





"""simple docstring"""


from __future__ import annotations

from typing import Any



class      __SCREAMING_SNAKE_CASE    :







  '''simple docstring'''


  def __init__(		self   :       List[str]					,   __a   :       int					,   __a   :       int					,   __a   :       float = 0	)		->				None:
        _UpperCamelCase,  _UpperCamelCase      :	Any						=       row, column
        _UpperCamelCase      :	List[str]						=       [[default_value for c in range(__a	)] for r in range(__a	)]

  def __str__(		self   :       Any	)		->				str:
        _UpperCamelCase      :	Optional[Any]						=       F'''Matrix consist of {self.row} rows and {self.column} columns\n'''

        # Make string identifier
        _UpperCamelCase      :	List[Any]						=       0
        for row_vector in self.array:
              for obj in row_vector:
                    _UpperCamelCase      :	Dict						=       max(__a					,   len(str(__a	)	)	)
        _UpperCamelCase      :	Dict						=       F'''%{max_element_length}s'''

        # Make string and return
        def single_line(__a   :       list[float]	) -> str:
              nonlocal string_format_identifier
              _UpperCamelCase      :	Any						=       "["
              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   :       List[Any]	)		->				str:
        return str(self	)

  def    __SCREAMING_SNAKE_CASE				(		self   :       List[str]					,   __a   :       tuple[int, int]	)		->				bool:
        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   :       Dict					,   __a   :       tuple[int, int]	)		->				Any:
        assert self.validate_indicies(__a	)
        return self.array[loc[0]][loc[1]]

  def __setitem__(		self   :       Tuple					,   __a   :       tuple[int, int]					,   __a   :       float	)		->				None:
        assert self.validate_indicies(__a	)
        _UpperCamelCase      :	List[Any]						=       value

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

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

  def __neg__(		self   :       str	)		->				Matrix:
        _UpperCamelCase      :	List[str]						=       Matrix(self.row					,   self.column	)
        for r in range(self.row	):
              for c in range(self.column	):
                    _UpperCamelCase      :	Tuple						=       -self[r, c]
        return result

  def __sub__(		self   :       Any					,   __a   :       Matrix	)		->				Matrix:
        return self + (-another)

  def __mul__(		self   :       Dict					,   __a   :       int | float | Matrix	)		->				Matrix:

        if isinstance(__a					,   (int, float)	):  # Scalar multiplication
              _UpperCamelCase      :	List[Any]						=       Matrix(self.row					,   self.column	)
              for r in range(self.row	):
                    for c in range(self.column	):
                          _UpperCamelCase      :	Dict						=       self[r, c] * another
              return result
        elif isinstance(__a					,   __a	):  # Matrix multiplication
              assert self.column == another.row
              _UpperCamelCase      :	Union[str, Any]						=       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:
              _UpperCamelCase      :	int						=       F'''Unsupported type given for another ({type(__a	)})'''
              raise TypeError(__a	)

  def    __SCREAMING_SNAKE_CASE				(		self   :       List[Any]	)		->				Matrix:
        _UpperCamelCase      :	Union[str, Any]						=       Matrix(self.column					,   self.row	)
        for r in range(self.row	):
              for c in range(self.column	):
                    _UpperCamelCase      :	Union[str, Any]						=       self[r, c]
        return result


  def    __SCREAMING_SNAKE_CASE				(		self   :       Optional[int]					,   __a   :       Matrix					,   __a   :       Matrix	)		->				Any:
        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
        _UpperCamelCase      :	int						=       v.transpose()
        _UpperCamelCase      :	Optional[int]						=       (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__    (					)					->		None:




        """simple docstring"""

        _UpperCamelCase      :	str						=       Matrix(3		,3		,0			)
        for i in range(3			):
              _UpperCamelCase      :	Dict						=       1
        print(F'''a^(-1) is {ainv}'''			)
        # u, v
        _UpperCamelCase      :	str						=       Matrix(3		,1		,0			)
        _UpperCamelCase,  _UpperCamelCase,  _UpperCamelCase      :	Any						=       1, 2, -3
        _UpperCamelCase      :	List[str]						=       Matrix(3		,1		,0			)
        _UpperCamelCase,  _UpperCamelCase,  _UpperCamelCase      :	List[str]						=       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__    (					)					->		None:




        """simple docstring"""

        import doctest

        doctest.testmod()

  testa()







"""simple docstring"""


from collections.abc import Iterator, MutableMapping
from dataclasses import dataclass
from typing import Generic, TypeVar

lowerCamelCase__				  =   TypeVar("KEY")
lowerCamelCase__				  =   TypeVar("VAL")



@dataclass(frozen=_UpperCamelCase		,  slots=_UpperCamelCase   )
class      __SCREAMING_SNAKE_CASE    (						Generic[KEY, VAL]   ):







  '''simple docstring'''


  SCREAMING_SNAKE_CASE__							:KEY
  SCREAMING_SNAKE_CASE__							:VAL





class      __SCREAMING_SNAKE_CASE    (						_Item   ):







  '''simple docstring'''


  def __init__(		self   :       List[str]	)		->				None:
        super().__init__(__a					,   __a	)


  def __bool__(		self   :       Dict	)		->				bool:
        return False





lowerCamelCase__				  =   _DeletedItem()



class      __SCREAMING_SNAKE_CASE    (						MutableMapping[KEY, VAL]   ):







  '''simple docstring'''


  def __init__(		self   :       int					,   __a   :       int = 8					,   __a   :       float = 0.75	)		->				None:
        _UpperCamelCase      :	str						=       initial_block_size
        _UpperCamelCase      :	list[_Item | None]						=       [None] * initial_block_size
        assert 0.0 < capacity_factor < 1.0
        _UpperCamelCase      :	List[str]						=       capacity_factor
        _UpperCamelCase      :	Dict						=       0

  def    __SCREAMING_SNAKE_CASE				(		self   :       int					,   __a   :       KEY	)		->				int:
        return hash(__a	) % len(self._buckets	)

  def    __SCREAMING_SNAKE_CASE				(		self   :       List[Any]					,   __a   :       int	)		->				int:
        return (ind + 1) % len(self._buckets	)

  def    __SCREAMING_SNAKE_CASE				(		self   :       Tuple					,   __a   :       int					,   __a   :       KEY					,   __a   :       VAL	)		->				bool:
        _UpperCamelCase      :	List[Any]						=       self._buckets[ind]
        if not stored:
              _UpperCamelCase      :	Tuple						=       _Item(__a					,   __a	)
              self._len += 1
              return True
        elif stored.key == key:
              _UpperCamelCase      :	Union[str, Any]						=       _Item(__a					,   __a	)
              return True
        else:
              return False

  def    __SCREAMING_SNAKE_CASE				(		self   :       List[str]	)		->				bool:
        _UpperCamelCase      :	Any						=       len(self._buckets	) * self._capacity_factor
        return len(self	) >= int(__a	)

  def    __SCREAMING_SNAKE_CASE				(		self   :       str	)		->				bool:
        if len(self._buckets	) <= self._initial_block_size:
              return False
        _UpperCamelCase      :	List[str]						=       len(self._buckets	) * self._capacity_factor / 2
        return len(self	) < limit

  def    __SCREAMING_SNAKE_CASE				(		self   :       Union[str, Any]					,   __a   :       int	)		->				None:
        _UpperCamelCase      :	Any						=       self._buckets
        _UpperCamelCase      :	List[Any]						=       [None] * new_size
        _UpperCamelCase      :	List[str]						=       0
        for item in old_buckets:
              if item:
                    self._add_item(item.key					,   item.val	)

  def    __SCREAMING_SNAKE_CASE				(		self   :       int	)		->				None:
        self._resize(len(self._buckets	) * 2	)

  def    __SCREAMING_SNAKE_CASE				(		self   :       Union[str, Any]	)		->				None:
        self._resize(len(self._buckets	) // 2	)

  def    __SCREAMING_SNAKE_CASE				(		self   :       List[Any]					,   __a   :       KEY	)		->				Iterator[int]:
        _UpperCamelCase      :	str						=       self._get_bucket_index(__a	)
        for _ in range(len(self._buckets	)	):
              yield ind
              _UpperCamelCase      :	Tuple						=       self._get_next_ind(__a	)

  def    __SCREAMING_SNAKE_CASE				(		self   :       Optional[int]					,   __a   :       KEY					,   __a   :       VAL	)		->				None:
        for ind in self._iterate_buckets(__a	):
              if self._try_set(__a					,   __a					,   __a	):
                    break

  def __setitem__(		self   :       int					,   __a   :       KEY					,   __a   :       VAL	)		->				None:
        if self._is_full():
              self._size_up()

        self._add_item(__a					,   __a	)

  def __delitem__(		self   :       str					,   __a   :       KEY	)		->				None:
        for ind in self._iterate_buckets(__a	):
              _UpperCamelCase      :	Tuple						=       self._buckets[ind]
              if item is None:
                    raise KeyError(__a	)
              if item is _deleted:
                    continue
              if item.key == key:
                    _UpperCamelCase      :	List[Any]						=       _deleted
                    self._len -= 1
                    break
        if self._is_sparse():
              self._size_down()

  def __getitem__(		self   :       str					,   __a   :       KEY	)		->				VAL:
        for ind in self._iterate_buckets(__a	):
              _UpperCamelCase      :	Tuple						=       self._buckets[ind]
              if item is None:
                    break
              if item is _deleted:
                    continue
              if item.key == key:
                    return item.val
        raise KeyError(__a	)

  def __len__(		self   :       List[Any]	)		->				int:
        return self._len

  def __iter__(		self   :       List[str]	)		->				Iterator[KEY]:
        yield from (item.key for item in self._buckets if item)


  def __repr__(		self   :       List[str]	)		->				str:
        _UpperCamelCase      :	Optional[int]						=       " ,".join(
            F'''{item.key}: {item.val}''' for item in self._buckets if item	)
        return F'''HashMap({val_string})'''
