




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     :		str								=       logging.get_logger(__name__)


class     UpperCamelCase_   (			UpperCAmelCase__					):

    '''simple docstring'''






    UpperCAmelCase__							  =				'''linear'''
    UpperCAmelCase__							  =				'''cosine'''
    UpperCAmelCase__							  =				'''cosine_with_restarts'''
    UpperCAmelCase__							  =				'''polynomial'''
    UpperCAmelCase__							  =				'''constant'''
    UpperCAmelCase__							  =				'''constant_with_warmup'''
    UpperCAmelCase__							  =				'''piecewise_constant'''







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_ = -1						)       ->	List[str]:



       """simple docstring"""

       return LambdaLR(lowercase_			,    lambda lowercase_						: 1			,    last_epoch=lowercase_						)







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_			,    lowercase_ = -1						)       ->	List[str]:



       """simple docstring"""

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

       return LambdaLR(lowercase_			,    lowercase_			,    last_epoch=lowercase_						)







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_			,    lowercase_ = -1						)       ->	List[str]:



       """simple docstring"""

       A__							=   {}
       A__							=   step_rules.split(''','''						)
       for rule_str in rule_list[:-1]:
              A__			,							A__							=   rule_str.split(''':'''						)
              A__							=   int(lowercase_						)
              A__							=   float(lowercase_						)
              A__							=   value
       A__							=   float(rule_list[-1]						)

       def create_rules_function(lowercase_			,    lowercase_						):
              def rule_func(lowercase_						) -> float:
                     A__							=   sorted(rules_dict.keys()						)
                     for i, sorted_step in enumerate(lowercase_						):
                            if steps < sorted_step:
                                   return rules_dict[sorted_steps[i]]
                     return last_lr_multiple

              return rule_func

       A__							=   create_rules_function(lowercase_			,    lowercase_						)

       return LambdaLR(lowercase_			,    lowercase_			,    last_epoch=lowercase_						)







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_			,    lowercase_			,    lowercase_=-1						)       ->	Optional[Any]:



       """simple docstring"""

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

       return LambdaLR(lowercase_			,    lowercase_			,    lowercase_						)







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_			,    lowercase_			,    lowercase_ = 0.5			,    lowercase_ = -1						)       ->	List[Any]:



       """simple docstring"""

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

       return LambdaLR(lowercase_			,    lowercase_			,    lowercase_						)







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_			,    lowercase_			,    lowercase_ = 1			,    lowercase_ = -1						)       ->	Tuple:



       """simple docstring"""

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

       return LambdaLR(lowercase_			,    lowercase_			,    lowercase_						)







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_			,    lowercase_			,    lowercase_=1E-7			,    lowercase_=1.0			,    lowercase_=-1						)       ->	Optional[Any]:



       """simple docstring"""

       A__							=   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(lowercase_						):
              if current_step < num_warmup_steps:
                     return float(lowercase_						) / float(max(1			,    lowercase_						)						)
              elif current_step > num_training_steps:
                     return lr_end / lr_init  # as LambdaLR multiplies by lr_init
              else:
                     A__							=   lr_init - lr_end
                     A__							=   num_training_steps - num_warmup_steps
                     A__							=   1 - (current_step - num_warmup_steps) / decay_steps
                     A__							=   lr_range * pct_remaining**power + lr_end
                     return decay / lr_init  # as LambdaLR multiplies by lr_init

       return LambdaLR(lowercase_			,    lowercase_			,    lowercase_						)


_lowerCamelCase     :		str								=       {
    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 SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_			,    lowercase_ = None			,    lowercase_ = None			,    lowercase_ = None			,    lowercase_ = 1			,    lowercase_ = 1.0			,    lowercase_ = -1			,    )       ->	List[str]:



       """simple docstring"""

       A__							=   SchedulerType(lowercase_						)
       A__							=   TYPE_TO_SCHEDULER_FUNCTION[name]
       if name == SchedulerType.CONSTANT:
              return schedule_func(lowercase_			,    last_epoch=lowercase_						)

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

       # 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(lowercase_			,    num_warmup_steps=lowercase_			,    last_epoch=lowercase_						)

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

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

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








from __future__ import annotations

from typing import Any


class     UpperCamelCase_   :

    '''simple docstring'''






    def __init__(      self				:     str ,			UpperCAmelCase__				:     int ,			UpperCAmelCase__				:     int ,			UpperCAmelCase__				:     float = 0)						->None:





           '''simple docstring'''

           A__			,							A__							=   row, column
           A__							=   [[default_value for c in range(UpperCAmelCase__)] for r in range(UpperCAmelCase__)]


    def __str__(      self				:     List[str])						->str:





           '''simple docstring'''

           A__							=   f"""Matrix consist of {self.row} rows and {self.column} columns\n"""

           # Make string identifier
           A__							=   0
           for row_vector in self.array:
                  for obj in row_vector:
                         A__							=   max(UpperCAmelCase__ ,			len(str(UpperCAmelCase__)))
           A__							=   f"""%{max_element_length}s"""

           # Make string and return
           def single_line(UpperCAmelCase__				:     list[float]) -> str:
                  nonlocal string_format_identifier
                  A__							=   '''['''
                  line += ", ".join(string_format_identifier % (obj,) for obj in row_vector)
                  line += "]"
                  return line

           s += "\n".join(single_line(UpperCAmelCase__) for row_vector in self.array)
           return s


    def __repr__(      self				:     Tuple)						->str:





           '''simple docstring'''

           return str(self)


    def 	SCREAMING_SNAKE_CASE							(      self				:     List[str] ,			UpperCAmelCase__				:     tuple[int, int])						->bool:





           '''simple docstring'''

           if not (isinstance(UpperCAmelCase__ ,			(list, tuple)) and len(UpperCAmelCase__) == 2):
                  return False
           elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
                  return False
           else:
                  return True


    def __getitem__(      self				:     List[Any] ,			UpperCAmelCase__				:     tuple[int, int])						->Any:





           '''simple docstring'''

           assert self.validate_indicies(UpperCAmelCase__)
           return self.array[loc[0]][loc[1]]


    def __setitem__(      self				:     List[Any] ,			UpperCAmelCase__				:     tuple[int, int] ,			UpperCAmelCase__				:     float)						->None:





           '''simple docstring'''

           assert self.validate_indicies(UpperCAmelCase__)
           A__							=   value


    def __add__(      self				:     Optional[int] ,			UpperCAmelCase__				:     Matrix)						->Matrix:





           '''simple docstring'''

           assert isinstance(UpperCAmelCase__ ,			UpperCAmelCase__)
           assert self.row == another.row and self.column == another.column

           # Add
           A__							=   Matrix(self.row ,			self.column)
           for r in range(self.row):
                  for c in range(self.column):
                         A__							=   self[r, c] + another[r, c]
           return result


    def __neg__(      self				:     str)						->Matrix:





           '''simple docstring'''

           A__							=   Matrix(self.row ,			self.column)
           for r in range(self.row):
                  for c in range(self.column):
                         A__							=   -self[r, c]
           return result


    def __sub__(      self				:     str ,			UpperCAmelCase__				:     Matrix)						->Matrix:





           '''simple docstring'''

           return self + (-another)


    def __mul__(      self				:     Union[str, Any] ,			UpperCAmelCase__				:     int | float | Matrix)						->Matrix:





           '''simple docstring'''

           if isinstance(UpperCAmelCase__ ,			(int, float)):  # Scalar multiplication
                  A__							=   Matrix(self.row ,			self.column)
                  for r in range(self.row):
                         for c in range(self.column):
                                A__							=   self[r, c] * another
                  return result
           elif isinstance(UpperCAmelCase__ ,			UpperCAmelCase__):  # Matrix multiplication
                  assert self.column == another.row
                  A__							=   Matrix(self.row ,			another.column)
                  for r in range(self.row):
                         for c in range(another.column):
                                for i in range(self.column):
                                       result[r, c] += self[r, i] * another[i, c]
                  return result
           else:
                  A__							=   f"""Unsupported type given for another ({type(UpperCAmelCase__)})"""
                  raise TypeError(UpperCAmelCase__)


    def 	SCREAMING_SNAKE_CASE							(      self				:     List[str])						->Matrix:





           '''simple docstring'''

           A__							=   Matrix(self.column ,			self.row)
           for r in range(self.row):
                  for c in range(self.column):
                         A__							=   self[r, c]
           return result





    def 	SCREAMING_SNAKE_CASE							(      self				:     Tuple ,			UpperCAmelCase__				:     Matrix ,			UpperCAmelCase__				:     Matrix)						->Any:





           '''simple docstring'''

           assert isinstance(UpperCAmelCase__ ,			UpperCAmelCase__) and isinstance(UpperCAmelCase__ ,			UpperCAmelCase__)
           assert self.row == self.column == u.row == v.row  # u, v should be column vector
           assert u.column == v.column == 1  # u, v should be column vector

           # Calculate
           A__							=   v.transpose()
           A__							=   (v_t * self * u)[0, 0] + 1
           if numerator_factor == 0:
                  return None  # It's not invertable
           return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":







  def SCREAMING_SNAKE_CASE    (	)       ->	None:



         """simple docstring"""

         A__							=   Matrix(3			,    3			,    0						)
         for i in range(3						):
                A__							=   1
         print(f"""a^(-1) is {ainv}"""						)
         # u, v
         A__							=   Matrix(3			,    1			,    0						)
         A__			,							A__			,							A__							=   1, 2, -3
         A__							=   Matrix(3			,    1			,    0						)
         A__			,							A__			,							A__							=   4, -2, 5
         print(f"""u is {u}"""						)
         print(f"""v is {v}"""						)
         print(f"""uv^T is {u * v.transpose()}"""						)
         # Sherman Morrison
         print(f"""(a + uv^T)^(-1) is {ainv.sherman_morrison(lowercase_			,    lowercase_						)}"""						)







  def SCREAMING_SNAKE_CASE    (	)       ->	None:



         """simple docstring"""

         import doctest

         doctest.testmod()
  testa()


