





"""simple docstring"""



from __future__ import annotations

from typing import Any






class 		__snake_case					:





 """simple docstring"""


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



     '''simple docstring'''




     __A ,       __A    :						Optional[int]						 =     row, column
     __A    :						Any						 =     [[default_value for c in range(__lowerCamelCase  )] for r in range(__lowerCamelCase  )]

 def __str__(    self  ):



     '''simple docstring'''




     __A    :						Tuple						 =     F"""Matrix consist of {self.row} rows and {self.column} columns\n"""

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

     # Make string and return
     def single_line(__lowerCamelCase  ) -> str:
         nonlocal string_format_identifier
         __A    :						List[Any]						 =     '''['''
         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  ):



     '''simple docstring'''




     return str(self  )

 def 					UpperCamelCase__(    self					,						__lowerCamelCase  ):



     '''simple docstring'''




     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  ):



     '''simple docstring'''




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

 def __setitem__(    self					,						__lowerCamelCase					,						__lowerCamelCase  ):



     '''simple docstring'''




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

 def __add__(    self					,						__lowerCamelCase  ):



     '''simple docstring'''




     assert isinstance(__lowerCamelCase					,						__lowerCamelCase  )
     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  ):



     '''simple docstring'''




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

 def __sub__(    self					,						__lowerCamelCase  ):



     '''simple docstring'''




     return self + (-another)

 def __mul__(    self					,						__lowerCamelCase  ):



     '''simple docstring'''




     if isinstance(__lowerCamelCase					,						(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(__lowerCamelCase					,						__lowerCamelCase  ):  # Matrix multiplication
         assert self.column == another.row
         __A    :						List[Any]						 =     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    :						Any						 =     F"""Unsupported type given for another ({type(__lowerCamelCase  )})"""
         raise TypeError(__lowerCamelCase  )

 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     __A    :						List[str]						 =     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 					UpperCamelCase__(    self					,						__lowerCamelCase					,						__lowerCamelCase  ):



     '''simple docstring'''




     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    :						Dict						 =     v.transpose()
     __A    :						Dict						 =     (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     (   )   ->None:



           '''simple docstring'''







           __A    :						int						 =     Matrix(3				,3				,0						)
           for i in range(3						):
               __A    :						Any						 =     1
           print(F"""a^(-1) is {ainv}"""						)
           # u, v
           __A    :						Optional[int]						 =     Matrix(3				,1				,0						)
           __A ,       __A ,       __A    :						List[str]						 =     1, 2, -3
           __A    :						Optional[int]						 =     Matrix(3				,1				,0						)
           __A ,       __A ,       __A    :						Tuple						 =     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(snake_case_				,snake_case_						)}"""						)







       def 		__lowercase     (   )   ->None:



           '''simple docstring'''







           import doctest

           doctest.testmod()




       testa()











"""simple docstring"""



def 		__lowercase     (   snake_case_  :  int						)   ->int:



    '''simple docstring'''







    assert (
        isinstance(snake_case_				,snake_case_						) and number_of_steps > 0
    ), F"""number_of_steps needs to be positive integer, your input {number_of_steps}"""
    if number_of_steps == 1:
        return 1
    __A ,       __A    :						List[Any]						 =     1, 1
    for _ in range(number_of_steps - 1						):
        __A ,       __A    :						List[str]						 =     current + previous, current
    return current


if __name__ == "__main__":
       import doctest

       doctest.testmod()




