



from math import factorial
class 				__A					:





			def __init__(self							,    __magic_name__							,    __magic_name__				):
						lowerCamelCase__ :      int								=		real
						if isinstance(__magic_name__							,    __magic_name__				):
									lowerCamelCase__ :      List[Any]								=		[1] * rank
						else:
									lowerCamelCase__ :      Tuple								=		rank





			def __repr__(self				):
						return (
						    f"{self.real}+"
						    f"{'+'.join(str(__magic_name__				)+'E'+str(n+1				)for n,dual in enumerate(self.duals				)				)}"
						)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Any								=		self.duals.copy()
						while cur[-1] == 0:
									cur.pop(-1				)
						return Dual(self.real							,    __magic_name__				)





			def __add__(self							,    __magic_name__				):
						if not isinstance(__magic_name__							,    __magic_name__				):
									return Dual(self.real + other							,    self.duals				)
						lowerCamelCase__ :      Any								=		self.duals.copy()
						lowerCamelCase__ :      List[str]								=		other.duals.copy()
						if len(__magic_name__				) > len(__magic_name__				):
									o_dual.extend([1] * (len(__magic_name__				) - len(__magic_name__				))				)
						elif len(__magic_name__				) < len(__magic_name__				):
									s_dual.extend([1] * (len(__magic_name__				) - len(__magic_name__				))				)
						lowerCamelCase__ :      Optional[Any]								=		[]
						for i in range(len(__magic_name__				)				):
									new_duals.append(s_dual[i] + o_dual[i]				)
						return Dual(self.real + other.real							,    __magic_name__				)

			UpperCamelCase					:Union[str, Any]     =			__add__





			def __sub__(self							,    __magic_name__				):
						return self + other * -1





			def __mul__(self							,    __magic_name__				):
						if not isinstance(__magic_name__							,    __magic_name__				):
									lowerCamelCase__ :      Tuple								=		[]
									for i in self.duals:
												new_duals.append(i * other				)
									return Dual(self.real * other							,    __magic_name__				)
						lowerCamelCase__ :      List[str]								=		[0] * (len(self.duals				) + len(other.duals				) + 1)
						for i, item in enumerate(self.duals				):
									for j, jtem in enumerate(other.duals				):
												new_duals[i + j + 1] += item * jtem
						for k in range(len(self.duals				)				):
									new_duals[k] += self.duals[k] * other.real
						for index in range(len(other.duals				)				):
									new_duals[index] += other.duals[index] * self.real
						return Dual(self.real * other.real							,    __magic_name__				)

			UpperCamelCase					:Tuple     =			__mul__





			def __truediv__(self							,    __magic_name__				):
						if not isinstance(__magic_name__							,    __magic_name__				):
									lowerCamelCase__ :      Optional[int]								=		[]
									for i in self.duals:
												new_duals.append(i / other				)
									return Dual(self.real / other							,    __magic_name__				)
						raise ValueError





			def __floordiv__(self							,    __magic_name__				):
						if not isinstance(__magic_name__							,    __magic_name__				):
									lowerCamelCase__ :      Optional[int]								=		[]
									for i in self.duals:
												new_duals.append(i // other				)
									return Dual(self.real // other							,    __magic_name__				)
						raise ValueError





			def __pow__(self							,    __magic_name__				):
						if n < 0 or isinstance(__magic_name__							,    __magic_name__				):
									raise ValueError("""power must be a positive integer"""				)
						if n == 0:
									return 1
						if n == 1:
									return self
						lowerCamelCase__ :      Optional[int]								=		self
						for _ in range(n - 1				):
									x *= self
						return x







def      _A				(UpperCamelCase		:      int      ,			UpperCamelCase		:      Union[str, Any]      ,			UpperCamelCase		:      Optional[int] ):



			'''simple docstring'''







			if not callable(UpperCamelCase ):
						raise ValueError("""differentiate() requires a function as input for func""" )
			if not isinstance(UpperCamelCase      ,			(float, int) ):
						raise ValueError("""differentiate() requires a float as input for position""" )
			if not isinstance(UpperCamelCase      ,			UpperCamelCase ):
						raise ValueError("""differentiate() requires an int as input for order""" )
			lowerCamelCase__ :      str								=		Dual(UpperCamelCase      ,			1 )
			lowerCamelCase__ :      Dict								=		func(UpperCamelCase )
			if order == 0:
						return result.real
			return result.duals[order - 1] * factorial(UpperCamelCase )


if __name__ == "__main__":
				import doctest

				doctest.testmod()






				def      _A				(UpperCamelCase		:      List[Any] ):



							'''simple docstring'''







							return y**2 * y**4
				print(differentiate(f, 9, 2))








import unittest

import numpy as np
import requests

from transformers.testing_utils import require_torch, require_vision
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
				import torch

				from transformers.pytorch_utils import is_torch_greater_or_equal_than_1_11
else:
				_lowercase     							=						False

if is_vision_available():
				from PIL import Image

				from transformers import PixaStructImageProcessor
class 				__A					( unittest.TestCase      ):





			def __init__(self							,    __magic_name__							,    __magic_name__=7							,    __magic_name__=3							,    __magic_name__=18							,    __magic_name__=30							,    __magic_name__=400							,    __magic_name__=None							,    __magic_name__=True							,    __magic_name__=True							,    __magic_name__=None							,    ):
						lowerCamelCase__ :      Optional[Any]								=		size if size is not None else {"""height""": 20, """width""": 20}
						lowerCamelCase__ :      List[str]								=		parent
						lowerCamelCase__ :      str								=		batch_size
						lowerCamelCase__ :      List[str]								=		num_channels
						lowerCamelCase__ :      Optional[int]								=		image_size
						lowerCamelCase__ :      Union[str, Any]								=		min_resolution
						lowerCamelCase__ :      List[Any]								=		max_resolution
						lowerCamelCase__ :      Optional[int]								=		size
						lowerCamelCase__ :      List[str]								=		do_normalize
						lowerCamelCase__ :      str								=		do_convert_rgb
						lowerCamelCase__ :      str								=		[512, 1024, 2048, 4096]
						lowerCamelCase__ :      Any								=		patch_size if patch_size is not None else {"""height""": 16, """width""": 16}





			def        _snake_case    (self				):
						return {"do_normalize": self.do_normalize, "do_convert_rgb": self.do_convert_rgb}





			def        _snake_case    (self				):
						lowerCamelCase__ :      List[str]								=		"""https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/tasks/australia.jpg"""
						lowerCamelCase__ :      int								=		Image.open(requests.get(__magic_name__							,    stream=__magic_name__				).raw				).convert("""RGB"""				)
						return raw_image







@unittest.skipIf(
    not is_torch_greater_or_equal_than_1_11					, reason='''`Pix2StructImageProcessor` requires `torch>=1.11.0`.'''					, )
@require_torch
@require_vision
class 				__A					( A_					, unittest.TestCase      ):
			UpperCamelCase					:Union[str, Any]     =			PixaStructImageProcessor if is_vision_available() else None





			def        _snake_case    (self				):
						lowerCamelCase__ :      List[str]								=		PixaStructImageProcessingTester(self				)





			@property
			def        _snake_case    (self				):
						return self.image_processor_tester.prepare_image_processor_dict()





			def        _snake_case    (self				):
						lowerCamelCase__ :      int								=		self.image_processing_class(**self.image_processor_dict				)
						self.assertTrue(hasattr(__magic_name__							,    """do_normalize"""				)				)
						self.assertTrue(hasattr(__magic_name__							,    """do_convert_rgb"""				)				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Tuple								=		self.image_processor_tester.prepare_dummy_image()

						lowerCamelCase__ :      Tuple								=		self.image_processing_class(**self.image_processor_dict				)
						lowerCamelCase__ :      List[str]								=		2048

						lowerCamelCase__ :      Any								=		image_processor(__magic_name__							,    return_tensors="""pt"""							,    max_patches=__magic_name__				)
						self.assertTrue(torch.allclose(inputs.flattened_patches.mean()							,    torch.tensor(0.06_06				)							,    atol=1E-3							,    rtol=1E-3				)				)





			def        _snake_case    (self				):
						# Initialize image_processor
						lowerCamelCase__ :      List[Any]								=		self.image_processing_class(**self.image_processor_dict				)
						# create random PIL images
						lowerCamelCase__ :      Optional[Any]								=		prepare_image_inputs(self.image_processor_tester							,    equal_resolution=__magic_name__				)
						for image in image_inputs:
									self.assertIsInstance(__magic_name__							,    Image.Image				)

						# Test not batched input
						lowerCamelCase__ :      Optional[Any]								=		(
						    (self.image_processor_tester.patch_size["""height"""] * self.image_processor_tester.patch_size["""width"""])
						    * self.image_processor_tester.num_channels
						) + 2

						for max_patch in self.image_processor_tester.max_patches:
									# Test not batched input
									lowerCamelCase__ :      Optional[Any]								=		image_processor(
									    image_inputs[0]							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (1, max_patch, expected_hidden_dim)							,    )

									# Test batched
									lowerCamelCase__ :      Optional[Any]								=		image_processor(
									    __magic_name__							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)							,    )





			def        _snake_case    (self				):
						# Initialize image_processor
						lowerCamelCase__ :      List[str]								=		self.image_processing_class(**self.image_processor_dict				)
						# create random PIL images
						lowerCamelCase__ :      Optional[Any]								=		prepare_image_inputs(self.image_processor_tester							,    equal_resolution=__magic_name__				)
						for image in image_inputs:
									self.assertIsInstance(__magic_name__							,    Image.Image				)

						# Test not batched input
						lowerCamelCase__ :      List[Any]								=		(
						    (self.image_processor_tester.patch_size["""height"""] * self.image_processor_tester.patch_size["""width"""])
						    * self.image_processor_tester.num_channels
						) + 2

						lowerCamelCase__ :      List[str]								=		True

						for max_patch in self.image_processor_tester.max_patches:
									# Test not batched input
									with self.assertRaises(__magic_name__				):
												lowerCamelCase__ :      Tuple								=		image_processor(
												    image_inputs[0]							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches

									lowerCamelCase__ :      Optional[Any]								=		"""Hello"""

									lowerCamelCase__ :      Dict								=		image_processor(
									    image_inputs[0]							,    return_tensors="""pt"""							,    max_patches=__magic_name__							,    header_text=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (1, max_patch, expected_hidden_dim)							,    )

									# Test batched
									lowerCamelCase__ :      Tuple								=		image_processor(
									    __magic_name__							,    return_tensors="""pt"""							,    max_patches=__magic_name__							,    header_text=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)							,    )





			def        _snake_case    (self				):
						# Initialize image_processor
						lowerCamelCase__ :      Any								=		self.image_processing_class(**self.image_processor_dict				)
						# create random numpy tensors
						lowerCamelCase__ :      Dict								=		prepare_image_inputs(self.image_processor_tester							,    equal_resolution=__magic_name__							,    numpify=__magic_name__				)
						for image in image_inputs:
									self.assertIsInstance(__magic_name__							,    np.ndarray				)

						lowerCamelCase__ :      Optional[int]								=		(
						    (self.image_processor_tester.patch_size["""height"""] * self.image_processor_tester.patch_size["""width"""])
						    * self.image_processor_tester.num_channels
						) + 2

						for max_patch in self.image_processor_tester.max_patches:
									# Test not batched input
									lowerCamelCase__ :      List[str]								=		image_processor(
									    image_inputs[0]							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (1, max_patch, expected_hidden_dim)							,    )

									# Test batched
									lowerCamelCase__ :      List[str]								=		image_processor(
									    __magic_name__							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)							,    )





			def        _snake_case    (self				):
						# Initialize image_processor
						lowerCamelCase__ :      Optional[int]								=		self.image_processing_class(**self.image_processor_dict				)
						# create random PyTorch tensors
						lowerCamelCase__ :      Dict								=		prepare_image_inputs(self.image_processor_tester							,    equal_resolution=__magic_name__							,    torchify=__magic_name__				)
						for image in image_inputs:
									self.assertIsInstance(__magic_name__							,    torch.Tensor				)

						# Test not batched input
						lowerCamelCase__ :      List[str]								=		(
						    (self.image_processor_tester.patch_size["""height"""] * self.image_processor_tester.patch_size["""width"""])
						    * self.image_processor_tester.num_channels
						) + 2

						for max_patch in self.image_processor_tester.max_patches:
									# Test not batched input
									lowerCamelCase__ :      Tuple								=		image_processor(
									    image_inputs[0]							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (1, max_patch, expected_hidden_dim)							,    )

									# Test batched
									lowerCamelCase__ :      Optional[Any]								=		image_processor(
									    __magic_name__							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)							,    )







@unittest.skipIf(
    not is_torch_greater_or_equal_than_1_11					, reason='''`Pix2StructImageProcessor` requires `torch>=1.11.0`.'''					, )
@require_torch
@require_vision
class 				__A					( A_					, unittest.TestCase      ):
			UpperCamelCase					:Optional[int]     =			PixaStructImageProcessor if is_vision_available() else None





			def        _snake_case    (self				):
						lowerCamelCase__ :      Optional[Any]								=		PixaStructImageProcessingTester(self							,    num_channels=4				)
						lowerCamelCase__ :      Optional[int]								=		3





			@property
			def        _snake_case    (self				):
						return self.image_processor_tester.prepare_image_processor_dict()





			def        _snake_case    (self				):
						lowerCamelCase__ :      Dict								=		self.image_processing_class(**self.image_processor_dict				)
						self.assertTrue(hasattr(__magic_name__							,    """do_normalize"""				)				)
						self.assertTrue(hasattr(__magic_name__							,    """do_convert_rgb"""				)				)





			def        _snake_case    (self				):
						# Initialize image_processor
						lowerCamelCase__ :      str								=		self.image_processing_class(**self.image_processor_dict				)
						# create random PIL images
						lowerCamelCase__ :      List[Any]								=		prepare_image_inputs(self.image_processor_tester							,    equal_resolution=__magic_name__				)
						for image in image_inputs:
									self.assertIsInstance(__magic_name__							,    Image.Image				)

						# Test not batched input
						lowerCamelCase__ :      List[str]								=		(
						    (self.image_processor_tester.patch_size["""height"""] * self.image_processor_tester.patch_size["""width"""])
						    * (self.image_processor_tester.num_channels - 1)
						) + 2

						for max_patch in self.image_processor_tester.max_patches:
									# Test not batched input
									lowerCamelCase__ :      Optional[Any]								=		image_processor(
									    image_inputs[0]							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (1, max_patch, expected_hidden_dim)							,    )

									# Test batched
									lowerCamelCase__ :      str								=		image_processor(
									    __magic_name__							,    return_tensors="""pt"""							,    max_patches=__magic_name__				).flattened_patches
									self.assertEqual(
									    encoded_images.shape							,    (self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)							,    )



