from ..utils import DummyObject, requires_backends




class    a (       metaclass=__lowerCamelCase				):



  """simple docstring"""
  __lowerCAmelCase				      =					["""torch""", """torchsde"""]







  def __init__(							self   ,    *snake_case_   ,    **snake_case_					):

    '''simple docstring'''







    requires_backends(self   ,    ["""torch""", """torchsde"""]					)







  @classmethod
  def    lowercase_  (							cls   ,    *snake_case_   ,    **snake_case_					):

    '''simple docstring'''







    requires_backends(cls   ,    ["""torch""", """torchsde"""]					)







  @classmethod
  def    lowercase_  (							cls   ,    *snake_case_   ,    **snake_case_					):

    '''simple docstring'''







    requires_backends(cls   ,    ["""torch""", """torchsde"""]					)
'''simple docstring'''






from __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload




class    a :



  """simple docstring"""







  def __init__(							self   ,    snake_case_ = None					):

    '''simple docstring'''







    if components is None:
      __UpperCAmelCase:					List[Any]		= []
    __UpperCAmelCase:					Tuple		= list(snake_case_					)







  def __len__(							self					):

    '''simple docstring'''







    return len(self.__components					)







  def __str__(							self					):

    '''simple docstring'''







    return "(" + ",".join(map(snake_case_   ,    self.__components					)					) + ")"







  def __add__(							self   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					int		= len(self					)
    if size == len(snake_case_					):
      __UpperCAmelCase:					str		= [self.__components[i] + other.component(snake_case_					) for i in range(snake_case_					)]
      return Vector(snake_case_					)
    else:
      raise Exception("""must have the same size"""					)







  def __sub__(							self   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					Dict		= len(self					)
    if size == len(snake_case_					):
      __UpperCAmelCase:					Dict		= [self.__components[i] - other.component(snake_case_					) for i in range(snake_case_					)]
      return Vector(snake_case_					)
    else:  # error case
      raise Exception("""must have the same size"""					)







  @overload
  def __mul__(							self   ,    snake_case_					):

    '''simple docstring'''







    ...







  @overload
  def __mul__(							self   ,    snake_case_					):

    '''simple docstring'''







    ...







  def __mul__(							self   ,    snake_case_					):

    '''simple docstring'''







    if isinstance(snake_case_   ,    (float, int)					):
      __UpperCAmelCase:					str		= [c * other for c in self.__components]
      return Vector(snake_case_					)
    elif isinstance(snake_case_   ,    snake_case_					) and len(self					) == len(snake_case_					):
      __UpperCAmelCase:					Dict		= len(self					)
      __UpperCAmelCase:					List[str]		= [self.__components[i] * other.component(snake_case_					) for i in range(snake_case_					)]
      return sum(snake_case_					)
    else:  # error case
      raise Exception("""invalid operand!"""					)







  def    lowercase_  (							self					):

    '''simple docstring'''







    return Vector(self.__components					)







  def    lowercase_  (							self   ,    snake_case_					):

    '''simple docstring'''







    if isinstance(snake_case_   ,    snake_case_					) and -len(self.__components					) <= i < len(self.__components					):
      return self.__components[i]
    else:
      raise Exception("""index out of range"""					)







  def    lowercase_  (							self   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    assert -len(self.__components					) <= pos < len(self.__components					)
    __UpperCAmelCase:					List[str]		= value







  def    lowercase_  (							self					):

    '''simple docstring'''







    if len(self.__components					) == 0:
      raise Exception("""Vector is empty"""					)
    __UpperCAmelCase:					Optional[Any]		= [c**2 for c in self.__components]
    return math.sqrt(sum(snake_case_					)					)







  def    lowercase_  (							self   ,    snake_case_   ,    snake_case_ = False					):

    '''simple docstring'''







    __UpperCAmelCase:					List[Any]		= self * other
    __UpperCAmelCase:					Any		= self.euclidean_length() * other.euclidean_length()
    if deg:
      return math.degrees(math.acos(num / den					)					)
    else:
      return math.acos(num / den					)






def  UpperCamelCase__					(					_lowercase    :				int     )							->	Vector:
  assert isinstance(_lowercase   ,    _lowercase     )
  return Vector([0] * dimension     )






def  UpperCamelCase__					(					_lowercase    :				int   ,    _lowercase    :				int     )							->	Vector:
  assert isinstance(_lowercase   ,    _lowercase     ) and (isinstance(_lowercase   ,    _lowercase     ))
  __UpperCAmelCase:					int		= [0] * dimension
  __UpperCAmelCase:					int		= 1
  return Vector(_lowercase     )






def  UpperCamelCase__					(					_lowercase    :				float   ,    _lowercase    :				Vector   ,    _lowercase    :				Vector     )							->	Vector:
  assert (
      isinstance(_lowercase   ,    _lowercase     )
      and isinstance(_lowercase   ,    _lowercase     )
      and (isinstance(_lowercase   ,    (int, float)     ))
  )
  return x * scalar + y






def  UpperCamelCase__					(					_lowercase    :				int   ,    _lowercase    :				int   ,    _lowercase    :				int     )							->	Vector:
  random.seed(_lowercase     )
  __UpperCAmelCase:					str		= [random.randint(_lowercase   ,    _lowercase     ) for _ in range(_lowercase     )]
  return Vector(_lowercase     )




class    a :



  """simple docstring"""







  def __init__(							self   ,    snake_case_   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    __UpperCAmelCase:					List[str]		= matrix
    __UpperCAmelCase:					Dict		= w
    __UpperCAmelCase:					Tuple		= h







  def __str__(							self					):

    '''simple docstring'''







    __UpperCAmelCase:					Optional[int]		= """"""
    for i in range(self.__height					):
      ans += "|"
      for j in range(self.__width					):
        if j < self.__width - 1:
          ans += str(self.__matrix[i][j]					) + ","
        else:
          ans += str(self.__matrix[i][j]					) + "|\n"
    return ans







  def __add__(							self   ,    snake_case_					):

    '''simple docstring'''







    if self.__width == other.width() and self.__height == other.height():
      __UpperCAmelCase:					List[str]		= []
      for i in range(self.__height					):
        __UpperCAmelCase:					List[Any]		= [
            self.__matrix[i][j] + other.component(snake_case_   ,    snake_case_					)
            for j in range(self.__width					)
        ]
        matrix.append(snake_case_					)
      return Matrix(snake_case_   ,    self.__width   ,    self.__height					)
    else:
      raise Exception("""matrix must have the same dimension!"""					)







  def __sub__(							self   ,    snake_case_					):

    '''simple docstring'''







    if self.__width == other.width() and self.__height == other.height():
      __UpperCAmelCase:					int		= []
      for i in range(self.__height					):
        __UpperCAmelCase:					Any		= [
            self.__matrix[i][j] - other.component(snake_case_   ,    snake_case_					)
            for j in range(self.__width					)
        ]
        matrix.append(snake_case_					)
      return Matrix(snake_case_   ,    self.__width   ,    self.__height					)
    else:
      raise Exception("""matrices must have the same dimension!"""					)







  @overload
  def __mul__(							self   ,    snake_case_					):

    '''simple docstring'''







    ...







  @overload
  def __mul__(							self   ,    snake_case_					):

    '''simple docstring'''







    ...







  def __mul__(							self   ,    snake_case_					):

    '''simple docstring'''







    if isinstance(snake_case_   ,    snake_case_					):  # matrix-vector
      if len(snake_case_					) == self.__width:
        __UpperCAmelCase:					Optional[Any]		= zero_vector(self.__height					)
        for i in range(self.__height					):
          __UpperCAmelCase:					Dict		= [
              self.__matrix[i][j] * other.component(snake_case_					)
              for j in range(self.__width					)
          ]
          ans.change_component(snake_case_   ,    sum(snake_case_					)					)
        return ans
      else:
        raise Exception(
            """vector must have the same size as the """
            """number of columns of the matrix!"""					)
    elif isinstance(snake_case_   ,    (int, float)					):  # matrix-scalar
      __UpperCAmelCase:					Dict		= [
          [self.__matrix[i][j] * other for j in range(self.__width					)]
          for i in range(self.__height					)
      ]
      return Matrix(snake_case_   ,    self.__width   ,    self.__height					)
    return None







  def    lowercase_  (							self					):

    '''simple docstring'''







    return self.__height







  def    lowercase_  (							self					):

    '''simple docstring'''







    return self.__width







  def    lowercase_  (							self   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    if 0 <= x < self.__height and 0 <= y < self.__width:
      return self.__matrix[x][y]
    else:
      raise Exception("""change_component: indices out of bounds"""					)







  def    lowercase_  (							self   ,    snake_case_   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    if 0 <= x < self.__height and 0 <= y < self.__width:
      __UpperCAmelCase:					int		= value
    else:
      raise Exception("""change_component: indices out of bounds"""					)







  def    lowercase_  (							self   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    if self.__height != self.__width:
      raise Exception("""Matrix is not square"""					)
    __UpperCAmelCase:					int		= self.__matrix[:x] + self.__matrix[x + 1 :]
    for i in range(len(snake_case_					)					):
      __UpperCAmelCase:					Optional[Any]		= minor[i][:y] + minor[i][y + 1 :]
    return Matrix(snake_case_   ,    self.__width - 1   ,    self.__height - 1					).determinant()







  def    lowercase_  (							self   ,    snake_case_   ,    snake_case_					):

    '''simple docstring'''







    if self.__height != self.__width:
      raise Exception("""Matrix is not square"""					)
    if 0 <= x < self.__height and 0 <= y < self.__width:
      return (-1) ** (x + y) * self.minor(snake_case_   ,    snake_case_					)
    else:
      raise Exception("""Indices out of bounds"""					)







  def    lowercase_  (							self					):

    '''simple docstring'''







    if self.__height != self.__width:
      raise Exception("""Matrix is not square"""					)
    if self.__height < 1:
      raise Exception("""Matrix has no element"""					)
    elif self.__height == 1:
      return self.__matrix[0][0]
    elif self.__height == 2:
      return (
          self.__matrix[0][0] * self.__matrix[1][1]
          - self.__matrix[0][1] * self.__matrix[1][0]
      )
    else:
      __UpperCAmelCase:					Any		= [
          self.__matrix[0][y] * self.cofactor(0   ,    snake_case_					) for y in range(self.__width					)
      ]
      return sum(snake_case_					)






def  UpperCamelCase__					(					_lowercase    :				int     )							->	Matrix:
  __UpperCAmelCase:					list[list[float]]		= [[0] * n for _ in range(_lowercase     )]
  return Matrix(_lowercase   ,    _lowercase   ,    _lowercase     )







def  UpperCamelCase__					(					_lowercase    :				int   ,    _lowercase    :				int   ,    _lowercase    :				int   ,    _lowercase    :				int     )							->	Matrix:
  random.seed(_lowercase     )
  __UpperCAmelCase:					list[list[float]]		= [
      [random.randint(_lowercase   ,    _lowercase     ) for _ in range(_lowercase     )] for _ in range(_lowercase     )
  ]
  return Matrix(_lowercase   ,    _lowercase   ,    _lowercase     )