prompt: We are currently solving the following issue within our repository. Here is the issue text:
  --- BEGIN ISSUE ---
  Adding the `pjit` in the comparison
  Some people are more familiar with using model parallel via [`pjit`](https://github.com/google/jax/blob/main/jax/experimental/pjit.py). What about adding one more rows [here](https://github.com/alpa-projects/alpa/blob/main/docs/gallery/tutorials/alpa_vs_pmap.py#L46-L52)?
  
  --- END ISSUE ---
  
  Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
  --- BEGIN FILES ---
  Path: `docs/gallery/tutorials/alpa_vs_pmap.py`
  Content:
  ```
  1 """
  2 Differences between alpa.parallelize and jax.pmap
  3 =================================================
  4 
  5 The most common tool for parallelization or distributed computing in jax is
  6 `pmap <https://jax.readthedocs.io/en/latest/jax.html#parallelization-pmap>`_.
  7 With several lines of code change, we can use ``pmap`` for data parallel
  8 training. However, we cannot use ``pmap`` for model parallel training,
  9 which is required for training large models with billions of parameters.
  10 
  11 On the contrary, ``alpa.parallelize`` supports both data parallelism and
  12 model parallelism in an automatic way. ``alpa.parallelize`` analyzes the
  13 jax computational graph and picks the best strategy.
  14 If data parallelism is more suitable, ``alpa.parallelize`` achieves the same
  15 performance as ``pmap`` but with less code change.
  16 If model parallelism is more suitable, ``alpa.parallelize`` achieves better performance
  17 and uses less memory than ``pmap``.
  18 
  19 In this tutorial, we are going to compare ``alpa.parallelize`` and ``pmap`` on two
  20 workloads. A more detailed comparison among ``alpa.parallelize``, ``pmap``, and ``xmap``
  21 is also attached at the end of the article.
  22 """
  23 
  24 ################################################################################
  25 # When data parallelism is prefered
  26 # ---------------------------------
  27 
  28 # TODO
  29 
  30 ################################################################################
  31 # When model parallelism is prefered
  32 # ----------------------------------
  33 
  34 # TODO
  35 
  36 ################################################################################
  37 # Comparing ``alpa.parallelize``, ``pmap``, and ``xmap``
  38 # ------------------------------------------------------
  39 # Besides ``pmap``, jax also provides
  40 # `xmap <https://jax.readthedocs.io/en/latest/notebooks/xmap_tutorial.html>`_
  41 # for more advanced parallelization.
  42 # The table below compares the features of ``alpa.parallelize``, ``pmap``, and ``xmap``.
  43 # In summary, ``alpa.parallelize`` supports more parallelism techniques in a
  44 # more automatic way.
  45 #
  46 # ================  ================ ==================== ==================== =========
  47 # Transformation    Data Parallelism Operator Parallelism Pipeline Parallelism Automated
  48 # ================  ================ ==================== ==================== =========
  49 # alpa.parallelize  yes              yes                  yes                  yes
  50 # pmap              yes              no                   no                   no
  51 # xmap              yes              yes                  no                   no
  52 # ================  ================ ==================== ==================== =========
  53 #
  54 # .. note::
  55 #   Operator parallelism and pipeline parallelism are two forms of model parallelism.
  56 #   Operator parallelism partitions the work in a single operator and assigns them
  57 #   to different devices. Pipeline parallelism partitions the computational
  58 #   graphs and assigns different operators to different devices.
  59
  ```
  --- END FILES ---
  
  Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.
  
  Here is an example:
  
  ```diff
  diff --git a/examples/server_async.py b/examples/server_async.py
  --- a/examples/server_async.py
  +++ b/examples/server_async.py
  @@ -313,4 +313,4 @@
   
   
   if __name__ == "__main__":
  -    asyncio.run(run_async_server("."), debug=True)
  +    asyncio.run(run_async_server(), debug=True)
  diff --git a/examples/server_sync.py b/examples/server_sync.py
  --- a/examples/server_sync.py
  +++ b/examples/server_sync.py
  @@ -313,5 +313,5 @@
   
   
   if __name__ == "__main__":
  -    server = run_sync_server(".")
  +    server = run_sync_server()
       server.shutdown()
  
  ```
  
golden_diff: diff --git a/docs/gallery/tutorials/alpa_vs_pmap.py b/docs/gallery/tutorials/alpa_vs_pmap.py
  --- a/docs/gallery/tutorials/alpa_vs_pmap.py
  +++ b/docs/gallery/tutorials/alpa_vs_pmap.py
  @@ -34,14 +34,15 @@
   # TODO
   
   ################################################################################
  -# Comparing ``alpa.parallelize``, ``pmap``, and ``xmap``
  -# ------------------------------------------------------
  +# Comparing ``alpa.parallelize``, ``pmap``, ``xmap``, and ``pjit``
  +# -----------------------------------------------------------------
   # Besides ``pmap``, jax also provides
  -# `xmap <https://jax.readthedocs.io/en/latest/notebooks/xmap_tutorial.html>`_
  +# `xmap <https://jax.readthedocs.io/en/latest/notebooks/xmap_tutorial.html>`_ and 
  +# `pjit <https://jax.readthedocs.io/en/latest/jax-101/08-pjit.html>`_
   # for more advanced parallelization.
  -# The table below compares the features of ``alpa.parallelize``, ``pmap``, and ``xmap``.
  -# In summary, ``alpa.parallelize`` supports more parallelism techniques in a
  -# more automatic way.
  +# The table below compares the features of ``alpa.parallelize``, ``pmap``, ``xmap`` 
  +# and ``pjit``. In summary, ``alpa.parallelize`` supports more parallelism 
  +# techniques in a more automatic way.
   #
   # ================  ================ ==================== ==================== =========
   # Transformation    Data Parallelism Operator Parallelism Pipeline Parallelism Automated
  @@ -49,6 +50,7 @@
   # alpa.parallelize  yes              yes                  yes                  yes
   # pmap              yes              no                   no                   no
   # xmap              yes              yes                  no                   no
  +# pjit              yes              yes                  no                   no
   # ================  ================ ==================== ==================== =========
   #
   # .. note::
  
verification_info: {"golden_diff": "diff --git a/docs/gallery/tutorials/alpa_vs_pmap.py b/docs/gallery/tutorials/alpa_vs_pmap.py\n--- a/docs/gallery/tutorials/alpa_vs_pmap.py\n+++ b/docs/gallery/tutorials/alpa_vs_pmap.py\n@@ -34,14 +34,15 @@\n # TODO\n \n ################################################################################\n-# Comparing ``alpa.parallelize``, ``pmap``, and ``xmap``\n-# ------------------------------------------------------\n+# Comparing ``alpa.parallelize``, ``pmap``, ``xmap``, and ``pjit``\n+# -----------------------------------------------------------------\n # Besides ``pmap``, jax also provides\n-# `xmap <https://jax.readthedocs.io/en/latest/notebooks/xmap_tutorial.html>`_\n+# `xmap <https://jax.readthedocs.io/en/latest/notebooks/xmap_tutorial.html>`_ and \n+# `pjit <https://jax.readthedocs.io/en/latest/jax-101/08-pjit.html>`_\n # for more advanced parallelization.\n-# The table below compares the features of ``alpa.parallelize``, ``pmap``, and ``xmap``.\n-# In summary, ``alpa.parallelize`` supports more parallelism techniques in a\n-# more automatic way.\n+# The table below compares the features of ``alpa.parallelize``, ``pmap``, ``xmap`` \n+# and ``pjit``. In summary, ``alpa.parallelize`` supports more parallelism \n+# techniques in a more automatic way.\n #\n # ================  ================ ==================== ==================== =========\n # Transformation    Data Parallelism Operator Parallelism Pipeline Parallelism Automated\n@@ -49,6 +50,7 @@\n # alpa.parallelize  yes              yes                  yes                  yes\n # pmap              yes              no                   no                   no\n # xmap              yes              yes                  no                   no\n+# pjit              yes              yes                  no                   no\n # ================  ================ ==================== ==================== =========\n #\n # .. note::\n", "issue": "Adding the `pjit` in the comparison\nSome people are more familiar with using model parallel via [`pjit`](https://github.com/google/jax/blob/main/jax/experimental/pjit.py). What about adding one more rows [here](https://github.com/alpa-projects/alpa/blob/main/docs/gallery/tutorials/alpa_vs_pmap.py#L46-L52)?\n", "before_files": [{"content": "\"\"\"\nDifferences between alpa.parallelize and jax.pmap\n=================================================\n\nThe most common tool for parallelization or distributed computing in jax is\n`pmap <https://jax.readthedocs.io/en/latest/jax.html#parallelization-pmap>`_.\nWith several lines of code change, we can use ``pmap`` for data parallel\ntraining. However, we cannot use ``pmap`` for model parallel training,\nwhich is required for training large models with billions of parameters.\n\nOn the contrary, ``alpa.parallelize`` supports both data parallelism and\nmodel parallelism in an automatic way. ``alpa.parallelize`` analyzes the\njax computational graph and picks the best strategy.\nIf data parallelism is more suitable, ``alpa.parallelize`` achieves the same\nperformance as ``pmap`` but with less code change.\nIf model parallelism is more suitable, ``alpa.parallelize`` achieves better performance\nand uses less memory than ``pmap``.\n\nIn this tutorial, we are going to compare ``alpa.parallelize`` and ``pmap`` on two\nworkloads. A more detailed comparison among ``alpa.parallelize``, ``pmap``, and ``xmap``\nis also attached at the end of the article.\n\"\"\"\n\n################################################################################\n# When data parallelism is prefered\n# ---------------------------------\n\n# TODO\n\n################################################################################\n# When model parallelism is prefered\n# ----------------------------------\n\n# TODO\n\n################################################################################\n# Comparing ``alpa.parallelize``, ``pmap``, and ``xmap``\n# ------------------------------------------------------\n# Besides ``pmap``, jax also provides\n# `xmap <https://jax.readthedocs.io/en/latest/notebooks/xmap_tutorial.html>`_\n# for more advanced parallelization.\n# The table below compares the features of ``alpa.parallelize``, ``pmap``, and ``xmap``.\n# In summary, ``alpa.parallelize`` supports more parallelism techniques in a\n# more automatic way.\n#\n# ================  ================ ==================== ==================== =========\n# Transformation    Data Parallelism Operator Parallelism Pipeline Parallelism Automated\n# ================  ================ ==================== ==================== =========\n# alpa.parallelize  yes              yes                  yes                  yes\n# pmap              yes              no                   no                   no\n# xmap              yes              yes                  no                   no\n# ================  ================ ==================== ==================== =========\n#\n# .. note::\n#   Operator parallelism and pipeline parallelism are two forms of model parallelism.\n#   Operator parallelism partitions the work in a single operator and assigns them\n#   to different devices. Pipeline parallelism partitions the computational\n#   graphs and assigns different operators to different devices.\n", "path": "docs/gallery/tutorials/alpa_vs_pmap.py"}], "after_files": [{"content": "\"\"\"\nDifferences between alpa.parallelize and jax.pmap\n=================================================\n\nThe most common tool for parallelization or distributed computing in jax is\n`pmap <https://jax.readthedocs.io/en/latest/jax.html#parallelization-pmap>`_.\nWith several lines of code change, we can use ``pmap`` for data parallel\ntraining. However, we cannot use ``pmap`` for model parallel training,\nwhich is required for training large models with billions of parameters.\n\nOn the contrary, ``alpa.parallelize`` supports both data parallelism and\nmodel parallelism in an automatic way. ``alpa.parallelize`` analyzes the\njax computational graph and picks the best strategy.\nIf data parallelism is more suitable, ``alpa.parallelize`` achieves the same\nperformance as ``pmap`` but with less code change.\nIf model parallelism is more suitable, ``alpa.parallelize`` achieves better performance\nand uses less memory than ``pmap``.\n\nIn this tutorial, we are going to compare ``alpa.parallelize`` and ``pmap`` on two\nworkloads. A more detailed comparison among ``alpa.parallelize``, ``pmap``, and ``xmap``\nis also attached at the end of the article.\n\"\"\"\n\n################################################################################\n# When data parallelism is prefered\n# ---------------------------------\n\n# TODO\n\n################################################################################\n# When model parallelism is prefered\n# ----------------------------------\n\n# TODO\n\n################################################################################\n# Comparing ``alpa.parallelize``, ``pmap``, ``xmap``, and ``pjit``\n# -----------------------------------------------------------------\n# Besides ``pmap``, jax also provides\n# `xmap <https://jax.readthedocs.io/en/latest/notebooks/xmap_tutorial.html>`_ and \n# `pjit <https://jax.readthedocs.io/en/latest/jax-101/08-pjit.html>`_\n# for more advanced parallelization.\n# The table below compares the features of ``alpa.parallelize``, ``pmap``, ``xmap`` \n# and ``pjit``. In summary, ``alpa.parallelize`` supports more parallelism \n# techniques in a more automatic way.\n#\n# ================  ================ ==================== ==================== =========\n# Transformation    Data Parallelism Operator Parallelism Pipeline Parallelism Automated\n# ================  ================ ==================== ==================== =========\n# alpa.parallelize  yes              yes                  yes                  yes\n# pmap              yes              no                   no                   no\n# xmap              yes              yes                  no                   no\n# pjit              yes              yes                  no                   no\n# ================  ================ ==================== ==================== =========\n#\n# .. note::\n#   Operator parallelism and pipeline parallelism are two forms of model parallelism.\n#   Operator parallelism partitions the work in a single operator and assigns them\n#   to different devices. Pipeline parallelism partitions the computational\n#   graphs and assigns different operators to different devices.\n", "path": "docs/gallery/tutorials/alpa_vs_pmap.py"}]}