


"""simple docstring"""






from __future__ import annotations





class      lowerCamelCase__   :







					"""simple docstring"""


					def __init__(       self    : Dict ,       UpperCamelCase    : list[list[int]]  ):
												'''simple docstring'''






												__UpperCAmelCase   :						Optional[int]      							=					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(UpperCamelCase  ) != 0:
																			__UpperCAmelCase   :						Union[str, Any]      							=					len(rows[0]  )
																			if cols == 0:
																										raise error
																			for row in rows:
																										if len(UpperCamelCase  ) != cols:
																																	raise error
																										for value in row:
																																	if not isinstance(UpperCamelCase ,       (int, float)  ):
																																								raise error
																			__UpperCAmelCase   :						Tuple      							=					rows
												else:
																			__UpperCAmelCase   :						List[Any]      							=					[]






					def lowerCamelCase__							(       self    : int  ):
												'''simple docstring'''






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






					@property
					def lowerCamelCase__							(       self    : Any  ):
												'''simple docstring'''






												return len(self.rows  )






					@property
					def lowerCamelCase__							(       self    : List[Any]  ):
												'''simple docstring'''






												return len(self.rows[0]  )






					@property
					def lowerCamelCase__							(       self    : List[str]  ):
												'''simple docstring'''






												return (self.num_rows, self.num_columns)






					@property
					def lowerCamelCase__							(       self    : Optional[int]  ):
												'''simple docstring'''






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






					def lowerCamelCase__							(       self    : Union[str, Any]  ):
												'''simple docstring'''






												__UpperCAmelCase   :						List[str]      							=					[
												    [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(UpperCamelCase  )






					def lowerCamelCase__							(       self    : 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 lowerCamelCase__							(       self    : List[Any]  ):
												'''simple docstring'''






												return bool(self.determinant()  )






					def lowerCamelCase__							(       self    : str ,       UpperCamelCase    : int ,       UpperCamelCase    : int  ):
												'''simple docstring'''






												__UpperCAmelCase   :						Any      							=					[
												    [
												        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(UpperCamelCase  ).determinant()






					def lowerCamelCase__							(       self    : Tuple ,       UpperCamelCase    : int ,       UpperCamelCase    : int  ):
												'''simple docstring'''






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






					def lowerCamelCase__							(       self    : List[Any]  ):
												'''simple docstring'''






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






					def lowerCamelCase__							(       self    : Union[str, 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 lowerCamelCase__							(       self    : int  ):
												'''simple docstring'''






												__UpperCAmelCase   :						Any      							=					[
												    [self.cofactors().rows[column][row] for column in range(self.num_columns  )]
												    for row in range(self.num_rows  )
												]
												return Matrix(UpperCamelCase  )






					def lowerCamelCase__							(       self    : Optional[Any]  ):
												'''simple docstring'''






												__UpperCAmelCase   :						Tuple      							=					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    : Optional[Any]  ):
												'''simple docstring'''






												return str(self.rows  )






					def __str__(       self    : Optional[Any]  ):
												'''simple docstring'''






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






					def lowerCamelCase__							(       self    : Optional[int] ,       UpperCamelCase    : list[int] ,       UpperCamelCase    : int | None = None  ):
												'''simple docstring'''






												__UpperCAmelCase   :						Union[str, Any]      							=					TypeError("""Row must be a list containing all ints and/or floats"""  )
												if not isinstance(UpperCamelCase ,       UpperCamelCase  ):
																			raise type_error
												for value in row:
																			if not isinstance(UpperCamelCase ,       (int, float)  ):
																										raise type_error
												if len(UpperCamelCase  ) != 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(UpperCamelCase  )
												else:
																			__UpperCAmelCase   :						str      							=					self.rows[0:position] + [row] + self.rows[position:]






					def lowerCamelCase__							(       self    : Tuple ,       UpperCamelCase    : list[int] ,       UpperCamelCase    : int | None = None  ):
												'''simple docstring'''






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






					def __eq__(       self    : str ,       UpperCamelCase    : object  ):
												'''simple docstring'''






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






					def __ne__(       self    : Dict ,       UpperCamelCase    : object  ):
												'''simple docstring'''






												return not self == other






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






												return self * -1






					def __add__(       self    : Optional[int] ,       UpperCamelCase    : 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    : Optional[Any] ,       UpperCamelCase    : 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    : Any ,       UpperCamelCase    : Matrix | int | float  ):
												'''simple docstring'''






												if isinstance(UpperCamelCase ,       (int, float)  ):
																			return Matrix(
																			    [[int(element * other  ) for element in row] for row in self.rows]  )
												elif isinstance(UpperCamelCase ,       UpperCamelCase  ):
																			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(UpperCamelCase ,       UpperCamelCase  ) 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    : Any ,       UpperCamelCase    : int  ):
												'''simple docstring'''






												if not isinstance(UpperCamelCase ,       UpperCamelCase  ):
																			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"""  )
												__UpperCAmelCase   :						Optional[int]      							=					self
												for _ in range(other - 1  ):
																			result *= self
												return result






					@classmethod
					def lowerCamelCase__							(       cls    : int ,       UpperCamelCase    : list[int] ,       UpperCamelCase    : list[int]  ):
												'''simple docstring'''






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


if __name__ == "__main__":
							import doctest

							doctest.testmod()




"""simple docstring"""






from collections.abc import Callable
def      lowerCamelCase       (     _UpperCamelCase		:      Callable[[float], float]       ,			_UpperCamelCase		:      float       ,			_UpperCamelCase		:      float							)		->       float:

							'''simple docstring'''



							__UpperCAmelCase   :						float      							=					a
							__UpperCAmelCase   :						float      							=					b
							if function(_UpperCamelCase							) == 0:  # one of the a or b is a root for the function
														return a
							elif function(_UpperCamelCase							) == 0:
														return b
							elif (
							    function(_UpperCamelCase							) * function(_UpperCamelCase							) > 0
							):  # if none of these are root and they are both positive or negative,
														# then this algorithm can't find the root
														raise ValueError("""could not find root in given interval."""							)
							else:
														__UpperCAmelCase   :						float      							=					start + (end - start) / 2.0
														while abs(start - mid							) > 1_0**-7:  # until precisely equals to 10^-7
																					if function(_UpperCamelCase							) == 0:
																												return mid
																					elif function(_UpperCamelCase							) * function(_UpperCamelCase							) < 0:
																												__UpperCAmelCase   :						Union[str, Any]      							=					mid
																					else:
																												__UpperCAmelCase   :						List[Any]      							=					mid
																					__UpperCAmelCase   :						Optional[Any]      							=					start + (end - start) / 2.0
														return mid
def      lowerCamelCase       (     _UpperCamelCase		:      float							)		->       float:

							'''simple docstring'''



							return x**3 - 2 * x - 5


if __name__ == "__main__":
							print(bisection(f, 1, 1000))

							import doctest

							doctest.testmod()
