From 2bd913fb84c555dbb07384b354af631ada6b8eb6 Mon Sep 17 00:00:00 2001 From: Unyi Daniel Date: Wed, 2 Mar 2022 19:19:55 +0000 Subject: [PATCH 01/13] Mesh Laplacian computation --- .pytest_cache/v/cache/lastfailed | 25 + .pytest_cache/v/cache/nodeids | 2065 +++++++++++++++++++ torch_geometric/utils/get_mesh_laplacian.py | 64 + 3 files changed, 2154 insertions(+) create mode 100644 .pytest_cache/v/cache/lastfailed create mode 100644 .pytest_cache/v/cache/nodeids create mode 100644 torch_geometric/utils/get_mesh_laplacian.py diff --git a/.pytest_cache/v/cache/lastfailed b/.pytest_cache/v/cache/lastfailed new file mode 100644 index 000000000000..a6ee27ce42cb --- /dev/null +++ b/.pytest_cache/v/cache/lastfailed @@ -0,0 +1,25 @@ +{ + "test/loader/test_cluster.py::test_cluster_gcn": true, + "test/nn/conv/test_appnp.py::test_appnp": true, + "test/nn/conv/test_arma_conv.py::test_arma_conv": true, + "test/nn/conv/test_cluster_gcn_conv.py::test_cluster_gcn_conv": true, + 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+ "test/utils/test_softmax.py::test_softmax", + "test/utils/test_softmax.py::test_softmax_dim", + "test/utils/test_sort_edge_index.py::test_sort_edge_index", + "test/utils/test_sparse.py::test_dense_to_sparse", + "test/utils/test_subgraph.py::test_get_num_hops", + "test/utils/test_subgraph.py::test_subgraph", + "test/utils/test_subgraph.py::test_k_hop_subgraph", + "test/utils/test_to_dense_adj.py::test_to_dense_adj", + "test/utils/test_to_dense_adj.py::test_to_dense_adj_with_duplicate_entries", + "test/utils/test_to_dense_batch.py::test_to_dense_batch", + "test/utils/test_train_test_split_edges.py::test_train_test_split_edges", + "test/utils/test_undirected.py::test_is_undirected", + "test/utils/test_undirected.py::test_to_undirected", + "test/visualization/test_influence.py::test_influence" +] \ No newline at end of file diff --git a/torch_geometric/utils/get_mesh_laplacian.py b/torch_geometric/utils/get_mesh_laplacian.py new file mode 100644 index 000000000000..eb0fdeebaf41 --- /dev/null +++ b/torch_geometric/utils/get_mesh_laplacian.py @@ -0,0 +1,64 @@ +import torch +from torch_scatter import scatter_add + +from torch_geometric.utils import add_self_loops + + +def get_mesh_laplacian(pos, face): + r""" Computes the mesh Laplacian of the mesh given by :obj:`pos` + and :obj:`face`. + + Args: + pos (Tensor): The node positions. + face (LongTensor): The face indices. + """ + + assert pos.shape[1] == 3 + assert face.shape[0] == 3 + + device = pos.device + dtype = pos.dtype + num_nodes = pos.shape[0] + cot_weight = torch.Tensor().to(dtype).to(device) + area_weight = torch.Tensor().to(dtype).to(device) + edge_index = torch.Tensor().long().to(device) + + def add_edge(left, centre, right): + left_pos, central_pos, right_pos = pos[left], pos[centre], pos[right] + left_vec = left_pos - central_pos + right_vec = right_pos - central_pos + dot = torch.einsum('ij, ij -> i', left_vec, right_vec) + cross = torch.norm(torch.cross(left_vec, right_vec, dim=1), dim=1) + cot = dot / cross # cos / sin + nonlocal cot_weight, area_weight, edge_index + cot_weight = torch.cat([cot_weight, cot / 2.0, cot / 2.0]) + # one-third of a triangle's area is cross / 6.0 + # since each edge is accounted twice, we compute cross / 12.0 instead + area_weight = torch.cat([area_weight, cross / 12.0, cross / 12.0]) + edge_index = torch.cat([ + edge_index, + torch.stack([left, right], dim=1), + torch.stack([right, left], dim=1) + ]) + + # add all 3 edges of the triangles + add_edge(face[2], face[0], face[1]) + add_edge(face[0], face[1], face[2]) + add_edge(face[1], face[2], face[0]) + + # eliminate duplicate matrix entries by adding them together + index_linearizer = torch.Tensor([num_nodes, 1]).to(device) + lin_index = torch.matmul(edge_index.float(), index_linearizer).long() + y, idx = lin_index.unique(return_inverse=True) + edge_index = torch.stack([y // num_nodes, y % num_nodes]) + cot_weight = scatter_add(cot_weight, idx, dim=0) + area_weight = scatter_add(area_weight, idx, dim=0) + + # compute the diagonal part + row, col = edge_index + cot_deg = scatter_add(cot_weight, row, dim=0, dim_size=num_nodes) + area_deg = scatter_add(area_weight, row, dim=0, dim_size=num_nodes) + deg = cot_deg / area_deg + edge_index, _ = add_self_loops(edge_index, num_nodes=num_nodes) + edge_weight = torch.cat([-cot_weight, deg], dim=0) + return edge_index, edge_weight From d55eb429f05401ff6281fe61727600737f2cbf06 Mon Sep 17 00:00:00 2001 From: Unyi Daniel Date: Thu, 3 Mar 2022 10:18:14 +0000 Subject: [PATCH 02/13] test: Mesh Laplacian computation --- test/utils/test_get_mesh_laplacian.py | 34 +++++++++++++++++++++++++++ torch_geometric/utils/__init__.py | 2 ++ 2 files changed, 36 insertions(+) create mode 100644 test/utils/test_get_mesh_laplacian.py diff --git a/test/utils/test_get_mesh_laplacian.py b/test/utils/test_get_mesh_laplacian.py new file mode 100644 index 000000000000..b264ff1ea38e --- /dev/null +++ b/test/utils/test_get_mesh_laplacian.py @@ -0,0 +1,34 @@ +import torch + +from torch_geometric.utils import get_mesh_laplacian + + +def test_get_mesh_laplacian(): + + # cube + pos = torch.Tensor([[1.0, 1.0, 1.0], [1.0, -1.0, 1.0], \ + [-1.0, -1.0, 1.0], [-1.0, 1.0, 1.0], \ + [1.0, 1.0, -1.0], [1.0, -1.0, -1.0], \ + [-1.0, -1.0, -1.0], [-1.0, 1.0, -1.0]]) + face = torch.Tensor([[0, 1, 2], [0, 3, 2], [4, 5, 1], \ + [4, 0, 1], [7, 6, 5], [7, 4, 5], \ + [3, 2, 6], [3, 7, 6], [4, 0, 3], \ + [4, 7, 3], [1, 5, 6], [1, 2, 6]]).long().t() + + lap = get_mesh_laplacian(pos, face) + assert torch.all(lap[0] == torch.Tensor([[0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, \ + 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, \ + 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, \ + 0, 1, 2, 3, 4, 5, 6, 7], + [1, 2, 3, 4, 0, 2, 4, 5, 6, 0, 1, 3, \ + 6, 0, 2, 4, 6, 7, 0, 1, 3, 5, 7, 1, \ + 4, 6, 7, 1, 2, 3, 5, 7, 3, 4, 5, 6, \ + 0, 1, 2, 3, 4, 5, 6, 7]])) + assert torch.allclose(lap[1], torch.Tensor([-1.0, -0.0, -1.0, -1.0, -1.0, -1.0, \ + -0.0, -1.0, -0.0, -0.0, -1.0, -1.0, \ + -1.0, -1.0, -1.0, -0.0, -0.0, -1.0, \ + -1.0, -0.0, -0.0, -1.0, -1.0, -1.0, \ + -1.0, -1.0, -0.0, -0.0, -1.0, -0.0, \ + -1.0, -1.0, -1.0, -1.0, -0.0, -1.0, \ + 1.125, 0.9, 1.125, 0.9, \ + 0.9, 1.125, 0.9, 1.125])) diff --git a/torch_geometric/utils/__init__.py b/torch_geometric/utils/__init__.py index 495eda85306b..8e13ce88235e 100644 --- a/torch_geometric/utils/__init__.py +++ b/torch_geometric/utils/__init__.py @@ -11,6 +11,7 @@ from .subgraph import get_num_hops, subgraph, k_hop_subgraph from .homophily import homophily from .get_laplacian import get_laplacian +from .get_mesh_laplacian import get_mesh_laplacian from .to_dense_batch import to_dense_batch from .to_dense_adj import to_dense_adj from .sparse import dense_to_sparse @@ -52,6 +53,7 @@ 'k_hop_subgraph', 'homophily', 'get_laplacian', + 'get_mesh_laplacian', 'to_dense_batch', 'to_dense_adj', 'dense_to_sparse', From 9b607c830697e7a55570070e524d7abec45492c8 Mon Sep 17 00:00:00 2001 From: Unyi Daniel Date: Thu, 3 Mar 2022 13:07:19 +0000 Subject: [PATCH 03/13] another test for mesh Laplacian computation --- .pytest_cache/v/cache/nodeids | 2064 +------------------------ test/utils/test_get_mesh_laplacian.py | 25 + 2 files changed, 26 insertions(+), 2063 deletions(-) diff --git a/.pytest_cache/v/cache/nodeids b/.pytest_cache/v/cache/nodeids index 4c6b2b59e983..d875f4e74146 100644 --- a/.pytest_cache/v/cache/nodeids +++ b/.pytest_cache/v/cache/nodeids @@ -1,2065 +1,3 @@ [ - "test/test_debug.py::test_debug", - "test/test_seed.py::test_seed_everything", - "test/data/test_batch.py::test_batch", - "test/data/test_batch.py::test_batching_with_new_dimension", - "test/data/test_batch.py::test_pickling", - "test/data/test_batch.py::test_recursive_batch", - "test/data/test_batch.py::test_batching_of_batches", - "test/data/test_batch.py::test_hetero_batch", - "test/data/test_batch.py::test_pair_data_batching", - "test/data/test_data.py::test_data", - "test/data/test_data.py::test_data_subgraph", - "test/data/test_data.py::test_copy_data", - 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"test/utils/test_convert.py::test_from_networkx_without_edges", - "test/utils/test_convert.py::test_from_networkx_with_same_node_and_edge_attributes", - "test/utils/test_convert.py::test_subgraph_convert", - "test/utils/test_convert.py::test_trimesh", - "test/utils/test_degree.py::test_degree", - "test/utils/test_dropout.py::test_dropout_adj", - "test/utils/test_geodesic.py::test_geodesic_distance", - "test/utils/test_get_laplacian.py::test_get_laplacian", - "test/utils/test_grid.py::test_grid", - "test/utils/test_homophily.py::test_homophily", - "test/utils/test_isolated.py::test_contains_isolated_nodes", - "test/utils/test_isolated.py::test_remove_isolated_nodes", - "test/utils/test_loop.py::test_contains_self_loops", - "test/utils/test_loop.py::test_remove_self_loops", - "test/utils/test_loop.py::test_segregate_self_loops", - "test/utils/test_loop.py::test_add_self_loops", - "test/utils/test_loop.py::test_add_remaining_self_loops", - "test/utils/test_loop.py::test_add_remaining_self_loops_without_initial_loops", - "test/utils/test_metric.py::test_metric", - "test/utils/test_metric.py::test_mean_iou", - "test/utils/test_negative_sampling.py::test_edge_index_to_vector_and_vice_versa", - "test/utils/test_negative_sampling.py::test_negative_sampling", - "test/utils/test_negative_sampling.py::test_bipartite_negative_sampling", - "test/utils/test_negative_sampling.py::test_batched_negative_sampling", - "test/utils/test_negative_sampling.py::test_bipartite_batched_negative_sampling", - "test/utils/test_negative_sampling.py::test_structured_negative_sampling", - "test/utils/test_negative_sampling.py::test_structured_negative_sampling_feasible", - "test/utils/test_normalized_cut.py::test_normalized_cut", - "test/utils/test_random.py::test_erdos_renyi_graph", - "test/utils/test_random.py::test_stochastic_blockmodel_graph", - "test/utils/test_random.py::test_barabasi_albert_graph", - "test/utils/test_repeat.py::test_repeat", - "test/utils/test_softmax.py::test_softmax", - "test/utils/test_softmax.py::test_softmax_dim", - "test/utils/test_sort_edge_index.py::test_sort_edge_index", - "test/utils/test_sparse.py::test_dense_to_sparse", - "test/utils/test_subgraph.py::test_get_num_hops", - "test/utils/test_subgraph.py::test_subgraph", - "test/utils/test_subgraph.py::test_k_hop_subgraph", - "test/utils/test_to_dense_adj.py::test_to_dense_adj", - "test/utils/test_to_dense_adj.py::test_to_dense_adj_with_duplicate_entries", - "test/utils/test_to_dense_batch.py::test_to_dense_batch", - "test/utils/test_train_test_split_edges.py::test_train_test_split_edges", - "test/utils/test_undirected.py::test_is_undirected", - "test/utils/test_undirected.py::test_to_undirected", - "test/visualization/test_influence.py::test_influence" + "test/utils/test_get_mesh_laplacian.py::test_get_mesh_laplacian" ] \ No newline at end of file diff --git a/test/utils/test_get_mesh_laplacian.py b/test/utils/test_get_mesh_laplacian.py index b264ff1ea38e..5ff49ff4ec66 100644 --- a/test/utils/test_get_mesh_laplacian.py +++ b/test/utils/test_get_mesh_laplacian.py @@ -32,3 +32,28 @@ def test_get_mesh_laplacian(): -1.0, -1.0, -1.0, -1.0, -0.0, -1.0, \ 1.125, 0.9, 1.125, 0.9, \ 0.9, 1.125, 0.9, 1.125])) + + # irregular triangular prism + pos = torch.Tensor([[0.0, 0.0, 0.0], [4.0, 0.0, 0.0], \ + [0.0, 0.0, -3.0], [1.0, 5.0, -1.0], \ + [3.0, 5.0, -1.0], [2.0, 5.0, -2.0]]) + face = torch.Tensor([[0, 1, 2], [3, 4, 5], [0, 1, 4], [0, 3, 4], \ + [1, 2, 5], [1, 4, 5], [2, 0, 3], [2, 5, 3]]).long().t() + + lap = get_mesh_laplacian(pos, face) + assert torch.all(lap[0] == torch.Tensor([[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, \ + 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, \ + 0, 1, 2, 3, 4, 5], + [1, 2, 3, 4, 0, 2, 4, 5, 0, 1, 3, 5, \ + 0, 2, 4, 5, 0, 1, 3, 5, 1, 2, 3, 4, \ + 0, 1, 2, 3, 4, 5]])) + assert torch.allclose(lap[1], torch.Tensor([-0.938834, -1.451131, -0.490290, \ + -0.000000, -0.938834, -0.378790, \ + -0.577017, -0.077878, -1.451131, \ + -0.378790, -0.163153, -0.344203, \ + -0.490290, -0.163153, -1.421842, \ + -2.387739, -0.000000, -0.577017, \ + -1.421842, -2.550610, -0.077878, \ + -0.344203, -2.387739, -2.550610, \ + 0.298518, 0.183356, 0.233502, \ + 0.761257, 0.688181, 0.768849])) From bed59d8b6f3dcb19c821f6e26b5bad607bbb0ea5 Mon Sep 17 00:00:00 2001 From: Unyi Daniel Date: Thu, 3 Mar 2022 13:51:49 +0000 Subject: [PATCH 04/13] formula in the documentation of get_mesh_Laplacian --- torch_geometric/utils/get_mesh_laplacian.py | 11 ++++++++++- 1 file changed, 10 insertions(+), 1 deletion(-) diff --git a/torch_geometric/utils/get_mesh_laplacian.py b/torch_geometric/utils/get_mesh_laplacian.py index eb0fdeebaf41..b52e93933146 100644 --- a/torch_geometric/utils/get_mesh_laplacian.py +++ b/torch_geometric/utils/get_mesh_laplacian.py @@ -6,7 +6,16 @@ def get_mesh_laplacian(pos, face): r""" Computes the mesh Laplacian of the mesh given by :obj:`pos` - and :obj:`face`. + and :obj:`face`. It is computed as :math:`\mathbf{L_{ij}} = + \begin{cases} + \frac{\cot \angle_{ikj} + \cot \angle_{ilj}}{2 a_{ij}} & + \mbox{if } \{i, j\} \mbox{ is an edge} \\ + \sum_{j \in N(i)}{L_{ij}} & + \mbox{if } \{i\} \mbox{ is in the diagonal} + \0 \mbox{ otherwise} + \end{cases}` + where :math:`a_{ij}` is the local area element, + i.e. one-third of the neighbouring triangle's area. Args: pos (Tensor): The node positions. From cad103c6f8aaca901a262268d1dd3e9d59b44ecf Mon Sep 17 00:00:00 2001 From: Unyi Daniel Date: Thu, 3 Mar 2022 14:22:29 +0000 Subject: [PATCH 05/13] formula in the documentation of get_mesh_Laplacian --- torch_geometric/utils/get_mesh_laplacian.py | 17 ++++++++--------- 1 file changed, 8 insertions(+), 9 deletions(-) diff --git a/torch_geometric/utils/get_mesh_laplacian.py b/torch_geometric/utils/get_mesh_laplacian.py index b52e93933146..1543789bc9cb 100644 --- a/torch_geometric/utils/get_mesh_laplacian.py +++ b/torch_geometric/utils/get_mesh_laplacian.py @@ -5,18 +5,17 @@ def get_mesh_laplacian(pos, face): - r""" Computes the mesh Laplacian of the mesh given by :obj:`pos` - and :obj:`face`. It is computed as :math:`\mathbf{L_{ij}} = - \begin{cases} + """ Computes the mesh Laplacian of the mesh given by :obj:`pos` + and :obj:`face`. + It is computed as :math:`\mathbf{L}_{ij} = \begin{cases} \frac{\cot \angle_{ikj} + \cot \angle_{ilj}}{2 a_{ij}} & - \mbox{if } \{i, j\} \mbox{ is an edge} \\ + \mbox{if } i, j \mbox{ is an edge,} \\ \sum_{j \in N(i)}{L_{ij}} & - \mbox{if } \{i\} \mbox{ is in the diagonal} - \0 \mbox{ otherwise} - \end{cases}` - where :math:`a_{ij}` is the local area element, + \mbox{if } i \mbox{ is in the diagonal,} \\ + 0 \mbox{ otherwise.} + \end{cases}` where :math:`a_{ij}` is the local area element, i.e. one-third of the neighbouring triangle's area. - + Args: pos (Tensor): The node positions. face (LongTensor): The face indices. From 2a3cc03019f58542357bf0f6e0e3d61176e12f23 Mon Sep 17 00:00:00 2001 From: Unyi Daniel Date: Thu, 3 Mar 2022 14:38:18 +0000 Subject: [PATCH 06/13] formula in the documentation of get_mesh_Laplacian --- torch_geometric/utils/get_mesh_laplacian.py | 19 ++++++++++--------- 1 file changed, 10 insertions(+), 9 deletions(-) diff --git a/torch_geometric/utils/get_mesh_laplacian.py b/torch_geometric/utils/get_mesh_laplacian.py index 1543789bc9cb..0bbe9b31deb9 100644 --- a/torch_geometric/utils/get_mesh_laplacian.py +++ b/torch_geometric/utils/get_mesh_laplacian.py @@ -5,15 +5,16 @@ def get_mesh_laplacian(pos, face): - """ Computes the mesh Laplacian of the mesh given by :obj:`pos` - and :obj:`face`. - It is computed as :math:`\mathbf{L}_{ij} = \begin{cases} - \frac{\cot \angle_{ikj} + \cot \angle_{ilj}}{2 a_{ij}} & - \mbox{if } i, j \mbox{ is an edge,} \\ - \sum_{j \in N(i)}{L_{ij}} & - \mbox{if } i \mbox{ is in the diagonal,} \\ - 0 \mbox{ otherwise.} - \end{cases}` where :math:`a_{ij}` is the local area element, + """ Computes the mesh Laplacian of the mesh given by + :obj:`pos` and :obj:`face`. It is computed as + :math:` \mathbf{L}_{ij} = \begin{cases} + \frac{\cot \angle_{ikj} + \cot \angle_{ilj}}{2 a_{ij}} & + \mbox{if } i, j \mbox{ is an edge,} \\ + \sum_{j \in N(i)}{L_{ij}} & + \mbox{if } i \mbox{ is in the diagonal,} \\ + 0 \mbox{ otherwise.} + \end{cases}` + where :math:`a_{ij}` is the local area element, i.e. one-third of the neighbouring triangle's area. Args: From af4bba115ed29e833288edc97b99e0c507097306 Mon Sep 17 00:00:00 2001 From: Unyi Daniel Date: Sat, 5 Mar 2022 13:06:15 +0000 Subject: [PATCH 07/13] improving documentation --- .pytest_cache/v/cache/lastfailed | 25 --------------------- torch_geometric/utils/get_mesh_laplacian.py | 11 +++++---- 2 files changed, 7 insertions(+), 29 deletions(-) delete mode 100644 .pytest_cache/v/cache/lastfailed diff --git a/.pytest_cache/v/cache/lastfailed b/.pytest_cache/v/cache/lastfailed deleted file mode 100644 index a6ee27ce42cb..000000000000 --- a/.pytest_cache/v/cache/lastfailed +++ /dev/null @@ -1,25 +0,0 @@ -{ - "test/loader/test_cluster.py::test_cluster_gcn": true, - "test/nn/conv/test_appnp.py::test_appnp": true, - "test/nn/conv/test_arma_conv.py::test_arma_conv": true, - "test/nn/conv/test_cluster_gcn_conv.py::test_cluster_gcn_conv": true, - "test/nn/conv/test_eg_conv.py::test_eg_conv": true, - "test/nn/conv/test_eg_conv.py::test_eg_conv_multiple_aggregators": true, - "test/nn/conv/test_gated_graph_conv.py::test_gated_graph_conv": true, - "test/nn/conv/test_gcn2_conv.py::test_gcn2_conv": true, - "test/nn/conv/test_gcn_conv.py::test_gcn_conv": true, - "test/nn/conv/test_gcn_conv.py::test_gcn_conv_with_decomposed_layers": true, - "test/nn/conv/test_gin_conv.py::test_gin_conv": true, - "test/nn/conv/test_graph_conv.py::test_graph_conv": true, - "test/nn/conv/test_lg_conv.py::test_lg_conv": true, - "test/nn/conv/test_mf_conv.py::test_mf_conv": true, - "test/nn/conv/test_pdn_conv.py::test_pdn_conv": true, - "test/nn/conv/test_rgcn_conv.py::test_rgcn_conv[RGCNConv-conf0]": true, - "test/nn/conv/test_rgcn_conv.py::test_rgcn_conv[RGCNConv-conf1]": true, - "test/nn/conv/test_rgcn_conv.py::test_rgcn_conv[RGCNConv-conf2]": true, - "test/nn/conv/test_sage_conv.py::test_sage_conv": true, - "test/nn/conv/test_sg_conv.py::test_sg_conv": true, - "test/nn/conv/test_signed_conv.py::test_signed_conv": true, - "test/nn/conv/test_tag_conv.py::test_tag_conv": true, - "test/nn/test_sequential.py::test_sequential_jittable": true -} \ No newline at end of file diff --git a/torch_geometric/utils/get_mesh_laplacian.py b/torch_geometric/utils/get_mesh_laplacian.py index 0bbe9b31deb9..8b3c0c28d45a 100644 --- a/torch_geometric/utils/get_mesh_laplacian.py +++ b/torch_geometric/utils/get_mesh_laplacian.py @@ -1,19 +1,22 @@ +from typing import Tuple + import torch +from torch import Tensor from torch_scatter import scatter_add from torch_geometric.utils import add_self_loops -def get_mesh_laplacian(pos, face): - """ Computes the mesh Laplacian of the mesh given by +def get_mesh_laplacian(pos: Tensor, face: Tensor) -> Tuple[Tensor, Tensor]: + r"""Computes the mesh Laplacian of the mesh given by :obj:`pos` and :obj:`face`. It is computed as - :math:` \mathbf{L}_{ij} = \begin{cases} + .. math:: \mathbf{L}_{ij} = \begin{cases} \frac{\cot \angle_{ikj} + \cot \angle_{ilj}}{2 a_{ij}} & \mbox{if } i, j \mbox{ is an edge,} \\ \sum_{j \in N(i)}{L_{ij}} & \mbox{if } i \mbox{ is in the diagonal,} \\ 0 \mbox{ otherwise.} - \end{cases}` + \end{cases} where :math:`a_{ij}` is the local area element, i.e. one-third of the neighbouring triangle's area. From d8607878dcbc02020efd2844b9695f7061628bf6 Mon Sep 17 00:00:00 2001 From: Unyi Daniel Date: Sun, 6 Mar 2022 22:20:17 +0000 Subject: [PATCH 08/13] improving code --- torch_geometric/utils/get_mesh_laplacian.py | 72 +++++++++++---------- 1 file changed, 37 insertions(+), 35 deletions(-) diff --git a/torch_geometric/utils/get_mesh_laplacian.py b/torch_geometric/utils/get_mesh_laplacian.py index 8b3c0c28d45a..a9fa0f1a1fd4 100644 --- a/torch_geometric/utils/get_mesh_laplacian.py +++ b/torch_geometric/utils/get_mesh_laplacian.py @@ -4,19 +4,23 @@ from torch import Tensor from torch_scatter import scatter_add -from torch_geometric.utils import add_self_loops +from torch_geometric.utils import add_self_loops, coalesce def get_mesh_laplacian(pos: Tensor, face: Tensor) -> Tuple[Tensor, Tensor]: r"""Computes the mesh Laplacian of the mesh given by :obj:`pos` and :obj:`face`. It is computed as - .. math:: \mathbf{L}_{ij} = \begin{cases} - \frac{\cot \angle_{ikj} + \cot \angle_{ilj}}{2 a_{ij}} & - \mbox{if } i, j \mbox{ is an edge,} \\ - \sum_{j \in N(i)}{L_{ij}} & - \mbox{if } i \mbox{ is in the diagonal,} \\ - 0 \mbox{ otherwise.} + + .. math:: + + \mathbf{L}_{ij} = \begin{cases} + \frac{\cot \angle_{ikj} + \cot \angle_{ilj}}{2 a_{ij}} & + \mbox{if } i, j \mbox{ is an edge,} \\ + \sum_{j \in N(i)}{L_{ij}} & + \mbox{if } i \mbox{ is in the diagonal,} \\ + 0 \mbox{ otherwise.} \end{cases} + where :math:`a_{ij}` is the local area element, i.e. one-third of the neighbouring triangle's area. @@ -28,43 +32,41 @@ def get_mesh_laplacian(pos: Tensor, face: Tensor) -> Tuple[Tensor, Tensor]: assert pos.shape[1] == 3 assert face.shape[0] == 3 - device = pos.device - dtype = pos.dtype num_nodes = pos.shape[0] - cot_weight = torch.Tensor().to(dtype).to(device) - area_weight = torch.Tensor().to(dtype).to(device) - edge_index = torch.Tensor().long().to(device) - def add_edge(left, centre, right): + def add_angles(left, centre, right): left_pos, central_pos, right_pos = pos[left], pos[centre], pos[right] left_vec = left_pos - central_pos right_vec = right_pos - central_pos dot = torch.einsum('ij, ij -> i', left_vec, right_vec) cross = torch.norm(torch.cross(left_vec, right_vec, dim=1), dim=1) - cot = dot / cross # cos / sin - nonlocal cot_weight, area_weight, edge_index - cot_weight = torch.cat([cot_weight, cot / 2.0, cot / 2.0]) - # one-third of a triangle's area is cross / 6.0 - # since each edge is accounted twice, we compute cross / 12.0 instead - area_weight = torch.cat([area_weight, cross / 12.0, cross / 12.0]) - edge_index = torch.cat([ - edge_index, - torch.stack([left, right], dim=1), - torch.stack([right, left], dim=1) - ]) + cot = dot / cross # cot = cos / sin + area = cross / 6.0 # one-third of a triangle's area is cross / 6.0 + return cot / 2.0, area / 2.0 + + # for each triangle face, add all 3 angles + cot_201, area_201 = add_angles(face[2], face[0], face[1]) + cot_012, area_012 = add_angles(face[0], face[1], face[2]) + cot_120, area_120 = add_angles(face[1], face[2], face[0]) + + cot_weight = torch.cat( + [cot_201, cot_201, cot_012, cot_012, cot_120, cot_120]) + area_weight = torch.cat( + [area_201, area_201, area_012, area_012, area_120, area_120]) + edge_index = torch.cat([ + torch.stack([face[2], face[1]], dim=1), + torch.stack([face[1], face[2]], dim=1), + torch.stack([face[0], face[2]], dim=1), + torch.stack([face[2], face[0]], dim=1), + torch.stack([face[1], face[0]], dim=1), + torch.stack([face[0], face[1]], dim=1) + ]) - # add all 3 edges of the triangles - add_edge(face[2], face[0], face[1]) - add_edge(face[0], face[1], face[2]) - add_edge(face[1], face[2], face[0]) + cot_edge_index, cot_weight = coalesce(edge_index.t(), cot_weight) + area_edge_index, area_weight = coalesce(edge_index.t(), area_weight) - # eliminate duplicate matrix entries by adding them together - index_linearizer = torch.Tensor([num_nodes, 1]).to(device) - lin_index = torch.matmul(edge_index.float(), index_linearizer).long() - y, idx = lin_index.unique(return_inverse=True) - edge_index = torch.stack([y // num_nodes, y % num_nodes]) - cot_weight = scatter_add(cot_weight, idx, dim=0) - area_weight = scatter_add(area_weight, idx, dim=0) + assert torch.all(cot_edge_index == area_edge_index) + edge_index = cot_edge_index # compute the diagonal part row, col = edge_index From addc8eb29a92c21c51a1bf655a68305644139a9c Mon Sep 17 00:00:00 2001 From: Unyi Daniel Date: Sun, 6 Mar 2022 22:54:43 +0000 Subject: [PATCH 09/13] minor code improvement --- .pytest_cache/v/cache/lastfailed | 1 + torch_geometric/utils/get_mesh_laplacian.py | 22 +++++++++------------ 2 files changed, 10 insertions(+), 13 deletions(-) create mode 100644 .pytest_cache/v/cache/lastfailed diff --git a/.pytest_cache/v/cache/lastfailed b/.pytest_cache/v/cache/lastfailed new file mode 100644 index 000000000000..9e26dfeeb6e6 --- /dev/null +++ b/.pytest_cache/v/cache/lastfailed @@ -0,0 +1 @@ +{} \ No newline at end of file diff --git a/torch_geometric/utils/get_mesh_laplacian.py b/torch_geometric/utils/get_mesh_laplacian.py index a9fa0f1a1fd4..8fc2af38ceb0 100644 --- a/torch_geometric/utils/get_mesh_laplacian.py +++ b/torch_geometric/utils/get_mesh_laplacian.py @@ -12,7 +12,6 @@ def get_mesh_laplacian(pos: Tensor, face: Tensor) -> Tuple[Tensor, Tensor]: :obj:`pos` and :obj:`face`. It is computed as .. math:: - \mathbf{L}_{ij} = \begin{cases} \frac{\cot \angle_{ikj} + \cot \angle_{ilj}}{2 a_{ij}} & \mbox{if } i, j \mbox{ is an edge,} \\ @@ -54,19 +53,16 @@ def add_angles(left, centre, right): area_weight = torch.cat( [area_201, area_201, area_012, area_012, area_120, area_120]) edge_index = torch.cat([ - torch.stack([face[2], face[1]], dim=1), - torch.stack([face[1], face[2]], dim=1), - torch.stack([face[0], face[2]], dim=1), - torch.stack([face[2], face[0]], dim=1), - torch.stack([face[1], face[0]], dim=1), - torch.stack([face[0], face[1]], dim=1) - ]) - - cot_edge_index, cot_weight = coalesce(edge_index.t(), cot_weight) - area_edge_index, area_weight = coalesce(edge_index.t(), area_weight) + torch.stack([face[2], face[1]], dim=0), + torch.stack([face[1], face[2]], dim=0), + torch.stack([face[0], face[2]], dim=0), + torch.stack([face[2], face[0]], dim=0), + torch.stack([face[1], face[0]], dim=0), + torch.stack([face[0], face[1]], dim=0) + ], dim=1) - assert torch.all(cot_edge_index == area_edge_index) - edge_index = cot_edge_index + _, cot_weight = coalesce(edge_index, cot_weight) + edge_index, area_weight = coalesce(edge_index, area_weight) # compute the diagonal part row, col = edge_index From b650a48cf3fbb7c13767cf729c412398ff4e5dc5 Mon Sep 17 00:00:00 2001 From: daniel-unyi-42 <63173826+daniel-unyi-42@users.noreply.github.com> Date: Mon, 7 Mar 2022 11:30:58 +0100 Subject: [PATCH 10/13] Ignore pytest_cache --- .gitignore | 1 + 1 file changed, 1 insertion(+) diff --git a/.gitignore b/.gitignore index 3e204eea9188..2e7c4c976eab 100644 --- a/.gitignore +++ b/.gitignore @@ -1,4 +1,5 @@ __pycache__/ +.pytest_cache/ data/ build/ dist/ From 323d66fdeabe1532621c9e2f7a5aec0a9032b6bc Mon Sep 17 00:00:00 2001 From: Unyi Daniel Date: Mon, 7 Mar 2022 11:04:59 +0000 Subject: [PATCH 11/13] documentation test --- torch_geometric/utils/get_mesh_laplacian.py | 15 ++++++++------- 1 file changed, 8 insertions(+), 7 deletions(-) diff --git a/torch_geometric/utils/get_mesh_laplacian.py b/torch_geometric/utils/get_mesh_laplacian.py index 8fc2af38ceb0..5bf2a45e593b 100644 --- a/torch_geometric/utils/get_mesh_laplacian.py +++ b/torch_geometric/utils/get_mesh_laplacian.py @@ -12,13 +12,13 @@ def get_mesh_laplacian(pos: Tensor, face: Tensor) -> Tuple[Tensor, Tensor]: :obj:`pos` and :obj:`face`. It is computed as .. math:: - \mathbf{L}_{ij} = \begin{cases} - \frac{\cot \angle_{ikj} + \cot \angle_{ilj}}{2 a_{ij}} & - \mbox{if } i, j \mbox{ is an edge,} \\ - \sum_{j \in N(i)}{L_{ij}} & - \mbox{if } i \mbox{ is in the diagonal,} \\ - 0 \mbox{ otherwise.} - \end{cases} + \mathbf{L}_{ij} = \begin{cases} + \frac{\cot \angle_{ikj} + \cot \angle_{ilj}}{2 a_{ij}} & + \mbox{if } i, j \mbox{ is an edge,} \\ + \sum_{j \in N(i)}{L_{ij}} & + \mbox{if } i \mbox{ is in the diagonal,} \\ + 0 \mbox{ otherwise.} + \end{cases} where :math:`a_{ij}` is the local area element, i.e. one-third of the neighbouring triangle's area. @@ -52,6 +52,7 @@ def add_angles(left, centre, right): [cot_201, cot_201, cot_012, cot_012, cot_120, cot_120]) area_weight = torch.cat( [area_201, area_201, area_012, area_012, area_120, area_120]) + edge_index = torch.cat([ torch.stack([face[2], face[1]], dim=0), torch.stack([face[1], face[2]], dim=0), From 235002975bc7d25b20276bc8ef6659c934eb941d Mon Sep 17 00:00:00 2001 From: Unyi Daniel Date: Mon, 7 Mar 2022 11:06:26 +0000 Subject: [PATCH 12/13] remove pytest_cache --- .pytest_cache/v/cache/lastfailed | 1 - .pytest_cache/v/cache/nodeids | 3 --- 2 files changed, 4 deletions(-) delete mode 100644 .pytest_cache/v/cache/lastfailed delete mode 100644 .pytest_cache/v/cache/nodeids diff --git a/.pytest_cache/v/cache/lastfailed b/.pytest_cache/v/cache/lastfailed deleted file mode 100644 index 9e26dfeeb6e6..000000000000 --- a/.pytest_cache/v/cache/lastfailed +++ /dev/null @@ -1 +0,0 @@ -{} \ No newline at end of file diff --git a/.pytest_cache/v/cache/nodeids b/.pytest_cache/v/cache/nodeids deleted file mode 100644 index d875f4e74146..000000000000 --- a/.pytest_cache/v/cache/nodeids +++ /dev/null @@ -1,3 +0,0 @@ -[ - "test/utils/test_get_mesh_laplacian.py::test_get_mesh_laplacian" -] \ No newline at end of file From 2ae2ac95f4929887e62abf19ad453533d079a92c Mon Sep 17 00:00:00 2001 From: rusty1s Date: Fri, 11 Mar 2022 23:05:32 +0100 Subject: [PATCH 13/13] re-format --- test/utils/test_get_mesh_laplacian.py | 147 +++++++++++++------- torch_geometric/utils/get_mesh_laplacian.py | 36 ++--- 2 files changed, 111 insertions(+), 72 deletions(-) diff --git a/test/utils/test_get_mesh_laplacian.py b/test/utils/test_get_mesh_laplacian.py index 5ff49ff4ec66..f438a26c3be5 100644 --- a/test/utils/test_get_mesh_laplacian.py +++ b/test/utils/test_get_mesh_laplacian.py @@ -3,57 +3,96 @@ from torch_geometric.utils import get_mesh_laplacian -def test_get_mesh_laplacian(): - - # cube - pos = torch.Tensor([[1.0, 1.0, 1.0], [1.0, -1.0, 1.0], \ - [-1.0, -1.0, 1.0], [-1.0, 1.0, 1.0], \ - [1.0, 1.0, -1.0], [1.0, -1.0, -1.0], \ - [-1.0, -1.0, -1.0], [-1.0, 1.0, -1.0]]) - face = torch.Tensor([[0, 1, 2], [0, 3, 2], [4, 5, 1], \ - [4, 0, 1], [7, 6, 5], [7, 4, 5], \ - [3, 2, 6], [3, 7, 6], [4, 0, 3], \ - [4, 7, 3], [1, 5, 6], [1, 2, 6]]).long().t() - - lap = get_mesh_laplacian(pos, face) - assert torch.all(lap[0] == torch.Tensor([[0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, \ - 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, \ - 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, \ - 0, 1, 2, 3, 4, 5, 6, 7], - [1, 2, 3, 4, 0, 2, 4, 5, 6, 0, 1, 3, \ - 6, 0, 2, 4, 6, 7, 0, 1, 3, 5, 7, 1, \ - 4, 6, 7, 1, 2, 3, 5, 7, 3, 4, 5, 6, \ - 0, 1, 2, 3, 4, 5, 6, 7]])) - assert torch.allclose(lap[1], torch.Tensor([-1.0, -0.0, -1.0, -1.0, -1.0, -1.0, \ - -0.0, -1.0, -0.0, -0.0, -1.0, -1.0, \ - -1.0, -1.0, -1.0, -0.0, -0.0, -1.0, \ - -1.0, -0.0, -0.0, -1.0, -1.0, -1.0, \ - -1.0, -1.0, -0.0, -0.0, -1.0, -0.0, \ - -1.0, -1.0, -1.0, -1.0, -0.0, -1.0, \ - 1.125, 0.9, 1.125, 0.9, \ - 0.9, 1.125, 0.9, 1.125])) - - # irregular triangular prism - pos = torch.Tensor([[0.0, 0.0, 0.0], [4.0, 0.0, 0.0], \ - [0.0, 0.0, -3.0], [1.0, 5.0, -1.0], \ - [3.0, 5.0, -1.0], [2.0, 5.0, -2.0]]) - face = torch.Tensor([[0, 1, 2], [3, 4, 5], [0, 1, 4], [0, 3, 4], \ - [1, 2, 5], [1, 4, 5], [2, 0, 3], [2, 5, 3]]).long().t() - - lap = get_mesh_laplacian(pos, face) - assert torch.all(lap[0] == torch.Tensor([[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, \ - 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, \ - 0, 1, 2, 3, 4, 5], - [1, 2, 3, 4, 0, 2, 4, 5, 0, 1, 3, 5, \ - 0, 2, 4, 5, 0, 1, 3, 5, 1, 2, 3, 4, \ - 0, 1, 2, 3, 4, 5]])) - assert torch.allclose(lap[1], torch.Tensor([-0.938834, -1.451131, -0.490290, \ - -0.000000, -0.938834, -0.378790, \ - -0.577017, -0.077878, -1.451131, \ - -0.378790, -0.163153, -0.344203, \ - -0.490290, -0.163153, -1.421842, \ - -2.387739, -0.000000, -0.577017, \ - -1.421842, -2.550610, -0.077878, \ - -0.344203, -2.387739, -2.550610, \ - 0.298518, 0.183356, 0.233502, \ - 0.761257, 0.688181, 0.768849])) +def test_get_mesh_laplacian_of_cube(): + pos = torch.tensor([ + [1.0, 1.0, 1.0], + [1.0, -1.0, 1.0], + [-1.0, -1.0, 1.0], + [-1.0, 1.0, 1.0], + [1.0, 1.0, -1.0], + [1.0, -1.0, -1.0], + [-1.0, -1.0, -1.0], + [-1.0, 1.0, -1.0], + ]) + + face = torch.tensor([ + [0, 1, 2], + [0, 3, 2], + [4, 5, 1], + [4, 0, 1], + [7, 6, 5], + [7, 4, 5], + [3, 2, 6], + [3, 7, 6], + [4, 0, 3], + [4, 7, 3], + [1, 5, 6], + [1, 2, 6], + ]) + + edge_index, edge_weight = get_mesh_laplacian(pos, face.t()) + + assert edge_index.tolist() == [ + [ + 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, + 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 0, 1, 2, 3, 4, 5, 6, 7 + ], + [ + 1, 2, 3, 4, 0, 2, 4, 5, 6, 0, 1, 3, 6, 0, 2, 4, 6, 7, 0, 1, 3, 5, + 7, 1, 4, 6, 7, 1, 2, 3, 5, 7, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7 + ], + ] + + assert torch.allclose( + edge_weight, + torch.tensor([ + -1.0, -0.0, -1.0, -1.0, -1.0, -1.0, -0.0, -1.0, -0.0, -0.0, -1.0, + -1.0, -1.0, -1.0, -1.0, -0.0, -0.0, -1.0, -1.0, -0.0, -0.0, -1.0, + -1.0, -1.0, -1.0, -1.0, -0.0, -0.0, -1.0, -0.0, -1.0, -1.0, -1.0, + -1.0, -0.0, -1.0, 1.125, 0.9, 1.125, 0.9, 0.9, 1.125, 0.9, 1.125 + ])) + + +def test_get_mesh_laplacian_of_irregular_triangular_prism(): + pos = torch.tensor([ + [0.0, 0.0, 0.0], + [4.0, 0.0, 0.0], + [0.0, 0.0, -3.0], + [1.0, 5.0, -1.0], + [3.0, 5.0, -1.0], + [2.0, 5.0, -2.0], + ]) + + face = torch.tensor([ + [0, 1, 2], + [3, 4, 5], + [0, 1, 4], + [0, 3, 4], + [1, 2, 5], + [1, 4, 5], + [2, 0, 3], + [2, 5, 3], + ]) + + edge_index, edge_weight = get_mesh_laplacian(pos, face.t()) + + assert edge_index.tolist() == [ + [ + 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, + 5, 5, 0, 1, 2, 3, 4, 5 + ], + [ + 1, 2, 3, 4, 0, 2, 4, 5, 0, 1, 3, 5, 0, 2, 4, 5, 0, 1, 3, 5, 1, 2, + 3, 4, 0, 1, 2, 3, 4, 5 + ], + ] + + assert torch.allclose( + edge_weight, + torch.tensor([ + -0.938834, -1.451131, -0.490290, -0.000000, -0.938834, -0.378790, + -0.577017, -0.077878, -1.451131, -0.378790, -0.163153, -0.344203, + -0.490290, -0.163153, -1.421842, -2.387739, -0.000000, -0.577017, + -1.421842, -2.550610, -0.077878, -0.344203, -2.387739, -2.550610, + 0.298518, 0.183356, 0.233502, 0.761257, 0.688181, 0.768849 + ])) diff --git a/torch_geometric/utils/get_mesh_laplacian.py b/torch_geometric/utils/get_mesh_laplacian.py index 5bf2a45e593b..2a44218ee881 100644 --- a/torch_geometric/utils/get_mesh_laplacian.py +++ b/torch_geometric/utils/get_mesh_laplacian.py @@ -8,28 +8,27 @@ def get_mesh_laplacian(pos: Tensor, face: Tensor) -> Tuple[Tensor, Tensor]: - r"""Computes the mesh Laplacian of the mesh given by - :obj:`pos` and :obj:`face`. It is computed as - + r"""Computes the mesh Laplacian of a mesh given by :obj:`pos` and + :obj:`face`. + It is computed as + .. math:: - \mathbf{L}_{ij} = \begin{cases} - \frac{\cot \angle_{ikj} + \cot \angle_{ilj}}{2 a_{ij}} & - \mbox{if } i, j \mbox{ is an edge,} \\ - \sum_{j \in N(i)}{L_{ij}} & - \mbox{if } i \mbox{ is in the diagonal,} \\ - 0 \mbox{ otherwise.} + \mathbf{L}_{ij} = \begin{cases} + \frac{\cot \angle_{ikj} + \cot \angle_{ilj}}{2 a_{ij}} & + \mbox{if } i, j \mbox{ is an edge} \\ + \sum_{j \in N(i)}{L_{ij}} & + \mbox{if } i \mbox{ is in the diagonal} \\ + 0 \mbox{ otherwise} \end{cases} - where :math:`a_{ij}` is the local area element, - i.e. one-third of the neighbouring triangle's area. + where :math:`a_{ij}` is the local area element, *i.e.* one-third of the + neighbouring triangle's area. Args: pos (Tensor): The node positions. face (LongTensor): The face indices. """ - - assert pos.shape[1] == 3 - assert face.shape[0] == 3 + assert pos.size(1) == 3 and face.size(0) == 3 num_nodes = pos.shape[0] @@ -43,7 +42,7 @@ def add_angles(left, centre, right): area = cross / 6.0 # one-third of a triangle's area is cross / 6.0 return cot / 2.0, area / 2.0 - # for each triangle face, add all 3 angles + # For each triangle face, add all three angles: cot_201, area_201 = add_angles(face[2], face[0], face[1]) cot_012, area_012 = add_angles(face[0], face[1], face[2]) cot_120, area_120 = add_angles(face[1], face[2], face[0]) @@ -62,14 +61,15 @@ def add_angles(left, centre, right): torch.stack([face[0], face[1]], dim=0) ], dim=1) - _, cot_weight = coalesce(edge_index, cot_weight) - edge_index, area_weight = coalesce(edge_index, area_weight) + edge_index, weight = coalesce(edge_index, [cot_weight, area_weight]) + cot_weight, area_weight = weight - # compute the diagonal part + # Compute the diagonal part: row, col = edge_index cot_deg = scatter_add(cot_weight, row, dim=0, dim_size=num_nodes) area_deg = scatter_add(area_weight, row, dim=0, dim_size=num_nodes) deg = cot_deg / area_deg edge_index, _ = add_self_loops(edge_index, num_nodes=num_nodes) edge_weight = torch.cat([-cot_weight, deg], dim=0) + return edge_index, edge_weight