






'''simple docstring'''

from __future__ import annotations

from typing import Any







class 	SCREAMING_SNAKE_CASE	:




       def __init__(					self      : int	,    A__      : int	,    A__      : int	,    A__      : float = 0					):


            """simple docstring"""







            __lowerCamelCase   ,      __lowerCamelCase						:       Tuple				   =				row, column
            __lowerCamelCase						:       List[str]				   =				[[default_value for c in range(UpperCamelCase__					)] for r in range(UpperCamelCase__					)]




       def __str__(					self      : List[str]					):


            """simple docstring"""







            __lowerCamelCase						:       Dict				   =				f"Matrix consist of {self.row} rows and {self.column} columns\n"

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

            # Make string and return
            def single_line(A__      : list[float]					) -> str:
                 nonlocal string_format_identifier
                 __lowerCamelCase						:       Tuple				   =				"""["""
                 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      : int					):


            """simple docstring"""







            return str(self					)




       def 					a_					(					self      : Tuple	,    A__      : tuple[int, int]					):


            """simple docstring"""







            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      : str	,    A__      : tuple[int, int]					):


            """simple docstring"""







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




       def __setitem__(					self      : Dict	,    A__      : tuple[int, int]	,    A__      : float					):


            """simple docstring"""







            assert self.validate_indicies(UpperCamelCase__					)
            __lowerCamelCase						:       Optional[Any]				   =				value




       def __add__(					self      : Optional[int]	,    A__      : Matrix					):


            """simple docstring"""







            assert isinstance(UpperCamelCase__	,    UpperCamelCase__					)
            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						:       Union[str, Any]				   =				self[r, c] + another[r, c]
            return result




       def __neg__(					self      : Optional[int]					):


            """simple docstring"""







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




       def __sub__(					self      : List[str]	,    A__      : Matrix					):


            """simple docstring"""







            return self + (-another)




       def __mul__(					self      : Any	,    A__      : int | float | Matrix					):


            """simple docstring"""







            if isinstance(UpperCamelCase__	,    (int, float)					):  # Scalar multiplication
                 __lowerCamelCase						:       Optional[Any]				   =				Matrix(self.row	,    self.column					)
                 for r in range(self.row					):
                      for c in range(self.column					):
                           __lowerCamelCase						:       List[Any]				   =				self[r, c] * another
                 return result
            elif isinstance(UpperCamelCase__	,    UpperCamelCase__					):  # Matrix multiplication
                 assert self.column == another.row
                 __lowerCamelCase						:       List[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						:       Tuple				   =				f"Unsupported type given for another ({type(UpperCamelCase__					)})"
                 raise TypeError(UpperCamelCase__					)




       def 					a_					(					self      : List[str]					):


            """simple docstring"""







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




       def 					a_					(					self      : Dict	,    A__      : Matrix	,    A__      : Matrix					):


            """simple docstring"""







            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						:       Optional[int]				   =				v.transpose()
            __lowerCamelCase						:       Optional[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  ()   ->     List[str]:


        """simple docstring"""
        # a^(-1)
        __lowerCamelCase						:       List[str]				   =				Matrix(3,						3,						0     )
        for i in range(3     ):
             __lowerCamelCase						:       Union[str, Any]				   =				1
        print(f"a^(-1) is {ainv}"     )
        # u, v
        __lowerCamelCase						:       List[Any]				   =				Matrix(3,						1,						0     )
        __lowerCamelCase   ,      __lowerCamelCase   ,      __lowerCamelCase						:       Tuple				   =				1, 2, -3
        __lowerCamelCase						:       str				   =				Matrix(3,						1,						0     )
        __lowerCamelCase   ,      __lowerCamelCase   ,      __lowerCamelCase						:       Optional[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  ()   ->     List[Any]:


        """simple docstring"""
        import doctest

        doctest.testmod()
   testa()











'''simple docstring'''

from __future__ import annotations

import typing
from collections.abc import Iterable

import numpy as np

UpperCAmelCase__						:List[str]          =			typing.Union[Iterable[float], Iterable[int], np.ndarray]  # noqa: UP007
UpperCAmelCase__						:Optional[int]          =			typing.Union[np.floataa, int, float]  # noqa: UP007
def     __lowercase  (_lowercase,						_lowercase     )   ->     VectorOut:


     """simple docstring"""
     return np.sqrt(np.sum((np.asarray(_lowercase     ) - np.asarray(_lowercase     )) ** 2     )     )
def     __lowercase  (_lowercase,						_lowercase     )   ->     VectorOut:


     """simple docstring"""
     return sum((va - va) ** 2 for va, va in zip(_lowercase,						_lowercase     )     ) ** (1 / 2)


if __name__ == "__main__":
   def     __lowercase  ()   ->     None:


        """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()



