



from __future__ import annotations

from typing import Any






class __A    :



 '''simple docstring'''







 def __init__(self				,     A				,     A				,     A = 0 )					->  None:


      """simple docstring"""



      _a						,					_a											=						row, column
      _a											=						[[default_value for c in range(A )] for r in range(A )]



 def __str__(self )					->  str:


      """simple docstring"""



      _a											=						f'''Matrix consist of {self.row} rows and {self.column} columns\n'''

      # Make string identifier
      _a											=						0
      for row_vector in self.array:
           for obj in row_vector:
                _a											=						max(A				,     len(str(A ) ) )
      _a											=						f'''%{max_element_length}s'''

      # Make string and return
      def single_line(A ) -> str:
           nonlocal string_format_identifier
           _a											=						'''['''
           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 )					->  str:


      """simple docstring"""



      return str(self )



 def       a__						(self				,     A )					->  bool:


      """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				,     A )					->  Any:


      """simple docstring"""



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



 def __setitem__(self				,     A				,     A )					->  None:


      """simple docstring"""



      assert self.validate_indicies(A )
      _a											=						value



 def __add__(self				,     A )					->  Matrix:


      """simple docstring"""



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

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



 def __neg__(self )					->  Matrix:


      """simple docstring"""



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



 def __sub__(self				,     A )					->  Matrix:


      """simple docstring"""



      return self + (-another)



 def __mul__(self				,     A )					->  Matrix:


      """simple docstring"""



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



 def       a__						(self )					->  Matrix:


      """simple docstring"""



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



 def       a__						(self				,     A				,     A )					->  Any:


      """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
      _a											=						v.transpose()
      _a											=						(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 lowerCAmelCase						():



       """simple docstring"""



       _a											=						Matrix(3						,			3						,			0)
       for i in range(3):
            _a											=						1
       print(F'''a^(-1) is {ainv}''')
       # u, v
       _a											=						Matrix(3						,			1						,			0)
       _a						,					_a						,					_a											=						1, 2, -3
       _a											=						Matrix(3						,			1						,			0)
       _a						,					_a						,					_a											=						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(__A						,			__A)}''')




  def lowerCAmelCase						():



       """simple docstring"""



       import doctest

       doctest.testmod()
  testa()








'''simple docstring'''





from __future__ import annotations

import typing
from collections.abc import Iterable

import numpy as np

lowercase_	 =						typing.Union[Iterable[float], Iterable[int], np.ndarray]  # noqa: UP007
lowercase_	 =						typing.Union[np.floataa, int, float]  # noqa: UP007




def lowerCAmelCase						(__A						,			__A):



     """simple docstring"""



     return np.sqrt(np.sum((np.asarray(__A) - np.asarray(__A)) ** 2))




def lowerCAmelCase						(__A						,			__A):



     """simple docstring"""



     return sum((va - va) ** 2 for va, va in zip(__A						,			__A)) ** (1 / 2)


if __name__ == "__main__":




  def lowerCAmelCase						():



       """simple docstring"""



       from timeit import timeit

       print('''Without Numpy''')
       print(
           timeit(
               '''euclidean_distance_no_np([1, 2, 3], [4, 5, 6])'''						,			number=10_000						,			globals=globals()						,			))
       print('''With Numpy''')
       print(
           timeit(
               '''euclidean_distance([1, 2, 3], [4, 5, 6])'''						,			number=10_000						,			globals=globals()						,			))
  benchmark()



