from typing import Any

import numpy as np


def SCREAMING_SNAKE_CASE					(  lowercase_:						np.ndarray					):
       assert np.shape(lowercase_					)[0] == np.shape(lowercase_					)[1]

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

       # Get eigenvalues and eignevectors for a symmetric matrix.
       _UpperCamelCase    ,   _UpperCamelCase  :							List[str]	    =	np.linalg.eigh(lowercase_					)

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


def SCREAMING_SNAKE_CASE					(  lowercase_:						int					):
       _UpperCamelCase  :							Dict	    =	np.random.randn(lowercase_		,    lowercase_					)
       _UpperCamelCase  :							Any	    =	np.dot(lowercase_		,    random_matrix.T					)
       assert _is_matrix_spd(lowercase_					)
       return spd_matrix


def SCREAMING_SNAKE_CASE					(  lowercase_:						np.ndarray		,    lowercase_:						np.ndarray		,    lowercase_:						int = 1000		,    lowercase_:						float = 1e-8		,    ):
       assert np.shape(lowercase_					)[0] == np.shape(lowercase_					)[1]
       assert np.shape(lowercase_					)[0] == np.shape(lowercase_					)[0]
       assert _is_matrix_spd(lowercase_					)

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

       # Set initial errors in solution guess and residual.
       _UpperCamelCase  :							Tuple	    =	1e9
       _UpperCamelCase  :							Optional[int]	    =	1e9
       _UpperCamelCase  :							List[str]	    =	1e9

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

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

              # The main algorithm.

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

              # Calculate errors.
              _UpperCamelCase  :							int	    =	np.linalg.norm(r - ra					)
              _UpperCamelCase  :							Union[str, Any]	    =	np.linalg.norm(x - xa					)
              _UpperCamelCase  :							Dict	    =	np.maximum(lowercase_		,    lowercase_					)

              # Update variables.
              _UpperCamelCase  :							Union[str, Any]	    =	np.copy(lowercase_					)
              _UpperCamelCase  :							Any	    =	np.copy(lowercase_					)
              _UpperCamelCase  :							Optional[Any]	    =	np.copy(lowercase_					)

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

       return x


def SCREAMING_SNAKE_CASE					(  ):
       _UpperCamelCase  :							Optional[Any]	    =	3
       _UpperCamelCase  :							List[str]	    =	_create_spd_matrix(lowercase_					)
       _UpperCamelCase  :							Tuple	    =	np.random.randn(lowercase_		,    1					)
       _UpperCamelCase  :							List[Any]	    =	np.dot(lowercase_		,    lowercase_					)

       # Numpy solution.
       _UpperCamelCase  :							int	    =	np.linalg.solve(lowercase_		,    lowercase_					)

       # Our implementation.
       _UpperCamelCase  :							List[Any]	    =	conjugate_gradient(lowercase_		,    lowercase_					)

       # 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 contextlib import contextmanager

from ...processing_utils import ProcessorMixin







class 							lowercase						(   SCREAMING_SNAKE_CASE__						):
							lowercase_			:			Dict			   =['''image_processor''', '''tokenizer''']
							lowercase_			:			List[str]			   ='''AutoImageProcessor'''
							lowercase_			:			Optional[Any]			   ='''AutoTokenizer'''




							def __init__(							self  ,A__=None  ,A__=None  ,**A__):
												lowercase		      =		None
												if "feature_extractor" in kwargs:
																	warnings.warn(
																	    '''The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`'''
																	    ''' instead.'''  ,A__  ,)
																	lowercase		      =		kwargs.pop('''feature_extractor''')

												lowercase		      =		image_processor if image_processor is not None else feature_extractor
												if image_processor is None:
																	raise ValueError('''You need to specify an `image_processor`.''')
												if tokenizer is None:
																	raise ValueError('''You need to specify a `tokenizer`.''')

												super().__init__(A__  ,A__)
												lowercase		      =		self.image_processor
												lowercase		      =		False




							def __call__(							self  ,*A__  ,**A__):
												# For backward compatibility
												if self._in_target_context_manager:
																	return self.current_processor(*A__  ,**A__)

												lowercase		      =		kwargs.pop('''images'''  ,A__)
												lowercase		      =		kwargs.pop('''text'''  ,A__)
												if len(A__) > 0:
																	lowercase		      =		args[0]
																	lowercase		      =		args[1:]

												if images is None and text is None:
																	raise ValueError('''You need to specify either an `images` or `text` input to process.''')

												if images is not None:
																	lowercase		      =		self.image_processor(A__  ,*A__  ,**A__)
												if text is not None:
																	lowercase		      =		self.tokenizer(A__  ,**A__)

												if text is None:
																	return inputs
												elif images is None:
																	return encodings
												else:
																	lowercase		      =		encodings['''input_ids''']
																	return inputs




							def 					A__ (							self  ,*A__  ,**A__):
												return self.tokenizer.batch_decode(*A__  ,**A__)




							def 					A__ (							self  ,*A__  ,**A__):
												return self.tokenizer.decode(*A__  ,**A__)




							@contextmanager
							def 					A__ (							self):
												warnings.warn(
												    '''`as_target_processor` is deprecated and will be removed in v5 of Transformers. You can process your '''
												    '''labels by using the argument `text` of the regular `__call__` method (either in the same call as '''
												    '''your images inputs, or in a separate call.''')
												lowercase		      =		True
												lowercase		      =		self.tokenizer
												yield
												lowercase		      =		self.image_processor
												lowercase		      =		False




							@property
							def 					A__ (							self):
												warnings.warn(
												    '''`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead.'''  ,A__  ,)
												return self.image_processor_class





							@property
							def 					A__ (							self):
												warnings.warn(
												    '''`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead.'''  ,A__  ,)
												return self.image_processor




