
from typing import Any

import numpy as np


def 			UpperCamelCase					(    __lowerCamelCase     : np.ndarray    ):
       return np.array_equal(__lowerCamelCase				,					matrix.conjugate().T    )


def 			UpperCamelCase					(    __lowerCamelCase     : np.ndarray				,					__lowerCamelCase     : np.ndarray    ):
       snake_case       :   Tuple							=      v.conjugate().T
       snake_case       :   Tuple							=      v_star.dot(__lowerCamelCase    )
       assert isinstance(__lowerCamelCase				,					np.ndarray    )
       return (v_star_dot.dot(__lowerCamelCase    )) / (v_star.dot(__lowerCamelCase    ))


def 			UpperCamelCase					(    ):
       snake_case       :   int							=      np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]    )
       snake_case       :   int							=      np.array([[1], [2], [3]]    )
       assert is_hermitian(__lowerCamelCase    ), f"""{a} is not hermitian."""
       print(rayleigh_quotient(__lowerCamelCase				,					__lowerCamelCase    )    )

       snake_case       :   Dict							=      np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]    )
       assert is_hermitian(__lowerCamelCase    ), f"""{a} is not hermitian."""
       assert rayleigh_quotient(__lowerCamelCase				,					__lowerCamelCase    ) == float(3    )


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   tests()







from typing import TYPE_CHECKING

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


if is_sentencepiece_available():
   from ..ta.tokenization_ta import TaTokenizer
else:
   from ...utils.dummy_sentencepiece_objects import TaTokenizer

__lowerCamelCase							=       TaTokenizer

if is_tokenizers_available():
   from ..ta.tokenization_ta_fast import TaTokenizerFast
else:
   from ...utils.dummy_tokenizers_objects import TaTokenizerFast

__lowerCamelCase							=       TaTokenizerFast

__lowerCamelCase							=       {"""configuration_mt5""": ["""MT5Config""", """MT5OnnxConfig"""]}

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   __lowerCamelCase							=       [
       """MT5EncoderModel""",
       """MT5ForConditionalGeneration""",
       """MT5ForQuestionAnswering""",
       """MT5Model""",
       """MT5PreTrainedModel""",
       """MT5Stack""",
   ]

try:
   if not is_tf_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   __lowerCamelCase							=       ["""TFMT5EncoderModel""", """TFMT5ForConditionalGeneration""", """TFMT5Model"""]

try:
   if not is_flax_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   __lowerCamelCase							=       ["""FlaxMT5EncoderModel""", """FlaxMT5ForConditionalGeneration""", """FlaxMT5Model"""]


if TYPE_CHECKING:
   from .configuration_mta import MTaConfig, MTaOnnxConfig

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_mta import (
          MTaEncoderModel,
          MTaForConditionalGeneration,
          MTaForQuestionAnswering,
          MTaModel,
          MTaPreTrainedModel,
          MTaStack,
      )

   try:
      if not is_tf_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_tf_mta import TFMTaEncoderModel, TFMTaForConditionalGeneration, TFMTaModel

   try:
      if not is_flax_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_flax_mta import FlaxMTaEncoderModel, FlaxMTaForConditionalGeneration, FlaxMTaModel

else:
   import sys

   __lowerCamelCase							=       _LazyModule(
       __name__,
       globals()["""__file__"""],
       _import_structure,
       extra_objects={"""MT5Tokenizer""": MTaTokenizer, """MT5TokenizerFast""": MTaTokenizerFast},
       module_spec=__spec__,
   )





