"""simple docstring"""


import tempfile

import torch

from diffusers import PNDMScheduler

from .test_schedulers import SchedulerCommonTest






class    a__    (   _a	):
   snake_case_							=      (PNDMScheduler,)
   snake_case_							=      (("num_inference_steps", 50),)


   def 	snake_case__	(     self,				**_UpperCAmelCase  ):
        '''simple docstring'''



        lowercase__				 =							{
            "num_train_timesteps": 1000,
            "beta_start": 0.0_001,
            "beta_end": 0.02,
            "beta_schedule": "linear",
        }

        config.update(**_UpperCAmelCase  )
        return config


   def 	snake_case__	(     self,				_UpperCAmelCase=0,				**_UpperCAmelCase  ):
        '''simple docstring'''



        lowercase__				 =							dict(self.forward_default_kwargs  )
        lowercase__				 =							kwargs.pop("num_inference_steps",				_UpperCAmelCase  )
        lowercase__				 =							self.dummy_sample
        lowercase__				 =							0.1 * sample
        lowercase__				 =							[residual + 0.2, residual + 0.15, residual + 0.1, residual + 0.05]

        for scheduler_class in self.scheduler_classes:
             lowercase__				 =							self.get_scheduler_config(**_UpperCAmelCase  )
             lowercase__				 =							scheduler_class(**_UpperCAmelCase  )
             scheduler.set_timesteps(_UpperCAmelCase  )
             # copy over dummy past residuals
             lowercase__				 =							dummy_past_residuals[:]

             with tempfile.TemporaryDirectory() as tmpdirname:
                  scheduler.save_config(_UpperCAmelCase  )
                  lowercase__				 =							scheduler_class.from_pretrained(_UpperCAmelCase  )
                  new_scheduler.set_timesteps(_UpperCAmelCase  )
                  # copy over dummy past residuals
                  lowercase__				 =							dummy_past_residuals[:]

             lowercase__				 =							scheduler.step_prk(_UpperCAmelCase,				_UpperCAmelCase,				_UpperCAmelCase,				**_UpperCAmelCase  ).prev_sample
             lowercase__				 =							new_scheduler.step_prk(_UpperCAmelCase,				_UpperCAmelCase,				_UpperCAmelCase,				**_UpperCAmelCase  ).prev_sample

             assert torch.sum(torch.abs(output - new_output  )  ) < 1E-5, "Scheduler outputs are not identical"

             lowercase__				 =							scheduler.step_plms(_UpperCAmelCase,				_UpperCAmelCase,				_UpperCAmelCase,				**_UpperCAmelCase  ).prev_sample
             lowercase__				 =							new_scheduler.step_plms(_UpperCAmelCase,				_UpperCAmelCase,				_UpperCAmelCase,				**_UpperCAmelCase  ).prev_sample

             assert torch.sum(torch.abs(output - new_output  )  ) < 1E-5, "Scheduler outputs are not identical"


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        pass


   def 	snake_case__	(     self,				_UpperCAmelCase=0,				**_UpperCAmelCase  ):
        '''simple docstring'''



        lowercase__				 =							dict(self.forward_default_kwargs  )
        lowercase__				 =							kwargs.pop("num_inference_steps",				_UpperCAmelCase  )
        lowercase__				 =							self.dummy_sample
        lowercase__				 =							0.1 * sample
        lowercase__				 =							[residual + 0.2, residual + 0.15, residual + 0.1, residual + 0.05]

        for scheduler_class in self.scheduler_classes:
             lowercase__				 =							self.get_scheduler_config()
             lowercase__				 =							scheduler_class(**_UpperCAmelCase  )
             scheduler.set_timesteps(_UpperCAmelCase  )

             # copy over dummy past residuals (must be after setting timesteps)
             lowercase__				 =							dummy_past_residuals[:]

             with tempfile.TemporaryDirectory() as tmpdirname:
                  scheduler.save_config(_UpperCAmelCase  )
                  lowercase__				 =							scheduler_class.from_pretrained(_UpperCAmelCase  )
                  # copy over dummy past residuals
                  new_scheduler.set_timesteps(_UpperCAmelCase  )

                  # copy over dummy past residual (must be after setting timesteps)
                  lowercase__				 =							dummy_past_residuals[:]

             lowercase__				 =							scheduler.step_prk(_UpperCAmelCase,				_UpperCAmelCase,				_UpperCAmelCase,				**_UpperCAmelCase  ).prev_sample
             lowercase__				 =							new_scheduler.step_prk(_UpperCAmelCase,				_UpperCAmelCase,				_UpperCAmelCase,				**_UpperCAmelCase  ).prev_sample

             assert torch.sum(torch.abs(output - new_output  )  ) < 1E-5, "Scheduler outputs are not identical"

             lowercase__				 =							scheduler.step_plms(_UpperCAmelCase,				_UpperCAmelCase,				_UpperCAmelCase,				**_UpperCAmelCase  ).prev_sample
             lowercase__				 =							new_scheduler.step_plms(_UpperCAmelCase,				_UpperCAmelCase,				_UpperCAmelCase,				**_UpperCAmelCase  ).prev_sample

             assert torch.sum(torch.abs(output - new_output  )  ) < 1E-5, "Scheduler outputs are not identical"


   def 	snake_case__	(     self,				**_UpperCAmelCase  ):
        '''simple docstring'''



        lowercase__				 =							self.scheduler_classes[0]
        lowercase__				 =							self.get_scheduler_config(**_UpperCAmelCase  )
        lowercase__				 =							scheduler_class(**_UpperCAmelCase  )

        lowercase__				 =							10
        lowercase__				 =							self.dummy_model()
        lowercase__				 =							self.dummy_sample_deter
        scheduler.set_timesteps(_UpperCAmelCase  )

        for i, t in enumerate(scheduler.prk_timesteps  ):
             lowercase__				 =							model(_UpperCAmelCase,				_UpperCAmelCase  )
             lowercase__				 =							scheduler.step_prk(_UpperCAmelCase,				_UpperCAmelCase,				_UpperCAmelCase  ).prev_sample

        for i, t in enumerate(scheduler.plms_timesteps  ):
             lowercase__				 =							model(_UpperCAmelCase,				_UpperCAmelCase  )
             lowercase__				 =							scheduler.step_plms(_UpperCAmelCase,				_UpperCAmelCase,				_UpperCAmelCase  ).prev_sample

        return sample


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        lowercase__				 =							dict(self.forward_default_kwargs  )

        lowercase__				 =							kwargs.pop("num_inference_steps",				_UpperCAmelCase  )

        for scheduler_class in self.scheduler_classes:
             lowercase__				 =							self.get_scheduler_config()
             lowercase__				 =							scheduler_class(**_UpperCAmelCase  )

             lowercase__				 =							self.dummy_sample
             lowercase__				 =							0.1 * sample

             if num_inference_steps is not None and hasattr(_UpperCAmelCase,				"set_timesteps"  ):
                  scheduler.set_timesteps(_UpperCAmelCase  )
             elif num_inference_steps is not None and not hasattr(_UpperCAmelCase,				"set_timesteps"  ):
                  lowercase__				 =							num_inference_steps

             # copy over dummy past residuals (must be done after set_timesteps)
             lowercase__				 =							[residual + 0.2, residual + 0.15, residual + 0.1, residual + 0.05]
             lowercase__				 =							dummy_past_residuals[:]

             lowercase__				 =							scheduler.step_prk(_UpperCAmelCase,				0,				_UpperCAmelCase,				**_UpperCAmelCase  ).prev_sample
             lowercase__				 =							scheduler.step_prk(_UpperCAmelCase,				1,				_UpperCAmelCase,				**_UpperCAmelCase  ).prev_sample

             self.assertEqual(output_a.shape,				sample.shape  )
             self.assertEqual(output_a.shape,				output_a.shape  )

             lowercase__				 =							scheduler.step_plms(_UpperCAmelCase,				0,				_UpperCAmelCase,				**_UpperCAmelCase  ).prev_sample
             lowercase__				 =							scheduler.step_plms(_UpperCAmelCase,				1,				_UpperCAmelCase,				**_UpperCAmelCase  ).prev_sample

             self.assertEqual(output_a.shape,				sample.shape  )
             self.assertEqual(output_a.shape,				output_a.shape  )


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        for timesteps in [100, 1000]:
             self.check_over_configs(num_train_timesteps=_UpperCAmelCase  )


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        for steps_offset in [0, 1]:
             self.check_over_configs(steps_offset=_UpperCAmelCase  )

        lowercase__				 =							self.scheduler_classes[0]
        lowercase__				 =							self.get_scheduler_config(steps_offset=1  )
        lowercase__				 =							scheduler_class(**_UpperCAmelCase  )
        scheduler.set_timesteps(10  )
        assert torch.equal(
            scheduler.timesteps,				torch.LongTensor(
                [901, 851, 851, 801, 801, 751, 751, 701, 701, 651, 651, 601, 601, 501, 401, 301, 201, 101, 1]  ),				)


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        for beta_start, beta_end in zip([0.0_001, 0.001],				[0.002, 0.02]  ):
             self.check_over_configs(beta_start=_UpperCAmelCase,				beta_end=_UpperCAmelCase  )


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        for schedule in ["linear", "squaredcos_cap_v2"]:
             self.check_over_configs(beta_schedule=_UpperCAmelCase  )


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        for prediction_type in ["epsilon", "v_prediction"]:
             self.check_over_configs(prediction_type=_UpperCAmelCase  )


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        for t in [1, 5, 10]:
             self.check_over_forward(time_step=_UpperCAmelCase  )


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        for t, num_inference_steps in zip([1, 5, 10],				[10, 50, 100]  ):
             self.check_over_forward(num_inference_steps=_UpperCAmelCase  )


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        lowercase__				 =							27

        for scheduler_class in self.scheduler_classes:
             lowercase__				 =							self.dummy_sample
             lowercase__				 =							0.1 * sample

             lowercase__				 =							self.get_scheduler_config()
             lowercase__				 =							scheduler_class(**_UpperCAmelCase  )

             scheduler.set_timesteps(_UpperCAmelCase  )

             # before power of 3 fix, would error on first step, so we only need to do two
             for i, t in enumerate(scheduler.prk_timesteps[:2]  ):
                  lowercase__				 =							scheduler.step_prk(_UpperCAmelCase,				_UpperCAmelCase,				_UpperCAmelCase  ).prev_sample


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        with self.assertRaises(_UpperCAmelCase  ):
             lowercase__				 =							self.scheduler_classes[0]
             lowercase__				 =							self.get_scheduler_config()
             lowercase__				 =							scheduler_class(**_UpperCAmelCase  )

             scheduler.step_plms(self.dummy_sample,				1,				self.dummy_sample  ).prev_sample


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        lowercase__				 =							self.full_loop()
        lowercase__				 =							torch.sum(torch.abs(_UpperCAmelCase  )  )
        lowercase__				 =							torch.mean(torch.abs(_UpperCAmelCase  )  )

        assert abs(result_sum.item() - 198.1_318  ) < 1E-2
        assert abs(result_mean.item() - 0.2_580  ) < 1E-3


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        lowercase__				 =							self.full_loop(prediction_type="v_prediction"  )
        lowercase__				 =							torch.sum(torch.abs(_UpperCAmelCase  )  )
        lowercase__				 =							torch.mean(torch.abs(_UpperCAmelCase  )  )

        assert abs(result_sum.item() - 67.3_986  ) < 1E-2
        assert abs(result_mean.item() - 0.0_878  ) < 1E-3


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        lowercase__				 =							self.full_loop(set_alpha_to_one=_UpperCAmelCase,				beta_start=0.01  )
        lowercase__				 =							torch.sum(torch.abs(_UpperCAmelCase  )  )
        lowercase__				 =							torch.mean(torch.abs(_UpperCAmelCase  )  )

        assert abs(result_sum.item() - 230.0_399  ) < 1E-2
        assert abs(result_mean.item() - 0.2_995  ) < 1E-3


   def 	snake_case__	(     self  ):
        '''simple docstring'''



        lowercase__				 =							self.full_loop(set_alpha_to_one=_UpperCAmelCase,				beta_start=0.01  )
        lowercase__				 =							torch.sum(torch.abs(_UpperCAmelCase  )  )
        lowercase__				 =							torch.mean(torch.abs(_UpperCAmelCase  )  )

        assert abs(result_sum.item() - 186.9_482  ) < 1E-2
        assert abs(result_mean.item() - 0.2_434  ) < 1E-3





"""simple docstring"""


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







def 					__a   (		A    ,				A    ,				A = "x"    ,				A = 10**-10    ,				A = 1    ,				):






     '''simple docstring'''



     lowercase__				 =							symbols(A      )
     lowercase__				 =							lambdify(A    ,				A      )
     lowercase__				 =							lambdify(A    ,				diff(A    ,				A      )      )

     lowercase__				 =							starting_point

     while True:
          if diff_function(A      ) != 0:
               lowercase__				 =							prev_guess - multiplicity * func(A      ) / diff_function(
                   A      )
          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

          lowercase__				 =							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)}')




