'''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


_lowercase		:				Optional[Any]	       =		logging.get_logger(__name__)





class 					__magic_name__		(					_UpperCAmelCase):
			UpperCamelCase__       = '''linear'''
			UpperCamelCase__       = '''cosine'''
			UpperCamelCase__       = '''cosine_with_restarts'''
			UpperCamelCase__       = '''polynomial'''
			UpperCamelCase__       = '''constant'''
			UpperCamelCase__       = '''constant_with_warmup'''
			UpperCamelCase__       = '''piecewise_constant'''




def 							lowerCamelCase			(   UpperCAmelCase__ :      Optimizer   ,   UpperCAmelCase__ :      int = -1				)    ->   Any:
							return LambdaLR(UpperCAmelCase__   ,   lambda UpperCAmelCase__				: 1   ,   last_epoch=UpperCAmelCase__				)




def 							lowerCamelCase			(   UpperCAmelCase__ :      Optimizer   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int = -1				)    ->   List[Any]:

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

							def create_rules_function(UpperCAmelCase__ :      Union[str, Any]   ,   UpperCAmelCase__ :      Optional[int]				):
														def rule_func(UpperCAmelCase__ :      int				) -> float:
																					lowercase_      :    List[str]       		= 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_      :    List[str]       		= create_rules_function(UpperCAmelCase__   ,   UpperCAmelCase__				)

							return LambdaLR(UpperCAmelCase__   ,   UpperCAmelCase__   ,   last_epoch=UpperCAmelCase__				)




def 							lowerCamelCase			(   UpperCAmelCase__ :      Optional[int]   ,   UpperCAmelCase__ :      Dict   ,   UpperCAmelCase__ :      Optional[Any]   ,   UpperCAmelCase__ :      int=-1				)    ->   Optional[int]:

							def lr_lambda(UpperCAmelCase__ :      int				):
														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 							lowerCamelCase			(   UpperCAmelCase__ :      Optimizer   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      float = 0.5   ,   UpperCAmelCase__ :      int = -1				)    ->   Optional[int]:

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

							return LambdaLR(UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__				)




def 							lowerCamelCase			(   UpperCAmelCase__ :      Optimizer   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int   ,   UpperCAmelCase__ :      int = 1   ,   UpperCAmelCase__ :      int = -1				)    ->   str:

							def lr_lambda(UpperCAmelCase__ :      Dict				):
														if current_step < num_warmup_steps:
																					return float(UpperCAmelCase__				) / float(max(1   ,   UpperCAmelCase__				)				)
														lowercase_      :    Optional[int]       		= 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 							lowerCamelCase			(   UpperCAmelCase__ :      Any   ,   UpperCAmelCase__ :      Any   ,   UpperCAmelCase__ :      Any   ,   UpperCAmelCase__ :      int=1e-7   ,   UpperCAmelCase__ :      Optional[Any]=1.0   ,   UpperCAmelCase__ :      Dict=-1				)    ->   List[str]:
							lowercase_      :    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(UpperCAmelCase__ :      int				):
														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_      :    str       		= lr_init - lr_end
																					lowercase_      :    str       		= num_training_steps - num_warmup_steps
																					lowercase_      :    Any       		= 1 - (current_step - num_warmup_steps) / decay_steps
																					lowercase_      :    Dict       		= lr_range * pct_remaining**power + lr_end
																					return decay / lr_init  # as LambdaLR multiplies by lr_init

							return LambdaLR(UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__				)


_lowercase		:				Tuple	       =		{
    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			(   UpperCAmelCase__ :      Union[str, SchedulerType]   ,   UpperCAmelCase__ :      Optimizer   ,   UpperCAmelCase__ :      Optional[str] = None   ,   UpperCAmelCase__ :      Optional[int] = None   ,   UpperCAmelCase__ :      Optional[int] = None   ,   UpperCAmelCase__ :      int = 1   ,   UpperCAmelCase__ :      float = 1.0   ,   UpperCAmelCase__ :      int = -1   ,   )    ->   str:
							lowercase_      :    Any       		= SchedulerType(UpperCAmelCase__				)
							lowercase_      :    Optional[int]       		= 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 collections.abc import Callable

import numpy as np




def 							lowerCamelCase			(   UpperCAmelCase__ :      Callable   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float				)    ->   np.array:
							lowercase_      :    Any       		= int(np.ceil((x_end - xa) / step_size				)				)
							lowercase_      :    List[Any]       		= np.zeros((n + 1,)				)
							lowercase_      :    List[Any]       		= ya
							lowercase_      :    List[str]       		= xa

							for k in range(UpperCAmelCase__				):
														lowercase_      :    Optional[Any]       		= y[k] + step_size * ode_func(UpperCAmelCase__   ,   y[k]				)
														lowercase_      :    List[Any]       		= y[k] + (
														    (step_size / 2) * (ode_func(UpperCAmelCase__   ,   y[k]				) + ode_func(x + step_size   ,   UpperCAmelCase__				))
														)
														x += step_size

							return y


if __name__ == "__main__":
						import doctest

						doctest.testmod()





