from typing import Any

import numpy as np
def    __magic_name__(	__UpperCAmelCase		)    ->     bool:



      '''simple docstring'''

      assert np.shape(__UpperCAmelCase		)[0] == np.shape(__UpperCAmelCase		)[1]

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

      # Get eigenvalues and eignevectors for a symmetric matrix.
      _lowerCamelCase     ,       _lowerCamelCase           =					np.linalg.eigh(__UpperCAmelCase		)

      # Check sign of all eigenvalues.
      # np.all returns a value of type np.bool_
      return bool(np.all(eigen_values > 0		)		)
def    __magic_name__(	__UpperCAmelCase		)    ->     Any:



      '''simple docstring'''

      _lowerCamelCase           =					np.random.randn(__UpperCAmelCase			,    __UpperCAmelCase		)
      _lowerCamelCase           =					np.dot(__UpperCAmelCase			,    random_matrix.T		)
      assert _is_matrix_spd(__UpperCAmelCase		)
      return spd_matrix
def    __magic_name__(	__UpperCAmelCase			,    __UpperCAmelCase			,    __UpperCAmelCase = 1000			,    __UpperCAmelCase = 1E-8			,    )    ->     Any:



      '''simple docstring'''

      assert np.shape(__UpperCAmelCase		)[0] == np.shape(__UpperCAmelCase		)[1]
      assert np.shape(__UpperCAmelCase		)[0] == np.shape(__UpperCAmelCase		)[0]
      assert _is_matrix_spd(__UpperCAmelCase		)

      # Initialize solution guess, residual, search direction.
      _lowerCamelCase           =					np.zeros((np.shape(__UpperCAmelCase		)[0], 1)		)
      _lowerCamelCase           =					np.copy(__UpperCAmelCase		)
      _lowerCamelCase           =					np.copy(__UpperCAmelCase		)

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

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

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

            # The main algorithm.

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

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

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

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

      return x
def    __magic_name__(	)    ->     None:



      '''simple docstring'''

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

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

      # Our implementation.
      _lowerCamelCase           =					conjugate_gradient(__UpperCAmelCase			,    __UpperCAmelCase		)

      # 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()
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,
)


snake_case__						      =			AttentionProcessor



class 			UpperCamelCase					(			__lowercase			):

     '''simple docstring'''

     def __init__(       self					,					*A_					,					**A_    )			->					Union[str, Any]:






           """simple docstring"""
           _lowerCamelCase           =					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'''					,					A_					,					standard_warn=A_    )
           super().__init__(*A_					,					**A_    )





class 			UpperCamelCase					(			__lowercase			):

     '''simple docstring'''

     def __init__(       self					,					*A_					,					**A_    )			->					List[Any]:






           """simple docstring"""
           _lowerCamelCase           =					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'''					,					A_					,					standard_warn=A_    )
           super().__init__(*A_					,					**A_    )





class 			UpperCamelCase					(			__lowercase			):

     '''simple docstring'''

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






           """simple docstring"""
           _lowerCamelCase           =					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'''					,					A_					,					standard_warn=A_    )
           super().__init__(*A_					,					**A_    )





class 			UpperCamelCase					(			__lowercase			):

     '''simple docstring'''

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






           """simple docstring"""
           _lowerCamelCase           =					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'''					,					A_					,					standard_warn=A_    )
           super().__init__(*A_					,					**A_    )





class 			UpperCamelCase					(			__lowercase			):

     '''simple docstring'''

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






           """simple docstring"""
           _lowerCamelCase           =					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'''					,					A_					,					standard_warn=A_    )
           super().__init__(*A_					,					**A_    )





class 			UpperCamelCase					(			__lowercase			):

     '''simple docstring'''

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






           """simple docstring"""
           _lowerCamelCase           =					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'''					,					A_					,					standard_warn=A_    )
           super().__init__(*A_					,					**A_    )





class 			UpperCamelCase					(			__lowercase			):

     '''simple docstring'''

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






           """simple docstring"""
           _lowerCamelCase           =					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'''					,					A_					,					standard_warn=A_    )
           super().__init__(*A_					,					**A_    )





class 			UpperCamelCase					(			__lowercase			):

     '''simple docstring'''

     def __init__(       self					,					*A_					,					**A_    )			->					Dict:






           """simple docstring"""
           _lowerCamelCase           =					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'''					,					A_					,					standard_warn=A_    )
           super().__init__(*A_					,					**A_    )