

"""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_	:    int            =      logging.get_logger(__name__)





class   UpperCamelCase_ (       a_  ):
  _A       :					Tuple				=	'linear'
  _A       :					Tuple				=	'cosine'
  _A       :					Union[str, Any]				=	'cosine_with_restarts'
  _A       :					Optional[Any]				=	'polynomial'
  _A       :					List[Any]				=	'constant'
  _A       :					List[str]				=	'constant_with_warmup'
  _A       :					List[str]				=	'piecewise_constant'






def       _lowerCAmelCase       (      lowerCAmelCase	,      lowerCAmelCase = -1		):







       '''simple docstring'''
       return LambdaLR(lowerCAmelCase	,      lambda lowerCAmelCase		: 1	,      last_epoch=lowerCAmelCase		)






def       _lowerCAmelCase       (      lowerCAmelCase	,      lowerCAmelCase	,      lowerCAmelCase = -1		):







       '''simple docstring'''

       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       _lowerCAmelCase       (      lowerCAmelCase	,      lowerCAmelCase	,      lowerCAmelCase = -1		):







       '''simple docstring'''
       UpperCAmelCase	    =			{}
       UpperCAmelCase	    =			step_rules.split(""","""		)
       for rule_str in rule_list[:-1]:
              UpperCAmelCase    ,       UpperCAmelCase	    =			rule_str.split(""":"""		)
              UpperCAmelCase	    =			int(lowerCAmelCase		)
              UpperCAmelCase	    =			float(lowerCAmelCase		)
              UpperCAmelCase	    =			value
       UpperCAmelCase	    =			float(rule_list[-1]		)

       def create_rules_function(lowerCAmelCase	,      lowerCAmelCase		):
              def rule_func(lowerCAmelCase		) -> float:
                     UpperCAmelCase	    =			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	    =			create_rules_function(lowerCAmelCase	,      lowerCAmelCase		)

       return LambdaLR(lowerCAmelCase	,      lowerCAmelCase	,      last_epoch=lowerCAmelCase		)






def       _lowerCAmelCase       (      lowerCAmelCase	,      lowerCAmelCase	,      lowerCAmelCase	,      lowerCAmelCase=-1		):







       '''simple docstring'''

       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       _lowerCAmelCase       (      lowerCAmelCase	,      lowerCAmelCase	,      lowerCAmelCase	,      lowerCAmelCase = 0.5	,      lowerCAmelCase = -1		):







       '''simple docstring'''

       def lr_lambda(lowerCAmelCase		):
              if current_step < num_warmup_steps:
                     return float(lowerCAmelCase		) / float(max(1	,      lowerCAmelCase		)		)
              UpperCAmelCase	    =			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	,      lowerCAmelCase	,      lowerCAmelCase	,      lowerCAmelCase = 1	,      lowerCAmelCase = -1		):







       '''simple docstring'''

       def lr_lambda(lowerCAmelCase		):
              if current_step < num_warmup_steps:
                     return float(lowerCAmelCase		) / float(max(1	,      lowerCAmelCase		)		)
              UpperCAmelCase	    =			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	,      lowerCAmelCase	,      lowerCAmelCase	,      lowerCAmelCase=1e-7	,      lowerCAmelCase=1.0	,      lowerCAmelCase=-1		):







       '''simple docstring'''
       UpperCAmelCase	    =			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:
                     UpperCAmelCase	    =			lr_init - lr_end
                     UpperCAmelCase	    =			num_training_steps - num_warmup_steps
                     UpperCAmelCase	    =			1 - (current_step - num_warmup_steps) / decay_steps
                     UpperCAmelCase	    =			lr_range * pct_remaining**power + lr_end
                     return decay / lr_init  # as LambdaLR multiplies by lr_init

       return LambdaLR(lowerCAmelCase	,      lowerCAmelCase	,      lowerCAmelCase		)


lowerCAmelCase_	:    Union[str, 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       _lowerCAmelCase       (      lowerCAmelCase	,      lowerCAmelCase	,      lowerCAmelCase = None	,      lowerCAmelCase = None	,      lowerCAmelCase = None	,      lowerCAmelCase = 1	,      lowerCAmelCase = 1.0	,      lowerCAmelCase = -1	,      ):







       '''simple docstring'''
       UpperCAmelCase	    =			SchedulerType(lowerCAmelCase		)
       UpperCAmelCase	    =			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		)








"""simple docstring"""







def       _lowerCAmelCase       (      lowerCAmelCase		):







       '''simple docstring'''
       UpperCAmelCase	    =			0
       UpperCAmelCase	    =			len(lowerCAmelCase		)

       for i in range(n - 1		):
              for j in range(i + 1	,      lowerCAmelCase		):
                     if arr[i] > arr[j]:
                            num_inversions += 1

       return num_inversions






def       _lowerCAmelCase       (      lowerCAmelCase		):







       '''simple docstring'''
       if len(lowerCAmelCase		) <= 1:
              return arr, 0
       UpperCAmelCase	    =			len(lowerCAmelCase		) // 2
       UpperCAmelCase	    =			arr[0:mid]
       UpperCAmelCase	    =			arr[mid:]

       UpperCAmelCase    ,       UpperCAmelCase	    =			count_inversions_recursive(lowerCAmelCase		)
       UpperCAmelCase    ,       UpperCAmelCase	    =			count_inversions_recursive(lowerCAmelCase		)
       UpperCAmelCase    ,       UpperCAmelCase	    =			_count_cross_inversions(lowerCAmelCase	,      lowerCAmelCase		)

       UpperCAmelCase	    =			inversion_p + inversions_q + cross_inversions
       return c, num_inversions






def       _lowerCAmelCase       (      lowerCAmelCase	,      lowerCAmelCase		):







       '''simple docstring'''
       UpperCAmelCase	    =			[]
       UpperCAmelCase	    =			UpperCAmelCase	    =			UpperCAmelCase	    =			0
       while i < len(lowerCAmelCase		) and j < len(lowerCAmelCase		):
              if p[i] > q[j]:
                     # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
                     # These are all inversions. The claim emerges from the
                     # property that P is sorted.
                     num_inversion += len(lowerCAmelCase		) - i
                     r.append(q[j]		)
                     j += 1
              else:
                     r.append(p[i]		)
                     i += 1

       if i < len(lowerCAmelCase		):
              r.extend(p[i:]		)
       else:
              r.extend(q[j:]		)

       return r, num_inversion






def       _lowerCAmelCase       (      ):







       '''simple docstring'''
       UpperCAmelCase	    =			[10, 2, 1, 5, 5, 2, 11]

       # this arr has 8 inversions:
       # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

       UpperCAmelCase	    =			count_inversions_bf(lowerCAmelCase		)
       UpperCAmelCase    ,       UpperCAmelCase	    =			count_inversions_recursive(lowerCAmelCase		)

       assert num_inversions_bf == num_inversions_recursive == 8

       print("""number of inversions = """	,      lowerCAmelCase		)

       # testing an array with zero inversion (a sorted arr_1)

       arr_a.sort()
       UpperCAmelCase	    =			count_inversions_bf(lowerCAmelCase		)
       UpperCAmelCase    ,       UpperCAmelCase	    =			count_inversions_recursive(lowerCAmelCase		)

       assert num_inversions_bf == num_inversions_recursive == 0
       print("""number of inversions = """	,      lowerCAmelCase		)

       # an empty list should also have zero inversions
       UpperCAmelCase	    =			[]
       UpperCAmelCase	    =			count_inversions_bf(lowerCAmelCase		)
       UpperCAmelCase    ,       UpperCAmelCase	    =			count_inversions_recursive(lowerCAmelCase		)

       assert num_inversions_bf == num_inversions_recursive == 0
       print("""number of inversions = """	,      lowerCAmelCase		)


if __name__ == "__main__":
 main()
