



from __future__ import annotations

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



class    UpperCAmelCase__:

   '''simple docstring'''




   def __init__(    self	:      Optional[int]      ,					lowerCAmelCase	:      Collection[float] | None = None)						->					None:




         """simple docstring"""

         if components is None:
               lowercase__  =	[]
         lowercase__  =	list(lowerCAmelCase)


   def __len__(    self	:      Tuple)						->					int:




         """simple docstring"""

         return len(self.__components)


   def __str__(    self	:      Optional[Any])						->					str:




         """simple docstring"""

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


   def __add__(    self	:      List[Any]      ,					lowerCAmelCase	:      Vector)						->					Vector:




         """simple docstring"""

         lowercase__  =	len(self)
         if size == len(lowerCAmelCase):
               lowercase__  =	[self.__components[i] + other.component(lowerCAmelCase) for i in range(lowerCAmelCase)]
               return Vector(lowerCAmelCase)
         else:
               raise Exception('must have the same size')


   def __sub__(    self	:      Optional[int]      ,					lowerCAmelCase	:      Vector)						->					Vector:




         """simple docstring"""

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


   @overload
   def __mul__(    self	:      int      ,					lowerCAmelCase	:      float)						->					Vector:




         """simple docstring"""

         ...


   @overload
   def __mul__(    self	:      Tuple      ,					lowerCAmelCase	:      Vector)						->					float:




         """simple docstring"""

         ...


   def __mul__(    self	:      List[str]      ,					lowerCAmelCase	:      float | Vector)						->					float | Vector:




         """simple docstring"""

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


   def       UpperCAmelCase		(    self	:      List[Any])						->					Vector:




         """simple docstring"""

         return Vector(self.__components)


   def       UpperCAmelCase		(    self	:      Any      ,					lowerCAmelCase	:      int)						->					float:




         """simple docstring"""

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


   def       UpperCAmelCase		(    self	:      List[Any]      ,					lowerCAmelCase	:      int      ,					lowerCAmelCase	:      float)						->					None:




         """simple docstring"""

         assert -len(self.__components) <= pos < len(self.__components)
         lowercase__  =	value


   def       UpperCAmelCase		(    self	:      int)						->					float:




         """simple docstring"""

         if len(self.__components) == 0:
               raise Exception('Vector is empty')
         lowercase__  =	[c**2 for c in self.__components]
         return math.sqrt(sum(lowerCAmelCase))



   def       UpperCAmelCase		(    self	:      List[str]      ,					lowerCAmelCase	:      Vector      ,					lowerCAmelCase	:      bool = False)						->					float:




         """simple docstring"""

         lowercase__  =	self * other
         lowercase__  =	self.euclidean_length() * other.euclidean_length()
         if deg:
               return math.degrees(math.acos(num / den))
         else:
               return math.acos(num / den)

def 	_lowerCAmelCase (    A__						):
      assert isinstance(A__    ,	A__						)
      return Vector([0] * dimension						)

def 	_lowerCAmelCase (    A__    ,	A__						):
      assert isinstance(A__    ,	A__						) and (isinstance(A__    ,	A__						))
      lowercase__  =	[0] * dimension
      lowercase__  =	1
      return Vector(A__						)

def 	_lowerCAmelCase (    A__    ,	A__    ,	A__						):
      assert (
          isinstance(A__    ,	A__						)
          and isinstance(A__    ,	A__						)
          and (isinstance(A__    ,	(int, float)						))
      )
      return x * scalar + y

def 	_lowerCAmelCase (    A__    ,	A__    ,	A__						):
      random.seed(A__						)
      lowercase__  =	[random.randint(A__    ,	A__						) for _ in range(A__						)]
      return Vector(A__						)



class    UpperCAmelCase__:

   '''simple docstring'''




   def __init__(    self	:      int      ,					lowerCAmelCase	:      list[list[float]]      ,					lowerCAmelCase	:      int      ,					lowerCAmelCase	:      int)						->					None:




         """simple docstring"""

         lowercase__  =	matrix
         lowercase__  =	w
         lowercase__  =	h


   def __str__(    self	:      List[str])						->					str:




         """simple docstring"""

         lowercase__  =	''
         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	:      List[str]      ,					lowerCAmelCase	:      Matrix)						->					Matrix:




         """simple docstring"""

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


   def __sub__(    self	:      List[Any]      ,					lowerCAmelCase	:      Matrix)						->					Matrix:




         """simple docstring"""

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


   @overload
   def __mul__(    self	:      Optional[Any]      ,					lowerCAmelCase	:      float)						->					Matrix:




         """simple docstring"""

         ...


   @overload
   def __mul__(    self	:      Tuple      ,					lowerCAmelCase	:      Vector)						->					Vector:




         """simple docstring"""

         ...


   def __mul__(    self	:      int      ,					lowerCAmelCase	:      float | Vector)						->					Vector | Matrix:




         """simple docstring"""

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


   def       UpperCAmelCase		(    self	:      Any)						->					int:




         """simple docstring"""

         return self.__height


   def       UpperCAmelCase		(    self	:      str)						->					int:




         """simple docstring"""

         return self.__width


   def       UpperCAmelCase		(    self	:      str      ,					lowerCAmelCase	:      int      ,					lowerCAmelCase	:      int)						->					float:




         """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       UpperCAmelCase		(    self	:      Dict      ,					lowerCAmelCase	:      int      ,					lowerCAmelCase	:      int      ,					lowerCAmelCase	:      float)						->					None:




         """simple docstring"""

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


   def       UpperCAmelCase		(    self	:      List[str]      ,					lowerCAmelCase	:      int      ,					lowerCAmelCase	:      int)						->					float:




         """simple docstring"""

         if self.__height != self.__width:
               raise Exception('Matrix is not square')
         lowercase__  =	self.__matrix[:x] + self.__matrix[x + 1 :]
         for i in range(len(lowerCAmelCase)):
               lowercase__  =	minor[i][:y] + minor[i][y + 1 :]
         return Matrix(lowerCAmelCase      ,					self.__width - 1      ,					self.__height - 1).determinant()


   def       UpperCAmelCase		(    self	:      Optional[int]      ,					lowerCAmelCase	:      int      ,					lowerCAmelCase	:      int)						->					float:




         """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(lowerCAmelCase      ,					lowerCAmelCase)
         else:
               raise Exception('Indices out of bounds')



   def       UpperCAmelCase		(    self	:      Any)						->					float:




         """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:
               lowercase__  =	[
                   self.__matrix[0][y] * self.cofactor(0      ,					lowerCAmelCase) for y in range(self.__width)
               ]
               return sum(lowerCAmelCase)

def 	_lowerCAmelCase (    A__						):
      lowercase__  =	[[0] * n for _ in range(A__						)]
      return Matrix(A__    ,	A__    ,	A__						)

def 	_lowerCAmelCase (    A__    ,	A__    ,	A__    ,	A__						):
      random.seed(A__						)
      lowercase__  =	[
          [random.randint(A__    ,	A__						) for _ in range(A__						)] for _ in range(A__						)
      ]
      return Matrix(A__    ,	A__    ,	A__						)





from datasets.utils.patching import _PatchedModuleObj, patch_submodule

from . import _test_patching

def 	_lowerCAmelCase (    ):
      import os as original_os
      from os import path as original_path
      from os import rename as original_rename
      from os.path import dirname as original_dirname
      from os.path import join as original_join

      assert _test_patching.os is original_os
      assert _test_patching.path is original_path
      assert _test_patching.join is original_join

      assert _test_patching.renamed_os is original_os
      assert _test_patching.renamed_path is original_path
      assert _test_patching.renamed_join is original_join

      lowercase__  =	'__test_patch_submodule_mock__'
      with patch_submodule(_test_patching    ,	'os.path.join'    ,	A__						):
            # Every way to access os.path.join must be patched, and the rest must stay untouched

            # check os.path.join
            assert isinstance(_test_patching.os    ,	_PatchedModuleObj						)
            assert isinstance(_test_patching.os.path    ,	_PatchedModuleObj						)
            assert _test_patching.os.path.join is mock

            # check path.join
            assert isinstance(_test_patching.path    ,	_PatchedModuleObj						)
            assert _test_patching.path.join is mock

            # check join
            assert _test_patching.join is mock

            # check that the other attributes are untouched
            assert _test_patching.os.rename is original_rename
            assert _test_patching.path.dirname is original_dirname
            assert _test_patching.os.path.dirname is original_dirname

            # Even renamed modules or objects must be patched

            # check renamed_os.path.join
            assert isinstance(_test_patching.renamed_os    ,	_PatchedModuleObj						)
            assert isinstance(_test_patching.renamed_os.path    ,	_PatchedModuleObj						)
            assert _test_patching.renamed_os.path.join is mock

            # check renamed_path.join
            assert isinstance(_test_patching.renamed_path    ,	_PatchedModuleObj						)
            assert _test_patching.renamed_path.join is mock

            # check renamed_join
            assert _test_patching.renamed_join is mock

            # check that the other attributes are untouched
            assert _test_patching.renamed_os.rename is original_rename
            assert _test_patching.renamed_path.dirname is original_dirname
            assert _test_patching.renamed_os.path.dirname is original_dirname

      # check that everthing is back to normal when the patch is over

      assert _test_patching.os is original_os
      assert _test_patching.path is original_path
      assert _test_patching.join is original_join

      assert _test_patching.renamed_os is original_os
      assert _test_patching.renamed_path is original_path
      assert _test_patching.renamed_join is original_join

def 	_lowerCAmelCase (    ):
      assert _test_patching.open is open

      lowercase__  =	'__test_patch_submodule_builtin_mock__'
      # _test_patching has "open" in its globals
      assert _test_patching.open is open
      with patch_submodule(_test_patching    ,	'open'    ,	A__						):
            assert _test_patching.open is mock

      # check that everthing is back to normal when the patch is over

      assert _test_patching.open is open

def 	_lowerCAmelCase (    ):
      # pandas.read_csv is not present in _test_patching
      lowercase__  =	'__test_patch_submodule_missing_mock__'
      with patch_submodule(_test_patching    ,	'pandas.read_csv'    ,	A__						):
            pass

def 	_lowerCAmelCase (    ):
      # builtin should always be mocked even if they're not in the globals
      # in case they're loaded at one point
      lowercase__  =	'__test_patch_submodule_missing_builtin_mock__'
      # _test_patching doesn't have "len" in its globals
      assert getattr(_test_patching    ,	'len'    ,	A__						) is None
      with patch_submodule(_test_patching    ,	'len'    ,	A__						):
            assert _test_patching.len is mock
      assert _test_patching.len is len

def 	_lowerCAmelCase (    ):
      lowercase__  =	'__test_patch_submodule_start_and_stop_mock__'
      lowercase__  =	patch_submodule(_test_patching    ,	'open'    ,	A__						)
      assert _test_patching.open is open
      patch.start()
      assert _test_patching.open is mock
      patch.stop()
      assert _test_patching.open is open

def 	_lowerCAmelCase (    ):
      from os import rename as original_rename
      from os.path import dirname as original_dirname
      from os.path import join as original_join

      lowercase__  =	'__test_patch_submodule_successive_join__'
      lowercase__  =	'__test_patch_submodule_successive_dirname__'
      lowercase__  =	'__test_patch_submodule_successive_rename__'
      assert _test_patching.os.path.join is original_join
      assert _test_patching.os.path.dirname is original_dirname
      assert _test_patching.os.rename is original_rename

      with patch_submodule(_test_patching    ,	'os.path.join'    ,	A__						):
            with patch_submodule(_test_patching    ,	'os.rename'    ,	A__						):
                  with patch_submodule(_test_patching    ,	'os.path.dirname'    ,	A__						):
                        assert _test_patching.os.path.join is mock_join
                        assert _test_patching.os.path.dirname is mock_dirname
                        assert _test_patching.os.rename is mock_rename

    # try another order
      with patch_submodule(_test_patching    ,	'os.rename'    ,	A__						):
            with patch_submodule(_test_patching    ,	'os.path.join'    ,	A__						):
                  with patch_submodule(_test_patching    ,	'os.path.dirname'    ,	A__						):
                        assert _test_patching.os.path.join is mock_join
                        assert _test_patching.os.path.dirname is mock_dirname
                        assert _test_patching.os.rename is mock_rename

      assert _test_patching.os.path.join is original_join
      assert _test_patching.os.path.dirname is original_dirname
      assert _test_patching.os.rename is original_rename

def 	_lowerCAmelCase (    ):
      lowercase__  =	'__test_patch_submodule_doesnt_exist_mock__'
      with patch_submodule(_test_patching    ,	'__module_that_doesn_exist__.__attribute_that_doesn_exist__'    ,	A__						):
            pass
      with patch_submodule(_test_patching    ,	'os.__attribute_that_doesn_exist__'    ,	A__						):
            pass
