


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 				__lowerCamelCase						( UpperCAmelCase_						:		Union[str, Any] ,  UpperCAmelCase_						:		Optional[int]=10						):




      """simple docstring"""





      a						:Union[str, Any] 							=       []
      for _ in range(UpperCAmelCase_						):
            lrs.append(scheduler.get_lr()[0]						)
            scheduler.step()
      return lrs
def 				__lowerCamelCase						( UpperCAmelCase_						:		Optional[Any] ,  UpperCAmelCase_						:		Tuple=10						):




      """simple docstring"""





      a						:Union[str, Any] 							=       []
      for step in range(UpperCAmelCase_						):
            lrs.append(scheduler.get_lr()[0]						)
            scheduler.step()
            if step == num_steps // 2:
                  with tempfile.TemporaryDirectory() as tmpdirname:
                        a						:Any 							=       os.path.join(UpperCAmelCase_ ,  '''schedule.bin'''						)
                        torch.save(scheduler.state_dict() ,  UpperCAmelCase_						)

                        a						:Union[str, Any] 							=       torch.load(UpperCAmelCase_						)
                        scheduler.load_state_dict(UpperCAmelCase_						)
      return lrs







@require_torch
class 		_snake_case  (      unittest.TestCase							):




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




 def        SCREAMING_SNAKE_CASE__				(		self    ):
       a						:Tuple 							=       torch.tensor([0.1, -0.2, -0.1]					,  requires_grad=_lowerCamelCase    )
       a						:int 							=       torch.tensor([0.4, 0.2, -0.5]    )
       a						:List[str] 							=       nn.MSELoss()
       # No warmup, constant schedule, no gradient clipping
       a						:List[Any] 							=       AdamW(params=[w]					,  lr=2e-1					,  weight_decay=0.0    )
       for _ in range(100    ):
             a						:Optional[Any] 							=       criterion(_lowerCamelCase					,  _lowerCamelCase    )
             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        SCREAMING_SNAKE_CASE__				(		self    ):
       a						:Any 							=       torch.tensor([0.1, -0.2, -0.1]					,  requires_grad=_lowerCamelCase    )
       a						:Tuple 							=       torch.tensor([0.4, 0.2, -0.5]    )
       a						:Optional[Any] 							=       nn.MSELoss()
       # No warmup, constant schedule, no gradient clipping
       a						:Dict 							=       Adafactor(
           params=[w]					,  lr=1e-2					,  eps=(1e-30, 1e-3)					,  clip_threshold=1.0					,  decay_rate=-0.8					,  betaa=_lowerCamelCase					,  weight_decay=0.0					,  relative_step=_lowerCamelCase					,  scale_parameter=_lowerCamelCase					,  warmup_init=_lowerCamelCase					,  )
       for _ in range(1000    ):
             a						:Tuple 							=       criterion(_lowerCamelCase					,  _lowerCamelCase    )
             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 		_snake_case  (      unittest.TestCase							):
 SCREAMING_SNAKE_CASE__      =       nn.Linear(50						,    50							) if is_torch_available() else None
 SCREAMING_SNAKE_CASE__      =       AdamW(m.parameters()						,    lr=10.0							) if is_torch_available() else None
 SCREAMING_SNAKE_CASE__      =       10




 def        SCREAMING_SNAKE_CASE__				(		self					,  _lowerCamelCase					,  _lowerCamelCase					,  _lowerCamelCase					,  _lowerCamelCase=None    ):
       self.assertEqual(len(_lowerCamelCase    )					,  len(_lowerCamelCase    )    )
       for a, b in zip(_lowerCamelCase					,  _lowerCamelCase    ):
             self.assertAlmostEqual(_lowerCamelCase					,  _lowerCamelCase					,  delta=_lowerCamelCase					,  msg=_lowerCamelCase    )




 def        SCREAMING_SNAKE_CASE__				(		self    ):
       a						:Any 							=       {'''num_warmup_steps''': 2, '''num_training_steps''': 10}
       # schedulers doct format
       # function: (sched_args_dict, expected_learning_rates)
       a						:Optional[Any] 							=       {
           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():
             a							,				a						:Optional[Any] 							=       data

             a						:Optional[int] 							=       scheduler_func(self.optimizer					,  **_lowerCamelCase    )
             self.assertEqual(len([scheduler.get_lr()[0]]    )					,  1    )
             a						:Union[str, Any] 							=       unwrap_schedule(_lowerCamelCase					,  self.num_steps    )
             self.assertListAlmostEqual(
                 _lowerCamelCase					,  _lowerCamelCase					,  tol=1e-2					,  msg=F'''failed for {scheduler_func} in normal scheduler'''					,  )

             a						:Union[str, Any] 							=       scheduler_func(self.optimizer					,  **_lowerCamelCase    )
             if scheduler_func.__name__ != "get_constant_schedule":
                   LambdaScheduleWrapper.wrap_scheduler(_lowerCamelCase    )  # wrap to test picklability of the schedule
             a						:Dict 							=       unwrap_and_save_reload_schedule(_lowerCamelCase					,  self.num_steps    )
             self.assertListEqual(_lowerCamelCase					,  _lowerCamelCase					,  msg=F'''failed for {scheduler_func} in save and reload'''    )







class 		_snake_case  :




 def __init__(		self					,  _lowerCamelCase    ):
       a						:str 							=       fn




 def __call__(		self					,  *_lowerCamelCase					,  **_lowerCamelCase    ):
       return self.fn(*_lowerCamelCase					,  **_lowerCamelCase    )




 @classmethod
 def        SCREAMING_SNAKE_CASE__				(		self					,  _lowerCamelCase    ):
       a						:List[str] 							=       list(map(self					,  scheduler.lr_lambdas    )    )









def 				__lowerCamelCase						( UpperCAmelCase_						:		int = 100_0000						):




      """simple docstring"""





      a						:Any 							=       set(range(3 ,  UpperCAmelCase_ ,  2						)						)
      primes.add(2						)
      for p in range(3 ,  UpperCAmelCase_ ,  2						):
            if p not in primes:
                  continue
            primes.difference_update(set(range(p * p ,  UpperCAmelCase_ ,  UpperCAmelCase_						)						)						)

      a						:Union[str, Any] 							=       [float(UpperCAmelCase_						) for n in range(limit + 1						)]

      for p in primes:
            for n in range(UpperCAmelCase_ ,  limit + 1 ,  UpperCAmelCase_						):
                  phi[n] *= 1 - 1 / p

      return int(sum(phi[2:]						)						)


if __name__ == "__main__":
     print(F"""{solution() = }""")





