Hello and welcome to the tutorial on Matrices.

All matrices operations are done using arrays.

We have already seen in previous session that how arrays are better suited for particular mathematical operations. In this session we are going to cover more details on Arrays, how to create/initialize them, how to manipulate and use them for solving given problem.

First thing first, we start with creating a normal array by:

a (equal to)= array([5, 8, 10, 13])

and we have a as array. we can cross the content by

a

Here a is single dimension array, that is it has only one row. We can create multi-dimensional arrays by

c = array([[11,12,13], [21,22,23], [31,32,33]])

both c and a are arrays but with different dimensions or shape

we can check shape of arrays by using shape attribute of arrays.

a.shape

c.shape

some other handy array initialization methods are also available to make life easier.

say we want to create a array of size 3x4 with all values initialized to be 1, we can use

b = ones((3, 4))

check value by

b

similarly, we already have a array, and we want to create one more array with same shape and initial values to be one, for that we will use

d = ones_like(c)

and d will be 3x3 array with all values 1

Similarly there are functions like zeros and zeros_like which initialize array with all values being 0. One more useful function available is 'identity', it create identity matrix(array) of given order

i = identity(3)

i

i = identity(5)

i

We have seen 

    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 []: 

    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 []: 

    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. 

On your Ipython terminal type a = array open parenthesis and then open square brackets 5,8,10,13 close square brackets and close parenthesis . This create an array a . You can see what a is by typing a on the terminal .

command.  type b= ones_like in parenthesis a .