notes on the envelope function

modelforge/tests/test_dimenet.py

@@ -60,7 +60,9 @@ def test_envelope():
     # Forward pass
     outputs = envelope(inputs)
     assert outputs.shape == inputs.shape
-    assert torch.allclose(outputs, torch.tensor([1.7109, 0.2539, 0.0000, 0.0000]), rtol=1e-3)
+    assert torch.allclose(
+        outputs, torch.tensor([1.7109, 0.2539, 0.0000, 0.0000]), rtol=1e-3
+    )
 
     # Script the model for optimization and deployment
     scripted_envelope = torch.jit.script(envelope)
@@ -70,12 +72,26 @@ def test_envelope():
     print(outputs_scripted)
     assert torch.allclose(outputs, outputs_scripted)
 
+    # ----------------------------------------- #
     # test for correct output computation
-    exponent=6 # Envelop function receives exponent = 5 but takes its increment and uses exponent = 6 -> why?
-    d_ij=0.5
-    u_05 = 1 - (exponent+1)*(exponent+2)/2*d_ij**exponent + exponent*(exponent+2)*d_ij**(exponent+1)- exponent*(exponent+1)/2*d_ij**(exponent+2)
-    u_05/=d_ij # this should not be done, but the Envelope function does this
+
+    exponent = (
+        5 + 1
+    )  # NOTE: Envelop function receives exponent = 5 but takes its increment and uses exponent = 6 FIXME: that seems strange ?
+    # start with test for float:
+    d_ij = 0.5
+    # generate envelope function of d_ij value
+    u_05 = (
+        1
+        - (exponent + 1) * (exponent + 2) / 2 * d_ij**exponent
+        + exponent * (exponent + 2) * d_ij ** (exponent + 1)
+        - exponent * (exponent + 1) / 2 * d_ij ** (exponent + 2)
+    )
+    u_05 /= d_ij  # NOTE: this is not in the paper, but in the DimNet++ implementation
+
+    # NOTE: this test passes, but only if you divide by d_ij at the end, which is not in the paper, but in the DimNet++ implementation
     u_05 = torch.tensor([u_05], dtype=torch.float32)
+
     assert torch.allclose(u_05, outputs[0], rtol=1e-3)
 
 
@@ -94,12 +110,16 @@ def test_bessel_basis():
 
     # Sample input tensor of distances
     num_pairs = 100
-    d_ij = torch.linspace(0, radial_cutoff, steps=num_pairs).unsqueeze(-1)  # Shape: (100,1)
+    d_ij = torch.linspace(0, radial_cutoff, steps=num_pairs).unsqueeze(
+        -1
+    )  # Shape: (100,1)
 
     # Forward pass
     outputs = bessel_layer(d_ij)  # Shape: (100, num_radial)
-    shape_tensor = torch.randn(num_pairs,num_radial) #output from besser_layer should have this size
-    assert shape_tensor.shape == outputs.shape # Should print: torch.Size([100, 6])
+    shape_tensor = torch.randn(
+        num_pairs, num_radial
+    )  # output from besser_layer should have this size
+    assert shape_tensor.shape == outputs.shape  # Should print: torch.Size([100, 6])
 
 
 def test_representation():