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+Functional Approach
+===================
+
+*Functions* allow us to enclose a set of statements and call the function again
+and again instead of repeating the group of statements everytime. Functions also
+allow us to isolate a piece of code from all the other code and provides the
+convenience of not polluting the global variables.
+
+*Function* in python is defined with the keyword **def** followed by the name
+of the function, in turn followed by a pair of parenthesis which encloses the
+list of parameters to the function. The definition line ends with a ':'. The
+definition line is followed by the body of the function intended by one block.
+The *Function* must return a value::
+
+ def factorial(n):
+ fact = 1
+ for i in range(2, n):
+ fact *= i
+
+ return fact
+
+The code snippet above defines a function with the name factorial, takes the
+number for which the factorial must be computed, computes the factorial and
+returns the value.
+
+A *Function* once defined can be used or called anywhere else in the program. We
+call a fucntion with its name followed by a pair of parenthesis which encloses
+the arguments to the function.
+
+The value that function returns can be assigned to a variable. Let's call the
+above function and store the factorial in a variable::
+
+ fact5 = factorial(5)
+
+The value of fact5 will now be 120, which is the factorial of 5. Note that we
+passed 5 as the argument to the function.
+
+It may be necessary to document what the function does, for each of the function
+to help the person who reads our code to understand it better. In order to do
+this Python allows the first line of the function body to be a string. This
+string is called as *Documentation String* or *docstring*. *docstrings* prove
+to be very handy since there are number of tools which can pull out all the
+docstrings from Python functions and generate the documentation automatically
+from it. *docstrings* for functions can be written as follows::
+
+ def factorial(n):
+ 'Returns the factorial for the number n.'
+ fact = 1
+ for i in range(2, n):
+ fact *= i
+
+ return fact
+
+An important point to note at this point is that, a function can return any
+Python value or a Python object, which also includes a *Tuple*. A *Tuple* is
+just a collection of values and those values themselves can be of any other
+valid Python datatypes, including *Lists*, *Tuples*, *Dictionaries* among other
+things. So effectively, if a function can return a tuple, it can return any
+number of values through a tuple
+
+Let us write a small function to swap two values::
+
+ def swap(a, b):
+ return b, a
+
+ c, d = swap(a, b)
+
+Function scope
+---------------
+The variables used inside the function are confined to the function's scope
+and doesn't pollute the variables of the same name outside the scope of the
+function. Also the arguments passed to the function are passed by-value if
+it is of basic Python data type::
+
+ def cant_change(n):
+ n = 10
+
+ n = 5
+ cant_change(n)
+
+Upon running this code, what do you think would have happened to value of n
+which was assigned 5 before the function call? If you have already tried out
+that snippet on the interpreter you already know that the value of n is not
+changed. This is true of any immutable types of Python like *Numbers*, *Strings*
+and *Tuples*. But when you pass mutable objects like *Lists* and *Dictionaries*
+the values are manipulated even outside the function::
+
+ >>> def can_change(n):
+ ... n[1] = James
+ ...
+
+ >>> name = ['Mr.', 'Steve', 'Gosling']
+ >>> can_change(name)
+ >>> name
+ ['Mr.', 'James', 'Gosling']
+
+If nothing is returned by the function explicitly, Python takes care to return
+None when the funnction is called.
+
+Default Arguments
+-----------------
+
+There may be situations where we need to allow the functions to take the
+arguments optionally. Python allows us to define function this way by providing
+a facility called *Default Arguments*. For example, we need to write a function
+that returns a list of fibonacci numbers. Since our function cannot generate an
+infinite list of fibonacci numbers, we need to specify the number of elements
+that the fibonacci sequence must contain. Suppose, additionally, we want to the
+function to return 10 numbers in the sequence if no option is specified we can
+define the function as follows::
+
+ def fib(n=10):
+ fib_list = [0, 1]
+ for i in range(n - 2):
+ next = fib_list[-2] + fib_list[-1]
+ fib_list.append(next)
+ return fib_list
+
+When we call this function, we can optionally specify the value for the
+parameter n, during the call as an argument. Calling with no argument and
+argument with n=5 returns the following fibonacci sequences::
+
+ fib()
+ [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]
+ fib(5)
+ [0, 1, 1, 2, 3]
+
+Keyword Arguments
+-----------------
+
+When a function takes a large number of arguments, it may be difficult to
+remember the order of the parameters in the function definition or it may
+be necessary to pass values to only certain parameters since others take
+the default value. In either of these cases, Python provides the facility
+of passing arguments by specifying the name of the parameter as defined in
+the function definition. This is known as *Keyword Arguments*.
+
+In a function call, *Keyword arguments* can be used for each argument, in the
+following fashion::
+
+ argument_name=argument_value
+ Also denoted as: keyword=argument
+
+ def wish(name='World', greetings='Hello'):
+ print "%s, %s!" % (greetings, name)
+
+This function can be called in one of the following ways. It is important to
+note that no restriction is imposed in the order in which *Keyword arguments*
+can be specified. Also note, that we have combined *Keyword arguments* with
+*Default arguments* in this example, however it is not necessary::
+
+ wish(name='Guido', greetings='Hey')
+ wish(greetings='Hey', name='Guido')
+
+Calling functions by specifying arguments in the order of parameters specified
+in the function definition is called as *Positional arguments*, as opposed to
+*Keyword arguments*. It is possible to use both *Positional arguments* and
+*Keyword arguments* in a single function call. But Python doesn't allow us to
+bungle up both of them. The arguments to the function, in the call, must always
+start with *Positional arguments* which is in turn followed by *Keyword
+arguments*::
+
+ def my_func(x, y, z, u, v, w):
+ # initialize variables.
+ ...
+ # do some stuff
+ ...
+ # return the value
+
+It is valid to call the above functions in the following ways::
+
+ my_func(10, 20, 30, u=1.0, v=2.0, w=3.0)
+ my_func(10, 20, 30, 1.0, 2.0, w=3.0)
+ my_func(10, 20, z=30, u=1.0, v=2.0, w=3.0)
+ my_func(x=10, y=20, z=30, u=1.0, v=2.0, w=3.0)
+
+Following lists some of the invalid calls::
+
+ my_func(10, 20, z=30, 1.0, 2.0, 3.0)
+ my_func(x=10, 20, z=30, 1.0, 2.0, 3.0)
+ my_func(x=10, y=20, z=30, u=1.0, v=2.0, 3.0)
+
+Parameter Packing and Unpacking
+-------------------------------
+
+The positional arguments passed to a function can be collected in a tuple
+parameter and keyword arguments can be collected in a dictionary. Since keyword
+arguments must always be the last set of arguments passed to a function, the
+keyword dictionary parameter must be the last parameter. The function definition
+must include a list explicit parameters, followed by tuple paramter collecting
+parameter, whose name is preceded by a *****, for collecting positional
+parameters, in turn followed by the dictionary collecting parameter, whose name
+is preceded by a ****** ::
+
+ def print_report(title, *args, **name):
+ """Structure of *args*
+ (age, email-id)
+ Structure of *name*
+ {
+ 'first': First Name
+ 'middle': Middle Name
+ 'last': Last Name
+ }
+ """
+
+ print "Title: %s" % (title)
+ print "Full name: %(first)s %(middle)s %(last)s" % name
+ print "Age: %d\nEmail-ID: %s" % args
+
+The above function can be called as. Note, the order of keyword parameters can
+be interchanged::
+
+ >>> print_report('Employee Report', 29, 'johny@example.com', first='Johny',
+ last='Charles', middle='Douglas')
+ Title: Employee Report
+ Full name: Johny Douglas Charles
+ Age: 29
+ Email-ID: johny@example.com
+
+The reverse of this can also be achieved by using a very identical syntax while
+calling the function. A tuple or a dictionary can be passed as arguments in
+place of a list of *Positional arguments* or *Keyword arguments* respectively
+using ***** or ****** ::
+
+ def print_report(title, age, email, first, middle, last):
+ print "Title: %s" % (title)
+ print "Full name: %s %s %s" % (first, middle, last)
+ print "Age: %d\nEmail-ID: %s" % (age, email)
+
+ >>> args = (29, 'johny@example.com')
+ >>> name = {
+ 'first': 'Johny',
+ 'middle': 'Charles',
+ 'last': 'Douglas'
+ }
+ >>> print_report('Employee Report', *args, **name)
+ Title: Employee Report
+ Full name: Johny Charles Douglas
+ Age: 29
+ Email-ID: johny@example.com
+
+Nested Functions and Scopes
+---------------------------
+
+Python allows nesting one function inside another. This style of programming
+turns out to be extremely flexible and powerful features when we use *Python
+decorators*. We will not talk about decorators is beyond the scope of this
+course. If you are interested in knowing more about *decorator programming* in
+Python you are suggested to read:
+
+| http://avinashv.net/2008/04/python-decorators-syntactic-sugar/
+| http://personalpages.tds.net/~kent37/kk/00001.html
+
+However, the following is an example for nested functions in Python::
+
+ def outer():
+ print "Outer..."
+ def inner():
+ print "Inner..."
+ print "Outer..."
+ inner()
+
+ >>> outer()
+
+map, reduce and filter functions
+--------------------------------
+
+Python provides several built-in functions for convenience. The **map()**,
+**reduce()** and **filter()** functions prove to be very useful with sequences like
+*Lists*.
+
+The **map** (*function*, *sequence*) function takes two arguments: *function*
+and a *sequence* argument. The *function* argument must be the name of the
+function which in turn takes a single argument, the individual element of the
+*sequence*. The **map** function calls *function(item)*, for each item in the
+sequence and returns a list of values, where each value is the value returned
+by each call to *function(item)*. **map()** function allows to pass more than
+one sequence. In this case, the first argument, *function* must take as many
+arguments as the number of sequences passed. This function is called with each
+corresponding element in the each of the sequences, or **None** if one of the
+sequence is exhausted::
+
+ def square(x):
+ return x*x
+
+ >>> map(square, [1, 2, 3, 4])
+ [1, 4, 9, 16]
+
+ def mul(x, y):
+ return x*y
+
+ >>> map(mul, [1, 2, 3, 4], [6, 7, 8, 9])
+
+The **filter** (*function*, *sequence*) function takes two arguments, similar to
+the **map()** function. The **filter** function calls *function(item)*, for each
+item in the sequence and returns all the elements in the sequence for which
+*function(item)* returned True::
+
+ def even(x):
+ if x % 2:
+ return True
+ else:
+ return False
+
+ >>> filter(even, range(1, 10))
+ [1, 3, 5, 7, 9]
+
+The **reduce** (*function*, *sequence*) function takes two arguments, similar to
+**map** function, however multiple sequences are not allowed. The **reduce**
+function calls *function* with first two consecutive elements in the sequence,
+obtains the result, calls *function* with the result and the subsequent element
+in the sequence and so on until the end of the list and returns the final result::
+
+ def mul(x, y):
+ return x*y
+
+ >>> reduce(mul, [1, 2, 3, 4])
+ 24
+
+List Comprehensions
+~~~~~~~~~~~~~~~~~~~
+
+List Comprehension is a convenvience utility provided by Python. It is a
+syntatic sugar to create *Lists*. Using *List Comprehensions* one can create
+*Lists* from other type of sequential data structures or other *Lists* itself.
+The syntax of *List Comprehensions* consists of a square brackets to indicate
+the result is a *List* within which we include at least one **for** clause and
+multiple **if** clauses. It will be more clear with an example::
+
+ >>> num = [1, 2, 3]
+ >>> sq = [x*x for x in num]
+ >>> sq
+ [1, 4, 9]
+ >>> all_num = [1, 2, 3, 4, 5, 6, 7, 8, 9]
+ >>> even = [x for x in all_num if x%2 == 0]
+
+The syntax used here is very clear from the way it is written. It can be
+translated into english as, "for each element x in the list all_num,
+if remainder of x divided by 2 is 0, add x to the list."