'''simple docstring'''

from __future__ import annotations

from typing import Any



class       UpperCAmelCase  :





       '''simple docstring'''



       def __init__(						self     ,       __lowerCAmelCase     ,       __lowerCAmelCase     ,       __lowerCAmelCase = 0			)  ->  None:
        lowercase__    :   List[str]						=				row, column
        lowercase__    :   Dict						=				[[default_value for c in range(__lowerCAmelCase			)] for r in range(__lowerCAmelCase			)]

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

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

        # Make string and return
        def single_line(__lowerCAmelCase			) -> str:
         nonlocal string_format_identifier
         lowercase__    :   int						=				'''['''
         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			)
        lowercase__    :   Any						=				value

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

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

       def __neg__(						self			)  ->  Matrix:
        lowercase__    :   Union[str, Any]						=				Matrix(self.row     ,       self.column			)
        for r in range(self.row			):
         for c in range(self.column			):
          lowercase__    :   Any						=				-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
         lowercase__    :   Any						=				Matrix(self.row     ,       self.column			)
         for r in range(self.row			):
          for c in range(self.column			):
           lowercase__    :   str						=				self[r, c] * another
         return result
        elif isinstance(__lowerCAmelCase     ,       __lowerCAmelCase			):  # Matrix multiplication
         assert self.column == another.row
         lowercase__    :   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:
         lowercase__    :   Union[str, Any]						=				F"""Unsupported type given for another ({type(__lowerCAmelCase			)})"""
         raise TypeError(__lowerCAmelCase			)

       def _lowerCAmelCase(						self			)  ->  Matrix:
        lowercase__    :   Tuple						=				Matrix(self.column     ,       self.row			)
        for r in range(self.row			):
         for c in range(self.column			):
          lowercase__    :   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
        lowercase__    :   Optional[Any]						=				v.transpose()
        lowercase__    :   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       __UpperCamelCase	(       ):
   # a^(-1)
   lowercase__    :   Any						=				Matrix(3		,					3		,					0					)
   for i in range(3					):
    lowercase__    :   int						=				1
   print(F"""a^(-1) is {ainv}"""					)
   # u, v
   lowercase__    :   str						=				Matrix(3		,					1		,					0					)
   lowercase__    :   List[Any]						=				1, 2, -3
   lowercase__    :   Optional[Any]						=				Matrix(3		,					1		,					0					)
   lowercase__    :   Union[str, 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(UpperCAmelCase		,					UpperCAmelCase					)}"""					)
  def       __UpperCamelCase	(       ):
   import doctest

   doctest.testmod()





  testa()


'''simple docstring'''

import numpy as np
def       __UpperCamelCase	(       UpperCAmelCase					):
 return 1 / (1 + np.exp(-vector					))
def       __UpperCamelCase	(       UpperCAmelCase					):
 return vector * sigmoid(UpperCAmelCase					)


if __name__ == "__main__":
  import doctest

  doctest.testmod()

