


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


UpperCAmelCase      =   logging.get_logger(__name__)







class lowerCAmelCase_						(			lowerCamelCase__	):

 '''simple docstring'''

 __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 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE = -1 )->  Tuple:




      """simple docstring"""

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






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE = -1 )->  Dict:




      """simple docstring"""

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

      return LambdaLR(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , last_epoch=SCREAMING_SNAKE_CASE )






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE = -1 )->  List[Any]:




      """simple docstring"""

      snake_case_	=				{}
      snake_case_	=				step_rules.split(''',''' )
      for rule_str in rule_list[:-1]:
            snake_case_	,   snake_case_	=				rule_str.split(''':''' )
            snake_case_	=				int(SCREAMING_SNAKE_CASE )
            snake_case_	=				float(SCREAMING_SNAKE_CASE )
            snake_case_	=				value
      snake_case_	=				float(rule_list[-1] )

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

            return rule_func

      snake_case_	=				create_rules_function(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )

      return LambdaLR(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , last_epoch=SCREAMING_SNAKE_CASE )






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE=-1 )->  str:




      """simple docstring"""

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

      return LambdaLR(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE = 0.5 , SCREAMING_SNAKE_CASE = -1 )->  Optional[Any]:




      """simple docstring"""

      def lr_lambda(SCREAMING_SNAKE_CASE ):
            if current_step < num_warmup_steps:
                  return float(SCREAMING_SNAKE_CASE ) / float(max(1 , SCREAMING_SNAKE_CASE ) )
            snake_case_	=				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(SCREAMING_SNAKE_CASE ) * 2.0 * progress )) )

      return LambdaLR(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE = 1 , SCREAMING_SNAKE_CASE = -1 )->  List[str]:




      """simple docstring"""

      def lr_lambda(SCREAMING_SNAKE_CASE ):
            if current_step < num_warmup_steps:
                  return float(SCREAMING_SNAKE_CASE ) / float(max(1 , SCREAMING_SNAKE_CASE ) )
            snake_case_	=				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(SCREAMING_SNAKE_CASE ) * progress) % 1.0) )) )

      return LambdaLR(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE=1E-7 , SCREAMING_SNAKE_CASE=1.0 , SCREAMING_SNAKE_CASE=-1 )->  Dict:




      """simple docstring"""

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

      return LambdaLR(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )


UpperCAmelCase      =   {
    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 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE = None , SCREAMING_SNAKE_CASE = None , SCREAMING_SNAKE_CASE = None , SCREAMING_SNAKE_CASE = 1 , SCREAMING_SNAKE_CASE = 1.0 , SCREAMING_SNAKE_CASE = -1 , )->  Union[str, Any]:




      """simple docstring"""

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

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

      # 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(SCREAMING_SNAKE_CASE , num_warmup_steps=SCREAMING_SNAKE_CASE , last_epoch=SCREAMING_SNAKE_CASE )

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

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

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



def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )->  int:




      """simple docstring"""

      return x if y == 0 else greatest_common_divisor(SCREAMING_SNAKE_CASE , x % y )






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )->  int:




      """simple docstring"""

      return (x * y) // greatest_common_divisor(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE = 20 )->  int:




      """simple docstring"""

      snake_case_	=				1
      for i in range(1 , n + 1 ):
            snake_case_	=				lcm(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )
      return g


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