
def    UpperCamelCase_ (	a_  ,				a_		)     ->Optional[Any]:
		# "Simpson Rule"
		# int(f) = delta_x/2 * (b-a)/3*(f1 + 4f2 + 2f_3 + ... + fn)
		A				=(boundary[1] - boundary[0]) / steps
		A				=boundary[0]
		A				=boundary[1]
		A				=make_points(__UpperCamelCase  ,				__UpperCamelCase  ,				__UpperCamelCase		)
		A				=0.0
		y += (h / 3.0) * f(__UpperCamelCase		)
		A				=2
		for i in x_i:
				y += (h / 3) * (4 - 2 * (cnt % 2)) * f(__UpperCamelCase		)
				cnt += 1
		y += (h / 3.0) * f(__UpperCamelCase		)
		return y

def    UpperCamelCase_ (	a_  ,				a_  ,				a_		)     ->Dict:
		A				=a + h
		while x < (b - h):
				yield x
				A				=x + h

def    UpperCamelCase_ (	a_		)     ->Optional[Any]:  # enter your function here
		A				=(x - 0) * (x - 0)
		return y

def    UpperCamelCase_ (	)     ->Dict:
		A				=0.0  # Lower bound of integration
		A				=1.0  # Upper bound of integration
		A				=10.0  # define number of steps or resolution
		A				=[a, b]  # define boundary of integration
		A				=method_a(__UpperCamelCase  ,				__UpperCamelCase		)
		print(f'''y = {y}'''		)


if __name__ == "__main__":
	main()






"""simple docstring"""


import unittest

import numpy as np
import PIL
import torch

from diffusers.image_processor import VaeImageProcessor







class 						lowerCamelCase__   (   unittest.TestCase							):





			'''simple docstring'''



			@property
			def    _lowerCAmelCase						(				self    )					->	List[str]:
				_lowerCAmelCase								=1
				_lowerCAmelCase								=3
				_lowerCAmelCase								=8
				_lowerCAmelCase								=8

				_lowerCAmelCase								=torch.rand((batch_size, num_channels, height, width)    )

				return sample



			def    _lowerCAmelCase						(				self	,	__UpperCAmelCase    )					->	Any:
				if isinstance(image[0]	,	PIL.Image.Image    ):
					return np.stack([np.array(__UpperCAmelCase    ) for i in image]	,	axis=0    )
				elif isinstance(__UpperCAmelCase	,	torch.Tensor    ):
					return image.cpu().numpy().transpose(0	,	2	,	3	,	1    )
				return image



			def    _lowerCAmelCase						(				self    )					->	Tuple:
				_lowerCAmelCase								=VaeImageProcessor(do_resize=__UpperCAmelCase	,	do_normalize=__UpperCAmelCase    )

				_lowerCAmelCase								=self.dummy_sample
				_lowerCAmelCase								=self.to_np(__UpperCAmelCase    )

				for output_type in ["pt", "np", "pil"]:
					_lowerCAmelCase								=image_processor.postprocess(
					    image_processor.preprocess(__UpperCAmelCase    )	,	output_type=__UpperCAmelCase	,	)
					_lowerCAmelCase								=self.to_np(__UpperCAmelCase    )
					_lowerCAmelCase								=(input_np * 2_55).round() if output_type == """pil""" else input_np
					assert (
					    np.abs(in_np - out_np    ).max() < 1e-6
					), f'''decoded output does not match input for output_type {output_type}'''



			def    _lowerCAmelCase						(				self    )					->	Union[str, Any]:
				_lowerCAmelCase								=VaeImageProcessor(do_resize=__UpperCAmelCase	,	do_normalize=__UpperCAmelCase    )
				_lowerCAmelCase								=self.dummy_sample.cpu().numpy().transpose(0	,	2	,	3	,	1    )

				for output_type in ["pt", "np", "pil"]:
					_lowerCAmelCase								=image_processor.postprocess(image_processor.preprocess(__UpperCAmelCase    )	,	output_type=__UpperCAmelCase    )

					_lowerCAmelCase								=self.to_np(__UpperCAmelCase    )
					_lowerCAmelCase								=(input_np * 2_55).round() if output_type == """pil""" else input_np
					assert (
					    np.abs(in_np - out_np    ).max() < 1e-6
					), f'''decoded output does not match input for output_type {output_type}'''



			def    _lowerCAmelCase						(				self    )					->	List[str]:
				_lowerCAmelCase								=VaeImageProcessor(do_resize=__UpperCAmelCase	,	do_normalize=__UpperCAmelCase    )

				_lowerCAmelCase								=self.dummy_sample.cpu().numpy().transpose(0	,	2	,	3	,	1    )
				_lowerCAmelCase								=image_processor.numpy_to_pil(__UpperCAmelCase    )

				for output_type in ["pt", "np", "pil"]:
					_lowerCAmelCase								=image_processor.postprocess(image_processor.preprocess(__UpperCAmelCase    )	,	output_type=__UpperCAmelCase    )
					for i, o in zip(__UpperCAmelCase	,	__UpperCAmelCase    ):
						_lowerCAmelCase								=np.array(__UpperCAmelCase    )
						_lowerCAmelCase								=self.to_np(__UpperCAmelCase    ) if output_type == """pil""" else (self.to_np(__UpperCAmelCase    ) * 2_55).round()
						assert (
						    np.abs(in_np - out_np    ).max() < 1e-6
						), f'''decoded output does not match input for output_type {output_type}'''



			def    _lowerCAmelCase						(				self    )					->	Tuple:
				_lowerCAmelCase								=VaeImageProcessor(do_resize=__UpperCAmelCase	,	do_normalize=__UpperCAmelCase    )

				_lowerCAmelCase								=self.dummy_sample
				_lowerCAmelCase								=input_pt_ad.squeeze(0    )

				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)
				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)

				_lowerCAmelCase								=self.to_np(self.dummy_sample    )
				_lowerCAmelCase								=input_np_ad.squeeze(0    )

				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)
				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)

				assert np.abs(out_pt_ad - out_pt_ad    ).max() < 1e-6
				assert np.abs(out_np_ad - out_np_ad    ).max() < 1e-6



			def    _lowerCAmelCase						(				self    )					->	Optional[Any]:
				_lowerCAmelCase								=VaeImageProcessor(do_resize=__UpperCAmelCase	,	do_normalize=__UpperCAmelCase    )

				_lowerCAmelCase								=self.dummy_sample
				_lowerCAmelCase								=list(__UpperCAmelCase    )

				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)

				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)

				_lowerCAmelCase								=self.to_np(self.dummy_sample    )
				list(__UpperCAmelCase    )

				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)

				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)

				assert np.abs(out_pt_ad - out_pt_list    ).max() < 1e-6
				assert np.abs(out_np_ad - out_np_list    ).max() < 1e-6



