


from __future__ import annotations







class 				snake_case__:







						'''simple docstring'''




						def __init__(				self   ,						__lowercase							)					->    Any:
										lowerCAmelCase_ :      Union[str, Any]    				=				TypeError(
										    '''Matrices must be formed from a list of zero or more lists containing at '''
										    '''least one and the same number of values, each of which must be of type '''
										    '''int or float.'''							)
										if len(__lowercase							) != 0:
														lowerCAmelCase_ :      Optional[Any]    				=				len(rows[0]							)
														if cols == 0:
																		raise error
														for row in rows:
																		if len(__lowercase							) != cols:
																						raise error
																		for value in row:
																						if not isinstance(__lowercase   ,						(int, float)							):
																										raise error
														lowerCAmelCase_ :      Optional[Any]    				=				rows
										else:
														lowerCAmelCase_ :      Optional[int]    				=				[]




						def 						lowercase_ (				self							)					->    list[list[int]]:
										return [[row[i] for row in self.rows] for i in range(len(self.rows[0]							)							)]




						@property
						def 						lowercase_ (				self							)					->    int:
										return len(self.rows							)




						@property
						def 						lowercase_ (				self							)					->    int:
										return len(self.rows[0]							)




						@property
						def 						lowercase_ (				self							)					->    tuple[int, int]:
										return (self.num_rows, self.num_columns)




						@property
						def 						lowercase_ (				self							)					->    bool:
										return self.order[0] == self.order[1]




						def 						lowercase_ (				self							)					->    Matrix:
										lowerCAmelCase_ :      List[str]    				=				[
										    [0 if column_num != row_num else 1 for column_num in range(self.num_rows							)]
										    for row_num in range(self.num_rows							)
										]
										return Matrix(__lowercase							)




						def 						lowercase_ (				self							)					->    int:
										if not self.is_square:
														return 0
										if self.order == (0, 0):
														return 1
										if self.order == (1, 1):
														return int(self.rows[0][0]							)
										if self.order == (2, 2):
														return int(
														    (self.rows[0][0] * self.rows[1][1])
														    - (self.rows[0][1] * self.rows[1][0])							)
										else:
														return sum(
														    self.rows[0][column] * self.cofactors().rows[0][column]
														    for column in range(self.num_columns							)							)




						def 						lowercase_ (				self							)					->    bool:
										return bool(self.determinant()							)




						def 						lowercase_ (				self   ,						__lowercase   ,						__lowercase							)					->    int:
										lowerCAmelCase_ :      Tuple    				=				[
										    [
										        self.rows[other_row][other_column]
										        for other_column in range(self.num_columns							)
										        if other_column != column
										    ]
										    for other_row in range(self.num_rows							)
										    if other_row != row
										]
										return Matrix(__lowercase							).determinant()




						def 						lowercase_ (				self   ,						__lowercase   ,						__lowercase							)					->    int:
										if (row + column) % 2 == 0:
														return self.get_minor(__lowercase   ,						__lowercase							)
										return -1 * self.get_minor(__lowercase   ,						__lowercase							)




						def 						lowercase_ (				self							)					->    Matrix:
										return Matrix(
										    [
										        [self.get_minor(__lowercase   ,						__lowercase							) for column in range(self.num_columns							)]
										        for row in range(self.num_rows							)
										    ]							)




						def 						lowercase_ (				self							)					->    Matrix:
										return Matrix(
										    [
										        [
										            self.minors().rows[row][column]
										            if (row + column) % 2 == 0
										            else self.minors().rows[row][column] * -1
										            for column in range(self.minors().num_columns							)
										        ]
										        for row in range(self.minors().num_rows							)
										    ]							)




						def 						lowercase_ (				self							)					->    Matrix:
										lowerCAmelCase_ :      Union[str, Any]    				=				[
										    [self.cofactors().rows[column][row] for column in range(self.num_columns							)]
										    for row in range(self.num_rows							)
										]
										return Matrix(__lowercase							)




						def 						lowercase_ (				self							)					->    Matrix:
										lowerCAmelCase_ :      Tuple    				=				self.determinant()
										if not determinant:
														raise TypeError('''Only matrices with a non-zero determinant have an inverse'''							)
										return self.adjugate() * (1 / determinant)




						def __repr__(				self							)					->    str:
										return str(self.rows							)




						def __str__(				self							)					->    str:
										if self.num_rows == 0:
														return "[]"
										if self.num_rows == 1:
														return "[[" + ". ".join(str(self.rows[0]							)							) + "]]"
										return (
										    "["
										    + "\n ".join(
										        [
										            '''[''' + '''. '''.join([str(__lowercase							) for value in row]							) + '''.]'''
										            for row in self.rows
										        ]							)
										    + "]"
										)




						def 						lowercase_ (				self   ,						__lowercase   ,						__lowercase = None							)					->    None:
										lowerCAmelCase_ :      Dict    				=				TypeError('''Row must be a list containing all ints and/or floats'''							)
										if not isinstance(__lowercase   ,						__lowercase							):
														raise type_error
										for value in row:
														if not isinstance(__lowercase   ,						(int, float)							):
																		raise type_error
										if len(__lowercase							) != self.num_columns:
														raise ValueError(
														    '''Row must be equal in length to the other rows in the matrix'''							)
										if position is None:
														self.rows.append(__lowercase							)
										else:
														lowerCAmelCase_ :      Optional[int]    				=				self.rows[0:position] + [row] + self.rows[position:]




						def 						lowercase_ (				self   ,						__lowercase   ,						__lowercase = None							)					->    None:
										lowerCAmelCase_ :      int    				=				TypeError(
										    '''Column must be a list containing all ints and/or floats'''							)
										if not isinstance(__lowercase   ,						__lowercase							):
														raise type_error
										for value in column:
														if not isinstance(__lowercase   ,						(int, float)							):
																		raise type_error
										if len(__lowercase							) != self.num_rows:
														raise ValueError(
														    '''Column must be equal in length to the other columns in the matrix'''							)
										if position is None:
														lowerCAmelCase_ :      Tuple    				=				[self.rows[i] + [column[i]] for i in range(self.num_rows							)]
										else:
														lowerCAmelCase_ :      Dict    				=				[
														    self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
														    for i in range(self.num_rows							)
														]




						def __eq__(				self   ,						__lowercase							)					->    bool:
										if not isinstance(__lowercase   ,						__lowercase							):
														return NotImplemented
										return self.rows == other.rows




						def __ne__(				self   ,						__lowercase							)					->    bool:
										return not self == other




						def __neg__(				self							)					->    Matrix:
										return self * -1




						def __add__(				self   ,						__lowercase							)					->    Matrix:
										if self.order != other.order:
														raise ValueError('''Addition requires matrices of the same order'''							)
										return Matrix(
										    [
										        [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns							)]
										        for i in range(self.num_rows							)
										    ]							)




						def __sub__(				self   ,						__lowercase							)					->    Matrix:
										if self.order != other.order:
														raise ValueError('''Subtraction requires matrices of the same order'''							)
										return Matrix(
										    [
										        [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns							)]
										        for i in range(self.num_rows							)
										    ]							)




						def __mul__(				self   ,						__lowercase							)					->    Matrix:
										if isinstance(__lowercase   ,						(int, float)							):
														return Matrix(
														    [[int(element * other							) for element in row] for row in self.rows]							)
										elif isinstance(__lowercase   ,						__lowercase							):
														if self.num_columns != other.num_rows:
																		raise ValueError(
																		    '''The number of columns in the first matrix must '''
																		    '''be equal to the number of rows in the second'''							)
														return Matrix(
														    [
														        [Matrix.dot_product(__lowercase   ,						__lowercase							) for column in other.columns()]
														        for row in self.rows
														    ]							)
										else:
														raise TypeError(
														    '''A Matrix can only be multiplied by an int, float, or another matrix'''							)




						def __pow__(				self   ,						__lowercase							)					->    Matrix:
										if not isinstance(__lowercase   ,						__lowercase							):
														raise TypeError('''A Matrix can only be raised to the power of an int'''							)
										if not self.is_square:
														raise ValueError('''Only square matrices can be raised to a power'''							)
										if other == 0:
														return self.identity()
										if other < 0:
														if self.is_invertable():
																		return self.inverse() ** (-other)
														raise ValueError(
														    '''Only invertable matrices can be raised to a negative power'''							)
										lowerCAmelCase_ :      Dict    				=				self
										for _ in range(other - 1							):
														result *= self
										return result




						@classmethod
						def 						lowercase_ (				cls   ,						__lowercase   ,						__lowercase							)					->    int:
										return sum(row[i] * column[i] for i in range(len(__lowercase							)							)							)


if __name__ == "__main__":
						import doctest

						doctest.testmod()



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			:  Tuple     =logging.get_logger(__name__)







class 				snake_case__(							UpperCAmelCase__							):







						'''simple docstring'''




						SCREAMING_SNAKE_CASE__      :  List[str]					=							"""linear"""
						SCREAMING_SNAKE_CASE__      :  Union[str, Any]					=							"""cosine"""
						SCREAMING_SNAKE_CASE__      :  Dict					=							"""cosine_with_restarts"""
						SCREAMING_SNAKE_CASE__      :  List[str]					=							"""polynomial"""
						SCREAMING_SNAKE_CASE__      :  Dict					=							"""constant"""
						SCREAMING_SNAKE_CASE__      :  List[str]					=							"""constant_with_warmup"""
						SCREAMING_SNAKE_CASE__      :  str					=							"""piecewise_constant"""






def 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ = -1 )-> Tuple:
				return LambdaLR(lowerCAmelCase_ ,   lambda lowerCAmelCase_ : 1 ,   last_epoch=lowerCAmelCase_ )



def 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ = -1 )-> List[Any]:

				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 )-> int:
				lowerCAmelCase_ :      Optional[int]    				=				{}
				lowerCAmelCase_ :      Union[str, Any]    				=				step_rules.split(''',''' )
				for rule_str in rule_list[:-1]:
								lowerCAmelCase_				,  lowerCAmelCase_ :      str    				=				rule_str.split(''':''' )
								lowerCAmelCase_ :      int    				=				int(lowerCAmelCase_ )
								lowerCAmelCase_ :      str    				=				float(lowerCAmelCase_ )
								lowerCAmelCase_ :      List[Any]    				=				value
				lowerCAmelCase_ :      int    				=				float(rule_list[-1] )

				def create_rules_function(lowerCAmelCase_ ,   lowerCAmelCase_ ):
								def rule_func(lowerCAmelCase_ ) -> float:
												lowerCAmelCase_ :      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

				lowerCAmelCase_ :      Tuple    				=				create_rules_function(lowerCAmelCase_ ,   lowerCAmelCase_ )

				return LambdaLR(lowerCAmelCase_ ,   lowerCAmelCase_ ,   last_epoch=lowerCAmelCase_ )



def 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_=-1 )-> Optional[int]:

				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 )-> List[Any]:

				def lr_lambda(lowerCAmelCase_ ):
								if current_step < num_warmup_steps:
												return float(lowerCAmelCase_ ) / float(max(1 ,   lowerCAmelCase_ ) )
								lowerCAmelCase_ :      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_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ = 1 ,   lowerCAmelCase_ = -1 )-> Dict:

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

				return LambdaLR(lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ )


_UpperCAmelCase			:  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 ,   )-> Optional[int]:
				lowerCAmelCase_ :      Union[str, Any]    				=				SchedulerType(lowerCAmelCase_ )
				lowerCAmelCase_ :      Optional[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_ )