Exceptions in Python

At run time, exceptional situations sometimes arise. In Python we can make allowance for them and indicate actions to take. (In contrast assertions should be used for conditions which should never happen.)
One such example is division by zero.
```
def invert1(n):
    return 1.0 / n
```

If we attempt to divide by zero, Python throws a ZeroDivisionError exception.

In [1]: invert1(3)
Out[1]: 0.3333333333333333

In [2]: invert1(0)
---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
<ipython-input-45-dcd5509b67f7> in <module>()
----> 1 invert1(0)

<ipython-input-43-2c7538fe7a03> in invert1(n)
      1 def invert1(n):
----> 2       return 1.0/n
      3

ZeroDivisionError: float division by zero

We could use invert1 in a function to invert a list of numbers.

def invert_list1(alon):
    return [invert1(n) for n in alon]

However if any of the numbers in the list is zero, Python just throws the exception and stops.

In [3]: list(range(-9, 10))
Out[3]: [-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

In [4]: invert_list1(list(range(-9, 9)))
---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
<ipython-input-53-a6f023733ca5> in <module>()
----> 1 invert_list1(list(range(-9, 9)))

/home/bon/projects/auc/courses/pyw2014/content/code/exceptions.py in invert_list1(alon)
      5
      6 def invert_list1(alon):
----> 7   return [invert1(n) for n in alon]
      8
      9 #----------------------------------------

<ipython-input-43-2c7538fe7a03> in invert1(n)
      1 def invert1(n):
----> 2       return 1.0/n
      3

ZeroDivisionError: float division by zero

Since it's not uncommon for this to happen when doing numerical calculations, we have a notion of not a number (abbreviated NaN). It is often used when the result of a numerical calculation is undefined as a float, such as 0/0, the various infinities, the square root of a negative number or for missing values.

The Python nan is generated by float('nan').

NaNs are contagious; most Python operations on floats return nan when at least one of their arguments is a nan. But see the Python manual for special cases.
As we have seen, division by zero throws an exception in Python. But we might prefer to return nan so that we can continue with our calculations:
```
def invert2(n):
    try:
        return 1.0 / n
    except ZeroDivisionError as e:
        print("Caught a zero:", e)
        return float("nan")
```
The Python construct try..except executes the code in the first subblock. If that block throws the exception indicated, then that exception is caught and the code in the second block is executed. Any other exception is thrown to top level in the usual way.

A try can have more than one except and can also have finally and else clauses. See the Python manual for details.

We can make a version of invert_list that uses this invert2

def invert_list2(alon):
    return [invert2(n) for n in alon]

Now we can invert our list without interruption.

In [5]: invert_list2(list(range(-9, 9)))
Caught a zero: float division by zero
Out[5]:
[-0.1111111111111111,
 -0.125,
 -0.14285714285714285,
 -0.16666666666666666,
 -0.2,
 -0.25,
 -0.3333333333333333,
 -0.5,
 -1.0,
 nan,
 1.0,
 0.5,
 0.3333333333333333,
 0.25,
 0.2,
 0.16666666666666666,
 0.14285714285714285,
 0.125]