Python - Numpy and Arrays

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.
• 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 languages like Python, specialized tools built up from these basic units live in libraries that can be called upon when needed.

In order to load our inflammation data, we need to import (that is, access) a library called NumPy. In general, you should use this library if you want to do fancy things with numbers, especially if you have matrices or arrays. We can import NumPy using:

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 you’ve imported the NumPy library, we can ask the library to read our data file for us.

Copying the data file

Before reading the data file, we need a local copy of the file. We can access many linux commands using the system function of the os library. Here, we will use the wget command.

import os
os.system('wget https://raw.githubusercontent.com/swcarpentry/python-novice-inflammation/gh-pages/data/python-novice-inflammation-data.zip')
os.system('unzip python-novice-inflammation-data.zip')
os.chdir('data')

Ok, now we can use NumPy to read the data file.

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

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 to refer to the parts of things as thing.component.

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, so we put them in quotes.

Since we haven’t told it to do anything else with the function’s output, the notebook 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). To save space, Python displays numbers as 1. instead of 1.0 when there’s nothing interesting after the decimal point.

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. Just as we can 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 its result:

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

This statement doesn’t produce any output because assignment doesn’t display anything. If we want to check that our data has been loaded, we can print the variable’s value:

print(data)

Now that our data is in memory, we can start doing things with it. First, let’s ask what type of thing data refers to:

print(type(data))

The output tells us that data currently refers to an N-dimensional array created 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. type will only tell you that a variable is a NumPy array. We can also find out the type of the data contained in the NumPy array.

print(data.dtype)

This tells us that the NumPy array’s elements are floating-point numbers.

We can see what the array’s shape is like this:

print(data.shape)

This tells us that data has 60 rows and 40 columns. When we created the variable data to store our arthritis data, we didn’t just 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, just as we do in math:

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

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

The expression data[30, 20] may not surprise you, but 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.

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.

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])

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])

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 just use ‘:’ on its own), the slice includes everything:

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

Exercise - Slicing Strings

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])

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’

Arrays also know how to perform common mathematical operations on their values. The simplest operations with data are arithmetic: add, subtract, multiply, and divide. When you do such operations on arrays, the operation is done on each individual element of the array. Thus:

doubledata = data * 2.0

will create a new array doubledata whose elements have the value of two times the value of the corresponding elements in data:

print('original:')
print(data[:3, 36:])
print('doubledata:')
print(doubledata[:3, 36:])

If, instead of taking an array and doing arithmetic with a single value (as above) you did the arithmetic operation with another array of the same shape, the operation will be done on corresponding elements of the two arrays. Thus:

tripledata = doubledata + data

will give you an array where tripledata[0,0] will equal doubledata[0,0] plus data[0,0], and so on for all other elements of the arrays.

print('tripledata:')
print(tripledata[:3, 36:])

Exercise

Create an array called datasquared which is the same size as data and every value in datasquared is the square of the corresponding value in data. Print a few values of both arrays to verify the contents of datasquared

Solution

datasquared = data * data
print( datasquared )

Keypoints:

• 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 an array.
• Array indices start at 0, not 1.
• Use low:high to specify a slice that includes the indices from low to high-1.
• All the indexing and slicing that works on arrays also works on strings.