



import copy
import re
class 				__A					:
						UpperCamelCase					:Union[str, Any]     =			'''hp'''
						UpperCamelCase					:Optional[Any]     =			{}
						UpperCamelCase					:Any     =			None





						@classmethod
						def        _snake_case    (cls							,    __magic_name__							,    __magic_name__				):
									lowerCamelCase__ :      Optional[int]								=		prefix
									lowerCamelCase__ :      List[str]								=		defaults
									cls.build_naming_info()





						@staticmethod
						def        _snake_case    (__magic_name__							,    __magic_name__				):
									if len(_UpperCAmelCase				) == 0:
												return ""
									lowerCamelCase__ :      Optional[int]								=		None
									if any(char.isdigit() for char in word				):
												raise Exception(f"Parameters should not contain numbers: '{word}' contains a number"				)
									if word in info["short_word"]:
												return info["short_word"][word]
									for prefix_len in range(1							,    len(_UpperCAmelCase				) + 1				):
												lowerCamelCase__ :      str								=		word[:prefix_len]
												if prefix in info["reverse_short_word"]:
															continue
												else:
															lowerCamelCase__ :      Tuple								=		prefix
															break

									if short_word is None:
												# Paranoid fallback
												def int_to_alphabetic(__magic_name__				):
															lowerCamelCase__ :      List[str]								=		''''''
															while integer != 0:
																		lowerCamelCase__ :      Union[str, Any]								=		chr(ord("""A"""				) + integer % 10				) + s
																		integer //= 10
															return s

												lowerCamelCase__ :      Optional[int]								=		0
												while True:
															lowerCamelCase__ :      List[str]								=		word + '''#''' + int_to_alphabetic(_UpperCAmelCase				)
															if sword in info["reverse_short_word"]:
																		continue
															else:
																		lowerCamelCase__ :      Optional[Any]								=		sword
																		break

									lowerCamelCase__ :      List[str]								=		short_word
									lowerCamelCase__ :      Dict								=		word
									return short_word





						@staticmethod
						def        _snake_case    (__magic_name__							,    __magic_name__				):
									lowerCamelCase__ :      str								=		param_name.split("""_"""				)

									lowerCamelCase__ :      str								=		[TrialShortNamer.shortname_for_word(_UpperCAmelCase							,    _UpperCAmelCase				) for word in words]

									# We try to create a separatorless short name, but if there is a collision we have to fallback
									# to a separated short name
									lowerCamelCase__ :      Dict								=		['''''', '''_''']

									for separator in separators:
												lowerCamelCase__ :      Union[str, Any]								=		separator.join(_UpperCAmelCase				)
												if shortname not in info["reverse_short_param"]:
															lowerCamelCase__ :      List[str]								=		shortname
															lowerCamelCase__ :      Union[str, Any]								=		param_name
															return shortname

									return param_name





						@staticmethod
						def        _snake_case    (__magic_name__							,    __magic_name__				):
									lowerCamelCase__ :      int								=		TrialShortNamer.shortname_for_key(_UpperCAmelCase							,    _UpperCAmelCase				)
									lowerCamelCase__ :      Optional[Any]								=		short_name
									lowerCamelCase__ :      Optional[Any]								=		param_name





						@classmethod
						def        _snake_case    (cls				):
									if cls.NAMING_INFO is not None:
												return

									lowerCamelCase__ :      Optional[Any]								=		{
									    '''short_word''': {},
									    '''reverse_short_word''': {},
									    '''short_param''': {},
									    '''reverse_short_param''': {},
									}

									lowerCamelCase__ :      List[str]								=		list(cls.DEFAULTS.keys()				)

									for k in field_keys:
												cls.add_new_param_name(_UpperCAmelCase							,    _UpperCAmelCase				)

									lowerCamelCase__ :      Optional[Any]								=		info





						@classmethod
						def        _snake_case    (cls							,    __magic_name__				):
									cls.build_naming_info()
									assert cls.PREFIX is not None
									lowerCamelCase__ :      str								=		[copy.copy(cls.PREFIX				)]

									for k, v in params.items():
												if k not in cls.DEFAULTS:
															raise Exception(f"You should provide a default value for the param name {k} with value {v}"				)
												if v == cls.DEFAULTS[k]:
															# The default value is not added to the name
															continue

												lowerCamelCase__ :      Union[str, Any]								=		cls.NAMING_INFO['''short_param'''][k]

												if isinstance(_UpperCAmelCase							,    _UpperCAmelCase				):
															lowerCamelCase__ :      str								=		1 if v else 0

												lowerCamelCase__ :      Tuple								=		'''''' if isinstance(_UpperCAmelCase							,    (int, float)				) else '''-'''
												lowerCamelCase__ :      Dict								=		f"{key}{sep}{v}"
												name.append(_UpperCAmelCase				)

									return "_".join(_UpperCAmelCase				)





						@classmethod
						def        _snake_case    (cls							,    __magic_name__				):
									lowerCamelCase__ :      List[Any]								=		repr[len(cls.PREFIX				) + 1 :]
									if repr == "":
												lowerCamelCase__ :      Tuple								=		[]
									else:
												lowerCamelCase__ :      str								=		repr.split("""_"""				)

									lowerCamelCase__ :      Optional[Any]								=		{}

									for value in values:
												if "-" in value:
															lowerCamelCase__ :      List[Any]								=		value.split("""-"""				)
												else:
															lowerCamelCase__ :      int								=		re.sub("""[0-9.]"""							,    """"""							,    _UpperCAmelCase				)
															lowerCamelCase__ :      Union[str, Any]								=		float(re.sub("""[^0-9.]"""							,    """"""							,    _UpperCAmelCase				)				)

												lowerCamelCase__ :      Dict								=		cls.NAMING_INFO['''reverse_short_param'''][p_k]

												lowerCamelCase__ :      Union[str, Any]								=		p_v

									for k in cls.DEFAULTS:
												if k not in parameters:
															lowerCamelCase__ :      Optional[int]								=		cls.DEFAULTS[k]

									return parameters








import unittest

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





			def        _snake_case    (self				):
						lowerCamelCase__ :      List[str]								=		Vector([1, 2, 3]				)
						self.assertEqual(x.component(0				)							,    1				)
						self.assertEqual(x.component(2				)							,    3				)
						lowerCamelCase__ :      str								=		Vector()





			def        _snake_case    (self				):
						lowerCamelCase__ :      Dict								=		Vector([0, 0, 0, 0, 0, 1]				)
						self.assertEqual(str(__magic_name__				)							,    """(0,0,0,0,0,1)"""				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Tuple								=		Vector([1, 2, 3, 4]				)
						self.assertEqual(len(__magic_name__				)							,    4				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Dict								=		Vector([1, 2]				)
						lowerCamelCase__ :      str								=		Vector([1, 2, 3, 4, 5]				)
						lowerCamelCase__ :      int								=		Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]				)
						lowerCamelCase__ :      int								=		Vector([1, -1, 1, -1, 2, -3, 4, -5]				)
						self.assertAlmostEqual(x.euclidean_length()							,    2.2_36							,    3				)
						self.assertAlmostEqual(y.euclidean_length()							,    7.4_16							,    3				)
						self.assertEqual(z.euclidean_length()							,    0				)
						self.assertAlmostEqual(w.euclidean_length()							,    7.6_16							,    3				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      str								=		Vector([1, 2, 3]				)
						lowerCamelCase__ :      Union[str, 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        _snake_case    (self				):
						lowerCamelCase__ :      Optional[int]								=		Vector([1, 2, 3]				)
						lowerCamelCase__ :      Any								=		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        _snake_case    (self				):
						lowerCamelCase__ :      Dict								=		Vector([1, 2, 3]				)
						lowerCamelCase__ :      int								=		Vector([2, -1, 4]				)  # for test of dot product
						lowerCamelCase__ :      List[Any]								=		Vector([1, -2, -1]				)
						self.assertEqual(str(x * 3.0				)							,    """(3.0,6.0,9.0)"""				)
						self.assertEqual((a * b)							,    0				)





			def        _snake_case    (self				):
						self.assertEqual(str(zero_vector(10				)				).count("""0"""				)							,    10				)





			def        _snake_case    (self				):
						self.assertEqual(str(unit_basis_vector(3							,    1				)				)							,    """(0,1,0)"""				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Any								=		Vector([1, 2, 3]				)
						lowerCamelCase__ :      str								=		Vector([1, 0, 1]				)
						self.assertEqual(str(axpy(2							,    __magic_name__							,    __magic_name__				)				)							,    """(3,4,7)"""				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Optional[Any]								=		Vector([1, 0, 0, 0, 0, 0]				)
						lowerCamelCase__ :      int								=		x.copy()
						self.assertEqual(str(__magic_name__				)							,    str(__magic_name__				)				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      int								=		Vector([1, 0, 0]				)
						x.change_component(0							,    0				)
						x.change_component(1							,    1				)
						self.assertEqual(str(__magic_name__				)							,    """(0,1,0)"""				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Optional[Any]								=		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        _snake_case    (self				):
						lowerCamelCase__ :      int								=		Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,    3							,    3				)
						lowerCamelCase__ :      int								=		[[-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        _snake_case    (self				):
						lowerCamelCase__ :      Any								=		Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,    3							,    3				)
						lowerCamelCase__ :      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(cofactors[x][y]							,    a.cofactor(__magic_name__							,    __magic_name__				)				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Optional[int]								=		Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,    3							,    3				)
						self.assertEqual(-5							,    a.determinant()				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      List[str]								=		Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]							,    3							,    3				)
						lowerCamelCase__ :      Optional[int]								=		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        _snake_case    (self				):
						lowerCamelCase__ :      str								=		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        _snake_case    (self				):
						lowerCamelCase__ :      List[Any]								=		Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,    3							,    3				)
						self.assertEqual(7							,    a.component(2							,    1				)							,    0.01				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Tuple								=		Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,    3							,    3				)
						lowerCamelCase__ :      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        _snake_case    (self				):
						lowerCamelCase__ :      str								=		Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,    3							,    3				)
						lowerCamelCase__ :      Optional[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        _snake_case    (self				):
						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()



