# Classes

All objects in Python are in fact implemented as classes, but you can program with objects without knowing about classes. Nevertheless, the class concept is a powerful tool and some basic knowledge will make it easier to understand much useful Python information that is floating around.

## A very simple class

A class packs together a set of variables and a set of functions. All functions can access all variables. The idea is to encapsulate variables and functions in logical units such that a larger program can be composed by combing such units (classes).

1: In classes, the functions are called methods and the variables are called attributes.

Here is a trivial class that has one variable a and one function dump that writes the contents of a:

class Trivial:
def __init__(self, a):
self.a = a

def dump(self):
print self.a


How can we use this class? First, we must make an instance (object) of the class:

t = Trivial(a=4)


The syntax Trivial(a=4) implies a call to the __init__ method (function) with 4 as the value of the argument a. Inside __init__, we store the value of a as an attribute in the class: self.a. If there were several methods in the class, all of them could then access self.a (as if a were some global variable in the class). The __init__ function is called a constructor since it is used to construct an instance (object) of the class.

Having an instance t of class Trivial, we can call the dump method as follows:

t.dump()


Even though both __init__ and dump have self as first argument, this argument is not used in a call.

The self argument. It takes time and experience to understand the self argument in class methods.
1. self must always be the first argument.
2. self is never used in calls.
3. self is used to access attributes and methods inside methods.
We refer to a more comprehensive text on classes for better explanation of self.

## A class for representing a mathematical function

The Python implementation of the mathematical function $$s(t; v_0, a) = v_0t + \frac{1}{2}at^2$$ can benefit from being implemented as a class. The reason is that $$s$$ is a function of one variable, $$t$$, so it should be called as $$s(t)$$, but the function also contains two parameters, $$v_0$$ and $$a$$. Using a class, we can pack $$v_0$$ and $$a$$ together with a function computing $$s(t)$$ and that can be called with one argument.

### The class code

class Distance:
def __init__(self, v0, a):
self.v0 = v0
self.a = a

def __call__(self, t):
v0, a = self.v0, self.a  # make local variables
return v0*t + 0.5*a*t**2


### Dissection

The class has two methods (functions). The name of a method can be freely chosen by the programmer, say dump as we used above, but here we have used three special names, starting and ending with double underscores, which allows us to use special attractive syntax in the calls (such methods are actually known as special methods).

The constructor __init__ has one purpose: storing data in class attributes, here self.v0 and self.a. We can then access these data in class methods.

The __call__ method is used to evaluate $$s(t)$$. It has one argument (self does not count since it is never used in calls). This special methods allows us to view a class instance as if were a function. Let us illustrate by some code:

s = Distance(v0=2, a=0.5)  # create instance
v = s(t=0.2)               # runs s.__call__(t=0.2)


The last line has some magic: s is a class instance, not a function, but still we can write s(t=0.2) or s(0.2) as if s were a function. This is the purpose of the special method __call__: to allow such syntax. Actually, s(0.2) means s.__call__(0.2). The nice result is that s looks like a function, it takes one argument t, as the mathematical function $$s(t)$$, but it also contains values of the two parameters $$v_0$$ and $$a$$.

In general, for a function $$f(x,y,z; p_1,p_2,\ldots,p_n)$$, here with three independent variables and $$n$$ parameters $$p_1,p_2,\ldots,p_n$$, we can pack the function and the parameters together in a class:

class F:
def __init__(self, p1, p2, ...):
self.p1 = p1
self.p2 = p2
...

def __call__(self, x, y, z):
# return formula involving x, y, z and self.p1, self.p2 ...


The $$f$$ function is initialized by

f = F(p1=..., p2=..., ...)


and later called as f(x, y, z).