"""simple docstring"""


import os
import tempfile
import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_torch


if is_torch_available():
 import torch
 from torch import nn

 from transformers import (
     Adafactor,
     AdamW,
     get_constant_schedule,
     get_constant_schedule_with_warmup,
     get_cosine_schedule_with_warmup,
     get_cosine_with_hard_restarts_schedule_with_warmup,
     get_inverse_sqrt_schedule,
     get_linear_schedule_with_warmup,
     get_polynomial_decay_schedule_with_warmup,
 )







def 					__a   (		A    ,				A=10      ):






     '''simple docstring'''



     lowercase__				 =							[]
     for _ in range(A      ):
          lrs.append(scheduler.get_lr()[0]      )
          scheduler.step()
     return lrs







def 					__a   (		A    ,				A=10      ):






     '''simple docstring'''



     lowercase__				 =							[]
     for step in range(A      ):
          lrs.append(scheduler.get_lr()[0]      )
          scheduler.step()
          if step == num_steps // 2:
               with tempfile.TemporaryDirectory() as tmpdirname:
                    lowercase__				 =							os.path.join(A    ,				"schedule.bin"      )
                    torch.save(scheduler.state_dict()    ,				A      )

                    lowercase__				 =							torch.load(A      )
                    scheduler.load_state_dict(A      )
     return lrs






@require_torch
class    a__    (   unittest.TestCase	):


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



        self.assertEqual(len(_UpperCAmelCase  ),				len(_UpperCAmelCase  )  )
        for a, b in zip(_UpperCAmelCase,				_UpperCAmelCase  ):
             self.assertAlmostEqual(_UpperCAmelCase,				_UpperCAmelCase,				delta=_UpperCAmelCase  )


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



        lowercase__				 =							torch.tensor([0.1, -0.2, -0.1],				requires_grad=_UpperCAmelCase  )
        lowercase__				 =							torch.tensor([0.4, 0.2, -0.5]  )
        lowercase__				 =							nn.MSELoss()
        # No warmup, constant schedule, no gradient clipping
        lowercase__				 =							AdamW(params=[w],				lr=2E-1,				weight_decay=0.0  )
        for _ in range(100  ):
             lowercase__				 =							criterion(_UpperCAmelCase,				_UpperCAmelCase  )
             loss.backward()
             optimizer.step()
             w.grad.detach_()  # No zero_grad() function on simple tensors. we do it ourselves.
             w.grad.zero_()
        self.assertListAlmostEqual(w.tolist(),				[0.4, 0.2, -0.5],				tol=1E-2  )


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



        lowercase__				 =							torch.tensor([0.1, -0.2, -0.1],				requires_grad=_UpperCAmelCase  )
        lowercase__				 =							torch.tensor([0.4, 0.2, -0.5]  )
        lowercase__				 =							nn.MSELoss()
        # No warmup, constant schedule, no gradient clipping
        lowercase__				 =							Adafactor(
            params=[w],				lr=1E-2,				eps=(1E-30, 1E-3),				clip_threshold=1.0,				decay_rate=-0.8,				betaa=_UpperCAmelCase,				weight_decay=0.0,				relative_step=_UpperCAmelCase,				scale_parameter=_UpperCAmelCase,				warmup_init=_UpperCAmelCase,				)
        for _ in range(1000  ):
             lowercase__				 =							criterion(_UpperCAmelCase,				_UpperCAmelCase  )
             loss.backward()
             optimizer.step()
             w.grad.detach_()  # No zero_grad() function on simple tensors. we do it ourselves.
             w.grad.zero_()
        self.assertListAlmostEqual(w.tolist(),				[0.4, 0.2, -0.5],				tol=1E-2  )






@require_torch
class    a__    (   unittest.TestCase	):
   snake_case_							=      nn.Linear(50					,					50	) if is_torch_available() else None
   snake_case_							=      AdamW(m.parameters()					,					lr=10.0	) if is_torch_available() else None
   snake_case_							=      10


   def 	snake_case__	(     self,				_UpperCAmelCase,				_UpperCAmelCase,				_UpperCAmelCase,				_UpperCAmelCase=None  ):
        '''simple docstring'''



        self.assertEqual(len(_UpperCAmelCase  ),				len(_UpperCAmelCase  )  )
        for a, b in zip(_UpperCAmelCase,				_UpperCAmelCase  ):
             self.assertAlmostEqual(_UpperCAmelCase,				_UpperCAmelCase,				delta=_UpperCAmelCase,				msg=_UpperCAmelCase  )


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



        lowercase__				 =							{"num_warmup_steps": 2, "num_training_steps": 10}
        # schedulers doct format
        # function: (sched_args_dict, expected_learning_rates)
        lowercase__				 =							{
            get_constant_schedule: ({}, [10.0] * self.num_steps),
            get_constant_schedule_with_warmup: (
                {"num_warmup_steps": 4},
                [0.0, 2.5, 5.0, 7.5, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0],
            ),
            get_linear_schedule_with_warmup: (
                {**common_kwargs},
                [0.0, 5.0, 10.0, 8.75, 7.5, 6.25, 5.0, 3.75, 2.5, 1.25],
            ),
            get_cosine_schedule_with_warmup: (
                {**common_kwargs},
                [0.0, 5.0, 10.0, 9.61, 8.53, 6.91, 5.0, 3.08, 1.46, 0.38],
            ),
            get_cosine_with_hard_restarts_schedule_with_warmup: (
                {**common_kwargs, "num_cycles": 2},
                [0.0, 5.0, 10.0, 8.53, 5.0, 1.46, 10.0, 8.53, 5.0, 1.46],
            ),
            get_polynomial_decay_schedule_with_warmup: (
                {**common_kwargs, "power": 2.0, "lr_end": 1E-7},
                [0.0, 5.0, 10.0, 7.656, 5.625, 3.906, 2.5, 1.406, 0.625, 0.156],
            ),
            get_inverse_sqrt_schedule: (
                {"num_warmup_steps": 2},
                [0.0, 5.0, 10.0, 8.165, 7.071, 6.325, 5.774, 5.345, 5.0, 4.714],
            ),
        }

        for scheduler_func, data in scheds.items():
             lowercase__ ,						lowercase__				 =							data

             lowercase__				 =							scheduler_func(self.optimizer,				**_UpperCAmelCase  )
             self.assertEqual(len([scheduler.get_lr()[0]]  ),				1  )
             lowercase__				 =							unwrap_schedule(_UpperCAmelCase,				self.num_steps  )
             self.assertListAlmostEqual(
                 _UpperCAmelCase,				_UpperCAmelCase,				tol=1E-2,				msg=F'''failed for {scheduler_func} in normal scheduler''',				)

             lowercase__				 =							scheduler_func(self.optimizer,				**_UpperCAmelCase  )
             if scheduler_func.__name__ != "get_constant_schedule":
                  LambdaScheduleWrapper.wrap_scheduler(_UpperCAmelCase  )  # wrap to test picklability of the schedule
             lowercase__				 =							unwrap_and_save_reload_schedule(_UpperCAmelCase,				self.num_steps  )
             self.assertListEqual(_UpperCAmelCase,				_UpperCAmelCase,				msg=F'''failed for {scheduler_func} in save and reload'''  )






class    a__    :


   def __init__(     self,				_UpperCAmelCase  ):
        '''simple docstring'''



        lowercase__				 =							fn


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



        return self.fn(*_UpperCAmelCase,				**_UpperCAmelCase  )


   @classmethod
   def 	snake_case__	(     self,				_UpperCAmelCase  ):
        '''simple docstring'''



        lowercase__				 =							list(map(self,				scheduler.lr_lambdas  )  )





"""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)}')




