* Arrays
*** Outline
***** Introduction
******* What do we want to do
********* We shall use arrays (mentioned before) which
********* shall be used for matrices in future
******* Arsenal Required
********* working knowledge of lists
***** Initializing matrices
******* Entering element-wise
******* using special functions
***** Accessing and Changing elements
******* Slicing??
******* Striding??
***** {{Simple operations??}}
*** Script
    Welcome to the Tutorial on arrays. 

    As mentioned in [the previous tutorial] arrays are much faster and
    more efficient. In this tutorial we shall look at creating arrays,
    accessing elements and changing them. 

    ---

    Let's start with creating simple arrays. We've already seen how to
    convert lists to arrays. Inputting a new array is similar to that. 

    In []: a = array([5, 8, 10, 13])

    Type /a/, to see what it is. 

    In []: a
    
    We enter a multi-dimensional array this way -
    
    In []: c = array([[11,12,13],
                     [21,22,23],
                      [31,32,33]])

    To see what c is, we just type c in the prompt. 
		      
    In []: c

    To see the dimensions of the array c, we use c.shape
    In []: c.shape 

    Now let us look at some special methods of creating an
    array. There are various functions that allow us to create special
    arrays. 

    The first one we shall look at is, /arange/. /arange/ is similar to
    the range command, except that it returns an array and accepts
    float arguments. 
    
    In []: a = arange(10)
    
    In []: a
    This is the array we just created. 
    
    In []: a.shape
    Note that /a/ is one dimensional and has 10 elements, as expected. 

    We could also use a.shape to change the shape of the array a. 
    In []: a.shape = 2,5
    Note that the total size of new array must be unchanged. 

    We type a, to see what it looks like
    In []: a

    ones command can be used to get an array with all the entries as
    ones. We pass it the shape of the array that we require. 
    
    In []: b = ones((3, 4))

    Look at b, by printing it out. 
    In []: b 

    To create an array with all entries as ones, with it's shape
    similar to an already existing array, we use the ones_like
    command.  
    In []: b = ones_like(a)

    zeros and zeros_like are similar commands that can give you arrays
    with all zeros. empty and empty_like give you empty arrays (arrays
    with no initialization done.)

    In []: b = zeros((3, 4))
    In []: b = zeros_like(a)

    The identity command can be used to obtain a square array with
    ones on the main diagonal. 
    
    In []: identity(3)

    To obtain a 2-D array, that is not necessarily square, eye command
    can be used. Look at the documentation of eye (using eye?) for
    more info. 

    ---
    
    Now that we have learnt how to create arrays, let's move on to
    accessing elements and changing them. 
    
    Let's work with the c, array which we had already created. 

    In []: c 

    Let's say we want to access the element 23 in c, we say

    In []: c[1][2]
    Note that this is similar to accessing an element inside a list of
    lists. Also, note that counting again starts from 0. 
    
    But arrays provide a more convenient way to access the elements. 
    In []: c[1, 2]
    
    Now, we can also change the element using a simple assignment. 
    In []: c[1, 2] = -23

    Let's look at accessing more than one elements at a time. We begin
    with accessing rows. 
    In []: c[1] gives us the second row. (counting starts from 0)

    To get a column, we use a syntax that is similar to the one used
    to access a single element. 
    In []: c[:,1], gives us the first column. 
    
    The colon specifies that we wish to obtain all elements in that
    dimension from the array.  

    So, we could use a more explicit way to access the second row of
    the array. 
    In []: c[1,:]
    
    The colon can be used to access specific portions of the array,
    similar to the way we do with lists. 
    In []: c[1,1:3]
    Observe that we get the second and third columns from the second
    row. As with lists, the number after the colon is excluded when
    slicing a portion of the array. 

    In []: c[1:3,1]
    Now, we get the second and third rows from the first column. 

    In []: c[1:3,1:3]
    We get the second and third rows and the second and third
    columns. 

    The numbers before and after the colons are optional. If the
    number before the colon is omitted, it is assumed to be zero by
    default. If the element after the colon is omitted, it is assumed
    to be until the end. 

    In []: c[1:, 1:]
    This is essentially similar to the previous example. We are using
    the default value i.e, the end, instead of specifying 3,
    explicitly. 

    In []: c[:2, :2]
    We have omitted specifying the zero before the colon, explicitly. 

    --- 
    
    You may have observed the similarity of the semi-colon notation to
    the notation used in lists. As expected, the semi-colon notation
    also provides a way to specify a jump. This {concept/idea} is
    termed as Striding. 

    To get every alternate row of c, starting from the first one, we say
    In []: c[::2,:]

    To get every alternate row of c, starting from the second one, we
    say 
    In []: c[1::2,:]


    In []: c[:,::2]
    In []: c[::2,::2]

    ---

    We come to the end of this tutorial on arrays. In this tutorial,
    you've learnt how to create arrays and access, change elements. 

    Thank you. 

*** Notes