### Introduction

The so-called magic methods have nothing to do with wizardry. You have already seen them in the previous chapters of our tutorial. They are special methods with fixed names. They are the methods with this clumsy syntax, i.e. the double underscores at the beginning and the end. They are also hard to talk about. How do you pronounce or say a method name like __init__? "Underscore underscore init underscore underscore" sounds horrible and is almost a tongue twister. "Double underscore init double underscore" is a lot better, but the ideal way is "dunder init dunder" That's why magic methods methods are sometimes called dunder methods!

So what's magic about the __init__ method? The answer is, you don't have to invoke it directly. The invocation is realized behind the scenes. When you create an instance x of a class A with the statement "x = A()", Python will do the necessary calls to __new__ and __init__.

Towards the end of this chapter of our tutorial we will introduce the __call__ method. It is overlooked by many beginners and even advanced programmers of Python. It is a functionality which many programming languages do not have, so programmers generally do not look for it. The __call__ method enables Python programmers to write classes where the instances behave like functions. Both functions and the instances of such classes are called callables.

We have encountered the concept of operator overloading many times in the course of this tutorial. We had used the plus sign to add numerical values, to concatenate strings or to combine lists:

4 + 5

Output::
9
3.8 + 9

Output::
12.8
"Peter" + " " + "Pan"

Output::
'Peter Pan'
[3,6,8] + [7,11,13]

Output::
[3, 6, 8, 7, 11, 13]

It's even possible to overload the "+" operator as well as all the other operators for the purposes of your own class. To do this, you need to understand the underlying mechanism. There is a special (or a "magic") method for every operator sign. The magic method for the "+" sign is the __add__ method. For "-" it is __sub__ and so on. We have a complete listing of all the magic methods a little further down.

The mechanism works like this: If we have an expression "x + y" and x is an instance of class K, then Python will check the class definition of K. If K has a method __add__ it will be called with x.__add__(y), otherwise we will get an error message:

Traceback (most recent call last):
File "", line 1, in
TypeError: unsupported operand type(s) for +: 'K' and 'K'



### Overview of Magic Methods

#### Binary Operators

Operator Method
- object.__sub__(self, other)
* object.__mul__(self, other)
// object.__floordiv__(self, other)
/ object.__truediv__(self, other)
% object.__mod__(self, other)
** object.__pow__(self, other[, modulo])
<< object.__lshift__(self, other)
>> object.__rshift__(self, other)
& object.__and__(self, other)
^ object.__xor__(self, other)
| object.__or__(self, other)

#### Extended Assignments

Operator Method
-= object.__isub__(self, other)
*= object.__imul__(self, other)
/= object.__idiv__(self, other)
//= object.__ifloordiv__(self, other)
%= object.__imod__(self, other)
**= object.__ipow__(self, other[, modulo])
<<= object.__ilshift__(self, other)
>>= object.__irshift__(self, other)
&= object.__iand__(self, other)
^= object.__ixor__(self, other)
|= object.__ior__(self, other)

#### Unary Operators

Operator Method
- object.__neg__(self)
+ object.__pos__(self)
abs() object.__abs__(self)
~ object.__invert__(self)
complex() object.__complex__(self)
int() object.__int__(self)
long() object.__long__(self)
float() object.__float__(self)
oct() object.__oct__(self)
hex() object.__hex__(self

#### Comparison Operators

Operator Method
< object.__lt__(self, other)
<= object.__le__(self, other)
== object.__eq__(self, other)
!= object.__ne__(self, other)
>= object.__ge__(self, other)
> object.__gt__(self, other)

### Example class: Length

We will demonstrate the Length class and how you can overload the "+" operator for your own class. To do this, we have to overload the __add__ method. Our class contains the __str__ and __repr__ methods as well. The instances of the class Length contain length or distance information. The attributes of an instance are self.value and self.unit.

This class allows us to calculate expressions with mixed units like this one:

2.56 m + 3 yd + 7.8 in + 7.03 cm

The class can be used like this:

from unit_conversions import Length
L = Length
print(L(2.56,"m") + L(3,"yd") + L(7.8,"in") + L(7.03,"cm"))

5.57162


The listing of the class:

class Length:

__metric = {"mm" : 0.001, "cm" : 0.01, "m" : 1, "km" : 1000,
"in" : 0.0254, "ft" : 0.3048, "yd" : 0.9144,
"mi" : 1609.344 }

def __init__(self, value, unit = "m" ):
self.value = value
self.unit = unit

def Converse2Metres(self):
return self.value * Length.__metric[self.unit]

l = self.Converse2Metres() + other.Converse2Metres()
return Length(l / Length.__metric[self.unit], self.unit )

def __str__(self):
return str(self.Converse2Metres())

def __repr__(self):
return "Length(" + str(self.value) + ", '" + self.unit + "')"

if __name__ == "__main__":
x = Length(4)
print(x)
y = eval(repr(x))

z = Length(4.5, "yd") + Length(1)
print(repr(z))
print(z)

4
Length(5.593613298337708, 'yd')
5.1148


We use the method __iadd__ to implement the extended assignment:

def __iadd__(self, other):
l = self.Converse2Metres() + other.Converse2Metres()
self.value = l / Length.__metric[self.unit]
return self


Now we are capable of writing the following assignments:

x += Length(1)
x += Length(4, "yd")


We added 1 metre in the example above by writing "x += Length(1))". Most certainly, you will agree with us that it would be more convenient to simply write "x += 1" instead. We also want to treat expressions like "Length(5,"yd") + 4.8" similarly. So, if somebody uses a type int or float, our class takes it automatically for "metre" and converts it into a Length object. It's easy to adapt our __add__ and __iadd__ method for this task. All we have to do is to check the type of the parameter "other":

def __add__(self, other):
if type(other) == int or type(other) == float:
l = self.Converse2Metres() + other
else:
l = self.Converse2Metres() + other.Converse2Metres()
return Length(l / Length.__metric[self.unit], self.unit )

if type(other) == int or type(other) == float:
l = self.Converse2Metres() + other
else:
l = self.Converse2Metres() + other.Converse2Metres()
self.value = l / Length.__metric[self.unit]
return self


It's a safe bet that if somebody works with adding integers and floats from the right side for a while, he or she will want to have the same from the left side! So let's try it out:

from unit_conversions import Length
x = Length(3, "yd") + 5
x = 5 + Length(3, "yd")

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-10-6f146ec16c5a> in <module>
1 from unit_conversions import Length
----> 2 x = Length(3, "yd") + 5
3 x = 5 + Length(3, "yd")

~\Dropbox (Bodenseo)\Bodenseo Team Folder\melisa\notebooks_en\unit_conversions.py in __add__(self, other)
13
---> 15         l = self.Converse2Metres() + other.Converse2Metres()
16         return Length(l / Length.__metric[self.unit], self.unit )
17

AttributeError: 'int' object has no attribute 'Converse2Metres'

Of course, the left side has to be of type "Length", because otherwise Python tries to apply the __add__ method from int, which can't cope with Length objects as second arguments!

Python provides a solution for this problem as well. It's the __radd__ method. It works like this: Python tries to evaluate the expression "5 + Length(3, 'yd')". First it calls int.__add__(5,Length(3, 'yd')), which will raise an exception. After this it will try to invoke Length.__radd__(Length(3, "yd"), 5). It's easy to recognize that the implementation of __radd__ is analogue to __add__:

In [ ]:
def __radd__(self, other):
if type(other) == int or type(other) == float:
l = self.Converse2Metres() + otherLength.__radd__(Length(3, "yd"), 5)
else:
l = self.Converse2Metres() + other.Converse2Metres()
return Length(l / Length.__metric[self.unit], self.unit )


It's advisable to make use of the __add__ method in the __radd__ method:

In [ ]:
def __radd__(self, other):


The following diagram illustrates the relationship between __add__ and __radd__:

### The call method

The __call__ method can be used to turn the instances of the class into callables. Functions are callable objects. A callable object is an object which can be used and behaves like a function but might not be a function. By using the __call__ method it is possible to define classes in a way that the instances will be callable objects. The __call__ method is called, if the instance is called "like a function", i.e. using brackets. The following class definition is the simplest possible way to define a class with a __call__ method.

In [ ]:
class FoodSupply:

def __call__(self):
return "spam"

foo = FoodSupply()
bar = FoodSupply()

print(foo(), bar())


The previous class example is extremely simple, but useless in practical terms. Whenever we create an instance of the class, we get a callable. These callables are always defining the same constant function. A function without any input and a constant output "spam". We'll now define a class which is slightly more useful. We define a class with the name TriangleArea. This class has only one method, which is the __call__method. The __call__ method calculates the area of an arbitrary triangle, if the length of the three sides are given.

In [ ]:
class TriangleArea:

def __call__(self, a, b, c):
p = (a + b + c) / 2
result = (p * (p - a) * (p - b) * (p - c)) ** 0.5
return result

area = TriangleArea()

print(area(3, 4, 5))


This program returns 6.0. This class is not very exciting, even though we can create an arbitrary number of instances where each instance just executes an unaltered __call__ function of the TrianlgeClass. We cannot pass parameters to the instanciation and the __call__ of each instance returns the value of the area of the triangle. So each instance behaves like the area function.

Our next example is a lot more exciting. The class FuzzyTriangleArea defines a __call__ method which implements a fuzzy behaviour in the calculations of the area. The result should be correct with a likelihood of p, e.g. 0.8. If the result is not correct the result will be in a range of ± v %. e.g. 0.1.

In [ ]:
import random

class FuzzyTriangleArea:

def __init__(self, p=0.8, v=0.1):
self.p, self.v = p, v

def __call__(self, a, b, c):
p = (a + b + c) / 2
result = (p * (p - a) * (p - b) * (p - c)) ** 0.5
if random.random() <= self.p:
return result
else:
return random.uniform(result-self.v,
result+self.v)

area1 = FuzzyTriangleArea()
area2 = FuzzyTriangleArea(0.5, 0.2)
for i in range(12):
print(f"{area1(3, 4, 5):4.3f}, {area2(3, 4, 5):4.2f}")


Beware that this output differs with every call! We can see the in most cases we get the right value for the area but sometimes not.

We can create many different instances of the previous class. Each of these behaves like an area function, which returns a value for the area, which may or may not be correct, depending on the instantiation parameters p and v. We can see those instances as experts (expert functions) which return in most cases the correct answer, if we use p values close to 1. If the value v is close to zero, the error will be small, if at all. The next task would be merging such experts, let's call them exp1, exp2, ..., expn to get an improved result. We can perform a vote on the results, i.e. we will return the value which is most often occuring, the correct value. Alternatively, we can calculate the arithmetic mean. We will implement both possibilities in our class FuzzyTriangleArea:

In [ ]:
from random import uniform, random
from collections import Counter

class FuzzyTriangleArea:

def __init__(self, p=0.8, v=0.1):
self.p, self.v = p, v

def __call__(self, a, b, c):
p = (a + b + c) / 2
result = (p * (p - a) * (p - b) * (p - c)) ** 0.5
if random.random() <= self.p:
return result
else:
return random.uniform(result-self.v,
result+self.v)

class MergeExperts:

def __init__(self, mode, *experts):
self.mode, self.experts = mode, experts

def __call__(self, a, b, c):
results= [exp(a, b, c) for exp in self.experts]
if self.mode == "vote":
c = Counter(results)
return c.most_common(1)[0][0]
elif self.mode == "mean":
return sum(results) / len(results)

rvalues = [(uniform(0.7, 0.9), uniform(0.05, 0.2)) for _ in range(20)]
experts = [FuzzyTriangleArea(p, v) for p, v in rvalues]
merger1 = MergeExperts("vote", *experts)
print(merger1(3, 4, 5))
merger2 = MergeExperts("mean", *experts)
print(merger2(3, 4, 5))


The following example defines a class with which we can create abitrary polynomial functions:

In [ ]:
class Polynomial:

def __init__(self, *coefficients):
self.coefficients = coefficients[::-1]

def __call__(self, x):
res = 0
for index, coeff in enumerate(self.coefficients):
res += coeff * x** index
return res

# a constant function
p1 = Polynomial(42)

# a straight Line
p2 = Polynomial(0.75, 2)

# a third degree Polynomial
p3 = Polynomial(1, -0.5, 0.75, 2)

for i in range(1, 10):
print(i, p1(i), p2(i), p3(i))


You will find further interesting examples of the __call__ function in our tutorial in the chapters Decorators and Memoization with Decorators. You may also consult our chapter on Polynomials.

### Standard Classes as Base Classes

It's possible to use standard classes - like int, float, dict or lists - as base classes as well.

We extend the list class by adding a push method:

In [ ]:
class Plist(list):

def __init__(self, l):
list.__init__(self, l)

def push(self, item):
self.append(item)

if __name__ == "__main__":
x = Plist([3,4])
x.push(47)
print(x)


This means that all the previously introduced binary and extended assignment operators exist in the "reversed" version as well:
__radd__ , __rsub__ , __rmul__ etc.

### Exercises

1) Write a class with the name Ccy, similar to the previously defined Length class.Ccy should contain values in various currencies, e.g. "EUR", "GBP" or "USD". An instance should contain the amount and the currency unit. The class, you are going to design as an exercise, might be best described with the following example session:

In [ ]:
from currencies import Ccy
v1 = Ccy(23.43, "EUR")
v2 = Ccy(19.97, "USD")
print(v1 + v2)

In [ ]:
print(v2 + v1)

In [ ]:
print(v1 + 3) # an int or a float is considered to be a EUR value

In [ ]:
print(3 + v1)


### Solutions to our Exercises

1)First exercise:

In [ ]:
"""

The class "Ccy" can be used to define money values in various currencies. A Ccy instance has the string attributes 'unit' (e.g. 'CHF', 'CAD' od 'EUR' and the 'value' as a float.
A currency object consists of a value and the corresponding unit.

"""

class Ccy:

currencies =  {'CHF': 1.0821202355817312,
'GBP': 0.8916546282920325,
'JPY': 114.38826536281809,
'EUR': 1.0,
'USD': 1.11123458162018}

def __init__(self, value, unit="EUR"):
self.value = value
self.unit = unit

def __str__(self):
return "{0:5.2f}".format(self.value) + " " + self.unit

def changeTo(self, new_unit):
"""
An Ccy object is transformed from the unit "self.unit" to "new_unit"
"""
self.value = (self.value / Ccy.currencies[self.unit] * Ccy.currencies[new_unit])
self.unit = new_unit

"""
Defines the '+' operator.
If other is a CCy object the currency values
are added and the result will be the unit of
self. If other is an int or a float, other will
be treated as a Euro value.
"""
if type(other) == int or type(other) == float:
x = (other * Ccy.currencies[self.unit])
else:
x = (other.value / Ccy.currencies[other.unit] * Ccy.currencies[self.unit])
return Ccy(x + self.value, self.unit)

"""
"""
if type(other) == int or type(other) == float:
x = (other * Ccy.currencies[self.unit])
else:
x = (other.value / Ccy.currencies[other.unit] * Ccy.currencies[self.unit])
self.value += x
return self

res = self + other
if self.unit != "EUR":
res.changeTo("EUR")
return res

# __sub__, __isub__ and __rsub__ can be defined analogue

x = Ccy(10,"USD")
y = Ccy(11)
z = Ccy(12.34, "JPY")
z = 7.8 + x + y + 255 + z
print(z)

lst = [Ccy(10,"USD"), Ccy(11), Ccy(12.34, "JPY"), Ccy(12.34, "CAD")]

z = sum(lst)

print(z)


Another interesting aspect of this currency converter class in Python can be shown, if we add multiplication. You will easily understand that it makes no sense to allow expressions like "12.4 € * 3.4 USD" (or in prefix notation: "€ 12.4 \$ 3.4"), but it makes perfect sense to evaluate "3 4.54 €". You can find the new currency converter class with the newly added methods for __mul__, __imul__ and __rmul__ in the following listing:

In [ ]:
"""

The class "Ccy" can be used to define money values in various currencies. A Ccy instance has the string attributes 'unit' (e.g. 'CHF', 'CAD' od 'EUR' and the 'value' as a float.
A currency object consists of a value and the corresponding unit.

"""

class Ccy:

currencies =  {'CHF': 1.0821202355817312,
'GBP': 0.8916546282920325,
'JPY': 114.38826536281809,
'EUR': 1.0,
'USD': 1.11123458162018}

def __init__(self, value, unit="EUR"):
self.value = value
self.unit = unit

def __str__(self):
return "{0:5.2f}".format(self.value) + " " + self.unit

def __repr__(self):
return 'Ccy(' + str(self.value) + ', "' + self.unit + '")'

def changeTo(self, new_unit):
"""
An Ccy object is transformed from the unit "self.unit" to "new_unit"
"""
self.value = (self.value / Ccy.currencies[self.unit] * Ccy.currencies[new_unit])
self.unit = new_unit

"""
Defines the '+' operator.
If other is a CCy object the currency values
are added and the result will be the unit of
self. If other is an int or a float, other will
be treated as a Euro value.
"""
if type(other) == int or type(other) == float:
x = (other * Ccy.currencies[self.unit])
else:
x = (other.value / Ccy.currencies[other.unit] * Ccy.currencies[self.unit])
return Ccy(x + self.value, self.unit)

"""
"""
if type(other) == int or type(other) == float:
x = (other * Ccy.currencies[self.unit])
else:
x = (other.value / Ccy.currencies[other.unit] * Ccy.currencies[self.unit])
self.value += x
return self

res = self + other
if self.unit != "EUR":
res.changeTo("EUR")
return res

# __sub__, __isub__ and __rsub__ can be defined analogue

def __mul__(self, other):
"""
Multiplication is only defined as a scalar multiplication,
i.e. a money value can be multiplied by an int or a float.
It is not possible to multiply to money values
"""
if type(other)==int or type(other)==float:
return Ccy(self.value * other, self.unit)
else:
raise TypeError("unsupported operand type(s) for *: 'Ccy' and " + type(other).__name__)

def __rmul__(self, other):
return self.__mul__(other)

def __imul__(self, other):
if type(other)==int or type(other)==float:
self.value *= other
return self
else:
raise TypeError("unsupported operand type(s) for *: 'Ccy' and " + type(other).__name__)


Assuming that you have saved the class under the name currency_converter, you can use it in the following way in the command shell:

In [ ]:
from currency_converter import Ccy
x = Ccy(10.00, "EUR")
y = Ccy(10.00, "GBP")
x + y

In [ ]:
print(x + y)

In [ ]:
print(2*x + y*0.9)


We can further improve our currency converter class by using a function get_currencies, which downloads the latest exchange rates from finance.yahoo.com. This function returns an exchange rates dictionary in our previously used format. The function is in a module called exchange_rates.py This is the code of the function exchange_rates.py:

from urllib.request import urlopen
from bs4 import BeautifulSoup

def get_currency_rates(base="USD"):
""" The file at location url is read in and the exchange rates are extracted """
url = "https://finance.yahoo.com/webservice/v1/symbols/allcurrencies/quote"
data = data.decode('utf-8')
soup = BeautifulSoup(data, 'html.parser')
data = soup.get_text()

flag = False
currencies = {}
for line in data.splitlines():
if flag:
value = float(line)
flag = False
currencies[currency] = value
if line.startswith("USD/"):
flag = True
currency = line[4:7]

currencies["USD"] =  1 # we must add it, because it's not included in file
if base != "USD":
base_currency_rate = currencies[base]
for currency in currencies:
currencies[currency] /= base_currency_rate

return currencies

  File "<tokenize>", line 6
url = "https://finance.yahoo.com/webservice/v1/symbols/allcurrencies/quote"
^
IndentationError: unindent does not match any outer indentation level


We can import this function from our module. (You have to save it somewhare in your Python path or the directory where your program runs):

In [ ]:
from exchange_rates import get_currency_rates

class Ccy:

currencies =  get_currencies()

#   continue with the code from the previous version


We save this version as currency_converter_web.

from currency_converter_web import Ccy
x = Ccy(1000, "JPY")
y = Ccy(10, "CHF")
print(2*x + 4.11*y + z)

---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
<ipython-input-11-06823ff39af5> in <module>
----> 1 from currency_converter_web import Ccy
2 x = Ccy(1000, "JPY")
3 y = Ccy(10, "CHF")
ModuleNotFoundError: No module named 'currency_converter_web'