from typing import Any

import numpy as np




def 				_snake_case     (       lowerCAmelCase							:       np.ndarray     ):
		"""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.
		SCREAMING_SNAKE_CASE_				,   SCREAMING_SNAKE_CASE_  :		Any    				=   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 				_snake_case     (       lowerCAmelCase							:       int     ):
		"""simple docstring"""







		SCREAMING_SNAKE_CASE_  :		Tuple    				=   np.random.randn(lowerCAmelCase       ,			lowerCAmelCase     )
		SCREAMING_SNAKE_CASE_  :		Tuple    				=   np.dot(lowerCAmelCase       ,			random_matrix.T     )
		assert _is_matrix_spd(lowerCAmelCase     )
		return spd_matrix




def 				_snake_case     (       lowerCAmelCase							:       np.ndarray       ,			lowerCAmelCase							:       np.ndarray       ,			lowerCAmelCase							:       int = 1_0_0_0       ,			lowerCAmelCase							:       float = 1E-8       ,			):
		"""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.
		SCREAMING_SNAKE_CASE_  :		Any    				=   np.zeros((np.shape(lowerCAmelCase     )[0], 1)     )
		SCREAMING_SNAKE_CASE_  :		Tuple    				=   np.copy(lowerCAmelCase     )
		SCREAMING_SNAKE_CASE_  :		int    				=   np.copy(lowerCAmelCase     )

		# Set initial errors in solution guess and residual.
		SCREAMING_SNAKE_CASE_  :		Optional[int]    				=   1E9
		SCREAMING_SNAKE_CASE_  :		Dict    				=   1E9
		SCREAMING_SNAKE_CASE_  :		List[str]    				=   1E9

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

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

				# The main algorithm.

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

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

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

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

		return x




def 				_snake_case     (       ):
		"""simple docstring"""







		SCREAMING_SNAKE_CASE_  :		str    				=   3
		SCREAMING_SNAKE_CASE_  :		str    				=   _create_spd_matrix(lowerCAmelCase     )
		SCREAMING_SNAKE_CASE_  :		List[Any]    				=   np.random.randn(lowerCAmelCase       ,			1     )
		SCREAMING_SNAKE_CASE_  :		str    				=   np.dot(lowerCAmelCase       ,			lowerCAmelCase     )

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

		# Our implementation.
		SCREAMING_SNAKE_CASE_  :		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()

import warnings

from ...utils import logging
from .image_processing_vit import ViTImageProcessor


__lowerCamelCase :     Tuple          =  logging.get_logger(__name__)






class 		a__						( A__ ):

					def __init__(   self				:	List[Any],*_A				:	Union[str, Any],**_A				:	List[Any]   ):







							"""simple docstring"""






							warnings.warn(
							    "The class ViTFeatureExtractor is deprecated and will be removed in version 5 of Transformers. Please"
							    " use ViTImageProcessor instead.",_A,)
							super().__init__(*_A,**_A   )
