LSESU Applicable Maths Python Lesson 7

6/12/16

In the last lesson of the term, we'll be looking at how to apply what we learnt last week with data manipulation with Numpy and Pandas to Data Visualisation with:

* Matplotlib
* Seaborn



In [ ]:

    
# Run this if you are using a Mac machine or have multiple versions of Python installed
!pip3 install numpy==1.11.1 pandas==0.19.1 matplotlib==1.5.3 seaborn==0.7.1 --upgrade



In [ ]:

    
# Run this if you are using a Windows machine
!pip install numpy==1.11.1 pandas==0.19.0 matplotlib==1.5.3 seaborn==0.7.1 --upgrade



In [ ]:

    
# Everyone run this block
import numpy as np
import pandas as pd
import matplotlib as mpl
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline

Matplotlib

Matplotlib is the standard package for 2D plot and graph generation in Python. Much of the interface is based on the interface for MATLAB, a powerful scripting language for scientific computing that I use everyday.

The matplotlib library, shortened to mpl, provides tools to create highly customisable figures and plots.
The pyplot, or plt, library is the interface section of mpl which provides the easy to use interactions with the rich mpl tools.

Here is a link to some official beginner tutorials from the Matplotlib project if you want to try something more complex than what we will do today.

Getting started

Let's plot a simple figure of a sine and a cosine wave. We'll go through each phase of creating the plot step by step.



In [ ]:

    
# Create a linearly spaced 1x256 vector between -pi to pi
X = np.linspace(-np.pi,np.pi,256,endpoint=True)

# Create sine and cosine wave vectors from the X vector
C,S = np.cos(X),np.sin(X)



In [ ]:

    
# Create a figure object. This is an abstract frame to plot things in
plt.figure()

# Plot the Cosine against X, and Sine against X
plt.plot(X,C)
plt.plot(X,S)

# Force the display of the figure
plt.show()

Cleaning up this plot



In [ ]:

    
X = np.linspace(-np.pi,np.pi,256,endpoint=True)
C,S = np.cos(X),np.sin(X)


# Create a figure object. This is an abstract frame to plot things in
plt.figure(figsize=(10,8),dpi=80)

# Plot the Cosine against X, and Sine against X
plt.plot(X,C,color='m',linewidth=2.3,linestyle=':',label='cos')
plt.plot(X,S,color='c',linewidth=5,linestyle='--',label='sin')

# Set the x and y axis limits
plt.xlim(X.min()*1.1,X.max()*1.1)
plt.ylim(C.min()*1.1,C.max()*1.1)

# Add figure labels
plt.title('Sine and Cosine waves from -$\pi$ to $\pi$',fontsize=20)
plt.xlabel('X axis')
plt.ylabel('Y axis')

# Set the x and y ticks
plt.xticks([-np.pi,-np.pi/2,0,np.pi/2,np.pi],
          ['$-\pi$','$-\pi/2$','$0$','$+\pi/2$','$+\pi$'],
          fontsize=20)
plt.yticks([-1,0,1],fontsize=20)

# Add a legend
plt.legend(loc='upper left',fontsize=20)

# Force the display of the figure
plt.show()

Challenge - Add a plot of the `tan(x)` function to the figure we just created.

Things to consider:

You will need to use the existing X vector and a new function
Declare all your code in between what is already written (don't just write it all at the end of the block!)
You might want to change the update the title, axis limits, line widths and color of your new line
You also might want to move the legend out of the axes! Here is a hint on how to do that

What else you can do with Matplotlib?

Scatter plot



In [ ]:

    
n = 1024
X = np.random.normal(0, 1, n)
Y = np.random.normal(0, 1, n)

T = np.arctan2(Y, X)
colors = mpl.cm.rainbow(np.linspace(0, 1,n)) # replace the rainbow arg with T

plt.axes([0.025, 0.025, 0.95, 0.95])
plt.scatter(X, Y, s=50, c=colors, alpha=0.5)

plt.xlim(-1.5, 1.5)
plt.xticks(())
plt.ylim(-1.5, 1.5)
plt.yticks(())

plt.show()

Sampling from a normal distribution



In [ ]:

    
# Define a normal distribution
mu, sigma = 0,1
samples = np.random.normal(mu,sigma,100000000)


count,bins,ignored = plt.hist(samples,30,normed=True)
plt.plot(bins,1/(sigma*np.sqrt(2*np.pi)) *
        np.exp(-(bins-mu)**2 / (2*sigma**2)),
        linewidth=3,linestyle=':',color='r')
plt.show()

3D Plots



In [ ]:

    
from mpl_toolkits.mplot3d import Axes3D

fig = plt.figure()
ax = Axes3D(fig)
X = np.arange(-4, 4, 0.25)
Y = np.arange(-4, 4, 0.25)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X ** 2 + Y ** 2)
Z = np.sin(R)

ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=plt.cm.rainbow)
ax.contourf(X, Y, Z, zdir='z', offset=-2, cmap=plt.cm.rainbow)
ax.set_zlim(-2, 2)

plt.show()

Seaborn

Seaborn is an alternative data visualisation library which has more of a focus on statistical graphs. Seaborn works really well with Pandas and if you create a Pandas DataFrame you can easily generate a Seaborn plot.



In [ ]:

    
sns.set() # Set up fig with default stylings

# Everybody help me fill in this dictionary!
birthdays = {
    'jan':{18:0,19:0,20:0,21:0,22:0,23:0,24:0,25:0,26:0,27:0,28:0,29:0,30:0},
    'feb':{18:0,19:0,20:0,21:0,22:0,23:0,24:0,25:0,26:0,27:0,28:0,29:0,30:0},
    'mar':{18:0,19:0,20:0,21:0,22:0,23:0,24:0,25:0,26:0,27:0,28:0,29:0,30:0},
    'apr':{18:0,19:0,20:0,21:0,22:0,23:0,24:0,25:0,26:0,27:0,28:0,29:0,30:0},
    'may':{18:0,19:0,20:0,21:0,22:0,23:0,24:0,25:0,26:0,27:0,28:0,29:0,30:0},
    'jun':{18:0,19:0,20:0,21:0,22:0,23:0,24:0,25:0,26:0,27:0,28:0,29:0,30:0},
    'jul':{18:0,19:0,20:0,21:0,22:0,23:0,24:0,25:0,26:0,27:0,28:0,29:0,30:0},
    'aug':{18:0,19:0,20:0,21:0,22:0,23:0,24:0,25:0,26:0,27:0,28:0,29:0,30:0},
    'sep':{18:0,19:0,20:0,21:0,22:0,23:0,24:0,25:0,26:0,27:0,28:0,29:0,30:0},
    'oct':{18:0,19:0,20:0,21:0,22:1,23:0,24:0,25:0,26:0,27:0,28:0,29:0,30:0},
    'nov':{18:0,19:0,20:0,21:0,22:0,23:0,24:0,25:0,26:0,27:0,28:0,29:0,30:0},
    'dec':{18:0,19:0,20:0,21:0,22:0,23:0,24:0,25:0,26:0,27:0,28:0,29:0,30:0}
}

df = pd.DataFrame.from_dict(birthdays)
df



In [ ]:

    
sns.heatmap(df)



In [ ]:

    
sns.heatmap(df,annot=True,fmt='d',linewidths=.5)

The Seaborn Tutorial Page has a lot of resources for helping you get started with this package

Challenge

Use NumPy to generate a random number array of an arbitrary size (square or near square arrays look best though), then use Seaborn to generate a heatmap of this information
How few lines of code do you need to do this?
Seaborn uses Matplotlib in the background, add a title to the figure using what we learnt about this other package



In [ ]:

    
# TO DO
sns.set()








# END TO DO