
import unittest

import numpy as np




def 				a						(							snake_case__:					Optional[Any]						,   snake_case__:					List[str]						,   snake_case__:					List[Any]						,   snake_case__:					Any = None						,   ):


				'''simple docstring'''
				lowercase_       =					np.shape(_UpperCamelCase					)
				lowercase_       =					np.shape(_UpperCamelCase					)
				lowercase_       =					np.shape(_UpperCamelCase					)

				if shape_a[0] != shape_b[0]:
								lowercase_       =					(
								    '''Expected the same number of rows for A and B. '''
								    F'''Instead found A of size {shape_a} and B of size {shape_b}'''
								)
								raise ValueError(_UpperCamelCase					)

				if shape_b[1] != shape_c[1]:
								lowercase_       =					(
								    '''Expected the same number of columns for B and C. '''
								    F'''Instead found B of size {shape_b} and C of size {shape_c}'''
								)
								raise ValueError(_UpperCamelCase					)

				lowercase_       =					pseudo_inv
				if a_inv is None:
								try:
												lowercase_       =					np.linalg.inv(_UpperCamelCase					)
								except np.linalg.LinAlgError:
												raise ValueError(
												    '''Input matrix A is not invertible. Cannot compute Schur complement.'''					)

				return mat_c - mat_b.T @ a_inv @ mat_b
class  lowercase__(				unittest.TestCase							):



	"""simple docstring"""




	def 						_lowercase  (       self  :			Tuple       )       ->     None:
					lowercase_       =					np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
					lowercase_       =					np.array([[0, 3], [3, 0], [2, 3]]       )
					lowercase_       =					np.array([[2, 1], [6, 3]]       )

					lowercase_       =					schur_complement(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       )

					lowercase_       =					np.block([[a, b], [b.T, c]]       )

					lowercase_       =					np.linalg.det(SCREAMING_SNAKE_CASE_       )
					lowercase_       =					np.linalg.det(SCREAMING_SNAKE_CASE_       )
					lowercase_       =					np.linalg.det(SCREAMING_SNAKE_CASE_       )

					self.assertAlmostEqual(SCREAMING_SNAKE_CASE_       ,							det_a * det_s       )
	def 						_lowercase  (       self  :			int       )       ->     None:
					lowercase_       =					np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
					lowercase_       =					np.array([[0, 3], [3, 0], [2, 3]]       )
					lowercase_       =					np.array([[2, 1], [6, 3]]       )

					with self.assertRaises(SCREAMING_SNAKE_CASE_       ):
									schur_complement(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       )




	def 						_lowercase  (       self  :			Tuple       )       ->     None:
					lowercase_       =					np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
					lowercase_       =					np.array([[0, 3], [3, 0], [2, 3]]       )
					lowercase_       =					np.array([[2, 1, 3], [6, 3, 5]]       )

					with self.assertRaises(SCREAMING_SNAKE_CASE_       ):
									schur_complement(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       )


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						unittest.main()











import PIL.Image
import PIL.ImageOps
from packaging import version
from PIL import Image


if version.parse(version.parse(PIL.__version__).base_version) >= version.parse('''9.1.0'''):
	lowerCAmelCase_    =				{
	    '''linear''': PIL.Image.Resampling.BILINEAR,
	    '''bilinear''': PIL.Image.Resampling.BILINEAR,
	    '''bicubic''': PIL.Image.Resampling.BICUBIC,
	    '''lanczos''': PIL.Image.Resampling.LANCZOS,
	    '''nearest''': PIL.Image.Resampling.NEAREST,
	}
else:
	lowerCAmelCase_    =				{
	    '''linear''': PIL.Image.LINEAR,
	    '''bilinear''': PIL.Image.BILINEAR,
	    '''bicubic''': PIL.Image.BICUBIC,
	    '''lanczos''': PIL.Image.LANCZOS,
	    '''nearest''': PIL.Image.NEAREST,
	}






def      lowerCamelCase_						(				_UpperCamelCase )		->						Optional[int]:






				"""simple docstring"""


				snake_case_						:    Dict				=  (images / 2 + 0.5).clamp(0 ,				1 )
				snake_case_						:    Dict				=  images.cpu().permute(0 ,				2 ,				3 ,				1 ).float().numpy()
				snake_case_						:    int				=  numpy_to_pil(_UpperCamelCase )
				return images






def      lowerCamelCase_						(				_UpperCamelCase )		->						List[Any]:






				"""simple docstring"""


				if images.ndim == 3:
								snake_case_						:    Optional[Any]				=  images[None, ...]
				snake_case_						:    Any				=  (images * 255).round().astype('''uint8''' )
				if images.shape[-1] == 1:
								# special case for grayscale (single channel) images
								snake_case_						:    str				=  [Image.fromarray(image.squeeze() ,				mode='''L''' ) for image in images]
				else:
								snake_case_						:    List[Any]				=  [Image.fromarray(_UpperCamelCase ) for image in images]

				return pil_images
