Assigned material 4

Complete before class on September 21

Outline

Part 1. Functions in Python

1.1. What are functions

1.2. Why use functions

1.3. User-defined functions

Part 2. Data visualization with matplotlib

2.1. Initialize figure

1.2. Plot simple vectors

1.3. Plot multiple vectors on the same graph

1.4. Plot functions

1.5. Organize your figures with subplots

Part 1. Functions in Python

1.1. What are functions?

A function is a set of statements that take inputs, do some specific computation and produces output. Function can takes a number of inputs—inputs can be scalars, lists, tuples or objects—and produces a number of outputs—outputs can be scalars, lists, tuples or objects.

1.2. Why use functions?

Programmer’s motto: DRY – don’t repeat yourself.
- Define it once and use it multiple times.
Functions are extremely useful for writing complex programs:
- divide complex operations into a combination of simpler steps.
- make programs easier to read and debug by abstracting out frequently repeated code.

There are three major types of functions in python: built-in function, user-defined function, and lambda function. In this section, we focus on user-defined functions.

1.3. User-defined function

We can use the built-in function to do many things. But once our program become complex, we will need to define functions according to our need.

In Python, a user-defined function's declaration begins with the keyword `def` and followed by the function name.
The function may take arguments(s) as input within the opening and closing parentheses, just after the function name followed by a colon.
After defining the function name and arguments(s) a block of program statement(s) start at the next line and these statement(s) must be indented.
You can give any name to a user defined function EXCEPT the Python keywords (such as print, if, vars, etc.)
To call a function, use the function name followed by parenthesis.

Suppose I wanted to check if a given integer is even or odd. I can define a function for this purpose.

In[1]:

def even_or_odd(x):
    if (x%2 ==0):
        print('even')
    else:
        print('odd')

# call the function
even_or_odd(9)
even_or_odd(12)

Out[1]:

odd
even

Next let's look at another (a bit more complex) example. We wanted to define a function to calculate the area of a circle.

In[1]:

def area_circle(radius):
    pi = 3.1415926
    area = pi * radius **2
    print(area)

In this example, we defined a function area_circle to calculate the area of circles. From this example, we can look at the components of a function:

the first line def area_circle(radius): is known as the function header
the radius inside the parentheses is the function parameter. This parameter is used just like a variable of the function.
the variable pi and area are known as local variables. They only exist within the function.

Once we defined the function, we can call it to do some calculation for us. when we call the function, simply type in the function name, and feed it with the argument (in this example, radius is the only input variable). The argument will then be passed to the parameter of the function and do the calculation for us.

In[2]:

area_circle(12.5)

Out[2]:

490.87384375

In this example, the function does the calculate for us, but it does not return any value. To let the function return a value, use the return keyword inside the function.

In[1]:

def area_circle(radius):
    pi = 3.1415926
    area = pi * radius **2
    return area

# now call the function to do calculate, and store the result.
result = area_circle(12.5)
print(result)

Out[1]:

490.87384375

Lastly, we can define functions that call other functions. Here is one example.

In[1]:

def labor_force(population, participation):
    labor = population*participation
    return labor

def unemployment_rate(population, participation, out_of_job):
    urate = out_of_job/labor_force(population,participation)
    return round(urate*100,2)

# specify arguments
population = 100
participation = 0.65
out_of_job = 10

result = unemployment_rate(population, participation, out_of_job)
print ("current unemployment rate is %s percent" %result)

Out[1]:

current unemployment rate is 15.38 percent.

In the above example, we defined two functions. The first function is labor_force, it takes population and participation as two inputs, and calculate the total labor force number. The second function is unemployment_rate, it take population, participation, and out_of_job as input variables, and calculate the unemployment rate. Note that inside the unemployment_rate function, we directly call the function labor_force to calculate the number of labor force. This is neat, as we don't have to repeat ourselves when calculating the unemployment rate.

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Part 2. Data Visualization with matplotlib

In this section, we start to explore data visualization in python. The library we are going to use is Matplotlib. Matplotlib is a comprehensive library for creating static, animated, and interactive visualizations. You can visit this website to see user guides, examples, gallery, and many other fun things.

Let's first import the required libraries for plotting.

In[1]:

import numpy as np
import matplotlib.pyplot as plt 
# plt is the commonly used alias of matplotlib

1.1. Initialize figure and subplots

In data visualization, it is common that we will need to plot many different figures and arrange them in certain ways. A good practice here is to use subplots to organize your art work. Let's look at the following block of code:

In[2]:

# initialize a figure
fig = plt.figure()
# set up your "paint canvas"
ax = fig.add_subplot(1,1,1)
# (1,1,1) stands for: 1 row x 1 col, first plot
# scatter the data
ax.scatter(np.linspace(0,1,5),np.linspace(0,5,5))
# show the plot
plt.show()

example figure 1

Here is what we just did:

we first initialized a figure, this is to create a space for your figure the computer's memory (Although computers are silly in general, but they are really good at memorizing things).
After you have the figure initialized, you can put as many "subplots" as you want into the figure. You can think of each subplot as a new painting canvas. we named the first painting canvas as ax; the .add_subplot( ) function is a neat way of adding subplot and specifying the positions. In this example, the (1,1,1) in the parentheses stands for (1 row, 1 column, 1st subplot). That is to say, we only created one painting canvas in this figure. we will see some more complex examples later.
we can then draw things on the canvas (i.e.,subplot) ax. Here, we put two simple vectors together and draw the scatter points.
Lastly, we tell python we are done with the art work, let's show the result.

1.2. Plot simple vectors

Suppose we want to visualize the trend of a virus pandemic. Let's draw a graph to illustrate how many new confirmed in each day. We first need to define a vector counts the days. This vector start from day 1, and counts to day 30. we can use the np.linspace() function to do this. Next, we need to create another vector capture the new confirmed cases in each day. For now, let's generate some random numbers between 30 and 50.

In[3]:

days = np.linspace(1,30,30)
random_number = np.random.randint(30, 50, 30)
# the syntax of generating random integer: 
# np.random.randint(lower_limit, upper_limit, number of elements)

With these two vectors, we can use the plot( ) function to draw the following figure:

In[4]:

# initialize a figure
fig = plt.figure()
# set up your "paint canvas"
ax = fig.add_subplot(1,1,1)
# (1,1,1) stands for: 1 row x 1 col, first plot
# scatter the data
ax.plot(days,random_number)
# add a title to the figure
ax.set_title("random number")
# show the plot
plt.show()

fig1

1.3. plot multiple vectors on the same graph.

In many situations, we want to plot multiple vectors on the same canvas. We can simply refer to the canvas name and then draw the picture. For example, I want to add a horizontal line equals to 45to the above graph. In addition, I want to create a label for each line. Below is the updated code:

In[5]:

# initialize a figure
fig = plt.figure()
# set up your "paint canvas"
ax = fig.add_subplot(1,1,1)
# (1,1,1) stands for: 1 row x 1 col, first plot
# scatter the data
ax.plot(days,random_number,label='some random number')

# add a horizontal line
ax.hlines(y=45,xmin=1,xmax=30,colors='red',label = 'a horizontal line')

# add a title to the figure
ax.set_title("random number")
# show the labels as legend, position at the lower right corner
ax.legend(loc='lower right')
# show the plot
plt.show()

fig2

1.4. plot functions

If we want to plot a more general function, then we first need to define a grid of x values and then calculate the corresponding y-values for each grid point. This results in x and y coordinates for a number of points that we can then add to a coordinate system. After connecting these points in the graph, we can get our function plot. Suppose we wanted to plot the function $LaTeX: y\:=\:x^3$

import matplotlib.pyplot as plt 
import numpy as np 

# 100 linearly spaced numbers 
x = np.linspace(-5,5,100) 

# the function, which is y = x^3 here 
y = x**3  

# initial the figure
fig = plt.figure() 

# set up the "paint canvas"
ax = fig.add_subplot(1, 1, 1) 

# plot the function 
ax.plot(x,y, 'g') 

# show the plot 
plt.show()

fig3

1.5. Organize your figures with subplots

In data visualization practice, it is common to "group" several figures and then present them together. We can do this by set up the correct number of "paint canvas". Recall that in the command fig.add_subplot(1,1,1), the (1,1,1) in the parentheses stands for (1 row, 1 column, 1st subplot). If we understand the this syntax, we can easily organize figures by changing the arguments.

import matplotlib.pyplot as plt 
import numpy as np 

# variables need to be plot
x = np.linspace(-5,5,100) 
y = x**3  
days = np.linspace(1,30,30)
random_number = np.random.randint(30, 50, 30)
# initial the figure
fig = plt.figure() 

# set up the "paint canvas", let's make a 2 row x 1 col figure

ax1 = fig.add_subplot(2, 1, 1) # 2x1 canvas, 1st subplot
# plot the first subplot
ax1.plot(x,y, 'g') 
ax1.set_title('first subplot')

ax2 = fig.add_subplot(2, 1, 2) # 2x1 canvas, 2st subplot
# plot the second subplot
ax2.plot(days,random_number) 
ax2.set_title('second subplot')

# show the plot 
plt.show()

fig4

There are many other decorations we can do to improve the quality of the graph. You can always customize the graph based on your need. Please see a cheatsheet of all the tricks here.

============================================================================================================== Study materials for September 17