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+++ b/arrays.org Tue Mar 30 14:53:58 2010 +0530
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+* Arrays
+*** Outline
+***** Introduction
+******* Why do we want to do that?
+******* We shall use arrays (introduced before) for matrices
+******* 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. Entering an array is similar to that.
+
+ a = array([5, 8, 10, 13])
+
+ 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. [is range covered?]
+
+ 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
+ 1s. 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 a 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.)
+
+ {Do an up arrow and quickly show them a couple of examples?}
+
+ 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 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 is a way to tell python to get all elements in that
+ dimension from the array.
+
+ So, we could use a more explicit way to access a row of a
+ In []: c[1,:]
+
+ We could use the colon to access specific portions of an array.
+ In []: c[1,1:2]
+ In []: c[1:2,1]
+ In []: c[1:2,1:2]
+ ...
+ [Oh, by the way this is termed as slicing. :)]
+ {How many examples should we show here?}
+
+ ---
+
+ You may have observed the similarity of the semi-colon notation to
+ the range command. 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]
+ {How many examples should we show here?}
+
+ ---
+
+ 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