





"""simple docstring"""

import unittest

import numpy as np



def        __a							(			A ,	A ,	A ,	A = None ,	)       ->						np.ndarray:



   '''simple docstring'''



   A__											=					np.shape(A )
   A__											=					np.shape(A )
   A__											=					np.shape(A )

   if shape_a[0] != shape_b[0]:
      A__											=					(
          '''Expected the same number of rows for A and B. '''
          f"""Instead found A of size {shape_a} and B of size {shape_b}"""
      )
      raise ValueError(A )

   if shape_b[1] != shape_c[1]:
      A__											=					(
          '''Expected the same number of columns for B and C. '''
          f"""Instead found B of size {shape_b} and C of size {shape_c}"""
      )
      raise ValueError(A )

   A__											=					pseudo_inv
   if a_inv is None:
      try:
         A__											=					np.linalg.inv(A )
      except np.linalg.LinAlgError:
         raise ValueError(
             "Input matrix A is not invertible. Cannot compute Schur complement." )

   return mat_c - mat_b.T @ a_inv @ mat_b


class       lowerCAmelCase__				(   unittest.TestCase  ):







 def  lowercase_       (   self					):

    '''simple docstring'''


    A__											=					np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]					)
    A__											=					np.array([[0, 3], [3, 0], [2, 3]]					)
    A__											=					np.array([[2, 1], [6, 3]]					)

    A__											=					schur_complement(UpperCAmelCase__		,	UpperCAmelCase__		,	UpperCAmelCase__					)

    A__											=					np.block([[a, b], [b.T, c]]					)

    A__											=					np.linalg.det(UpperCAmelCase__					)
    A__											=					np.linalg.det(UpperCAmelCase__					)
    A__											=					np.linalg.det(UpperCAmelCase__					)

    self.assertAlmostEqual(UpperCAmelCase__		,	det_a * det_s					)







 def  lowercase_       (   self					):

    '''simple docstring'''


    A__											=					np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]					)
    A__											=					np.array([[0, 3], [3, 0], [2, 3]]					)
    A__											=					np.array([[2, 1], [6, 3]]					)

    with self.assertRaises(UpperCAmelCase__					):
       schur_complement(UpperCAmelCase__		,	UpperCAmelCase__		,	UpperCAmelCase__					)







 def  lowercase_       (   self					):

    '''simple docstring'''


    A__											=					np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]					)
    A__											=					np.array([[0, 3], [3, 0], [2, 3]]					)
    A__											=					np.array([[2, 1, 3], [6, 3, 5]]					)

    with self.assertRaises(UpperCAmelCase__					):
       schur_complement(UpperCAmelCase__		,	UpperCAmelCase__		,	UpperCAmelCase__					)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 unittest.main()


'''simple docstring'''





import re

from flax.core.frozen_dict import freeze
from flax.traverse_util import flatten_dict, unflatten_dict
from jax.experimental import PartitionSpec as P


# Sentinels
UpperCamelCase_    						=       object()

# For specifying empty leaf dict `{}`
UpperCamelCase_    						=       object()






def 				_lowerCAmelCase			(   __magic_name__						:     int   , __magic_name__						:     int						)				->  Optional[int]:
						lowercase :							Optional[Any]    		=tuple((re.compile(x + '''$'''						) for x in qs)						)
						for i in range(len(__magic_name__						) - len(__magic_name__						) + 1						):
												lowercase :							Union[str, Any]    		=[x.match(__magic_name__						) for x, y in zip(__magic_name__   , ks[i:]						)]
												if matches and all(__magic_name__						):
																		return True
						return False






def 				_lowerCAmelCase			(   __magic_name__						:     Dict						)				->  List[str]:
						def replace(__magic_name__						:     Optional[int]   , __magic_name__						:     Optional[Any]						):
												for rule, replacement in rules:
																		if _match(__magic_name__   , __magic_name__						):
																								return replacement
												return val

						return replace






def 				_lowerCAmelCase			(   )				->  int:
						return [
						    # embeddings
						    (("transformer", "wpe", "embedding"), P('''mp'''   , __magic_name__						)),
						    (("transformer", "wte", "embedding"), P('''mp'''   , __magic_name__						)),
						    # atention
						    (("attention", "(q_proj|k_proj|v_proj)", "kernel"), P(__magic_name__   , '''mp'''						)),
						    (("attention", "out_proj", "kernel"), P('''mp'''   , __magic_name__						)),
						    (("attention", "out_proj", "bias"), None),
						    # mlp
						    (("mlp", "c_fc", "kernel"), P(__magic_name__   , '''mp'''						)),
						    (("mlp", "c_fc", "bias"), P('''mp'''						)),
						    (("mlp", "c_proj", "kernel"), P('''mp'''   , __magic_name__						)),
						    (("mlp", "c_proj", "bias"), None),
						    # layer norms
						    ((r"ln_\d+", "bias"), None),
						    ((r"\d+", r"ln_\d+", "scale"), None),
						    (("ln_f", "bias"), None),
						    (("ln_f", "scale"), None),
						]







def 				_lowerCAmelCase			(   __magic_name__						:     str						)				->  int:
						lowercase :							int    		=_get_partition_rules()
						lowercase :							Tuple    		=_replacement_rules(__magic_name__						)
						lowercase :							Any    		={k: _unmatched for k in flatten_dict(__magic_name__						)}
						lowercase :							Any    		={k: replace(__magic_name__   , __magic_name__						) for k, v in initd.items()}
						assert _unmatched not in result.values(), "Incomplete partition spec."
						return freeze(unflatten_dict(__magic_name__						)						)





