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operator overloading

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%% Cell type:markdown id: tags:
# Operator overloading
> This practical assumes you are familiar with the basics of object-oriented
> programming in Python.
Operator overloading, in an object-oriented programming language, is the
process of customising the behaviour of _operators_ (e.g. `+`, `*`, `/` and
`-`) on user-defined types. This practical aims to show you that operator
overloading is __very__ easy to do in Python.
overloading is **very** easy to do in Python.
This practical gives a brief overview of the operators which you may be most
interested in implementing. However, there are many operators (and other
special methods) which you can support in your own classes - the [official
documentation](https://docs.python.org/3.5/reference/datamodel.html#basic-customization)
documentation](https://docs.python.org/3/reference/datamodel.html#basic-customization)
is the best reference if you are interested in learning more.
* [Overview](#overview)
* [Arithmetic operators](#arithmetic-operators)
* [Equality and comparison operators](#equality-and-comparison-operators)
* [The indexing operator `[]`](#the-indexing-operator)
* [The call operator `()`](#the-call-operator)
* [The dot operator `.`](#the-dot-operator)
<a class="anchor" id="overview"></a>
## Overview
In Python, when you add two numbers together:
%% Cell type:code id: tags:
```
a = 5
b = 10
r = a + b
print(r)
```
%% Cell type:markdown id: tags:
What actually goes on behind the scenes is this:
%% Cell type:code id: tags:
```
r = a.__add__(b)
print(r)
```
%% Cell type:markdown id: tags:
In other words, whenever you use the `+` operator on two variables (the
operands to the `+` operator), the Python interpreter calls the `__add__`
method of the first operand (`a`), and passes the second operand (`b`) as an
argument.
So it is very easy to use the `+` operator with our own classes - all we have
to do is implement a method called `__add__`.
<a class="anchor" id="arithmetic-operators"></a>
## Arithmetic operators
Let's play with an example - a class which represents a 2D vector:
%% Cell type:code id: tags:
```
class Vector2D(object):
def __init__(self, x, y):
self.x = x
self.y = y
def __str__(self):
return 'Vector2D({}, {})'.format(self.x, self.y)
```
%% Cell type:markdown id: tags:
> Note that we have implemented the special `__str__` method, which allows our
> `Vector2D` instances to be converted into strings.
If we try to use the `+` operator on this class, we are bound to get an error:
%% Cell type:code id: tags:
```
v1 = Vector2D(2, 3)
v2 = Vector2D(4, 5)
print(v1 + v2)
```
%% Cell type:markdown id: tags:
But all we need to do to support the `+` operator is to implement a method
called `__add__`:
%% Cell type:code id: tags:
```
class Vector2D(object):
def __init__(self, x, y):
self.x = x
self.y = y
def __str__(self):
return 'Vector2D({}, {})'.format(self.x, self.y)
def __add__(self, other):
return Vector2D(self.x + other.x,
self.y + other.y)
```
%% Cell type:markdown id: tags:
And now we can use `+` on `Vector2D` objects - it's that easy:
%% Cell type:code id: tags:
```
v1 = Vector2D(2, 3)
v2 = Vector2D(4, 5)
print('{} + {} = {}'.format(v1, v2, v1 + v2))
```
%% Cell type:markdown id: tags:
Our `__add__` method creates and returns a new `Vector2D` which contains the
sum of the `x` and `y` components of the `Vector2D` on which it is called, and
the `Vector2D` which is passed in. We could also make the `__add__` method
work with scalars, by extending its definition a bit:
%% Cell type:code id: tags:
```
class Vector2D(object):
def __init__(self, x, y):
self.x = x
self.y = y
def __add__(self, other):
if isinstance(other, Vector2D):
return Vector2D(self.x + other.x,
self.y + other.y)
else:
return Vector2D(self.x + other, self.y + other)
def __str__(self):
return 'Vector2D({}, {})'.format(self.x, self.y)
```
%% Cell type:markdown id: tags:
So now we can add both `Vector2D` instances and scalars numbers together:
%% Cell type:code id: tags:
```
v1 = Vector2D(2, 3)
v2 = Vector2D(4, 5)
n = 6
print('{} + {} = {}'.format(v1, v2, v1 + v2))
print('{} + {} = {}'.format(v1, n, v1 + n))
```
%% Cell type:markdown id: tags:
Other numeric and logical operators can be supported by implementing the
appropriate method, for example:
- Multiplication (`*`): `__mul__`
- Division (`/`): `__div__`
- Negation (`-`): `__neg__`
- In-place addition (`+=`): `__iadd__`
- Exclusive or (`^`): `__xor__`
When an operator is applied to operands of different types, a set of fall-back
rules are followed depending on the set of methods implemented on the
operands. For example, in the expression `a + b`, if `a.__add__` is not
implemented, but but `b.__radd__` is implemented, then the latter will be
called. Take a look at the [official
documentation](https://docs.python.org/3.5/reference/datamodel.html#emulating-numeric-types)
documentation](https://docs.python.org/3/reference/datamodel.html#emulating-numeric-types)
for further details, including a full list of the arithmetic and logical
operators that your classes can support.
<a class="anchor" id="equality-and-comparison-operators"></a>
## Equality and comparison operators
Adding support for equality (`==`, `!=`) and comparison (e.g. `>=`) operators
is just as easy. Imagine that we have a class called `Label`, which represents
a label in a lookup table. Our `Label` has an integer label, a name, and an
RGB colour:
%% Cell type:code id: tags:
```
class Label(object):
def __init__(self, label, name, colour):
self.label = label
self.name = name
self.colour = colour
```
%% Cell type:markdown id: tags:
In order to ensure that a list of `Label` objects is ordered by their label
values, we can implement a set of functions, so that `Label` classes can be
compared using the standard comparison operators:
%% Cell type:code id: tags:
```
import functools
# Don't worry about this statement
# just yet - it is explained below
@functools.total_ordering
class Label(object):
def __init__(self, label, name, colour):
self.label = label
self.name = name
self.colour = colour
def __str__(self):
rgb = ''.join(['{:02x}'.format(c) for c in self.colour])
return 'Label({}, {}, #{})'.format(self.label, self.name, rgb)
def __repr__(self):
return str(self)
# implement Label == Label
def __eq__(self, other):
return self.label == other.label
# implement Label < Label
def __lt__(self, other):
return self.label < other.label
```
%% Cell type:markdown id: tags:
> We also added `__str__` and `__repr__` methods to the `Label` class so that
> `Label` instances will be printed nicely.
Now we can compare and sort our `Label` instances:
%% Cell type:code id: tags:
```
l1 = Label(1, 'Parietal', (255, 0, 0))
l2 = Label(2, 'Occipital', ( 0, 255, 0))
l3 = Label(3, 'Temporal', ( 0, 0, 255))
print('{} > {}: {}'.format(l1, l2, l1 > l2))
print('{} < {}: {}'.format(l1, l3, l1 <= l3))
print('{} != {}: {}'.format(l2, l3, l2 != l3))
print(sorted((l3, l1, l2)))
```
%% Cell type:markdown id: tags:
The
[`@functools.total_ordering`](https://docs.python.org/3.5/library/functools.html#functools.total_ordering)
[`@functools.total_ordering`](https://docs.python.org/3/library/functools.html#functools.total_ordering)
is a convenience
[decorator](https://docs.python.org/3.5/glossary.html#term-decorator) which,
[decorator](https://docs.python.org/3/glossary.html#term-decorator) which,
given a class that implements equality and a single comparison function
(`__lt__` in the above code), will "fill in" the remainder of the comparison
operators. If you need very specific or complicated behaviour, then you can
provide methods for _all_ of the comparison operators, e.g. `__gt__` for `>`,
`__ge__` for `>=`, etc.).
> Decorators are introduced in another practical.
But if you just want the operators to work in the conventional manner, you can
simply use the `@functools.total_ordering` decorator, and provide `__eq__`,
and just one of `__lt__`, `__le__`, `__gt__` or `__ge__`.
Refer to the [official
documentation](https://docs.python.org/3.5/reference/datamodel.html#object.__lt__)
documentation](https://docs.python.org/3/reference/datamodel.html#object.__lt__)
for all of the details on supporting comparison operators.
> You may see the `__cmp__` method in older code bases - this provides a
> C-style comparison function which returns `<0`, `0`, or `>0` based on
> comparing two items. This has been superseded by the rich comparison
> operators introduced here, and is no longer supported in Python 3.
<a class="anchor" id="the-indexing-operator"></a>
## The indexing operator `[]`
The indexing operator (`[]`) is generally used by "container" types, such as
the built-in `list` and `dict` classes.
At its essence, there are only three types of behaviours that are possible
with the `[]` operator. All that is needed to support them are to implement
three special methods in your class, regardless of whether your class will be
indexed by sequential integers (like a `list`) or by
[hashable](https://docs.python.org/3.5/glossary.html#term-hashable) values
[hashable](https://docs.python.org/3/glossary.html#term-hashable) values
(like a `dict`):
- __Retrieval__ is performed by the `__getitem__` method
- __Assignment__ is performed by the `__setitem__` method
- __Deletion__ is performed by the `__delitem__` method
- **Retrieval** is performed by the `__getitem__` method
- **Assignment** is performed by the `__setitem__` method
- **Deletion** is performed by the `__delitem__` method
Note that, if you implement these methods in your own class, there is no
requirement for them to actually provide any form of data storage or
retrieval. However if you don't, you will probably confuse users of your code
who are used to how the `list` and `dict` types work. Whenever you deviate
from conventional behaviour, make sure you explain it well in your
documentation!
The following contrived example demonstrates all three behaviours:
%% Cell type:code id: tags:
```
class TwoTimes(object):
def __init__(self):
self.__deleted = set()
self.__assigned = {}
def __getitem__(self, key):
if key in self.__deleted:
raise KeyError('{} has been deleted!'.format(key))
elif key in self.__assigned:
return self.__assigned[key]
else:
return key * 2
def __setitem__(self, key, value):
self.__assigned[key] = value
def __delitem__(self, key):
self.__deleted.add(key)
```
%% Cell type:markdown id: tags:
Guess what happens whenever we index a `TwoTimes` object:
%% Cell type:code id: tags:
```
tt = TwoTimes()
print('TwoTimes[{}] = {}'.format(2, tt[2]))
print('TwoTimes[{}] = {}'.format(6, tt[6]))
print('TwoTimes[{}] = {}'.format('abc', tt['abc']))
```
%% Cell type:markdown id: tags:
The `TwoTimes` class allows us to override the value for a specific key:
%% Cell type:code id: tags:
```
print(tt[4])
tt[4] = 'this is not 4 * 4'
print(tt[4])
```
%% Cell type:markdown id: tags:
And we can also "delete" keys:
%% Cell type:code id: tags:
```
print(tt['12345'])
del tt['12345']
# this is going to raise an error
print(tt['12345'])
```
%% Cell type:markdown id: tags:
If you wish to support the Python `start:stop:step` [slice
notation](https://docs.python.org/3.5/library/functions.html#slice), you
notation](https://docs.python.org/3/library/functions.html#slice), you
simply need to write your `__getitem__` and `__setitem__` methods so that they
can detect `slice` objects:
%% Cell type:code id: tags:
```
class TwoTimes(object):
def __init__(self, max):
self.__max = max
def __getitem__(self, key):
if isinstance(key, slice):
start = key.start or 0
stop = key.stop or self.__max
step = key.step or 1
else:
start = key
stop = key + 1
step = 1
return [i * 2 for i in range(start, stop, step)]
```
%% Cell type:markdown id: tags:
Now we can "slice" a `TwoTimes` instance:
%% Cell type:code id: tags:
```
tt = TwoTimes(10)
print(tt[5])
print(tt[3:7])
print(tt[::2])
```
%% Cell type:markdown id: tags:
> It is possible to sub-class the built-in `list` and `dict` classes if you
> wish to extend their functionality in some way. However, if you are writing
> a class that should mimic the one of the `list` or `dict` classes, but work
> in a different way internally (e.g. a `dict`-like object which uses a
> different hashing algorithm), the `Sequence` and `MutableMapping` classes
> are [a better choice](https://stackoverflow.com/a/7148602) - you can find
> them in the
> [`collections.abc`](https://docs.python.org/3.5/library/collections.abc.html)
> [`collections.abc`](https://docs.python.org/3/library/collections.abc.html)
> module.
<a class="anchor" id="the-call-operator"></a>
## The call operator `()`
Remember how everything in Python is an object, even functions? When you call
a function, a method called `__call__` is called on the function object. We can
implement the `__call__` method on our own class, which will allow us to "call"
objects as if they are functions.
For example, the `TimedFunction` class allows us to calculate the execution
time of any function:
%% Cell type:code id: tags:
```
import time
class TimedFunction(object):
def __init__(self, func):
self.func = func
def __call__(self, *args, **kwargs):
print('Timing {}...'.format(self.func.__name__))
start = time.time()
retval = self.func(*args, **kwargs)
end = time.time()
print('Elapsed time: {:0.2f} seconds'.format(end - start))
return retval
```
%% Cell type:markdown id: tags:
Let's see how the `TimedFunction` behaves:
%% Cell type:code id: tags:
```
import numpy as np
import numpy.linalg as npla
def inverse(data):
return npla.inv(data)
tf = TimedFunction(inverse)
data = np.random.random((5000, 5000))
# Wait a few seconds after
# running this code block!
inv = tf(data)
```
%% Cell type:markdown id: tags:
> The `TimedFunction` class is conceptually very similar to a
> [decorator](https://docs.python.org/3.5/glossary.html#term-decorator) -
> [decorator](https://docs.python.org/3/glossary.html#term-decorator) -
> decorators are covered in another practical.
<a class="anchor" id="the-dot-operator"></a>
## The dot operator `.`
Python allows us to override the `.` (dot) operator which is used to access
the attributes and methods of an object. This is very powerful, but is also
quite a niche feature, and it is easy to trip yourself up, so if you wish to
use this in your own project, make sure that you carefully read (and
understand) [the
documentation](https://docs.python.org/3.5/reference/datamodel.html#customizing-attribute-access),
documentation](https://docs.python.org/3/reference/datamodel.html#customizing-attribute-access),
and test your code comprehensively!
For this example, we need a little background information. OpenGL includes
the native data types `vec2`, `vec3`, and `vec4`, which can be used to
represent 2, 3, or 4 component vectors respectively. These data types have a
neat feature called [_swizzling_][glslref], which allows you to access any
component (`x`,`y`, `z`, `w` for vectors, or `r`, `g`, `b`, `a` for colours)
in any order, with a syntax similar to attribute access in Python.
[glslref]: https://www.khronos.org/opengl/wiki/Data_Type_(GLSL)#Swizzling
So here is an example which implements this swizzle-style attribute access on
a class called `Vector`, in which we have customised the behaviour of the `.`
operator:
%% Cell type:code id: tags:
```
class Vector(object):
def __init__(self, xyz):
self.__xyz = list(xyz)
def __str__(self):
return 'Vector({})'.format(self.__xyz)
def __getattr__(self, key):
# Swizzling behaviour only occurs when
# the attribute name is entirely comprised
# of 'x', 'y', and 'z'.
if not all([c in 'xyz' for c in key]):
raise AttributeError(key)
key = ['xyz'.index(c) for c in key]
return [self.__xyz[c] for c in key]
def __setattr__(self, key, value):
# Restrict swizzling behaviour as above
if not all([c in 'xyz' for c in key]):
return super().__setattr__(key, value)
if len(key) == 1:
value = (value,)
idxs = ['xyz'.index(c) for c in key]
for i, v in sorted(zip(idxs, value)):
self.__xyz[i] = v
```
%% Cell type:markdown id: tags:
And here it is in action:
%% Cell type:code id: tags:
```
v = Vector((1, 2, 3))
print('v: ', v)
print('xyz: ', v.xyz)
print('zy: ', v.zy)
print('xx: ', v.xx)
v.xz = 10, 30
print(v)
v.y = 20
print(v)
```
......
advanced_topics/04_operator_overloading.md
+ 14
− 14
View file @ 21e785f3
......@@ -8,13 +8,13 @@
Operator overloading, in an object-oriented programming language, is the
process of customising the behaviour of _operators_ (e.g. `+`, `*`, `/` and
`-`) on user-defined types. This practical aims to show you that operator
overloading is __very__ easy to do in Python.
overloading is **very** easy to do in Python.
This practical gives a brief overview of the operators which you may be most
interested in implementing. However, there are many operators (and other
special methods) which you can support in your own classes - the [official
documentation](https://docs.python.org/3.5/reference/datamodel.html#basic-customization)
documentation](https://docs.python.org/3/reference/datamodel.html#basic-customization)
is the best reference if you are interested in learning more.
......@@ -173,7 +173,7 @@ rules are followed depending on the set of methods implemented on the
operands. For example, in the expression `a + b`, if `a.__add__` is not
implemented, but but `b.__radd__` is implemented, then the latter will be
called. Take a look at the [official
documentation](https://docs.python.org/3.5/reference/datamodel.html#emulating-numeric-types)
documentation](https://docs.python.org/3/reference/datamodel.html#emulating-numeric-types)
for further details, including a full list of the arithmetic and logical
operators that your classes can support.
......@@ -252,9 +252,9 @@ print(sorted((l3, l1, l2)))
The
[`@functools.total_ordering`](https://docs.python.org/3.5/library/functools.html#functools.total_ordering)
[`@functools.total_ordering`](https://docs.python.org/3/library/functools.html#functools.total_ordering)
is a convenience
[decorator](https://docs.python.org/3.5/glossary.html#term-decorator) which,
[decorator](https://docs.python.org/3/glossary.html#term-decorator) which,
given a class that implements equality and a single comparison function
(`__lt__` in the above code), will "fill in" the remainder of the comparison
operators. If you need very specific or complicated behaviour, then you can
......@@ -271,7 +271,7 @@ and just one of `__lt__`, `__le__`, `__gt__` or `__ge__`.
Refer to the [official
documentation](https://docs.python.org/3.5/reference/datamodel.html#object.__lt__)
documentation](https://docs.python.org/3/reference/datamodel.html#object.__lt__)
for all of the details on supporting comparison operators.
......@@ -293,13 +293,13 @@ At its essence, there are only three types of behaviours that are possible
with the `[]` operator. All that is needed to support them are to implement
three special methods in your class, regardless of whether your class will be
indexed by sequential integers (like a `list`) or by
[hashable](https://docs.python.org/3.5/glossary.html#term-hashable) values
[hashable](https://docs.python.org/3/glossary.html#term-hashable) values
(like a `dict`):
- __Retrieval__ is performed by the `__getitem__` method
- __Assignment__ is performed by the `__setitem__` method
- __Deletion__ is performed by the `__delitem__` method
- **Retrieval** is performed by the `__getitem__` method
- **Assignment** is performed by the `__setitem__` method
- **Deletion** is performed by the `__delitem__` method
Note that, if you implement these methods in your own class, there is no
......@@ -370,7 +370,7 @@ print(tt['12345'])
If you wish to support the Python `start:stop:step` [slice
notation](https://docs.python.org/3.5/library/functions.html#slice), you
notation](https://docs.python.org/3/library/functions.html#slice), you
simply need to write your `__getitem__` and `__setitem__` methods so that they
can detect `slice` objects:
......@@ -414,7 +414,7 @@ print(tt[::2])
> different hashing algorithm), the `Sequence` and `MutableMapping` classes
> are [a better choice](https://stackoverflow.com/a/7148602) - you can find
> them in the
> [`collections.abc`](https://docs.python.org/3.5/library/collections.abc.html)
> [`collections.abc`](https://docs.python.org/3/library/collections.abc.html)
> module.
......@@ -472,7 +472,7 @@ inv = tf(data)
> The `TimedFunction` class is conceptually very similar to a
> [decorator](https://docs.python.org/3.5/glossary.html#term-decorator) -
> [decorator](https://docs.python.org/3/glossary.html#term-decorator) -
> decorators are covered in another practical.
......@@ -485,7 +485,7 @@ the attributes and methods of an object. This is very powerful, but is also
quite a niche feature, and it is easy to trip yourself up, so if you wish to
use this in your own project, make sure that you carefully read (and
understand) [the
documentation](https://docs.python.org/3.5/reference/datamodel.html#customizing-attribute-access),
documentation](https://docs.python.org/3/reference/datamodel.html#customizing-attribute-access),
and test your code comprehensively!
......
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