


'''simple docstring'''






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






def 	_A				(lowerCAmelCase__  :str				,						lowerCAmelCase__  :complex				,						lowerCAmelCase__  :str = "x"				,						lowerCAmelCase__  :float = 10**-10				,						lowerCAmelCase__  :int = 1				,						)   ->  complex:




     '''simple docstring'''



     _a			      =							symbols(lowerCAmelCase__		)
     _a			      =							lambdify(lowerCAmelCase__				,						lowerCAmelCase__		)
     _a			      =							lambdify(lowerCAmelCase__				,						diff(lowerCAmelCase__				,						lowerCAmelCase__		)		)

     _a			      =							starting_point

     while True:
          if diff_function(lowerCAmelCase__		) != 0:
               _a			      =							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

          _a			      =							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', 1_0, precision=0.005)}''',
 )

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





'''simple docstring'''






import gc
import unittest

import numpy as np
import torch

from diffusers import AutoencoderKL, DDIMScheduler, DiTPipeline, DPMSolverMultistepScheduler, TransformeraDModel
from diffusers.utils import is_xformers_available, load_numpy, slow, torch_device
from diffusers.utils.testing_utils import enable_full_determinism, require_torch_gpu

from ..pipeline_params import (
    CLASS_CONDITIONED_IMAGE_GENERATION_BATCH_PARAMS,
    CLASS_CONDITIONED_IMAGE_GENERATION_PARAMS,
)
from ..test_pipelines_common import PipelineTesterMixin


enable_full_determinism()




class  a     (     _SCREAMING_SNAKE_CASE  ,				unittest.TestCase       ):
 _lowerCAmelCase 					=	DiTPipeline
 _lowerCAmelCase 					=	CLASS_CONDITIONED_IMAGE_GENERATION_PARAMS
 _lowerCAmelCase 					=	PipelineTesterMixin.required_optional_params - {
     """latents""",
     """num_images_per_prompt""",
     """callback""",
     """callback_steps""",
 }
 _lowerCAmelCase 					=	CLASS_CONDITIONED_IMAGE_GENERATION_BATCH_PARAMS
 _lowerCAmelCase 					=	False
 def 							__UpperCAmelCase		( self						)					->							Dict:
      torch.manual_seed(0						)
      _a			      =							TransformeraDModel(
          sample_size=16      ,				num_layers=2      ,				patch_size=4      ,				attention_head_dim=8      ,				num_attention_heads=2      ,				in_channels=4      ,				out_channels=8      ,				attention_bias=__magic_name__      ,				activation_fn='gelu-approximate'      ,				num_embeds_ada_norm=10_00      ,				norm_type='ada_norm_zero'      ,				norm_elementwise_affine=__magic_name__      ,				)
      _a			      =							AutoencoderKL()
      _a			      =							DDIMScheduler()
      _a			      =							{'transformer': transformer.eval(), 'vae': vae.eval(), 'scheduler': scheduler}
      return components
 def 							__UpperCAmelCase		( self      ,				__magic_name__      ,				__magic_name__=0						)					->							Union[str, Any]:
      if str(__magic_name__						).startswith('mps'						):
           _a			      =							torch.manual_seed(__magic_name__						)
      else:
           _a			      =							torch.Generator(device=__magic_name__						).manual_seed(__magic_name__						)
      _a			      =							{
          'class_labels': [1],
          'generator': generator,
          'num_inference_steps': 2,
          'output_type': 'numpy',
      }
      return inputs
 def 							__UpperCAmelCase		( self						)					->							Tuple:
      _a			      =							'cpu'

      _a			      =							self.get_dummy_components()
      _a			      =							self.pipeline_class(**__magic_name__						)
      pipe.to(__magic_name__						)
      pipe.set_progress_bar_config(disable=__magic_name__						)

      _a			      =							self.get_dummy_inputs(__magic_name__						)
      _a			      =							pipe(**__magic_name__						).images
      _a			      =							image[0, -3:, -3:, -1]

      self.assertEqual(image.shape      ,				(1, 16, 16, 3)						)
      _a			      =							np.array([0.2_9_4_6, 0.6_6_0_1, 0.4_3_2_9, 0.3_2_9_6, 0.4_1_4_4, 0.5_3_1_9, 0.7_2_7_3, 0.5_0_1_3, 0.4_4_5_7]						)
      _a			      =							np.abs(image_slice.flatten() - expected_slice						).max()
      self.assertLessEqual(__magic_name__      ,				1e-3						)
 def 							__UpperCAmelCase		( self						)					->							Any:
      self._test_inference_batch_single_identical(relax_max_difference=__magic_name__      ,				expected_max_diff=1e-3						)




 @unittest.skipIf(
     torch_device != 'cuda' or not is_xformers_available()      ,				reason='XFormers attention is only available with CUDA and `xformers` installed'      ,				)
 def 							__UpperCAmelCase		( self						)					->							Any:
      self._test_xformers_attention_forwardGenerator_pass(expected_max_diff=1e-3						)





@require_torch_gpu
@slow
class  a     (     unittest.TestCase       ):
 def 							__UpperCAmelCase		( self						)					->							List[str]:
      super().tearDown()
      gc.collect()
      torch.cuda.empty_cache()
 def 							__UpperCAmelCase		( self						)					->							Union[str, Any]:
      _a			      =							torch.manual_seed(0						)

      _a			      =							DiTPipeline.from_pretrained('facebook/DiT-XL-2-256'						)
      pipe.to('cuda'						)

      _a			      =							['vase', 'umbrella', 'white shark', 'white wolf']
      _a			      =							pipe.get_label_ids(__magic_name__						)

      _a			      =							pipe(__magic_name__      ,				generator=__magic_name__      ,				num_inference_steps=40      ,				output_type='np'						).images

      for word, image in zip(__magic_name__      ,				__magic_name__						):
           _a			      =							load_numpy(
               f'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/dit/{word}.npy'						)
           assert np.abs((expected_image - image).max()						) < 1e-2




 def 							__UpperCAmelCase		( self						)					->							Any:
      _a			      =							DiTPipeline.from_pretrained('facebook/DiT-XL-2-512'						)
      _a			      =							DPMSolverMultistepScheduler.from_config(pipe.scheduler.config						)
      pipe.to('cuda'						)

      _a			      =							['vase', 'umbrella']
      _a			      =							pipe.get_label_ids(__magic_name__						)

      _a			      =							torch.manual_seed(0						)
      _a			      =							pipe(__magic_name__      ,				generator=__magic_name__      ,				num_inference_steps=25      ,				output_type='np'						).images

      for word, image in zip(__magic_name__      ,				__magic_name__						):
           _a			      =							load_numpy(
               'https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main'
               f'/dit/{word}_512.npy'						)

           assert np.abs((expected_image - image).max()						) < 1e-1

