


'''simple docstring'''







from __future__ import annotations


class  lowerCAmelCase_						:





  """simple docstring"""



  def __init__(					self     :							str				,							SCREAMING_SNAKE_CASE__     :							list[list[int]]						):





       '''simple docstring'''

       __a       =   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(SCREAMING_SNAKE_CASE__						) != 0:
            __a       =   len(rows[0]						)
            if cols == 0:
                 raise error
            for row in rows:
                 if len(SCREAMING_SNAKE_CASE__						) != cols:
                      raise error
                 for value in row:
                      if not isinstance(SCREAMING_SNAKE_CASE__				,							(int, float)						):
                           raise error
            __a       =   rows
       else:
            __a       =   []

  def __a						(					self     :							str						):





       '''simple docstring'''

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

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





       '''simple docstring'''

       return len(self.rows						)

  @property
  def __a						(					self     :							Any						):





       '''simple docstring'''

       return len(self.rows[0]						)

  @property
  def __a						(					self     :							str						):





       '''simple docstring'''

       return (self.num_rows, self.num_columns)

  @property
  def __a						(					self     :							List[str]						):





       '''simple docstring'''

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

  def __a						(					self     :							List[Any]						):





       '''simple docstring'''

       __a       =   [
           [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(SCREAMING_SNAKE_CASE__						)

  def __a						(					self     :							List[Any]						):





       '''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     :							List[Any]						):





       '''simple docstring'''

       return bool(self.determinant()						)

  def __a						(					self     :							Optional[Any]				,							SCREAMING_SNAKE_CASE__     :							int				,							SCREAMING_SNAKE_CASE__     :							int						):





       '''simple docstring'''

       __a       =   [
           [
               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(SCREAMING_SNAKE_CASE__						).determinant()

  def __a						(					self     :							Any				,							SCREAMING_SNAKE_CASE__     :							int				,							SCREAMING_SNAKE_CASE__     :							int						):





       '''simple docstring'''

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

  def __a						(					self     :							List[Any]						):





       '''simple docstring'''

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

  def __a						(					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 __a						(					self     :							Optional[Any]						):





       '''simple docstring'''

       __a       =   [
           [self.cofactors().rows[column][row] for column in range(self.num_columns						)]
           for row in range(self.num_rows						)
       ]
       return Matrix(SCREAMING_SNAKE_CASE__						)

  def __a						(					self     :							Optional[Any]						):





       '''simple docstring'''

       __a       =   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     :							Any						):





       '''simple docstring'''

       return str(self.rows						)

  def __str__(					self     :							Optional[int]						):





       '''simple docstring'''

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

  def __a						(					self     :							List[str]				,							SCREAMING_SNAKE_CASE__     :							list[int]				,							SCREAMING_SNAKE_CASE__     :							int | None = None						):





       '''simple docstring'''

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

  def __a						(					self     :							Any				,							SCREAMING_SNAKE_CASE__     :							list[int]				,							SCREAMING_SNAKE_CASE__     :							int | None = None						):





       '''simple docstring'''

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

  def __eq__(					self     :							Optional[int]				,							SCREAMING_SNAKE_CASE__     :							object						):





       '''simple docstring'''

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

  def __ne__(					self     :							Union[str, Any]				,							SCREAMING_SNAKE_CASE__     :							object						):





       '''simple docstring'''

       return not self == other

  def __neg__(					self     :							Optional[int]						):





       '''simple docstring'''

       return self * -1

  def __add__(					self     :							int				,							SCREAMING_SNAKE_CASE__     :							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				,							SCREAMING_SNAKE_CASE__     :							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				,							SCREAMING_SNAKE_CASE__     :							Matrix | int | float						):





       '''simple docstring'''

       if isinstance(SCREAMING_SNAKE_CASE__				,							(int, float)						):
            return Matrix(
                [[int(element * other						) for element in row] for row in self.rows]						)
       elif isinstance(SCREAMING_SNAKE_CASE__				,							SCREAMING_SNAKE_CASE__						):
            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(SCREAMING_SNAKE_CASE__				,							SCREAMING_SNAKE_CASE__						) 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     :							Optional[Any]				,							SCREAMING_SNAKE_CASE__     :							int						):





       '''simple docstring'''

       if not isinstance(SCREAMING_SNAKE_CASE__				,							SCREAMING_SNAKE_CASE__						):
            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"""						)
       __a       =   self
       for _ in range(other - 1						):
            result *= self
       return result


  @classmethod
  def __a						(					cls     :							List[str]				,							SCREAMING_SNAKE_CASE__     :							list[int]				,							SCREAMING_SNAKE_CASE__     :							list[int]						):





       '''simple docstring'''

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


if __name__ == "__main__":
 import doctest

 doctest.testmod()










'''simple docstring'''







import math
import random
from typing import Any

from .hill_climbing import SearchProblem




def        __lowercase						(      __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE = True				,  __SCREAMING_SNAKE_CASE = math.inf				,  __SCREAMING_SNAKE_CASE = -math.inf				,  __SCREAMING_SNAKE_CASE = math.inf				,  __SCREAMING_SNAKE_CASE = -math.inf				,  __SCREAMING_SNAKE_CASE = False				,  __SCREAMING_SNAKE_CASE = 100				,  __SCREAMING_SNAKE_CASE = 0.01				,  __SCREAMING_SNAKE_CASE = 1				,  )				->					Any:
     """simple docstring"""




     __a       =   False
     __a       =   search_prob
     __a       =   start_temperate
     __a       =   []
     __a       =   0
     __a       =   None

     while not search_end:
          __a       =   current_state.score()
          if best_state is None or current_score > best_state.score():
               __a       =   current_state
          scores.append(__SCREAMING_SNAKE_CASE		)
          iterations += 1
          __a       =   None
          __a       =   current_state.get_neighbors()
          while (
              next_state is None and neighbors
          ):  # till we do not find a neighbor that we can move to
               __a       =   random.randint(0				,  len(__SCREAMING_SNAKE_CASE		) - 1		)  # picking a random neighbor
               __a       =   neighbors.pop(__SCREAMING_SNAKE_CASE		)
               __a       =   picked_neighbor.score() - current_score

               if (
                   picked_neighbor.x > max_x
                   or picked_neighbor.x < min_x
                   or picked_neighbor.y > max_y
                   or picked_neighbor.y < min_y
               ):
                    continue  # neighbor outside our bounds

               if not find_max:
                    __a       =   change * -1  # in case we are finding minimum
               if change > 0:  # improves the solution
                    __a       =   picked_neighbor
               else:
                    __a       =   (math.e) ** (
                        change / current_temp
                    )  # probability generation function
                    if random.random() < probability:  # random number within probability
                         __a       =   picked_neighbor
          __a       =   current_temp - (current_temp * rate_of_decrease)

          if current_temp < threshold_temp or next_state is None:
               # temperature below threshold, or could not find a suitable neighbor
               __a       =   True
          else:
               __a       =   next_state

     if visualization:
          from matplotlib import pyplot as plt

          plt.plot(range(__SCREAMING_SNAKE_CASE		)				,  __SCREAMING_SNAKE_CASE		)
          plt.xlabel("""Iterations"""		)
          plt.ylabel("""Function values"""		)
          plt.show()
     return best_state


if __name__ == "__main__":




 def        __lowercase						(      __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE		)				->					int:
      """simple docstring"""




      return (x**2) + (y**2)

 # starting the problem with initial coordinates (12, 47)
 SCREAMING_SNAKE_CASE_      =			SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
 SCREAMING_SNAKE_CASE_      =			simulated_annealing(
     prob, find_max=False, max_x=1_00, min_x=5, max_y=50, min_y=-5, visualization=True
 )
 print(
     'The minimum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 '
     f"""and 50 > y > - 5 found via hill climbing: {local_min.score()}"""
 )

 # starting the problem with initial coordinates (12, 47)
 SCREAMING_SNAKE_CASE_      =			SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
 SCREAMING_SNAKE_CASE_      =			simulated_annealing(
     prob, find_max=True, max_x=1_00, min_x=5, max_y=50, min_y=-5, visualization=True
 )
 print(
     'The maximum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 '
     f"""and 50 > y > - 5 found via hill climbing: {local_min.score()}"""
 )




 def        __lowercase						(      __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE		)				->					int:
      """simple docstring"""




      return (3 * x**2) - (6 * y)

 SCREAMING_SNAKE_CASE_      =			SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
 SCREAMING_SNAKE_CASE_      =			simulated_annealing(prob, find_max=False, visualization=True)
 print(
     'The minimum score for f(x, y) = 3*x^2 - 6*y found via hill climbing: '
     f"""{local_min.score()}"""
 )

 SCREAMING_SNAKE_CASE_      =			SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
 SCREAMING_SNAKE_CASE_      =			simulated_annealing(prob, find_max=True, visualization=True)



 print(
     'The maximum score for f(x, y) = 3*x^2 - 6*y found via hill climbing: '
     f"""{local_min.score()}"""
 )






