

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__      		=			logging.get_logger(__name__)






class     lowercase_			(_UpperCAmelCase   ):




  """simple docstring"""




  SCREAMING_SNAKE_CASE					:						Union[str, Any]           =    'linear'
  SCREAMING_SNAKE_CASE					:						List[Any]           =    'cosine'
  SCREAMING_SNAKE_CASE					:						List[Any]           =    'cosine_with_restarts'
  SCREAMING_SNAKE_CASE					:						Union[str, Any]           =    'polynomial'
  SCREAMING_SNAKE_CASE					:						Any           =    'constant'
  SCREAMING_SNAKE_CASE					:						str           =    'constant_with_warmup'
  SCREAMING_SNAKE_CASE					:						Any           =    'piecewise_constant'


def 	_A  (					A__  ,       A__ = -1   ):






 """simple docstring"""



 return LambdaLR(UpperCAmelCase__  ,       lambda A__   : 1  ,       last_epoch=UpperCAmelCase__   )


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






 """simple docstring"""



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

 return LambdaLR(UpperCAmelCase__  ,       UpperCAmelCase__  ,       last_epoch=UpperCAmelCase__   )


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






 """simple docstring"""



 __lowercase													=				{}
 __lowercase													=				step_rules.split(''','''   )
 for rule_str in rule_list[:-1]:
  __lowercase													=				rule_str.split(''':'''   )
  __lowercase													=				int(UpperCAmelCase__   )
  __lowercase													=				float(UpperCAmelCase__   )
  __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(UpperCAmelCase__   ):
    if steps < sorted_step:
     return rules_dict[sorted_steps[i]]
   return last_lr_multiple

  return rule_func

 __lowercase													=				create_rules_function(UpperCAmelCase__  ,       UpperCAmelCase__   )

 return LambdaLR(UpperCAmelCase__  ,       UpperCAmelCase__  ,       last_epoch=UpperCAmelCase__   )


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






 """simple docstring"""



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

 return LambdaLR(UpperCAmelCase__  ,       UpperCAmelCase__  ,       UpperCAmelCase__   )


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






 """simple docstring"""



 def lr_lambda(A__   ):
  if current_step < num_warmup_steps:
   return float(UpperCAmelCase__   ) / float(max(1  ,       UpperCAmelCase__   )   )
  __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(UpperCAmelCase__   ) * 2.0 * progress   ))   )

 return LambdaLR(UpperCAmelCase__  ,       UpperCAmelCase__  ,       UpperCAmelCase__   )


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






 """simple docstring"""



 def lr_lambda(A__   ):
  if current_step < num_warmup_steps:
   return float(UpperCAmelCase__   ) / float(max(1  ,       UpperCAmelCase__   )   )
  __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(UpperCAmelCase__   ) * progress) % 1.0)   ))   )

 return LambdaLR(UpperCAmelCase__  ,       UpperCAmelCase__  ,       UpperCAmelCase__   )


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(UpperCAmelCase__   ) / float(max(1  ,       UpperCAmelCase__   )   )
  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(UpperCAmelCase__  ,       UpperCAmelCase__  ,       UpperCAmelCase__   )


lowerCAmelCase__      		=			{
    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(UpperCAmelCase__   )
 __lowercase													=				TYPE_TO_SCHEDULER_FUNCTION[name]
 if name == SchedulerType.CONSTANT:
  return schedule_func(UpperCAmelCase__  ,       last_epoch=UpperCAmelCase__   )

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

 # 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(UpperCAmelCase__  ,       num_warmup_steps=UpperCAmelCase__  ,       last_epoch=UpperCAmelCase__   )

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

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

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




'''simple docstring'''






from __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
lowerCAmelCase__      		=			numpy.array([0, 0])
lowerCAmelCase__      		=			numpy.array([0.5, 0.8_660_254])
lowerCAmelCase__      		=			numpy.array([1, 0])
lowerCAmelCase__      		=			[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]


def 	_A  (					A__  ,       A__   ):






 """simple docstring"""



 __lowercase													=				initial_vectors
 for _ in range(A__   ):
  __lowercase													=				iteration_step(A__   )
 return vectors


def 	_A  (					A__   ):






 """simple docstring"""



 __lowercase													=				[]
 for i, start_vector in enumerate(vectors[:-1]   ):
  __lowercase													=				vectors[i + 1]
  new_vectors.append(A__   )
  __lowercase													=				end_vector - start_vector
  new_vectors.append(start_vector + difference_vector / 3   )
  new_vectors.append(
      start_vector + difference_vector / 3 + rotate(difference_vector / 3  ,       60   )   )
  new_vectors.append(start_vector + difference_vector * 2 / 3   )
 new_vectors.append(vectors[-1]   )
 return new_vectors


def 	_A  (					A__  ,       A__   ):






 """simple docstring"""



 __lowercase													=				numpy.radians(A__   )
 __lowercase						,			__lowercase													=				numpy.cos(A__   ), numpy.sin(A__   )
 __lowercase													=				numpy.array(((c, -s), (s, c))   )
 return numpy.dot(A__  ,       A__   )


def 	_A  (					A__   ):






 """simple docstring"""



 __lowercase													=				plt.gca()
 axes.set_aspect('''equal'''   )

 # matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
 # y-coordinates as inputs, which are constructed from the vector-list using
 # zip()
 __lowercase						,			__lowercase													=				zip(*A__   )
 plt.plot(A__  ,       A__   )
 plt.show()


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 lowerCAmelCase__      		=			iterate(INITIAL_VECTORS, 5)
 plot(processed_vectors)

