update multivector examples

classes/multivector_v5.py

@@ -0,0 +1,270 @@
+"""
+A multi-dimensional ``MultiVector`` class, take 2
+
+A ``MultiVector`` is built from an iterable of numbers::
+
+    >>> MultiVector([3.1, 4.2])
+    MultiVector([3.1, 4.2])
+    >>> MultiVector((3, 4, 5))
+    MultiVector([3.0, 4.0, 5.0])
+    >>> MultiVector(range(10))
+    MultiVector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
+
+
+Tests with 2-dimensions (same results as ``vector_v1.py``)::
+
+    >>> v1 = MultiVector([3, 4])
+    >>> x, y = v1
+    >>> x, y
+    (3.0, 4.0)
+    >>> v1
+    MultiVector([3.0, 4.0])
+    >>> v1_clone = eval(repr(v1))
+    >>> v1 == v1_clone
+    True
+    >>> print(v1)
+    (3.0, 4.0)
+    >>> octets = bytes(v1)
+    >>> octets
+    b'\\x00\\x00\\x00\\x00\\x00\\x00\\x08@\\x00\\x00\\x00\\x00\\x00\\x00\\x10@'
+    >>> abs(v1)
+    5.0
+    >>> bool(v1), bool(MultiVector([0, 0]))
+    (True, False)
+
+
+Test of ``.frombytes()`` class method:
+
+    >>> v1_clone = MultiVector.frombytes(bytes(v1))
+    >>> v1_clone
+    MultiVector([3.0, 4.0])
+    >>> v1 == v1_clone
+    True
+
+
+Tests with 3-dimensions::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> x, y, z = v1
+    >>> x, y, z
+    (3.0, 4.0, 5.0)
+    >>> v1
+    MultiVector([3.0, 4.0, 5.0])
+    >>> v1_clone = eval(repr(v1))
+    >>> v1 == v1_clone
+    True
+    >>> print(v1)
+    (3.0, 4.0, 5.0)
+    >>> abs(v1)  # doctest:+ELLIPSIS
+    7.071067811...
+    >>> bool(v1), bool(MultiVector([0, 0, 0]))
+    (True, False)
+
+
+Tests with many dimensions::
+
+    >>> v7 = MultiVector(range(7))
+    >>> v7
+    MultiVector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
+    >>> abs(v7)  # doctest:+ELLIPSIS
+    9.53939201...
+
+
+Test of ``.__bytes__`` and ``.frombytes()`` methods::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> v1_clone = MultiVector.frombytes(bytes(v1))
+    >>> v1_clone
+    MultiVector([3.0, 4.0, 5.0])
+    >>> v1 == v1_clone
+    True
+
+
+Tests of sequence behavior::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> len(v1)
+    3
+    >>> v1[0], v1[len(v1)-1], v1[-1]
+    (3.0, 5.0, 5.0)
+
+
+Test of slicing::
+
+    >>> v7 = MultiVector(range(7))
+    >>> v7[-1]
+    6.0
+    >>> v7[1:4]
+    MultiVector([1.0, 2.0, 3.0])
+    >>> v7[-1:]
+    MultiVector([6.0])
+    >>> v7[1,2]
+    Traceback (most recent call last):
+      ...
+    TypeError: MultiVector indices must be integers
+
+
+Tests of dynamic attribute access::
+
+    >>> v7 = MultiVector(range(10))
+    >>> v7.x
+    0.0
+    >>> v7.y, v7.z, v7.t, v7.u, v7.v, v7.w
+    (1.0, 2.0, 3.0, 4.0, 5.0, 6.0)
+
+Dynamic attribute lookup failures::
+
+    >>> v7.k
+    Traceback (most recent call last):
+      ...
+    AttributeError: 'MultiVector' object has no attribute 'k'
+    >>> v3 = MultiVector(range(3))
+    >>> v3.t
+    Traceback (most recent call last):
+      ...
+    AttributeError: 'MultiVector' object has no attribute 't'
+    >>> v3.spam
+    Traceback (most recent call last):
+      ...
+    AttributeError: 'MultiVector' object has no attribute 'spam'
+
+
+Tests of hashing::
+
+    >>> v1 = MultiVector([3, 4])
+    >>> v2 = MultiVector([3.1, 4.2])
+    >>> v3 = MultiVector([3, 4, 5])
+    >>> v6 = MultiVector(range(6))
+    >>> hash(v1), hash(v2), hash(v3), hash(v6)
+    (7, 384307168202284039, 2, 1)
+    >>> len(set([v1, v2, v3, v6]))
+    4
+
+
+Tests of ``format()`` with Cartesian coordinates in 2D:
+
+    >>> v1 = MultiVector([3, 4])
+    >>> format(v1)
+    '(3.0, 4.0)'
+    >>> format(v1, '.2f')
+    '(3.00, 4.00)'
+    >>> format(v1, '.3e')
+    '(3.000e+00, 4.000e+00)'
+
+
+Tests of ``format()`` with Cartesian coordinates in 3D and 7D:
+
+    >>> v3 = MultiVector([3, 4, 5])
+    >>> format(v3)
+    '(3.0, 4.0, 5.0)'
+    >>> format(MultiVector(range(7)))
+    '(0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0)'
+
+
+Tests of the ``angle`` method::
+
+    >>> MultiVector([0, 0]).angle()
+    0.0
+    >>> MultiVector([1, 0]).angle()
+    0.0
+    >>> epsilon = 10**-8
+    >>> abs(MultiVector([0, 1]).angle() - math.pi/2) < epsilon
+    True
+    >>> abs(MultiVector([1, 1]).angle() - math.pi/4) < epsilon
+    True
+
+
+Tests of ``format()`` with polar coordinates:
+
+    >>> format(MultiVector([1, 1]), 'p')  # doctest:+ELLIPSIS
+    '<1.414213..., 0.785398...>'
+    >>> format(MultiVector([1, 1]), '.3ep')
+    '<1.414e+00, 7.854e-01>'
+    >>> format(MultiVector([1, 1]), '0.5fp')
+    '<1.41421, 0.78540>'
+
+
+"""
+
+from array import array
+import reprlib
+import math
+import functools
+import operator
+
+
+class MultiVector:
+    typecode = 'd'
+
+    def __init__(self, components):
+        self._components = array(self.typecode, components)
+
+    def __iter__(self):
+        return iter(self._components)
+
+    def __repr__(self):
+        components = reprlib.repr(self._components)
+        components = components[components.find('['):-1]
+        return 'MultiVector({})'.format(components)
+
+    def __str__(self):
+        return str(tuple(self))
+
+    def __bytes__(self):
+        return bytes(self._components)
+
+    def __eq__(self, other):
+        return tuple(self) == tuple(other)
+
+    def __hash__(self):
+        hashes = (hash(x) for x in self)
+        return functools.reduce(operator.xor, hashes)
+
+    def __abs__(self):
+        return math.sqrt(sum(x * x for x in self))
+
+    def __bool__(self):
+        return bool(abs(self))
+
+    def __len__(self):
+        return len(self._components)
+
+    def __getitem__(self, index):
+        cls = type(self)
+        if isinstance(index, slice):
+            return cls(self._components[index])
+        elif isinstance(index, int):
+            return self._components[index]
+        else:
+            msg = '{.__name__} indices must be integers'
+            raise TypeError(msg.format(cls))
+
+    shortcut_names = 'xyztuvw'
+
+    def __getattr__(self, name):
+        cls = type(self)
+        if len(name) == 1:
+            pos = cls.shortcut_names.find(name)
+            if 0 <= pos < len(self._components):
+                return self._components[pos]
+        msg = '{.__name__!r} object has no attribute {!r}'
+        raise AttributeError(msg.format(cls, name))
+
+    def angle(self):
+        return math.atan2(self.y, self.x)  # <1>
+
+    def __format__(self, fmt_spec=''):
+        if fmt_spec.endswith('p'):
+            fmt_spec = fmt_spec[:-1]
+            coords = (abs(self), self.angle())
+            outer_fmt = '<{}>'  # <2>
+        else:
+            coords = self
+            outer_fmt = '({})'  # <3>
+        components = (format(c, fmt_spec) for c in coords)
+        return outer_fmt.format(', '.join(components))  # <4>
+
+    @classmethod
+    def frombytes(cls, octets):
+        memv = memoryview(octets).cast(cls.typecode)
+        return cls(memv)

classes/vector_v2.py

@@ -28,7 +28,7 @@ Test of ``.frombytes()`` class method:
     >>> v1 == v1_clone
     True
 
-Tests of ``format()`` with rectangular coordinates:
+Tests of ``format()`` with Cartesian coordinates:
 
     >>> format(v1)
     '(3.0, 4.0)'
@@ -37,6 +37,7 @@ Tests of ``format()`` with rectangular coordinates:
     >>> format(v1, '.3e')
     '(3.000e+00, 4.000e+00)'
 
+
 Tests of the ``angle`` method::
 
     >>> Vector(0, 0).angle()
@@ -49,6 +50,7 @@ Tests of the ``angle`` method::
     >>> abs(Vector(1, 1).angle() - math.pi/4) < epsilon
     True
 
+
 Tests of ``format()`` with polar coordinates:
 
     >>> format(Vector(1, 1), 'p')  # doctest:+ELLIPSIS

classes/vector_v2_fmt_snippet.py

@@ -20,6 +20,7 @@ A 2-dimensional vector class
     >>> bool(v1), bool(Vector(0, 0))
     (True, False)
 
+
 Test of ``.frombytes()`` class method:
 
     >>> v1_clone = Vector.frombytes(bytes(v1))
@@ -28,7 +29,8 @@ Test of ``.frombytes()`` class method:
     >>> v1 == v1_clone
     True
 
-Tests of ``format()`` with rectangular coordinates:
+
+Tests of ``format()`` with Cartesian coordinates:
 
     >>> format(v1)
     '(3.0, 4.0)'
@@ -37,6 +39,7 @@ Tests of ``format()`` with rectangular coordinates:
     >>> format(v1, '.3e')
     '(3.000e+00, 4.000e+00)'
 
+
 Tests of the ``angle`` method::
 
     >>> Vector(0, 0).angle()
@@ -49,6 +52,7 @@ Tests of the ``angle`` method::
     >>> abs(Vector(1, 1).angle() - math.pi/4) < epsilon
     True
 
+
 Tests of ``format()`` with polar coordinates:
 
     >>> format(Vector(1, 1), 'p')  # doctest:+ELLIPSIS

classes/vector_v3.py

@@ -28,6 +28,38 @@ Test of .frombytes() class method:
     >>> 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::
+
+    >>> Vector(0, 0).angle()
+    0.0
+    >>> Vector(1, 0).angle()
+    0.0
+    >>> epsilon = 10**-8
+    >>> abs(Vector(0, 1).angle() - math.pi/2) < epsilon
+    True
+    >>> abs(Vector(1, 1).angle() - math.pi/4) < epsilon
+    True
+
+
+Tests of ``format()`` with polar coordinates:
+
+    >>> format(Vector(1, 1), 'p')  # doctest:+ELLIPSIS
+    '<1.414213..., 0.785398...>'
+    >>> format(Vector(1, 1), '.3ep')
+    '<1.414e+00, 7.854e-01>'
+    >>> format(Vector(1, 1), '0.5fp')
+    '<1.41421, 0.78540>'
+
 # BEGIN VECTOR_V3_DEMO
 Test of `x` and `y` read-only properties:
 

classes/vector_v3_slots.py

@@ -20,6 +20,7 @@ A 2-dimensional vector class
     >>> bool(v1), bool(Vector(0, 0))  #<7>
     (True, False)
 
+
 Test of .frombytes() class method:
 
     >>> v1_clone = Vector.frombytes(bytes(v1))
@@ -28,6 +29,39 @@ Test of .frombytes() class method:
     >>> 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::
+
+    >>> Vector(0, 0).angle()
+    0.0
+    >>> Vector(1, 0).angle()
+    0.0
+    >>> epsilon = 10**-8
+    >>> abs(Vector(0, 1).angle() - math.pi/2) < epsilon
+    True
+    >>> abs(Vector(1, 1).angle() - math.pi/4) < epsilon
+    True
+
+
+Tests of ``format()`` with polar coordinates:
+
+    >>> format(Vector(1, 1), 'p')  # doctest:+ELLIPSIS
+    '<1.414213..., 0.785398...>'
+    >>> format(Vector(1, 1), '.3ep')
+    '<1.414e+00, 7.854e-01>'
+    >>> format(Vector(1, 1), '0.5fp')
+    '<1.41421, 0.78540>'
+
 # BEGIN VECTOR_V3_DEMO
 Test of `x` and `y` read-only properties: