[Feature] Reduce messages with scatter_add in PyTorch (#427)

* implement pytorch spmm with gather and scatter add

* fix

* replace torch take with index_select

* comments

* comment about pytorch __getitem__ operator pitfall

* typo

python/dgl/backend/pytorch/tensor.py

@@ -135,15 +135,17 @@ def zeros_like(input):
 def ones(shape, dtype, ctx):
     return th.ones(shape, dtype=dtype, device=ctx)
 
-if TH_VERSION.version[0] == 0:
-    # TODO(minjie): note this does not support autograd on the `x` tensor.
-    #               should adopt a workaround using custom op.
-    def spmm(x, y):
-        return th.spmm(x, y)
-else:
-    # torch v1.0+
-    def spmm(x, y):
-        return th.sparse.mm(x, y)
+def spmm(x, y):
+    dst, src = x._indices()
+    # scatter index
+    index = dst.view(-1, 1).expand(-1, y.shape[1])
+    # zero tensor to be scatter_add to
+    out = y.new_full((x.shape[0], y.shape[1]), 0)
+    # look up src features and multiply by edge features
+    # Note: using y[src] instead of index_select will lead to terrible
+    #       performance in backward
+    feature = th.index_select(y, 0, src) * x._values().unsqueeze(-1)
+    return out.scatter_add(0, index, feature)
 
 def unsorted_1d_segment_sum(input, seg_id, n_segs, dim):
     y = th.zeros(n_segs, *input.shape[1:]).to(input)