Improve AUC numeric stability

CHANGELOG.md

@@ -49,6 +49,9 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Fixed `PSNR` not working with `DDP` ([#214](https://github.com/PyTorchLightning/metrics/pull/214))
 
 
+- Fixed `AUC` sometimes raises errors even for sorted imput due to numerical instability ([#224](https://github.com/PyTorchLightning/metrics/pull/224))
+
+
 - Fixed metric calculation with unequal batch sizes ([#220](https://github.com/PyTorchLightning/metrics/pull/220))
 
 

torchmetrics/functional/classification/auc.py

@@ -31,16 +31,16 @@ def _auc_update(x: Tensor, y: Tensor) -> Tuple[Tensor, Tensor]:
     return x, y
 
 
-def _auc_compute(x: Tensor, y: Tensor, reorder: bool = False) -> Tensor:
+def _auc_compute(x: Tensor, y: Tensor, reorder: bool = False, tol: float = 1e-6) -> Tensor:
     with torch.no_grad():
         if reorder:
             # TODO: include stable=True arg when pytorch v1.9 is released
             x, x_idx = torch.sort(x)
             y = y[x_idx]
 
         dx = x[1:] - x[:-1]
-        if (dx < 0).any():
-            if (dx <= 0).all():
+        if (dx + tol < 0).any():
+            if (dx <= tol).all():
                 direction = -1.
             else:
                 raise ValueError(