arrays.org
author Santosh G. Vattam <vattam.santosh@gmail.com>
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* Arrays
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*** Outline
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***** Introduction
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******* What do we want to do
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********* We shall use arrays (mentioned before) which
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********* shall be used for matrices in future
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******* Arsenal Required
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********* working knowledge of lists
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***** Initializing matrices
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******* Entering element-wise
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******* using special functions
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***** Accessing and Changing elements
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******* Slicing??
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******* Striding??
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***** {{Simple operations??}}
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*** Script
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    Welcome to the Tutorial on arrays. 
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    As mentioned in [the previous tutorial] arrays are much faster and
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    more efficient. In this tutorial we shall look at creating arrays,
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    accessing elements and changing them. 
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    ---
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    Let's start with creating simple arrays. We've already seen how to
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    convert lists to arrays. Inputting a new array is similar to that. 
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    In []: a = array([5, 8, 10, 13])
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    Type /a/, to see what it is. 
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    In []: a
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    We enter a multi-dimensional array this way -
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    In []: c = array([[11,12,13],
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                     [21,22,23],
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                      [31,32,33]])
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    To see what c is, we just type c in the prompt. 
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    In []: c
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    To see the dimensions of the array c, we use c.shape
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    In []: c.shape 
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    Now let us look at some special methods of creating an
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    array. There are various functions that allow us to create special
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    arrays. 
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    The first one we shall look at is, /arange/. /arange/ is similar to
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    the range command, except that it returns an array and accepts
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    float arguments. 
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    In []: a = arange(10)
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    In []: a
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    This is the array we just created. 
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    In []: a.shape
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    Note that /a/ is one dimensional and has 10 elements, as expected. 
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    We could also use a.shape to change the shape of the array a. 
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    In []: a.shape = 2,5
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    Note that the total size of new array must be unchanged. 
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    We type a, to see what it looks like
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    In []: a
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    ones command can be used to get an array with all the entries as
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    ones. We pass it the shape of the array that we require. 
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    In []: b = ones((3, 4))
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    Look at b, by printing it out. 
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    In []: b 
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    To create an array with all entries as ones, with it's shape
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    similar to an already existing array, we use the ones_like
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    command.  
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    In []: b = ones_like(a)
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    zeros and zeros_like are similar commands that can give you arrays
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    with all zeros. empty and empty_like give you empty arrays (arrays
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    with no initialization done.)
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    In []: b = zeros((3, 4))
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    In []: b = zeros_like(a)
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    The identity command can be used to obtain a square array with
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    ones on the main diagonal. 
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    In []: identity(3)
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    To obtain a 2-D array, that is not necessarily square, eye command
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    can be used. Look at the documentation of eye (using eye?) for
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    more info. 
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    ---
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    Now that we have learnt how to create arrays, let's move on to
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    accessing elements and changing them. 
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    Let's work with the c, array which we had already created. 
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    In []: c 
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    Let's say we want to access the element 23 in c, we say
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    In []: c[1][2]
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    Note that this is similar to accessing an element inside a list of
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    lists. Also, note that counting again starts from 0. 
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    But arrays provide a more convenient way to access the elements. 
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    In []: c[1, 2]
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    Now, we can also change the element using a simple assignment. 
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    In []: c[1, 2] = -23
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    Let's look at accessing more than one elements at a time. We begin
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    with accessing rows. 
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    In []: c[1] gives us the second row. (counting starts from 0)
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    To get a column, we use a syntax that is similar to the one used
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    to access a single element. 
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    In []: c[:,1], gives us the first column. 
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    The colon specifies that we wish to obtain all elements in that
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    dimension from the array.  
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    So, we could use a more explicit way to access the second row of
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    the array. 
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    In []: c[1,:]
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    The colon can be used to access specific portions of the array,
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    similar to the way we do with lists. 
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    In []: c[1,1:3]
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    Observe that we get the second and third columns from the second
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    row. As with lists, the number after the colon is excluded when
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    slicing a portion of the array. 
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    In []: c[1:3,1]
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    Now, we get the second and third rows from the first column. 
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    In []: c[1:3,1:3]
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    We get the second and third rows and the second and third
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    columns. 
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    The numbers before and after the colons are optional. If the
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    number before the colon is omitted, it is assumed to be zero by
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    default. If the element after the colon is omitted, it is assumed
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    to be until the end. 
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    In []: c[1:, 1:]
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    This is essentially similar to the previous example. We are using
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    the default value i.e, the end, instead of specifying 3,
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    explicitly. 
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    In []: c[:2, :2]
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    We have omitted specifying the zero before the colon, explicitly. 
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    --- 
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    You may have observed the similarity of the semi-colon notation to
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    the notation used in lists. As expected, the semi-colon notation
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    also provides a way to specify a jump. This {concept/idea} is
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    termed as Striding. 
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    To get every alternate row of c, starting from the first one, we say
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    In []: c[::2,:]
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    To get every alternate row of c, starting from the second one, we
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    say 
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    In []: c[1::2,:]
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    In []: c[:,::2]
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    In []: c[::2,::2]
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    ---
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    We come to the end of this tutorial on arrays. In this tutorial,
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    you've learnt how to create arrays and access, change elements. 
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    Thank you. 
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*** Notes