Converting flat indices to 3D indices in Python

Question

I have an array of flat indices and I want to get the corresponding 3D indices. I want to avoid using a for-loop to convert each flat index to a 3D index one by one.

I tried to use the numpy's np.unravel_index() method to compute the 3D indices as shown below:

   import numpy as np

   # Column vector of flat indices
   test_flat_indices = np.array([[3957], [8405], [9161], [11105], [969]])

   # Shape of 3D array
   num_rows = 51
   num_cols = 51
   num_frames = 8

   # Convert flat indices to 3D indices
   indices_3d = np.unravel_index(test_flat_indices, (num_rows, num_cols, num_frames))

   # Format the result to [row, col, frame] format
   indices_3d = np.column_stack(np.array(indices_3d))

   print(indices_3d)

The above code produces the following output:

   array([[ 9, 35,  5],
          [20, 30,  5],
          [22, 23,  1],
          [27, 11,  1],
          [ 2, 19,  1]], dtype=int64)

Problem: The above out seems wrong because if I try to convert the 3D indices above to flat indices back (for verification) then, the values does not match. For example, the output value [9, 35, 5] should represent 9th-row, 35th-column and 5th-frame, which would actually result in (5x51x51 + 9x51 + 35) = 13499, which is wrong (the correct value should be 3957).

NOTE: If I change the unravel_index() method arguments to np.unravel_index(test_flat_indices, (num_frames, num_rows, num_cols)) then, the output is correct, which is:

   array([[ 1, 26, 30],
          [ 3, 11, 41],
          [ 3, 26, 32],
          [ 4, 13, 38],
          [ 0, 19,  0]], dtype=int64)

but why do I need to put the number of frames first?