"""simple docstring"""


import math
from enum import Enum
from typing import Optional, Union

from torch.optim import Optimizer
from torch.optim.lr_scheduler import LambdaLR

from .utils import logging


lowerCAmelCase_:					Tuple     =					logging.get_logger(__name__)






class    a__    (   a__	):
   snake_case_							=      "linear"
   snake_case_							=      "cosine"
   snake_case_							=      "cosine_with_restarts"
   snake_case_							=      "polynomial"
   snake_case_							=      "constant"
   snake_case_							=      "constant_with_warmup"
   snake_case_							=      "piecewise_constant"







def 					__a   (		A    ,				A = -1      ):






     '''simple docstring'''



     return LambdaLR(A    ,				lambda A      : 1    ,				last_epoch=A      )







def 					__a   (		A    ,				A    ,				A = -1      ):






     '''simple docstring'''



     def lr_lambda(A      ):
          if current_step < num_warmup_steps:
               return float(A      ) / float(max(1.0    ,				A      )      )
          return 1.0

     return LambdaLR(A    ,				A    ,				last_epoch=A      )







def 					__a   (		A    ,				A    ,				A = -1      ):






     '''simple docstring'''



     lowercase__				 =							{}
     lowercase__				 =							step_rules.split(","      )
     for rule_str in rule_list[:-1]:
          lowercase__ ,						lowercase__				 =							rule_str.split(":"      )
          lowercase__				 =							int(A      )
          lowercase__				 =							float(A      )
          lowercase__				 =							value
     lowercase__				 =							float(rule_list[-1]      )

     def create_rules_function(A    ,				A      ):
          def rule_func(A      ) -> float:
               lowercase__				 =							sorted(rules_dict.keys()      )
               for i, sorted_step in enumerate(A      ):
                    if steps < sorted_step:
                         return rules_dict[sorted_steps[i]]
               return last_lr_multiple

          return rule_func

     lowercase__				 =							create_rules_function(A    ,				A      )

     return LambdaLR(A    ,				A    ,				last_epoch=A      )







def 					__a   (		A    ,				A    ,				A    ,				A=-1      ):






     '''simple docstring'''



     def lr_lambda(A      ):
          if current_step < num_warmup_steps:
               return float(A      ) / float(max(1    ,				A      )      )
          return max(
              0.0    ,				float(num_training_steps - current_step      ) / float(max(1    ,				num_training_steps - num_warmup_steps      )      )      )

     return LambdaLR(A    ,				A    ,				A      )







def 					__a   (		A    ,				A    ,				A    ,				A = 0.5    ,				A = -1      ):






     '''simple docstring'''



     def lr_lambda(A      ):
          if current_step < num_warmup_steps:
               return float(A      ) / float(max(1    ,				A      )      )
          lowercase__				 =							float(current_step - num_warmup_steps      ) / float(max(1    ,				num_training_steps - num_warmup_steps      )      )
          return max(0.0    ,				0.5 * (1.0 + math.cos(math.pi * float(A      ) * 2.0 * progress      ))      )

     return LambdaLR(A    ,				A    ,				A      )







def 					__a   (		A    ,				A    ,				A    ,				A = 1    ,				A = -1      ):






     '''simple docstring'''



     def lr_lambda(A      ):
          if current_step < num_warmup_steps:
               return float(A      ) / float(max(1    ,				A      )      )
          lowercase__				 =							float(current_step - num_warmup_steps      ) / float(max(1    ,				num_training_steps - num_warmup_steps      )      )
          if progress >= 1.0:
               return 0.0
          return max(0.0    ,				0.5 * (1.0 + math.cos(math.pi * ((float(A      ) * progress) % 1.0)      ))      )

     return LambdaLR(A    ,				A    ,				A      )







def 					__a   (		A    ,				A    ,				A    ,				A=1e-7    ,				A=1.0    ,				A=-1      ):






     '''simple docstring'''



     lowercase__				 =							optimizer.defaults["lr"]
     if not (lr_init > lr_end):
          raise ValueError(f'''lr_end ({lr_end}) must be be smaller than initial lr ({lr_init})'''      )

     def lr_lambda(A      ):
          if current_step < num_warmup_steps:
               return float(A      ) / float(max(1    ,				A      )      )
          elif current_step > num_training_steps:
               return lr_end / lr_init  # as LambdaLR multiplies by lr_init
          else:
               lowercase__				 =							lr_init - lr_end
               lowercase__				 =							num_training_steps - num_warmup_steps
               lowercase__				 =							1 - (current_step - num_warmup_steps) / decay_steps
               lowercase__				 =							lr_range * pct_remaining**power + lr_end
               return decay / lr_init  # as LambdaLR multiplies by lr_init

     return LambdaLR(A    ,				A    ,				A      )


lowerCAmelCase_:					Optional[Any]     =					{
    SchedulerType.LINEAR: get_linear_schedule_with_warmup,
    SchedulerType.COSINE: get_cosine_schedule_with_warmup,
    SchedulerType.COSINE_WITH_RESTARTS: get_cosine_with_hard_restarts_schedule_with_warmup,
    SchedulerType.POLYNOMIAL: get_polynomial_decay_schedule_with_warmup,
    SchedulerType.CONSTANT: get_constant_schedule,
    SchedulerType.CONSTANT_WITH_WARMUP: get_constant_schedule_with_warmup,
    SchedulerType.PIECEWISE_CONSTANT: get_piecewise_constant_schedule,
}







def 					__a   (		A    ,				A    ,				A = None    ,				A = None    ,				A = None    ,				A = 1    ,				A = 1.0    ,				A = -1    ,				):






     '''simple docstring'''



     lowercase__				 =							SchedulerType(A      )
     lowercase__				 =							TYPE_TO_SCHEDULER_FUNCTION[name]
     if name == SchedulerType.CONSTANT:
          return schedule_func(A    ,				last_epoch=A      )

     if name == SchedulerType.PIECEWISE_CONSTANT:
          return schedule_func(A    ,				step_rules=A    ,				last_epoch=A      )

     # All other schedulers require `num_warmup_steps`
     if num_warmup_steps is None:
          raise ValueError(f'''{name} requires `num_warmup_steps`, please provide that argument.'''      )

     if name == SchedulerType.CONSTANT_WITH_WARMUP:
          return schedule_func(A    ,				num_warmup_steps=A    ,				last_epoch=A      )

     # All other schedulers require `num_training_steps`
     if num_training_steps is None:
          raise ValueError(f'''{name} requires `num_training_steps`, please provide that argument.'''      )

     if name == SchedulerType.COSINE_WITH_RESTARTS:
          return schedule_func(
              A    ,				num_warmup_steps=A    ,				num_training_steps=A    ,				num_cycles=A    ,				last_epoch=A    ,				)

     if name == SchedulerType.POLYNOMIAL:
          return schedule_func(
              A    ,				num_warmup_steps=A    ,				num_training_steps=A    ,				power=A    ,				last_epoch=A    ,				)

     return schedule_func(
         A    ,				num_warmup_steps=A    ,				num_training_steps=A    ,				last_epoch=A      )





"""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)}')




