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"""

A 2-dimensional vector class

>>> v1 = Vector2d(3, 4)

>>> print(v1.x, v1.y)

3.0 4.0

>>> x, y = v1

>>> x, y

(3.0, 4.0)

>>> v1

Vector2d(3.0, 4.0)

>>> v1_clone = eval(repr(v1))

>>> v1 == v1_clone

True

>>> print(v1)

(3.0, 4.0)

>>> octets = bytes(v1)

>>> octets

b'd\\x00\\x00\\x00\\x00\\x00\\x00\\x08@\\x00\\x00\\x00\\x00\\x00\\x00\\x10@'

>>> abs(v1)

5.0

>>> bool(v1), bool(Vector2d(0, 0))

(True, False)

Test of ``.frombytes()`` class method:

>>> v1_clone = Vector2d.frombytes(bytes(v1))

>>> v1_clone

Vector2d(3.0, 4.0)

>>> v1 == v1_clone

True

Tests of ``format()`` with Cartesian coordinates:

>>> format(v1)

'(3.0, 4.0)'

>>> format(v1, '.2f')

'(3.00, 4.00)'

>>> format(v1, '.3e')

'(3.000e+00, 4.000e+00)'

Tests of the ``angle`` method::

>>> Vector2d(0, 0).angle()

0.0

>>> Vector2d(1, 0).angle()

0.0

>>> epsilon = 10**-8

>>> abs(Vector2d(0, 1).angle() - math.pi/2) < epsilon

True

>>> abs(Vector2d(1, 1).angle() - math.pi/4) < epsilon

True

Tests of ``format()`` with polar coordinates:

>>> format(Vector2d(1, 1), 'p') # doctest:+ELLIPSIS

'<1.414213..., 0.785398...>'

>>> format(Vector2d(1, 1), '.3ep')

'<1.414e+00, 7.854e-01>'

>>> format(Vector2d(1, 1), '0.5fp')

'<1.41421, 0.78540>'

Tests of `x` and `y` read-only properties:

>>> v1.x, v1.y

(3.0, 4.0)

>>> v1.x = 123

Traceback (most recent call last):

...

AttributeError: can't set attribute 'x'

Tests of hashing:

>>> v1 = Vector2d(3, 4)

>>> v2 = Vector2d(3.1, 4.2)

>>> len({v1, v2})

2

"""

from array import array

import math

# tag::VECTOR2D_V3_SLOTS[]

class Vector2d:

__match_args__ = ('x', 'y') # <1>

__slots__ = ('__x', '__y') # <2>

typecode = 'd'

# end::VECTOR2D_V3_SLOTS[]

def __init__(self, x, y):

self.__x = float(x)

self.__y = float(y)

@property

def x(self):

return self.__x

@property

def y(self):

return self.__y

def __iter__(self):

return (i for i in (self.x, self.y))

def __repr__(self):

class_name = type(self).__name__

return '{}({!r}, {!r})'.format(class_name, *self)

def __str__(self):

return str(tuple(self))

def __bytes__(self):

return (bytes([ord(self.typecode)]) +

bytes(array(self.typecode, self)))

def __eq__(self, other):

return tuple(self) == tuple(other)

def __hash__(self):

return hash((self.x, self.y))

def __abs__(self):

return math.hypot(self.x, self.y)

def __bool__(self):

return bool(abs(self))

def angle(self):

return math.atan2(self.y, self.x)

def __format__(self, fmt_spec=''):

if fmt_spec.endswith('p'):

fmt_spec = fmt_spec[:-1]

coords = (abs(self), self.angle())

outer_fmt = '<{}, {}>'

else:

coords = self

outer_fmt = '({}, {})'

components = (format(c, fmt_spec) for c in coords)

return outer_fmt.format(*components)

@classmethod

def frombytes(cls, octets):

typecode = chr(octets[0])

memv = memoryview(octets[1:]).cast(typecode)

return cls(*memv)