






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


a						:			Optional[int]     	=					logging.get_logger(__name__)
class        a       (					lowercase__  ):



      """simple docstring"""


      a    :					Tuple							=      'linear'
      a    :					int							=      'cosine'
      a    :					Optional[Any]							=      'cosine_with_restarts'
      a    :					Dict							=      'polynomial'
      a    :					Tuple							=      'constant'
      a    :					Dict							=      'constant_with_warmup'
      a    :					Any							=      'piecewise_constant'






def 							lowerCamelCase__ (       __lowerCamelCase     :	Optimizer    ,						__lowerCamelCase     :	int = -1						):
  return LambdaLR(__lowerCamelCase    ,						lambda __lowerCamelCase						: 1    ,						last_epoch=__lowerCamelCase						)






def 							lowerCamelCase__ (       __lowerCamelCase     :	Optimizer    ,						__lowerCamelCase     :	int    ,						__lowerCamelCase     :	int = -1						):

  def lr_lambda(__lowerCamelCase     :	int						):
    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 							lowerCamelCase__ (       __lowerCamelCase     :	Optimizer    ,						__lowerCamelCase     :	str    ,						__lowerCamelCase     :	int = -1						):
  __UpperCAmelCase				:      Union[str, Any]	 =    {}
  __UpperCAmelCase				:      Tuple	 =    step_rules.split(""","""						)
  for rule_str in rule_list[:-1]:
    __UpperCAmelCase ,					__UpperCAmelCase				:      List[str]	 =    rule_str.split(""":"""						)
    __UpperCAmelCase				:      Any	 =    int(__lowerCamelCase						)
    __UpperCAmelCase				:      List[str]	 =    float(__lowerCamelCase						)
    __UpperCAmelCase				:      int	 =    value
  __UpperCAmelCase				:      Any	 =    float(rule_list[-1]						)

  def create_rules_function(__lowerCamelCase     :	Dict    ,						__lowerCamelCase     :	List[Any]						):
    def rule_func(__lowerCamelCase     :	int						) -> float:
      __UpperCAmelCase				:      Tuple	 =    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

  __UpperCAmelCase				:      str	 =    create_rules_function(__lowerCamelCase    ,						__lowerCamelCase						)

  return LambdaLR(__lowerCamelCase    ,						__lowerCamelCase    ,						last_epoch=__lowerCamelCase						)






def 							lowerCamelCase__ (       __lowerCamelCase     :	Optional[Any]    ,						__lowerCamelCase     :	str    ,						__lowerCamelCase     :	Tuple    ,						__lowerCamelCase     :	List[Any]=-1						):

  def lr_lambda(__lowerCamelCase     :	int						):
    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 							lowerCamelCase__ (       __lowerCamelCase     :	Optimizer    ,						__lowerCamelCase     :	int    ,						__lowerCamelCase     :	int    ,						__lowerCamelCase     :	float = 0.5    ,						__lowerCamelCase     :	int = -1						):

  def lr_lambda(__lowerCamelCase     :	Dict						):
    if current_step < num_warmup_steps:
      return float(__lowerCamelCase						) / float(max(1    ,						__lowerCamelCase						)						)
    __UpperCAmelCase				:      Tuple	 =    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 							lowerCamelCase__ (       __lowerCamelCase     :	Optimizer    ,						__lowerCamelCase     :	int    ,						__lowerCamelCase     :	int    ,						__lowerCamelCase     :	int = 1    ,						__lowerCamelCase     :	int = -1						):

  def lr_lambda(__lowerCamelCase     :	Union[str, Any]						):
    if current_step < num_warmup_steps:
      return float(__lowerCamelCase						) / float(max(1    ,						__lowerCamelCase						)						)
    __UpperCAmelCase				:      Union[str, Any]	 =    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 							lowerCamelCase__ (       __lowerCamelCase     :	str    ,						__lowerCamelCase     :	List[str]    ,						__lowerCamelCase     :	Tuple    ,						__lowerCamelCase     :	List[Any]=1E-7    ,						__lowerCamelCase     :	List[Any]=1.0    ,						__lowerCamelCase     :	int=-1						):
  __UpperCAmelCase				:      Tuple	 =    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     :	int						):
    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:
      __UpperCAmelCase				:      Optional[Any]	 =    lr_init - lr_end
      __UpperCAmelCase				:      Union[str, Any]	 =    num_training_steps - num_warmup_steps
      __UpperCAmelCase				:      int	 =    1 - (current_step - num_warmup_steps) / decay_steps
      __UpperCAmelCase				:      Optional[int]	 =    lr_range * pct_remaining**power + lr_end
      return decay / lr_init  # as LambdaLR multiplies by lr_init

  return LambdaLR(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase						)


a						:			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 							lowerCamelCase__ (       __lowerCamelCase     :	Union[str, SchedulerType]    ,						__lowerCamelCase     :	Optimizer    ,						__lowerCamelCase     :	Optional[str] = None    ,						__lowerCamelCase     :	Optional[int] = None    ,						__lowerCamelCase     :	Optional[int] = None    ,						__lowerCamelCase     :	int = 1    ,						__lowerCamelCase     :	float = 1.0    ,						__lowerCamelCase     :	int = -1    ,						):
  __UpperCAmelCase				:      Union[str, Any]	 =    SchedulerType(__lowerCamelCase						)
  __UpperCAmelCase				:      int	 =    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						)










def     a     (		lowerCamelCase_						,  lowerCamelCase_							):






				'''simple docstring'''
				lowercase__  					=     len(lowerCamelCase_							)
				lowercase__  					=     [[False] * (required_sum + 1) for _ in range(arr_len + 1							)]

				# for each arr value, a sum of zero(0) can be formed by not taking any element
				# hence True/1
				for i in range(arr_len + 1							):
								lowercase__  					=     True

				# sum is not zero and set is empty then false
				for i in range(1						,  required_sum + 1							):
								lowercase__  					=     False

				for i in range(1						,  arr_len + 1							):
								for j in range(1						,  required_sum + 1							):
												if arr[i - 1] > j:
																lowercase__  					=     subset[i - 1][j]
												if arr[i - 1] <= j:
																lowercase__  					=     subset[i - 1][j] or subset[i - 1][j - arr[i - 1]]

				return subset[arr_len][required_sum]


if __name__ == "__main__":
							import doctest

							doctest.testmod()




