


'''simple docstring'''






# limitations under the License.

# NOTE: This file is deprecated and will be removed in a future version.
# It only exists so that temporarely `from diffusers.pipelines import DiffusionPipeline` works

from .pipelines import DiffusionPipeline, ImagePipelineOutput  # noqa: F401
from .utils import deprecate


deprecate(
    'pipelines_utils',
    '0.22.0',
    'Importing `DiffusionPipeline` or `ImagePipelineOutput` from diffusers.pipeline_utils is deprecated. Please import from diffusers.pipelines.pipeline_utils instead.',
    standard_warn=False,
    stacklevel=3,
)





'''simple docstring'''






from typing import Any

import numpy as np





def lowerCamelCase__     (		__lowerCamelCase			:				np.ndarray				):







   '''simple docstring'''




   return np.array_equal(__lowerCamelCase			,       matrix.conjugate().T				)





def lowerCamelCase__     (		__lowerCamelCase			:				np.ndarray			,       __lowerCamelCase			:				np.ndarray				):







   '''simple docstring'''




   _UpperCAmelCase  :  str				       =v.conjugate().T
   _UpperCAmelCase  :  Optional[int]				       =v_star.dot(__lowerCamelCase				)
   assert isinstance(__lowerCamelCase			,       np.ndarray				)
   return (v_star_dot.dot(__lowerCamelCase				)) / (v_star.dot(__lowerCamelCase				))





def lowerCamelCase__     (		):







   '''simple docstring'''




   _UpperCAmelCase  :  Optional[Any]				       =np.array([[2, 2 + 1J, 4], [2 - 1J, 3, 1J], [4, -1J, 1]]				)
   _UpperCAmelCase  :  List[str]				       =np.array([[1], [2], [3]]				)
   assert is_hermitian(__lowerCamelCase				), f"{a} is not hermitian."
   print(rayleigh_quotient(__lowerCamelCase			,       __lowerCamelCase				)				)

   _UpperCAmelCase  :  List[str]				       =np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]				)
   assert is_hermitian(__lowerCamelCase				), f"{a} is not hermitian."
   assert rayleigh_quotient(__lowerCamelCase			,       __lowerCamelCase				) == float(3				)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 tests()

