Make _get_perspective_coeffs more numerically stable (#8249)

Co-authored-by: Nicolas Hug <nh.nicolas.hug@gmail.com>

torchvision/transforms/functional.py

@@ -676,14 +676,19 @@ def _get_perspective_coeffs(startpoints: List[List[int]], endpoints: List[List[i
     Returns:
         octuple (a, b, c, d, e, f, g, h) for transforming each pixel.
     """
-    a_matrix = torch.zeros(2 * len(startpoints), 8, dtype=torch.float)
+    if len(startpoints) != 4 or len(endpoints) != 4:
+        raise ValueError(
+            f"Please provide exactly four corners, got {len(startpoints)} startpoints and {len(endpoints)} endpoints."
+        )
+    a_matrix = torch.zeros(2 * len(startpoints), 8, dtype=torch.float64)
 
     for i, (p1, p2) in enumerate(zip(endpoints, startpoints)):
         a_matrix[2 * i, :] = torch.tensor([p1[0], p1[1], 1, 0, 0, 0, -p2[0] * p1[0], -p2[0] * p1[1]])
         a_matrix[2 * i + 1, :] = torch.tensor([0, 0, 0, p1[0], p1[1], 1, -p2[1] * p1[0], -p2[1] * p1[1]])
 
-    b_matrix = torch.tensor(startpoints, dtype=torch.float).view(8)
-    res = torch.linalg.lstsq(a_matrix, b_matrix, driver="gels").solution
+    b_matrix = torch.tensor(startpoints, dtype=torch.float64).view(8)
+    # do least squares in double precision to prevent numerical issues
+    res = torch.linalg.lstsq(a_matrix, b_matrix, driver="gels").solution.to(torch.float32)
 
     output: List[float] = res.tolist()
     return output