






import unittest

from .lib import (
    Matrix,
    Vector,
    axpy,
    square_zero_matrix,
    unit_basis_vector,
    zero_vector,
)
class 		SCREAMING_SNAKE_CASE__	(  unittest.TestCase     ):

  '''simple docstring'''







  def  lowerCamelCase       (      self		:			Union[str, Any]							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    Vector([1, 2, 3]							)
         self.assertEqual(x.component(0							)       ,				1							)
         self.assertEqual(x.component(2							)       ,				3							)
         _UpperCAmelCase							=    Vector()


  def  lowerCamelCase       (      self		:			Tuple							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    Vector([0, 0, 0, 0, 0, 1]							)
         self.assertEqual(str(lowerCamelCase							)       ,				"""(0,0,0,0,0,1)"""							)


  def  lowerCamelCase       (      self		:			Optional[int]							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    Vector([1, 2, 3, 4]							)
         self.assertEqual(len(lowerCamelCase							)       ,				4							)


  def  lowerCamelCase       (      self		:			Tuple							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    Vector([1, 2]							)
         _UpperCAmelCase							=    Vector([1, 2, 3, 4, 5]							)
         _UpperCAmelCase							=    Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]							)
         _UpperCAmelCase							=    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  lowerCamelCase       (      self		:			Dict							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    Vector([1, 2, 3]							)
         _UpperCAmelCase							=    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  lowerCamelCase       (      self		:			Dict							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    Vector([1, 2, 3]							)
         _UpperCAmelCase							=    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  lowerCamelCase       (      self		:			int							)						->	None:


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


  def  lowerCamelCase       (      self		:			Optional[int]							)						->	None:


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


  def  lowerCamelCase       (      self		:			Optional[Any]							)						->	None:


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


  def  lowerCamelCase       (      self		:			Any							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    Vector([1, 2, 3]							)
         _UpperCAmelCase							=    Vector([1, 0, 1]							)
         self.assertEqual(str(axpy(2       ,				lowerCamelCase       ,				lowerCamelCase							)							)       ,				"""(3,4,7)"""							)


  def  lowerCamelCase       (      self		:			Union[str, Any]							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    Vector([1, 0, 0, 0, 0, 0]							)
         _UpperCAmelCase							=    x.copy()
         self.assertEqual(str(lowerCamelCase							)       ,				str(lowerCamelCase							)							)


  def  lowerCamelCase       (      self		:			Tuple							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    Vector([1, 0, 0]							)
         x.change_component(0       ,				0							)
         x.change_component(1       ,				1							)
         self.assertEqual(str(lowerCamelCase							)       ,				"""(0,1,0)"""							)


  def  lowerCamelCase       (      self		:			Union[str, Any]							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    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(lowerCamelCase							)							)


  def  lowerCamelCase       (      self		:			str							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]       ,				3       ,				3							)
         _UpperCAmelCase							=    [[-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(lowerCamelCase       ,				lowerCamelCase							)							)


  def  lowerCamelCase       (      self		:			str							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]       ,				3       ,				3							)
         _UpperCAmelCase							=    [[-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(lowerCamelCase       ,				lowerCamelCase							)							)


  def  lowerCamelCase       (      self		:			List[str]							)						->	None:


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


  def  lowerCamelCase       (      self		:			List[str]							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]       ,				3       ,				3							)
         _UpperCAmelCase							=    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  lowerCamelCase       (      self		:			Any							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    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(lowerCamelCase							)							)


  def  lowerCamelCase       (      self		:			int							)						->	None:


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


  def  lowerCamelCase       (      self		:			Optional[Any]							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]       ,				3       ,				3							)
         _UpperCAmelCase							=    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  lowerCamelCase       (      self		:			Tuple							)						->	None:


         """simple docstring"""
         _UpperCAmelCase							=    Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]       ,				3       ,				3							)
         _UpperCAmelCase							=    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  lowerCamelCase       (      self		:			List[str]							)						->	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()







from __future__ import annotations







def     a_   (__A      )				->						int:



					"""simple docstring"""
					__a					:						List[Any]      =					len(__A      ) // 2

					# choose the middle 3 elements
					__a					:						Any      =					lst[m - 1 : m + 2]

					# if middle element is peak
					if three[1] > three[0] and three[1] > three[2]:
										return three[1]

					# if increasing, recurse on right
					elif three[0] < three[2]:
										if len(lst[:m]      ) == 2:
															m -= 1
										return peak(lst[m:]      )

					# decreasing
					else:
										if len(lst[:m]      ) == 2:
															m += 1
										return peak(lst[:m]      )


if __name__ == "__main__":
			import doctest

			doctest.testmod()





