Python Fundamentals

Overview

Teaching: 0 min
Exercises: 0 min

Questions

What basic data types can I work with in Python?

How can I create a new variable in Python?

Can I change the value associated with a variable after I create it?

Objectives

Assign values to variables.

Variables

Any Python interpreter can be used as a calculator:

3 + 5 * 4

This is great but not very interesting. To do anything useful with data, we need to assign its value to a variable. In Python, we can assign a value to a variable, using the equals sign =. For example, to assign value 60 to a variable weight_kg, we would execute:

weight_kg = 60

From now on, whenever we use weight_kg, Python will substitute the value we assigned to it. In layman’s terms, a variable is a name for a value.

In Python, variable names:

can include letters, digits, and underscores
cannot start with a digit
are case sensitive.

This means that, for example:

weight0 is a valid variable name, whereas 0weight is not
weight and Weight are different variables

Types of data

Python knows various types of data. Three common ones are:

integer numbers
floating point numbers, and
strings.

In the example above, variable weight_kg has an integer value of 60. To create a variable with a floating point value, we can execute:

weight_kg = 60.0

And to create a string, we add single or double quotes around some text, for example:

weight_kg_text = 'weight in kilograms:'

Using Variables in Python

To display the value of a variable to the screen in Python, we can use the print function:

print(weight_kg)

60.0

We can display multiple things at once using only one print command:

print(weight_kg_text, weight_kg)

weight in kilograms: 60.0

Moreover, we can do arithmetic with variables right inside the print function:

print('weight in pounds:', 2.2 * weight_kg)

weight in pounds: 132.0

The above command, however, did not change the value of weight_kg:

print(weight_kg)

60.0

To change the value of the weight_kg variable, we have to assign weight_kg a new value using the equals = sign:

weight_kg = 65.0
print('weight in kilograms is now:', weight_kg)

weight in kilograms is now: 65.0

Check Your Understanding

What values do the variables mass and age have after each statement in the following program? Test your answers by executing the commands.
mass = 47.5
age = 122
mass = mass * 2.0
age = age - 20
print(mass, age)
Solution
95.0 102

Sorting Out References

What does the following program print out?
first, second = 'Grace', 'Hopper'
third, fourth = second, first
print(third, fourth)
Solution
Hopper Grace

Key Points

Basic data types in Python include integers, strings, and floating-point numbers.

Use variable = value to assign a value to a variable in order to record it in memory.

Variables are created on demand whenever a value is assigned to them.

Use print(something) to display the value of something.

Analyzing Patient Data

Overview

Teaching: 0 min
Exercises: 0 min

Questions

How can I process tabular data files in Python?

Objectives

Explain what a library is and what libraries are used for.

Import a Python library and use the functions it contains.

Read tabular data from a file into a program.

Select individual values and subsections from data.

Perform operations on arrays of data.

Words are useful, but what’s more useful are the sentences and stories we build with them. Similarly, while a lot of powerful, general tools are built into Python, specialized tools built up from these basic units live in libraries that can be called upon when needed.

Loading data into Python

To begin processing inflammation data, we need to load it into Python. We can do that using a library called NumPy, which stands for Numerical Python. In general, you should use this library when you want to do anything involving numbers, matrices or arrays. To tell Python that we’d like to start using NumPy, we need to import it:

import numpy

Importing a library is like getting a piece of lab equipment out of a storage locker and setting it up on the bench. Libraries provide additional functionality to the basic Python package, much like a new piece of equipment adds functionality to a lab space. Just like in the lab, importing too many libraries can sometimes complicate and slow down your programs - so we only import what we need for each program.

Once we’ve imported the library, we can ask the library to read our data file for us:

numpy.loadtxt(fname='inflammation-01.csv', delimiter=',')

array([[ 0.,  0.,  1., ...,  3.,  0.,  0.],
       [ 0.,  1.,  2., ...,  1.,  0.,  1.],
       [ 0.,  1.,  1., ...,  2.,  1.,  1.],
       ...,
       [ 0.,  1.,  1., ...,  1.,  1.,  1.],
       [ 0.,  0.,  0., ...,  0.,  2.,  0.],
       [ 0.,  0.,  1., ...,  1.,  1.,  0.]])

The expression numpy.loadtxt(...) is a function call that asks Python to run the function loadtxt which belongs to the numpy library. This dotted notation is used everywhere in Python: the thing that appears before the dot contains the thing that appears after.

numpy.loadtxt has two parameters: the name of the file we want to read and the delimiter that separates values on a line. These both need to be character strings (or strings for short), so we put them in quotes.

Since we haven’t told it to do anything else with the function’s output, Python just displays it. In this case, that output is the data we just loaded. By default, only a few rows and columns are shown (with ... to omit elements when displaying big arrays). Note that, to save space when displaying NumPy arrays, Python does not show us trailing zeros, so 1.0 becomes 1..

Importing libraries with shortcuts

In this lesson we use the import numpy syntax to import NumPy. However, shortcuts such as import numpy as np are frequently used. Importing NumPy this way means that after the inital import, rather than writing numpy.loadtxt(...), you can now write np.loadtxt(...). Some people prefer this as it is quicker to type and results in shorter lines of code - especially for libraries with long names! You will frequently see Python code online using a NumPy function with np, and it’s because they’ve used this shortcut. It makes no difference which approach you choose to take, but you must be consistent as if you use import numpy as np then numpy.loadtxt(...) will not work, and you must use np.loadtxt(...) instead. Because of this, when working with other people it is important you agree on how libraries are imported.

Our call to numpy.loadtxt read our file but didn’t save the data in memory. To do that, we need to assign the array to a variable. In a similar manner to how we assign a single value to a variable, we can also assign an array of values to a variable using the same syntax. Let’s re-run numpy.loadtxt and save the returned data:

data = numpy.loadtxt(fname='inflammation-01.csv', delimiter=',')

This statement doesn’t produce any output because we’ve assigned the output to the variable data. If we want to check that the data have been loaded, we can print the variable’s value:

print(data)

[[ 0.  0.  1. ...,  3.  0.  0.]
 [ 0.  1.  2. ...,  1.  0.  1.]
 [ 0.  1.  1. ...,  2.  1.  1.]
 ...,
 [ 0.  1.  1. ...,  1.  1.  1.]
 [ 0.  0.  0. ...,  0.  2.  0.]
 [ 0.  0.  1. ...,  1.  1.  0.]]

Now that the data are in memory, we can manipulate them. First, let’s ask what type of thing data refers to:

print(type(data))

<class 'numpy.ndarray'>

The output tells us that data currently refers to an N-dimensional array, the functionality for which is provided by the NumPy library. These data correspond to arthritis patients’ inflammation. The rows are the individual patients, and the columns are their daily inflammation measurements.

Data Type

A Numpy array contains one or more elements of the same type. The type function will only tell you that a variable is a NumPy array but won’t tell you the type of thing inside the array. We can find out the type of the data contained in the NumPy array.
print(data.dtype)
float64
This tells us that the NumPy array’s elements are floating-point numbers.

With the following command, we can see the array’s shape:

print(data.shape)

(60, 40)

The output tells us that the data array variable contains 60 rows and 40 columns. When we created the variable data to store our arthritis data, we did not only create the array; we also created information about the array, called members or attributes. This extra information describes data in the same way an adjective describes a noun. data.shape is an attribute of data which describes the dimensions of data. We use the same dotted notation for the attributes of variables that we use for the functions in libraries because they have the same part-and-whole relationship.

If we want to get a single number from the array, we must provide an index in square brackets after the variable name, just as we do in math when referring to an element of a matrix. Our inflammation data has two dimensions, so we will need to use two indices to refer to one specific value:

print('first value in data:', data[0, 0])

first value in data: 0.0

print('middle value in data:', data[30, 20])

middle value in data: 13.0

The expression data[30, 20] accesses the element at row 30, column 20. While this expression may not surprise you, data[0, 0] might. Programming languages like Fortran, MATLAB and R start counting at 1 because that’s what human beings have done for thousands of years. Languages in the C family (including C++, Java, Perl, and Python) count from 0 because it represents an offset from the first value in the array (the second value is offset by one index from the first value). This is closer to the way that computers represent arrays (if you are interested in the historical reasons behind counting indices from zero, you can read Mike Hoye’s blog post). As a result, if we have an M×N array in Python, its indices go from 0 to M-1 on the first axis and 0 to N-1 on the second. It takes a bit of getting used to, but one way to remember the rule is that the index is how many steps we have to take from the start to get the item we want.

In the Corner

What may also surprise you is that when Python displays an array, it shows the element with index [0, 0] in the upper left corner rather than the lower left. This is consistent with the way mathematicians draw matrices but different from the Cartesian coordinates. The indices are (row, column) instead of (column, row) for the same reason, which can be confusing when plotting data.

Slicing data

An index like [30, 20] selects a single element of an array, but we can select whole sections as well. For example, we can select the first ten days (columns) of values for the first four patients (rows) like this:

print(data[0:4, 0:10])

[[ 0.  0.  1.  3.  1.  2.  4.  7.  8.  3.]
 [ 0.  1.  2.  1.  2.  1.  3.  2.  2.  6.]
 [ 0.  1.  1.  3.  3.  2.  6.  2.  5.  9.]
 [ 0.  0.  2.  0.  4.  2.  2.  1.  6.  7.]]

The slice 0:4 means, “Start at index 0 and go up to, but not including, index 4”. Again, the up-to-but-not-including takes a bit of getting used to, but the rule is that the difference between the upper and lower bounds is the number of values in the slice.

We don’t have to start slices at 0:

print(data[5:10, 0:10])

[[ 0.  0.  1.  2.  2.  4.  2.  1.  6.  4.]
 [ 0.  0.  2.  2.  4.  2.  2.  5.  5.  8.]
 [ 0.  0.  1.  2.  3.  1.  2.  3.  5.  3.]
 [ 0.  0.  0.  3.  1.  5.  6.  5.  5.  8.]
 [ 0.  1.  1.  2.  1.  3.  5.  3.  5.  8.]]

We also don’t have to include the upper and lower bound on the slice. If we don’t include the lower bound, Python uses 0 by default; if we don’t include the upper, the slice runs to the end of the axis, and if we don’t include either (i.e., if we use ‘:’ on its own), the slice includes everything:

small = data[:3, 36:]
print('small is:')
print(small)

The above example selects rows 0 through 2 and columns 36 through to the end of the array.

small is:
[[ 2.  3.  0.  0.]
 [ 1.  1.  0.  1.]
 [ 2.  2.  1.  1.]]

Analyzing data

NumPy has several useful functions that take an array as input to perform operations on its values. If we want to find the average inflammation for all patients on all days, for example, we can ask NumPy to compute data’s mean value:

print(numpy.mean(data))

6.14875

mean is a function that takes an array as an argument.

Not All Functions Have Input

Generally, a function uses inputs to produce outputs. However, some functions produce outputs without needing any input. For example, checking the current time doesn’t require any input.
import time
print(time.ctime())
Sat Mar 26 13:07:33 2016
For functions that don’t take in any arguments, we still need parentheses (()) to tell Python to go and do something for us.

Let’s use three other NumPy functions to get some descriptive values about the dataset. We’ll also use multiple assignment, a convenient Python feature that will enable us to do this all in one line.

maxval, minval, stdval = numpy.max(data), numpy.min(data), numpy.std(data)

print('maximum inflammation:', maxval)
print('minimum inflammation:', minval)
print('standard deviation:', stdval)

Here we’ve assigned the return value from numpy.max(data) to the variable maxval, the value from numpy.min(data) to minval, and so on.

maximum inflammation: 20.0
minimum inflammation: 0.0
standard deviation: 4.61383319712

When analyzing data, though, we often want to look at variations in statistical values, such as the maximum inflammation per patient or the average inflammation per day. One way to do this is to create a new temporary array of the data we want, then ask it to do the calculation:

patient_0 = data[0, :] # 0 on the first axis (rows), everything on the second (columns)
print('maximum inflammation for patient 0:', numpy.max(patient_0))

maximum inflammation for patient 0: 18.0

Everything in a line of code following the ‘#’ symbol is a comment that is ignored by Python. Comments allow programmers to leave explanatory notes for other programmers or their future selves.

We don’t actually need to store the row in a variable of its own. Instead, we can combine the selection and the function call:

print('maximum inflammation for patient 2:', numpy.max(data[2, :]))

maximum inflammation for patient 2: 19.0

What if we need the maximum inflammation for each patient over all days (as in the next diagram on the left) or the average for each day (as in the diagram on the right)? As the diagram below shows, we want to perform the operation across an axis:

Per-patient maximum inflammation is computed row-wise across all columns using numpy.max(data, axis=1).
Per-day average inflammation is computed column-wise across all rows using numpy.mean(data, axis=0).

To support this functionality, most array functions allow us to specify the axis we want to work on. If we ask for the average across axis 0 (rows in our 2D example), we get:

print(numpy.mean(data, axis=0))

[  0.           0.45         1.11666667   1.75         2.43333333   3.15
8          3.88333333   5.23333333   5.51666667   5.95         5.9
35         7.73333333   8.36666667   9.5          9.58333333
63333333  11.56666667  12.35        13.25        11.96666667
03333333  10.16666667  10.           8.66666667   9.15         7.25
33333333   6.58333333   6.06666667   5.95         5.11666667   3.6
3          3.56666667   2.48333333   1.5          1.13333333
56666667]

As a quick check, we can ask this array what its shape is:

print(numpy.mean(data, axis=0).shape)

(40,)

The expression (40,) tells us we have an N×1 vector, so this is the average inflammation per day for all patients. If we average across axis 1 (columns in our 2D example), we get:

print(numpy.mean(data, axis=1))

[ 5.45   5.425  6.1    5.9    5.55   6.225  5.975  6.65   6.625  6.525
775  5.8    6.225  5.75   5.225  6.3    6.55   5.7    5.85   6.55
775  5.825  6.175  6.1    5.8    6.425  6.05   6.025  6.175  6.55
175  6.35   6.725  6.125  7.075  5.725  5.925  6.15   6.075  5.75
975  5.725  6.3    5.9    6.75   5.925  7.225  6.15   5.95   6.275  5.7
1    6.825  5.975  6.725  5.7    6.25   6.4    7.05   5.9  ]

which is the average inflammation per patient across all days.

Slicing Strings

A section of an array is called a slice. We can take slices of character strings as well:
element = 'oxygen'
print('first three characters:', element[0:3])
print('last three characters:', element[3:6])
first three characters: oxy
last three characters: gen
What is the value of element[:4]? What about element[4:]? Or element[:]?
Solution
oxyg
en
oxygen
What is element[-1]? What is element[-2]?
Solution
n
e
Given those answers, explain what element[1:-1] does.

Solution

Creates a substring from index 1 up to (not including) the final index, effectively removing the first and last letters from ‘oxygen’

How can we rewrite the slice for getting the last three characters of element, so that it works even if we assign a different string to element? Test your solution with the following strings: carpentry, clone, hi.
Solution
element = 'oxygen'
print('last three characters:', element[-3:])
element = 'carpentry'
print('last three characters:', element[-3:])
element = 'clone'
print('last three characters:', element[-3:])
element = 'hi'
print('last three characters:', element[-3:])
last three characters: gen
last three characters: try
last three characters: one
last three characters: hi

Key Points

Import a library into a program using import libraryname.

Use the numpy library to work with arrays in Python.

The expression array.shape gives the shape of an array.

Use array[x, y] to select a single element from a 2D array.

Array indices start at 0, not 1.

Use low:high to specify a slice that includes the indices from low to high-1.

Use # some kind of explanation to add comments to programs.

Use numpy.mean(array), numpy.max(array), and numpy.min(array) to calculate simple statistics.

Use numpy.mean(array, axis=0) or numpy.mean(array, axis=1) to calculate statistics across the specified axis.

Visualizing Tabular Data

Overview

Teaching: 0 min
Exercises: 0 min

Questions

How can I visualize tabular data in Python?

How can I group several plots together?

Objectives

Plot simple graphs from data.

Group several graphs in a single figure.

Visualizing data

The mathematician Richard Hamming once said, “The purpose of computing is insight, not numbers,” and the best way to develop insight is often to visualize data. Visualization deserves an entire lecture of its own, but we can explore a few features of Python’s matplotlib library here. While there is no official plotting library, matplotlib is the de facto standard. First, we will import the pyplot module from matplotlib and use two of its functions to create and display a heat map of our data:

import matplotlib.pyplot
image = matplotlib.pyplot.imshow(data)
matplotlib.pyplot.show()

Heatmap of the Data

Blue pixels in this heat map represent low values, while yellow pixels represent high values. As we can see, inflammation rises and falls over a 40-day period. Let’s take a look at the average inflammation over time:

ave_inflammation = numpy.mean(data, axis=0)
ave_plot = matplotlib.pyplot.plot(ave_inflammation)
matplotlib.pyplot.show()

Average Inflammation Over Time

Here, we have put the average inflammation per day across all patients in the variable ave_inflammation, then asked matplotlib.pyplot to create and display a line graph of those values. The result is a roughly linear rise and fall, which is suspicious: we might instead expect a sharper rise and slower fall. Let’s have a look at two other statistics:

max_plot = matplotlib.pyplot.plot(numpy.max(data, axis=0))
matplotlib.pyplot.show()

Key Points

Use the pyplot module from the matplotlib library for creating simple visualizations.

Programming Review and Python Intro Part 1

Python Fundamentals

Overview

Variables

Types of data

Using Variables in Python

Check Your Understanding

Solution

Sorting Out References

Solution

Key Points

Analyzing Patient Data

Overview

Loading data into Python

Importing libraries with shortcuts

Data Type

In the Corner

Slicing data

Analyzing data

Not All Functions Have Input

Slicing Strings

Solution

Solution

Solution

Solution

Key Points

Visualizing Tabular Data

Overview

Visualizing data

Key Points