code: def vmap_with_axes(
      target: "flax.linen.transforms.Target",
      variable_axes: Mapping[
          flax.core.lift.CollectionFilter, flax.core.lift.InOutAxis
      ],
      split_rngs: Mapping[flax.core.lift.PRNGSequenceFilter, bool] = {},
      in_axes=0,
      out_axes=0,
      axis_size: Optional[int] = None,
      axis_name: Optional[str] = None,
      partitioning_axis_names: Mapping[Any, str] = {},
      spmd_axis_name: Optional[str] = None,
      methods=None,
  ) -> "flax.linen.transforms.Target":
      """Wrapped version of nn.vmap that handles logical axis metadata."""
  
      # tell normal vmap to broadcast axis metadata.
      variable_axes = dict(variable_axes)  # shallow copy
      for name in partitioning_axis_names:
          variable_axes[f"{name}_axes"] = None
  
      # perform usual lifted vmap
      vmapped = flax.linen.transforms.lift_transform(
          flax.core.lift.vmap,
          target,
          variable_axes=variable_axes,
          split_rngs=split_rngs,
          in_axes=in_axes,
          out_axes=out_axes,
          axis_size=axis_size,
          axis_name=axis_name,
          spmd_axis_name=spmd_axis_name,
          methods=methods,
      )
  
      for collection_name, axis in variable_axes.items():
          if collection_name in partitioning_axis_names:
              vmapped = _add_axis_to_metadata(  # pylint: disable=protected-access
                  vmapped,
                  axis_pos=axis,
                  axis_name=partitioning_axis_names[collection_name],
                  axis_col=f"{collection_name}_axes",
              )
  
      return vmapped
  
imports: import functools
  import re
  from typing import Any, Callable, Mapping, Optional, Tuple
  import flax
  from flax import linen
  from flax import struct
  from flax.core.frozen_dict import freeze
  from flax.core.frozen_dict import unfreeze
  from flax.core.lift import In
  from flax.core.lift import Out
  from flax.linen.spmd import _axis_rules
  from flax.linen.spmd import _AxisRules
  from flax.linen.spmd import _is_logical_spec
  from flax.linen.spmd import _with_sharding_constraint
  from flax.linen.spmd import Array
  from flax.linen.spmd import ArrayPytree
  from flax.linen.spmd import get_logical_axis_rules
  from flax.linen.spmd import logical_axis_rules
  from flax.linen.spmd import logical_to_mesh
  from flax.linen.spmd import logical_to_mesh_axes
  from flax.linen.spmd import LogicalPartitionSpec
  from flax.linen.spmd import LogicalPartitionSpecPytree
  from flax.linen.spmd import LogicalRules
  from flax.linen.spmd import PartitionSpecPytree
  from flax.linen.spmd import RulesFallback
  from flax.linen.spmd import set_logical_axis_rules
  from flax.linen.spmd import with_logical_constraint
  from flax.traverse_util import flatten_dict
  from flax.traverse_util import unflatten_dict
  import jax
label_desc: Use image node_id 10 for calling a global function with example usage: vmap_with_axes(target, variable_axes, split_rngs, in_axes, out_axes, axis_size, axis_name, partitioning_axis_names, spmd_axis_name, methods) and returns: vmapped