


"""simple docstring"""
from typing import TYPE_CHECKING

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


SCREAMING_SNAKE_CASE					:       str							   =							{
    """auto_factory""": ["""get_values"""],
    """configuration_auto""": ["""ALL_PRETRAINED_CONFIG_ARCHIVE_MAP""", """CONFIG_MAPPING""", """MODEL_NAMES_MAPPING""", """AutoConfig"""],
    """feature_extraction_auto""": ["""FEATURE_EXTRACTOR_MAPPING""", """AutoFeatureExtractor"""],
    """image_processing_auto""": ["""IMAGE_PROCESSOR_MAPPING""", """AutoImageProcessor"""],
    """processing_auto""": ["""PROCESSOR_MAPPING""", """AutoProcessor"""],
    """tokenization_auto""": ["""TOKENIZER_MAPPING""", """AutoTokenizer"""],
}

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			SCREAMING_SNAKE_CASE					:       Any							   =							[
			    """MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING""",
			    """MODEL_FOR_AUDIO_FRAME_CLASSIFICATION_MAPPING""",
			    """MODEL_FOR_AUDIO_XVECTOR_MAPPING""",
			    """MODEL_FOR_BACKBONE_MAPPING""",
			    """MODEL_FOR_CAUSAL_IMAGE_MODELING_MAPPING""",
			    """MODEL_FOR_CAUSAL_LM_MAPPING""",
			    """MODEL_FOR_CTC_MAPPING""",
			    """MODEL_FOR_DOCUMENT_QUESTION_ANSWERING_MAPPING""",
			    """MODEL_FOR_DEPTH_ESTIMATION_MAPPING""",
			    """MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING""",
			    """MODEL_FOR_IMAGE_SEGMENTATION_MAPPING""",
			    """MODEL_FOR_INSTANCE_SEGMENTATION_MAPPING""",
			    """MODEL_FOR_MASKED_IMAGE_MODELING_MAPPING""",
			    """MODEL_FOR_MASKED_LM_MAPPING""",
			    """MODEL_FOR_MASK_GENERATION_MAPPING""",
			    """MODEL_FOR_MULTIPLE_CHOICE_MAPPING""",
			    """MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING""",
			    """MODEL_FOR_OBJECT_DETECTION_MAPPING""",
			    """MODEL_FOR_PRETRAINING_MAPPING""",
			    """MODEL_FOR_QUESTION_ANSWERING_MAPPING""",
			    """MODEL_FOR_SEMANTIC_SEGMENTATION_MAPPING""",
			    """MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING""",
			    """MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING""",
			    """MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING""",
			    """MODEL_FOR_TABLE_QUESTION_ANSWERING_MAPPING""",
			    """MODEL_FOR_TEXT_ENCODING_MAPPING""",
			    """MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING""",
			    """MODEL_FOR_UNIVERSAL_SEGMENTATION_MAPPING""",
			    """MODEL_FOR_VIDEO_CLASSIFICATION_MAPPING""",
			    """MODEL_FOR_VISION_2_SEQ_MAPPING""",
			    """MODEL_FOR_VISUAL_QUESTION_ANSWERING_MAPPING""",
			    """MODEL_MAPPING""",
			    """MODEL_WITH_LM_HEAD_MAPPING""",
			    """MODEL_FOR_ZERO_SHOT_IMAGE_CLASSIFICATION_MAPPING""",
			    """MODEL_FOR_ZERO_SHOT_OBJECT_DETECTION_MAPPING""",
			    """AutoModel""",
			    """AutoBackbone""",
			    """AutoModelForAudioClassification""",
			    """AutoModelForAudioFrameClassification""",
			    """AutoModelForAudioXVector""",
			    """AutoModelForCausalLM""",
			    """AutoModelForCTC""",
			    """AutoModelForDepthEstimation""",
			    """AutoModelForImageClassification""",
			    """AutoModelForImageSegmentation""",
			    """AutoModelForInstanceSegmentation""",
			    """AutoModelForMaskGeneration""",
			    """AutoModelForTextEncoding""",
			    """AutoModelForMaskedImageModeling""",
			    """AutoModelForMaskedLM""",
			    """AutoModelForMultipleChoice""",
			    """AutoModelForNextSentencePrediction""",
			    """AutoModelForObjectDetection""",
			    """AutoModelForPreTraining""",
			    """AutoModelForQuestionAnswering""",
			    """AutoModelForSemanticSegmentation""",
			    """AutoModelForSeq2SeqLM""",
			    """AutoModelForSequenceClassification""",
			    """AutoModelForSpeechSeq2Seq""",
			    """AutoModelForTableQuestionAnswering""",
			    """AutoModelForTokenClassification""",
			    """AutoModelForUniversalSegmentation""",
			    """AutoModelForVideoClassification""",
			    """AutoModelForVision2Seq""",
			    """AutoModelForVisualQuestionAnswering""",
			    """AutoModelForDocumentQuestionAnswering""",
			    """AutoModelWithLMHead""",
			    """AutoModelForZeroShotImageClassification""",
			    """AutoModelForZeroShotObjectDetection""",
			]

try:
			if not is_tf_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			SCREAMING_SNAKE_CASE					:       List[str]							   =							[
			    """TF_MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING""",
			    """TF_MODEL_FOR_CAUSAL_LM_MAPPING""",
			    """TF_MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING""",
			    """TF_MODEL_FOR_MASK_GENERATION_MAPPING""",
			    """TF_MODEL_FOR_MASKED_IMAGE_MODELING_MAPPING""",
			    """TF_MODEL_FOR_MASKED_LM_MAPPING""",
			    """TF_MODEL_FOR_MULTIPLE_CHOICE_MAPPING""",
			    """TF_MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING""",
			    """TF_MODEL_FOR_PRETRAINING_MAPPING""",
			    """TF_MODEL_FOR_QUESTION_ANSWERING_MAPPING""",
			    """TF_MODEL_FOR_DOCUMENT_QUESTION_ANSWERING_MAPPING""",
			    """TF_MODEL_FOR_SEMANTIC_SEGMENTATION_MAPPING""",
			    """TF_MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING""",
			    """TF_MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING""",
			    """TF_MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING""",
			    """TF_MODEL_FOR_TABLE_QUESTION_ANSWERING_MAPPING""",
			    """TF_MODEL_FOR_TEXT_ENCODING_MAPPING""",
			    """TF_MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING""",
			    """TF_MODEL_FOR_VISION_2_SEQ_MAPPING""",
			    """TF_MODEL_FOR_ZERO_SHOT_IMAGE_CLASSIFICATION_MAPPING""",
			    """TF_MODEL_MAPPING""",
			    """TF_MODEL_WITH_LM_HEAD_MAPPING""",
			    """TFAutoModel""",
			    """TFAutoModelForAudioClassification""",
			    """TFAutoModelForCausalLM""",
			    """TFAutoModelForImageClassification""",
			    """TFAutoModelForMaskedImageModeling""",
			    """TFAutoModelForMaskedLM""",
			    """TFAutoModelForMaskGeneration""",
			    """TFAutoModelForMultipleChoice""",
			    """TFAutoModelForNextSentencePrediction""",
			    """TFAutoModelForPreTraining""",
			    """TFAutoModelForDocumentQuestionAnswering""",
			    """TFAutoModelForQuestionAnswering""",
			    """TFAutoModelForSemanticSegmentation""",
			    """TFAutoModelForSeq2SeqLM""",
			    """TFAutoModelForSequenceClassification""",
			    """TFAutoModelForSpeechSeq2Seq""",
			    """TFAutoModelForTableQuestionAnswering""",
			    """TFAutoModelForTextEncoding""",
			    """TFAutoModelForTokenClassification""",
			    """TFAutoModelForVision2Seq""",
			    """TFAutoModelForZeroShotImageClassification""",
			    """TFAutoModelWithLMHead""",
			]

try:
			if not is_flax_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			SCREAMING_SNAKE_CASE					:       str							   =							[
			    """FLAX_MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING""",
			    """FLAX_MODEL_FOR_CAUSAL_LM_MAPPING""",
			    """FLAX_MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING""",
			    """FLAX_MODEL_FOR_MASKED_LM_MAPPING""",
			    """FLAX_MODEL_FOR_MULTIPLE_CHOICE_MAPPING""",
			    """FLAX_MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING""",
			    """FLAX_MODEL_FOR_PRETRAINING_MAPPING""",
			    """FLAX_MODEL_FOR_QUESTION_ANSWERING_MAPPING""",
			    """FLAX_MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING""",
			    """FLAX_MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING""",
			    """FLAX_MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING""",
			    """FLAX_MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING""",
			    """FLAX_MODEL_FOR_VISION_2_SEQ_MAPPING""",
			    """FLAX_MODEL_MAPPING""",
			    """FlaxAutoModel""",
			    """FlaxAutoModelForCausalLM""",
			    """FlaxAutoModelForImageClassification""",
			    """FlaxAutoModelForMaskedLM""",
			    """FlaxAutoModelForMultipleChoice""",
			    """FlaxAutoModelForNextSentencePrediction""",
			    """FlaxAutoModelForPreTraining""",
			    """FlaxAutoModelForQuestionAnswering""",
			    """FlaxAutoModelForSeq2SeqLM""",
			    """FlaxAutoModelForSequenceClassification""",
			    """FlaxAutoModelForSpeechSeq2Seq""",
			    """FlaxAutoModelForTokenClassification""",
			    """FlaxAutoModelForVision2Seq""",
			]


if TYPE_CHECKING:
			from .auto_factory import get_values
			from .configuration_auto import ALL_PRETRAINED_CONFIG_ARCHIVE_MAP, CONFIG_MAPPING, MODEL_NAMES_MAPPING, AutoConfig
			from .feature_extraction_auto import FEATURE_EXTRACTOR_MAPPING, AutoFeatureExtractor
			from .image_processing_auto import IMAGE_PROCESSOR_MAPPING, AutoImageProcessor
			from .processing_auto import PROCESSOR_MAPPING, AutoProcessor
			from .tokenization_auto import TOKENIZER_MAPPING, AutoTokenizer

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_auto import (
						    MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING,
						    MODEL_FOR_AUDIO_FRAME_CLASSIFICATION_MAPPING,
						    MODEL_FOR_AUDIO_XVECTOR_MAPPING,
						    MODEL_FOR_BACKBONE_MAPPING,
						    MODEL_FOR_CAUSAL_IMAGE_MODELING_MAPPING,
						    MODEL_FOR_CAUSAL_LM_MAPPING,
						    MODEL_FOR_CTC_MAPPING,
						    MODEL_FOR_DEPTH_ESTIMATION_MAPPING,
						    MODEL_FOR_DOCUMENT_QUESTION_ANSWERING_MAPPING,
						    MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING,
						    MODEL_FOR_IMAGE_SEGMENTATION_MAPPING,
						    MODEL_FOR_INSTANCE_SEGMENTATION_MAPPING,
						    MODEL_FOR_MASK_GENERATION_MAPPING,
						    MODEL_FOR_MASKED_IMAGE_MODELING_MAPPING,
						    MODEL_FOR_MASKED_LM_MAPPING,
						    MODEL_FOR_MULTIPLE_CHOICE_MAPPING,
						    MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING,
						    MODEL_FOR_OBJECT_DETECTION_MAPPING,
						    MODEL_FOR_PRETRAINING_MAPPING,
						    MODEL_FOR_QUESTION_ANSWERING_MAPPING,
						    MODEL_FOR_SEMANTIC_SEGMENTATION_MAPPING,
						    MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING,
						    MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING,
						    MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING,
						    MODEL_FOR_TABLE_QUESTION_ANSWERING_MAPPING,
						    MODEL_FOR_TEXT_ENCODING_MAPPING,
						    MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING,
						    MODEL_FOR_UNIVERSAL_SEGMENTATION_MAPPING,
						    MODEL_FOR_VIDEO_CLASSIFICATION_MAPPING,
						    MODEL_FOR_VISION_2_SEQ_MAPPING,
						    MODEL_FOR_VISUAL_QUESTION_ANSWERING_MAPPING,
						    MODEL_FOR_ZERO_SHOT_IMAGE_CLASSIFICATION_MAPPING,
						    MODEL_FOR_ZERO_SHOT_OBJECT_DETECTION_MAPPING,
						    MODEL_MAPPING,
						    MODEL_WITH_LM_HEAD_MAPPING,
						    AutoBackbone,
						    AutoModel,
						    AutoModelForAudioClassification,
						    AutoModelForAudioFrameClassification,
						    AutoModelForAudioXVector,
						    AutoModelForCausalLM,
						    AutoModelForCTC,
						    AutoModelForDepthEstimation,
						    AutoModelForDocumentQuestionAnswering,
						    AutoModelForImageClassification,
						    AutoModelForImageSegmentation,
						    AutoModelForInstanceSegmentation,
						    AutoModelForMaskedImageModeling,
						    AutoModelForMaskedLM,
						    AutoModelForMaskGeneration,
						    AutoModelForMultipleChoice,
						    AutoModelForNextSentencePrediction,
						    AutoModelForObjectDetection,
						    AutoModelForPreTraining,
						    AutoModelForQuestionAnswering,
						    AutoModelForSemanticSegmentation,
						    AutoModelForSeqaSeqLM,
						    AutoModelForSequenceClassification,
						    AutoModelForSpeechSeqaSeq,
						    AutoModelForTableQuestionAnswering,
						    AutoModelForTextEncoding,
						    AutoModelForTokenClassification,
						    AutoModelForUniversalSegmentation,
						    AutoModelForVideoClassification,
						    AutoModelForVisionaSeq,
						    AutoModelForVisualQuestionAnswering,
						    AutoModelForZeroShotImageClassification,
						    AutoModelForZeroShotObjectDetection,
						    AutoModelWithLMHead,
						)

			try:
						if not is_tf_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_tf_auto import (
						    TF_MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING,
						    TF_MODEL_FOR_CAUSAL_LM_MAPPING,
						    TF_MODEL_FOR_DOCUMENT_QUESTION_ANSWERING_MAPPING,
						    TF_MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING,
						    TF_MODEL_FOR_MASK_GENERATION_MAPPING,
						    TF_MODEL_FOR_MASKED_IMAGE_MODELING_MAPPING,
						    TF_MODEL_FOR_MASKED_LM_MAPPING,
						    TF_MODEL_FOR_MULTIPLE_CHOICE_MAPPING,
						    TF_MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING,
						    TF_MODEL_FOR_PRETRAINING_MAPPING,
						    TF_MODEL_FOR_QUESTION_ANSWERING_MAPPING,
						    TF_MODEL_FOR_SEMANTIC_SEGMENTATION_MAPPING,
						    TF_MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING,
						    TF_MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING,
						    TF_MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING,
						    TF_MODEL_FOR_TABLE_QUESTION_ANSWERING_MAPPING,
						    TF_MODEL_FOR_TEXT_ENCODING_MAPPING,
						    TF_MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING,
						    TF_MODEL_FOR_VISION_2_SEQ_MAPPING,
						    TF_MODEL_FOR_ZERO_SHOT_IMAGE_CLASSIFICATION_MAPPING,
						    TF_MODEL_MAPPING,
						    TF_MODEL_WITH_LM_HEAD_MAPPING,
						    TFAutoModel,
						    TFAutoModelForAudioClassification,
						    TFAutoModelForCausalLM,
						    TFAutoModelForDocumentQuestionAnswering,
						    TFAutoModelForImageClassification,
						    TFAutoModelForMaskedImageModeling,
						    TFAutoModelForMaskedLM,
						    TFAutoModelForMaskGeneration,
						    TFAutoModelForMultipleChoice,
						    TFAutoModelForNextSentencePrediction,
						    TFAutoModelForPreTraining,
						    TFAutoModelForQuestionAnswering,
						    TFAutoModelForSemanticSegmentation,
						    TFAutoModelForSeqaSeqLM,
						    TFAutoModelForSequenceClassification,
						    TFAutoModelForSpeechSeqaSeq,
						    TFAutoModelForTableQuestionAnswering,
						    TFAutoModelForTextEncoding,
						    TFAutoModelForTokenClassification,
						    TFAutoModelForVisionaSeq,
						    TFAutoModelForZeroShotImageClassification,
						    TFAutoModelWithLMHead,
						)

			try:
						if not is_flax_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_flax_auto import (
						    FLAX_MODEL_FOR_AUDIO_CLASSIFICATION_MAPPING,
						    FLAX_MODEL_FOR_CAUSAL_LM_MAPPING,
						    FLAX_MODEL_FOR_IMAGE_CLASSIFICATION_MAPPING,
						    FLAX_MODEL_FOR_MASKED_LM_MAPPING,
						    FLAX_MODEL_FOR_MULTIPLE_CHOICE_MAPPING,
						    FLAX_MODEL_FOR_NEXT_SENTENCE_PREDICTION_MAPPING,
						    FLAX_MODEL_FOR_PRETRAINING_MAPPING,
						    FLAX_MODEL_FOR_QUESTION_ANSWERING_MAPPING,
						    FLAX_MODEL_FOR_SEQ_TO_SEQ_CAUSAL_LM_MAPPING,
						    FLAX_MODEL_FOR_SEQUENCE_CLASSIFICATION_MAPPING,
						    FLAX_MODEL_FOR_SPEECH_SEQ_2_SEQ_MAPPING,
						    FLAX_MODEL_FOR_TOKEN_CLASSIFICATION_MAPPING,
						    FLAX_MODEL_FOR_VISION_2_SEQ_MAPPING,
						    FLAX_MODEL_MAPPING,
						    FlaxAutoModel,
						    FlaxAutoModelForCausalLM,
						    FlaxAutoModelForImageClassification,
						    FlaxAutoModelForMaskedLM,
						    FlaxAutoModelForMultipleChoice,
						    FlaxAutoModelForNextSentencePrediction,
						    FlaxAutoModelForPreTraining,
						    FlaxAutoModelForQuestionAnswering,
						    FlaxAutoModelForSeqaSeqLM,
						    FlaxAutoModelForSequenceClassification,
						    FlaxAutoModelForSpeechSeqaSeq,
						    FlaxAutoModelForTokenClassification,
						    FlaxAutoModelForVisionaSeq,
						)

else:
			import sys

			SCREAMING_SNAKE_CASE					:       Dict							   =							_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)









from typing import Any

import numpy as np






def  _UpperCAmelCase						( __lowerCamelCase							)		->bool:


 '''simple docstring'''
 assert np.shape(__lowerCamelCase							)[0] == np.shape(__lowerCamelCase							)[1]

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

 # Get eigenvalues and eignevectors for a symmetric matrix.
 snake_case	,       snake_case :			int							=   np.linalg.eigh(__lowerCamelCase							)

 # Check sign of all eigenvalues.
 # np.all returns a value of type np.bool_
 return bool(np.all(eigen_values > 0							)							)






def  _UpperCAmelCase						( __lowerCamelCase							)		->Any:


 '''simple docstring'''
 snake_case :			Dict							=   np.random.randn(__lowerCamelCase			,  __lowerCamelCase							)
 snake_case :			List[Any]							=   np.dot(__lowerCamelCase			,  random_matrix.T							)
 assert _is_matrix_spd(__lowerCamelCase							)
 return spd_matrix






def  _UpperCAmelCase						( __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase = 1000			,  __lowerCamelCase = 1E-8			,  )		->Any:


 '''simple docstring'''
 assert np.shape(__lowerCamelCase							)[0] == np.shape(__lowerCamelCase							)[1]
 assert np.shape(__lowerCamelCase							)[0] == np.shape(__lowerCamelCase							)[0]
 assert _is_matrix_spd(__lowerCamelCase							)

 # Initialize solution guess, residual, search direction.
 snake_case :			Any							=   np.zeros((np.shape(__lowerCamelCase							)[0], 1)							)
 snake_case :			Optional[int]							=   np.copy(__lowerCamelCase							)
 snake_case :			Optional[Any]							=   np.copy(__lowerCamelCase							)

 # Set initial errors in solution guess and residual.
 snake_case :			Optional[Any]							=   1E9
 snake_case :			List[Any]							=   1E9
 snake_case :			List[str]							=   1E9

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

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

  # The main algorithm.

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

  # Calculate errors.
  snake_case :			List[Any]							=   np.linalg.norm(r - ra							)
  snake_case :			Any							=   np.linalg.norm(x - xa							)
  snake_case :			str							=   np.maximum(__lowerCamelCase			,  __lowerCamelCase							)

  # Update variables.
  snake_case :			Tuple							=   np.copy(__lowerCamelCase							)
  snake_case :			Tuple							=   np.copy(__lowerCamelCase							)
  snake_case :			List[str]							=   np.copy(__lowerCamelCase							)

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

 return x






def  _UpperCAmelCase						( )		->None:


 '''simple docstring'''
 snake_case :			str							=   3
 snake_case :			Dict							=   _create_spd_matrix(__lowerCamelCase							)
 snake_case :			str							=   np.random.randn(__lowerCamelCase			,  1							)
 snake_case :			str							=   np.dot(__lowerCamelCase			,  __lowerCamelCase							)

 # Numpy solution.
 snake_case :			Any							=   np.linalg.solve(__lowerCamelCase			,  __lowerCamelCase							)

 # Our implementation.
 snake_case :			List[str]							=   conjugate_gradient(__lowerCamelCase			,  __lowerCamelCase							)

 # 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()






