





from __future__ import annotations

from typing import Any

class      lowerCAmelCase							:
 def __init__(   self						:   List[Any]    ,  UpperCAmelCase						:   int    ,  UpperCAmelCase						:   int    ,  UpperCAmelCase						:   float = 0			)    ->			None:
     lowerCamelCase__				,							lowerCamelCase__					:   List[str]      				=	row, column
     lowerCamelCase__					:   List[Any]      				=	[[default_value for c in range(UpperCAmelCase			)] for r in range(UpperCAmelCase			)]
 def __str__(   self						:   Optional[Any]			)    ->			str:
     lowerCamelCase__					:   Dict      				=	F"""Matrix consist of {self.row} rows and {self.column} columns\n"""

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

     # Make string and return
     def single_line(UpperCAmelCase						:   list[float]			) -> str:
         nonlocal string_format_identifier
         lowerCamelCase__					:   str      				=	'['
         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						:   List[Any]			)    ->			str:
     return str(self			)
 def   A_			(   self						:   Any    ,  UpperCAmelCase						:   tuple[int, int]			)    ->			bool:
     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						:   Any    ,  UpperCAmelCase						:   tuple[int, int]			)    ->			Any:
     assert self.validate_indicies(UpperCAmelCase			)
     return self.array[loc[0]][loc[1]]
 def __setitem__(   self						:   Optional[Any]    ,  UpperCAmelCase						:   tuple[int, int]    ,  UpperCAmelCase						:   float			)    ->			None:
     assert self.validate_indicies(UpperCAmelCase			)
     lowerCamelCase__					:   Dict      				=	value
 def __add__(   self						:   Dict    ,  UpperCAmelCase						:   Matrix			)    ->			Matrix:
     assert isinstance(UpperCAmelCase    ,  UpperCAmelCase			)
     assert self.row == another.row and self.column == another.column

     # Add
     lowerCamelCase__					:   int      				=	Matrix(self.row    ,  self.column			)
     for r in range(self.row			):
         for c in range(self.column			):
             lowerCamelCase__					:   str      				=	self[r, c] + another[r, c]
     return result
 def __neg__(   self						:   str			)    ->			Matrix:
     lowerCamelCase__					:   int      				=	Matrix(self.row    ,  self.column			)
     for r in range(self.row			):
         for c in range(self.column			):
             lowerCamelCase__					:   List[Any]      				=	-self[r, c]
     return result
 def __sub__(   self						:   Optional[int]    ,  UpperCAmelCase						:   Matrix			)    ->			Matrix:
     return self + (-another)
 def __mul__(   self						:   List[Any]    ,  UpperCAmelCase						:   int | float | Matrix			)    ->			Matrix:

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







 def   A_			(   self						:   Optional[Any]    ,  UpperCAmelCase						:   Matrix    ,  UpperCAmelCase						:   Matrix			)    ->			Any:
     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
     lowerCamelCase__					:   Dict      				=	v.transpose()
     lowerCamelCase__					:   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  SCREAMING_SNAKE_CASE   ( )    ->  None:
        # a^(-1)
        lowerCamelCase__					:   str      				=	Matrix(3		,			3		,			0				)
        for i in range(3				):
            lowerCamelCase__					:   Tuple      				=	1
        print(F"""a^(-1) is {ainv}"""				)
        # u, v
        lowerCamelCase__					:   List[Any]      				=	Matrix(3		,			1		,			0				)
        lowerCamelCase__				,							lowerCamelCase__				,							lowerCamelCase__					:   Dict      				=	1, 2, -3
        lowerCamelCase__					:   Optional[int]      				=	Matrix(3		,			1		,			0				)
        lowerCamelCase__				,							lowerCamelCase__				,							lowerCamelCase__					:   Dict      				=	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  SCREAMING_SNAKE_CASE   ( )    ->  None:
        import doctest

        doctest.testmod()


    testa()












from pathlib import Path

import fire


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase		,			_UpperCAmelCase		,			_UpperCAmelCase				)    ->  Optional[int]:
    lowerCamelCase__					:   Union[str, Any]      				=	Path(_UpperCAmelCase				)
    lowerCamelCase__					:   int      				=	Path(_UpperCAmelCase				)
    dest_dir.mkdir(exist_ok=_UpperCAmelCase				)
    for path in src_dir.iterdir():
        lowerCamelCase__					:   Tuple      				=	[x.rstrip() for x in list(path.open().readlines()				)][:n]
        lowerCamelCase__					:   Optional[int]      				=	dest_dir.joinpath(path.name				)
        print(_UpperCAmelCase				)
        dest_path.open('w'				).write('\n'.join(_UpperCAmelCase				)				)


if __name__ == "__main__":
    fire.Fire(minify)





