




'''simple docstring'''



from typing import Any

import numpy as np







def 			_UpperCamelCase (_lowerCamelCase							:     np.ndarray	)->   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    					=  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							:     int	)->   Any:




     '''simple docstring'''





     __snake_case    					=  np.random.randn(_lowerCamelCase   ,	_lowerCamelCase	)
     __snake_case    					=  np.dot(_lowerCamelCase   ,	random_matrix.T	)
     assert _is_matrix_spd(_lowerCamelCase	)
     return spd_matrix







def 			_UpperCamelCase (_lowerCamelCase							:     np.ndarray   ,	_lowerCamelCase							:     np.ndarray   ,	_lowerCamelCase							:     int = 10_00   ,	_lowerCamelCase							:     float = 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    					=  np.zeros((np.shape(_lowerCamelCase	)[0], 1)	)
     __snake_case    					=  np.copy(_lowerCamelCase	)
     __snake_case    					=  np.copy(_lowerCamelCase	)

     # Set initial errors in solution guess and residual.
     __snake_case    					=  1E9
     __snake_case    					=  1E9
     __snake_case    					=  1E9

     # Set iteration counter to threshold number of iterations.
     __snake_case    					=  0

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

          # The main algorithm.

          # Update search direction magnitude.
          __snake_case    					=  np.dot(ra.T   ,	_lowerCamelCase	) / np.dot(pa.T   ,	_lowerCamelCase	)
          # Update solution guess.
          __snake_case    					=  xa + alpha * pa
          # Calculate new residual.
          __snake_case    					=  ra - alpha * w
          # Calculate new Krylov subspace scale.
          __snake_case    					=  np.dot(r.T   ,	_lowerCamelCase	) / np.dot(ra.T   ,	_lowerCamelCase	)
          # Calculate new A conjuage search direction.
          __snake_case    					=  r + beta * pa

          # Calculate errors.
          __snake_case    					=  np.linalg.norm(r - ra	)
          __snake_case    					=  np.linalg.norm(x - xa	)
          __snake_case    					=  np.maximum(_lowerCamelCase   ,	_lowerCamelCase	)

          # Update variables.
          __snake_case    					=  np.copy(_lowerCamelCase	)
          __snake_case    					=  np.copy(_lowerCamelCase	)
          __snake_case    					=  np.copy(_lowerCamelCase	)

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

     return x







def 			_UpperCamelCase ()->   None:




     '''simple docstring'''





     __snake_case    					=  3
     __snake_case    					=  _create_spd_matrix(_lowerCamelCase	)
     __snake_case    					=  np.random.randn(_lowerCamelCase   ,	1	)
     __snake_case    					=  np.dot(_lowerCamelCase   ,	_lowerCamelCase	)

     # Numpy solution.
     __snake_case    					=  np.linalg.solve(_lowerCamelCase   ,	_lowerCamelCase	)

     # Our implementation.
     __snake_case    					=  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()












'''simple docstring'''



from ..utils import deprecate
from .attention_processor import (  # noqa: F401
    Attention,
    AttentionProcessor,
    AttnAddedKVProcessor,
    AttnProcessor2_0,
    LoRAAttnProcessor,
    LoRALinearLayer,
    LoRAXFormersAttnProcessor,
    SlicedAttnAddedKVProcessor,
    SlicedAttnProcessor,
    XFormersAttnProcessor,
)
from .attention_processor import AttnProcessor as AttnProcessorRename  # noqa: F401


deprecate(
    '''cross_attention''',
    '''0.20.0''',
    '''Importing from cross_attention is deprecated. Please import from diffusers.models.attention_processor instead.''',
    standard_warn=False,
)


UpperCAmelCase_       :  Optional[int]      =		AttentionProcessor





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  Optional[int]:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  Any:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  Tuple:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  Optional[Any]:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  Optional[int]:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  Tuple:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  int:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  List[str]:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )






