diff --git a/Makefile b/Makefile index 734a8d34..e21d433a 100644 --- a/Makefile +++ b/Makefile @@ -26,6 +26,12 @@ tests: @echo " Running all tests" @FIREDRAKE_USE_FUSE=1 python3 -m coverage run -p -m pytest -rx test +mini_tests: + @FIREDRAKE_USE_FUSE=1 python3 -m pytest test/test_2d_examples_docs.py + @FIREDRAKE_USE_FUSE=1 python3 -m pytest test/test_convert_to_fiat.py::test_1d + @FIREDRAKE_USE_FUSE=1 python3 -m pytest test/test_orientations.py::test_surface_vec_rt + @FIREDRAKE_USE_FUSE=1 python3 -m pytest test/test_convert_to_fiat.py::test_projection_convergence_3d\[construct_tet_ned-N1curl-1-0.8\] + coverage: @python3 -m coverage combine @python3 -m coverage report -m diff --git a/fuse/__init__.py b/fuse/__init__.py index 8855d8d2..f7e89d39 100644 --- a/fuse/__init__.py +++ b/fuse/__init__.py @@ -1,4 +1,5 @@ -from fuse.cells import Point, Edge, polygon, make_tetrahedron, constructCellComplex + +from fuse.cells import Point, Edge, polygon, line, make_tetrahedron, constructCellComplex, TensorProductPoint from fuse.groups import S1, S2, S3, D4, Z3, Z4, C3, C4, S4, A4, diff_C3, tet_edges, tet_faces, sq_edges, GroupRepresentation, PermutationSetRepresentation, get_cyc_group, get_sym_group from fuse.dof import DeltaPairing, DOF, L2Pairing, FuseFunction, PointKernel, VectorKernel, BarycentricPolynomialKernel, PolynomialKernel, ComponentKernel from fuse.triples import ElementTriple, DOFGenerator, immerse diff --git a/fuse/cells.py b/fuse/cells.py index 31345ad4..7d34981a 100644 --- a/fuse/cells.py +++ b/fuse/cells.py @@ -151,6 +151,13 @@ def compute_scaled_verts(d, n): raise ValueError("Dimension {} not supported".format(d)) +def line(): + """ + Constructs the default 1D interval + """ + return Point(1, [Point(0), Point(0)], vertex_num=2) + + def polygon(n): """ Constructs the 2D default cell with n sides/vertices @@ -373,6 +380,7 @@ def compute_cell_group(self): """ verts = self.ordered_vertices() v_coords = [self.get_node(v, return_coords=True) for v in verts] + n = len(verts) max_group = SymmetricGroup(n) edges = [edge.ordered_vertices() for edge in self.edges()] @@ -502,6 +510,15 @@ def get_starter_ids(self): min_ids = [min(dimension) for dimension in structure] return min_ids + def local_id(self, node): + structure = [sorted(generation) for generation in nx.topological_generations(self.G)] + structure.reverse() + min_id = self.get_starter_ids() + for d in range(len(structure)): + if node.id in structure[d]: + return node.id - min_id[d] + raise ValueError("Node not found in cell") + def graph_dim(self): if self.oriented: dim = self.dimension + 1 @@ -648,7 +665,6 @@ def basis_vectors(self, return_coords=True, entity=None, order=False, norm=True) self_levels = [generation for generation in nx.topological_generations(self.G)] vertices = entity.ordered_vertices() if self.dimension == 0: - # return [[] raise ValueError("Dimension 0 entities cannot have Basis Vectors") if self.oriented: # ordered_vertices() handles the orientation so we want to drop the orientation node @@ -822,7 +838,7 @@ def attachment(self, source, dst): return lambda *x: fold_reduce(attachments[0], *x) - def attachment_J(self, source, dst): + def attachment_J_det(self, source, dst): attachment = self.attachment(source, dst) symbol_names = ["x", "y", "z"] symbols = [] @@ -831,7 +847,7 @@ def attachment_J(self, source, dst): for i in range(self.dim_of_node(dst)): symbols += [sp.Symbol(symbol_names[i])] J = sp.Matrix(attachment(*symbols)).jacobian(sp.Matrix(symbols)) - return J + return np.sqrt(abs(float(sp.det(J.T * J)))) def quadrature(self, degree): fiat_el = self.to_fiat() @@ -903,6 +919,13 @@ def dict_id(self): def _from_dict(o_dict): return Point(o_dict["dim"], o_dict["edges"], oriented=o_dict["oriented"], cell_id=o_dict["id"]) + def equivalent(self, other): + if self.dimension != other.dimension: + return False + if set(self.ordered_vertex_coords()) != set(other.ordered_vertex_coords()): + return False + return self.get_topology() == other.get_topology() + class Edge(): """ @@ -926,7 +949,12 @@ def __call__(self, *x): if hasattr(self.attachment, '__iter__'): res = [] for attach_comp in self.attachment: - res.append(sympy_to_numpy(attach_comp, syms, x)) + if len(attach_comp.atoms(sp.Symbol)) <= len(x): + res.append(sympy_to_numpy(attach_comp, syms, x)) + else: + res_val = attach_comp.subs({syms[i]: x[i] for i in range(len(x))}) + res.append(res_val) + return tuple(res) return sympy_to_numpy(self.attachment, syms, x) return x @@ -957,50 +985,182 @@ def _from_dict(o_dict): class TensorProductPoint(): + id_iter = itertools.count() - def __init__(self, A, B, flat=False): + def __init__(self, A, B): + self.id = next(self.id_iter) self.A = A self.B = B self.dimension = self.A.dimension + self.B.dimension - self.flat = flat + self.flat = False + self.fiat_elem = None + self.group = self.compute_cell_group() + self.entities = {} + for d in [(a_d, b_d) for a_d in range(self.A.dimension + 1) for b_d in range(self.B.dimension + 1)]: + if d == (self.A.dimension, self.B.dimension): + self.entities[d] = [self] + else: + self.entities[d] = [TensorProductPoint(e_a, e_b) for e_a in self.A.d_entities(d[0], True) for e_b in self.B.d_entities(d[1], True)] def ordered_vertices(self): return self.A.ordered_vertices() + self.B.ordered_vertices() + def component_orientations(self): + from fuse.utils import orientation_value + self.component_os_to_os = {} + for dim in self.to_fiat().get_topology(): + self.component_os_to_os[dim] = {} + a_ent = self.A.d_entities(dim[0])[0] + b_ent = self.B.d_entities(dim[1])[0] + verts = [(v_a, v_b) for v_a in a_ent.vertices() for v_b in b_ent.vertices()] + ident = [i for i in range(len(verts))] + group = [(g_a, g_b) for g_a in a_ent.group.members() for g_b in b_ent.group.members()] + for g_a, g_b in group: + new_verts = [(v_a, v_b) for v_a in g_a.permute(a_ent.vertices()) for v_b in g_b.permute(b_ent.vertices())] + perm = [verts.index(v) for v in new_verts] + o_val = orientation_value(ident, perm) + if sum(dim) == self.dimension and self.group.group_rep_numbering is not None: + o_val = self.group.group_rep_numbering[o_val] + self.component_os_to_os[dim][(g_a.numeric_rep(), g_b.numeric_rep())] = o_val + return self.component_os_to_os + + def compute_cell_group(self): + """ + Systematically work out the symmetry group of the tensor product cell. + """ + verts = self.vertices() + group = [(g_a, g_b) for g_a in self.A.group.members() for g_b in self.B.group.members()] + perms = [] + for g_a, g_b in group: + new_verts = [(v_a, v_b) for v_a in g_a.permute(self.A.vertices()) for v_b in g_b.permute(self.B.vertices())] + perm = [verts.index(v) for v in new_verts] + perms += [fuse_groups.Permutation(perm)] + + grp = fuse_groups.PermutationSetRepresentation(perms).add_cell(self) + return grp + + def get_starter_ids(self): + # this doesn't actually make sense - remove when confirmed all changes to eliminate min ids from triple is done + a_starts = self.A.get_starter_ids() + b_starts = self.B.get_starter_ids() + ids = [] + for a, b in zip(a_starts, b_starts): + ids += [max(a, b)] + return ids + def get_spatial_dimension(self): return self.dimension def get_sub_entities(self): - self.A.get_sub_entities() - self.B.get_sub_entities() + return self.to_fiat().sub_entities - def dimension(self): - return tuple(self.A.dimension, self.B.dimension) + def dim(self): + return (self.A.dimension, self.B.dimension) def d_entities(self, d, get_class=True): + if isinstance(d, tuple): + if get_class: + return self.entities[d] + return [e.id for e in self.entities[d]] + raise NotImplementedError("not sure this is right") return self.A.d_entities(d, get_class) + self.B.d_entities(d, get_class) def vertices(self, get_class=True, return_coords=False): # TODO maybe refactor with get_node - verts = self.d_entities(0, get_class) if return_coords: a_verts = self.A.vertices(return_coords=return_coords) b_verts = self.B.vertices(return_coords=return_coords) return [a + b for a in a_verts for b in b_verts] - return verts + return [(a, b) for a in self.A.vertices() for b in self.B.vertices()] def to_ufl(self, name=None): - if self.flat: - return CellComplexToUFL(self, "quadrilateral") return TensorProductCell(self.A.to_ufl(), self.B.to_ufl()) def to_fiat(self, name=None): - if self.flat: - return CellComplexToFiatHypercube(self, CellComplexToFiatTensorProduct(self, name)) - return CellComplexToFiatTensorProduct(self, name) + if self.fiat_elem is None: + self.fiat_elem = CellComplexToFiatTensorProduct(self, name) + return self.fiat_elem + + def flatten(self): + assert self.A.equivalent(self.B) + return FlattenedPoint(self.A, self.B) + + +class FlattenedPoint(Point, TensorProductPoint): + + def __init__(self, A, B): + self.A = A + self.B = B + self.dimension = self.A.dimension + self.B.dimension + self.flat = True + fuse_edges = self.construct_fuse_rep() + super().__init__(self.dimension, fuse_edges) + + def to_ufl(self, name=None): + return CellComplexToUFL(self, "quadrilateral") + + def to_fiat(self, name=None): + # TODO this should check if it actually is a hypercube + fiat = CellComplexToFiatHypercube(self, CellComplexToFiatTensorProduct(self, name)) + return fiat + + def construct_fuse_rep(self): + sub_cells = [self.A, self.B] + dims = (self.A.dimension, self.B.dimension) + + points = {cell: {i: [] for i in range(max(dims) + 1)} for cell in sub_cells} + attachments = {cell: {i: [] for i in range(max(dims) + 1)} for cell in sub_cells} + + for d in range(max(dims) + 1): + for cell in sub_cells: + if d <= cell.dimension: + sub_ent = cell.d_entities(d, get_class=True) + points[cell][d].extend(sub_ent) + for s in sub_ent: + attachments[cell][d].extend(s.connections) + + prod_points = list(itertools.product(*[points[cell][0] for cell in sub_cells])) + # temp = prod_points[1] + # prod_points[1] = prod_points[2] + # prod_points[2] = temp + point_cls = [Point(0) for i in range(len(prod_points))] + edges = [] + + # generate edges of tensor product result + for a in prod_points: + for b in prod_points: + # of all combinations of point, take those where at least one changes and at least one is the same + if any(a[i] == b[i] for i in range(len(a))) and any(a[i] != b[i] for i in range(len(sub_cells))): + # ensure if they change, that edge exists in the existing topology + if all([a[i] == b[i] or (sub_cells[i].local_id(a[i]), sub_cells[i].local_id(b[i])) in list(sub_cells[i]._topology[1].values()) for i in range(len(sub_cells))]): + edges.append((a, b)) + # hasse level 1 + edge_cls1 = {e: None for e in edges} + for i in range(len(sub_cells)): + for (a, b) in edges: + a_idx = prod_points.index(a) + b_idx = prod_points.index(b) + if a[i] != b[i]: + a_edge = [att for att in attachments[sub_cells[i]][1] if att.point == a[i]][0] + b_edge = [att for att in attachments[sub_cells[i]][1] if att.point == b[i]][0] + edge_cls1[(a, b)] = Point(1, [Edge(point_cls[a_idx], a_edge.attachment, a_edge.o), + Edge(point_cls[b_idx], b_edge.attachment, b_edge.o)]) + edge_cls2 = [] + # hasse level 2 + for i in range(len(sub_cells)): + for (a, b) in edges: + if a[i] == b[i]: + x = sp.Symbol("x") + a_edge = [att for att in attachments[sub_cells[i]][1] if att.point == a[i]][0] + if i == 0: + attach = (x,) + a_edge.attachment + else: + attach = a_edge.attachment + (x,) + edge_cls2.append(Edge(edge_cls1[(a, b)], attach, a_edge.o)) + return edge_cls2 def flatten(self): - return TensorProductPoint(self.A, self.B, True) + return self class CellComplexToFiatSimplex(Simplex): @@ -1190,9 +1350,8 @@ def constructCellComplex(name): return polygon(3).to_ufl(name) # return ufc_triangle().to_ufl(name) elif name == "quadrilateral": - interval = Point(1, [Point(0), Point(0)], vertex_num=2) - return TensorProductPoint(interval, interval).flatten().to_ufl(name) - # return ufc_quad().to_ufl(name) + return TensorProductPoint(line(), line()).flatten().to_ufl(name) + # return firedrake_quad().to_ufl(name) # return polygon(4).to_ufl(name) elif name == "tetrahedron": # return ufc_tetrahedron().to_ufl(name) diff --git a/fuse/dof.py b/fuse/dof.py index 7c64d70d..2c6cad0a 100644 --- a/fuse/dof.py +++ b/fuse/dof.py @@ -190,11 +190,16 @@ def __call__(self, *args): return self.pt def evaluate(self, Qpts, Qwts, basis_change, immersed, dim, value_shape): - if isinstance(self.pt, int): - return Qpts, np.array([wt*self.pt for wt in Qwts]).astype(np.float64), [[(i,) for i in range(dim)] for pt in Qpts] + if len(value_shape) == 0: + comps = [[tuple()] for pt in Qpts] + else: + comps = [[(i,) for v in value_shape for i in range(v)] for pt in Qpts] + + if not isinstance(self.pt, tuple): + return Qpts, np.array([wt*self.pt for wt in Qwts]).astype(np.float64), comps if not immersed: - return Qpts, np.array([wt*np.matmul(self.pt, basis_change)for wt in Qwts]).astype(np.float64), [[(i,) for i in range(dim)] for pt in Qpts] - return Qpts, np.array([wt*immersed(np.matmul(self.pt, basis_change))for wt in Qwts]).astype(np.float64), [[(i,) for i in range(dim)] for pt in Qpts] + return Qpts, np.array([wt*np.matmul(self.pt, basis_change)for wt in Qwts]).astype(np.float64), comps + return Qpts, np.array([wt*immersed(np.matmul(self.pt, basis_change))for wt in Qwts]).astype(np.float64), comps def _to_dict(self): o_dict = {"pt": self.pt} @@ -274,10 +279,14 @@ class PolynomialKernel(BaseKernel): def __init__(self, fn, g=None, symbols=[]): if hasattr(fn, "__iter__"): - if len(symbols) != 0 and any(not sp.sympify(fn[i]).as_poly() for i in range(len(fn))): - raise ValueError("Function components must be able to be interpreted as a sympy polynomial") - self.fn = [sp.sympify(fn[i]).as_poly() for i in range(len(fn))] - self.shape = len(fn) + shape = len(fn) + else: + shape = 0 + if len(symbols) != 0 and (shape != 0 and any(not sp.sympify(fn[i]).as_poly() for i in range(shape))) and not sp.sympify(fn).as_poly(): + raise ValueError("Function argument or its components must be able to be interpreted as a sympy polynomial") + if shape != 0: + self.fn = [sp.sympify(fn[i]).as_poly() for i in range(shape)] + self.shape = shape else: self.fn = sp.sympify(fn) self.shape = 0 @@ -304,9 +313,7 @@ def __call__(self, *args): if self.shape == 0: res = sympy_to_numpy(self.fn, self.syms, args[:len(self.syms)]) else: - res = [] - for i in range(self.shape): - res += [sympy_to_numpy(self.fn[i], self.syms, args[:len(self.syms)])] + res = [sympy_to_numpy(self.fn[i], self.syms, args[:len(self.syms)]) for i in range(self.shape)] return res def evaluate(self, Qpts, Qwts, basis_change, immersed, dim, value_shape): @@ -411,9 +418,9 @@ def add_context(self, dof_gen, cell, space, g, overall_id=None, generator_id=Non self.pairing = self.pairing.add_entity(cell) if self.target_space is None: self.target_space = space - if self.id is None and overall_id is not None: + if overall_id is not None: self.id = overall_id - if self.sub_id is None and generator_id is not None: + if generator_id is not None: self.sub_id = generator_id def convert_to_fiat(self, ref_el, interpolant_degree, value_shape=tuple()): @@ -452,20 +459,21 @@ def immersed(pt): pts, wts, comps = self.kernel.evaluate(Qpts, Qwts, basis_change, immersed, self.cell.dimension, value_shape) if self.immersed: - # need to compute jacobian from attachment. pts = np.array([self.cell.attachment(self.cell.id, self.cell_defined_on.id)(*pt) for pt in pts]) - # J_det = self.cell.attachment_J_det(self.cell.id, self.cell_defined_on.id) - J_det = 1 + J_det = self.cell.attachment_J_det(self.cell.id, self.cell_defined_on.id) if not np.allclose(J_det, 1): raise ValueError("Jacobian Determinant is not 1 did you do something wrong") + # if self.pairing.orientation: + # immersion = self.target_space.tabulate(wts, self.pairing.entity.orient(self.pairing.orientation))[0] + # else: immersion = self.target_space.tabulate(pts, self.cell_defined_on) + # Special case - force evaluation on different orientation of entity for construction of matrix transforms + # if self.entity_o: + # immersion = self.target_space.tabulate(wts, self.pairing.entity.orient(self.entity_o)) if isinstance(self.target_space, TrH1): - new_wts = wts + new_wts = wts * J_det else: new_wts = np.outer(wts * J_det, immersion) - # shape is wrong for 2d face on tet - # if isinstance(self.kernel, BarycentricPolynomialKernel) and self.kernel.shape > 1: - # new_wts = np.array([self.cell.attachment(self.cell.id, self.cell_defined_on.id)(*pt) for pt in new_wts]) else: new_wts = wts # pt dict is { pt: [(weight, component)]} diff --git a/fuse/groups.py b/fuse/groups.py index 6ca40b3c..f0d6e561 100644 --- a/fuse/groups.py +++ b/fuse/groups.py @@ -65,9 +65,15 @@ def compute_perm(self, base_val=None): return val, val_list def numeric_rep(self): + """ Uses a standard formula to number permutations in the group. + For the case where this doesn't automatically number from 0..n (ie the group is not the full symmetry group), + a mapping is constructed on group creation""" identity = self.group.identity.perm.array_form m_array = self.perm.array_form - return orientation_value(identity, m_array) + val = orientation_value(identity, m_array) + if self.group.group_rep_numbering is not None: + return self.group.group_rep_numbering[val] + return val def __eq__(self, x): assert isinstance(x, GroupMemberRep) @@ -144,6 +150,11 @@ def __init__(self, perm_list, cell=None): counter += 1 # self._members = sorted(self._members, key=lambda g: g.numeric_rep()) + self.group_rep_numbering = None + numeric_reps = [m.numeric_rep() for m in self.members()] + if sorted(numeric_reps) != list(range(len(numeric_reps))): + self.group_rep_numbering = {a: b for a, b in zip(sorted(numeric_reps), list(range(len(numeric_reps))))} + def add_cell(self, cell): return PermutationSetRepresentation(self.perm_list, cell=cell) @@ -268,6 +279,11 @@ def __init__(self, base_group, cell=None): self.identity = p_rep counter += 1 + self.group_rep_numbering = None + numeric_reps = [m.numeric_rep() for m in self.members()] + if sorted(numeric_reps) != list(range(len(numeric_reps))): + self.group_rep_numbering = {a: b for a, b in zip(sorted(numeric_reps), list(range(len(numeric_reps))))} + # this order produces simpler generator lists # self.generators.reverse() diff --git a/fuse/spaces/element_sobolev_spaces.py b/fuse/spaces/element_sobolev_spaces.py index 2a3aa4fb..b5964d9d 100644 --- a/fuse/spaces/element_sobolev_spaces.py +++ b/fuse/spaces/element_sobolev_spaces.py @@ -1,4 +1,5 @@ from functools import total_ordering +from ufl.sobolevspace import H1, HDiv, HCurl, L2, H2 @total_ordering @@ -55,6 +56,9 @@ def __init__(self, cell): def __repr__(self): return "H1" + def to_ufl(self): + return H1 + class CellHDiv(ElementSobolevSpace): @@ -64,6 +68,9 @@ def __init__(self, cell): def __repr__(self): return "HDiv" + def to_ufl(self): + return HDiv + class CellHCurl(ElementSobolevSpace): @@ -73,6 +80,9 @@ def __init__(self, cell): def __repr__(self): return "HCurl" + def to_ufl(self): + return HCurl + class CellH2(ElementSobolevSpace): @@ -82,6 +92,9 @@ def __init__(self, cell): def __repr__(self): return "H2" + def to_ufl(self): + return H2 + class CellL2(ElementSobolevSpace): @@ -90,3 +103,6 @@ def __init__(self, cell): def __repr__(self): return "L2" + + def to_ufl(self): + return L2 diff --git a/fuse/spaces/polynomial_spaces.py b/fuse/spaces/polynomial_spaces.py index 422cf053..c7f8d369 100644 --- a/fuse/spaces/polynomial_spaces.py +++ b/fuse/spaces/polynomial_spaces.py @@ -1,13 +1,16 @@ from FIAT.polynomial_set import ONPolynomialSet +from FIAT.expansions import morton_index2, morton_index3 from FIAT.quadrature_schemes import create_quadrature from FIAT.reference_element import cell_to_simplex from FIAT import expansions, polynomial_set, reference_element from itertools import chain -from fuse.utils import tabulate_sympy, max_deg_sp_mat +from fuse.utils import tabulate_sympy, max_deg_sp_expr import sympy as sp import numpy as np from functools import total_ordering +morton_index = {2: morton_index2, 3: morton_index3} + @total_ordering class PolynomialSpace(object): @@ -47,7 +50,6 @@ def degree(self): return self.maxdegree def to_ON_polynomial_set(self, ref_el, k=None): - # how does super/sub degrees work here if not isinstance(ref_el, reference_element.Cell): ref_el = ref_el.to_fiat() sd = ref_el.get_spatial_dimension() @@ -56,18 +58,25 @@ def to_ON_polynomial_set(self, ref_el, k=None): shape = (sd,) else: shape = tuple() + base_ON = ONPolynomialSet(ref_el, self.maxdegree, shape, scale="orthonormal") + indices = None if self.mindegree > 0: - base_ON = ONPolynomialSet(ref_el, self.maxdegree, shape, scale="orthonormal") dimPmin = expansions.polynomial_dimension(ref_el, self.mindegree) dimPmax = expansions.polynomial_dimension(ref_el, self.maxdegree) if self.set_shape: indices = list(chain(*(range(i * dimPmin, i * dimPmax) for i in range(sd)))) else: indices = list(range(dimPmin, dimPmax)) - restricted_ON = base_ON.take(indices) - return restricted_ON - return ONPolynomialSet(ref_el, self.maxdegree, shape, scale="orthonormal") + + if self.contains != self.maxdegree and self.contains != -1: + indices = [morton_index[sd](p, q) for p in range(self.contains + 1) for q in range(self.contains + 1)] + + if indices is None: + return base_ON + + restricted_ON = base_ON.take(indices) + return restricted_ON def __repr__(self): res = "" @@ -87,9 +96,7 @@ def __mul__(self, x): the sympy object on the right. This is due to Sympy's implementation of __mul__ not passing to this handler as it should. """ - if isinstance(x, sp.Symbol): - return ConstructedPolynomialSpace([x], [self]) - elif isinstance(x, sp.Matrix): + if isinstance(x, sp.Symbol) or isinstance(x, sp.Expr) or isinstance(x, sp.Matrix): return ConstructedPolynomialSpace([x], [self]) else: raise TypeError(f'Cannot multiply a PolySpace with {type(x)}') @@ -148,7 +155,7 @@ def __init__(self, weights, spaces): self.weights = weights self.spaces = spaces - weight_degrees = [0 if not (isinstance(w, sp.Expr) or isinstance(w, sp.Matrix)) else max_deg_sp_mat(w) for w in self.weights] + weight_degrees = [0 if not (isinstance(w, sp.Expr) or isinstance(w, sp.Matrix)) else max_deg_sp_expr(w) for w in self.weights] maxdegree = max([space.maxdegree + w_deg for space, w_deg in zip(spaces, weight_degrees)]) mindegree = min([space.mindegree + w_deg for space, w_deg in zip(spaces, weight_degrees)]) @@ -163,37 +170,49 @@ def to_ON_polynomial_set(self, ref_el): if not isinstance(ref_el, reference_element.Cell): ref_el = ref_el.to_fiat() k = max([s.maxdegree for s in self.spaces]) - space_poly_sets = [s.to_ON_polynomial_set(ref_el) for s in self.spaces] sd = ref_el.get_spatial_dimension() ref_el = cell_to_simplex(ref_el) - if all([w == 1 for w in self.weights]): - weighted_sets = space_poly_sets - # otherwise have to work on this through tabulation - Q = create_quadrature(ref_el, 2 * (k + 1)) - Qpts, Qwts = Q.get_points(), Q.get_weights() weighted_sets = [] - for (space, w) in zip(space_poly_sets, self.weights): + for (s, w) in zip(self.spaces, self.weights): + space = s.to_ON_polynomial_set(ref_el) + if s.set_shape: + shape = (sd,) + else: + shape = tuple() if not (isinstance(w, sp.Expr) or isinstance(w, sp.Matrix)): weighted_sets.append(space) else: - w_deg = max_deg_sp_mat(w) - Pkpw = ONPolynomialSet(ref_el, space.degree + w_deg, scale="orthonormal") - vec_Pkpw = ONPolynomialSet(ref_el, space.degree + w_deg, (sd,), scale="orthonormal") + if isinstance(w, sp.Expr): + w = sp.Matrix([[w]]) + vec = False + else: + vec = True + w_deg = max_deg_sp_expr(w) + Q = create_quadrature(ref_el, 2 * (k + w_deg + 1)) + Qpts, Qwts = Q.get_points(), Q.get_weights() + Pkpw = ONPolynomialSet(ref_el, space.degree + w_deg, shape, scale="orthonormal") + # vec_Pkpw = ONPolynomialSet(ref_el, space.degree + w_deg, (sd,), scale="orthonormal") space_at_Qpts = space.tabulate(Qpts)[(0,) * sd] Pkpw_at_Qpts = Pkpw.tabulate(Qpts)[(0,) * sd] tabulated_expr = tabulate_sympy(w, Qpts).T - scaled_at_Qpts = space_at_Qpts[:, None, :] * tabulated_expr[None, :, :] + if s.set_shape or vec: + scaled_at_Qpts = space_at_Qpts[:, None, :] * tabulated_expr[None, :, :] + else: + scaled_at_Qpts = space_at_Qpts[:, None, :] * tabulated_expr[None, :, :] + scaled_at_Qpts = scaled_at_Qpts.squeeze() PkHw_coeffs = np.dot(np.multiply(scaled_at_Qpts, Qwts), Pkpw_at_Qpts.T) + if len(PkHw_coeffs.shape) == 1: + PkHw_coeffs = PkHw_coeffs.reshape(1, -1) weighted_sets.append(polynomial_set.PolynomialSet(ref_el, space.degree + w_deg, space.degree + w_deg, - vec_Pkpw.get_expansion_set(), + Pkpw.get_expansion_set(), PkHw_coeffs)) combined_sets = weighted_sets[0] for i in range(1, len(weighted_sets)): diff --git a/fuse/tensor_products.py b/fuse/tensor_products.py index cf16e247..25407856 100644 --- a/fuse/tensor_products.py +++ b/fuse/tensor_products.py @@ -1,17 +1,25 @@ -from fuse.triples import ElementTriple +from fuse.triples import ElementTriple, compute_form_degree +from fuse.traces import TrHCurl, TrHDiv from fuse.cells import TensorProductPoint -from finat.ufl import TensorProductElement, FuseElement +import numpy as np +from finat.ufl import TensorProductElement, FuseElement, HDivElement, HCurlElement -def tensor_product(A, B): +def tensor_product(A, B, matrices=True): if not (isinstance(A, ElementTriple) and isinstance(B, ElementTriple)): raise ValueError("Both components of Tensor Product need to be a Fuse Triple.") - return TensorProductTriple(A, B) + return TensorProductTriple(A, B, matrices=matrices) + + +def symmetric_tensor_product(A, B): + if not (isinstance(A, ElementTriple) and isinstance(B, ElementTriple)): + raise ValueError("Both components of Tensor Product need to be a Fuse Triple.") + return TensorProductTriple(A, B, symmetric=True) class TensorProductTriple(ElementTriple): - def __init__(self, A, B, flat=False): + def __init__(self, A, B, flat=False, symmetric=True, matrices=True): self.A = A self.B = B self.spaces = [] @@ -20,9 +28,17 @@ def __init__(self, A, B, flat=False): self.DOFGenerator = [A.DOFGenerator, B.DOFGenerator] self.cell = TensorProductPoint(A.cell, B.cell) + self.symmetric = symmetric self.flat = flat - self.apply_matrices = False + if self.flat: + self.unflat_cell = self.cell + self.cell = self.cell.flatten() + self.mat_transformer = None + self.apply_matrices = matrices + if self.apply_matrices: + self.setup_matrices() + @property def sub_elements(self): return [self.A, self.B] @@ -30,25 +46,206 @@ def __repr__(self): return "TensorProd(%s, %s)" % (repr(self.A), repr(self.B)) def setup_matrices(self): - oriented_mats_by_entity, flat_by_entity = self._initialise_entity_dicts(self.A.generate() + self.B.generate()) - breakpoint() - for dim in range(self.cell.dimension): - for dimA in range(self.A.cell.dimension): - pass - for dimB in range(self.B.cell_dimension): - pass - return super().setup_matrices() + if self.A.cell.dimension > 1 or self.B.cell.dimension > 1: + raise NotImplementedError("Combining of matrices not implemented in 3D") + if self.cell.flat: + raise NotImplementedError("Matrices for flattened cells not yet implemented") + self.A.to_ufl() + self.B.to_ufl() + oriented_mats_by_entity, flat_by_entity = self._initialise_entity_dicts(self.generate()) + if self.flat: + top = self.unflat_cell.to_fiat().get_topology() + else: + top = self.cell.to_fiat().get_topology() + for dim in top.keys(): + a_ents = self.A.cell.get_topology()[dim[0]].keys() + b_ents = self.B.cell.get_topology()[dim[1]].keys() + ents = [(a, b) for a in a_ents for b in b_ents] + comp_os = self.cell.component_orientations() + for e, (a, b) in enumerate(ents): + ent_dofs = self.entity_dofs[dim][(a, b)] + if len(ent_dofs) >= 1: + sub_mat = oriented_mats_by_entity[dim][e] + a_mat = self.A.matrices[dim[0]][a] + a_ent_ids = self.A.entity_ids[dim[0]][a] + b_mat = self.B.matrices[dim[1]][b] + b_ent_ids = self.B.entity_ids[dim[1]][b] + + os = [(o_a, o_b) for o_a in a_mat.keys() for o_b in b_mat.keys()] + for o in os: + a_sub_mat = a_mat[o[0]][np.ix_(a_ent_ids, a_ent_ids)] + b_sub_mat = b_mat[o[1]][np.ix_(b_ent_ids, b_ent_ids)] + if self.mat_transformer is not None: + o_classes = (self.A.cell.group.get_member_by_val(o[0]), self.B.cell.group.get_member_by_val(o[1])) + combined_sub_mat = self.mat_transformer(a_sub_mat, b_sub_mat, o_classes) + else: + combined_sub_mat = np.kron(a_sub_mat, b_sub_mat) + new_o = comp_os[dim][o] + sub_mat[new_o][np.ix_(ent_dofs, ent_dofs)] = np.matmul(sub_mat[new_o][np.ix_(ent_dofs, ent_dofs)], combined_sub_mat) + # from collections import defaultdict + # from FIAT.reference_element import tuple_sum + self.matrices = oriented_mats_by_entity + self.reversed_matrices = self.reverse_dof_perms(self.matrices) + + def generate(self): + a_dofs = self.A.generate() + b_dofs = self.B.generate() + a_ent_assocs, _, _ = self.A._entity_associations(a_dofs, overall=False) + b_ent_assocs, _, _ = self.B._entity_associations(b_dofs, overall=False) + if self.flat: + top = self.unflat_cell.to_fiat().get_topology() + else: + top = self.cell.to_fiat().get_topology() + self.entity_dofs = {} + dofs = [] + counter = 0 + for dim in top.keys(): + ents_A = a_ent_assocs[dim[0]].keys() + ents_B = b_ent_assocs[dim[1]].keys() + self.entity_dofs[dim] = {(a_e, b_e): tuple() for a_e in ents_A for b_e in ents_B} + for a_e, b_e in self.entity_dofs[dim].keys(): + a_dofs = [d for dofs in a_ent_assocs[dim[0]][a_e].values() for d in dofs] + b_dofs = [d for dofs in b_ent_assocs[dim[1]][b_e].values() for d in dofs] + new_dofs = [(a, b) for a in a_dofs for b in b_dofs] + dofs += new_dofs + self.entity_dofs[dim][(a_e, b_e)] = [i + counter for i in range(len(new_dofs))] + counter += len(new_dofs) + self.dofs = dofs + return dofs def to_ufl(self): if self.flat: - return FuseElement(self, self.cell.flatten().to_ufl()) - ufl_sub_elements = [e.to_ufl() for e in self.sub_elements()] - # self.setup_matrices() - # breakpoint() - return TensorProductElement(*ufl_sub_elements, cell=self.cell.to_ufl()) + return FuseElement(self, self.cell.to_ufl()) + ufl_sub_elements = [e.to_ufl() for e in self.sub_elements] + return TensorProductElement(*ufl_sub_elements, cell=self.cell.to_ufl(), triple=self) def flatten(self): - return TensorProductTriple(self.A, self.B, flat=True) + return TensorProductTriple(self.A, self.B, flat=True, symmetric=self.symmetric, matrices=self.apply_matrices) def unflatten(self): - return TensorProductTriple(self.A, self.B, flat=False) + return TensorProductTriple(self.A, self.B, flat=False, symmetric=self.symmetric, matrices=self.apply_matrices) + + +def compute_matrix_transform(trace, cell, o): + bvs = np.array(cell.basis_vectors()) + new_bvs = np.array(cell.orient(~o).basis_vectors()) + basis_change = np.matmul(new_bvs, np.linalg.inv(bvs)) + # if len(ent_dofs_ids) == basis_change.shape[0]: + # sub_mat = basis_change + # elif len(dof_gen_class[dim].g2.members()) == 2 and len(ent_dofs_ids) == 1: + # # equivalently g1 trivial + # sub_mat = trace.manipulate_basis(basis_change) + # else: + # case where value change is a restriction of the full transformation of the basis + value_change = trace(cell).manipulate_basis(basis_change) + # sub_mat = np.kron((~o).matrix_form(), value_change) + return value_change + + +class HDiv(TensorProductTriple): + + def __init__(self, tensor_element): + self.gem_transformer, self.mat_transformer = self.select_fuse_hdiv_transformer(tensor_element) + self.trace = TrHDiv + super(HDiv, self).__init__(tensor_element.A, tensor_element.B, tensor_element.flat, tensor_element.symmetric, tensor_element.matrices) + self.spaces[1] = TrHDiv + + def to_ufl(self): + return HDivElement(super(HDiv, self).to_ufl(), self.gem_transformer) + + def select_fuse_hdiv_transformer(self, element): + # Assume: something x interval + import gem + assert len(element.sub_elements) == 2 + assert element.sub_elements[1].cell.get_shape() == 1 + # Globally consistent edge orientations of the reference + # quadrilateral: rightward horizontally, upward vertically. + # Their rotation by 90 degrees anticlockwise is interpreted as the + # positive direction for normal vectors. + ks = tuple(compute_form_degree(fe.cell, fe.spaces) for fe in element.sub_elements) + transform = lambda cell, o: compute_matrix_transform(element.trace, cell, o) + if ks == (0, 1): + # Make the scalar value the right hand rule normal on the + # y-aligned edges. + cell = element.sub_elements[1].cell + bv = cell.basis_vectors()[0] + return lambda v: [gem.Product(gem.Literal(bv[0]), v), gem.Zero()], lambda m_a, m_b, o: np.kron(transform(cell, o[1]) @ m_a, m_b) + elif ks == (1, 0): + # Make the scalar value the upward-pointing normal on the + # x-aligned edges. + cell = element.sub_elements[0].cell + bv = cell.basis_vectors()[0][0] + return lambda v: [gem.Zero(), gem.Product(gem.Literal(bv), v)], lambda m_a, m_b, o: np.kron(m_a, transform(cell, o[0]) @ m_b) + # elif ks == (2, 0): + # # Same for 3D, so z-plane. + # return lambda v: [gem.Zero(), gem.Zero(), v] + # elif ks == (1, 1): + # if element.mapping == "contravariant piola": + # # Pad the 2-vector normal on the "base" cell into a + # # 3-vector, maintaining direction. + # return lambda v: [gem.Indexed(v, (0,)), + # gem.Indexed(v, (1,)), + # gem.Zero()] + # elif element.mapping == "covariant piola": + # # Rotate the 2-vector tangential component on the "base" + # # cell 90 degrees anticlockwise into a 3-vector and pad. + # return lambda v: [gem.Indexed(v, (1,)), + # gem.Product(gem.Literal(-1), gem.Indexed(v, (0,))), + # gem.Zero()] + # else: + # assert False, "Unexpected original mapping!" + else: + raise NotImplementedError("Unexpected original mapping!") + assert False, "Unexpected form degree combination!" + + +class HCurl(TensorProductTriple): + + def __init__(self, tensor_element): + self.gem_transformer, self.mat_transformer = self.select_fuse_hcurl_transformer(tensor_element) + self.trace = TrHCurl + super(HDiv, self).__init__(tensor_element.A, tensor_element.B, tensor_element.flat, tensor_element.symmetric, tensor_element.matrices) + self.spaces[1] = TrHCurl + + def to_ufl(self): + return HCurlElement(super(HDiv, self).to_ufl(), self.gem_transformer) + + def select_fuse_hcurl_transformer(element): + import gem + # Assume: something x interval + assert len(element.sub_elements) == 2 + assert element.sub_elements[1].cell.get_shape() == 1 + + # Globally consistent edge orientations of the reference + # quadrilateral: rightward horizontally, upward vertically. + # Tangential vectors interpret these as the positive direction. + dim = element.cell.get_spatial_dimension() + ks = tuple(compute_form_degree(fe.cell, fe.spaces) for fe in element.sub_elements) + if all(str(fe.spaces[1]) == "H1" or str(fe.spaces[1]) == "L2" for fe in element.sub_elements): # affine mapping + if ks == (1, 0): + # Can only be 2D. Make the scalar value the + # tangential following the cell edge direction on the x-aligned edges. + bv = element.sub_elements[0].cell.basis_vectors()[0][0] + return lambda v: [gem.Product(gem.Literal(bv), v), gem.Zero()] + elif ks == (0, 1): + # Can be any spatial dimension. Make the scalar value the + # tangential following the cell edge direction . + bv = element.sub_elements[1].cell.basis_vectors()[0][0] + return lambda v: [gem.Zero()] * (dim - 1) + [gem.Product(gem.Literal(bv), v)] + else: + assert False + # elif any(str(fe.spaces[1]) == "HCurl" for fe in element.sub_elements): # Covariant Piola mapping + # # Second factor must be continuous interval. Just padding. + # return lambda v: [gem.Indexed(v, (0,)), + # gem.Indexed(v, (1,)), + # gem.Zero()] + # elif any(str(fe.spaces[1]) == "HDiv" for fe in element.sub_elements): # Contravariant Piola mapping + # # Second factor must be continuous interval. Rotate the + # # 2-vector tangential component on the "base" cell 90 degrees + # # clockwise into a 3-vector and pad. + # return lambda v: [gem.Product(gem.Literal(-1), gem.Indexed(v, (1,))), + # gem.Indexed(v, (0,)), + # gem.Zero()] + else: + raise NotImplementedError("Unexpected original mapping!") + assert False, "Unexpected original mapping!" diff --git a/fuse/triples.py b/fuse/triples.py index 3c1607cf..3054ee5e 100644 --- a/fuse/triples.py +++ b/fuse/triples.py @@ -18,6 +18,21 @@ from functools import cache +def compute_form_degree(cell, spaces): + if str(spaces[1]) == "L2": + return cell.dimension + elif str(spaces[1]) == "H1": + return 0 + if cell.dimension < 2: + raise ValueError(f"Cells of dimension {cell.dimension} can only be 0 or 1 forms") + if cell.dimension == 2: + return 1 + elif str(spaces[1]) == "HDiv": + return 1 + elif str(spaces[1]) == "HCurl": + return 2 + + class ElementTriple(): """ Class to represent the three core parts of the element @@ -157,7 +172,8 @@ def to_ufl(self): def to_fiat(self): # call this to ensure set up is complete self.to_ufl() - form_degree = 1 if self.spaces[0].set_shape else 0 + # form_degree = 1 if self.spaces[0].set_shape else 0 + form_degree = compute_form_degree(self.cell, self.spaces) degree = self.spaces[0].degree() # sanity check that the dofs span the space original_V, original_basis = self.compute_dense_matrix(self.ref_el, self.entity_ids, self.nodes, self.poly_set) @@ -343,9 +359,8 @@ def make_overall_dense_matrices(self, ref_el, entity_ids, nodes, poly_set): res_dict[dim][e_id][val] = np.matmul(transformed_basis, original_V.T) return res_dict - def _entity_associations(self, dofs): - min_ids = self.cell.get_starter_ids() - entity_associations = {dim: {e.id - min_ids[dim]: {} for e in self.cell.d_entities(dim)} + def _entity_associations(self, dofs, overall=True): + entity_associations = {dim: {i: {} for i, e in enumerate(self.cell.d_entities(dim))} for dim in range(self.cell.dim() + 1)} cell_dim = self.cell.dim() cell_dict = entity_associations[cell_dim][0] @@ -355,8 +370,13 @@ def _entity_associations(self, dofs): # construct mapping of entities to the dof generators and the dofs they generate for d in dofs: sub_dim = d.cell_defined_on.dim() - sub_dict = entity_associations[sub_dim][d.cell_defined_on.id - min_ids[sub_dim]] - for dim in set([sub_dim, cell_dim]): + cell_defined_on_id = self.cell.d_entities_ids(sub_dim).index(d.cell_defined_on.id) + sub_dict = entity_associations[sub_dim][cell_defined_on_id] + if overall: + dims = set([sub_dim, cell_dim]) + else: + dims = [sub_dim] + for dim in dims: dof_gen = str(d.generation[dim]) if not len(d.generation[dim].g2.members()) == 1: @@ -369,7 +389,6 @@ def _entity_associations(self, dofs): sub_dict[dof_gen] += [d] elif dim < cell_dim or not d.immersed: sub_dict[dof_gen] = [d] - if dof_gen in cell_dict.keys() and dim == cell_dim and d.immersed: cell_dict[dof_gen] += [d] elif dim == cell_dim and d.immersed: @@ -377,16 +396,21 @@ def _entity_associations(self, dofs): return entity_associations, pure_perm, sub_pure_perm def _initialise_entity_dicts(self, dofs): - min_ids = self.cell.get_starter_ids() + # min_ids = self.cell.get_starter_ids() dof_id_mat = np.eye(len(dofs)) oriented_mats_by_entity = {} flat_by_entity = {} - for dim in range(self.cell.dim() + 1): + if isinstance(self.cell, TensorProductPoint): + dims = [(a_d, b_d) for a_d in range(self.cell.A.dimension + 1) for b_d in range(self.cell.B.dimension + 1)] + else: + dims = [i for i in range(self.cell.dimension + 1)] + for dim in dims: oriented_mats_by_entity[dim] = {} flat_by_entity[dim] = {} + ents = self.cell.d_entities(dim) - for e in ents: - e_id = e.id - min_ids[dim] + for e_id, e in enumerate(ents): + # old_e_id = e.id - min_ids[dim] members = e.group.members() oriented_mats_by_entity[dim][e_id] = {} flat_by_entity[dim][e_id] = {} @@ -411,8 +435,10 @@ def make_dof_perms(self, ref_el, entity_ids, nodes, poly_set): # dof mapping according to the generation for dim in range(self.cell.dim() + 1): ents = self.cell.d_entities(dim) - for e in ents: - e_id = e.id - min_ids[dim] + for e_id, e in enumerate(ents): + old_e_id = e.id - min_ids[dim] + if e_id != old_e_id: + raise ValueError("e id problems") members = e.group.members() for g in members: val = g.numeric_rep() @@ -421,7 +447,7 @@ def make_dof_perms(self, ref_el, entity_ids, nodes, poly_set): ent_dofs = entity_associations[dim][e_id][dof_gen] ent_dofs_ids = np.array([self.dof_id_to_fiat_id[ed.id] for ed in ent_dofs], dtype=int) # (dof_gen, ent_dofs) - total_ent_dof_ids += [self.dof_id_to_fiat_id[ed.id] for ed in ent_dofs if ed.id not in total_ent_dof_ids] + total_ent_dof_ids += [self.dof_id_to_fiat_id[ed.id] for ed in ent_dofs if self.dof_id_to_fiat_id[ed.id] not in total_ent_dof_ids] # dof_idx = [total_ent_dof_ids.index(id) for id in ent_dofs_ids] dof_gen_class = ent_dofs[0].generation @@ -480,7 +506,10 @@ def make_dof_perms(self, ref_el, entity_ids, nodes, poly_set): g_sub_mat = perm_list_to_matrix(identity, [sub_e for sub_e, _ in permuted_ents]) for sub_e, sub_g in permuted_ents: sub_e = self.cell.get_node(sub_e) - sub_e_id = sub_e.id - min_ids[sub_e.dim()] + old_sub_e_id = sub_e.id - min_ids[sub_e.dim()] + sub_e_id = self.cell.d_entities(sub_e.dim(), get_class=False).index(sub_e.id) + if sub_e_id != old_sub_e_id: + raise ValueError("sub e id problems") sub_ent_ids = [] for (k, v) in entity_associations[immersed_dim][sub_e_id].items(): sub_ent_ids += [self.dof_id_to_fiat_id[e.id] for e in v] @@ -525,13 +554,14 @@ def orient_mat_perms(self): num_ents += len(ents) def reverse_dof_perms(self, matrices): - min_ids = self.cell.get_starter_ids() + # min_ids = self.cell.get_starter_ids() reversed_mats = {} for dim in matrices.keys(): reversed_mats[dim] = {} ents = self.cell.d_entities(dim) for e in ents: - e_id = e.id - min_ids[dim] + # old_e_id = e.id - min_ids[dim] + e_id = self.cell.d_entities(e.dim(), get_class=False).index(e.id) perms_copy = matrices[dim][e_id].copy() members = e.group.members() for m in members: @@ -539,6 +569,21 @@ def reverse_dof_perms(self, matrices): reversed_mats[dim][e_id] = perms_copy return reversed_mats + def __add__(self, other): + """ Construct a new element triple by combining the degrees of freedom + This implementation does not make assertions about the properties + of the resulting element. + + Elements being adding must be defined over the same cell and have the same + value shape and mapping""" + assert self.cell == other.cell + assert self.spaces[0].set_shape == other.spaces[0].set_shape + assert str(self.spaces[1]) == str(other.spaces[1]) + + spaces = (self.spaces[0] + other.spaces[0], self.spaces[1], max([self.spaces[2], other.spaces[2]])) + + return ElementTriple(self.cell, spaces, self.DOFGenerator + other.DOFGenerator) + def _to_dict(self): o_dict = {"cell": self.cell, "spaces": self.spaces, "dofs": self.DOFGenerator} return o_dict @@ -576,21 +621,20 @@ def num_dofs(self): return self.dof_numbers def generate(self, cell, space, id_counter): - if self.ls is None: - self.ls = [] - for l_g in self.x: - i = 0 - for g in self.g1.members(): - generated = l_g(g) - if not isinstance(generated, list): - generated = [generated] - for dof in generated: - dof.add_context(self, cell, space, g, id_counter, i) - id_counter += 1 - i += 1 - self.ls.extend(generated) - self.dof_numbers = len(self.ls) - self.dof_ids = [dof.id for dof in self.ls] + self.ls = [] + for l_g in self.x: + i = 0 + for g in self.g1.members(): + generated = l_g(g) + if not isinstance(generated, list): + generated = [generated] + for dof in generated: + dof.add_context(self, cell, space, g, id_counter, i) + id_counter += 1 + i += 1 + self.ls.extend(generated) + self.dof_numbers = len(self.ls) + self.dof_ids = [dof.id for dof in self.ls] return self.ls def make_entity_ids(self): diff --git a/fuse/utils.py b/fuse/utils.py index fcfa3d9e..0d0ee9a9 100644 --- a/fuse/utils.py +++ b/fuse/utils.py @@ -29,7 +29,7 @@ def sympy_to_numpy(array, symbols, values): """ substituted = array.subs({symbols[i]: values[i] for i in range(len(values))}) - if len(array.atoms(sp.Symbol)) == len(values) and all(not isinstance(v, sp.Expr) for v in values): + if len(array.atoms(sp.Symbol)) <= len(values) and all(not isinstance(v, sp.Expr) for v in values): nparray = np.array(substituted).astype(np.float64) if len(nparray.shape) > 1: @@ -47,7 +47,7 @@ def tabulate_sympy(expr, pts): # expr: sp matrix expression in x,y,z for components of R^d # pts: n values in R^d # returns: evaluation of expr at pts - res = np.array(pts) + res = np.zeros((pts.shape[0],) + (expr.shape[-1],)) i = 0 syms = ["x", "y", "z"] for pt in pts: @@ -57,16 +57,20 @@ def tabulate_sympy(expr, pts): subbed = np.array(subbed).astype(np.float64) res[i] = subbed[0] i += 1 - final = res.squeeze() - return final + # final = res.squeeze() + return res -def max_deg_sp_mat(sp_mat): +def max_deg_sp_expr(sp_expr): degs = [] - for comp in sp_mat: - # only compute degree if component is a polynomial - if sp.sympify(comp).as_poly(): - degs += [sp.sympify(comp).as_poly().degree()] + if isinstance(sp_expr, sp.Matrix): + for comp in sp_expr: + # only compute degree if component is a polynomial + if sp.sympify(comp).as_poly(): + degs += [sp.sympify(comp).as_poly().total_degree()] + else: + if sp.sympify(sp_expr).as_poly(): + degs += [sp.sympify(sp_expr).as_poly().total_degree()] return max(degs) diff --git a/test/test_2d_examples_docs.py b/test/test_2d_examples_docs.py index c1d8ce16..9754bb42 100644 --- a/test/test_2d_examples_docs.py +++ b/test/test_2d_examples_docs.py @@ -1,6 +1,7 @@ from fuse import * import sympy as sp import numpy as np +import pytest np.set_printoptions(legacy="1.25") @@ -30,6 +31,33 @@ def construct_dg1(): return dg1 +def construct_dg0_integral(edge=None): + if not edge: + edge = Point(1, [Point(0), Point(0)], vertex_num=2) + xs = [DOF(L2Pairing(), VectorKernel(0.5))] + dg0 = ElementTriple(edge, (P0, CellL2, C0), DOFGenerator(xs, S1, S1)) + return dg0 + + +def construct_dg1_integral(cell=None): + edge = Point(1, [Point(0), Point(0)], vertex_num=2) + x = sp.Symbol("x") + xs = [DOF(L2Pairing(), PolynomialKernel((1/2)*(x + 1), symbols=(x,)))] + dg1 = ElementTriple(edge, (P1, CellL2, C0), DOFGenerator(xs, S2, S1)) + return dg1 + + +def construct_dg2_integral(cell=None): + edge = Point(1, [Point(0), Point(0)], vertex_num=2) + x = sp.Symbol("x") + xs = [DOF(L2Pairing(), PolynomialKernel((x/2)*(x + 1), symbols=(x,)))] + centre = [DOF(L2Pairing(), PolynomialKernel((1 - x**2), symbols=(x,)))] + + dofs = [DOFGenerator(xs, S2, S1), DOFGenerator(centre, S1, S1)] + dg2 = ElementTriple(edge, (PolynomialSpace(2), CellL2, C0), dofs) + return dg2 + + def plot_dg1(): dg1 = construct_dg1() dg1.plot() @@ -78,9 +106,11 @@ def test_dg_examples(): assert any(np.isclose(val, dof.eval(test_func)) for val in dof_vals) -def construct_cg1(): +def construct_cg1(edge=None): + # [test_cg1 0] - edge = Point(1, [Point(0), Point(0)], vertex_num=2) + if not edge: + edge = Point(1, [Point(0), Point(0)], vertex_num=2) vert = edge.vertices()[0] xs = [DOF(DeltaPairing(), PointKernel(()))] @@ -392,6 +422,15 @@ def test_rt_example(): rt.to_fiat() +@pytest.mark.parametrize(["triple", "expected"], [(construct_dg1_integral(), 1), + (construct_cg1(), 0), + (construct_rt(), 1), + (construct_dg1_tri(), 2)]) +def test_form_degree(triple, expected): + from fuse.triples import compute_form_degree + assert compute_form_degree(triple.cell, triple.spaces) == expected + + def construct_hermite(): tri = polygon(3) vert = tri.vertices()[0] diff --git a/test/test_algebra.py b/test/test_algebra.py new file mode 100644 index 00000000..53049276 --- /dev/null +++ b/test/test_algebra.py @@ -0,0 +1,36 @@ +from fuse import * +from firedrake import * +import numpy as np +import sympy as sp +from test_convert_to_fiat import create_cg2_tri, construct_cg3 + + +def construct_bubble(cell=None): + if cell is None: + cell = polygon(3) + x = sp.Symbol("x") + y = sp.Symbol("y") + f = (3*np.sqrt(3)/4)*(y + np.sqrt(3)/3)*(np.sqrt(3)*x + y - 2*np.sqrt(3)/3)*(-np.sqrt(3)*x + y - 2*np.sqrt(3)/3) + space = PolynomialSpace(3).restrict(0, 0)*f + xs = [DOF(DeltaPairing(), PointKernel((0, 0)))] + bubble = ElementTriple(cell, (space, CellL2, L2), DOFGenerator(xs, S1, S1)) + return bubble + + +def test_bubble(): + mesh = UnitTriangleMesh() + x = SpatialCoordinate(mesh) + + tri = polygon(3) + bub = construct_bubble(tri) + cg2 = create_cg2_tri(tri) + p2b3 = bub + cg2 + V = FunctionSpace(mesh, p2b3.to_ufl()) + W = FunctionSpace(mesh, construct_cg3().to_ufl()) + + bubble_func = 27*x[0]*x[1]*(1-x[0]-x[1]) + u = project(bubble_func, V) + exact = Function(W) + exact.interpolate(bubble_func, W) + # make sure that these are the same + assert sqrt(assemble((u-exact)*(u-exact)*dx)) < 1e-14 diff --git a/test/test_cells.py b/test/test_cells.py index 929ec0bf..3576c1d4 100644 --- a/test/test_cells.py +++ b/test/test_cells.py @@ -1,9 +1,9 @@ from fuse import * from firedrake import * -from fuse.cells import ufc_triangle, ufc_tetrahedron +from fuse.cells import ufc_triangle import pytest import numpy as np -from FIAT.reference_element import default_simplex, ufc_simplex +from FIAT.reference_element import default_simplex from test_convert_to_fiat import helmholtz_solve @@ -195,117 +195,11 @@ def test_comparison(): # print(tensor_product1 >= tensor_product1) -@pytest.mark.parametrize(["cell"], [(ufc_triangle(),), (polygon(3),)]) -def test_connectivity(cell): - cell = cell.to_fiat() - for dim0 in range(cell.get_spatial_dimension()+1): - connectivity = cell.get_connectivity()[(dim0, 0)] - topology = cell.get_topology()[dim0] - assert len(connectivity) == len(topology) - - assert all(connectivity[i] == t for i, t in topology.items()) - - -def test_tensor_connectivity(): - from test_2d_examples_docs import construct_cg1 - A = construct_cg1() - B = construct_cg1() - cell = tensor_product(A, B).cell - cell = cell.to_fiat() - for dim0 in [(0, 0), (1, 0), (0, 1), (1, 1)]: - connectivity = cell.get_connectivity()[(dim0, (0, 0))] - topology = cell.get_topology()[dim0] - assert len(connectivity) == len(topology) - - assert all(connectivity[i] == t for i, t in topology.items()) - - -@pytest.mark.parametrize(["cell"], [(ufc_triangle(),), (polygon(3),), (make_tetrahedron(), ), (make_tetrahedron(), )]) -def test_new_connectivity(cell): - cell = cell.to_fiat() - for dim0 in range(cell.get_dimension() + 1): - connectivity = cell.get_connectivity()[(dim0, 0)] - topology = cell.get_topology()[dim0] - assert len(connectivity) == len(topology) - for i, t in topology.items(): - print(connectivity[i]) - print(t) - assert all(connectivity[i] == t for i, t in topology.items()) - - -def test_compare_tris(): - fuse_tet = polygon(3) - ufc_tet = ufc_triangle() - fiat_tet = ufc_simplex(2) - - print(fiat_tet.get_topology()) - print(fuse_tet.get_topology()) - print(ufc_tet.get_topology()) - fiat_connectivity = fiat_tet.get_connectivity() - fuse_connectivity = fuse_tet.to_fiat().get_connectivity() - ufc_connectivity = ufc_tet.to_fiat().get_connectivity() - _dim = fiat_tet.get_dimension() - print("fiat") - print(make_entity_cone_lists(fiat_tet)) - for dim0 in range(_dim): - connectivity = fiat_connectivity[(dim0+1, dim0)] - print(connectivity) - print("fuse") - print(make_entity_cone_lists(fuse_tet.to_fiat())) - for dim0 in range(_dim): - connectivity = fuse_connectivity[(dim0+1, dim0)] - print(connectivity) - print("fuse ufc") - print(make_entity_cone_lists(ufc_tet.to_fiat())) - for dim0 in range(_dim): - connectivity = ufc_connectivity[(dim0+1, dim0)] - print(connectivity) - - -def test_compare_tets(): - tet = make_tetrahedron() - # perm = tet.group.get_member([1, 2, 0, 3]) - fuse_tet = tet - ufc_tet = ufc_tetrahedron() - fiat_tet = ufc_simplex(3) - # breakpoint() - print(fiat_tet.get_topology()) - print(fuse_tet.get_topology()) - print(ufc_tet.get_topology()) - fiat_connectivity = fiat_tet.get_connectivity() - fuse_connectivity = fuse_tet.to_fiat().get_connectivity() - ufc_connectivity = ufc_tet.to_fiat().get_connectivity() - _dim = fiat_tet.get_dimension() - print("fiat") - print(make_entity_cone_lists(fiat_tet)) - for dim0 in range(_dim): - connectivity = fiat_connectivity[(dim0+1, dim0)] - print(connectivity) - print("fuse") - print(make_entity_cone_lists(fuse_tet.to_fiat())) - for dim0 in range(_dim): - connectivity = fuse_connectivity[(dim0+1, dim0)] - print(connectivity) - print("fuse ufc") - print(make_entity_cone_lists(ufc_tet.to_fiat())) - for dim0 in range(_dim): - connectivity = ufc_connectivity[(dim0+1, dim0)] - print(connectivity) - - -def make_entity_cone_lists(fiat_cell): - _dim = fiat_cell.get_dimension() - _connectivity = fiat_cell.connectivity - _list = [] - _offset_list = [0 for _ in _connectivity[(0, 0)]] # vertices have no cones - _offset = 0 - _n = 0 # num. of entities up to dimension = _d - for _d in range(_dim): - _n1 = len(_offset_list) - for _conn in _connectivity[(_d + 1, _d)]: - _list += [_c + _n for _c in _conn] # These are indices into cell_closure[some_cell] - _offset_list.append(_offset) - _offset += len(_conn) - _n = _n1 - _offset_list.append(_offset) - return _list, _offset_list +def test_self_equality(C): + assert C == C + + +@pytest.mark.parametrize(["A", "B", "res"], [(ufc_triangle(), polygon(3), False), + (line(), line(), True),]) +def test_equivalence(A, B, res): + assert A.equivalent(B) == res diff --git a/test/test_convert_to_fiat.py b/test/test_convert_to_fiat.py index e59f57ef..5a6d3487 100644 --- a/test/test_convert_to_fiat.py +++ b/test/test_convert_to_fiat.py @@ -5,7 +5,7 @@ from firedrake import * from sympy.combinatorics import Permutation from FIAT.quadrature_schemes import create_quadrature -from test_2d_examples_docs import construct_cg1, construct_nd, construct_rt, construct_cg3 +from test_2d_examples_docs import construct_cg1, construct_nd, construct_rt, construct_cg3, construct_dg0_integral, construct_dg1_integral, construct_dg2_integral from test_3d_examples_docs import (construct_tet_rt, construct_tet_rt2, construct_tet_rt3, construct_tet_ned, construct_tet_ned_2nd_kind, construct_tet_ned_2nd_kind_2, construct_tet_ned_2nd_kind_2_non_bary, @@ -113,13 +113,11 @@ def create_cg1(cell): def create_cg1_quad(): deg = 1 - cell = polygon(4) - # cell = constructCellComplex("quadrilateral").cell_complex - - vert_dg = create_dg0(cell.vertices()[0]) + cell = TensorProductPoint(line(), line()).flatten() + print(cell, type(cell)) + vert_dg = create_dg1(cell.vertices()[0]) xs = [immerse(cell, vert_dg, TrH1)] - - Pk = PolynomialSpace(deg, deg + 1) + Pk = PolynomialSpace(deg + 1, deg) cg = ElementTriple(cell, (Pk, CellL2, C0), DOFGenerator(xs, get_cyc_group(len(cell.vertices())), S1)) return cg @@ -145,7 +143,9 @@ def create_cg1_flipped(cell): return cg -def create_cg2(cell): +def create_cg2(cell=None): + if cell is None: + cell = line() deg = 2 if cell.dim() > 1: raise NotImplementedError("This method is for cg2 on edges, please use create_cg2_tri for triangles") @@ -363,6 +363,9 @@ def test_entity_perms(elem_gen, cell): @pytest.mark.parametrize("elem_gen,elem_code,deg", [(create_cg1, "CG", 1), (create_dg1, "DG", 1), + pytest.param(construct_dg0_integral, "DG", 0, marks=pytest.mark.xfail(reason='Passes locally, fails in CI, probably same as dg2')), + (construct_dg1_integral, "DG", 1), + (construct_dg2_integral, "DG", 2), pytest.param(create_dg2, "DG", 2, marks=pytest.mark.xfail(reason='Need to update TSFC in CI')), (create_cg2, "CG", 2) ]) @@ -506,6 +509,7 @@ def helmholtz_solve(V, mesh): def poisson_solve(r, elem, parameters={}, quadrilateral=False): # Create mesh and define function space m = UnitSquareMesh(2 ** r, 2 ** r, quadrilateral=quadrilateral) + x = SpatialCoordinate(m) V = FunctionSpace(m, elem) @@ -526,6 +530,29 @@ def poisson_solve(r, elem, parameters={}, quadrilateral=False): return sqrt(assemble(inner(u - f, u - f) * dx)) +def run_test_original(r, elem_code, deg, parameters={}, quadrilateral=False): + # Create mesh and define function space + m = UnitSquareMesh(2 ** r, 2 ** r, quadrilateral=quadrilateral) + + x = SpatialCoordinate(m) + V = FunctionSpace(m, elem_code, deg) + # Define variational problem + u = Function(V) + v = TestFunction(V) + a = inner(grad(u), grad(v)) * dx + + bcs = [DirichletBC(V, Constant(0), 3), + DirichletBC(V, Constant(42), 4)] + + # Compute solution + solve(a == 0, u, solver_parameters=parameters, bcs=bcs) + + f = Function(V) + f.interpolate(42*x[1]) + + return sqrt(assemble(inner(u - f, u - f) * dx)) + + @pytest.mark.parametrize(['params', 'elem_gen'], [(p, d) for p in [{}, {'snes_type': 'ksponly', 'ksp_type': 'preonly', 'pc_type': 'lu'}] @@ -537,7 +564,7 @@ def test_poisson_analytic(params, elem_gen): @pytest.mark.parametrize(['elem_gen'], - [(create_cg1_quad_tensor,), pytest.param(create_cg1_quad, marks=pytest.mark.xfail(reason='Need to allow generation on tensor product quads'))]) + [(create_cg1_quad_tensor,), pytest.param(create_cg1_quad, marks=pytest.mark.xfail(reason='Issue with cell/mesh'))]) def test_quad(elem_gen): elem = elem_gen() r = 0 @@ -545,8 +572,13 @@ def test_quad(elem_gen): assert (poisson_solve(r, ufl_elem, parameters={}, quadrilateral=True) < 1.e-9) +@pytest.mark.xfail(reason="Issue with quad cell") def test_non_tensor_quad(): - create_cg1_quad() + elem = create_cg1_quad() + # ufl_elem = elem.to_ufl() + print(elem.to_fiat().entity_permutations()) + # elem.cell.hasse_diagram(filename="cg1quad.png") + assert (run_test_original(1, "CG", 1, parameters={}, quadrilateral=True) < 1.e-9) def project(U, mesh, func): diff --git a/test/test_dofs.py b/test/test_dofs.py index 8b2e0cae..bf29ad45 100644 --- a/test/test_dofs.py +++ b/test/test_dofs.py @@ -220,6 +220,6 @@ def test_generate_quadrature(): print("fiat", d.pt_dict) print() for d in elem.generate(): - print("fuse", d.to_quadrature(degree, (2,))) + print("fuse", d.to_quadrature(degree, value_shape=(2,))) elem.to_fiat() diff --git a/test/test_groups.py b/test/test_groups.py index 1b26787e..0c207039 100644 --- a/test/test_groups.py +++ b/test/test_groups.py @@ -117,3 +117,10 @@ def test_perm_mat_conversion(): mat_form = g.matrix_form() array_form = perm_matrix_to_perm_array(mat_form) assert np.allclose(g.perm.array_form, array_form) + + +def test_numeric_reps(): + cell = polygon(4) + rot4 = get_cyc_group(4).add_cell(cell) + + assert sorted([m.numeric_rep() for m in rot4.members()]) == list(range(len(rot4.members()))) diff --git a/test/test_perms.py b/test/test_perms.py index 4b0531d3..25c71231 100644 --- a/test/test_perms.py +++ b/test/test_perms.py @@ -3,7 +3,6 @@ from test_2d_examples_docs import construct_cg3 import pytest import numpy as np -import sympy as sp vert = Point(0) edge = Point(1, [Point(0), Point(0)], vertex_num=2) diff --git a/test/test_polynomial_space.py b/test/test_polynomial_space.py index e7dad66d..baf81206 100644 --- a/test/test_polynomial_space.py +++ b/test/test_polynomial_space.py @@ -41,6 +41,7 @@ def test_restriction(): res_on_set = restricted.to_ON_polynomial_set(cell) P3_on_set = P3.to_ON_polynomial_set(cell) + assert res_on_set.get_num_members() < P3_on_set.get_num_members() not_restricted = P3.restrict(0, 3) @@ -48,6 +49,16 @@ def test_restriction(): assert not_restricted.mindegree == 0 +def test_square_space(): + cell = polygon(3) + q2 = PolynomialSpace(3, 1) + + q2_on_set = q2.to_ON_polynomial_set(cell) + P3_on_set = P3.to_ON_polynomial_set(cell) + + assert q2_on_set.get_num_members() < P3_on_set.get_num_members() + + @pytest.mark.parametrize("deg", [1, 2, 3, 4]) def test_complete_space(deg): cell = polygon(3) diff --git a/test/test_tensor_prod.py b/test/test_tensor_prod.py index 7c527203..713c9621 100644 --- a/test/test_tensor_prod.py +++ b/test/test_tensor_prod.py @@ -2,10 +2,27 @@ import numpy as np from fuse import * from firedrake import * -from test_2d_examples_docs import construct_cg1, construct_dg1 +from test_2d_examples_docs import construct_cg1, construct_dg1, construct_dg0_integral, construct_dg1_integral +from test_convert_to_fiat import create_cg2, create_dg0 # from test_convert_to_fiat import create_cg1 +def create_cg3_interval(cell=None): + if cell is None: + cell = line() + deg = 3 + if cell.dim() > 1: + raise NotImplementedError("This method is for cg3 on edges, please use construct_cg3 for triangles") + vert_dg = create_dg0(cell.vertices()[0]) + xs = [immerse(cell, vert_dg, TrH1)] + interior = [DOF(DeltaPairing(), PointKernel((-1/np.sqrt(5), )))] + + Pk = PolynomialSpace(deg) + cg = ElementTriple(cell, (Pk, CellL2, C0), [DOFGenerator(xs, get_cyc_group(len(cell.vertices())), S1), + DOFGenerator(interior, S2, S1)]) + return cg + + def helmholtz_solve(mesh, V): u = TrialFunction(V) v = TestFunction(V) @@ -32,38 +49,48 @@ def mass_solve(U): assemble(L) solve(a == L, out) assert np.allclose(out.dat.data, f.dat.data, rtol=1e-5) + return out.dat.data -@pytest.mark.parametrize("generator, code, deg", [(construct_cg1, "CG", 1), (construct_dg1, "DG", 1)]) -def test_tensor_product_ext_mesh(generator, code, deg): +@pytest.mark.parametrize("generator1, generator2, code1, code2, deg1, deg2", + [(construct_cg1, construct_cg1, "CG", "CG", 1, 1), + (construct_dg1, construct_dg1, "DG", "DG", 1, 1), + (construct_dg1, construct_cg1, "DG", "CG", 1, 1), + (construct_dg1_integral, construct_cg1, "DG", "CG", 1, 1)]) +def test_ext_mesh(generator1, generator2, code1, code2, deg1, deg2): m = UnitIntervalMesh(2) mesh = ExtrudedMesh(m, 2) # manual method of creating tensor product elements - horiz_elt = FiniteElement(code, as_cell("interval"), deg) - vert_elt = FiniteElement(code, as_cell("interval"), deg) + horiz_elt = FiniteElement(code1, as_cell("interval"), deg1) + vert_elt = FiniteElement(code2, as_cell("interval"), deg2) elt = TensorProductElement(horiz_elt, vert_elt) U = FunctionSpace(mesh, elt) - mass_solve(U) + res1 = mass_solve(U) # fuseonic way of creating tensor product elements - A = generator() - B = generator() + A = generator1() + B = generator2() elem = tensor_product(A, B) U = FunctionSpace(mesh, elem.to_ufl()) - mass_solve(U) + res2 = mass_solve(U) + + assert np.allclose(res1, res2) -def test_helmholtz(): +@pytest.mark.parametrize(["elem_gen", "elem_code", "deg", "conv_rate"], [(construct_cg1, "CG", 1, 1.8), + (create_cg2, "CG", 2, 3.8), + (create_cg3_interval, "CG", 3, 4.8)]) +def test_helmholtz(elem_gen, elem_code, deg, conv_rate): vals = range(3, 6) res = [] for r in vals: m = UnitIntervalMesh(2**r) mesh = ExtrudedMesh(m, 2**r) - A = construct_cg1() - B = construct_cg1() + A = elem_gen() + B = elem_gen() elem = tensor_product(A, B) U = FunctionSpace(mesh, elem.to_ufl()) @@ -72,7 +99,7 @@ def test_helmholtz(): res = np.array(res) conv = np.log2(res[:-1] / res[1:]) print("convergence order:", conv) - assert (np.array(conv) > 1.8).all() + assert (np.array(conv) > conv_rate).all() def test_on_quad_mesh(): @@ -90,7 +117,10 @@ def test_on_quad_mesh(): mass_solve(U) -def test_quad_mesh_helmholtz(): +@pytest.mark.parametrize(["elem_gen", "elem_code", "deg", "conv_rate"], [(construct_cg1, "CG", 1, 1.8), + (create_cg2, "CG", 2, 3.8), + (create_cg3_interval, "CG", 3, 4.8)]) +def test_quad_mesh_helmholtz(elem_gen, elem_code, deg, conv_rate): quadrilateral = True vals = range(3, 6) res_fuse = [] @@ -98,22 +128,166 @@ def test_quad_mesh_helmholtz(): for r in vals: mesh = UnitSquareMesh(2 ** r, 2 ** r, quadrilateral=quadrilateral) - A = construct_cg1() - B = construct_cg1() - elem = tensor_product(A, B).flatten() + A = elem_gen() + B = elem_gen() + elem = tensor_product(A, B, matrices=False).flatten() U = FunctionSpace(mesh, elem.to_ufl()) res_fuse += [helmholtz_solve(mesh, U)] - - U = FunctionSpace(mesh, "CG", 1) + U = FunctionSpace(mesh, elem_code, deg) res_fire += [helmholtz_solve(mesh, U)] - print("l2 error norms:", res_fuse) + + print("Fuse l2 error norms:", res_fuse) res = np.array(res_fuse) conv = np.log2(res[:-1] / res[1:]) - print("convergence order:", conv) - assert (np.array(conv) > 1.8).all() + print("Fuse convergence order:", conv) + assert (np.array(conv) > conv_rate).all() - print("l2 error norms:", res_fire) + print("FIAT l2 error norms:", res_fire) res = np.array(res_fire) conv = np.log2(res[:-1] / res[1:]) - print("convergence order:", conv) - assert (np.array(conv) > 1.8).all() + print("Fiat convergence order:", conv) + assert (np.array(conv) > conv_rate).all() + + +@pytest.mark.parametrize(["A", "B", "res"], [(Point(0), line(), False), + (line(), line(), True), + (polygon(3), line(), False),]) +def test_flattening(A, B, res): + tensor_cell = TensorProductPoint(A, B) + if not res: + with pytest.raises(AssertionError): + tensor_cell.flatten() + else: + cell = tensor_cell.flatten() + cell.construct_fuse_rep() + + +def test_cg1_dg0(): + A = construct_cg1() + B = construct_dg1_integral() + non_sym = tensor_product(A, B) + # non_sym2 = tensor_product(B, A).flatten() + # from finat.element_factory import convert + # non_sym, _ = convert(non_sym.to_ufl(), shift_axes=0) + # non_sym2, _ = convert(non_sym2.to_ufl(), shift_axes=0) + # from FIAT.reference_element import flatten_entities + # print() + # print(non_sym.entity_dofs()) + # print(non_sym2.entity_dofs()) + # print(flatten_entities(non_sym.entity_dofs())) + # print(flatten_entities(non_sym2.entity_dofs())) + print(non_sym) + A = construct_dg1_integral() + B = construct_dg1_integral() + non_sym1 = tensor_product(A, B) + print(non_sym1) + breakpoint() + + +def test_trace_galerkin_projection(): + mesh = UnitSquareMesh(10, 10, quadrilateral=True) + + x, y = SpatialCoordinate(mesh) + A = construct_cg1() + B = construct_dg1_integral() + elem = tensor_product(A, B).flatten() + elem2 = tensor_product(B, A).flatten() + + # Define the Trace Space + T = FunctionSpace(mesh, elem.to_ufl() + elem2.to_ufl()) + + # Define trial and test functions + lambdar = TrialFunction(T) + gammar = TestFunction(T) + + # Define right hand side function + + V = FunctionSpace(mesh, "CG", 1) + f = Function(V) + f.interpolate(cos(x*pi*2)*cos(y*pi*2)) + + # Construct bilinear form + a = inner(lambdar, gammar) * ds + inner(lambdar('+'), gammar('+')) * dS + + # Construct linear form + l = inner(f, gammar) * ds + inner(f('+'), gammar('+')) * dS + + # Compute the solution + t = Function(T) + solve(a == l, t, solver_parameters={'ksp_rtol': 1e-14}) + + # Compute error in trace norm + trace_error = sqrt(assemble(FacetArea(mesh)*inner((t - f)('+'), (t - f)('+')) * dS)) + + assert trace_error < 1e-13 + + +def test_hdiv(): + from fuse.tensor_products import HDiv + np.set_printoptions(linewidth=90, precision=4, suppress=True) + m = UnitIntervalMesh(2) + mesh = ExtrudedMesh(m, 2) + # CG_1 = FiniteElement("CG", "interval", 1) + # DG_0 = FiniteElement("DG", "interval", 0) + cg1 = construct_cg1() + dg0 = construct_dg0_integral() + p1p0 = HDiv(tensor_product(cg1, dg0)) + # P1P0 = TensorProductElement(CG_1, DG_0) + # RT_horiz = HDivElement(p1p0.to_ufl(), transform=hdiv_transform(p1p0)) + RT_horiz = p1p0.to_ufl() + # RT_horiz = HDivElement(P1P0) + # p0p1 = HDiv(tensor_product(dg0, cg1)) + # P0P1 = TensorProductElement(DG_0, CG_1) + # RT_vert = p0p1.to_ufl() + # RT_vert = HDivElement(P0P1) + elt = RT_horiz + # + RT_vert + # + RT_vert + # mesh = UnitSquareMesh(1, 1, quadrilateral=True) + V = FunctionSpace(mesh, elt) + u = TrialFunction(V) + v = TestFunction(V) + f = Function(V) + x, y = SpatialCoordinate(mesh) + # f_vec = as_vector(((1+8*pi*pi)*cos(x*pi*2)*cos(y*pi*2), (1+8*pi*pi)*cos(x*pi*2)*cos(y*pi*2))) + f_vec = as_vector((2, 3)) + f = project(f_vec, V) + a = (inner(grad(u), grad(v)) + inner(u, v)) * dx + L = inner(f, v) * dx + u = Function(V) + solve(a == L, u) + breakpoint() + # f.interpolate(cos(x*pi*2)*cos(y*pi*2)) + # V.finat_element.basis_evaluation(1, [(0, 0)]) + # tabulation = V.finat_element.fiat_equivalent.tabulate(0, [(0, 0), (1, 0)]) + # for ent, arr in tabulation.items(): + # print(ent) + # for comp in arr: + # print(comp[0], comp[1]) + + +def test_transforms(): + edge = Point(1, [Point(0), Point(0)], vertex_num=2) + rev_edge = edge.orient(edge.group.members()[1]) + from fuse.tensor_products import HDiv, HCurl + cg1 = construct_cg1() + rev_cg1 = construct_cg1(rev_edge) + dg0 = construct_dg0_integral() + rev_dg0 = construct_dg0_integral(rev_edge) + import gem + v = gem.Literal(5) + print("HCurl") + print(HCurl(tensor_product(dg0, cg1))(v)) + print(HCurl(tensor_product(rev_dg0, cg1))(v)) + print(HCurl(tensor_product(cg1, dg0))(v)) + print(HCurl(tensor_product(cg1, rev_dg0))(v)) + print(HCurl(tensor_product(dg0, rev_cg1))(v)) + print(HCurl(tensor_product(rev_cg1, dg0))(v)) + print("HDiv") + print(HDiv(tensor_product(dg0, cg1))(v)) + print(HDiv(tensor_product(rev_dg0, cg1))(v)) + print(HDiv(tensor_product(cg1, dg0))(v)) + print(HDiv(tensor_product(cg1, rev_dg0))(v)) + print(HDiv(tensor_product(dg0, rev_cg1))(v)) + print(HDiv(tensor_product(rev_cg1, dg0))(v)) + breakpoint()