import numpy as np





def 	__lowerCamelCase							(UpperCAmelCase__     :							np.ndarray      , UpperCAmelCase__     :							np.ndarray      , UpperCAmelCase__     :							float = 1e-12      , UpperCAmelCase__     :							int = 1_0_0      , ):
					assert np.shape(UpperCAmelCase__  )[0] == np.shape(UpperCAmelCase__  )[1]
					# Ensure proper dimensionality.
					assert np.shape(UpperCAmelCase__  )[0] == np.shape(UpperCAmelCase__  )[0]
					# Ensure inputs are either both complex or both real
					assert np.iscomplexobj(UpperCAmelCase__  ) == np.iscomplexobj(UpperCAmelCase__  )
					SCREAMING_SNAKE_CASE    			=       np.iscomplexobj(UpperCAmelCase__  )
					if is_complex:
										# Ensure complex input_matrix is Hermitian
										assert np.array_equal(UpperCAmelCase__      , input_matrix.conj().T  )

					# Set convergence to False. Will define convergence when we exceed max_iterations
					# or when we have small changes from one iteration to next.

					SCREAMING_SNAKE_CASE    			=       False
					SCREAMING_SNAKE_CASE    			=       0
					SCREAMING_SNAKE_CASE    			=       0
					SCREAMING_SNAKE_CASE    			=       1e12

					while not convergence:
										# Multiple matrix by the vector.
										SCREAMING_SNAKE_CASE    			=       np.dot(UpperCAmelCase__      , UpperCAmelCase__  )
										# Normalize the resulting output vector.
										SCREAMING_SNAKE_CASE    			=       w / np.linalg.norm(UpperCAmelCase__  )
										# Find rayleigh quotient
										# (faster than usual b/c we know vector is normalized already)
										SCREAMING_SNAKE_CASE    			=       vector.conj().T if is_complex else vector.T
										SCREAMING_SNAKE_CASE    			=       np.dot(UpperCAmelCase__      , np.dot(UpperCAmelCase__      , UpperCAmelCase__  )  )

										# Check convergence.
										SCREAMING_SNAKE_CASE    			=       np.abs(lambda_ - lambda_previous  ) / lambda_
										iterations += 1

										if error <= error_tol or iterations >= max_iterations:
															SCREAMING_SNAKE_CASE    			=       True

										SCREAMING_SNAKE_CASE    			=       lambda_

					if is_complex:
										SCREAMING_SNAKE_CASE    			=       np.real(lambda_  )

					return lambda_, vector





def 	__lowerCamelCase							():
					SCREAMING_SNAKE_CASE    			=       np.array([[4_1, 4, 2_0], [4, 2_6, 3_0], [2_0, 3_0, 5_0]]  )
					SCREAMING_SNAKE_CASE    			=       np.array([4_1, 4, 2_0]  )
					SCREAMING_SNAKE_CASE    			=       real_input_matrix.astype(np.complexaaa  )
					SCREAMING_SNAKE_CASE    			=       np.triu(1j * complex_input_matrix      , 1  )
					complex_input_matrix += imag_matrix
					complex_input_matrix += -1 * imag_matrix.T
					SCREAMING_SNAKE_CASE    			=       np.array([4_1, 4, 2_0]  ).astype(np.complexaaa  )

					for problem_type in ["real", "complex"]:
										if problem_type == "real":
															SCREAMING_SNAKE_CASE    			=       real_input_matrix
															SCREAMING_SNAKE_CASE    			=       real_vector
										elif problem_type == "complex":
															SCREAMING_SNAKE_CASE    			=       complex_input_matrix
															SCREAMING_SNAKE_CASE    			=       complex_vector

										# Our implementation.
										SCREAMING_SNAKE_CASE			,   SCREAMING_SNAKE_CASE    			=       power_iteration(UpperCAmelCase__      , UpperCAmelCase__  )

										# Numpy implementation.

										# Get eigenvalues and eigenvectors using built-in numpy
										# eigh (eigh used for symmetric or hermetian matrices).
										SCREAMING_SNAKE_CASE			,   SCREAMING_SNAKE_CASE    			=       np.linalg.eigh(UpperCAmelCase__  )
										# Last eigenvalue is the maximum one.
										SCREAMING_SNAKE_CASE    			=       eigen_values[-1]
										# Last column in this matrix is eigenvector corresponding to largest eigenvalue.
										SCREAMING_SNAKE_CASE    			=       eigen_vectors[:, -1]

										# Check our implementation and numpy gives close answers.
										assert np.abs(eigen_value - eigen_value_max  ) <= 1e-6
										# Take absolute values element wise of each eigenvector.
										# as they are only unique to a minus sign.
										assert np.linalg.norm(np.abs(UpperCAmelCase__  ) - np.abs(UpperCAmelCase__  )  ) <= 1e-6


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							test_power_iteration()





from typing import TYPE_CHECKING

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


_lowerCamelCase					:   Optional[int]							=		{
    '''configuration_blenderbot''': [
        '''BLENDERBOT_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''BlenderbotConfig''',
        '''BlenderbotOnnxConfig''',
    ],
    '''tokenization_blenderbot''': ['''BlenderbotTokenizer'''],
}

try:
							if not is_tokenizers_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							_lowerCamelCase					:   List[Any]							=		['''BlenderbotTokenizerFast''']

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							_lowerCamelCase					:   Tuple							=		[
							    '''BLENDERBOT_PRETRAINED_MODEL_ARCHIVE_LIST''',
							    '''BlenderbotForCausalLM''',
							    '''BlenderbotForConditionalGeneration''',
							    '''BlenderbotModel''',
							    '''BlenderbotPreTrainedModel''',
							]


try:
							if not is_tf_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							_lowerCamelCase					:   List[str]							=		[
							    '''TFBlenderbotForConditionalGeneration''',
							    '''TFBlenderbotModel''',
							    '''TFBlenderbotPreTrainedModel''',
							]


try:
							if not is_flax_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							_lowerCamelCase					:   Optional[int]							=		[
							    '''FlaxBlenderbotForConditionalGeneration''',
							    '''FlaxBlenderbotModel''',
							    '''FlaxBlenderbotPreTrainedModel''',
							]


if TYPE_CHECKING:
							from .configuration_blenderbot import (
							    BLENDERBOT_PRETRAINED_CONFIG_ARCHIVE_MAP,
							    BlenderbotConfig,
							    BlenderbotOnnxConfig,
							)
							from .tokenization_blenderbot import BlenderbotTokenizer

							try:
														if not is_tokenizers_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .tokenization_blenderbot_fast import BlenderbotTokenizerFast

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_blenderbot import (
														    BLENDERBOT_PRETRAINED_MODEL_ARCHIVE_LIST,
														    BlenderbotForCausalLM,
														    BlenderbotForConditionalGeneration,
														    BlenderbotModel,
														    BlenderbotPreTrainedModel,
														)

							try:
														if not is_tf_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_tf_blenderbot import (
														    TFBlenderbotForConditionalGeneration,
														    TFBlenderbotModel,
														    TFBlenderbotPreTrainedModel,
														)

							try:
														if not is_flax_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_flax_blenderbot import (
														    FlaxBlenderbotForConditionalGeneration,
														    FlaxBlenderbotModel,
														    FlaxBlenderbotPreTrainedModel,
														)

else:
							import sys

							_lowerCamelCase					:   Dict							=		_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)




