


'''simple docstring'''







from __future__ import annotations

from typing import Any
class 	UpperCamelCase__					:



     """simple docstring"""






     def __init__( self      ,	snake_case__      ,	snake_case__      ,	snake_case__ = 0   ):

            '''simple docstring'''

            _lowerCAmelCase			,     _lowerCAmelCase    :							List[Any]   			=       row, column
            _lowerCAmelCase    :							Any   			=       [[default_value for c in range(__A   )] for r in range(__A   )]







     def __str__( self   ):

            '''simple docstring'''

            _lowerCAmelCase    :							Dict   			=       F'Matrix consist of {self.row} rows and {self.column} columns\n'

            # Make string identifier
            _lowerCAmelCase    :							List[Any]   			=       0
            for row_vector in self.array:
                   for obj in row_vector:
                          _lowerCAmelCase    :							Any   			=       max(__A      ,	len(str(__A   )   )   )
            _lowerCAmelCase    :							Union[str, Any]   			=       F'%{max_element_length}s'

            # Make string and return
            def single_line(snake_case__   ) -> str:
                   nonlocal string_format_identifier
                   _lowerCAmelCase    :							List[Any]   			=       '['
                   line += ", ".join(string_format_identifier % (obj,) for obj in row_vector   )
                   line += "]"
                   return line

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







     def __repr__( self   ):

            '''simple docstring'''

            return str(self   )







     def a	( self      ,	snake_case__   ):

            '''simple docstring'''

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







     def __getitem__( self      ,	snake_case__   ):

            '''simple docstring'''

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







     def __setitem__( self      ,	snake_case__      ,	snake_case__   ):

            '''simple docstring'''

            assert self.validate_indicies(__A   )
            _lowerCAmelCase    :							int   			=       value







     def __add__( self      ,	snake_case__   ):

            '''simple docstring'''

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

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







     def __neg__( self   ):

            '''simple docstring'''

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







     def __sub__( self      ,	snake_case__   ):

            '''simple docstring'''

            return self + (-another)







     def __mul__( self      ,	snake_case__   ):

            '''simple docstring'''

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







     def a	( self   ):

            '''simple docstring'''

            _lowerCAmelCase    :							Tuple   			=       Matrix(self.column      ,	self.row   )
            for r in range(self.row   ):
                   for c in range(self.column   ):
                          _lowerCAmelCase    :							Union[str, Any]   			=       self[r, c]
            return result







     def a	( self      ,	snake_case__      ,	snake_case__   ):

            '''simple docstring'''

            assert isinstance(__A      ,	__A   ) and isinstance(__A      ,	__A   )
            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
            _lowerCAmelCase    :							Optional[int]   			=       v.transpose()
            _lowerCAmelCase    :							List[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 			lowercase				():







              """simple docstring"""







              _lowerCAmelCase    :							Any   			=       Matrix(3   ,						3   ,						0					)
              for i in range(3					):
                     _lowerCAmelCase    :							Dict   			=       1
              print(f'a^(-1) is {ainv}'					)
              # u, v
              _lowerCAmelCase    :							List[str]   			=       Matrix(3   ,						1   ,						0					)
              _lowerCAmelCase			,     _lowerCAmelCase			,     _lowerCAmelCase    :							List[str]   			=       1, 2, -3
              _lowerCAmelCase    :							Tuple   			=       Matrix(3   ,						1   ,						0					)
              _lowerCAmelCase			,     _lowerCAmelCase			,     _lowerCAmelCase    :							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(_lowercase   ,						_lowercase					)}'					)






       def 			lowercase				():







              """simple docstring"""







              import doctest

              doctest.testmod()
       testa()





'''simple docstring'''







def 			lowercase				(_A   ,						_A					):







       """simple docstring"""







       _lowerCAmelCase    :							Optional[int]   			=       (boundary[1] - boundary[0]) / steps
       _lowerCAmelCase    :							Any   			=       boundary[0]
       _lowerCAmelCase    :							List[str]   			=       boundary[1]
       _lowerCAmelCase    :							Tuple   			=       make_points(_A   ,						_A   ,						_A					)
       _lowerCAmelCase    :							Tuple   			=       0.0
       y += (h / 2.0) * f(_A					)
       for i in x_i:
              # print(i)
              y += h * f(_A					)
       y += (h / 2.0) * f(_A					)
       return y






def 			lowercase				(_A   ,						_A   ,						_A					):







       """simple docstring"""







       _lowerCAmelCase    :							Tuple   			=       a + h
       while x < (b - h):
              yield x
              _lowerCAmelCase    :							Any   			=       x + h






def 			lowercase				(_A					):  # enter your function here







       """simple docstring"""







       _lowerCAmelCase    :							int   			=       (x - 0) * (x - 0)
       return y






def 			lowercase				():







       """simple docstring"""







       _lowerCAmelCase    :							Optional[Any]   			=       0.0  # Lower bound of integration
       _lowerCAmelCase    :							Dict   			=       1.0  # Upper bound of integration
       _lowerCAmelCase    :							Optional[Any]   			=       10.0  # define number of steps or resolution
       _lowerCAmelCase    :							Optional[int]   			=       [a, b]  # define boundary of integration
       _lowerCAmelCase    :							List[Any]   			=       method_a(_A   ,						_A					)
       print(f'y = {y}'					)


if __name__ == "__main__":
       main()

