


from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403



def       _lowerCAmelCase    (				lowerCAmelCase_				:str		,    lowerCAmelCase_				:complex		,    lowerCAmelCase_				:str = "x"		,    lowerCAmelCase_				:float = 10**-10		,    lowerCAmelCase_				:int = 1		,    )->complex:
   '''simple docstring'''






   snake_case_            =       symbols(lowerCAmelCase_				)
   snake_case_            =       lambdify(lowerCAmelCase_		,    lowerCAmelCase_				)
   snake_case_            =       lambdify(lowerCAmelCase_		,    diff(lowerCAmelCase_		,    lowerCAmelCase_				)				)

   snake_case_            =       starting_point

   while True:
      if diff_function(lowerCAmelCase_				) != 0:
         snake_case_            =       prev_guess - multiplicity * func(lowerCAmelCase_				) / diff_function(
             lowerCAmelCase_				)
      else:
         raise ZeroDivisionError("Could not find root"				) from None

      # Precision is checked by comparing the difference of consecutive guesses
      if abs(next_guess - prev_guess				) < precision:
         return next_guess

      snake_case_            =       next_guess


# Let's Execute
if __name__ == "__main__":
   # Find root of trigonometric function
   # Find value of pi
   print(F'''The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}''')

   # Find root of polynomial
   # Find fourth Root of 5
   print(F'''The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5J)}''')

   # Find value of e
   print(
       '''The root of log(y) - 1 = 0 is ''',
       F'''{newton_raphson('log(y) - 1', 2, variable='y')}''',
   )

   # Exponential Roots
   print(
       '''The root of exp(x) - 1 = 0 is''',
       F'''{newton_raphson('exp(x) - 1', 10, precision=0.005)}''',
   )

   # Find root of cos(x)
   print(F'''The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}''')








import json
import os
import tempfile
import unittest

import numpy as np
from datasets import load_dataset

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

from ...test_image_processing_common import ImageProcessingSavingTestMixin


if is_torch_available():
   import torch

if is_vision_available():
   from PIL import Image

   from transformers import ImageGPTImageProcessor


class      __lowerCAmelCase  (			unittest.TestCase       ):






  """simple docstring"""





  def __init__(  self							:							Union[str, Any]     ,					_lowerCAmelCase							:							List[Any]     ,					_lowerCAmelCase							:							List[Any]=7     ,					_lowerCAmelCase							:							Any=3     ,					_lowerCAmelCase							:							Dict=1_8     ,					_lowerCAmelCase							:							Tuple=3_0     ,					_lowerCAmelCase							:							Optional[int]=4_0_0     ,					_lowerCAmelCase							:							Optional[int]=True     ,					_lowerCAmelCase							:							Any=None     ,					_lowerCAmelCase							:							List[Any]=True     ,					) ->			Dict:




     """simple docstring"""
     snake_case_            =       size if size is not None else {"height": 1_8, "width": 1_8}
     snake_case_            =       parent
     snake_case_            =       batch_size
     snake_case_            =       num_channels
     snake_case_            =       image_size
     snake_case_            =       min_resolution
     snake_case_            =       max_resolution
     snake_case_            =       do_resize
     snake_case_            =       size
     snake_case_            =       do_normalize



  def        lowerCAmelCase__	(  self							:							str	) ->			Optional[int]:




     """simple docstring"""
     return {
         # here we create 2 clusters for the sake of simplicity
         "clusters": np.asarray(
             [
                 [0.8_866_443_634_033_203, 0.6_618_829_369_544_983, 0.3_891_746_401_786_804],
                 [-0.6_042_559_146_881_104, -0.02_295_008_860_528_469, 0.5_423_797_369_003_296],
             ]	),
         "do_resize": self.do_resize,
         "size": self.size,
         "do_normalize": self.do_normalize,
     }






@require_torch
@require_vision
class      __lowerCAmelCase  (			a			,	unittest.TestCase       ):






  """simple docstring"""





  _SCREAMING_SNAKE_CASE		     =							ImageGPTImageProcessor if is_vision_available() else None



  def        lowerCAmelCase__	(  self							:							Union[str, Any]	) ->			List[Any]:




     """simple docstring"""
     snake_case_            =       ImageGPTImageProcessingTester(self	)



  @property
  def        lowerCAmelCase__	(  self							:							str	) ->			Union[str, Any]:




     """simple docstring"""
     return self.image_processor_tester.prepare_image_processor_dict()



  def        lowerCAmelCase__	(  self							:							List[Any]	) ->			int:




     """simple docstring"""
     snake_case_            =       self.image_processing_class(**self.image_processor_dict	)
     self.assertTrue(hasattr(_lowerCAmelCase     ,					"clusters"	)	)
     self.assertTrue(hasattr(_lowerCAmelCase     ,					"do_resize"	)	)
     self.assertTrue(hasattr(_lowerCAmelCase     ,					"size"	)	)
     self.assertTrue(hasattr(_lowerCAmelCase     ,					"do_normalize"	)	)



  def        lowerCAmelCase__	(  self							:							int	) ->			Any:




     """simple docstring"""
     snake_case_            =       self.image_processing_class.from_dict(self.image_processor_dict	)
     self.assertEqual(image_processor.size     ,					{"height": 1_8, "width": 1_8}	)

     snake_case_            =       self.image_processing_class.from_dict(self.image_processor_dict     ,					size=4_2	)
     self.assertEqual(image_processor.size     ,					{"height": 4_2, "width": 4_2}	)



  def        lowerCAmelCase__	(  self							:							Tuple	) ->			Any:




     """simple docstring"""
     snake_case_            =       self.image_processing_class(**self.image_processor_dict	)
     snake_case_            =       json.loads(image_processor.to_json_string()	)
     for key, value in self.image_processor_dict.items():
        if key == "clusters":
           self.assertTrue(np.array_equal(_lowerCAmelCase     ,					obj[key]	)	)
        else:
           self.assertEqual(obj[key]     ,					_lowerCAmelCase	)



  def        lowerCAmelCase__	(  self							:							int	) ->			Optional[Any]:




     """simple docstring"""
     snake_case_            =       self.image_processing_class(**self.image_processor_dict	)

     with tempfile.TemporaryDirectory() as tmpdirname:
        snake_case_            =       os.path.join(_lowerCAmelCase     ,					"image_processor.json"	)
        image_processor_first.to_json_file(_lowerCAmelCase	)
        snake_case_            =       self.image_processing_class.from_json_file(_lowerCAmelCase	).to_dict()

     snake_case_            =       image_processor_first.to_dict()
     for key, value in image_processor_first.items():
        if key == "clusters":
           self.assertTrue(np.array_equal(_lowerCAmelCase     ,					image_processor_second[key]	)	)
        else:
           self.assertEqual(image_processor_first[key]     ,					_lowerCAmelCase	)



  def        lowerCAmelCase__	(  self							:							Optional[int]	) ->			Union[str, Any]:




     """simple docstring"""
     snake_case_            =       self.image_processing_class(**self.image_processor_dict	)

     with tempfile.TemporaryDirectory() as tmpdirname:
        image_processor_first.save_pretrained(_lowerCAmelCase	)
        snake_case_            =       self.image_processing_class.from_pretrained(_lowerCAmelCase	).to_dict()

     snake_case_            =       image_processor_first.to_dict()
     for key, value in image_processor_first.items():
        if key == "clusters":
           self.assertTrue(np.array_equal(_lowerCAmelCase     ,					image_processor_second[key]	)	)
        else:
           self.assertEqual(image_processor_first[key]     ,					_lowerCAmelCase	)



  @unittest.skip("ImageGPT requires clusters at initialization"	)
  def        lowerCAmelCase__	(  self							:							List[str]	) ->			int:




     """simple docstring"""
     pass






def       _lowerCAmelCase    (				)->Optional[Any]:
   '''simple docstring'''






   snake_case_            =       load_dataset("hf-internal-testing/fixtures_image_utils"		,    split="test"				)

   snake_case_            =       Image.open(dataset[4]["file"]				)
   snake_case_            =       Image.open(dataset[5]["file"]				)

   snake_case_            =       [imagea, imagea]

   return images



@require_vision
@require_torch
class      __lowerCAmelCase  (			unittest.TestCase       ):






  """simple docstring"""





  @slow
  def        lowerCAmelCase__	(  self							:							List[str]	) ->			int:




     """simple docstring"""
     snake_case_            =       ImageGPTImageProcessor.from_pretrained("openai/imagegpt-small"	)

     snake_case_            =       prepare_images()

     # test non-batched
     snake_case_            =       image_processing(images[0]     ,					return_tensors="pt"	)

     self.assertIsInstance(encoding.input_ids     ,					torch.LongTensor	)
     self.assertEqual(encoding.input_ids.shape     ,					(1, 1_0_2_4)	)

     snake_case_            =       [3_0_6, 1_9_1, 1_9_1]
     self.assertEqual(encoding.input_ids[0, :3].tolist()     ,					_lowerCAmelCase	)

     # test batched
     snake_case_            =       image_processing(_lowerCAmelCase     ,					return_tensors="pt"	)

     self.assertIsInstance(encoding.input_ids     ,					torch.LongTensor	)
     self.assertEqual(encoding.input_ids.shape     ,					(2, 1_0_2_4)	)

     snake_case_            =       [3_0_3, 1_3, 1_3]
     self.assertEqual(encoding.input_ids[1, -3:].tolist()     ,					_lowerCAmelCase	)




