code: def _logical_1d_to_physical_subspace_auto(
      sizes_and_strides, physical_shape
  ):
      """Maps logical 1d mesh to subspace of physical nd mesh.
  
      We are mapping a 1d logical mesh to a subspace (a strided slice containing the
      origin) of a n-dimensional physical mesh.
  
      output[i] contains the coordinate-tuple in the physical mesh for the i-th
      logical processor.
  
      sizes_and_strides is a list of (size, stride) pairs specifying the dimensions
      of the strided slice. For example,
        sizes_and_strides=[(2, 16), (4, 1)] would represent the slice containing
        [(0, 0), (0, 1), (0, 2), (0, 3),
         (16, 0), (16, 1), (16, 2), (16, 3)]
  
      This function heuristically picks an order, with the goal of optimizing
      allreduce performance.
  
      Args:
        sizes_and_strides: a list of n (size, stride) pairs
        physical_shape: ignored
      Returns:
        a list of coordinate-lists
      """
      del physical_shape
      ndims = len(sizes_and_strides)
      sizes = [p[0] for p in sizes_and_strides]
      strides = [p[1] for p in sizes_and_strides]
      n = mtf.list_product(sizes)
      if ndims >= 2 and sizes[0] > 1 and sizes[1] > 1:
          ring = _ring_2d(sizes[0], sizes[1])
          ret = []
          sizes_combined = [sizes[0] * sizes[1]] + sizes[2:]
          for logical_pnum in range(n):
              logical_coord = mtf.pnum_to_processor_coordinates(
                  sizes_combined, logical_pnum
              )
              ret.append(
                  list(ring[logical_coord[0]]) + logical_coord[1:]
              )
      else:
          ret = [
              mtf.pnum_to_processor_coordinates(sizes, logical_pnum)
              for logical_pnum in range(n)
          ]
      # multiply by strides
      ret = [
          [x * stride for x, stride in zip(pcoord, strides)]
          for pcoord in ret
      ]
      return ret
  
imports: from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  import math
  import os
  import gin
  from mesh_tensorflow import ops_with_redefined_builtins
  from mesh_tensorflow import tpu_variables
  from mesh_tensorflow import utils
  from six.moves import xrange
  import tensorflow.compat.v1
  from tensorflow.python.tpu.ops import tpu_ops
label_desc: Use image node_id 2 for calling a global function with example usage: _logical_1d_to_physical_subspace_auto(sizes_and_strides, physical_shape) and returns: ret