Mention singledispatch, fix footnote numbering

61687a57 · Paul McCarthy · 8144d67c · 61687a57 · 61687a57
Commit 61687a57 authored 7 years ago by Paul McCarthy
--- a/advanced_topics/object_oriented_programming.ipynb
+++ b/advanced_topics/object_oriented_programming.ipynb
@@ -1052,10 +1052,10 @@
    "The `NumberOperator` class has also overridden the `preprocess` method, to\n",
    "ensure that all values handled by the `Operator` are numbers. This method gets\n",
    "called within the `Operator.run` method - for a `NumberOperator` instance, the\n",
-    "`NumberOperator.preprocess` method will get called<sup>1</sup>.\n",
+    "`NumberOperator.preprocess` method will get called<sup>3</sup>.\n",
    "\n",
    "\n",
-    "> <sup>1</sup> When a sub-class overrides a base-class method, it is still\n",
+    "> <sup>3</sup> When a sub-class overrides a base-class method, it is still\n",
    "> possible to access the base-class implementation [via the `super()`\n",
    "> function](https://stackoverflow.com/a/4747427) (the preferred method), or by\n",
    "> [explicitly calling the base-class\n",
@@ -1658,7 +1658,8 @@
    "\n",
    "However, because a Python method can be written to accept any number or type\n",
    "of arguments, it is very easy to to build your own overloading logic by\n",
-    "writing a \"dispatch\" method. Here is YACE (Yet Another Contrived Example):"
+    "writing a \"dispatch\" method<sup>4</sup>. Here is YACE (Yet Another Contrived\n",
+    "Example):"
   ]
  },
  {
@@ -1697,6 +1698,12 @@
   "cell_type": "markdown",
   "metadata": {},
   "source": [
+    "> <sup>4</sup>Another option is the [`functools.singledispatch`\n",
+    "> decorator](https://docs.python.org/3.5/library/functools.html#functools.singledispatch),\n",
+    "> which is more complicated, but may allow you to write your dispatch logic in\n",
+    "> a more concise manner.\n",
+    "\n",
+    "\n",
    "<a class=\"anchor\" id=\"useful-references\"></a>\n",
    "## Useful references\n",
    "\n",

 %% Cell type:markdown id: tags:
 # Object-oriented programming in Python
 By now you might have realised that __everything__ in Python is an
 object. Strings are objects, numbers are objects, functions are objects,
 modules are objects - __everything__ is an object!
 But this does not mean that you have to use Python in an object-oriented
 fashion. You can stick with functions and statements, and get quite a lot
 done. But some problems are just easier to solve, and to reason about, when
 you use an object-oriented approach.
 * [Objects versus classes](#objects-versus-classes)
 * [Defining a class](#defining-a-class)
 * [Object creation - the `__init__` method](#object-creation-the-init-method)
 * [Our method is called `__init__`, but we didn't actually call the `__init__` method!](#our-method-is-called-init)
 * [We didn't specify the `self` argument - what gives?!?](#we-didnt-specify-the-self-argument)
 * [Attributes](#attributes)
 * [Methods](#methods)
 * [Protecting attribute access](#protecting-attribute-access)
 * [A better way - properties](#a-better-way-properties])
 * [Inheritance](#inheritance)
 * [The basics](#the-basics)
 * [Code re-use and problem decomposition](#code-re-use-and-problem-decomposition)
 * [Polymorphism](#polymorphism)
 * [Multiple inheritance](#multiple-inheritance)
 * [Class attributes and methods](#class-attributes-and-methods)
 * [Class attributes](#class-attributes)
 * [Class methods](#class-methods)
 * [Appendix: The `object` base-class](#appendix-the-object-base-class)
 * [Appendix: `__init__` versus `__new__`](#appendix-init-versus-new)
 * [Appendix: Monkey-patching](#appendix-monkey-patching)
 * [Appendix: Method overloading](#appendix-method-overloading)
 * [Useful references](#useful-references)
 <a class="anchor" id="objects-versus-classes"></a>
 ## Objects versus classes
 If you are versed in C++, Java, C#, or some other object-oriented language,
 then this should all hopefully sound familiar, and you can skip to the next
 section.
 If you have not done any object-oriented programming before, your first step
 is to understand the difference between _objects_ (also known as
 _instances_) and _classes_ (also known as _types_).
 If you have some experience in C, then you can start off by thinking of a
 class as like a `struct` definition - a `struct` is a specification for the
 layout of a chunk of memory. For example, here is a typical struct definition:
 > ```
 > /**
 >  * Struct representing a stack.
 >  */
 > typedef struct __stack {
 >   uint8_t capacity; /**< the maximum capacity of this stack */
 >   uint8_t size;     /**< the current size of this stack     */
 >   void  **top;      /**< pointer to the top of this stack   */
 > } stack_t;
 > ```
 Now, an _object_ is not a definition, but rather a thing which resides in
 memory. An object can have _attributes_ (pieces of information), and _methods_
 (functions associated with the object). You can pass objects around your code,
 manipulate their attributes, and call their methods.
 Returning to our C metaphor, you can think of an object as like an
 instantiation of a struct:
 > ```
 > stack_t stack;
 > stack.capacity = 10;
 > ```
 One of the major differences between a `struct` in C, and a `class` in Python
 and other object oriented languages, is that you can't (easily) add functions
 to a `struct` - it is just a chunk of memory. Whereas in Python, you can add
 functions to your class definition, which will then be added as methods when
 you create an object from that class.
 Of course there are many more differences between C structs and classes (most
 notably [inheritance](todo), [polymorphism](todo), and [access
 protection](todo)). But if you can understand the difference between a
 _definition_ of a C struct, and an _instantiation_ of that struct, then you
 are most of the way towards understanding the difference between a _class_,
 and an _object_.
 > But just to confuse you, remember that in Python, __everything__ is an
 > object - even classes!
 <a class="anchor" id="defining-a-class"></a>
 ## Defining a class
 Defining a class in Python is simple. Let's take on a small project, by
 developing a class which can be used in place of the `fslmaths` shell command.
 %% Cell type:code id: tags:
 ``` 
 class FSLMaths(object):
    pass
 ```
 %% Cell type:markdown id: tags:
 In this statement, we defined a new class called `FSLMaths`, which inherits
 from the built-in `object` base-class (see [below](inheritance) for more
 details on inheritance).
 Now that we have defined our class, we can create objects - instances of that
 class - by calling the class itself, as if it were a function:
 %% Cell type:code id: tags:
 ``` 
 fm1 = FSLMaths()
 fm2 = FSLMaths()
 print(fm1)
 print(fm2)
 ```
 %% Cell type:markdown id: tags:
 Although these objects are not of much use at this stage. Let's do some more
 work.
 <a class="anchor" id="object-creation-the-init-method"></a>
 ## Object creation - the `__init__` method
 The first thing that our `fslmaths` replacement will need is an input image.
 It makes sense to pass this in when we create an `FSLMaths` object:
 %% Cell type:code id: tags:
 ``` 
 class FSLMaths(object):
    def __init__(self, inimg):
        self.img = inimg
 ```
 %% Cell type:markdown id: tags:
 Here we have added a _method_ called `__init__` to our class (remember that a
 _method_ is just a function which is defined in a class, and which can be
 called on instances of that class).  This method expects two arguments -
 `self`, and `inimg`. So now, when we create an instance of the `FSLMaths`
 class, we will need to provide an input image:
 %% Cell type:code id: tags:
 ``` 
 import nibabel as nib
 import os.path as op
 fpath = op.expandvars('$FSLDIR/data/standard/MNI152_T1_2mm.nii.gz')
 inimg = nib.load(fpath)
 fm    = FSLMaths(inimg)
 ```
 %% Cell type:markdown id: tags:
 There are a couple of things to note here...
 <a class="anchor" id="our-method-is-called-init"></a>
 ### Our method is called `__init__`, but we didn't actually call the `__init__` method!
 `__init__` is a special method in Python - it is called when an instance of a
 class is created. And recall that we can create an instance of a class by
 calling the class in the same way that we call a function.
 There are a number of "special" methods that you can add to a class in Python
 to customise various aspects of how instances of the class behave.  One of the
 first ones you may come across is the `__str__` method, which defines how an
 object should be printed (more specifically, how an object gets converted into
 a string). For example, we could add a `__str__` method to our `FSLMaths`
 class like so:
 %% Cell type:code id: tags:
 ``` 
 class FSLMaths(object):
    def __init__(self, inimg):
        self.img = inimg
    def __str__(self):
        return 'FSLMaths({})'.format(self.img.get_filename())
 fpath = op.expandvars('$FSLDIR/data/standard/MNI152_T1_2mm.nii.gz')
 inimg = nib.load(fpath)
 fm    = FSLMaths(inimg)
 print(fm)
 ```
 %% Cell type:markdown id: tags:
 Refer to the [official
 docs](https://docs.python.org/3.5/reference/datamodel.html#special-method-names)
 for details on all of the special methods that can be defined in a class. And
 take a look at the appendix for some more details on [how Python objects get
 created](appendix-init-versus-new).
 <a class="anchor" id="we-didnt-specify-the-self-argument"></a>
 ### We didn't specify the `self` argument - what gives?!?
 The `self` argument is a special argument for methods in Python. If you are
 coming from C++, Java, C# or similar, `self` in Python is equivalent to `this`
 in those languages.
 In a method, the `self` argument is a reference to the object that the method
 was called on. So in this line of code:
 %% Cell type:code id: tags:
 ``` 
 fm = FSLMaths(inimg)
 ```
 %% Cell type:markdown id: tags:
 the `self` argument in `__init__` will be a reference to the `FSLMaths` object
 that has been created (and is then assigned to the `fm` variable, after the
 `__init__` method has finished).
 But note that you __do not__ need to explicitly provide the `self` argument
 when you call a method on an object, or when you create a new object. The
 Python runtime will take care of passing the instance to its method, as the
 first argument to the method.
 But when you are writing a class, you __do__ need to explicitly list `self` as
 the first argument to all of the methods of the class.
 <a class="anchor" id="attributes"></a>
 ## Attributes
 In Python, the term __attribute__ is used to refer to a piece of information
 that is associated with an object. An attribute is generally a reference to
 another object (which might be a string, a number, or a list, or some other
 more complicated object).
 Remember that we modified our `FSLMaths` class so that it is passed an input
 image on creation:
 %% Cell type:code id: tags:
 ``` 
 class FSLMaths(object):
    def __init__(self, inimg):
        self.img = inimg
 fpath = op.expandvars('$FSLDIR/data/standard/MNI152_T1_2mm.nii.gz')
 fm    = FSLMaths(nib.load(fpath))
 ```
 %% Cell type:markdown id: tags:
 Take a look at what is going on in the `__init__` method - we take the `inimg`
 argument, and create a reference to it called `self.img`. We have added an
 _attribute_ to the `FSLMaths` instance, called `img`, and we can access that
 attribute like so:
 %% Cell type:code id: tags:
 ``` 
 print('Input for our FSLMaths instance: {}'.format(fm.img.get_filename()))
 ```
 %% Cell type:markdown id: tags:
 And that concludes the section on adding attributes to Python objects.
 Just kidding. But it really is that simple. This is one aspect of Python which
 might be quite jarring to you if you are coming from a language with more
 rigid semantics, such as C++ or Java. In those languages, you must pre-specify
 all of the attributes and methods that are a part of a class. But Python is
 much more flexible - you can simply add attributes to an object after it has
 been created.  In fact, you can even do this outside of the class
 definition<sup>1</sup>:
 %% Cell type:code id: tags:
 ``` 
 fm = FSLMaths(inimg)
 fm.another_attribute = 'Haha'
 print(fm.another_attribute)
 ```
 %% Cell type:markdown id: tags:
 __But ...__ while attributes can be added to a Python object at any time, it is
 good practice (and makes for more readable and maintainable code) to add all
 of an object's attributes within the `__init__` method.
 > <sup>1</sup>This not possible with many of the built-in types, such as
 > `list` and `dict` objects, nor with types that are defined in Python
 > extensions (Python modules that are written in C).
 <a class="anchor" id="methods"></a>
 ## Methods
 We've been dilly-dallying on this little `FSLMaths` project for a while now,
 but our class still can't actually do anything. Let's start adding some
 functionality:
 %% Cell type:code id: tags:
 ``` 
 class FSLMaths(object):
    def __init__(self, inimg):
        self.img        = inimg
        self.operations = []
    def add(self, value):
        self.operations.append(('add', value))
    def mul(self, value):
        self.operations.append(('mul', value))
    def div(self, value):
        self.operations.append(('div', value))
 ```
 %% Cell type:markdown id: tags:
 Woah woah, [slow down egg-head!](https://www.youtube.com/watch?v=yz-TemWooa4)
 We've modified `__init__` so that a second attribute called `operations` is
 added to our object - this `operations` attribute is simply a list.
 Then, we added a handful of methods - `add`, `mul`, and `div` - which each
 append a tuple to that `operations` list.
 > Note that, just like in the `__init__` method, the first argument that will
 > be passed to these methods is `self` - a reference to the object that the
 > method has been called on.
 The idea behind this design is that our `FSLMaths` class will not actually do
 anything when we call the `add`, `mul` or `div` methods. Instead, it will
 "stage" each operation, and then perform them all in one go. So let's add
 another method, `run`, which actually does the work:
 %% Cell type:code id: tags:
 ``` 
 import numpy   as np
 import nibabel as nib
 class FSLMaths(object):
    def __init__(self, inimg):
        self.img        = inimg
        self.operations = []
    def add(self, value):
        self.operations.append(('add', value))
    def mul(self, value):
        self.operations.append(('mul', value))
    def div(self, value):
        self.operations.append(('div', value))
    def run(self, output=None):
        data = np.array(self.img.get_data())
        for oper, value in self.operations:
            # Value could be an image.
            # If not, we assume that
            # it is a scalar/numpy array.
            if isinstance(value, nib.nifti1.Nifti1Image):
                value = value.get_data()
            if oper == 'add':
                data = data + value
            elif oper == 'mul':
                data = data * value
            elif oper == 'div':
                data = data / value
        # turn final output into a nifti,
        # and save it to disk if an
        # 'output' has been specified.
        outimg = nib.nifti1.Nifti1Image(data, inimg.affine)
        if output is not None:
            nib.save(outimg, output)
        return outimg
 ```
 %% Cell type:markdown id: tags:
 We now have a useable (but not very useful) `FSLMaths` class!
 %% Cell type:code id: tags:
 ``` 
 fpath = op.expandvars('$FSLDIR/data/standard/MNI152_T1_2mm.nii.gz')
 fmask = op.expandvars('$FSLDIR/data/standard/MNI152_T1_2mm_brain_mask.nii.gz')
 inimg = nib.load(fpath)
 mask  = nib.load(fmask)
 fm    = FSLMaths(inimg)
 fm.mul(mask)
 fm.add(-10)
 outimg = fm.run()
 norigvox = (inimg .get_data() > 0).sum()
 nmaskvox = (outimg.get_data() > 0).sum()
 print('Number of voxels >0 in original image: {}'.format(norigvox))
 print('Number of voxels >0 in masked image:   {}'.format(nmaskvox))
 ```
 %% Cell type:markdown id: tags:
 <a class="anchor" id="protecting-attribute-access"></a>
 ## Protecting attribute access
 In our `FSLMaths` class, the input image was added as an attribute called
 `img` to `FSLMaths` objects. We saw that it is easy to read the attributes
 of an object - if we have a `FSLMaths` instance called `fm`, we can read its
 input image via `fm.img`.
 But it is just as easy to write the attributes of an object. What's to stop
 some sloppy research assistant from overwriting our `img` attribute?
 %% Cell type:code id: tags:
 ``` 
 inimg = nib.load(op.expandvars('$FSLDIR/data/standard/MNI152_T1_2mm.nii.gz'))
 fm = FSLMaths(inimg)
 fm.img = None
 fm.run()
 ```
 %% Cell type:markdown id: tags:
 Well, the scary answer is ... there is __nothing__ stopping you from doing
 whatever you want to a Python object. You can add, remove, and modify
 attributes at will. You can even replace the methods of an existing object if
 you like:
 %% Cell type:code id: tags:
 ``` 
 fm = FSLMaths(inimg)
 def myadd(value):
    print('Oh no, I\'m not going to add {} to '
          'your image. Go away!'.format(value))
 fm.add = myadd
 fm.add(123)
 fm.mul = None
 fm.mul(123)
 ```
 %% Cell type:markdown id: tags:
 But you really shouldn't get into the habit of doing devious things like
 this. Think of the poor souls who inherit your code years after you have left
 the lab - if you go around overwriting all of the methods and attributes of
 your objects, they are not going to have a hope in hell of understanding what
 your code is actually doing, and they are not going to like you very
 much. Take a look at the appendix for a [brief discussion on this
 topic](appendix-monkey-patching).
 Python tends to assume that programmers are "responsible adults", and hence
 doesn't do much in the way of restricting access to the attributes or methods
 of an object. This is in contrast to languages like C++ and Java, where the
 notion of a private attribute or method is strictly enforced by the language.
 However, there are a couple of conventions in Python that are [universally
 adhered
 to](https://docs.python.org/3.5/tutorial/classes.html#private-variables):
 * Class-level attributes and methods, and module-level attributes, functions,
  and classes, which begin with a single underscore (`_`), should be
  considered __protected__ - they are intended for internal use only, and
  should not be considered part of the public API of a class or module.  This
  is not enforced by the language in any way<sup>2</sup> - remember, we are
  all responsible adults here!
 * Class-level attributes and methods which begin with a double-underscore
  (`__`) should be considered __private__. Python provides a weak form of
  enforcement for this rule - any attribute or method with such a name will
  actually be _renamed_ (in a standardised manner) at runtime, so that it is
  not accessible through its original name (it is still accessible via its
  [mangled
  name](https://docs.python.org/3.5/tutorial/classes.html#private-variables)
  though).
 > <sup>2</sup> With the exception that module-level fields which begin with a
 > single underscore will not be imported into the local scope via the
 > `from [module] import *` techinque.
 So with all of this in mind, we can adjust our `FSLMaths` class to discourage
 our sloppy research assistant from overwriting the `img` attribute:
 %% Cell type:code id: tags:
 ``` 
 # remainder of definition omitted for brevity
 class FSLMaths(object):
    def __init__(self, inimg):
        self.__img        = inimg
        self.__operations = []
 ```
 %% Cell type:markdown id: tags:
 But now we have lost the ability to read our `__img` attribute:
 %% Cell type:code id: tags:
 ``` 
 inimg = nib.load(op.expandvars('$FSLDIR/data/standard/MNI152_T1_2mm.nii.gz'))
 fm = FSLMaths(inimg)
 print(fm.__img)
 ```
 %% Cell type:markdown id: tags:
 <a class="anchor" id="a-better-way-properties"></a>
 ### A better way - properties
 Python has a feature called
 [`properties`](https://docs.python.org/3.5/library/functions.html#property),
 which is a nice way of controlling access to the attributes of an object. We
 can use properties by defining a "getter" method which can be used to access
 our attributes, and "decorating" them with the `@property` decorator (we will
 cover decorators in a later practical).
 %% Cell type:code id: tags:
 ``` 
 class FSLMaths(object):
    def __init__(self, inimg):
        self.__img        = inimg
        self.__operations = []
    @property
    def img(self):
        return self.__img
 ```
 %% Cell type:markdown id: tags:
 So we are still storing our input image as a private attribute, but now we
 have made it available in a read-only manner via the public `img` property:
 %% Cell type:code id: tags:
 ``` 
 fpath = op.expandvars('$FSLDIR/data/standard/MNI152_T1_2mm.nii.gz')
 inimg = nib.load(fpath)
 fm    = FSLMaths(inimg)
 print(fm.img.get_filename())
 ```
 %% Cell type:markdown id: tags:
 Note that, even though we have defined `img` as a method, we can access it
 like an attribute - this is due to the magic behind the `@property` decorator.
 We can also define "setter" methods for a property. For example, we might wish
 to add the ability for a user of our `FSLMaths` class to change the input
 image after creation.
 %% Cell type:code id: tags:
 ``` 
 class FSLMaths(object):
    def __init__(self, inimg):
        self.__img        = None
        self.__operations = []
        self.img          = inimg
    @property
    def img(self):
        return self.__img
    @img.setter
    def img(self, value):
        if not isinstance(value, nib.nifti1.Nifti1Image):
            raise ValueError('value must be a NIFTI image!')
        self.__img = value
 ```
 %% Cell type:markdown id: tags:
 > Note that we used the `img` setter method within `__init__` to validate the
 > initial `inimg` that was passed in during creation.
 Property setters are a nice way to add validation logic for when an attribute
 is assigned a value. In this example, an error will be raised if the new input
 is not a NIFTI image.
 %% Cell type:code id: tags:
 ``` 
 fpath = op.expandvars('$FSLDIR/data/standard/MNI152_T1_2mm.nii.gz')
 inimg = nib.load(fpath)
 fm    = FSLMaths(inimg)
 print('Input:     ', fm.img.get_filename())
 # let's change the input
 # to a different image
 fpath2 = op.expandvars('$FSLDIR/data/standard/MNI152_T1_2mm_brain.nii.gz')
 inimg2 = nib.load(fpath2)
 fm.img = inimg2
 print('New input: ', fm.img.get_filename())
 print('This is going to explode')
 fm.img = 'abcde'
 ```
 %% Cell type:markdown id: tags:
 <a class="anchor" id="inheritance"></a>
 ## Inheritance
 One of the major advantages of an object-oriented programming approach is
 _inheritance_ - the ability to define hierarchical relationships between
 classes and instances.
 <a class="anchor" id="the-basics"></a>
 ### The basics
 My local veterinary surgery runs some Python code which looks like the
 following, to assist the nurses in identifying an animal when it arrives at
 the surgery:
 %% Cell type:code id: tags:
 ``` 
 class Animal(object):
    def noiseMade(self):
        raise NotImplementedError('This method must be '
                                  'implemented by sub-classes')
 class Dog(Animal):
    def noiseMade(self):
        return 'Woof'
 class TalkingDog(Dog):
    def noiseMade(self):
        return 'Hi Homer, find your soulmate!'
 class Cat(Animal):
    def noiseMade(self):
        return 'Meow'
 class Labrador(Dog):
    pass
 class Chihuahua(Dog):
    def noiseMade(self):
        return 'Yap yap yap'
 ```
 %% Cell type:markdown id: tags:
 Hopefully this example doesn't need much in the way of explanation - this
 collection of classes captures a hierarchical relationship which exists in the
 real world (and also captures the inherently annoying nature of
 chihuahuas). For example, in the real world, all dogs are animals, but not all
 animals are dogs.  Therefore in our model, the `Dog` class has specified
 `Animal` as its base class. We say that the `Dog` class _extends_, _derives
 from_, or _inherits from_, the `Animal` class, and that all `Dog` instances
 are also `Animal` instances (but not vice-versa).
 What does that `noiseMade` method do?  There is a `noiseMade` method defined
 on the `Animal` class, but it has been re-implemented, or _overridden_ in the
 `Dog`,
 [`TalkingDog`](https://twitter.com/simpsonsqotd/status/427941665836630016?lang=en),
 `Cat`, and `Chihuahua` classes (but not on the `Labrador` class).  We can call
 the `noiseMade` method on any `Animal` instance, but the specific behaviour
 that we get is dependent on the specific type of animal.
 %% Cell type:code id: tags:
 ``` 
 d  = Dog()
 l  = Labrador()
 c  = Cat()
 ch = Chihuahua()
 print('Noise made by dogs:       {}'.format(d .noiseMade()))
 print('Noise made by labradors:  {}'.format(l .noiseMade()))
 print('Noise made by cats:       {}'.format(c .noiseMade()))
 print('Noise made by chihuahuas: {}'.format(ch.noiseMade()))
 ```
 %% Cell type:markdown id: tags:
 Note that calling the `noiseMade` method on a `Labrador` instance resulted in
 the `Dog.noiseMade` implementation being called.
 <a class="anchor" id="code-re-use-and-problem-decomposition"></a>
 ### Code re-use and problem decomposition
 Inheritance allows us to split a problem into smaller problems, and to re-use
 code.  Let's demonstrate this with a more involved (and even more contrived)
 example.  Imagine that a former colleague had written a class called
 `Operator`:
 %% Cell type:code id: tags:
 ``` 
 class Operator(object):
    def __init__(self):
        super().__init__() # this line will be explained later
        self.__operations = []
        self.__opFuncs    = {}
    @property
    def operations(self):
        return list(self.__operations)
    @property
    def functions(self):
        return dict(self.__opFuncs)
    def addFunction(self, name, func):
        self.__opFuncs[name] = func
    def do(self, name, *values):
        self.__operations.append((name, values))
    def preprocess(self, value):
        return value
    def run(self, input):
        data = self.preprocess(input)
        for oper, vals in self.__operations:
            func = self.__opFuncs[oper]
            vals = [self.preprocess(v) for v in vals]
            data = func(data, *vals)
        return data
 ```
 %% Cell type:markdown id: tags:
 This `Operator` class provides an interface and logic to execute a chain of
 operations - an operation is some function which accepts one or more inputs,
 and produce one output.
 But it stops short of defining any operations. Instead, we can create another
 class - a sub-class - which derives from the `Operator` class. This sub-class
 will define the operations that will ultimately be executed by the `Operator`
 class. All that the `Operator` class does is:
 - Allow functions to be registered with the `addFunction` method - all
  registered functions can be used via the `do` method.
 - Stage an operation (using a registered function) via the `do` method. Note
  that `do` allows any number of values to be passed to it, as we used the `*`
  operator when specifying the `values` argument.
 - Run all staged operations via the `run` method - it passes an input through
  all of the operations that have been staged, and then returns the final
  result.
 Let's define a sub-class:
 %% Cell type:code id: tags:
 ``` 
 class NumberOperator(Operator):
    def __init__(self):
        super().__init__()
        self.addFunction('add',    self.add)
        self.addFunction('mul',    self.mul)
        self.addFunction('negate', self.negate)
    def preprocess(self, value):
        return float(value)
    def add(self, a, b):
        return a + b
    def mul(self, a, b):
        return a * b
    def negate(self, a):
        return -a
 ```
 %% Cell type:markdown id: tags:
 The `NumberOperator` is a sub-class of `Operator`, which we can use for basic
 numerical calculations. It provides a handful of simple numerical methods, but
 the most interesting stuff is inside `__init__`.
 > ```
 > super().__init__()
 > ```
 This line invokes `Operator.__init__` - the initialisation method for the
 `Operator` base-class.
 In Python, we can use the [built-in `super`
 method](https://docs.python.org/3.5/library/functions.html#super) to take care
 of correctly calling methods that are defined in an object's base-class (or
 classes, in the case of [multiple inheritance](multiple-inheritance)).
 > The `super` function is one thing which changed between Python 2 and 3 -
 > in Python 2, it was necessary to pass both the type and the instance
 > to `super`. So it is common to see code that looks like this:
 >
 > ```
 > def __init__(self):
 >     super(NumberOperator, self).__init__()
 > ```
 >
 > Fortunately things are a lot cleaner in Python 3.
 Let's move on to the next few lines in `__init__`:
 > ```
 > self.addFunction('add',    self.add)
 > self.addFunction('mul',    self.mul)
 > self.addFunction('negate', self.negate)
 > ```
 Here we are registering all of the functionality that is provided by the
 `NumberOperator` class, via the `Operator.addFunction` method.
 The `NumberOperator` class has also overridden the `preprocess` method, to
 ensure that all values handled by the `Operator` are numbers. This method gets
 called within the `Operator.run` method - for a `NumberOperator` instance, the
-`NumberOperator.preprocess` method will get called<sup>1</sup>.
+`NumberOperator.preprocess` method will get called<sup>3</sup>.
-> <sup>1</sup> When a sub-class overrides a base-class method, it is still
+> <sup>3</sup> When a sub-class overrides a base-class method, it is still
 > possible to access the base-class implementation [via the `super()`
 > function](https://stackoverflow.com/a/4747427) (the preferred method), or by
 > [explicitly calling the base-class
 > implementation](https://stackoverflow.com/a/2421325).
 Now let's see what our `NumberOperator` class does:
 %% Cell type:code id: tags:
 ``` 
 no = NumberOperator()
 no.do('add', 10)
 no.do('mul', 2)
 no.do('negate')
 print('Operations on {}: {}'.format(10,  no.run(10)))
 print('Operations on {}: {}'.format(2.5, no.run(5)))
 ```
 %% Cell type:markdown id: tags:
 It works! While this is a contrived example, hopefully you can see how
 inheritance can be used to break a problem down into sub-problems:
 - The `Operator` class provides all of the logic needed to manage and execute
  operations, without caring about what those operations are actually doing.
 - This leaves the `NumberOperator` class free to concentrate on implementing
  the functions that are specific to its task, and not having to worry about
  how they are executed.
 We could also easily implement other `Operator` sub-classes to work on
 different data types, such as arrays, images, or even non-numeric data such as
 strings:
 %% Cell type:code id: tags:
 ``` 
 class StringOperator(Operator):
    def __init__(self):
        super().__init__()
        self.addFunction('capitalise', self.capitalise)
        self.addFunction('concat',     self.concat)
    def preprocess(self, value):
        return str(value)
    def capitalise(self, s):
        return ' '.join([w[0].upper() + w[1:] for w in s.split()])
    def concat(self, s1, s2):
        return s1 + s2
 so = StringOperator()
 so.do('capitalise')
 so.do('concat', '!')
 print(so.run('python is an ok language'))
 ```
 %% Cell type:markdown id: tags:
 <a class="anchor" id="polymorphism"></a>
 ### Polymorphism
 Inheritance also allows us to take advantage of _polymorphism_, which refers
 to idea that, in an object-oriented language, we should be able to use an
 object without having complete knowledge about the class, or type, of that
 object. For example, we should be able to write a function which expects an
 `Operator` instance, but which will work on an instance of any `Operator`
 sub-classs. As an example, let's write a function which prints a summary of an
 `Operator` instance:
 %% Cell type:code id: tags:
 ``` 
 def operatorSummary(o):
    print(type(o).__name__)
    print('  All functions: ')
    for fname in o.functions.keys():
        print('    {}'.format(fname))
    print('  Staged operations: ')
    for i, (fname, vals) in enumerate(o.operations):
        vals = ', '.join([str(v) for v in vals])
        print('    {}: {}({})'.format(i + 1, fname, vals))
 ```
 %% Cell type:markdown id: tags:
 Because the `operatorSummary` function only uses methods that are defined
 in the `Operator` base-class, we can use it on _any_ `Operator` instance,
 regardless of its specific type:
 %% Cell type:code id: tags:
 ``` 
 operatorSummary(no)
 operatorSummary(so)
 ```
 %% Cell type:markdown id: tags:
 <a class="anchor" id="multiple-inheritance"></a>
 ### Multiple inheritance
 Python allows you to define a class which has multiple base classes - this is
 known as _multiple inheritance_. For example, we might want to build a
 notification mechanisim into our `StringOperator` class, so that listeners can
 be notified whenever the `capitalise` method gets called. It so happens that
 our old colleague of `Operator` class fame also wrote a `Notifier` class which
 allows listeners to register to be notified when an event occurs:
 %% Cell type:code id: tags:
 ``` 
 class Notifier(object):
    def __init__(self):
        super().__init__()
        self.__listeners = {}
    def register(self, name, func):
        self.__listeners[name] = func
    def notify(self, *args, **kwargs):
        for func in self.__listeners.values():
            func(*args, **kwargs)
 ```
 %% Cell type:markdown id: tags:
 Let's modify the `StringOperator` class to use the functionality of the
 `Notifier ` class:
 %% Cell type:code id: tags:
 ``` 
 class StringOperator(Operator, Notifier):
    def __init__(self):
        super().__init__()
        self.addFunction('capitalise', self.capitalise)
        self.addFunction('concat',     self.concat)
    def preprocess(self, value):
        return str(value)
    def capitalise(self, s):
        result = ' '.join([w[0].upper() + w[1:] for w in s.split()])
        self.notify(result)
        return result
    def concat(self, s1, s2):
        return s1 + s2
 ```
 %% Cell type:markdown id: tags:
 Now, anything which is interested in uses of the `capitalise` method can
 register as a listener on a `StringOperator` instance:
 %% Cell type:code id: tags:
 ``` 
 so = StringOperator()
 def capitaliseCalled(result):
    print('Capitalise operation called: {}'.format(result))
 so.register('mylistener', capitaliseCalled)
 so.do('capitalise')
 so.do('concat', '?')
 print(so.run('did you notice that functions are objects too'))
 ```
 %% Cell type:markdown id: tags:
 If you wish to use multiple inheritance in your design, it is important to be
 aware of the mechanism that Python uses to determine how base class methods
 are called (and which base class method will be called, in the case of naming
 conflicts). This is referred to as the Method Resolution Order (MRO) - further
 details on the topic can be found
 [here](https://www.python.org/download/releases/2.3/mro/), and a more concise
 summary
 [here](http://python-history.blogspot.co.uk/2010/06/method-resolution-order.html).
 Note also that for base class `__init__` methods to be correctly called in a
 design which uses multiple inheritance, _all_ classes in the hierarchy must
 invoke `super().__init__()`. This can become complicated when some base
 classes expect to be passed arguments to their `__init__` method. In scenarios
 like this it may be prefereable to manually invoke the base class `__init__`
 methods instead of using `super()`. For example:
 > ```
 > class StringOperator(Operator, Notifier):
 >     def __init__(self):
 >         Operator.__init__(self)
 >         Notifier.__init__(self)
 > ```
 This approach has the disadvantage that if the base classes change, you will
 have to change these invocations. But the advantage is that you know exactly
 how the class hierarchy will be initialised. In general though, doing
 everything with `super()` will result in more maintainable code.
 <a class="anchor" id="class-attributes-and-methods"></a>
 ## Class attributes and methods
 Up to this point we have been covering how to add attributes and methods to an
 _object_. But it is also possible to add methods and attributes to a _class_
 (`static` methods and fields, for those of you familiar with C++ or Java).
 Class attributes and methods can be accessed without having to create an
 instance of the class - they are not associated with individual objects, but
 rather with the class itself.
 Class methods and attributes can be useful in several scenarios - as a
 hypothetical, not very useful example, let's say that we want to gain usage
 statistics for how many times each type of operation is used on instances of
 our `FSLMaths` class. We might, for example, use this information in a grant
 application to show evidence that more research is needed to optimise the
 performance of the `add` operation.
 <a class="anchor" id="class-attributes"></a>
 ### Class attributes
 Let's add a `dict` called `opCounters` as a class attribute to the `FSLMaths`
 class - whenever an operation is called on a `FSLMaths` instance, the counter
 for that operation will be incremented:
 %% Cell type:code id: tags:
 ``` 
 import numpy   as np
 import nibabel as nib
 class FSLMaths(object):
    # It's this easy to add a class-level
    # attribute. This dict is associated
    # with the FSLMaths *class*, not with
    # any individual FSLMaths instance.
    opCounters = {}
    def __init__(self, inimg):
        self.img        = inimg
        self.operations = []
    def add(self, value):
        self.operations.append(('add', value))
    def mul(self, value):
        self.operations.append(('mul', value))
    def div(self, value):
        self.operations.append(('div', value))
    def run(self, output=None):
        data = np.array(self.img.get_data())
        for oper, value in self.operations:
            # Code omitted for brevity
            # Increment the usage counter
            # for this operation. We can
            # access class attributes (and
            # methods) through the class
            # itself.
            FSLMaths.opCounters[oper] = self.opCounters.get(oper, 0) + 1
 ```
 %% Cell type:markdown id: tags:
 So let's see it in action:
 %% Cell type:code id: tags:
 ``` 
 fpath = op.expandvars('$FSLDIR/data/standard/MNI152_T1_2mm.nii.gz')
 fmask = op.expandvars('$FSLDIR/data/standard/MNI152_T1_2mm_brain_mask.nii.gz')
 inimg = nib.load(fpath)
 mask  = nib.load(fmask)
 fm1 = FSLMaths(inimg)
 fm2 = FSLMaths(inimg)
 fm1.mul(mask)
 fm1.add(15)
 fm2.add(25)
 fm1.div(1.5)
 fm1.run()
 fm2.run()
 print('FSLMaths usage statistics')
 for oper in ('add', 'div', 'mul'):
    print('  {} : {}'.format(oper, FSLMaths.opCounters.get(oper, 0)))
 ```
 %% Cell type:markdown id: tags:
 <a class="anchor" id="class-methods"></a>
 ### Class methods
 It is just as easy to add a method to a class - let's take our reporting code
 from above, and add it as a method to the `FSLMaths` class.
 A class method is denoted by the
 [`@classmethod`](https://docs.python.org/3.5/library/functions.html#classmethod)
 decorator. Note that, where a regular method which is called on an instance
 will be passed the instance as its first argument (`self`), a class method
 will be passed the class itself as the first argument - the standard
 convention is to call this argument `cls`:
 %% Cell type:code id: tags:
 ``` 
 class FSLMaths(object):
    opCounters = {}
    @classmethod
    def usage(cls):
        print('FSLMaths usage statistics')
        for oper in ('add', 'div', 'mul'):
            print('  {} : {}'.format(oper, FSLMaths.opCounters.get(oper, 0)))
    def __init__(self, inimg):
        self.img        = inimg
        self.operations = []
    def add(self, value):
        self.operations.append(('add', value))
    def mul(self, value):
        self.operations.append(('mul', value))
    def div(self, value):
        self.operations.append(('div', value))
    def run(self, output=None):
        data = np.array(self.img.get_data())
        for oper, value in self.operations:
            FSLMaths.opCounters[oper] = self.opCounters.get(oper, 0) + 1
 ```
 %% Cell type:markdown id: tags:
 > There is another decorator -
 > [`@staticmethod`](https://docs.python.org/3.5/library/functions.html#staticmethod) -
 > which can be used on methods defined within a class. The difference
 > between a `@classmethod` and a `@staticmethod` is that the latter will _not_
 > be passed the class (`cls`).
 calling a class method is the same as accessing a class attribute:
 %% Cell type:code id: tags:
 ``` 
 fpath = op.expandvars('$FSLDIR/data/standard/MNI152_T1_2mm.nii.gz')
 fmask = op.expandvars('$FSLDIR/data/standard/MNI152_T1_2mm_brain_mask.nii.gz')
 inimg = nib.load(fpath)
 mask  = nib.load(fmask)
 fm1 = FSLMaths(inimg)
 fm2 = FSLMaths(inimg)
 fm1.mul(mask)
 fm1.add(15)
 fm2.add(25)
 fm1.div(1.5)
 fm1.run()
 fm2.run()
 FSLMaths.usage()
 ```
 %% Cell type:markdown id: tags:
 Note that it is also possible to access class attributes and methods through
 instances:
 %% Cell type:code id: tags:
 ``` 
 print(fm1.opCounters)
 fm1.usage()
 ```
 %% Cell type:markdown id: tags:
 <a class="anchor" id="appendix-the-object-base-class"></a>
 ## Appendix: The `object` base-class
 When you are defining a class, you need to specify the base-class from which
 your class inherits. If your class does not inherit from a particular class,
 then it should inherit from the built-in `object` class:
 > ```
 > class MyClass(object):
 >     ...
 > ```
 However, in older code bases, you might see class definitions that look like
 this, without explicitly inheriting from the `object` base class:
 > ```
 > class MyClass:
 >     ...
 > ```
 This syntax is a [throwback to older versions of
 Python](https://docs.python.org/2/reference/datamodel.html#new-style-and-classic-classes).
 In Python 3 there is actually no difference in defining classes in the
 "new-style" way we have used throughout this tutorial, or the "old-style" way
 mentioned in this appendix.
 But if you are writing code which needs to run on both Python 2 and 3, you
 __must__ define your classes in the new-style convention, i.e. by explicitly
 inheriting from the `object` base class. Therefore, the safest approach is to
 always use the new-style format.
 <a class="anchor" id="appendix-init-versus-new"></a>
 ## Appendix: `__init__` versus `__new__`
 In Python, object creation is actually a two-stage process - _creation_, and
 then _initialisation_. The `__init__` method gets called during the
 _initialisation_ stage - its job is to initialise the state of the object. But
 note that, by the time `__init__` gets called, the object has already been
 created.
 You can also define a method called `__new__` if you need to control the
 creation stage, although this is very rarely needed. One example of where you
 might need to implement the `__new__` method is if you wish to create a
 [subclass of a
 `numpy.array`](https://docs.scipy.org/doc/numpy-1.14.0/user/basics.subclassing.html)
 (although you might alternatively want to think about redefining your problem
 so that this is not necessary).
 A brief explanation on
 the difference between `__new__` and `__init__` can be found
 [here](https://www.reddit.com/r/learnpython/comments/2s3pms/what_is_the_difference_between_init_and_new/cnm186z/),
 and you may also wish to take a look at the [official Python
 docs](https://docs.python.org/3.5/reference/datamodel.html#basic-customization).
 <a class="anchor" id="appendix-monkey-patching"></a>
 ## Appendix: Monkey-patching
 The act of run-time modification of objects or class definitions is referred
 to as [_monkey-patching_](https://en.wikipedia.org/wiki/Monkey_patch) and,
 whilst it is allowed by the Python programming language, it is generally
 considered quite bad practice.
 Just because you _can_ do something doesn't mean that you _should_. Python
 gives you the flexibility to write your software in whatever manner you deem
 suitable.  __But__ if you want to write software that will be used, adopted,
 maintained, and enjoyed by other people, you should be polite, write your code
 in a clear, readable fashion, and avoid the use of devious tactics such as
 monkey-patching.
 __However__, while monkey-patching may seem like a horrific programming
 practice to those of you coming from the realms of C++, Java, and the like,
 (and it is horrific in many cases), it can be _extremely_ useful in certain
 circumstances.  For instance, monkey-patching makes [unit testing a
 breeze in Python](https://docs.python.org/3.5/library/unittest.mock.html).
 As another example, consider the scenario where you are dependent on a third
 party library which has bugs in it. No problem - while you are waiting for the
 library author to release a new version of the library, you can write your own
 working implementation and [monkey-patch it
 in!](https://git.fmrib.ox.ac.uk/fsl/fsleyes/fsleyes/blob/0.21.0/fsleyes/views/viewpanel.py#L726)
 <a class="anchor" id="appendix-method-overloading"></a>
 ## Appendix: Method overloading
 Method overloading (defining multiple methods with the same name in a class,
 but each accepting different arguments) is one of the only object-oriented
 features that is not present in Python. Becuase Python does not perform any
 runtime checks on the types of arguments that are passed to a method, or the
 compatibility of the method to accept the arguments, it would not be possible
 to determine which implementation of a method is to be called. In other words,
 in Python only the name of a method is used to identify that method, unlike in
 C++ and Java, where the full method signature (name, input types and return
 types) is used.
 However, because a Python method can be written to accept any number or type
 of arguments, it is very easy to to build your own overloading logic by
-writing a "dispatch" method. Here is YACE (Yet Another Contrived Example):
+writing a "dispatch" method<sup>4</sup>. Here is YACE (Yet Another Contrived
+Example):
 %% Cell type:code id: tags:
 ``` 
 class Adder(object):
    def add(self, *args):
        if   len(args) == 2: return self.__add2(*args)
        elif len(args) == 3: return self.__add3(*args)
        elif len(args) == 4: return self.__add4(*args)
        else:
            raise AttributeError('No method available to accept {} '
                                 'arguments'.format(len(args)))
    def __add2(self, a, b):
        return a + b
    def __add3(self, a, b, c):
        return a + b + c
    def __add4(self, a, b, c, d):
        return a + b + c + d
 a = Adder()
 print('Add two:   {}'.format(a.add(1, 2)))
 print('Add three: {}'.format(a.add(1, 2, 3)))
 print('Add four:  {}'.format(a.add(1, 2, 3, 4)))
 ```
 %% Cell type:markdown id: tags:
+> <sup>4</sup>Another option is the [`functools.singledispatch`
+> decorator](https://docs.python.org/3.5/library/functools.html#functools.singledispatch),
+> which is more complicated, but may allow you to write your dispatch logic in
+> a more concise manner.
 <a class="anchor" id="useful-references"></a>
 ## Useful references
 The official Python documentation has a wealth of information on the internal
 workings of classes and objects, so these pages are worth a read:
 * https://docs.python.org/3.5/tutorial/classes.html
 * https://docs.python.org/3.5/reference/datamodel.html

--- a/advanced_topics/object_oriented_programming.md
+++ b/advanced_topics/object_oriented_programming.md
@@ -853,10 +853,10 @@ Here we are registering all of the functionality that is provided by the
 The `NumberOperator` class has also overridden the `preprocess` method, to
 ensure that all values handled by the `Operator` are numbers. This method gets
 called within the `Operator.run` method - for a `NumberOperator` instance, the
-`NumberOperator.preprocess` method will get called<sup>1</sup>.
+`NumberOperator.preprocess` method will get called<sup>3</sup>.
-> <sup>1</sup> When a sub-class overrides a base-class method, it is still
+> <sup>3</sup> When a sub-class overrides a base-class method, it is still
 > possible to access the base-class implementation [via the `super()`
 > function](https://stackoverflow.com/a/4747427) (the preferred method), or by
 > [explicitly calling the base-class
@@ -1361,7 +1361,8 @@ types) is used.
 However, because a Python method can be written to accept any number or type
 of arguments, it is very easy to to build your own overloading logic by
-writing a "dispatch" method. Here is YACE (Yet Another Contrived Example):
+writing a "dispatch" method<sup>4</sup>. Here is YACE (Yet Another Contrived
+Example):
 ```
@@ -1391,6 +1392,11 @@ print('Add three: {}'.format(a.add(1, 2, 3)))
 print('Add four:  {}'.format(a.add(1, 2, 3, 4)))
 ```
+> <sup>4</sup>Another option is the [`functools.singledispatch`
+> decorator](https://docs.python.org/3.5/library/functools.html#functools.singledispatch),
+> which is more complicated, but may allow you to write your dispatch logic in
+> a more concise manner.
 <a class="anchor" id="useful-references"></a>
 ## Useful references