





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


SCREAMING_SNAKE_CASE__       :			Union[str, Any]			      =						logging.get_logger(__name__)







class   __lowerCAmelCase			(					_UpperCamelCase  ):
   _UpperCamelCase :						List[Any]     		=				"""linear"""
   _UpperCamelCase :						List[Any]     		=				"""cosine"""
   _UpperCamelCase :						Tuple     		=				"""cosine_with_restarts"""
   _UpperCamelCase :						Optional[Any]     		=				"""polynomial"""
   _UpperCamelCase :						int     		=				"""constant"""
   _UpperCamelCase :						Optional[int]     		=				"""constant_with_warmup"""
   _UpperCamelCase :						Optional[int]     		=				"""piecewise_constant"""







def       _A  (      lowerCamelCase							, lowerCamelCase = -1   ):
   return LambdaLR(lowerCamelCase							, lambda lowerCamelCase   : 1							, last_epoch=lowerCamelCase   )






def       _A  (      lowerCamelCase							, lowerCamelCase							, lowerCamelCase = -1   ):

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

   return LambdaLR(lowerCamelCase							, lowerCamelCase							, last_epoch=lowerCamelCase   )






def       _A  (      lowerCamelCase							, lowerCamelCase							, lowerCamelCase = -1   ):
   a__	:						Tuple      		=  {}
   a__	:						str      		=  step_rules.split(","   )
   for rule_str in rule_list[:-1]:
      a__		,     a__	:						Dict      		=  rule_str.split(":"   )
      a__	:						List[Any]      		=  int(lowerCamelCase   )
      a__	:						Optional[int]      		=  float(lowerCamelCase   )
      a__	:						List[str]      		=  value
   a__	:						int      		=  float(rule_list[-1]   )

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

      return rule_func

   a__	:						int      		=  create_rules_function(lowerCamelCase							, lowerCamelCase   )

   return LambdaLR(lowerCamelCase							, lowerCamelCase							, last_epoch=lowerCamelCase   )






def       _A  (      lowerCamelCase							, lowerCamelCase							, lowerCamelCase							, lowerCamelCase=-1   ):

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

   return LambdaLR(lowerCamelCase							, lowerCamelCase							, lowerCamelCase   )






def       _A  (      lowerCamelCase							, lowerCamelCase							, lowerCamelCase							, lowerCamelCase = 0.5							, lowerCamelCase = -1   ):

   def lr_lambda(lowerCamelCase   ):
      if current_step < num_warmup_steps:
         return float(lowerCamelCase   ) / float(max(1							, lowerCamelCase   )   )
      a__	:						Optional[Any]      		=  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(lowerCamelCase   ) * 2.0 * progress   ))   )

   return LambdaLR(lowerCamelCase							, lowerCamelCase							, lowerCamelCase   )






def       _A  (      lowerCamelCase							, lowerCamelCase							, lowerCamelCase							, lowerCamelCase = 1							, lowerCamelCase = -1   ):

   def lr_lambda(lowerCamelCase   ):
      if current_step < num_warmup_steps:
         return float(lowerCamelCase   ) / float(max(1							, lowerCamelCase   )   )
      a__	:						List[str]      		=  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(lowerCamelCase   ) * progress) % 1.0)   ))   )

   return LambdaLR(lowerCamelCase							, lowerCamelCase							, lowerCamelCase   )






def       _A  (      lowerCamelCase							, lowerCamelCase							, lowerCamelCase							, lowerCamelCase=1E-7							, lowerCamelCase=1.0							, lowerCamelCase=-1   ):
   a__	:						Optional[Any]      		=  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(lowerCamelCase   ):
      if current_step < num_warmup_steps:
         return float(lowerCamelCase   ) / float(max(1							, lowerCamelCase   )   )
      elif current_step > num_training_steps:
         return lr_end / lr_init  # as LambdaLR multiplies by lr_init
      else:
         a__	:						Any      		=  lr_init - lr_end
         a__	:						List[str]      		=  num_training_steps - num_warmup_steps
         a__	:						Optional[Any]      		=  1 - (current_step - num_warmup_steps) / decay_steps
         a__	:						Optional[int]      		=  lr_range * pct_remaining**power + lr_end
         return decay / lr_init  # as LambdaLR multiplies by lr_init

   return LambdaLR(lowerCamelCase							, lowerCamelCase							, lowerCamelCase   )


SCREAMING_SNAKE_CASE__       :			Optional[int]			      =						{
    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  (      lowerCamelCase							, lowerCamelCase							, lowerCamelCase = None							, lowerCamelCase = None							, lowerCamelCase = None							, lowerCamelCase = 1							, lowerCamelCase = 1.0							, lowerCamelCase = -1							, ):
   a__	:						List[Any]      		=  SchedulerType(lowerCamelCase   )
   a__	:						Dict      		=  TYPE_TO_SCHEDULER_FUNCTION[name]
   if name == SchedulerType.CONSTANT:
      return schedule_func(lowerCamelCase							, last_epoch=lowerCamelCase   )

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

   # 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(lowerCamelCase							, num_warmup_steps=lowerCamelCase							, last_epoch=lowerCamelCase   )

   # 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(
          lowerCamelCase							, num_warmup_steps=lowerCamelCase							, num_training_steps=lowerCamelCase							, num_cycles=lowerCamelCase							, last_epoch=lowerCamelCase							, )

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

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








from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean






def       _A  (      lowerCamelCase   ):

   # A local function to see if a dot lands in the circle.
   def is_in_circle(lowerCamelCase							, lowerCamelCase   ) -> bool:
      a__	:						Any      		=  sqrt((x**2) + (y**2)   )
      # Our circle has a radius of 1, so a distance
      # greater than 1 would land outside the circle.
      return distance_from_centre <= 1

   # The proportion of guesses that landed in the circle
   a__	:						Union[str, Any]      		=  mean(
       int(is_in_circle(uniform(-1.0							, 1.0   )							, uniform(-1.0							, 1.0   )   )   )
       for _ in range(lowerCamelCase   )   )
   # The ratio of the area for circle to square is pi/4.
   a__	:						Any      		=  proportion * 4
   print(F"""The estimated value of pi is {pi_estimate}"""   )
   print(F"""The numpy value of pi is {pi}"""   )
   print(F"""The total error is {abs(pi - pi_estimate   )}"""   )






def       _A  (      lowerCamelCase							, lowerCamelCase							, lowerCamelCase = 0.0							, lowerCamelCase = 1.0							, ):
   return mean(
       function_to_integrate(uniform(lowerCamelCase							, lowerCamelCase   )   ) for _ in range(lowerCamelCase   )   ) * (max_value - min_value)






def       _A  (      lowerCamelCase							, lowerCamelCase = 0.0							, lowerCamelCase = 1.0   ):

   def identity_function(lowerCamelCase   ) -> float:
      return x

   a__	:						int      		=  area_under_curve_estimator(
       lowerCamelCase							, lowerCamelCase							, lowerCamelCase							, lowerCamelCase   )
   a__	:						int      		=  (max_value * max_value - min_value * min_value) / 2

   print("******************"   )
   print(F"""Estimating area under y=x where x varies from {min_value} to {max_value}"""   )
   print(F"""Estimated value is {estimated_value}"""   )
   print(F"""Expected value is {expected_value}"""   )
   print(F"""Total error is {abs(estimated_value - expected_value   )}"""   )
   print("******************"   )






def       _A  (      lowerCamelCase   ):

   def function_to_integrate(lowerCamelCase   ) -> float:
      return sqrt(4.0 - x * x   )

   a__	:						int      		=  area_under_curve_estimator(
       lowerCamelCase							, lowerCamelCase							, 0.0							, 2.0   )

   print("******************"   )
   print("Estimating pi using area_under_curve_estimator"   )
   print(F"""Estimated value is {estimated_value}"""   )
   print(F"""Expected value is {pi}"""   )
   print(F"""Total error is {abs(estimated_value - pi   )}"""   )
   print("******************"   )


if __name__ == "__main__":
  import doctest

  doctest.testmod()

