



'''simple docstring'''




from typing import Any

import numpy as np






def 		_lowerCAmelCase				(_lowercase			):

       """simple docstring"""

       return np.array_equal(lowerCamelCase__   ,					matrix.conjugate().T			)






def 		_lowerCAmelCase				(_lowercase   ,					_lowercase			):

       """simple docstring"""

       a__								= v.conjugate().T
       a__								= v_star.dot(lowerCamelCase__			)
       assert isinstance(lowerCamelCase__   ,					np.ndarray			)
       return (v_star_dot.dot(lowerCamelCase__			)) / (v_star.dot(lowerCamelCase__			))






def 		_lowerCAmelCase				():

       """simple docstring"""

       a__								= np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]			)
       a__								= np.array([[1], [2], [3]]			)
       assert is_hermitian(lowerCamelCase__			), F'{a} is not hermitian.'
       print(rayleigh_quotient(lowerCamelCase__   ,					lowerCamelCase__			)			)

       a__								= 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_tokenizers_available, is_torch_available


UpperCAmelCase   :    Any     =		{
    "configuration_roc_bert": ["ROC_BERT_PRETRAINED_CONFIG_ARCHIVE_MAP", "RoCBertConfig"],
    "tokenization_roc_bert": ["RoCBertTokenizer"],
}

try:
		if not is_tokenizers_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		pass

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		UpperCAmelCase   :    Union[str, Any]     =		[
		    "ROC_BERT_PRETRAINED_MODEL_ARCHIVE_LIST",
		    "RoCBertForCausalLM",
		    "RoCBertForMaskedLM",
		    "RoCBertForMultipleChoice",
		    "RoCBertForPreTraining",
		    "RoCBertForQuestionAnswering",
		    "RoCBertForSequenceClassification",
		    "RoCBertForTokenClassification",
		    "RoCBertLayer",
		    "RoCBertModel",
		    "RoCBertPreTrainedModel",
		    "load_tf_weights_in_roc_bert",
		]

if TYPE_CHECKING:
		from .configuration_roc_bert import ROC_BERT_PRETRAINED_CONFIG_ARCHIVE_MAP, RoCBertConfig
		from .tokenization_roc_bert import RoCBertTokenizer

		try:
				if not is_tokenizers_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				raise OptionalDependencyNotAvailable()

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_roc_bert import (
				    ROC_BERT_PRETRAINED_MODEL_ARCHIVE_LIST,
				    RoCBertForCausalLM,
				    RoCBertForMaskedLM,
				    RoCBertForMultipleChoice,
				    RoCBertForPreTraining,
				    RoCBertForQuestionAnswering,
				    RoCBertForSequenceClassification,
				    RoCBertForTokenClassification,
				    RoCBertLayer,
				    RoCBertModel,
				    RoCBertPreTrainedModel,
				    load_tf_weights_in_roc_bert,
				)


else:
		import sys

		UpperCAmelCase   :    Tuple     =		_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)

