






'''simple docstring'''

from __future__ import annotations







class 	SCREAMING_SNAKE_CASE	:




       def __init__(					self      : Any	,    A__      : list[list[int]]					):


            """simple docstring"""







            __lowerCamelCase						:       List[str]				   =				TypeError(
                """Matrices must be formed from a list of zero or more lists containing at """
                """least one and the same number of values, each of which must be of type """
                """int or float."""					)
            if len(A__					) != 0:
                 __lowerCamelCase						:       Optional[int]				   =				len(rows[0]					)
                 if cols == 0:
                      raise error
                 for row in rows:
                      if len(A__					) != cols:
                           raise error
                      for value in row:
                           if not isinstance(A__	,    (int, float)					):
                                raise error
                 __lowerCamelCase						:       Tuple				   =				rows
            else:
                 __lowerCamelCase						:       Optional[int]				   =				[]




       def 					a_					(					self      : Optional[Any]					):


            """simple docstring"""







            return [[row[i] for row in self.rows] for i in range(len(self.rows[0]					)					)]




       @property
       def 					a_					(					self      : List[Any]					):


            """simple docstring"""







            return len(self.rows					)




       @property
       def 					a_					(					self      : Tuple					):


            """simple docstring"""







            return len(self.rows[0]					)




       @property
       def 					a_					(					self      : Optional[int]					):


            """simple docstring"""







            return (self.num_rows, self.num_columns)




       @property
       def 					a_					(					self      : int					):


            """simple docstring"""







            return self.order[0] == self.order[1]




       def 					a_					(					self      : Tuple					):


            """simple docstring"""







            __lowerCamelCase						:       List[Any]				   =				[
                [0 if column_num != row_num else 1 for column_num in range(self.num_rows					)]
                for row_num in range(self.num_rows					)
            ]
            return Matrix(A__					)




       def 					a_					(					self      : List[str]					):


            """simple docstring"""







            if not self.is_square:
                 return 0
            if self.order == (0, 0):
                 return 1
            if self.order == (1, 1):
                 return int(self.rows[0][0]					)
            if self.order == (2, 2):
                 return int(
                     (self.rows[0][0] * self.rows[1][1])
                     - (self.rows[0][1] * self.rows[1][0])					)
            else:
                 return sum(
                     self.rows[0][column] * self.cofactors().rows[0][column]
                     for column in range(self.num_columns					)					)




       def 					a_					(					self      : Dict					):


            """simple docstring"""







            return bool(self.determinant()					)




       def 					a_					(					self      : List[Any]	,    A__      : int	,    A__      : int					):


            """simple docstring"""







            __lowerCamelCase						:       Dict				   =				[
                [
                    self.rows[other_row][other_column]
                    for other_column in range(self.num_columns					)
                    if other_column != column
                ]
                for other_row in range(self.num_rows					)
                if other_row != row
            ]
            return Matrix(A__					).determinant()




       def 					a_					(					self      : Any	,    A__      : int	,    A__      : int					):


            """simple docstring"""







            if (row + column) % 2 == 0:
                 return self.get_minor(A__	,    A__					)
            return -1 * self.get_minor(A__	,    A__					)




       def 					a_					(					self      : Tuple					):


            """simple docstring"""







            return Matrix(
                [
                    [self.get_minor(A__	,    A__					) for column in range(self.num_columns					)]
                    for row in range(self.num_rows					)
                ]					)




       def 					a_					(					self      : Optional[Any]					):


            """simple docstring"""







            return Matrix(
                [
                    [
                        self.minors().rows[row][column]
                        if (row + column) % 2 == 0
                        else self.minors().rows[row][column] * -1
                        for column in range(self.minors().num_columns					)
                    ]
                    for row in range(self.minors().num_rows					)
                ]					)




       def 					a_					(					self      : Optional[Any]					):


            """simple docstring"""







            __lowerCamelCase						:       Optional[int]				   =				[
                [self.cofactors().rows[column][row] for column in range(self.num_columns					)]
                for row in range(self.num_rows					)
            ]
            return Matrix(A__					)




       def 					a_					(					self      : Union[str, Any]					):


            """simple docstring"""







            __lowerCamelCase						:       Dict				   =				self.determinant()
            if not determinant:
                 raise TypeError("""Only matrices with a non-zero determinant have an inverse"""					)
            return self.adjugate() * (1 / determinant)




       def __repr__(					self      : List[str]					):


            """simple docstring"""







            return str(self.rows					)




       def __str__(					self      : str					):


            """simple docstring"""







            if self.num_rows == 0:
                 return "[]"
            if self.num_rows == 1:
                 return "[[" + ". ".join(str(self.rows[0]					)					) + "]]"
            return (
                "["
                + "\n ".join(
                    [
                        """[""" + """. """.join([str(A__					) for value in row]					) + """.]"""
                        for row in self.rows
                    ]					)
                + "]"
            )




       def 					a_					(					self      : List[Any]	,    A__      : list[int]	,    A__      : int | None = None					):


            """simple docstring"""







            __lowerCamelCase						:       List[str]				   =				TypeError("""Row must be a list containing all ints and/or floats"""					)
            if not isinstance(A__	,    A__					):
                 raise type_error
            for value in row:
                 if not isinstance(A__	,    (int, float)					):
                      raise type_error
            if len(A__					) != self.num_columns:
                 raise ValueError(
                     """Row must be equal in length to the other rows in the matrix"""					)
            if position is None:
                 self.rows.append(A__					)
            else:
                 __lowerCamelCase						:       Tuple				   =				self.rows[0:position] + [row] + self.rows[position:]




       def 					a_					(					self      : Optional[Any]	,    A__      : list[int]	,    A__      : int | None = None					):


            """simple docstring"""







            __lowerCamelCase						:       str				   =				TypeError(
                """Column must be a list containing all ints and/or floats"""					)
            if not isinstance(A__	,    A__					):
                 raise type_error
            for value in column:
                 if not isinstance(A__	,    (int, float)					):
                      raise type_error
            if len(A__					) != self.num_rows:
                 raise ValueError(
                     """Column must be equal in length to the other columns in the matrix"""					)
            if position is None:
                 __lowerCamelCase						:       Optional[Any]				   =				[self.rows[i] + [column[i]] for i in range(self.num_rows					)]
            else:
                 __lowerCamelCase						:       Union[str, Any]				   =				[
                     self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
                     for i in range(self.num_rows					)
                 ]




       def __eq__(					self      : Any	,    A__      : object					):


            """simple docstring"""







            if not isinstance(A__	,    A__					):
                 return NotImplemented
            return self.rows == other.rows




       def __ne__(					self      : List[str]	,    A__      : object					):


            """simple docstring"""







            return not self == other




       def __neg__(					self      : Union[str, Any]					):


            """simple docstring"""







            return self * -1




       def __add__(					self      : List[Any]	,    A__      : Matrix					):


            """simple docstring"""







            if self.order != other.order:
                 raise ValueError("""Addition requires matrices of the same order"""					)
            return Matrix(
                [
                    [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns					)]
                    for i in range(self.num_rows					)
                ]					)




       def __sub__(					self      : int	,    A__      : Matrix					):


            """simple docstring"""







            if self.order != other.order:
                 raise ValueError("""Subtraction requires matrices of the same order"""					)
            return Matrix(
                [
                    [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns					)]
                    for i in range(self.num_rows					)
                ]					)




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


            """simple docstring"""







            if isinstance(A__	,    (int, float)					):
                 return Matrix(
                     [[int(element * other					) for element in row] for row in self.rows]					)
            elif isinstance(A__	,    A__					):
                 if self.num_columns != other.num_rows:
                      raise ValueError(
                          """The number of columns in the first matrix must """
                          """be equal to the number of rows in the second"""					)
                 return Matrix(
                     [
                         [Matrix.dot_product(A__	,    A__					) for column in other.columns()]
                         for row in self.rows
                     ]					)
            else:
                 raise TypeError(
                     """A Matrix can only be multiplied by an int, float, or another matrix"""					)




       def __pow__(					self      : List[str]	,    A__      : int					):


            """simple docstring"""







            if not isinstance(A__	,    A__					):
                 raise TypeError("""A Matrix can only be raised to the power of an int"""					)
            if not self.is_square:
                 raise ValueError("""Only square matrices can be raised to a power"""					)
            if other == 0:
                 return self.identity()
            if other < 0:
                 if self.is_invertable():
                      return self.inverse() ** (-other)
                 raise ValueError(
                     """Only invertable matrices can be raised to a negative power"""					)
            __lowerCamelCase						:       Union[str, Any]				   =				self
            for _ in range(other - 1					):
                 result *= self
            return result




       @classmethod
       def 					a_					(					cls      : Union[str, Any]	,    A__      : list[int]	,    A__      : list[int]					):


            """simple docstring"""







            return sum(row[i] * column[i] for i in range(len(A__					)					)					)


if __name__ == "__main__":
   import doctest

   doctest.testmod()











'''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()



