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Lists, Arrays and Matrices and their Visualization


What You Will Learn

  • You will create lists, arrays and matrices using scipy
  • You will learn to slice, reverse, append and plot arrays

Lists in Python

Type in the code at the Ipython console
  • from scipy import *
  • x=[1,2,3,4,5]
  • The first line imports all modules in scipy. The second line creates a list in the variable x.
  • Type x at the console and observe the list
  • Type x[0:2] at the console and observe the first two values in the list
  • Type x[3:5] at the console and observe a slice of the list
  • Type x[::-1] at the console and observe the reversed list
  • Type len(x) at the console and observe the length of the list x
  • Type y=[4,5,6] and then type x+y observe the two lists getting concatenated.
  • Type append(x,y) observe a similar result
  • Type z=['apple','orange','pear'] to create a list of strings

Arrays using Scipy

scipy and numpy provide arrays that support mathematical operations.

  • Type x=array([1,2,3,4,5]) at the console and observe the array
  • Type x[0:2] at the console and observe the first two values in the array
  • Type x[3:5] at the console and observe a slice of the array
  • Type x[::-1] at the console and observe the reversed array
  • Type len(x) at the console and observe the length of the array x
  • Type y=[4,5,6,5,7] and then type x+y observe the point wise sum of the two arrays.
  • Type append(x,y) observe the concatenated array
  • Type concatenate(x,y) and observe a similar result.
  • Type x*y and observe the point wise multiplication
  • Type sum(x*y) and observe the dot product between x and y

Plots of Arrays

Matplotlib is an excellent tool for visualizing two and three dimensional data. It imported as
from pylab import *
Stem plot of x can be made as
from scipy import *
from pylab import *
x=array([1,2,3,4,5])
y=array([2.4,4.6,3.765,8.7,5.4])
stem(range(0,len(x)),x,'b')
stem(range(0,len(y)),y,'r')
grid('on')
savefig('figure.pdf')
show()
The first two lines import all modules in scipy and pylab. Lines 3 and 4 creates two arrays of real numbers. Lines 5 and 6 create the stem plots of x and y in blue and red colors respectively. The x axis if formed by integers from 0 to length of x and y respectively. The grid command places a grid on the GUI. savefig commands saves the pot as pdf (or .eps) file in the present working directory. Replace stem by plot to observe continuous plots of x and y. See the stem plots in Fig. 1.
Fig.1 - Discrete plots of one dimensional arrays using matplotlib

Two Dimensional Arrays and Matrices

Two dimensional array (also called image) is created as
from scipy import *
from pylab import *
x=array([[1,2,3],[4,5,6],[7,8,9]])
Type x and observe the two dimensional array. The array can be visualized as an image by
imshow(x)
show()
The two dimensional representation od the array is shown as Fig. 2.
Fig.2 - Image of the 2-D array

The above two dimensional array can be made into a matrix as

x=mat([[1,2,3],[4,5,6],[7,8,9]])
It can be visualized by
matshow(x)
show()
The plot looks like what we had in Fig. 2.

What You Learned

  • You created lists, arrays and matrices using scipy
  • You learned to slice, reverse, append and plot arrays and matrices

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