





import unittest

from .lib import (
    Matrix,
    Vector,
    axpy,
    square_zero_matrix,
    unit_basis_vector,
    zero_vector,
)






class     lowercase__       (	unittest.TestCase				):

   '''simple docstring'''


   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Optional[Any]          =      Vector([1, 2, 3]							)
       self.assertEqual(x.component(0							),		1							)
       self.assertEqual(x.component(2							),		3							)
       UpperCamelCase__							:				Any          =      Vector()




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Dict          =      Vector([0, 0, 0, 0, 0, 1]							)
       self.assertEqual(str(__magic_name__							),		'''(0,0,0,0,0,1)'''							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				str          =      Vector([1, 2, 3, 4]							)
       self.assertEqual(len(__magic_name__							),		4							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Any          =      Vector([1, 2]							)
       UpperCamelCase__							:				int          =      Vector([1, 2, 3, 4, 5]							)
       UpperCamelCase__							:				Optional[Any]          =      Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]							)
       UpperCamelCase__							:				Any          =      Vector([1, -1, 1, -1, 2, -3, 4, -5]							)
       self.assertAlmostEqual(x.euclidean_length(),		2.236,		3							)
       self.assertAlmostEqual(y.euclidean_length(),		7.416,		3							)
       self.assertEqual(z.euclidean_length(),		0							)
       self.assertAlmostEqual(w.euclidean_length(),		7.616,		3							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Optional[Any]          =      Vector([1, 2, 3]							)
       UpperCamelCase__							:				List[Any]          =      Vector([1, 1, 1]							)
       self.assertEqual((x + y).component(0							),		2							)
       self.assertEqual((x + y).component(1							),		3							)
       self.assertEqual((x + y).component(2							),		4							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Any          =      Vector([1, 2, 3]							)
       UpperCamelCase__							:				Dict          =      Vector([1, 1, 1]							)
       self.assertEqual((x - y).component(0							),		0							)
       self.assertEqual((x - y).component(1							),		1							)
       self.assertEqual((x - y).component(2							),		2							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				str          =      Vector([1, 2, 3]							)
       UpperCamelCase__							:				int          =      Vector([2, -1, 4]							)  # for test of dot product
       UpperCamelCase__							:				List[str]          =      Vector([1, -2, -1]							)
       self.assertEqual(str(x * 3.0							),		'''(3.0,6.0,9.0)'''							)
       self.assertEqual((a * b),		0							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       self.assertEqual(str(zero_vector(10							)							).count('''0'''							),		10							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       self.assertEqual(str(unit_basis_vector(3,		1							)							),		'''(0,1,0)'''							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Tuple          =      Vector([1, 2, 3]							)
       UpperCamelCase__							:				str          =      Vector([1, 0, 1]							)
       self.assertEqual(str(axpy(2,		__magic_name__,		__magic_name__							)							),		'''(3,4,7)'''							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Any          =      Vector([1, 0, 0, 0, 0, 0]							)
       UpperCamelCase__							:				List[str]          =      x.copy()
       self.assertEqual(str(__magic_name__							),		str(__magic_name__							)							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Any          =      Vector([1, 0, 0]							)
       x.change_component(0,		0							)
       x.change_component(1,		1							)
       self.assertEqual(str(__magic_name__							),		'''(0,1,0)'''							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				str          =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]],		3,		3							)
       self.assertEqual('''|1,2,3|\n|2,4,5|\n|6,7,8|\n''',		str(__magic_name__							)							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Union[str, Any]          =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]],		3,		3							)
       UpperCamelCase__							:				Optional[Any]          =      [[-3, -14, -10], [-5, -10, -5], [-2, -1, 0]]
       for x in range(a.height()							):
           for y in range(a.width()							):
               self.assertEqual(minors[x][y],		a.minor(__magic_name__,		__magic_name__							)							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Optional[int]          =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]],		3,		3							)
       UpperCamelCase__							:				Union[str, Any]          =      [[-3, 14, -10], [5, -10, 5], [-2, 1, 0]]
       for x in range(a.height()							):
           for y in range(a.width()							):
               self.assertEqual(cofactors[x][y],		a.cofactor(__magic_name__,		__magic_name__							)							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Any          =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]],		3,		3							)
       self.assertEqual(-5,		a.determinant()							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				int          =      Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]],		3,		3							)
       UpperCamelCase__							:				List[str]          =      Vector([1, 2, 3]							)
       self.assertEqual('''(14,32,50)''',		str(a * x							)							)
       self.assertEqual('''|2,4,6|\n|8,10,12|\n|14,16,18|\n''',		str(a * 2							)							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Tuple          =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]],		3,		3							)
       a.change_component(0,		2,		5							)
       self.assertEqual('''|1,2,5|\n|2,4,5|\n|6,7,8|\n''',		str(__magic_name__							)							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Optional[Any]          =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]],		3,		3							)
       self.assertEqual(7,		a.component(2,		1							),		0.01							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Optional[Any]          =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]],		3,		3							)
       UpperCamelCase__							:				Optional[int]          =      Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]],		3,		3							)
       self.assertEqual('''|2,4,10|\n|4,8,10|\n|12,14,18|\n''',		str(a + b							)							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       UpperCamelCase__							:				Optional[int]          =      Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]],		3,		3							)
       UpperCamelCase__							:				List[Any]          =      Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]],		3,		3							)
       self.assertEqual('''|0,0,-4|\n|0,0,0|\n|0,0,-2|\n''',		str(a - b							)							)




   def       UpperCamelCase__  (    self							) ->      None:






       """simple docstring"""
       self.assertEqual(
           '''|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n''',		str(square_zero_matrix(5							)							),		)


if __name__ == "__main__":
  unittest.main()








import random




def 		lowerCAmelCase_    (  __UpperCAmelCase:			list		,   __UpperCAmelCase:			Optional[int]      )      ->	tuple:
    UpperCamelCase__   ,UpperCamelCase__   ,UpperCamelCase__							:				List[Any]          =      [], [], []
    for element in data:
        if element < pivot:
            less.append(__UpperCAmelCase      )
        elif element > pivot:
            greater.append(__UpperCAmelCase      )
        else:
            equal.append(__UpperCAmelCase      )
    return less, equal, greater





def 		lowerCAmelCase_    (  __UpperCAmelCase:			list		,   __UpperCAmelCase:			int      )      ->	List[str]:
    # index = len(items) // 2 when trying to find the median
    #   (value of index when items is sorted)

    # invalid input
    if index >= len(__UpperCAmelCase      ) or index < 0:
        return None

    UpperCamelCase__							:				List[str]          =      items[random.randint(0		,   len(__UpperCAmelCase      ) - 1      )]
    UpperCamelCase__							:				List[Any]          =      0
    UpperCamelCase__   ,UpperCamelCase__   ,UpperCamelCase__							:				int          =      _partition(__UpperCAmelCase		,   __UpperCAmelCase      )
    UpperCamelCase__							:				Union[str, Any]          =      len(__UpperCAmelCase      )
    UpperCamelCase__							:				Dict          =      len(__UpperCAmelCase      )

    # index is the pivot
    if m <= index < m + count:
        return pivot
    # must be in smaller
    elif m > index:
        return quick_select(__UpperCAmelCase		,   __UpperCAmelCase      )
    # must be in larger
    else:
        return quick_select(__UpperCAmelCase		,   index - (m + count)      )

