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ramalhoramalho
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update multivector examples
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‎classes/multivector_v5.py‎

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"""
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A multi-dimensional ``MultiVector`` class, take 2
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A ``MultiVector`` is built from an iterable of numbers::
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>>> MultiVector([3.1, 4.2])
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MultiVector([3.1, 4.2])
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>>> MultiVector((3, 4, 5))
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MultiVector([3.0, 4.0, 5.0])
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>>> MultiVector(range(10))
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MultiVector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
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Tests with 2-dimensions (same results as ``vector_v1.py``)::
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>>> v1 = MultiVector([3, 4])
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>>> x, y = v1
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>>> x, y
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(3.0, 4.0)
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>>> v1
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MultiVector([3.0, 4.0])
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>>> v1_clone = eval(repr(v1))
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>>> v1 == v1_clone
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True
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>>> print(v1)
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(3.0, 4.0)
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>>> octets = bytes(v1)
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>>> octets
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b'\\x00\\x00\\x00\\x00\\x00\\x00\\x08@\\x00\\x00\\x00\\x00\\x00\\x00\\x10@'
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>>> abs(v1)
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5.0
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>>> bool(v1), bool(MultiVector([0, 0]))
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(True, False)
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Test of ``.frombytes()`` class method:
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>>> v1_clone = MultiVector.frombytes(bytes(v1))
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>>> v1_clone
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MultiVector([3.0, 4.0])
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>>> v1 == v1_clone
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True
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Tests with 3-dimensions::
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>>> v1 = MultiVector([3, 4, 5])
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>>> x, y, z = v1
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>>> x, y, z
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(3.0, 4.0, 5.0)
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>>> v1
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MultiVector([3.0, 4.0, 5.0])
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>>> v1_clone = eval(repr(v1))
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>>> v1 == v1_clone
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True
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>>> print(v1)
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(3.0, 4.0, 5.0)
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>>> abs(v1) # doctest:+ELLIPSIS
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7.071067811...
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>>> bool(v1), bool(MultiVector([0, 0, 0]))
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(True, False)
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Tests with many dimensions::
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>>> v7 = MultiVector(range(7))
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>>> v7
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MultiVector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
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>>> abs(v7) # doctest:+ELLIPSIS
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9.53939201...
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Test of ``.__bytes__`` and ``.frombytes()`` methods::
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>>> v1 = MultiVector([3, 4, 5])
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>>> v1_clone = MultiVector.frombytes(bytes(v1))
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>>> v1_clone
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MultiVector([3.0, 4.0, 5.0])
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>>> v1 == v1_clone
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True
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Tests of sequence behavior::
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>>> v1 = MultiVector([3, 4, 5])
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>>> len(v1)
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3
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>>> v1[0], v1[len(v1)-1], v1[-1]
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(3.0, 5.0, 5.0)
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Test of slicing::
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>>> v7 = MultiVector(range(7))
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>>> v7[-1]
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6.0
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>>> v7[1:4]
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MultiVector([1.0, 2.0, 3.0])
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>>> v7[-1:]
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MultiVector([6.0])
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>>> v7[1,2]
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Traceback (most recent call last):
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...
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TypeError: MultiVector indices must be integers
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Tests of dynamic attribute access::
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>>> v7 = MultiVector(range(10))
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>>> v7.x
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0.0
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>>> v7.y, v7.z, v7.t, v7.u, v7.v, v7.w
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(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)
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Dynamic attribute lookup failures::
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>>> v7.k
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Traceback (most recent call last):
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...
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AttributeError: 'MultiVector' object has no attribute 'k'
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>>> v3 = MultiVector(range(3))
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>>> v3.t
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Traceback (most recent call last):
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...
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AttributeError: 'MultiVector' object has no attribute 't'
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>>> v3.spam
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Traceback (most recent call last):
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...
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AttributeError: 'MultiVector' object has no attribute 'spam'
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Tests of hashing::
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>>> v1 = MultiVector([3, 4])
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>>> v2 = MultiVector([3.1, 4.2])
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>>> v3 = MultiVector([3, 4, 5])
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>>> v6 = MultiVector(range(6))
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>>> hash(v1), hash(v2), hash(v3), hash(v6)
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(7, 384307168202284039, 2, 1)
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>>> len(set([v1, v2, v3, v6]))
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4
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Tests of ``format()`` with Cartesian coordinates in 2D:
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>>> v1 = MultiVector([3, 4])
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>>> format(v1)
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'(3.0, 4.0)'
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>>> format(v1, '.2f')
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'(3.00, 4.00)'
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>>> format(v1, '.3e')
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'(3.000e+00, 4.000e+00)'
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Tests of ``format()`` with Cartesian coordinates in 3D and 7D:
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>>> v3 = MultiVector([3, 4, 5])
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>>> format(v3)
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'(3.0, 4.0, 5.0)'
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>>> format(MultiVector(range(7)))
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'(0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0)'
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Tests of the ``angle`` method::
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>>> MultiVector([0, 0]).angle()
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0.0
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>>> MultiVector([1, 0]).angle()
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0.0
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>>> epsilon = 10**-8
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>>> abs(MultiVector([0, 1]).angle() - math.pi/2) < epsilon
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True
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>>> abs(MultiVector([1, 1]).angle() - math.pi/4) < epsilon
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True
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Tests of ``format()`` with polar coordinates:
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>>> format(MultiVector([1, 1]), 'p') # doctest:+ELLIPSIS
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'<1.414213..., 0.785398...>'
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>>> format(MultiVector([1, 1]), '.3ep')
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'<1.414e+00, 7.854e-01>'
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>>> format(MultiVector([1, 1]), '0.5fp')
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'<1.41421, 0.78540>'
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"""
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from array import array
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import reprlib
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import math
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import functools
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import operator
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class MultiVector:
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typecode = 'd'
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def __init__(self, components):
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self._components = array(self.typecode, components)
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def __iter__(self):
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return iter(self._components)
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def __repr__(self):
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components = reprlib.repr(self._components)
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components = components[components.find('['):-1]
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return 'MultiVector({})'.format(components)
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def __str__(self):
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return str(tuple(self))
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def __bytes__(self):
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return bytes(self._components)
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def __eq__(self, other):
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return tuple(self) == tuple(other)
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def __hash__(self):
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hashes = (hash(x) for x in self)
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return functools.reduce(operator.xor, hashes)
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def __abs__(self):
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return math.sqrt(sum(x * x for x in self))
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def __bool__(self):
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return bool(abs(self))
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def __len__(self):
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return len(self._components)
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def __getitem__(self, index):
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cls = type(self)
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if isinstance(index, slice):
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return cls(self._components[index])
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elif isinstance(index, int):
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return self._components[index]
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else:
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msg = '{.__name__} indices must be integers'
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raise TypeError(msg.format(cls))
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shortcut_names = 'xyztuvw'
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def __getattr__(self, name):
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cls = type(self)
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if len(name) == 1:
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pos = cls.shortcut_names.find(name)
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if 0 <= pos < len(self._components):
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return self._components[pos]
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msg = '{.__name__!r} object has no attribute {!r}'
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raise AttributeError(msg.format(cls, name))
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def angle(self):
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return math.atan2(self.y, self.x) # <1>
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def __format__(self, fmt_spec=''):
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if fmt_spec.endswith('p'):
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fmt_spec = fmt_spec[:-1]
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coords = (abs(self), self.angle())
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outer_fmt = '<{}>' # <2>
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else:
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coords = self
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outer_fmt = '({})' # <3>
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components = (format(c, fmt_spec) for c in coords)
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return outer_fmt.format(', '.join(components)) # <4>
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@classmethod
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def frombytes(cls, octets):
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memv = memoryview(octets).cast(cls.typecode)
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return cls(memv)

‎classes/vector_v2.py‎

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>>> v1 == v1_clone
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True
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Tests of ``format()`` with rectangular coordinates:
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Tests of ``format()`` with Cartesian coordinates:
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>>> format(v1)
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'(3.0, 4.0)'
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>>> format(v1, '.3e')
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'(3.000e+00, 4.000e+00)'
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Tests of the ``angle`` method::
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>>> Vector(0, 0).angle()
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>>> abs(Vector(1, 1).angle() - math.pi/4) < epsilon
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True
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Tests of ``format()`` with polar coordinates:
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>>> format(Vector(1, 1), 'p') # doctest:+ELLIPSIS

‎classes/vector_v2_fmt_snippet.py‎

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>>> bool(v1), bool(Vector(0, 0))
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(True, False)
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Test of ``.frombytes()`` class method:
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>>> v1_clone = Vector.frombytes(bytes(v1))
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>>> v1 == v1_clone
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True
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Tests of ``format()`` with rectangular coordinates:
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Tests of ``format()`` with Cartesian coordinates:
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>>> format(v1)
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'(3.0, 4.0)'
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>>> format(v1, '.3e')
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'(3.000e+00, 4.000e+00)'
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Tests of the ``angle`` method::
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>>> Vector(0, 0).angle()
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>>> abs(Vector(1, 1).angle() - math.pi/4) < epsilon
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True
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Tests of ``format()`` with polar coordinates:
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>>> format(Vector(1, 1), 'p') # doctest:+ELLIPSIS

‎classes/vector_v3.py‎

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>>> v1 == v1_clone
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True
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Tests of ``format()`` with Cartesian coordinates:
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>>> format(v1)
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'(3.0, 4.0)'
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>>> format(v1, '.2f')
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'(3.00, 4.00)'
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>>> format(v1, '.3e')
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'(3.000e+00, 4.000e+00)'
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Tests of the ``angle`` method::
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>>> Vector(0, 0).angle()
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0.0
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>>> Vector(1, 0).angle()
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0.0
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>>> epsilon = 10**-8
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>>> abs(Vector(0, 1).angle() - math.pi/2) < epsilon
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True
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>>> abs(Vector(1, 1).angle() - math.pi/4) < epsilon
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True
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Tests of ``format()`` with polar coordinates:
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>>> format(Vector(1, 1), 'p') # doctest:+ELLIPSIS
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'<1.414213..., 0.785398...>'
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>>> format(Vector(1, 1), '.3ep')
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'<1.414e+00, 7.854e-01>'
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>>> format(Vector(1, 1), '0.5fp')
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'<1.41421, 0.78540>'
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# BEGIN VECTOR_V3_DEMO
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Test of `x` and `y` read-only properties:
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