feat(treespec): add tree broadcast functions broadcast_common, tree_broadcast_common, tree_broadcast_map, and tree_broadcast_map_with_path

[XuehaiPan]

Description

Describe your changes in detail.

Add new methods and functions:

• PyTreeSpec.broadcast_to_common_suffix()
• tree_broadcast_common()
• broadcast_common()
• tree_broadcast_map()
• tree_broadcast_map_with_path()

>>> import optree
>>> spec1 = optree.tree_structure({'a': 1, 'b': (2, 3), 'c': [4, 5]})
>>> spec1
PyTreeSpec({'a': *, 'b': (*, *), 'c': [*, *]})
>>> spec2 = optree.tree_structure({'a': (1, 2), 'b': 3, 'c': [4, 5]})
>>> spec2
PyTreeSpec({'a': (*, *), 'b': *, 'c': [*, *]})
>>> spec3 = spec1.broadcast_to_common_suffix(spec2)
>>> spec3
PyTreeSpec({'a': (*, *), 'b': (*, *), 'c': [*, *]})
>>> spec1.is_prefix(spec3)
True
>>> spec2.is_prefix(spec3)
True

>>> import optree
>>> spec1 = optree.tree_structure({'a': 1, 'b': (2, 3), 'c': [4, None]})
>>> spec1
PyTreeSpec({'a': *, 'b': (*, *), 'c': [*, None]})
>>> spec2 = optree.tree_structure({'a': (1, 2), 'b': 3, 'c': [None, 5]})
>>> spec2
PyTreeSpec({'a': (*, *), 'b': *, 'c': [None, *]})
>>> spec3 = spec1.broadcast_to_common_suffix(spec2)
>>> spec3
PyTreeSpec({'a': (*, *), 'b': (*, *), 'c': [None, None]})
>>> spec1.is_prefix(spec3)
True
>>> spec2.is_prefix(spec3)
True

>>> import optree
>>> optree.tree_broadcast_common([1, (2, 3), 4], [5, 6, (7, 8)])
([1, (2, 3), (4, 4)], [5, (6, 6), (7, 8)])
>>> optree.tree_broadcast_map(lambda x, y: x * y, [5, 6, (3, 4)], [{'a': 7, 'b': 9}, [1, 2], 8])
[{'a': 35, 'b': 45}, [6, 12], (24, 32)]
>>> optree.tree_broadcast_map_with_path(lambda p, x, y: (p, x * y), [5, 6, (3, 4)], [{'a': 7, 'b': 9}, [1, 2], 8])
[{'a': ((0, 'a'), 35), 'b': ((0, 'b'), 45)},
 [((1, 0), 6), ((1, 1), 12)],
 (((2, 0), 24), ((2, 1), 32))]

Motivation and Context

Why is this change required? What problem does it solve?
If it fixes an open issue, please link to the issue here.
You can use the syntax close #15213 if this solves the issue #15213

• I have raised an issue to propose this change (required for new features and bug fixes)

Types of changes

What types of changes does your code introduce? Put an x in all the boxes that apply:

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds core functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation (update in the documentation)

Checklist

Go over all the following points, and put an x in all the boxes that apply.
If you are unsure about any of these, don't hesitate to ask. We are here to help!

• I have read the CONTRIBUTION guide. (required)
• My change requires a change to the documentation.
• I have updated the tests accordingly. (required for a bug fix or a new feature)
• I have updated the documentation accordingly.
• I have reformatted the code using make format. (required)
• I have checked the code using make lint. (required)
• I have ensured make test pass. (required)

[codecov]

Codecov Report

All modified lines are covered by tests ✅

Comparison is base (e5ed81c) 100.00% compared to head (7823670) 100.00%.

Additional details and impacted files

@@            Coverage Diff            @@
##              main       #87   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files            4         4           
  Lines          428       468   +40     
=========================================
+ Hits           428       468   +40     

Flag	Coverage Δ
unittests	100.00% <100.00%> (ø)

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Files	Coverage Δ
optree/__init__.py	100.00% <ø> (ø)
optree/ops.py	100.00% <100.00%> (ø)

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