
from typing import TYPE_CHECKING

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


lowerCamelCase__        =						{
    """configuration_bart""": ["""BART_PRETRAINED_CONFIG_ARCHIVE_MAP""", """BartConfig""", """BartOnnxConfig"""],
    """tokenization_bart""": ["""BartTokenizer"""],
}

try:
					if not is_tokenizers_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					lowerCamelCase__        =						["""BartTokenizerFast"""]

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					lowerCamelCase__        =						[
					    """BART_PRETRAINED_MODEL_ARCHIVE_LIST""",
					    """BartForCausalLM""",
					    """BartForConditionalGeneration""",
					    """BartForQuestionAnswering""",
					    """BartForSequenceClassification""",
					    """BartModel""",
					    """BartPretrainedModel""",
					    """PretrainedBartModel""",
					]

try:
					if not is_tf_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					lowerCamelCase__        =						[
					    """TFBartForConditionalGeneration""",
					    """TFBartForSequenceClassification""",
					    """TFBartModel""",
					    """TFBartPretrainedModel""",
					]

try:
					if not is_flax_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					lowerCamelCase__        =						[
					    """FlaxBartDecoderPreTrainedModel""",
					    """FlaxBartForCausalLM""",
					    """FlaxBartForConditionalGeneration""",
					    """FlaxBartForQuestionAnswering""",
					    """FlaxBartForSequenceClassification""",
					    """FlaxBartModel""",
					    """FlaxBartPreTrainedModel""",
					]

if TYPE_CHECKING:
					from .configuration_bart import BART_PRETRAINED_CONFIG_ARCHIVE_MAP, BartConfig, BartOnnxConfig
					from .tokenization_bart import BartTokenizer

					try:
										if not is_tokenizers_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .tokenization_bart_fast import BartTokenizerFast

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_bart import (
										    BART_PRETRAINED_MODEL_ARCHIVE_LIST,
										    BartForCausalLM,
										    BartForConditionalGeneration,
										    BartForQuestionAnswering,
										    BartForSequenceClassification,
										    BartModel,
										    BartPretrainedModel,
										    PretrainedBartModel,
										)

					try:
										if not is_tf_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_tf_bart import (
										    TFBartForConditionalGeneration,
										    TFBartForSequenceClassification,
										    TFBartModel,
										    TFBartPretrainedModel,
										)

					try:
										if not is_flax_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_flax_bart import (
										    FlaxBartDecoderPreTrainedModel,
										    FlaxBartForCausalLM,
										    FlaxBartForConditionalGeneration,
										    FlaxBartForQuestionAnswering,
										    FlaxBartForSequenceClassification,
										    FlaxBartModel,
										    FlaxBartPreTrainedModel,
										)

else:
					import sys

					lowerCamelCase__        =						_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)

from typing import Any

import numpy as np
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_	)							->						bool:
			assert np.shape(SCREAMING_SNAKE_CASE_	)[0] == np.shape(SCREAMING_SNAKE_CASE_	)[1]

			# If matrix not symmetric, exit right away.
			if np.allclose(SCREAMING_SNAKE_CASE_			,				matrix.T	) is False:
						return False

			# Get eigenvalues and eignevectors for a symmetric matrix.
			lowerCAmelCase__ ,							lowerCAmelCase__ : Optional[int]   =						np.linalg.eigh(SCREAMING_SNAKE_CASE_	)

			# Check sign of all eigenvalues.
			# np.all returns a value of type np.bool_
			return bool(np.all(eigen_values > 0	)	)
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_	)							->						Any:
			lowerCAmelCase__ : List[Any]   =						np.random.randn(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)
			lowerCAmelCase__ : Any   =						np.dot(SCREAMING_SNAKE_CASE_			,				random_matrix.T	)
			assert _is_matrix_spd(SCREAMING_SNAKE_CASE_	)
			return spd_matrix
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_ = 1_000			,				SCREAMING_SNAKE_CASE_ = 1e-8			,				)							->						Any:
			assert np.shape(SCREAMING_SNAKE_CASE_	)[0] == np.shape(SCREAMING_SNAKE_CASE_	)[1]
			assert np.shape(SCREAMING_SNAKE_CASE_	)[0] == np.shape(SCREAMING_SNAKE_CASE_	)[0]
			assert _is_matrix_spd(SCREAMING_SNAKE_CASE_	)

			# Initialize solution guess, residual, search direction.
			lowerCAmelCase__ : Optional[Any]   =						np.zeros((np.shape(SCREAMING_SNAKE_CASE_	)[0], 1)	)
			lowerCAmelCase__ : str   =						np.copy(SCREAMING_SNAKE_CASE_	)
			lowerCAmelCase__ : Dict   =						np.copy(SCREAMING_SNAKE_CASE_	)

			# Set initial errors in solution guess and residual.
			lowerCAmelCase__ : Union[str, Any]   =						1e9
			lowerCAmelCase__ : int   =						1e9
			lowerCAmelCase__ : Union[str, Any]   =						1e9

			# Set iteration counter to threshold number of iterations.
			lowerCAmelCase__ : List[str]   =						0

			while error > tol:
						# Save this value so we only calculate the matrix-vector product once.
						lowerCAmelCase__ : int   =						np.dot(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)

						# The main algorithm.

						# Update search direction magnitude.
						lowerCAmelCase__ : List[str]   =						np.dot(ra.T			,				SCREAMING_SNAKE_CASE_	) / np.dot(pa.T			,				SCREAMING_SNAKE_CASE_	)
						# Update solution guess.
						lowerCAmelCase__ : Dict   =						xa + alpha * pa
						# Calculate new residual.
						lowerCAmelCase__ : Tuple   =						ra - alpha * w
						# Calculate new Krylov subspace scale.
						lowerCAmelCase__ : str   =						np.dot(r.T			,				SCREAMING_SNAKE_CASE_	) / np.dot(ra.T			,				SCREAMING_SNAKE_CASE_	)
						# Calculate new A conjuage search direction.
						lowerCAmelCase__ : Dict   =						r + beta * pa

						# Calculate errors.
						lowerCAmelCase__ : List[str]   =						np.linalg.norm(r - ra	)
						lowerCAmelCase__ : Tuple   =						np.linalg.norm(x - xa	)
						lowerCAmelCase__ : str   =						np.maximum(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)

						# Update variables.
						lowerCAmelCase__ : List[Any]   =						np.copy(SCREAMING_SNAKE_CASE_	)
						lowerCAmelCase__ : Dict   =						np.copy(SCREAMING_SNAKE_CASE_	)
						lowerCAmelCase__ : str   =						np.copy(SCREAMING_SNAKE_CASE_	)

						# Update number of iterations.
						iterations += 1
						if iterations > max_iterations:
									break

			return x
def 					lowerCAmelCase__     (    )							->						None:
			lowerCAmelCase__ : Optional[Any]   =						3
			lowerCAmelCase__ : Optional[int]   =						_create_spd_matrix(SCREAMING_SNAKE_CASE_	)
			lowerCAmelCase__ : Tuple   =						np.random.randn(SCREAMING_SNAKE_CASE_			,				1	)
			lowerCAmelCase__ : int   =						np.dot(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)

			# Numpy solution.
			lowerCAmelCase__ : Optional[Any]   =						np.linalg.solve(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)

			# Our implementation.
			lowerCAmelCase__ : Optional[int]   =						conjugate_gradient(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)

			# Ensure both solutions are close to x_true (and therefore one another).
			assert np.linalg.norm(x_numpy - x_true	) <= 1e-6
			assert np.linalg.norm(x_conjugate_gradient - x_true	) <= 1e-6


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					test_conjugate_gradient()