Make _get_perspective_coeffs more numerically stable

[Parskatt]

See #8248

cc @vfdev-5

[pytorch-bot]

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✅ You can merge normally! (17 Unrelated Failures)

As of commit fb78e35 with merge base ae14789 ():

FLAKY - The following jobs failed but were likely due to flakiness present on trunk:

• CMake / linux (linux.g5.4xlarge.nvidia.gpu, cuda, 11.8) / linux-job (gh)
  The process '/usr/bin/git' failed with exit code 128
• CMake / macos (macos-12) / macos-job (gh)
  The process '/usr/local/bin/git' failed with exit code 128
• CMake / macos (macos-m1-stable) / macos-job (gh)
  The process '/usr/bin/git' failed with exit code 128
• CMake / windows (windows.4xlarge, cpu) / windows-job (gh)
  The process 'C:\Program Files\Git\cmd\git.exe' failed with exit code 128
• Prototype tests on Linux / unittests-prototype (3.8, linux.g5.4xlarge.nvidia.gpu, cuda, 11.8) / linux-job (gh)
  The process '/usr/bin/git' failed with exit code 128
• Tests / unittests-linux (3.8, linux.g5.4xlarge.nvidia.gpu, cuda, 11.8) / linux-job (gh)
  The process '/usr/bin/git' failed with exit code 128
• Tests / unittests-macos (3.10, macos-12) / macos-job (gh)
  The process '/usr/local/bin/git' failed with exit code 128
• Tests / unittests-macos (3.11, macos-12) / macos-job (gh)
  The process '/usr/local/bin/git' failed with exit code 128
• Tests / unittests-macos (3.8, macos-12) / macos-job (gh)
  The process '/usr/local/bin/git' failed with exit code 128
• Tests / unittests-macos (3.8, macos-m1-stable) / macos-job (gh)
  The process '/usr/bin/git' failed with exit code 128
• Tests / unittests-macos (3.9, macos-12) / macos-job (gh)
  The process '/usr/local/bin/git' failed with exit code 128
• Tests / unittests-windows (3.10, windows.4xlarge, cpu) / windows-job (gh)
  The process 'C:\Program Files\Git\cmd\git.exe' failed with exit code 128
• Tests / unittests-windows (3.11, windows.4xlarge, cpu) / windows-job (gh)
  The process 'C:\Program Files\Git\cmd\git.exe' failed with exit code 128
• Tests / unittests-windows (3.8, windows.4xlarge, cpu) / windows-job (gh)
  The process 'C:\Program Files\Git\cmd\git.exe' failed with exit code 128
• Tests / unittests-windows (3.9, windows.4xlarge, cpu) / windows-job (gh)
  The process 'C:\Program Files\Git\cmd\git.exe' failed with exit code 128

BROKEN TRUNK - The following jobs failed but were present on the merge base:

👉 Rebase onto the `viable/strict` branch to avoid these failures

• Build Windows Conda / pytorch/vision / conda-py3_8-cpu (gh)
  Process completed with exit code 1.
• CMake / windows (windows.g5.4xlarge.nvidia.gpu, cuda, 11.8) / windows-job (gh)
  ##[error]The operation was canceled.

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[NicolasHug]

Thanks for the report and for the fix @Parskatt . This looks good, just some minor comments below, LMK what you think

[NicolasHug]

Feel free to address this here!

[Parskatt]

made a simple check for 4 corners

[NicolasHug]

Instead of creating a_matrix and b_matrix as float and then converting them as double, should we just create both as double?

[Parskatt]

sounds good, changed

[NicolasHug]

Thanks @Parskatt . Looks like there's still a minor lint issue. I tried pushing directly to your PR branch but I don't have persmission. This diff should fix it, if you don't mind applying it manually

diff --git a/torchvision/transforms/functional.py b/torchvision/transforms/functional.py
index c67a45001f..b5c242c1e6 100644
--- a/torchvision/transforms/functional.py
+++ b/torchvision/transforms/functional.py
@@ -679,7 +679,7 @@ def _get_perspective_coeffs(startpoints: List[List[int]], endpoints: List[List[i
     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)):

[NicolasHug]

There are some CI failures but they're unrelated so this is good to merge. Thanks a lot for the report and for the fix @Parskatt