



'''simple docstring'''






from __future__ import annotations

from typing import Any

class 							a__:







    def __init__(   self				:						int		,    __snake_case				:						int		,    __snake_case				:						int		,    __snake_case				:						float = 0			):
      a     ,			a		:      Optional[int]       =  row, column
      a		:      Union[str, Any]       =  [[default_value for c in range(UpperCamelCase__			)] for r in range(UpperCamelCase__			)]







    def __str__(   self				:						List[str]			):
      a		:      Optional[int]       =  F"""Matrix consist of {self.row} rows and {self.column} columns\n"""

      # Make string identifier
      a		:      Union[str, Any]       =  0
      for row_vector in self.array:
        for obj in row_vector:
          a		:      Optional[int]       =  max(UpperCamelCase__		,    len(str(UpperCamelCase__			)			)			)
      a		:      Optional[Any]       =  F"""%{max_element_length}s"""

      # Make string and return
      def single_line(__snake_case				:						list[float]			) -> str:
        nonlocal string_format_identifier
        a		:      Optional[Any]       =  '['
        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				:						int			):
      return str(self			)







    def     lowercase_ (   self				:						Tuple		,    __snake_case				:						tuple[int, int]			):







      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				:						str		,    __snake_case				:						tuple[int, int]			):
      assert self.validate_indicies(UpperCamelCase__			)
      return self.array[loc[0]][loc[1]]







    def __setitem__(   self				:						Dict		,    __snake_case				:						tuple[int, int]		,    __snake_case				:						float			):
      assert self.validate_indicies(UpperCamelCase__			)
      a		:      Optional[Any]       =  value







    def __add__(   self				:						Optional[int]		,    __snake_case				:						Matrix			):
      assert isinstance(UpperCamelCase__		,    UpperCamelCase__			)
      assert self.row == another.row and self.column == another.column

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







    def __neg__(   self				:						Optional[int]			):
      a		:      Dict       =  Matrix(self.row		,    self.column			)
      for r in range(self.row			):
        for c in range(self.column			):
          a		:      Optional[Any]       =  -self[r, c]
      return result







    def __sub__(   self				:						List[str]		,    __snake_case				:						Matrix			):
      return self + (-another)







    def __mul__(   self				:						Any		,    __snake_case				:						int | float | Matrix			):







      if isinstance(UpperCamelCase__		,    (int, float)			):  # Scalar multiplication
        a		:      Dict       =  Matrix(self.row		,    self.column			)
        for r in range(self.row			):
          for c in range(self.column			):
            a		:      List[Any]       =  self[r, c] * another
        return result
      elif isinstance(UpperCamelCase__		,    UpperCamelCase__			):  # Matrix multiplication
        assert self.column == another.row
        a		:      Tuple       =  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		:      Dict       =  F"""Unsupported type given for another ({type(UpperCamelCase__			)})"""
        raise TypeError(UpperCamelCase__			)







    def     lowercase_ (   self				:						List[str]			):
      a		:      Optional[int]       =  Matrix(self.column		,    self.row			)
      for r in range(self.row			):
        for c in range(self.column			):
          a		:      str       =  self[r, c]
      return result







    def     lowercase_ (   self				:						Dict		,    __snake_case				:						Matrix		,    __snake_case				:						Matrix			):
      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		:      List[Any]       =  v.transpose()
      a		:      Tuple       =  (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    lowerCamelCase__ (		):
       # a^(-1)
       a		:      Optional[Any]       =  Matrix(3				,    3				,    0       )
       for i in range(3       ):
         a		:      List[Any]       =  1
       print(f"""a^(-1) is {ainv}"""       )
       # u, v
       a		:      Union[str, Any]       =  Matrix(3				,    1				,    0       )
       a     ,			a     ,			a		:      Union[str, Any]       =  1, 2, -3
       a		:      str       =  Matrix(3				,    1				,    0       )
       a     ,			a     ,			a		:      List[Any]       =  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(_A				,    _A       )}"""       )
     def    lowerCamelCase__ (		):
       import doctest

       doctest.testmod()

     testa()










'''simple docstring'''






from math import factorial, pi
def    lowerCamelCase__ (		_A				,    _A = 30       ):

  if not isinstance(_A				,    (int, float)       ):
    raise ValueError('maclaurin_sin() requires either an int or float for theta'       )

  if not isinstance(_A				,    _A       ) or accuracy <= 0:
    raise ValueError('maclaurin_sin() requires a positive int for accuracy'       )

  a		:      List[Any]       =  float(_A       )
  a		:      Optional[int]       =  theta // (2 * pi)
  theta -= 2 * div * pi
  return sum(
      (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1       ) for r in range(_A       )       )
def    lowerCamelCase__ (		_A				,    _A = 30       ):

  if not isinstance(_A				,    (int, float)       ):
    raise ValueError('maclaurin_cos() requires either an int or float for theta'       )

  if not isinstance(_A				,    _A       ) or accuracy <= 0:
    raise ValueError('maclaurin_cos() requires a positive int for accuracy'       )

  a		:      List[str]       =  float(_A       )
  a		:      List[str]       =  theta // (2 * pi)
  theta -= 2 * div * pi
  return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r       ) for r in range(_A       )       )


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     print(maclaurin_sin(1_0))
     print(maclaurin_sin(-1_0))
     print(maclaurin_sin(1_0, 1_5))
     print(maclaurin_sin(-1_0, 1_5))

     print(maclaurin_cos(5))
     print(maclaurin_cos(-5))
     print(maclaurin_cos(1_0, 1_5))
     print(maclaurin_cos(-1_0, 1_5))