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"""

The `+` operator produces a `Vector` result.

>>> v1 = Vector(2, 4)

>>> v2 = Vector(2, 1)

>>> v1 + v2

Vector(4, 5)

We can also implemement the `*` operator to perform scalar multiplication

or elementwise multiplication.

>>> v = Vector(3, 4)

>>> abs(v)

5.0

>>> v * 3

Vector(9, 12)

>>> abs(v * 3)

15.0

>>> v25 = Vector(2, 5)

>>> v71 = Vector(7, 1)

>>> v71 * v25

Vector(14, 5)

A vector can be used in a boolean context, where it will be considered

_falsy_ if it has magnitude zero, otherwise it is _truthy_::

>>> bool(v)

True

>>> bool(Vector(0, 0))

False

Vectors can have n-dimensions::

>>> v3 = Vector(1, 2, 3)

>>> len(v3)

3

>>> v3

Vector(1, 2, 3)

>>> abs(v3) # doctest:+ELLIPSIS

3.74165738...

>>> v3 + Vector(4, 5, 6)

Vector(5, 7, 9)

>>> v3 * 5

Vector(5, 10, 15)

>>> v2 + v3

Traceback (most recent call last):

...

ValueError: Addition applies only to vectors of equal dimensions.

The `repr` of a Vector is produced with the help of the `reprlib.repr`

function, limiting the size of the output string:

>>> Vector(*range(100))

Vector(0, 1, 2, 3, 4, 5, ...)

"""

# BEGIN VECTOR_ITER

import math

import numbers

import reprlib

EQ_DIMENSIONS_MSG = '%s applies only to vectors of equal dimensions.'

class Vector:

"""An n-dimensional vector"""

def __init__(self, *components): # <1>

self._components = tuple(components) # <2>

def __repr__(self):

return 'Vector' + (reprlib.repr(self._components)) # <3>

def __iter__(self):

return iter(self._components) # <4>

def __abs__(self):

return math.sqrt(sum(comp*comp for comp in self)) # <5>

def __len__(self):

return len(self._components) # <6>

def __add__(self, other):

if len(self) != len(other):

raise ValueError(EQ_DIMENSIONS_MSG % 'Addition')

return Vector(*(a+b for a, b in zip(self, other))) # <7>

def __mul__(self, other):

if isinstance(other, numbers.Number):

return Vector(*(comp*other for comp in self)) # <8>

else:

return self.elementwise_mul(other) # <9>

def elementwise_mul(self, other):

if len(self) != len(other):

raise ValueError(EQ_DIMENSIONS_MSG %

'Elementwise multiplication')

return Vector(*(a*b for a, b in zip(self, other))) # <10>

def __bool__(self):

return any(self) # <11>

# END VECTOR_ITER