F.grid_sample produced unexpected results

vision
1

When I use the normalized grid corresponding to the original coordinate system, as expected, the output should be the same as the original input.
However, the actual output results are slightly different. Perhaps it is a precision issue?

h_coord, w_coord = torch.meshgrid(torch.arange(7), torch.arange(7))
h_coord = h_coord.reshape(1, 7, 7, 1)
w_coord = w_coord.reshape(1, 7, 7, 1)
grid = torch.cat(
    [
        2 * torch.clamp(w_coord, 0, 6) / (7 - 1) - 1,
        2 * torch.clamp(h_coord, 0, 6) / (7 - 1) - 1,
    ],
    dim=-1,
)
grid_sampled_shift = F.grid_sample(pad_x[:, :2], grid, mode="bilinear", align_corners=True)

print(grid)
print(pad_x[:, :2])
print(grid_sampled_shift)


'''
tensor([[[[-1.0000, -1.0000],
          [-0.6667, -1.0000],
          [-0.3333, -1.0000],
          [ 0.0000, -1.0000],
          [ 0.3333, -1.0000],
          [ 0.6667, -1.0000],
          [ 1.0000, -1.0000]],

         [[-1.0000, -0.6667],
          [-0.6667, -0.6667],
          [-0.3333, -0.6667],
          [ 0.0000, -0.6667],
          [ 0.3333, -0.6667],
          [ 0.6667, -0.6667],
          [ 1.0000, -0.6667]],

         [[-1.0000, -0.3333],
          [-0.6667, -0.3333],
          [-0.3333, -0.3333],
          [ 0.0000, -0.3333],
          [ 0.3333, -0.3333],
          [ 0.6667, -0.3333],
          [ 1.0000, -0.3333]],

         [[-1.0000,  0.0000],
          [-0.6667,  0.0000],
          [-0.3333,  0.0000],
          [ 0.0000,  0.0000],
          [ 0.3333,  0.0000],
          [ 0.6667,  0.0000],
          [ 1.0000,  0.0000]],

         [[-1.0000,  0.3333],
          [-0.6667,  0.3333],
          [-0.3333,  0.3333],
          [ 0.0000,  0.3333],
          [ 0.3333,  0.3333],
          [ 0.6667,  0.3333],
          [ 1.0000,  0.3333]],

         [[-1.0000,  0.6667],
          [-0.6667,  0.6667],
          [-0.3333,  0.6667],
          [ 0.0000,  0.6667],
          [ 0.3333,  0.6667],
          [ 0.6667,  0.6667],
          [ 1.0000,  0.6667]],

         [[-1.0000,  1.0000],
          [-0.6667,  1.0000],
          [-0.3333,  1.0000],
          [ 0.0000,  1.0000],
          [ 0.3333,  1.0000],
          [ 0.6667,  1.0000],
          [ 1.0000,  1.0000]]]])

tensor([[[[0., 0., 0., 0., 0., 0., 0.],
          [0., 0., 0., 0., 0., 0., 0.],
          [1., 1., 1., 1., 1., 1., 1.],
          [2., 2., 2., 2., 2., 2., 2.],
          [3., 3., 3., 3., 3., 3., 3.],
          [4., 4., 4., 4., 4., 4., 4.],
          [4., 4., 4., 4., 4., 4., 4.]],

         [[0., 0., 1., 2., 3., 4., 4.],
          [0., 0., 1., 2., 3., 4., 4.],
          [0., 0., 1., 2., 3., 4., 4.],
          [0., 0., 1., 2., 3., 4., 4.],
          [0., 0., 1., 2., 3., 4., 4.],
          [0., 0., 1., 2., 3., 4., 4.],
          [0., 0., 1., 2., 3., 4., 4.]]]])
          
tensor([[[[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00,
           0.0000e+00, 0.0000e+00],
          [1.1921e-07, 1.1921e-07, 1.1921e-07, 1.1921e-07, 1.1921e-07,
           1.1921e-07, 1.1921e-07],
          [1.0000e+00, 1.0000e+00, 1.0000e+00, 1.0000e+00, 1.0000e+00,
           1.0000e+00, 1.0000e+00],
          [2.0000e+00, 2.0000e+00, 2.0000e+00, 2.0000e+00, 2.0000e+00,
           2.0000e+00, 2.0000e+00],
          [3.0000e+00, 3.0000e+00, 3.0000e+00, 3.0000e+00, 3.0000e+00,
           3.0000e+00, 3.0000e+00],
          [4.0000e+00, 4.0000e+00, 4.0000e+00, 4.0000e+00, 4.0000e+00,
           4.0000e+00, 4.0000e+00],
          [4.0000e+00, 4.0000e+00, 4.0000e+00, 4.0000e+00, 4.0000e+00,
           4.0000e+00, 4.0000e+00]],

         [[0.0000e+00, 1.1921e-07, 1.0000e+00, 2.0000e+00, 3.0000e+00,
           4.0000e+00, 4.0000e+00],
          [0.0000e+00, 1.1921e-07, 1.0000e+00, 2.0000e+00, 3.0000e+00,
           4.0000e+00, 4.0000e+00],
          [0.0000e+00, 1.1921e-07, 1.0000e+00, 2.0000e+00, 3.0000e+00,
           4.0000e+00, 4.0000e+00],
          [0.0000e+00, 1.1921e-07, 1.0000e+00, 2.0000e+00, 3.0000e+00,
           4.0000e+00, 4.0000e+00],
          [0.0000e+00, 1.1921e-07, 1.0000e+00, 2.0000e+00, 3.0000e+00,
           4.0000e+00, 4.0000e+00],
          [0.0000e+00, 1.1921e-07, 1.0000e+00, 2.0000e+00, 3.0000e+00,
           4.0000e+00, 4.0000e+00],
          [0.0000e+00, 1.1921e-07, 1.0000e+00, 2.0000e+00, 3.0000e+00,
           4.0000e+00, 4.0000e+00]]]])
'''
2

Yes, I believe the small absolute errors are created by the limited floating point precision.
I.e. the grid will contain floating point values, which might not be exactly representable. Using mode="bilinear" would then most likely try to interpolate the source values. You could use mode="nearest" to get the same output.

3

Okay, thanks. It is a good idea to use nearest neighbor interpolation.