


from __future__ import annotations

from typing import Any







class      lowerCAmelCase__       :




     '''simple docstring'''


     def __init__(						self ,						__lowerCamelCase ,						__lowerCamelCase ,						__lowerCamelCase = 0)			->				None:
            _A    ,			_A      :       Any				    = row, column
            _A      :       str				    = [[default_value for c in range(__lowerCamelCase)] for r in range(__lowerCamelCase)]


     def __str__(						self)			->				str:
            _A      :       Any				    = F"Matrix consist of {self.row} rows and {self.column} columns\n"

            # Make string identifier
            _A      :       List[str]				    = 0
            for row_vector in self.array:
                   for obj in row_vector:
                          _A      :       Any				    = max(__lowerCamelCase ,						len(str(__lowerCamelCase)))
            _A      :       Tuple				    = F"%{max_element_length}s"

            # Make string and return
            def single_line(__lowerCamelCase) -> str:
                   nonlocal string_format_identifier
                   _A      :       Tuple				    = "["
                   line += ", ".join(string_format_identifier % (obj,) for obj in row_vector)
                   line += "]"
                   return line

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


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


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


     def __getitem__(						self ,						__lowerCamelCase)			->				Any:
            assert self.validate_indicies(__lowerCamelCase)
            return self.array[loc[0]][loc[1]]


     def __setitem__(						self ,						__lowerCamelCase ,						__lowerCamelCase)			->				None:
            assert self.validate_indicies(__lowerCamelCase)
            _A      :       Optional[int]				    = value


     def __add__(						self ,						__lowerCamelCase)			->				Matrix:
            assert isinstance(__lowerCamelCase ,						__lowerCamelCase)
            assert self.row == another.row and self.column == another.column

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


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


     def __sub__(						self ,						__lowerCamelCase)			->				Matrix:
            return self + (-another)


     def __mul__(						self ,						__lowerCamelCase)			->				Matrix:

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


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


     def  _lowerCamelCase (						self ,						__lowerCamelCase ,						__lowerCamelCase)			->				Any:
            assert isinstance(__lowerCamelCase ,						__lowerCamelCase) and isinstance(__lowerCamelCase ,						__lowerCamelCase)
            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      :       Any				    = v.transpose()
            _A      :       Optional[Any]				    = (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 							_UpperCAmelCase				():
           # a^(-1)
           _A      :       int				    = Matrix(3				,							3				,							0						)
           for i in range(3						):
                  _A      :       Tuple				    = 1
           print(f"a^(-1) is {ainv}"						)
           # u, v
           _A      :       List[Any]				    = Matrix(3				,							1				,							0						)
           _A    ,			_A    ,			_A      :       Optional[Any]				    = 1, 2, -3
           _A      :       Tuple				    = Matrix(3				,							1				,							0						)
           _A    ,			_A    ,			_A      :       Optional[int]				    = 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(UpperCamelCase__				,							UpperCamelCase__						)}"						)
    def 							_UpperCAmelCase				():
           import doctest

           doctest.testmod()






    testa()




def 							_UpperCAmelCase				(UpperCamelCase__     :  Optional[Any]				,							UpperCamelCase__     :  Union[str, Any]						):
       # "extended trapezoidal rule"
       # int(f) = dx/2 * (f1 + 2f2 + ... + fn)
       _A      :       int				    = (boundary[1] - boundary[0]) / steps
       _A      :       Any				    = boundary[0]
       _A      :       List[Any]				    = boundary[1]
       _A      :       str				    = make_points(UpperCamelCase__				,							UpperCamelCase__				,							UpperCamelCase__						)
       _A      :       str				    = 0.0
       y += (h / 2.0) * f(UpperCamelCase__						)
       for i in x_i:
              # print(i)
              y += h * f(UpperCamelCase__						)
       y += (h / 2.0) * f(UpperCamelCase__						)
       return y
def 							_UpperCAmelCase				(UpperCamelCase__     :  List[str]				,							UpperCamelCase__     :  Optional[int]				,							UpperCamelCase__     :  Any						):
       _A      :       Optional[int]				    = a + h
       while x < (b - h):
              yield x
              _A      :       Dict				    = x + h
def 							_UpperCAmelCase				(UpperCamelCase__     :  Optional[int]						):  # enter your function here
       _A      :       Any				    = (x - 0) * (x - 0)
       return y
def 							_UpperCAmelCase				():
       _A      :       Optional[Any]				    = 0.0  # Lower bound of integration
       _A      :       Optional[int]				    = 1.0  # Upper bound of integration
       _A      :       List[Any]				    = 10.0  # define number of steps or resolution
       _A      :       Any				    = [a, b]  # define boundary of integration
       _A      :       Tuple				    = method_a(UpperCamelCase__				,							UpperCamelCase__						)
       print(f"y = {y}"						)


if __name__ == "__main__":
    main()
