Let’s try an experiment with lists:
>>> a = [1, 2, 3, 4]
>>> a + 1
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: can only concatenate list (not "int") to list
>>>
Our idea is to check whether it is possible to add 1 to each element of the list by simply writing:
a + 1
Unfortunately, Python does not let us do this (there is very good reason as to why the language behaves in this way). But that does not mean that there is no way to do arithmetic on a sequence of numbers; Python offers powerful Numeric Arrays using which we can do all kinds of tricky number sequence manipulations. But before we use Numeric Arrays, we have to understand how to use modules in Python.
Try this experiment:
>>> sin(0)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
NameError: name 'sin' is not defined
>>>
We are unable to calculate sin of 0 - Python tells us that name `sin’ is not defined! The reason is simple; functions like sin, cos etc are not part of the core Python language. They are defined in additional modules (also called libraries). We have to use a special notation to tell Python that we wish to use the functions defined in a module:
>>> from math import *
>>> sin(0)
0.0
>>> cos(0)
1.0
>>>
Note
Functions like sin, cos etc need angles to be specified in radian.
The first line:
from math import *
simply means:
Use all the functions available in a module called `math'.
The star symbol should not be interpreted as a multiplication operator in this context - it simply means ALL.
In general, if you wish to use all the functions defined in a module called xyz, just type:
from xyz import *
One of the things which makes programming languages tricky to learn is that there will be many different ways to express the same idea. Here is another way to use a module:
>>> import math
>>> sin(0)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
NameError: name 'sin' is not defined
>>> math.sin(0)
0.0
>>> math.cos(0)
1.0
>>>
The statement:
import math
is similar to the one which we saw in the previous section - the difference is that now we have to write math.sin and math.cos instead of simply sin and cos.
What do you do if you wish to get a list of all the functions present in a module?:
>>> import math
>>> dir(math)
['__doc__', '__file__', '__name__', '__package__',
'acos', 'acosh', 'asin', 'asinh', 'atan', 'atan2',
'atanh', 'ceil', 'copysign', 'cos', 'cosh', 'degrees',
'e', 'exp', 'fabs', 'factorial', 'floor', 'fmod',
'frexp', 'fsum', 'hypot', 'isinf', 'isnan', 'ldexp',
'log', 'log10', 'log1p', 'modf', 'pi', 'pow', 'radians',
'sin', 'sinh', 'sqrt', 'tan', 'tanh', 'trunc']
The function dir can be used to display list of all functions defined in a module. You can ignore the names starting with two underscore signs in the above list.
The working of many of these functions should be evident from their names. If you wish, you can get information about what the function actually does by using help:
>>> help(math.hypot)
hypot(...)
hypot(x,y)
Return the Euclidean distance, sqrt(x*x + y*y).
>>>
A Python Numeric Array looks like a list - with the difference that it is more suited for mathematical computations. Here is how you can create a Numeric array:
>>> from pylab import *
>>> a = [10, 20, 30, 40]
>>> b = array(a)
>>> b
array([10, 20, 30, 40])
>>> b + 1
array([11, 21, 31, 41])
>>> b * 2
array([20, 40, 60, 80])
>>>
The first statement:
from pylab import *
simply makes available all the functions in a module called pylab. If you get an error while executing this statement, it means the module is not installed on your system. Read the Appendix of this book to learn how you can install additional software on your GNU/Linux system.
We are making use of only one function from the pylab module in the above example; a function called array. What does array do? It acts on an ordinary Python list a and produces a Numeric sequence called (in this example) b. You can now add 1 to all the elements of the sequence by just writing:
b + 1
Similarly, you can multiply all the elements of b with 2 by doing:
b * 2
Now, just relax for a moment and think of the power that you have in your hands! A numeric array (like b above) can contain hundreds of thousands of numbers. With a simple statement like “b+1”, you can operate on all the elements of the sequence! Working with a million numbers at once has become as easy as working with one or two numbers.
You will see how to use this power to do some interesting math in the next chapter!