ) argument_multiindex, = argument_multiindices return_variable, = coarse_builder.set_arguments((ufl.TestFunction(Vc), ), argument_multiindices) integration_dim, entity_ids = lower_integral_type(Vce.cell, "cell") # Midpoint quadrature for jacobian on coarse cell. quadrature_rule = make_quadrature(Vce.cell, 0) coarse_cfg = dict(interface=coarse_builder, ufl_cell=Vc.ufl_cell(), precision=parameters["precision"], integration_dim=integration_dim, entity_ids=entity_ids, index_cache=index_cache, quadrature_rule=quadrature_rule) X = ufl.SpatialCoordinate(Vc.mesh()) K = ufl_utils.preprocess_expression(ufl.JacobianInverse(Vc.mesh())) C_0, = fem.compile_ufl(X, **coarse_cfg) K, = fem.compile_ufl(K, **coarse_cfg) i = gem.Index() j = gem.Index() C_0 = gem.Indexed(C_0, (j, )) C_0 = gem.index_sum(C_0, quadrature_rule.point_set.indices) C_a = gem.Indexed(C_a, (j, )) X_a = gem.Sum(C_0, gem.Product(gem.Literal(-1), C_a)) K_ij = gem.Indexed(K, (i, j)) K_ij = gem.index_sum(K_ij, quadrature_rule.point_set.indices) X_a = gem.index_sum(gem.Product(K_ij, X_a), (j, )) C_0, = quadrature_rule.point_set.points C_0 = gem.Indexed(gem.Literal(C_0), (i, )) # fine quad points in coarse reference space. X_a = gem.Sum(C_0, gem.Product(gem.Literal(-1), X_a)) X_a = gem.ComponentTensor(X_a, (i, )) # Coarse basis function evaluated at fine quadrature points phi_c = fem.fiat_to_ufl( Vce.point_evaluation(0, X_a, (Vce.cell.get_dimension(), 0)), 0) tensor_indices = tuple(gem.Index(extent=d) for d in f.ufl_shape) phi_c = gem.Indexed(phi_c, argument_multiindex + tensor_indices) fexpr = gem.Indexed(fexpr, tensor_indices) quadrature_weight = macro_quadrature_rule.weight_expression expr = gem.Product(gem.IndexSum(gem.Product(phi_c, fexpr), tensor_indices), gem.Product(macro_detJ, quadrature_weight)) quadrature_indices = macro_builder.indices + macro_quadrature_rule.point_set.indices reps = spectral.Integrals([expr], quadrature_indices, argument_multiindices, parameters) assignments = spectral.flatten([(return_variable, reps)], index_cache) return_variables, expressions = zip(*assignments) expressions = impero_utils.preprocess_gem(expressions, **spectral.finalise_options) assignments = list(zip(return_variables, expressions)) impero_c = impero_utils.compile_gem(assignments, quadrature_indices + argument_multiindex, remove_zeros=True) index_names = [] def name_index(index, name): index_names.append((index, name)) if index in index_cache: for multiindex, suffix in zip(index_cache[index], string.ascii_lowercase): name_multiindex(multiindex, name + suffix) def name_multiindex(multiindex, name): if len(multiindex) == 1: name_index(multiindex[0], name) else: for i, index in enumerate(multiindex): name_index(index, name + str(i)) name_multiindex(quadrature_indices, 'ip') for multiindex, name in zip(argument_multiindices, ['j', 'k']): name_multiindex(multiindex, name) index_names.extend(zip(macro_builder.indices, ["entity"])) body = generate_coffee(impero_c, index_names, parameters["precision"], ScalarType_c) retarg = ast.Decl(ScalarType_c, ast.Symbol("R", rank=(Vce.space_dimension(), ))) local_tensor = coarse_builder.local_tensor local_tensor.init = ast.ArrayInit( numpy.zeros(Vce.space_dimension(), dtype=ScalarType_c)) body.children.insert(0, local_tensor) args = [retarg] + macro_builder.kernel_args + [ macro_builder.coordinates_arg, coarse_builder.coordinates_arg ] # Now we have the kernel that computes <f, phi_c>dx_c # So now we need to hit it with the inverse mass matrix on dx_c u = TrialFunction(Vc) v = TestFunction(Vc) expr = Tensor(ufl.inner(u, v) * ufl.dx).inv * AssembledVector( ufl.Coefficient(Vc)) Ainv, = compile_expression(expr) Ainv = Ainv.kinfo.kernel A = ast.Symbol(local_tensor.sym.symbol) R = ast.Symbol("R") body.children.append( ast.FunCall(Ainv.name, R, coarse_builder.coordinates_arg.sym, A)) from coffee.base import Node assert isinstance(Ainv._code, Node) return op2.Kernel(ast.Node([ Ainv._code, ast.FunDecl("void", "pyop2_kernel_injection_dg", args, body, pred=["static", "inline"]) ]), name="pyop2_kernel_injection_dg", cpp=True, include_dirs=Ainv._include_dirs, headers=Ainv._headers)
def sum(self, o, *ops): shape, = set(o.shape for o in ops) indices = gem.indices(len(shape)) return gem.ComponentTensor( gem.Sum(*[gem.Indexed(op, indices) for op in ops]), indices)
def compile_expression_dual_evaluation(expression, to_element, *, domain=None, interface=None, parameters=None, coffee=False): """Compile a UFL expression to be evaluated against a compile-time known reference element's dual basis. Useful for interpolating UFL expressions into e.g. N1curl spaces. :arg expression: UFL expression :arg to_element: A FInAT element for the target space :arg domain: optional UFL domain the expression is defined on (required when expression contains no domain). :arg interface: backend module for the kernel interface :arg parameters: parameters object :arg coffee: compile coffee kernel instead of loopy kernel """ import coffee.base as ast import loopy as lp # Just convert FInAT element to FIAT for now. # Dual evaluation in FInAT will bring a thorough revision. to_element = to_element.fiat_equivalent if any(len(dual.deriv_dict) != 0 for dual in to_element.dual_basis()): raise NotImplementedError( "Can only interpolate onto dual basis functionals without derivative evaluation, sorry!" ) if parameters is None: parameters = default_parameters() else: _ = default_parameters() _.update(parameters) parameters = _ # Determine whether in complex mode complex_mode = is_complex(parameters["scalar_type"]) # Find out which mapping to apply try: mapping, = set(to_element.mapping()) except ValueError: raise NotImplementedError( "Don't know how to interpolate onto zany spaces, sorry") expression = apply_mapping(expression, mapping, domain) # Apply UFL preprocessing expression = ufl_utils.preprocess_expression(expression, complex_mode=complex_mode) # Initialise kernel builder if interface is None: if coffee: import tsfc.kernel_interface.firedrake as firedrake_interface_coffee interface = firedrake_interface_coffee.ExpressionKernelBuilder else: # Delayed import, loopy is a runtime dependency import tsfc.kernel_interface.firedrake_loopy as firedrake_interface_loopy interface = firedrake_interface_loopy.ExpressionKernelBuilder builder = interface(parameters["scalar_type"]) arguments = extract_arguments(expression) argument_multiindices = tuple( builder.create_element(arg.ufl_element()).get_indices() for arg in arguments) # Replace coordinates (if any) unless otherwise specified by kwarg if domain is None: domain = expression.ufl_domain() assert domain is not None # Collect required coefficients first_coefficient_fake_coords = False coefficients = extract_coefficients(expression) if has_type(expression, GeometricQuantity) or any( fem.needs_coordinate_mapping(c.ufl_element()) for c in coefficients): # Create a fake coordinate coefficient for a domain. coords_coefficient = ufl.Coefficient( ufl.FunctionSpace(domain, domain.ufl_coordinate_element())) builder.domain_coordinate[domain] = coords_coefficient builder.set_cell_sizes(domain) coefficients = [coords_coefficient] + coefficients first_coefficient_fake_coords = True builder.set_coefficients(coefficients) # Split mixed coefficients expression = ufl_utils.split_coefficients(expression, builder.coefficient_split) # Translate to GEM kernel_cfg = dict( interface=builder, ufl_cell=domain.ufl_cell(), # FIXME: change if we ever implement # interpolation on facets. integral_type="cell", argument_multiindices=argument_multiindices, index_cache={}, scalar_type=parameters["scalar_type"]) if all( isinstance(dual, PointEvaluation) for dual in to_element.dual_basis()): # This is an optimisation for point-evaluation nodes which # should go away once FInAT offers the interface properly qpoints = [] # Everything is just a point evaluation. for dual in to_element.dual_basis(): ptdict = dual.get_point_dict() qpoint, = ptdict.keys() (qweight, component), = ptdict[qpoint] assert allclose(qweight, 1.0) assert component == () qpoints.append(qpoint) point_set = PointSet(qpoints) config = kernel_cfg.copy() config.update(point_set=point_set) # Allow interpolation onto QuadratureElements to refer to the quadrature # rule they represent if isinstance(to_element, FIAT.QuadratureElement): assert allclose(asarray(qpoints), asarray(to_element._points)) quad_rule = QuadratureRule(point_set, to_element._weights) config["quadrature_rule"] = quad_rule expr, = fem.compile_ufl(expression, **config, point_sum=False) # In some cases point_set.indices may be dropped from expr, but nothing # new should now appear assert set(expr.free_indices) <= set( chain(point_set.indices, *argument_multiindices)) shape_indices = tuple(gem.Index() for _ in expr.shape) basis_indices = point_set.indices ir = gem.Indexed(expr, shape_indices) else: # This is general code but is more unrolled than necssary. dual_expressions = [] # one for each functional broadcast_shape = len(expression.ufl_shape) - len( to_element.value_shape()) shape_indices = tuple(gem.Index() for _ in expression.ufl_shape[:broadcast_shape]) expr_cache = {} # Sharing of evaluation of the expression at points for dual in to_element.dual_basis(): pts = tuple(sorted(dual.get_point_dict().keys())) try: expr, point_set = expr_cache[pts] except KeyError: point_set = PointSet(pts) config = kernel_cfg.copy() config.update(point_set=point_set) expr, = fem.compile_ufl(expression, **config, point_sum=False) # In some cases point_set.indices may be dropped from expr, but # nothing new should now appear assert set(expr.free_indices) <= set( chain(point_set.indices, *argument_multiindices)) expr = gem.partial_indexed(expr, shape_indices) expr_cache[pts] = expr, point_set weights = collections.defaultdict(list) for p in pts: for (w, cmp) in dual.get_point_dict()[p]: weights[cmp].append(w) qexprs = gem.Zero() for cmp in sorted(weights): qweights = gem.Literal(weights[cmp]) qexpr = gem.Indexed(expr, cmp) qexpr = gem.index_sum( gem.Indexed(qweights, point_set.indices) * qexpr, point_set.indices) qexprs = gem.Sum(qexprs, qexpr) assert qexprs.shape == () assert set(qexprs.free_indices) == set( chain(shape_indices, *argument_multiindices)) dual_expressions.append(qexprs) basis_indices = (gem.Index(), ) ir = gem.Indexed(gem.ListTensor(dual_expressions), basis_indices) # Build kernel body return_indices = basis_indices + shape_indices + tuple( chain(*argument_multiindices)) return_shape = tuple(i.extent for i in return_indices) return_var = gem.Variable('A', return_shape) if coffee: return_arg = ast.Decl(parameters["scalar_type"], ast.Symbol('A', rank=return_shape)) else: return_arg = lp.GlobalArg("A", dtype=parameters["scalar_type"], shape=return_shape) return_expr = gem.Indexed(return_var, return_indices) # TODO: one should apply some GEM optimisations as in assembly, # but we don't for now. ir, = impero_utils.preprocess_gem([ir]) impero_c = impero_utils.compile_gem([(return_expr, ir)], return_indices) index_names = dict( (idx, "p%d" % i) for (i, idx) in enumerate(basis_indices)) # Handle kernel interface requirements builder.register_requirements([ir]) # Build kernel tuple return builder.construct_kernel(return_arg, impero_c, index_names, first_coefficient_fake_coords)