

'''simple docstring'''

import unittest

import numpy as np





def       A_     (       snake_case					,				snake_case					,				snake_case					,				snake_case = None					,				):
  SCREAMING_SNAKE_CASE:List[str]  					=    np.shape(__snake_case       )
  SCREAMING_SNAKE_CASE:List[Any]  					=    np.shape(__snake_case       )
  SCREAMING_SNAKE_CASE:Optional[Any]  					=    np.shape(__snake_case       )

  if shape_a[0] != shape_b[0]:
    SCREAMING_SNAKE_CASE:Optional[int]  					=    (
        "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(__snake_case       )

  if shape_b[1] != shape_c[1]:
    SCREAMING_SNAKE_CASE:Union[str, Any]  					=    (
        "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(__snake_case       )

  SCREAMING_SNAKE_CASE:Union[str, Any]  					=    pseudo_inv
  if a_inv is None:
    try:
      SCREAMING_SNAKE_CASE:str  					=    np.linalg.inv(__snake_case       )
    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 							_snake_case       (				unittest.TestCase  ):
   def 			__UpperCamelCase  (       self	:					Optional[Any]							):
     SCREAMING_SNAKE_CASE:Optional[int]  					=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
     SCREAMING_SNAKE_CASE:Union[str, Any]  					=    np.array([[0, 3], [3, 0], [2, 3]]							)
     SCREAMING_SNAKE_CASE:str  					=    np.array([[2, 1], [6, 3]]							)

     SCREAMING_SNAKE_CASE:int  					=    schur_complement(_a   ,_a   ,_a							)

     SCREAMING_SNAKE_CASE:Union[str, Any]  					=    np.block([[a, b], [b.T, c]]							)

     SCREAMING_SNAKE_CASE:Optional[int]  					=    np.linalg.det(_a							)
     SCREAMING_SNAKE_CASE:Any  					=    np.linalg.det(_a							)
     SCREAMING_SNAKE_CASE:List[str]  					=    np.linalg.det(_a							)

     self.assertAlmostEqual(_a   ,det_a * det_s							)
   def 			__UpperCamelCase  (       self	:					str							):
     SCREAMING_SNAKE_CASE:List[str]  					=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
     SCREAMING_SNAKE_CASE:List[Any]  					=    np.array([[0, 3], [3, 0], [2, 3]]							)
     SCREAMING_SNAKE_CASE:Union[str, Any]  					=    np.array([[2, 1], [6, 3]]							)

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







   def 			__UpperCamelCase  (       self	:					str							):
     SCREAMING_SNAKE_CASE:Union[str, Any]  					=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
     SCREAMING_SNAKE_CASE:int  					=    np.array([[0, 3], [3, 0], [2, 3]]							)
     SCREAMING_SNAKE_CASE:Tuple  					=    np.array([[2, 1, 3], [6, 3, 5]]							)

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


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    unittest.main()








"""simple docstring"""




from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
)


_A			:       Optional[int]   		=       {
    """configuration_llama""": ["""LLAMA_PRETRAINED_CONFIG_ARCHIVE_MAP""", """LlamaConfig"""],
}

try:
   if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   _A			:       Union[str, Any]   		=       ["""LlamaTokenizer"""]

try:
   if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   _A			:       Dict   		=       ["""LlamaTokenizerFast"""]

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   _A			:       int   		=       [
       """LlamaForCausalLM""",
       """LlamaModel""",
       """LlamaPreTrainedModel""",
       """LlamaForSequenceClassification""",
   ]


if TYPE_CHECKING:
   from .configuration_llama import LLAMA_PRETRAINED_CONFIG_ARCHIVE_MAP, LlamaConfig

   try:
      if not is_sentencepiece_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_llama import LlamaTokenizer

   try:
      if not is_tokenizers_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_llama_fast import LlamaTokenizerFast

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_llama import LlamaForCausalLM, LlamaForSequenceClassification, LlamaModel, LlamaPreTrainedModel


else:
   import sys

   _A			:       str   		=       _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)


