Content from Python Fundamentals

## Overview

### Questions

• What basic data types can I work with in Python?
• How can I create a new variable in Python?
• How do I use a function?
• 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:

### PYTHON

3 + 5 * 4

### OUTPUT

23

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, we can track the weight of a patient who weighs 60 kilograms by assigning the value 60 to a variable weight_kg:

### PYTHON

weight_kg = 60

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

In Python, variable names:

• can include letters, digits, and underscores
• 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. If we want to more precisely track the weight of our patient, we can use a floating point value by executing:

### PYTHON

weight_kg = 60.3

To create a string, we add single or double quotes around some text. To identify and track a patient throughout our study, we can assign each person a unique identifier by storing it in a string:

### PYTHON

patient_id = '001'

## Using Variables in Python

Once we have data stored with variable names, we can make use of it in calculations. We may want to store our patient’s weight in pounds as well as kilograms:

### PYTHON

weight_lb = 2.2 * weight_kg

We might decide to add a prefix to our patient identifier:

### PYTHON

patient_id = 'inflam_' + patient_id

## Built-in Python functions

To carry out common tasks with data and variables in Python, the language provides us with several built-in functions. To display information to the screen, we use the print function:

### PYTHON

print(weight_lb)
print(patient_id)

### OUTPUT

132.66
inflam_001

When we want to make use of a function, referred to as calling the function, we follow its name by parentheses. The parentheses are important: if you leave them off, the function doesn’t actually run! Sometimes you will include values or variables inside the parentheses for the function to use. In the case of print, we use the parentheses to tell the function what value we want to display. We will learn more about how functions work and how to create our own in later episodes.

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

### PYTHON

print(patient_id, 'weight in kilograms:', weight_kg)

### OUTPUT

inflam_001 weight in kilograms: 60.3

We can also call a function inside of another function call. For example, Python has a built-in function called type that tells you a value’s data type:

### PYTHON

print(type(60.3))
print(type(patient_id))

### OUTPUT

<class 'float'>
<class 'str'>

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

### PYTHON

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

### OUTPUT

weight in pounds: 132.66

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

### PYTHON

print(weight_kg)

### OUTPUT

60.3

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

### PYTHON

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

### OUTPUT

weight in kilograms is now: 65.0

### Variables as Sticky Notes

A variable in Python is analogous to a sticky note with a name written on it: assigning a value to a variable is like putting that sticky note on a particular value.

Using this analogy, we can investigate how assigning a value to one variable does not change values of other, seemingly related, variables. For example, let’s store the subject’s weight in pounds in its own variable:

### PYTHON

# There are 2.2 pounds per kilogram
weight_lb = 2.2 * weight_kg
print('weight in kilograms:', weight_kg, 'and in pounds:', weight_lb)

### OUTPUT

weight in kilograms: 65.0 and in pounds: 143.0

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.

Similar to above, the expression 2.2 * weight_kg is evaluated to 143.0, and then this value is assigned to the variable weight_lb (i.e. the sticky note weight_lb is placed on 143.0). At this point, each variable is “stuck” to completely distinct and unrelated values.

Let’s now change weight_kg:

### PYTHON

weight_kg = 100.0
print('weight in kilograms is now:', weight_kg, 'and weight in pounds is still:', weight_lb)

### OUTPUT

weight in kilograms is now: 100.0 and weight in pounds is still: 143.0

Since weight_lb doesn’t “remember” where its value comes from, it is not updated when we change weight_kg.

What values do the variables mass and age have after each of the following statements? Test your answer by executing the lines.

### PYTHON

mass = 47.5
age = 122
mass = mass * 2.0
age = age - 20

### OUTPUT

mass holds a value of 47.5, age does not exist
mass still holds a value of 47.5, age holds a value of 122
mass now has a value of 95.0, age's value is still 122
mass still has a value of 95.0, age now holds 102

### Sorting Out References

Python allows you to assign multiple values to multiple variables in one line by separating the variables and values with commas. What does the following program print out?

### PYTHON

first, second = 'Grace', 'Hopper'
third, fourth = second, first
print(third, fourth)

### OUTPUT

Hopper Grace

### Seeing Data Types

What are the data types of the following variables?

### PYTHON

planet = 'Earth'
apples = 5
distance = 10.5

### PYTHON

print(type(planet))
print(type(apples))
print(type(distance))

### OUTPUT

<class 'str'>
<class 'int'>
<class 'float'>

### 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.
• Use # some kind of explanation to add comments to programs.
• Built-in functions are always available to use.

Content from Analyzing Patient Data

## Overview

### 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.

To begin processing the clinical trial 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 fancy things with lots of numbers, especially if you have matrices or arrays. To tell Python that we’d like to start using NumPy, we need to import it:

### PYTHON

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:

### PYTHON

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

### OUTPUT

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. The dot notation in Python is used most of all as an object attribute/property specifier or for invoking its method. object.property will give you the object.property value, object_name.method() will invoke on object_name method.

As an example, John Smith is the John that belongs to the Smith family. We could use the dot notation to write his name smith.john, just as loadtxt is a function that belongs to the numpy library.

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, 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). Note that, to save space when displaying NumPy arrays, Python does not show us trailing zeros, so 1.0 becomes 1..

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:

### PYTHON

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:

### PYTHON

print(data)

### OUTPUT

[[ 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:

### PYTHON

print(type(data))

### OUTPUT

<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.

### PYTHON

print(data.dtype)

### OUTPUT

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:

### PYTHON

print(data.shape)

### OUTPUT

(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:

### PYTHON

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

### OUTPUT

first value in data: 0.0

### PYTHON

print('middle value in data:', data[29, 19])

### OUTPUT

middle value in data: 16.0

The expression data[29, 19] 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:

### PYTHON

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

### OUTPUT

[[ 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:

### PYTHON

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

### OUTPUT

[[ 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:

### PYTHON

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.

### OUTPUT

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:

### PYTHON

print(numpy.mean(data))

### OUTPUT

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.

### PYTHON

import time
print(time.ctime())

### OUTPUT

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.

### PYTHON

maxval, minval, stdval = numpy.amax(data), numpy.amin(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.amax(data) to the variable maxval, the value from numpy.amin(data) to minval, and so on.

### OUTPUT

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

### Mystery Functions in IPython

How did we know what functions NumPy has and how to use them? If you are working in IPython or in a Jupyter Notebook, there is an easy way to find out. If you type the name of something followed by a dot, then you can use tab completion (e.g. type numpy. and then press Tab) to see a list of all functions and attributes that you can use. After selecting one, you can also add a question mark (e.g. numpy.cumprod?), and IPython will return an explanation of the method! This is the same as doing help(numpy.cumprod). Similarly, if you are using the “plain vanilla” Python interpreter, you can type numpy. and press the Tab key twice for a listing of what is available. You can then use the help() function to see an explanation of the function you’re interested in, for example: help(numpy.cumprod).

### Confusing Function Names

One might wonder why the functions are called amax and amin and not max and min or why the other is called mean and not amean. The package numpy does provide functions max and min that are fully equivalent to amax and amin, but they share a name with standard library functions max and min that come with Python itself. Referring to the functions like we did above, that is numpy.max for example, does not cause problems, but there are other ways to refer to them that could. In addition, text editors might highlight (color) these functions like standard library function, even though they belong to NumPy, which can be confusing and lead to errors. Since there is no function called mean in the standard library, there is no function called amean.

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:

### PYTHON

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

### OUTPUT

maximum inflammation for patient 0: 18.0

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:

### PYTHON

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

### OUTPUT

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:

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:

### PYTHON

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

### OUTPUT

[  0.           0.45         1.11666667   1.75         2.43333333   3.15
3.8          3.88333333   5.23333333   5.51666667   5.95         5.9
8.35         7.73333333   8.36666667   9.5          9.58333333
10.63333333  11.56666667  12.35        13.25        11.96666667
11.03333333  10.16666667  10.           8.66666667   9.15         7.25
7.33333333   6.58333333   6.06666667   5.95         5.11666667   3.6
3.3          3.56666667   2.48333333   1.5          1.13333333
0.56666667]

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

### PYTHON

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

### OUTPUT

(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:

### PYTHON

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

### OUTPUT

[ 5.45   5.425  6.1    5.9    5.55   6.225  5.975  6.65   6.625  6.525
6.775  5.8    6.225  5.75   5.225  6.3    6.55   5.7    5.85   6.55
5.775  5.825  6.175  6.1    5.8    6.425  6.05   6.025  6.175  6.55
6.175  6.35   6.725  6.125  7.075  5.725  5.925  6.15   6.075  5.75
5.975  5.725  6.3    5.9    6.75   5.925  7.225  6.15   5.95   6.275  5.7
6.1    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:

### PYTHON

element = 'oxygen'
print('first three characters:', element[0:3])
print('last three characters:', element[3:6])

### OUTPUT

first three characters: oxy
last three characters: gen

What is the value of element[:4]? What about element[4:]? Or element[:]?

### OUTPUT

oxyg
en
oxygen

### Slicing Strings(continued)

What is element[-1]? What is element[-2]?

### OUTPUT

n
e

### Slicing Strings(continued)

Given those answers, explain what element[1:-1] does.

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

### Slicing Strings(continued)

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.

### PYTHON

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:])

### OUTPUT

last three characters: gen
last three characters: try
last three characters: one
last three characters: hi

### Thin Slices

The expression element[3:3] produces an empty string, i.e., a string that contains no characters. If data holds our array of patient data, what does data[3:3, 4:4] produce? What about data[3:3, :]?

### OUTPUT

array([], shape=(0, 0), dtype=float64)
array([], shape=(0, 40), dtype=float64)

### Stacking Arrays

Arrays can be concatenated and stacked on top of one another, using NumPy’s vstack and hstack functions for vertical and horizontal stacking, respectively.

### PYTHON

import numpy

A = numpy.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
print('A = ')
print(A)

B = numpy.hstack([A, A])
print('B = ')
print(B)

C = numpy.vstack([A, A])
print('C = ')
print(C)

### OUTPUT

A =
[[1 2 3]
[4 5 6]
[7 8 9]]
B =
[[1 2 3 1 2 3]
[4 5 6 4 5 6]
[7 8 9 7 8 9]]
C =
[[1 2 3]
[4 5 6]
[7 8 9]
[1 2 3]
[4 5 6]
[7 8 9]]

Write some additional code that slices the first and last columns of A, and stacks them into a 3x2 array. Make sure to print the results to verify your solution.

A ‘gotcha’ with array indexing is that singleton dimensions are dropped by default. That means A[:, 0] is a one dimensional array, which won’t stack as desired. To preserve singleton dimensions, the index itself can be a slice or array. For example, A[:, :1] returns a two dimensional array with one singleton dimension (i.e. a column vector).

### PYTHON

D = numpy.hstack((A[:, :1], A[:, -1:]))
print('D = ')
print(D)

### OUTPUT

D =
[[1 3]
[4 6]
[7 9]]

An alternative way to achieve the same result is to use Numpy’s delete function to remove the second column of A. If you’re not sure what the parameters of numpy.delete mean, use the help files.

### PYTHON

D = numpy.delete(arr=A, obj=1, axis=1)
print('D = ')
print(D)

### OUTPUT

D =
[[1 3]
[4 6]
[7 9]]

### Change In Inflammation

The patient data is longitudinal in the sense that each row represents a series of observations relating to one individual. This means that the change in inflammation over time is a meaningful concept. Let’s find out how to calculate changes in the data contained in an array with NumPy.

The numpy.diff() function takes an array and returns the differences between two successive values. Let’s use it to examine the changes each day across the first week of patient 3 from our inflammation dataset.

### PYTHON

patient3_week1 = data[3, :7]
print(patient3_week1)

### OUTPUT

 [0. 0. 2. 0. 4. 2. 2.]

Calling numpy.diff(patient3_week1) would do the following calculations

### PYTHON

[ 0 - 0, 2 - 0, 0 - 2, 4 - 0, 2 - 4, 2 - 2 ]

and return the 6 difference values in a new array.

### PYTHON

numpy.diff(patient3_week1)

### OUTPUT

array([ 0.,  2., -2.,  4., -2.,  0.])

Note that the array of differences is shorter by one element (length 6).

When calling numpy.diff with a multi-dimensional array, an axis argument may be passed to the function to specify which axis to process. When applying numpy.diff to our 2D inflammation array data, which axis would we specify?

Since the row axis (0) is patients, it does not make sense to get the difference between two arbitrary patients. The column axis (1) is in days, so the difference is the change in inflammation – a meaningful concept.

### PYTHON

numpy.diff(data, axis=1)

### Change In Inflammation(continued)

If the shape of an individual data file is (60, 40) (60 rows and 40 columns), what would the shape of the array be after you run the diff() function and why?

The shape will be (60, 39) because there is one fewer difference between columns than there are columns in the data.

### Change In Inflammation(continued)

How would you find the largest change in inflammation for each patient? Does it matter if the change in inflammation is an increase or a decrease?

By using the numpy.amax() function after you apply the numpy.diff() function, you will get the largest difference between days.

### PYTHON

numpy.amax(numpy.diff(data, axis=1), axis=1)

### PYTHON

array([  7.,  12.,  11.,  10.,  11.,  13.,  10.,   8.,  10.,  10.,   7.,
7.,  13.,   7.,  10.,  10.,   8.,  10.,   9.,  10.,  13.,   7.,
12.,   9.,  12.,  11.,  10.,  10.,   7.,  10.,  11.,  10.,   8.,
11.,  12.,  10.,   9.,  10.,  13.,  10.,   7.,   7.,  10.,  13.,
12.,   8.,   8.,  10.,  10.,   9.,   8.,  13.,  10.,   7.,  10.,
8.,  12.,  10.,   7.,  12.])

If inflammation values decrease along an axis, then the difference from one element to the next will be negative. If you are interested in the magnitude of the change and not the direction, the numpy.absolute() function will provide that.

Notice the difference if you get the largest absolute difference between readings.

### PYTHON

numpy.amax(numpy.absolute(numpy.diff(data, axis=1)), axis=1)

### PYTHON

array([ 12.,  14.,  11.,  13.,  11.,  13.,  10.,  12.,  10.,  10.,  10.,
12.,  13.,  10.,  11.,  10.,  12.,  13.,   9.,  10.,  13.,   9.,
12.,   9.,  12.,  11.,  10.,  13.,   9.,  13.,  11.,  11.,   8.,
11.,  12.,  13.,   9.,  10.,  13.,  11.,  11.,  13.,  11.,  13.,
13.,  10.,   9.,  10.,  10.,   9.,   9.,  13.,  10.,   9.,  10.,
11.,  13.,  10.,  10.,  12.])

### 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.amax(array), and numpy.amin(array) to calculate simple statistics.
• Use numpy.mean(array, axis=0) or numpy.mean(array, axis=1) to calculate statistics across the specified axis.

Content from Visualizing Tabular Data

## Overview

### Questions

• How can I visualize tabular data in Python?
• How can I group several plots together?

### Objectives

• Plot simple graphs from data.
• Plot multiple 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:

### Episode Prerequisites

If you are continuing in the same notebook from the previous episode, you already have a data variable and have imported numpy. If you are starting a new notebook at this point, you need the following two lines:

### PYTHON

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

### PYTHON

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

Each row in the heat map corresponds to a patient in the clinical trial dataset, and each column corresponds to a day in the dataset. Blue pixels in this heat map represent low values, while yellow pixels represent high values. As we can see, the general number of inflammation flare-ups for the patients rises and falls over a 40-day period.

So far so good as this is in line with our knowledge of the clinical trial and Dr. Maverick’s claims:

• the patients take their medication once their inflammation flare-ups begin
• it takes around 3 weeks for the medication to take effect and begin reducing flare-ups
• and flare-ups appear to drop to zero by the end of the clinical trial.

Now let’s take a look at the average inflammation over time:

### PYTHON

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

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 reasonably linear rise and fall, in line with Dr. Maverick’s claim that the medication takes 3 weeks to take effect. But a good data scientist doesn’t just consider the average of a dataset, so let’s have a look at two other statistics:

### PYTHON

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

### PYTHON

min_plot = matplotlib.pyplot.plot(numpy.amin(data, axis=0))
matplotlib.pyplot.show()

The maximum value rises and falls linearly, while the minimum seems to be a step function. Neither trend seems particularly likely, so either there’s a mistake in our calculations or something is wrong with our data. This insight would have been difficult to reach by examining the numbers themselves without visualization tools.

### Grouping plots

You can group similar plots in a single figure using subplots. This script below uses a number of new commands. The function matplotlib.pyplot.figure() creates a space into which we will place all of our plots. The parameter figsize tells Python how big to make this space. Each subplot is placed into the figure using its add_subplot method. The add_subplot method takes 3 parameters. The first denotes how many total rows of subplots there are, the second parameter refers to the total number of subplot columns, and the final parameter denotes which subplot your variable is referencing (left-to-right, top-to-bottom). Each subplot is stored in a different variable (axes1, axes2, axes3). Once a subplot is created, the axes can be titled using the set_xlabel() command (or set_ylabel()). Here are our three plots side by side:

### PYTHON

import numpy
import matplotlib.pyplot

fig = matplotlib.pyplot.figure(figsize=(10.0, 3.0))

axes1.set_ylabel('average')
axes1.plot(numpy.mean(data, axis=0))

axes2.set_ylabel('max')
axes2.plot(numpy.amax(data, axis=0))

axes3.set_ylabel('min')
axes3.plot(numpy.amin(data, axis=0))

fig.tight_layout()

matplotlib.pyplot.savefig('inflammation.png')
matplotlib.pyplot.show()

The call to loadtxt reads our data, and the rest of the program tells the plotting library how large we want the figure to be, that we’re creating three subplots, what to draw for each one, and that we want a tight layout. (If we leave out that call to fig.tight_layout(), the graphs will actually be squeezed together more closely.)

The call to savefig stores the plot as a graphics file. This can be a convenient way to store your plots for use in other documents, web pages etc. The graphics format is automatically determined by Matplotlib from the file name ending we specify; here PNG from ‘inflammation.png’. Matplotlib supports many different graphics formats, including SVG, PDF, and JPEG.

### Importing libraries with shortcuts

In this lesson we use the import matplotlib.pyplot syntax to import the pyplot module of matplotlib. However, shortcuts such as import matplotlib.pyplot as plt are frequently used. Importing pyplot this way means that after the initial import, rather than writing matplotlib.pyplot.plot(...), you can now write plt.plot(...). Another common convention is to use the shortcut import numpy as np when importing the NumPy library. We then can write np.loadtxt(...) instead of numpy.loadtxt(...), for example.

Some people prefer these shortcuts 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 pyplot function with plt, or 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 matplotlib.pyplot as plt then matplotlib.pyplot.plot(...) will not work, and you must use plt.plot(...) instead. Because of this, when working with other people it is important you agree on how libraries are imported.

### Plot Scaling

Why do all of our plots stop just short of the upper end of our graph?

Because matplotlib normally sets x and y axes limits to the min and max of our data (depending on data range)

### Plot Scaling(continued)

If we want to change this, we can use the set_ylim(min, max) method of each ‘axes’, for example:

### PYTHON

axes3.set_ylim(0, 6)

Update your plotting code to automatically set a more appropriate scale. (Hint: you can make use of the max and min methods to help.)

### PYTHON

# One method
axes3.set_ylabel('min')
axes3.plot(numpy.amin(data, axis=0))
axes3.set_ylim(0, 6)

### PYTHON

# A more automated approach
min_data = numpy.amin(data, axis=0)
axes3.set_ylabel('min')
axes3.plot(min_data)
axes3.set_ylim(numpy.amin(min_data), numpy.amax(min_data) * 1.1)

### Drawing Straight Lines

In the center and right subplots above, we expect all lines to look like step functions because non-integer value are not realistic for the minimum and maximum values. However, you can see that the lines are not always vertical or horizontal, and in particular the step function in the subplot on the right looks slanted. Why is this?

Because matplotlib interpolates (draws a straight line) between the points. One way to do avoid this is to use the Matplotlib drawstyle option:

### PYTHON

import numpy
import matplotlib.pyplot

fig = matplotlib.pyplot.figure(figsize=(10.0, 3.0))

axes1.set_ylabel('average')
axes1.plot(numpy.mean(data, axis=0), drawstyle='steps-mid')

axes2.set_ylabel('max')
axes2.plot(numpy.amax(data, axis=0), drawstyle='steps-mid')

axes3.set_ylabel('min')
axes3.plot(numpy.amin(data, axis=0), drawstyle='steps-mid')

fig.tight_layout()

matplotlib.pyplot.show()

Create a plot showing the standard deviation (numpy.std) of the inflammation data for each day across all patients.

### PYTHON

std_plot = matplotlib.pyplot.plot(numpy.std(data, axis=0))
matplotlib.pyplot.show()

### Moving Plots Around

Modify the program to display the three plots on top of one another instead of side by side.

### PYTHON

import numpy
import matplotlib.pyplot

# change figsize (swap width and height)
fig = matplotlib.pyplot.figure(figsize=(3.0, 10.0))

# change add_subplot (swap first two parameters)

axes1.set_ylabel('average')
axes1.plot(numpy.mean(data, axis=0))

axes2.set_ylabel('max')
axes2.plot(numpy.amax(data, axis=0))

axes3.set_ylabel('min')
axes3.plot(numpy.amin(data, axis=0))

fig.tight_layout()

matplotlib.pyplot.show()

### Key Points

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

Content from Storing Multiple Values in Lists

## Overview

### Questions

• How can I store many values together?

### Objectives

• Explain what a list is.
• Create and index lists of simple values.
• Change the values of individual elements
• Append values to an existing list
• Reorder and slice list elements
• Create and manipulate nested lists

In the previous episode, we analyzed a single file of clinical trial inflammation data. However, after finding some peculiar and potentially suspicious trends in the trial data we ask Dr. Maverick if they have performed any other clinical trials. Surprisingly, they say that they have and provide us with 11 more CSV files for a further 11 clinical trials they have undertaken since the initial trial.

Our goal now is to process all the inflammation data we have, which means that we still have eleven more files to go!

The natural first step is to collect the names of all the files that we have to process. In Python, a list is a way to store multiple values together. In this episode, we will learn how to store multiple values in a list as well as how to work with lists.

## Python lists

Unlike NumPy arrays, lists are built into the language so we do not have to load a library to use them. We create a list by putting values inside square brackets and separating the values with commas:

### PYTHON

odds = [1, 3, 5, 7]
print('odds are:', odds)

### OUTPUT

odds are: [1, 3, 5, 7]

We can access elements of a list using indices – numbered positions of elements in the list. These positions are numbered starting at 0, so the first element has an index of 0.

### PYTHON

print('first element:', odds[0])
print('last element:', odds[3])
print('"-1" element:', odds[-1])

### OUTPUT

first element: 1
last element: 7
"-1" element: 7

Yes, we can use negative numbers as indices in Python. When we do so, the index -1 gives us the last element in the list, -2 the second to last, and so on. Because of this, odds[3] and odds[-1] point to the same element here.

There is one important difference between lists and strings: we can change the values in a list, but we cannot change individual characters in a string. For example:

### PYTHON

names = ['Curie', 'Darwing', 'Turing']  # typo in Darwin's name
print('names is originally:', names)
names[1] = 'Darwin'  # correct the name
print('final value of names:', names)

### OUTPUT

names is originally: ['Curie', 'Darwing', 'Turing']
final value of names: ['Curie', 'Darwin', 'Turing']

works, but:

### PYTHON

name = 'Darwin'
name[0] = 'd'

### ERROR

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-8-220df48aeb2e> in <module>()
1 name = 'Darwin'
----> 2 name[0] = 'd'

TypeError: 'str' object does not support item assignment

does not.

### Ch-Ch-Ch-Ch-Changes

Data which can be modified in place is called mutable, while data which cannot be modified is called immutable. Strings and numbers are immutable. This does not mean that variables with string or number values are constants, but when we want to change the value of a string or number variable, we can only replace the old value with a completely new value.

Lists and arrays, on the other hand, are mutable: we can modify them after they have been created. We can change individual elements, append new elements, or reorder the whole list. For some operations, like sorting, we can choose whether to use a function that modifies the data in-place or a function that returns a modified copy and leaves the original unchanged.

Be careful when modifying data in-place. If two variables refer to the same list, and you modify the list value, it will change for both variables!

### PYTHON

mild_salsa = ['peppers', 'onions', 'cilantro', 'tomatoes']
hot_salsa = mild_salsa        # <-- mild_salsa and hot_salsa point to the *same* list data in memory
hot_salsa[0] = 'hot peppers'
print('Ingredients in mild salsa:', mild_salsa)
print('Ingredients in hot salsa:', hot_salsa)

### OUTPUT

Ingredients in mild salsa: ['hot peppers', 'onions', 'cilantro', 'tomatoes']
Ingredients in hot salsa: ['hot peppers', 'onions', 'cilantro', 'tomatoes']

If you want variables with mutable values to be independent, you must make a copy of the value when you assign it.

### PYTHON

mild_salsa = ['peppers', 'onions', 'cilantro', 'tomatoes']
hot_salsa = list(mild_salsa)        # <-- makes a *copy* of the list
hot_salsa[0] = 'hot peppers'
print('Ingredients in mild salsa:', mild_salsa)
print('Ingredients in hot salsa:', hot_salsa)

### OUTPUT

Ingredients in mild salsa: ['peppers', 'onions', 'cilantro', 'tomatoes']
Ingredients in hot salsa: ['hot peppers', 'onions', 'cilantro', 'tomatoes']

Because of pitfalls like this, code which modifies data in place can be more difficult to understand. However, it is often far more efficient to modify a large data structure in place than to create a modified copy for every small change. You should consider both of these aspects when writing your code.

### Nested Lists

Since a list can contain any Python variables, it can even contain other lists.

For example, you could represent the products on the shelves of a small grocery shop as a nested list called veg:

To store the contents of the shelf in a nested list, you write it this way:

### PYTHON

veg = [['lettuce', 'lettuce', 'peppers', 'zucchini'],
['lettuce', 'lettuce', 'peppers', 'zucchini'],
['lettuce', 'cilantro', 'peppers', 'zucchini']]

Here are some visual examples of how indexing a list of lists veg works. First, you can reference each row on the shelf as a separate list. For example, veg[2] represents the bottom row, which is a list of the baskets in that row.

Index operations using the image would work like this:

### PYTHON

print(veg[2])

### OUTPUT

['lettuce', 'cilantro', 'peppers', 'zucchini']

### PYTHON

print(veg[0])

### OUTPUT

['lettuce', 'lettuce', 'peppers', 'zucchini']

To reference a specific basket on a specific shelf, you use two indexes. The first index represents the row (from top to bottom) and the second index represents the specific basket (from left to right).

### PYTHON

print(veg[0][0])

### OUTPUT

'lettuce'

### PYTHON

print(veg[1][2])

### OUTPUT

'peppers'

### Heterogeneous Lists

Lists in Python can contain elements of different types. Example:

### PYTHON

sample_ages = [10, 12.5, 'Unknown']

There are many ways to change the contents of lists besides assigning new values to individual elements:

### PYTHON

odds.append(11)
print('odds after adding a value:', odds)

### OUTPUT

odds after adding a value: [1, 3, 5, 7, 11]

### PYTHON

removed_element = odds.pop(0)
print('odds after removing the first element:', odds)
print('removed_element:', removed_element)

### OUTPUT

odds after removing the first element: [3, 5, 7, 11]
removed_element: 1

### PYTHON

odds.reverse()
print('odds after reversing:', odds)

### OUTPUT

odds after reversing: [11, 7, 5, 3]

While modifying in place, it is useful to remember that Python treats lists in a slightly counter-intuitive way.

As we saw earlier, when we modified the mild_salsa list item in-place, if we make a list, (attempt to) copy it and then modify this list, we can cause all sorts of trouble. This also applies to modifying the list using the above functions:

### PYTHON

odds = [3, 5, 7]
primes = odds
primes.append(2)
print('primes:', primes)
print('odds:', odds)

### OUTPUT

primes: [3, 5, 7, 2]
odds: [3, 5, 7, 2]

This is because Python stores a list in memory, and then can use multiple names to refer to the same list. If all we want to do is copy a (simple) list, we can again use the list function, so we do not modify a list we did not mean to:

### PYTHON

odds = [3, 5, 7]
primes = list(odds)
primes.append(2)
print('primes:', primes)
print('odds:', odds)

### OUTPUT

primes: [3, 5, 7, 2]
odds: [3, 5, 7]

Subsets of lists and strings can be accessed by specifying ranges of values in brackets, similar to how we accessed ranges of positions in a NumPy array. This is commonly referred to as “slicing” the list/string.

### PYTHON

binomial_name = 'Drosophila melanogaster'
group = binomial_name[0:10]
print('group:', group)

species = binomial_name[11:23]
print('species:', species)

chromosomes = ['X', 'Y', '2', '3', '4']
autosomes = chromosomes[2:5]
print('autosomes:', autosomes)

last = chromosomes[-1]
print('last:', last)

### OUTPUT

group: Drosophila
species: melanogaster
autosomes: ['2', '3', '4']
last: 4

### Slicing From the End

Use slicing to access only the last four characters of a string or entries of a list.

### PYTHON

string_for_slicing = 'Observation date: 02-Feb-2013'
list_for_slicing = [['fluorine', 'F'],
['chlorine', 'Cl'],
['bromine', 'Br'],
['iodine', 'I'],
['astatine', 'At']]

### OUTPUT

'2013'
[['chlorine', 'Cl'], ['bromine', 'Br'], ['iodine', 'I'], ['astatine', 'At']]

Would your solution work regardless of whether you knew beforehand the length of the string or list (e.g. if you wanted to apply the solution to a set of lists of different lengths)? If not, try to change your approach to make it more robust.

Hint: Remember that indices can be negative as well as positive

Use negative indices to count elements from the end of a container (such as list or string):

### PYTHON

string_for_slicing[-4:]
list_for_slicing[-4:]

### Non-Continuous Slices

So far we’ve seen how to use slicing to take single blocks of successive entries from a sequence. But what if we want to take a subset of entries that aren’t next to each other in the sequence?

You can achieve this by providing a third argument to the range within the brackets, called the step size. The example below shows how you can take every third entry in a list:

### PYTHON

primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]
subset = primes[0:12:3]
print('subset', subset)

### OUTPUT

subset [2, 7, 17, 29]

Notice that the slice taken begins with the first entry in the range, followed by entries taken at equally-spaced intervals (the steps) thereafter. If you wanted to begin the subset with the third entry, you would need to specify that as the starting point of the sliced range:

### PYTHON

primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]
subset = primes[2:12:3]
print('subset', subset)

### OUTPUT

subset [5, 13, 23, 37]

Use the step size argument to create a new string that contains only every other character in the string “In an octopus’s garden in the shade”. Start with creating a variable to hold the string:

### PYTHON

beatles = "In an octopus's garden in the shade"

What slice of beatles will produce the following output (i.e., the first character, third character, and every other character through the end of the string)?

### OUTPUT

I notpssgre ntesae

To obtain every other character you need to provide a slice with the step size of 2:

### PYTHON

beatles[0:35:2]

You can also leave out the beginning and end of the slice to take the whole string and provide only the step argument to go every second element:

### PYTHON

beatles[::2]

If you want to take a slice from the beginning of a sequence, you can omit the first index in the range:

### PYTHON

date = 'Monday 4 January 2016'
day = date[0:6]
print('Using 0 to begin range:', day)
day = date[:6]
print('Omitting beginning index:', day)

### OUTPUT

Using 0 to begin range: Monday
Omitting beginning index: Monday

And similarly, you can omit the ending index in the range to take a slice to the very end of the sequence:

### PYTHON

months = ['jan', 'feb', 'mar', 'apr', 'may', 'jun', 'jul', 'aug', 'sep', 'oct', 'nov', 'dec']
sond = months[8:12]
print('With known last position:', sond)
sond = months[8:len(months)]
print('Using len() to get last entry:', sond)
sond = months[8:]
print('Omitting ending index:', sond)

### OUTPUT

With known last position: ['sep', 'oct', 'nov', 'dec']
Using len() to get last entry: ['sep', 'oct', 'nov', 'dec']
Omitting ending index: ['sep', 'oct', 'nov', 'dec']

+ usually means addition, but when used on strings or lists, it means “concatenate”. Given that, what do you think the multiplication operator * does on lists? In particular, what will be the output of the following code?

### PYTHON

counts = [2, 4, 6, 8, 10]
repeats = counts * 2
print(repeats)
1. [2, 4, 6, 8, 10, 2, 4, 6, 8, 10]
2. [4, 8, 12, 16, 20]
3. [[2, 4, 6, 8, 10], [2, 4, 6, 8, 10]]
4. [2, 4, 6, 8, 10, 4, 8, 12, 16, 20]

The technical term for this is operator overloading: a single operator, like + or *, can do different things depending on what it’s applied to.

The multiplication operator * used on a list replicates elements of the list and concatenates them together:

### OUTPUT

[2, 4, 6, 8, 10, 2, 4, 6, 8, 10]

It’s equivalent to:

### PYTHON

counts + counts

### Key Points

• [value1, value2, value3, ...] creates a list.
• Lists can contain any Python object, including lists (i.e., list of lists).
• Lists are indexed and sliced with square brackets (e.g., list[0] and list[2:9]), in the same way as strings and arrays.
• Lists are mutable (i.e., their values can be changed in place).
• Strings are immutable (i.e., the characters in them cannot be changed).

Content from Repeating Actions with Loops

## Overview

### Questions

• How can I do the same operations on many different values?

### Objectives

• Explain what a for loop does.
• Correctly write for loops to repeat simple calculations.
• Trace changes to a loop variable as the loop runs.
• Trace changes to other variables as they are updated by a for loop.

In the episode about visualizing data, we wrote Python code that plots values of interest from our first inflammation dataset (inflammation-01.csv), which revealed some suspicious features in it.

We have a dozen data sets right now and potentially more on the way if Dr. Maverick can keep up their surprisingly fast clinical trial rate. We want to create plots for all of our data sets with a single statement. To do that, we’ll have to teach the computer how to repeat things.

An example task that we might want to repeat is accessing numbers in a list, which we will do by printing each number on a line of its own.

### PYTHON

odds = [1, 3, 5, 7]

In Python, a list is basically an ordered collection of elements, and every element has a unique number associated with it — its index. This means that we can access elements in a list using their indices. For example, we can get the first number in the list odds, by using odds[0]. One way to print each number is to use four print statements:

### PYTHON

print(odds[0])
print(odds[1])
print(odds[2])
print(odds[3])

### OUTPUT

1
3
5
7

This is a bad approach for three reasons:

1. Not scalable. Imagine you need to print a list that has hundreds of elements. It might be easier to type them in manually.

2. Difficult to maintain. If we want to decorate each printed element with an asterisk or any other character, we would have to change four lines of code. While this might not be a problem for small lists, it would definitely be a problem for longer ones.

3. Fragile. If we use it with a list that has more elements than what we initially envisioned, it will only display part of the list’s elements. A shorter list, on the other hand, will cause an error because it will be trying to display elements of the list that do not exist.

### PYTHON

odds = [1, 3, 5]
print(odds[0])
print(odds[1])
print(odds[2])
print(odds[3])

### OUTPUT

1
3
5

### ERROR

---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-3-7974b6cdaf14> in <module>()
3 print(odds[1])
4 print(odds[2])
----> 5 print(odds[3])

IndexError: list index out of range

Here’s a better approach: a for loop

### PYTHON

odds = [1, 3, 5, 7]
for num in odds:
print(num)

### OUTPUT

1
3
5
7

This is shorter — certainly shorter than something that prints every number in a hundred-number list — and more robust as well:

### PYTHON

odds = [1, 3, 5, 7, 9, 11]
for num in odds:
print(num)

### OUTPUT

1
3
5
7
9
11

The improved version uses a for loop to repeat an operation — in this case, printing — once for each thing in a sequence. The general form of a loop is:

### PYTHON

for variable in collection:
# do things using variable, such as print

Using the odds example above, the loop might look like this:

where each number (num) in the variable odds is looped through and printed one number after another. The other numbers in the diagram denote which loop cycle the number was printed in (1 being the first loop cycle, and 6 being the final loop cycle).

We can call the loop variable anything we like, but there must be a colon at the end of the line starting the loop, and we must indent anything we want to run inside the loop. Unlike many other languages, there is no command to signify the end of the loop body (e.g. end for); everything indented after the for statement belongs to the loop.

### What’s in a name?

In the example above, the loop variable was given the name num as a mnemonic; it is short for ‘number’. We can choose any name we want for variables. We might just as easily have chosen the name banana for the loop variable, as long as we use the same name when we invoke the variable inside the loop:

### PYTHON

odds = [1, 3, 5, 7, 9, 11]
for banana in odds:
print(banana)

### OUTPUT

1
3
5
7
9
11

It is a good idea to choose variable names that are meaningful, otherwise it would be more difficult to understand what the loop is doing.

Here’s another loop that repeatedly updates a variable:

### PYTHON

length = 0
names = ['Curie', 'Darwin', 'Turing']
for value in names:
length = length + 1
print('There are', length, 'names in the list.')

### OUTPUT

There are 3 names in the list.

It’s worth tracing the execution of this little program step by step. Since there are three names in names, the statement on line 4 will be executed three times. The first time around, length is zero (the value assigned to it on line 1) and value is Curie. The statement adds 1 to the old value of length, producing 1, and updates length to refer to that new value. The next time around, value is Darwin and length is 1, so length is updated to be 2. After one more update, length is 3; since there is nothing left in names for Python to process, the loop finishes and the print function on line 5 tells us our final answer.

Note that a loop variable is a variable that is being used to record progress in a loop. It still exists after the loop is over, and we can re-use variables previously defined as loop variables as well:

### PYTHON

name = 'Rosalind'
for name in ['Curie', 'Darwin', 'Turing']:
print(name)
print('after the loop, name is', name)

### OUTPUT

Curie
Darwin
Turing
after the loop, name is Turing

Note also that finding the length of an object is such a common operation that Python actually has a built-in function to do it called len:

### PYTHON

print(len([0, 1, 2, 3]))

### OUTPUT

4

len is much faster than any function we could write ourselves, and much easier to read than a two-line loop; it will also give us the length of many other things that we haven’t met yet, so we should always use it when we can.

### From 1 to N

Python has a built-in function called range that generates a sequence of numbers. range can accept 1, 2, or 3 parameters.

• If one parameter is given, range generates a sequence of that length, starting at zero and incrementing by 1. For example, range(3) produces the numbers 0, 1, 2.
• If two parameters are given, range starts at the first and ends just before the second, incrementing by one. For example, range(2, 5) produces 2, 3, 4.
• If range is given 3 parameters, it starts at the first one, ends just before the second one, and increments by the third one. For example, range(3, 10, 2) produces 3, 5, 7, 9.

Using range, write a loop that prints the first 3 natural numbers:

### PYTHON

1
2
3

### PYTHON

for number in range(1, 4):
print(number)

### Understanding the loops

Given the following loop:

### PYTHON

word = 'oxygen'
for letter in word:
print(letter)

How many times is the body of the loop executed?

• 3 times
• 4 times
• 5 times
• 6 times

The body of the loop is executed 6 times.

### Computing Powers With Loops

Exponentiation is built into Python:

### PYTHON

print(5 ** 3)

### OUTPUT

125

Write a loop that calculates the same result as 5 ** 3 using multiplication (and without exponentiation).

### PYTHON

result = 1
for number in range(0, 3):
result = result * 5
print(result)

### Summing a list

Write a loop that calculates the sum of elements in a list by adding each element and printing the final value, so [124, 402, 36] prints 562

### PYTHON

numbers = [124, 402, 36]
summed = 0
for num in numbers:
summed = summed + num
print(summed)

### Computing the Value of a Polynomial

The built-in function enumerate takes a sequence (e.g. a list) and generates a new sequence of the same length. Each element of the new sequence is a pair composed of the index (0, 1, 2,…) and the value from the original sequence:

### PYTHON

for idx, val in enumerate(a_list):
# Do something using idx and val

The code above loops through a_list, assigning the index to idx and the value to val.

Suppose you have encoded a polynomial as a list of coefficients in the following way: the first element is the constant term, the second element is the coefficient of the linear term, the third is the coefficient of the quadratic term, etc.

### PYTHON

x = 5
coefs = [2, 4, 3]
y = coefs[0] * x**0 + coefs[1] * x**1 + coefs[2] * x**2
print(y)

### OUTPUT

97

Write a loop using enumerate(coefs) which computes the value y of any polynomial, given x and coefs.

### PYTHON

y = 0
for idx, coef in enumerate(coefs):
y = y + coef * x**idx

### Key Points

• Use for variable in sequence to process the elements of a sequence one at a time.
• The body of a for loop must be indented.
• Use len(thing) to determine the length of something that contains other values.

Content from Analyzing Data from Multiple Files

## Overview

### Questions

• How can I do the same operations on many different files?

### Objectives

• Use a library function to get a list of filenames that match a wildcard pattern.
• Write a for loop to process multiple files.

As a final piece to processing our inflammation data, we need a way to get a list of all the files in our data directory whose names start with inflammation- and end with .csv. The following library will help us to achieve this:

### PYTHON

import glob

The glob library contains a function, also called glob, that finds files and directories whose names match a pattern. We provide those patterns as strings: the character * matches zero or more characters, while ? matches any one character. We can use this to get the names of all the CSV files in the current directory:

### PYTHON

print(glob.glob('inflammation*.csv'))

### OUTPUT

['inflammation-05.csv', 'inflammation-11.csv', 'inflammation-12.csv', 'inflammation-08.csv',
'inflammation-03.csv', 'inflammation-06.csv', 'inflammation-09.csv', 'inflammation-07.csv',
'inflammation-10.csv', 'inflammation-02.csv', 'inflammation-04.csv', 'inflammation-01.csv']

As these examples show, glob.glob’s result is a list of file and directory paths in arbitrary order. This means we can loop over it to do something with each filename in turn. In our case, the “something” we want to do is generate a set of plots for each file in our inflammation dataset.

If we want to start by analyzing just the first three files in alphabetical order, we can use the sorted built-in function to generate a new sorted list from the glob.glob output:

### PYTHON

import glob
import numpy
import matplotlib.pyplot

filenames = sorted(glob.glob('inflammation*.csv'))
filenames = filenames[0:3]
for filename in filenames:
print(filename)

fig = matplotlib.pyplot.figure(figsize=(10.0, 3.0))

axes1.set_ylabel('average')
axes1.plot(numpy.mean(data, axis=0))

axes2.set_ylabel('max')
axes2.plot(numpy.amax(data, axis=0))

axes3.set_ylabel('min')
axes3.plot(numpy.amin(data, axis=0))

fig.tight_layout()
matplotlib.pyplot.show()

### OUTPUT

inflammation-01.csv

### OUTPUT

inflammation-02.csv

### OUTPUT

inflammation-03.csv

The plots generated for the second clinical trial file look very similar to the plots for the first file: their average plots show similar “noisy” rises and falls; their maxima plots show exactly the same linear rise and fall; and their minima plots show similar staircase structures.

The third dataset shows much noisier average and maxima plots that are far less suspicious than the first two datasets, however the minima plot shows that the third dataset minima is consistently zero across every day of the trial. If we produce a heat map for the third data file we see the following:

We can see that there are zero values sporadically distributed across all patients and days of the clinical trial, suggesting that there were potential issues with data collection throughout the trial. In addition, we can see that the last patient in the study didn’t have any inflammation flare-ups at all throughout the trial, suggesting that they may not even suffer from arthritis!

### Plotting Differences

Plot the difference between the average inflammations reported in the first and second datasets (stored in inflammation-01.csv and inflammation-02.csv, correspondingly), i.e., the difference between the leftmost plots of the first two figures.

### PYTHON

import glob
import numpy
import matplotlib.pyplot

filenames = sorted(glob.glob('inflammation*.csv'))

fig = matplotlib.pyplot.figure(figsize=(10.0, 3.0))

matplotlib.pyplot.ylabel('Difference in average')
matplotlib.pyplot.plot(numpy.mean(data0, axis=0) - numpy.mean(data1, axis=0))

fig.tight_layout()
matplotlib.pyplot.show()

### Generate Composite Statistics

Use each of the files once to generate a dataset containing values averaged over all patients by completing the code inside the loop given below:

### PYTHON

filenames = glob.glob('inflammation*.csv')
composite_data = numpy.zeros((60, 40))
for filename in filenames:
# sum each new file's data into composite_data as it's read
#
# and then divide the composite_data by number of samples
composite_data = composite_data / len(filenames)

Then use pyplot to generate average, max, and min for all patients.

### PYTHON

import glob
import numpy
import matplotlib.pyplot

filenames = glob.glob('inflammation*.csv')
composite_data = numpy.zeros((60, 40))

for filename in filenames:
data = numpy.loadtxt(fname = filename, delimiter=',')
composite_data = composite_data + data

composite_data = composite_data / len(filenames)

fig = matplotlib.pyplot.figure(figsize=(10.0, 3.0))

axes1.set_ylabel('average')
axes1.plot(numpy.mean(composite_data, axis=0))

axes2.set_ylabel('max')
axes2.plot(numpy.amax(composite_data, axis=0))

axes3.set_ylabel('min')
axes3.plot(numpy.amin(composite_data, axis=0))

fig.tight_layout()

matplotlib.pyplot.show()

After spending some time investigating the heat map and statistical plots, as well as doing the above exercises to plot differences between datasets and to generate composite patient statistics, we gain some insight into the twelve clinical trial datasets.

The datasets appear to fall into two categories:

• seemingly “ideal” datasets that agree excellently with Dr. Maverick’s claims, but display suspicious maxima and minima (such as inflammation-01.csv and inflammation-02.csv)
• “noisy” datasets that somewhat agree with Dr. Maverick’s claims, but show concerning data collection issues such as sporadic missing values and even an unsuitable candidate making it into the clinical trial.

In fact, it appears that all three of the “noisy” datasets (inflammation-03.csv, inflammation-08.csv, and inflammation-11.csv) are identical down to the last value. Armed with this information, we confront Dr. Maverick about the suspicious data and duplicated files.

Dr. Maverick has admitted to fabricating the clinical data for their drug trial. They did this after discovering that the initial trial had several issues, including unreliable data recording and poor participant selection. In order to prove the efficacy of their drug, they created fake data. When asked for additional data, they attempted to generate more fake datasets, and also included the original poor-quality dataset several times in order to make the trials seem more realistic.

Congratulations! We’ve investigated the inflammation data and proven that the datasets have been synthetically generated.

But it would be a shame to throw away the synthetic datasets that have taught us so much already, so we’ll forgive the imaginary Dr. Maverick and continue to use the data to learn how to program.

### Key Points

• Use glob.glob(pattern) to create a list of files whose names match a pattern.
• Use * in a pattern to match zero or more characters, and ? to match any single character.

Content from Making Choices

## Overview

### Questions

• How can my programs do different things based on data values?

### Objectives

• Write conditional statements including if, elif, and else branches.
• Correctly evaluate expressions containing and and or.

In our last lesson, we discovered something suspicious was going on in our inflammation data by drawing some plots. How can we use Python to automatically recognize the different features we saw, and take a different action for each? In this lesson, we’ll learn how to write code that runs only when certain conditions are true.

## Conditionals

We can ask Python to take different actions, depending on a condition, with an if statement:

### PYTHON

num = 37
if num > 100:
print('greater')
else:
print('not greater')
print('done')

### OUTPUT

not greater
done

The second line of this code uses the keyword if to tell Python that we want to make a choice. If the test that follows the if statement is true, the body of the if (i.e., the set of lines indented underneath it) is executed, and “greater” is printed. If the test is false, the body of the else is executed instead, and “not greater” is printed. Only one or the other is ever executed before continuing on with program execution to print “done”:

Conditional statements don’t have to include an else. If there isn’t one, Python simply does nothing if the test is false:

### PYTHON

num = 53
print('before conditional...')
if num > 100:
print(num, 'is greater than 100')
print('...after conditional')

### OUTPUT

before conditional...
...after conditional

We can also chain several tests together using elif, which is short for “else if”. The following Python code uses elif to print the sign of a number.

### PYTHON

num = -3

if num > 0:
print(num, 'is positive')
elif num == 0:
print(num, 'is zero')
else:
print(num, 'is negative')

### OUTPUT

-3 is negative

Note that to test for equality we use a double equals sign == rather than a single equals sign = which is used to assign values.

### Comparing in Python

Along with the > and == operators we have already used for comparing values in our conditionals, there are a few more options to know about:

• >: greater than
• <: less than
• ==: equal to
• !=: does not equal
• >=: greater than or equal to
• <=: less than or equal to

We can also combine tests using and and or. and is only true if both parts are true:

### PYTHON

if (1 > 0) and (-1 >= 0):
print('both parts are true')
else:
print('at least one part is false')

### OUTPUT

at least one part is false

while or is true if at least one part is true:

### PYTHON

if (1 < 0) or (1 >= 0):
print('at least one test is true')

### OUTPUT

at least one test is true

### TrueandFalse

True and False are special words in Python called booleans, which represent truth values. A statement such as 1 < 0 returns the value False, while -1 < 0 returns the value True.

## Checking our Data

Now that we’ve seen how conditionals work, we can use them to check for the suspicious features we saw in our inflammation data. We are about to use functions provided by the numpy module again. Therefore, if you’re working in a new Python session, make sure to load the module and data with:

### PYTHON

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

From the first couple of plots, we saw that maximum daily inflammation exhibits a strange behavior and raises one unit a day. Wouldn’t it be a good idea to detect such behavior and report it as suspicious? Let’s do that! However, instead of checking every single day of the study, let’s merely check if maximum inflammation in the beginning (day 0) and in the middle (day 20) of the study are equal to the corresponding day numbers.

### PYTHON

max_inflammation_0 = numpy.amax(data, axis=0)[0]
max_inflammation_20 = numpy.amax(data, axis=0)[20]

if max_inflammation_0 == 0 and max_inflammation_20 == 20:
print('Suspicious looking maxima!')

We also saw a different problem in the third dataset; the minima per day were all zero (looks like a healthy person snuck into our study). We can also check for this with an elif condition:

### PYTHON

elif numpy.sum(numpy.amin(data, axis=0)) == 0:
print('Minima add up to zero!')

And if neither of these conditions are true, we can use else to give the all-clear:

### PYTHON

else:
print('Seems OK!')

Let’s test that out:

### PYTHON

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

max_inflammation_0 = numpy.amax(data, axis=0)[0]
max_inflammation_20 = numpy.amax(data, axis=0)[20]

if max_inflammation_0 == 0 and max_inflammation_20 == 20:
print('Suspicious looking maxima!')
elif numpy.sum(numpy.amin(data, axis=0)) == 0:
else:
print('Seems OK!')

### OUTPUT

Suspicious looking maxima!

### PYTHON

data = numpy.loadtxt(fname='inflammation-03.csv', delimiter=',')

max_inflammation_0 = numpy.amax(data, axis=0)[0]
max_inflammation_20 = numpy.amax(data, axis=0)[20]

if max_inflammation_0 == 0 and max_inflammation_20 == 20:
print('Suspicious looking maxima!')
elif numpy.sum(numpy.amin(data, axis=0)) == 0:
else:
print('Seems OK!')

### OUTPUT

Minima add up to zero!

In this way, we have asked Python to do something different depending on the condition of our data. Here we printed messages in all cases, but we could also imagine not using the else catch-all so that messages are only printed when something is wrong, freeing us from having to manually examine every plot for features we’ve seen before.

### How Many Paths?

Consider this code:

### PYTHON

if 4 > 5:
print('A')
elif 4 == 5:
print('B')
elif 4 < 5:
print('C')

Which of the following would be printed if you were to run this code? Why did you pick this answer?

1. A
2. B
3. C
4. B and C

C gets printed because the first two conditions, 4 > 5 and 4 == 5, are not true, but 4 < 5 is true. In this case only one of these conditions can be true for at a time, but in other scenarios multiple elif conditions could be met. In these scenarios only the action associated with the first true elif condition will occur, starting from the top of the conditional section. This contrasts with the case of multiple if statements, where every action can occur as long as their condition is met.

### What Is Truth?

True and False booleans are not the only values in Python that are true and false. In fact, any value can be used in an if or elif. After reading and running the code below, explain what the rule is for which values are considered true and which are considered false.

### PYTHON

if '':
print('empty string is true')
if 'word':
print('word is true')
if []:
print('empty list is true')
if [1, 2, 3]:
print('non-empty list is true')
if 0:
print('zero is true')
if 1:
print('one is true')

### That’s Not Not What I Meant

Sometimes it is useful to check whether some condition is not true. The Boolean operator not can do this explicitly. After reading and running the code below, write some if statements that use not to test the rule that you formulated in the previous challenge.

### PYTHON

if not '':
print('empty string is not true')
if not 'word':
print('word is not true')
if not not True:
print('not not True is true')

### Close Enough

Write some conditions that print True if the variable a is within 10% of the variable b and False otherwise. Compare your implementation with your partner’s: do you get the same answer for all possible pairs of numbers?

There is a built-in function abs that returns the absolute value of a number:

### PYTHON

print(abs(-12))

### OUTPUT

12

### PYTHON

a = 5
b = 5.1

if abs(a - b) <= 0.1 * abs(b):
print('True')
else:
print('False')

### PYTHON

print(abs(a - b) <= 0.1 * abs(b))

This works because the Booleans True and False have string representations which can be printed.

### In-Place Operators

Python (and most other languages in the C family) provides in-place operators that work like this:

### PYTHON

x = 1  # original value
x += 1 # add one to x, assigning result back to x
x *= 3 # multiply x by 3
print(x)

### OUTPUT

6

Write some code that sums the positive and negative numbers in a list separately, using in-place operators. Do you think the result is more or less readable than writing the same without in-place operators?

### PYTHON

positive_sum = 0
negative_sum = 0
test_list = [3, 4, 6, 1, -1, -5, 0, 7, -8]
for num in test_list:
if num > 0:
positive_sum += num
elif num == 0:
pass
else:
negative_sum += num
print(positive_sum, negative_sum)

Here pass means “don’t do anything”. In this particular case, it’s not actually needed, since if num == 0 neither sum needs to change, but it illustrates the use of elif and pass.

### Sorting a List Into Buckets

In our data folder, large data sets are stored in files whose names start with “inflammation-” and small data sets – in files whose names start with “small-”. We also have some other files that we do not care about at this point. We’d like to break all these files into three lists called large_files, small_files, and other_files, respectively.

Add code to the template below to do this. Note that the string method startswith returns True if and only if the string it is called on starts with the string passed as an argument, that is:

### PYTHON

'String'.startswith('Str')

### OUTPUT

True

But

### PYTHON

'String'.startswith('str')

### OUTPUT

False

Use the following Python code as your starting point:

### PYTHON

filenames = ['inflammation-01.csv',
'myscript.py',
'inflammation-02.csv',
'small-01.csv',
'small-02.csv']
large_files = []
small_files = []
other_files = []

1. loop over the names of the files
2. figure out which group each filename belongs in
3. append the filename to that list

In the end the three lists should be:

### PYTHON

large_files = ['inflammation-01.csv', 'inflammation-02.csv']
small_files = ['small-01.csv', 'small-02.csv']
other_files = ['myscript.py']

### PYTHON

for filename in filenames:
if filename.startswith('inflammation-'):
large_files.append(filename)
elif filename.startswith('small-'):
small_files.append(filename)
else:
other_files.append(filename)

print('large_files:', large_files)
print('small_files:', small_files)
print('other_files:', other_files)

### Counting Vowels

1. Write a loop that counts the number of vowels in a character string.
2. Test it on a few individual words and full sentences.
3. Once you are done, compare your solution to your neighbor’s. Did you make the same decisions about how to handle the letter ‘y’ (which some people think is a vowel, and some do not)?

### PYTHON

vowels = 'aeiouAEIOU'
sentence = 'Mary had a little lamb.'
count = 0
for char in sentence:
if char in vowels:
count += 1

print('The number of vowels in this string is ' + str(count))

### Key Points

• Use if condition to start a conditional statement, elif condition to provide additional tests, and else to provide a default.
• The bodies of the branches of conditional statements must be indented.
• Use == to test for equality.
• X and Y is only true if both X and Y are true.
• X or Y is true if either X or Y, or both, are true.
• Zero, the empty string, and the empty list are considered false; all other numbers, strings, and lists are considered true.
• True and False represent truth values.

Content from Creating Functions

## Overview

### Questions

• How can I define new functions?
• What’s the difference between defining and calling a function?
• What happens when I call a function?

### Objectives

• Define a function that takes parameters.
• Return a value from a function.
• Test and debug a function.
• Set default values for function parameters.
• Explain why we should divide programs into small, single-purpose functions.

At this point, we’ve seen that code can have Python make decisions about what it sees in our data. What if we want to convert some of our data, like taking a temperature in Fahrenheit and converting it to Celsius. We could write something like this for converting a single number

### PYTHON

fahrenheit_val = 99
celsius_val = ((fahrenheit_val - 32) * (5/9))

and for a second number we could just copy the line and rename the variables

### PYTHON

fahrenheit_val = 99
celsius_val = ((fahrenheit_val - 32) * (5/9))

fahrenheit_val2 = 43
celsius_val2 = ((fahrenheit_val2 - 32) * (5/9))

But we would be in trouble as soon as we had to do this more than a couple times. Cutting and pasting it is going to make our code get very long and very repetitive, very quickly. We’d like a way to package our code so that it is easier to reuse, a shorthand way of re-executing longer pieces of code. In Python we can use ‘functions’. Let’s start by defining a function fahr_to_celsius that converts temperatures from Fahrenheit to Celsius:

### PYTHON

def explicit_fahr_to_celsius(temp):
# Assign the converted value to a variable
converted = ((temp - 32) * (5/9))
# Return the value of the new variable
return converted

def fahr_to_celsius(temp):
# Return converted value more efficiently using the return
# function without creating a new variable. This code does
# the same thing as the previous function but it is more explicit
# in explaining how the return command works.
return ((temp - 32) * (5/9))

The function definition opens with the keyword def followed by the name of the function (fahr_to_celsius) and a parenthesized list of parameter names (temp). The body of the function — the statements that are executed when it runs — is indented below the definition line. The body concludes with a return keyword followed by the return value.

When we call the function, the values we pass to it are assigned to those variables so that we can use them inside the function. Inside the function, we use a return statement to send a result back to whoever asked for it.

Let’s try running our function.

### PYTHON

fahr_to_celsius(32)

This command should call our function, using “32” as the input and return the function value.

In fact, calling our own function is no different from calling any other function:

### PYTHON

print('freezing point of water:', fahr_to_celsius(32), 'C')
print('boiling point of water:', fahr_to_celsius(212), 'C')

### OUTPUT

freezing point of water: 0.0 C
boiling point of water: 100.0 C

We’ve successfully called the function that we defined, and we have access to the value that we returned.

## Composing Functions

Now that we’ve seen how to turn Fahrenheit into Celsius, we can also write the function to turn Celsius into Kelvin:

### PYTHON

def celsius_to_kelvin(temp_c):
return temp_c + 273.15

print('freezing point of water in Kelvin:', celsius_to_kelvin(0.))

### OUTPUT

freezing point of water in Kelvin: 273.15

What about converting Fahrenheit to Kelvin? We could write out the formula, but we don’t need to. Instead, we can compose the two functions we have already created:

### PYTHON

def fahr_to_kelvin(temp_f):
temp_c = fahr_to_celsius(temp_f)
temp_k = celsius_to_kelvin(temp_c)
return temp_k

print('boiling point of water in Kelvin:', fahr_to_kelvin(212.0))

### OUTPUT

boiling point of water in Kelvin: 373.15

This is our first taste of how larger programs are built: we define basic operations, then combine them in ever-larger chunks to get the effect we want. Real-life functions will usually be larger than the ones shown here — typically half a dozen to a few dozen lines — but they shouldn’t ever be much longer than that, or the next person who reads it won’t be able to understand what’s going on.

## Variable Scope

In composing our temperature conversion functions, we created variables inside of those functions, temp, temp_c, temp_f, and temp_k. We refer to these variables as local variables because they no longer exist once the function is done executing. If we try to access their values outside of the function, we will encounter an error:

### PYTHON

print('Again, temperature in Kelvin was:', temp_k)

### ERROR

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-1-eed2471d229b> in <module>
----> 1 print('Again, temperature in Kelvin was:', temp_k)

NameError: name 'temp_k' is not defined

If you want to reuse the temperature in Kelvin after you have calculated it with fahr_to_kelvin, you can store the result of the function call in a variable:

### PYTHON

temp_kelvin = fahr_to_kelvin(212.0)
print('temperature in Kelvin was:', temp_kelvin)

### OUTPUT

temperature in Kelvin was: 373.15

The variable temp_kelvin, being defined outside any function, is said to be global.

Inside a function, one can read the value of such global variables:

### PYTHON

def print_temperatures():
print('temperature in Fahrenheit was:', temp_fahr)
print('temperature in Kelvin was:', temp_kelvin)

temp_fahr = 212.0
temp_kelvin = fahr_to_kelvin(temp_fahr)

print_temperatures()

### OUTPUT

temperature in Fahrenheit was: 212.0
temperature in Kelvin was: 373.15

## Tidying up

Now that we know how to wrap bits of code up in functions, we can make our inflammation analysis easier to read and easier to reuse. First, let’s make a visualize function that generates our plots:

### PYTHON

def visualize(filename):

fig = matplotlib.pyplot.figure(figsize=(10.0, 3.0))

axes1.set_ylabel('average')
axes1.plot(numpy.mean(data, axis=0))

axes2.set_ylabel('max')
axes2.plot(numpy.amax(data, axis=0))

axes3.set_ylabel('min')
axes3.plot(numpy.amin(data, axis=0))

fig.tight_layout()
matplotlib.pyplot.show()

and another function called detect_problems that checks for those systematics we noticed:

### PYTHON

def detect_problems(filename):

if numpy.amax(data, axis=0)[0] == 0 and numpy.amax(data, axis=0)[20] == 20:
print('Suspicious looking maxima!')
elif numpy.sum(numpy.amin(data, axis=0)) == 0:
else:
print('Seems OK!')

Wait! Didn’t we forget to specify what both of these functions should return? Well, we didn’t. In Python, functions are not required to include a return statement and can be used for the sole purpose of grouping together pieces of code that conceptually do one thing. In such cases, function names usually describe what they do, e.g. visualize, detect_problems.

Notice that rather than jumbling this code together in one giant for loop, we can now read and reuse both ideas separately. We can reproduce the previous analysis with a much simpler for loop:

### PYTHON

filenames = sorted(glob.glob('inflammation*.csv'))

for filename in filenames[:3]:
print(filename)
visualize(filename)
detect_problems(filename)

By giving our functions human-readable names, we can more easily read and understand what is happening in the for loop. Even better, if at some later date we want to use either of those pieces of code again, we can do so in a single line.

## Testing and Documenting

Once we start putting things in functions so that we can re-use them, we need to start testing that those functions are working correctly. To see how to do this, let’s write a function to offset a dataset so that it’s mean value shifts to a user-defined value:

### PYTHON

def offset_mean(data, target_mean_value):
return (data - numpy.mean(data)) + target_mean_value

We could test this on our actual data, but since we don’t know what the values ought to be, it will be hard to tell if the result was correct. Instead, let’s use NumPy to create a matrix of 0’s and then offset its values to have a mean value of 3:

### PYTHON

z = numpy.zeros((2, 2))
print(offset_mean(z, 3))

### OUTPUT

[[ 3.  3.]
[ 3.  3.]]

That looks right, so let’s try offset_mean on our real data:

### PYTHON

data = numpy.loadtxt(fname='inflammation-01.csv', delimiter=',')
print(offset_mean(data, 0))

### OUTPUT

[[-6.14875 -6.14875 -5.14875 ... -3.14875 -6.14875 -6.14875]
[-6.14875 -5.14875 -4.14875 ... -5.14875 -6.14875 -5.14875]
[-6.14875 -5.14875 -5.14875 ... -4.14875 -5.14875 -5.14875]
...
[-6.14875 -5.14875 -5.14875 ... -5.14875 -5.14875 -5.14875]
[-6.14875 -6.14875 -6.14875 ... -6.14875 -4.14875 -6.14875]
[-6.14875 -6.14875 -5.14875 ... -5.14875 -5.14875 -6.14875]]

It’s hard to tell from the default output whether the result is correct, but there are a few tests that we can run to reassure us:

### PYTHON

print('original min, mean, and max are:', numpy.amin(data), numpy.mean(data), numpy.amax(data))
offset_data = offset_mean(data, 0)
print('min, mean, and max of offset data are:',
numpy.amin(offset_data),
numpy.mean(offset_data),
numpy.amax(offset_data))

### OUTPUT

original min, mean, and max are: 0.0 6.14875 20.0
min, mean, and max of offset data are: -6.14875 2.842170943040401e-16 13.85125

That seems almost right: the original mean was about 6.1, so the lower bound from zero is now about -6.1. The mean of the offset data isn’t quite zero, but it’s pretty close. We can even go further and check that the standard deviation hasn’t changed:

### PYTHON

print('std dev before and after:', numpy.std(data), numpy.std(offset_data))

### OUTPUT

std dev before and after: 4.613833197118566 4.613833197118566

Those values look the same, but we probably wouldn’t notice if they were different in the sixth decimal place. Let’s do this instead:

### PYTHON

print('difference in standard deviations before and after:',
numpy.std(data) - numpy.std(offset_data))

### OUTPUT

difference in standard deviations before and after: 0.0

Everything looks good, and we should probably get back to doing our analysis. We have one more task first, though: we should write some documentation for our function to remind ourselves later what it’s for and how to use it.

### PYTHON

# offset_mean(data, target_mean_value):
# return a new array containing the original data with its mean offset to match the desired value.
def offset_mean(data, target_mean_value):
return (data - numpy.mean(data)) + target_mean_value

There’s a better way, though. If the first thing in a function is a string that isn’t assigned to a variable, that string is attached to the function as its documentation:

### PYTHON

def offset_mean(data, target_mean_value):
"""Return a new array containing the original data
with its mean offset to match the desired value."""
return (data - numpy.mean(data)) + target_mean_value

This is better because we can now ask Python’s built-in help system to show us the documentation for the function:

### PYTHON

help(offset_mean)

### OUTPUT

Help on function offset_mean in module __main__:

offset_mean(data, target_mean_value)
Return a new array containing the original data with its mean offset to match the desired value.

A string like this is called a docstring. We don’t need to use triple quotes when we write one, but if we do, we can break the string across multiple lines:

### PYTHON

def offset_mean(data, target_mean_value):
"""Return a new array containing the original data
with its mean offset to match the desired value.

Examples
--------
>>> offset_mean([1, 2, 3], 0)
array([-1.,  0.,  1.])
"""
return (data - numpy.mean(data)) + target_mean_value

help(offset_mean)

### OUTPUT

Help on function offset_mean in module __main__:

offset_mean(data, target_mean_value)
Return a new array containing the original data
with its mean offset to match the desired value.

Examples
--------
>>> offset_mean([1, 2, 3], 0)
array([-1.,  0.,  1.])

## Defining Defaults

We have passed parameters to functions in two ways: directly, as in type(data), and by name, as in numpy.loadtxt(fname='something.csv', delimiter=','). In fact, we can pass the filename to loadtxt without the fname=:

### PYTHON

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

### OUTPUT

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.]])

but we still need to say delimiter=:

### PYTHON

numpy.loadtxt('inflammation-01.csv', ',')

### ERROR

Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/Users/username/anaconda3/lib/python3.6/site-packages/numpy/lib/npyio.py", line 1041, in loa
dtxt
dtype = np.dtype(dtype)
_commastring
newitem = (dtype, eval(repeats))
File "<string>", line 1
,
^
SyntaxError: unexpected EOF while parsing

To understand what’s going on, and make our own functions easier to use, let’s re-define our offset_mean function like this:

### PYTHON

def offset_mean(data, target_mean_value=0.0):
"""Return a new array containing the original data
with its mean offset to match the desired value, (0 by default).

Examples
--------
>>> offset_mean([1, 2, 3])
array([-1.,  0.,  1.])
"""
return (data - numpy.mean(data)) + target_mean_value

The key change is that the second parameter is now written target_mean_value=0.0 instead of just target_mean_value. If we call the function with two arguments, it works as it did before:

### PYTHON

test_data = numpy.zeros((2, 2))
print(offset_mean(test_data, 3))

### OUTPUT

[[ 3.  3.]
[ 3.  3.]]

But we can also now call it with just one parameter, in which case target_mean_value is automatically assigned the default value of 0.0:

### PYTHON

more_data = 5 + numpy.zeros((2, 2))
print('data before mean offset:')
print(more_data)
print('offset data:')
print(offset_mean(more_data))

### OUTPUT

data before mean offset:
[[ 5.  5.]
[ 5.  5.]]
offset data:
[[ 0.  0.]
[ 0.  0.]]

This is handy: if we usually want a function to work one way, but occasionally need it to do something else, we can allow people to pass a parameter when they need to but provide a default to make the normal case easier. The example below shows how Python matches values to parameters:

### PYTHON

def display(a=1, b=2, c=3):
print('a:', a, 'b:', b, 'c:', c)

print('no parameters:')
display()
print('one parameter:')
display(55)
print('two parameters:')
display(55, 66)

### OUTPUT

no parameters:
a: 1 b: 2 c: 3
one parameter:
a: 55 b: 2 c: 3
two parameters:
a: 55 b: 66 c: 3

As this example shows, parameters are matched up from left to right, and any that haven’t been given a value explicitly get their default value. We can override this behavior by naming the value as we pass it in:

### PYTHON

print('only setting the value of c')
display(c=77)

### OUTPUT

only setting the value of c
a: 1 b: 2 c: 77

With that in hand, let’s look at the help for numpy.loadtxt:

### PYTHON

help(numpy.loadtxt)

### OUTPUT

Help on function loadtxt in module numpy.lib.npyio:

cols=None, unpack=False, ndmin=0, encoding='bytes')
Load data from a text file.

Each row in the text file must have the same number of values.

Parameters
----------
...

There’s a lot of information here, but the most important part is the first couple of lines:

### OUTPUT

loadtxt(fname, dtype=<class 'float'>, comments='#', delimiter=None, converters=None, skiprows=0, use
cols=None, unpack=False, ndmin=0, encoding='bytes')

This tells us that loadtxt has one parameter called fname that doesn’t have a default value, and eight others that do. If we call the function like this:

### PYTHON

numpy.loadtxt('inflammation-01.csv', ',')

then the filename is assigned to fname (which is what we want), but the delimiter string ',' is assigned to dtype rather than delimiter, because dtype is the second parameter in the list. However ',' isn’t a known dtype so our code produced an error message when we tried to run it. When we call loadtxt we don’t have to provide fname= for the filename because it’s the first item in the list, but if we want the ',' to be assigned to the variable delimiter, we do have to provide delimiter= for the second parameter since delimiter is not the second parameter in the list.

Consider these two functions:

### PYTHON

def s(p):
a = 0
for v in p:
a += v
m = a / len(p)
d = 0
for v in p:
d += (v - m) * (v - m)
return numpy.sqrt(d / (len(p) - 1))

def std_dev(sample):
sample_sum = 0
for value in sample:
sample_sum += value

sample_mean = sample_sum / len(sample)

sum_squared_devs = 0
for value in sample:
sum_squared_devs += (value - sample_mean) * (value - sample_mean)

return numpy.sqrt(sum_squared_devs / (len(sample) - 1))

The functions s and std_dev are computationally equivalent (they both calculate the sample standard deviation), but to a human reader, they look very different. You probably found std_dev much easier to read and understand than s.

As this example illustrates, both documentation and a programmer’s coding style combine to determine how easy it is for others to read and understand the programmer’s code. Choosing meaningful variable names and using blank spaces to break the code into logical “chunks” are helpful techniques for producing readable code. This is useful not only for sharing code with others, but also for the original programmer. If you need to revisit code that you wrote months ago and haven’t thought about since then, you will appreciate the value of readable code!

### Combining Strings

“Adding” two strings produces their concatenation: 'a' + 'b' is 'ab'. Write a function called fence that takes two parameters called original and wrapper and returns a new string that has the wrapper character at the beginning and end of the original. A call to your function should look like this:

### PYTHON

print(fence('name', '*'))

### OUTPUT

*name*

### PYTHON

def fence(original, wrapper):
return wrapper + original + wrapper

### Return versus print

Note that return and print are not interchangeable. print is a Python function that prints data to the screen. It enables us, users, see the data. return statement, on the other hand, makes data visible to the program. Let’s have a look at the following function:

### PYTHON

def add(a, b):
print(a + b)

Question: What will we see if we execute the following commands?

### PYTHON

A = add(7, 3)
print(A)

Python will first execute the function add with a = 7 and b = 3, and, therefore, print 10. However, because function add does not have a line that starts with return (no return “statement”), it will, by default, return nothing which, in Python world, is called None. Therefore, A will be assigned to None and the last line (print(A)) will print None. As a result, we will see:

### OUTPUT

10
None

### Selecting Characters From Strings

If the variable s refers to a string, then s[0] is the string’s first character and s[-1] is its last. Write a function called outer that returns a string made up of just the first and last characters of its input. A call to your function should look like this:

### PYTHON

print(outer('helium'))

### OUTPUT

hm

### PYTHON

def outer(input_string):
return input_string[0] + input_string[-1]

### Rescaling an Array

Write a function rescale that takes an array as input and returns a corresponding array of values scaled to lie in the range 0.0 to 1.0. (Hint: If L and H are the lowest and highest values in the original array, then the replacement for a value v should be (v-L) / (H-L).)

### PYTHON

def rescale(input_array):
L = numpy.amin(input_array)
H = numpy.amax(input_array)
output_array = (input_array - L) / (H - L)
return output_array

### Testing and Documenting Your Function

Run the commands help(numpy.arange) and help(numpy.linspace) to see how to use these functions to generate regularly-spaced values, then use those values to test your rescale function. Once you’ve successfully tested your function, add a docstring that explains what it does.

### PYTHON

"""Takes an array as input, and returns a corresponding array scaled so
that 0 corresponds to the minimum and 1 to the maximum value of the input array.

Examples:
>>> rescale(numpy.arange(10.0))
array([ 0.        ,  0.11111111,  0.22222222,  0.33333333,  0.44444444,
0.55555556,  0.66666667,  0.77777778,  0.88888889,  1.        ])
>>> rescale(numpy.linspace(0, 100, 5))
array([ 0.  ,  0.25,  0.5 ,  0.75,  1.  ])
"""

### Defining Defaults

Rewrite the rescale function so that it scales data to lie between 0.0 and 1.0 by default, but will allow the caller to specify lower and upper bounds if they want. Compare your implementation to your neighbor’s: do the two functions always behave the same way?

### PYTHON

def rescale(input_array, low_val=0.0, high_val=1.0):
"""rescales input array values to lie between low_val and high_val"""
L = numpy.amin(input_array)
H = numpy.amax(input_array)
intermed_array = (input_array - L) / (H - L)
output_array = intermed_array * (high_val - low_val) + low_val
return output_array

### Variables Inside and Outside Functions

What does the following piece of code display when run — and why?

### PYTHON

f = 0
k = 0

def f2k(f):
k = ((f - 32) * (5.0 / 9.0)) + 273.15
return k

print(f2k(8))
print(f2k(41))
print(f2k(32))

print(k)

### OUTPUT

259.81666666666666
278.15
273.15
0

k is 0 because the k inside the function f2k doesn’t know about the k defined outside the function. When the f2k function is called, it creates a local variable k. The function does not return any values and does not alter k outside of its local copy. Therefore the original value of k remains unchanged. Beware that a local k is created because f2k internal statements affect a new value to it. If k was only read, it would simply retrieve the global k value.

### Mixing Default and Non-Default Parameters

Given the following code:

### PYTHON

def numbers(one, two=2, three, four=4):
n = str(one) + str(two) + str(three) + str(four)
return n

print(numbers(1, three=3))

what do you expect will be printed? What is actually printed? What rule do you think Python is following?

1. 1234
2. one2three4
3. 1239
4. SyntaxError

Given that, what does the following piece of code display when run?

### PYTHON

def func(a, b=3, c=6):
print('a: ', a, 'b: ', b, 'c:', c)

func(-1, 2)
1. a: b: 3 c: 6
2. a: -1 b: 3 c: 6
3. a: -1 b: 2 c: 6
4. a: b: -1 c: 2

Attempting to define the numbers function results in 4. SyntaxError. The defined parameters two and four are given default values. Because one and three are not given default values, they are required to be included as arguments when the function is called and must be placed before any parameters that have default values in the function definition.

The given call to func displays a: -1 b: 2 c: 6. -1 is assigned to the first parameter a, 2 is assigned to the next parameter b, and c is not passed a value, so it uses its default value 6.

Revise a function you wrote for one of the previous exercises to try to make the code more readable. Then, collaborate with one of your neighbors to critique each other’s functions and discuss how your function implementations could be further improved to make them more readable.

### Key Points

• Define a function using def function_name(parameter).
• The body of a function must be indented.
• Call a function using function_name(value).
• Numbers are stored as integers or floating-point numbers.
• Variables defined within a function can only be seen and used within the body of the function.
• Variables created outside of any function are called global variables.
• Within a function, we can access global variables.
• Variables created within a function override global variables if their names match.
• Use help(thing) to view help for something.
• Put docstrings in functions to provide help for that function.
• Specify default values for parameters when defining a function using name=value in the parameter list.
• Parameters can be passed by matching based on name, by position, or by omitting them (in which case the default value is used).
• Put code whose parameters change frequently in a function, then call it with different parameter values to customize its behavior.

Content from Errors and Exceptions

## Overview

### Questions

• How can I handle errors in Python programs?

### Objectives

• To be able to read a traceback, and determine where the error took place and what type it is.
• To be able to describe the types of situations in which syntax errors, indentation errors, name errors, index errors, and missing file errors occur.

Every programmer encounters errors, both those who are just beginning, and those who have been programming for years. Encountering errors and exceptions can be very frustrating at times, and can make coding feel like a hopeless endeavour. However, understanding what the different types of errors are and when you are likely to encounter them can help a lot. Once you know why you get certain types of errors, they become much easier to fix.

Errors in Python have a very specific form, called a traceback. Let’s examine one:

### PYTHON

# This code has an intentional error. You can type it directly or
# use it for reference to understand the error message below.
def favorite_ice_cream():
ice_creams = [
'chocolate',
'vanilla',
'strawberry'
]
print(ice_creams[3])

favorite_ice_cream()

### ERROR

---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-1-70bd89baa4df> in <module>()
9     print(ice_creams[3])
10
----> 11 favorite_ice_cream()

<ipython-input-1-70bd89baa4df> in favorite_ice_cream()
7         'strawberry'
8     ]
----> 9     print(ice_creams[3])
10
11 favorite_ice_cream()

IndexError: list index out of range

This particular traceback has two levels. You can determine the number of levels by looking for the number of arrows on the left hand side. In this case:

1. The first shows code from the cell above, with an arrow pointing to Line 11 (which is favorite_ice_cream()).

2. The second shows some code in the function favorite_ice_cream, with an arrow pointing to Line 9 (which is print(ice_creams[3])).

The last level is the actual place where the error occurred. The other level(s) show what function the program executed to get to the next level down. So, in this case, the program first performed a function call to the function favorite_ice_cream. Inside this function, the program encountered an error on Line 6, when it tried to run the code print(ice_creams[3]).

### Long Tracebacks

Sometimes, you might see a traceback that is very long -- sometimes they might even be 20 levels deep! This can make it seem like something horrible happened, but the length of the error message does not reflect severity, rather, it indicates that your program called many functions before it encountered the error. Most of the time, the actual place where the error occurred is at the bottom-most level, so you can skip down the traceback to the bottom.

So what error did the program actually encounter? In the last line of the traceback, Python helpfully tells us the category or type of error (in this case, it is an IndexError) and a more detailed error message (in this case, it says “list index out of range”).

If you encounter an error and don’t know what it means, it is still important to read the traceback closely. That way, if you fix the error, but encounter a new one, you can tell that the error changed. Additionally, sometimes knowing where the error occurred is enough to fix it, even if you don’t entirely understand the message.

If you do encounter an error you don’t recognize, try looking at the official documentation on errors. However, note that you may not always be able to find the error there, as it is possible to create custom errors. In that case, hopefully the custom error message is informative enough to help you figure out what went wrong.

Read the Python code and the resulting traceback below, and answer the following questions:

1. How many levels does the traceback have?
2. What is the function name where the error occurred?
3. On which line number in this function did the error occur?
4. What is the type of error?
5. What is the error message?

### PYTHON

# This code has an intentional error. Do not type it directly;
# use it for reference to understand the error message below.
def print_message(day):
messages = [
'Hello, world!',
'Today is Tuesday!',
'It is the middle of the week.',
'Today is Donnerstag in German!',
'Last day of the week!',
'Hooray for the weekend!',
'Aw, the weekend is almost over.'
]
print(messages[day])

def print_sunday_message():
print_message(7)

print_sunday_message()

### ERROR

---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
16     print_message(7)
17
---> 18 print_sunday_message()
19

14
15 def print_sunday_message():
---> 16     print_message(7)
17
18 print_sunday_message()

11         'Aw, the weekend is almost over.'
12     ]
---> 13     print(messages[day])
14
15 def print_sunday_message():

IndexError: list index out of range
1. 3 levels
2. print_message
3. 13
4. IndexError
5. list index out of range You can then infer that 7 is not the right index to use with messages.

### Better errors on newer Pythons

Newer versions of Python have improved error printouts. If you are debugging errors, it is often helpful to use the latest Python version, even if you support older versions of Python.

## Syntax Errors

When you forget a colon at the end of a line, accidentally add one space too many when indenting under an if statement, or forget a parenthesis, you will encounter a syntax error. This means that Python couldn’t figure out how to read your program. This is similar to forgetting punctuation in English: for example, this text is difficult to read there is no punctuation there is also no capitalization why is this hard because you have to figure out where each sentence ends you also have to figure out where each sentence begins to some extent it might be ambiguous if there should be a sentence break or not

People can typically figure out what is meant by text with no punctuation, but people are much smarter than computers. If Python doesn’t know how to read the program, it will give up and inform you with an error. For example:

### PYTHON

def some_function()
msg = 'hello, world!'
print(msg)
return msg

### ERROR

  File "<ipython-input-3-6bb841ea1423>", line 1
def some_function()
^
SyntaxError: invalid syntax

Here, Python tells us that there is a SyntaxError on line 1, and even puts a little arrow in the place where there is an issue. In this case the problem is that the function definition is missing a colon at the end.

Actually, the function above has two issues with syntax. If we fix the problem with the colon, we see that there is also an IndentationError, which means that the lines in the function definition do not all have the same indentation:

### PYTHON

def some_function():
msg = 'hello, world!'
print(msg)
return msg

### ERROR

  File "<ipython-input-4-ae290e7659cb>", line 4
return msg
^
IndentationError: unexpected indent

Both SyntaxError and IndentationError indicate a problem with the syntax of your program, but an IndentationError is more specific: it always means that there is a problem with how your code is indented.

### Tabs and Spaces

Some indentation errors are harder to spot than others. In particular, mixing spaces and tabs can be difficult to spot because they are both whitespace. In the example below, the first two lines in the body of the function some_function are indented with tabs, while the third line — with spaces. If you’re working in a Jupyter notebook, be sure to copy and paste this example rather than trying to type it in manually because Jupyter automatically replaces tabs with spaces.

### PYTHON

def some_function():
msg = 'hello, world!'
print(msg)
return msg

Visually it is impossible to spot the error. Fortunately, Python does not allow you to mix tabs and spaces.

### ERROR

  File "<ipython-input-5-653b36fbcd41>", line 4
return msg
^
TabError: inconsistent use of tabs and spaces in indentation

## Variable Name Errors

Another very common type of error is called a NameError, and occurs when you try to use a variable that does not exist. For example:

### PYTHON

print(a)

### ERROR

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
----> 1 print(a)

NameError: name 'a' is not defined

Variable name errors come with some of the most informative error messages, which are usually of the form “name ‘the_variable_name’ is not defined”.

Why does this error message occur? That’s a harder question to answer, because it depends on what your code is supposed to do. However, there are a few very common reasons why you might have an undefined variable. The first is that you meant to use a string, but forgot to put quotes around it:

### PYTHON

print(hello)

### ERROR

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-8-9553ee03b645> in <module>()
----> 1 print(hello)

NameError: name 'hello' is not defined

The second reason is that you might be trying to use a variable that does not yet exist. In the following example, count should have been defined (e.g., with count = 0) before the for loop:

### PYTHON

for number in range(10):
count = count + number
print('The count is:', count)

### ERROR

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-9-dd6a12d7ca5c> in <module>()
1 for number in range(10):
----> 2     count = count + number
3 print('The count is:', count)

NameError: name 'count' is not defined

Finally, the third possibility is that you made a typo when you were writing your code. Let’s say we fixed the error above by adding the line Count = 0 before the for loop. Frustratingly, this actually does not fix the error. Remember that variables are case-sensitive, so the variable count is different from Count. We still get the same error, because we still have not defined count:

### PYTHON

Count = 0
for number in range(10):
count = count + number
print('The count is:', count)

### ERROR

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-10-d77d40059aea> in <module>()
1 Count = 0
2 for number in range(10):
----> 3     count = count + number
4 print('The count is:', count)

NameError: name 'count' is not defined

## Index Errors

Next up are errors having to do with containers (like lists and strings) and the items within them. If you try to access an item in a list or a string that does not exist, then you will get an error. This makes sense: if you asked someone what day they would like to get coffee, and they answered “caturday”, you might be a bit annoyed. Python gets similarly annoyed if you try to ask it for an item that doesn’t exist:

### PYTHON

letters = ['a', 'b', 'c']
print('Letter #1 is', letters[0])
print('Letter #2 is', letters[1])
print('Letter #3 is', letters[2])
print('Letter #4 is', letters[3])

### OUTPUT

Letter #1 is a
Letter #2 is b
Letter #3 is c

### ERROR

---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-11-d817f55b7d6c> in <module>()
3 print('Letter #2 is', letters[1])
4 print('Letter #3 is', letters[2])
----> 5 print('Letter #4 is', letters[3])

IndexError: list index out of range

Here, Python is telling us that there is an IndexError in our code, meaning we tried to access a list index that did not exist.

## File Errors

The last type of error we’ll cover today are those associated with reading and writing files: FileNotFoundError. If you try to read a file that does not exist, you will receive a FileNotFoundError telling you so. If you attempt to write to a file that was opened read-only, Python 3 returns an UnsupportedOperationError. More generally, problems with input and output manifest as OSErrors, which may show up as a more specific subclass; you can see the list in the Python docs. They all have a unique UNIX errno, which is you can see in the error message.

### PYTHON

file_handle = open('myfile.txt', 'r')

### ERROR

---------------------------------------------------------------------------
FileNotFoundError                         Traceback (most recent call last)
<ipython-input-14-f6e1ac4aee96> in <module>()
----> 1 file_handle = open('myfile.txt', 'r')

FileNotFoundError: [Errno 2] No such file or directory: 'myfile.txt'

One reason for receiving this error is that you specified an incorrect path to the file. For example, if I am currently in a folder called myproject, and I have a file in myproject/writing/myfile.txt, but I try to open myfile.txt, this will fail. The correct path would be writing/myfile.txt. It is also possible that the file name or its path contains a typo.

A related issue can occur if you use the “read” flag instead of the “write” flag. Python will not give you an error if you try to open a file for writing when the file does not exist. However, if you meant to open a file for reading, but accidentally opened it for writing, and then try to read from it, you will get an UnsupportedOperation error telling you that the file was not opened for reading:

### PYTHON

file_handle = open('myfile.txt', 'w')
file_handle.read()

### ERROR

---------------------------------------------------------------------------
UnsupportedOperation                      Traceback (most recent call last)
<ipython-input-15-b846479bc61f> in <module>()
1 file_handle = open('myfile.txt', 'w')

UnsupportedOperation: not readable

These are the most common errors with files, though many others exist. If you get an error that you’ve never seen before, searching the Internet for that error type often reveals common reasons why you might get that error.

### Identifying Syntax Errors

1. Read the code below, and (without running it) try to identify what the errors are.
2. Run the code, and read the error message. Is it a SyntaxError or an IndentationError?
3. Fix the error.
4. Repeat steps 2 and 3, until you have fixed all the errors.

### PYTHON

def another_function
print('Syntax errors are annoying.')
print('But at least Python tells us about them!')
print('So they are usually not too hard to fix.')

SyntaxError for missing (): at end of first line, IndentationError for mismatch between second and third lines. A fixed version is:

### PYTHON

def another_function():
print('Syntax errors are annoying.')
print('But at least Python tells us about them!')
print('So they are usually not too hard to fix.')

### Identifying Variable Name Errors

1. Read the code below, and (without running it) try to identify what the errors are.
2. Run the code, and read the error message. What type of NameError do you think this is? In other words, is it a string with no quotes, a misspelled variable, or a variable that should have been defined but was not?
3. Fix the error.
4. Repeat steps 2 and 3, until you have fixed all the errors.

### PYTHON

for number in range(10):
# use a if the number is a multiple of 3, otherwise use b
if (Number % 3) == 0:
message = message + a
else:
message = message + 'b'
print(message)

3 NameErrors for number being misspelled, for message not defined, and for a not being in quotes.

Fixed version:

### PYTHON

message = ''
for number in range(10):
# use a if the number is a multiple of 3, otherwise use b
if (number % 3) == 0:
message = message + 'a'
else:
message = message + 'b'
print(message)

### Identifying Index Errors

1. Read the code below, and (without running it) try to identify what the errors are.
2. Run the code, and read the error message. What type of error is it?
3. Fix the error.

### PYTHON

seasons = ['Spring', 'Summer', 'Fall', 'Winter']
print('My favorite season is ', seasons[4])

IndexError; the last entry is seasons[3], so seasons[4] doesn’t make sense. A fixed version is:

### PYTHON

seasons = ['Spring', 'Summer', 'Fall', 'Winter']
print('My favorite season is ', seasons[-1])

### Key Points

• Tracebacks can look intimidating, but they give us a lot of useful information about what went wrong in our program, including where the error occurred and what type of error it was.
• An error having to do with the ‘grammar’ or syntax of the program is called a SyntaxError. If the issue has to do with how the code is indented, then it will be called an IndentationError.
• A NameError will occur when trying to use a variable that does not exist. Possible causes are that a variable definition is missing, a variable reference differs from its definition in spelling or capitalization, or the code contains a string that is missing quotes around it.
• Containers like lists and strings will generate errors if you try to access items in them that do not exist. This type of error is called an IndexError.
• Trying to read a file that does not exist will give you an FileNotFoundError. Trying to read a file that is open for writing, or writing to a file that is open for reading, will give you an IOError.

Content from Defensive Programming

## Overview

### Questions

• How can I make my programs more reliable?

### Objectives

• Explain what an assertion is.
• Add assertions that check the program’s state is correct.
• Correctly add precondition and postcondition assertions to functions.
• Explain what test-driven development is, and use it when creating new functions.
• Explain why variables should be initialized using actual data values rather than arbitrary constants.

Our previous lessons have introduced the basic tools of programming: variables and lists, file I/O, loops, conditionals, and functions. What they haven’t done is show us how to tell whether a program is getting the right answer, and how to tell if it’s still getting the right answer as we make changes to it.

To achieve that, we need to:

• Write programs that check their own operation.
• Write and run tests for widely-used functions.
• Make sure we know what “correct” actually means.

The good news is, doing these things will speed up our programming, not slow it down. As in real carpentry — the kind done with lumber — the time saved by measuring carefully before cutting a piece of wood is much greater than the time that measuring takes.

## Assertions

The first step toward getting the right answers from our programs is to assume that mistakes will happen and to guard against them. This is called defensive programming, and the most common way to do it is to add assertions to our code so that it checks itself as it runs. An assertion is simply a statement that something must be true at a certain point in a program. When Python sees one, it evaluates the assertion’s condition. If it’s true, Python does nothing, but if it’s false, Python halts the program immediately and prints the error message if one is provided. For example, this piece of code halts as soon as the loop encounters a value that isn’t positive:

### PYTHON

numbers = [1.5, 2.3, 0.7, -0.001, 4.4]
total = 0.0
for num in numbers:
assert num > 0.0, 'Data should only contain positive values'
total += num
print('total is:', total)

### ERROR

---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
<ipython-input-19-33d87ea29ae4> in <module>()
2 total = 0.0
3 for num in numbers:
----> 4     assert num > 0.0, 'Data should only contain positive values'
5     total += num
6 print('total is:', total)

AssertionError: Data should only contain positive values

Programs like the Firefox browser are full of assertions: 10-20% of the code they contain are there to check that the other 80–90% are working correctly. Broadly speaking, assertions fall into three categories:

• A precondition is something that must be true at the start of a function in order for it to work correctly.

• A postcondition is something that the function guarantees is true when it finishes.

• An invariant is something that is always true at a particular point inside a piece of code.

For example, suppose we are representing rectangles using a tuple of four coordinates (x0, y0, x1, y1), representing the lower left and upper right corners of the rectangle. In order to do some calculations, we need to normalize the rectangle so that the lower left corner is at the origin and the longest side is 1.0 units long. This function does that, but checks that its input is correctly formatted and that its result makes sense:

### PYTHON

def normalize_rectangle(rect):
"""Normalizes a rectangle so that it is at the origin and 1.0 units long on its longest axis.
Input should be of the format (x0, y0, x1, y1).
(x0, y0) and (x1, y1) define the lower left and upper right corners
of the rectangle, respectively."""
assert len(rect) == 4, 'Rectangles must contain 4 coordinates'
x0, y0, x1, y1 = rect
assert x0 < x1, 'Invalid X coordinates'
assert y0 < y1, 'Invalid Y coordinates'

dx = x1 - x0
dy = y1 - y0
if dx > dy:
scaled = dx / dy
upper_x, upper_y = 1.0, scaled
else:
scaled = dx / dy
upper_x, upper_y = scaled, 1.0

assert 0 < upper_x <= 1.0, 'Calculated upper X coordinate invalid'
assert 0 < upper_y <= 1.0, 'Calculated upper Y coordinate invalid'

return (0, 0, upper_x, upper_y)

The preconditions on lines 6, 8, and 9 catch invalid inputs:

### PYTHON

print(normalize_rectangle( (0.0, 1.0, 2.0) )) # missing the fourth coordinate

### ERROR

---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
<ipython-input-2-1b9cd8e18a1f> in <module>
----> 1 print(normalize_rectangle( (0.0, 1.0, 2.0) )) # missing the fourth coordinate

<ipython-input-1-c94cf5b065b9> in normalize_rectangle(rect)
4     (x0, y0) and (x1, y1) define the lower left and upper right corners
5     of the rectangle, respectively."""
----> 6     assert len(rect) == 4, 'Rectangles must contain 4 coordinates'
7     x0, y0, x1, y1 = rect
8     assert x0 < x1, 'Invalid X coordinates'

AssertionError: Rectangles must contain 4 coordinates

### PYTHON

print(normalize_rectangle( (4.0, 2.0, 1.0, 5.0) )) # X axis inverted

### ERROR

---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
<ipython-input-3-325036405532> in <module>
----> 1 print(normalize_rectangle( (4.0, 2.0, 1.0, 5.0) )) # X axis inverted

<ipython-input-1-c94cf5b065b9> in normalize_rectangle(rect)
6     assert len(rect) == 4, 'Rectangles must contain 4 coordinates'
7     x0, y0, x1, y1 = rect
----> 8     assert x0 < x1, 'Invalid X coordinates'
9     assert y0 < y1, 'Invalid Y coordinates'
10

AssertionError: Invalid X coordinates

The post-conditions on lines 20 and 21 help us catch bugs by telling us when our calculations might have been incorrect. For example, if we normalize a rectangle that is taller than it is wide everything seems OK:

### PYTHON

print(normalize_rectangle( (0.0, 0.0, 1.0, 5.0) ))

### OUTPUT

(0, 0, 0.2, 1.0)

but if we normalize one that’s wider than it is tall, the assertion is triggered:

### PYTHON

print(normalize_rectangle( (0.0, 0.0, 5.0, 1.0) ))

### ERROR

---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
<ipython-input-5-8d4a48f1d068> in <module>
----> 1 print(normalize_rectangle( (0.0, 0.0, 5.0, 1.0) ))

<ipython-input-1-c94cf5b065b9> in normalize_rectangle(rect)
19
20     assert 0 < upper_x <= 1.0, 'Calculated upper X coordinate invalid'
---> 21     assert 0 < upper_y <= 1.0, 'Calculated upper Y coordinate invalid'
22
23     return (0, 0, upper_x, upper_y)

AssertionError: Calculated upper Y coordinate invalid

Re-reading our function, we realize that line 14 should divide dy by dx rather than dx by dy. In a Jupyter notebook, you can display line numbers by typing Ctrl+M followed by L. If we had left out the assertion at the end of the function, we would have created and returned something that had the right shape as a valid answer, but wasn’t. Detecting and debugging that would almost certainly have taken more time in the long run than writing the assertion.

But assertions aren’t just about catching errors: they also help people understand programs. Each assertion gives the person reading the program a chance to check (consciously or otherwise) that their understanding matches what the code is doing.

Most good programmers follow two rules when adding assertions to their code. The first is, fail early, fail often. The greater the distance between when and where an error occurs and when it’s noticed, the harder the error will be to debug, so good code catches mistakes as early as possible.

The second rule is, turn bugs into assertions or tests. Whenever you fix a bug, write an assertion that catches the mistake should you make it again. If you made a mistake in a piece of code, the odds are good that you have made other mistakes nearby, or will make the same mistake (or a related one) the next time you change it. Writing assertions to check that you haven’t regressed (i.e., haven’t re-introduced an old problem) can save a lot of time in the long run, and helps to warn people who are reading the code (including your future self) that this bit is tricky.

## Test-Driven Development

An assertion checks that something is true at a particular point in the program. The next step is to check the overall behavior of a piece of code, i.e., to make sure that it produces the right output when it’s given a particular input. For example, suppose we need to find where two or more time series overlap. The range of each time series is represented as a pair of numbers, which are the time the interval started and ended. The output is the largest range that they all include:

Most novice programmers would solve this problem like this:

1. Write a function range_overlap.
2. Call it interactively on two or three different inputs.
3. If it produces the wrong answer, fix the function and re-run that test.

This clearly works — after all, thousands of scientists are doing it right now — but there’s a better way:

1. Write a short function for each test.
2. Write a range_overlap function that should pass those tests.
3. If range_overlap produces any wrong answers, fix it and re-run the test functions.

Writing the tests before writing the function they exercise is called test-driven development (TDD). Its advocates believe it produces better code faster because:

1. If people write tests after writing the thing to be tested, they are subject to confirmation bias, i.e., they subconsciously write tests to show that their code is correct, rather than to find errors.
2. Writing tests helps programmers figure out what the function is actually supposed to do.

We start by defining an empty function range_overlap:

### PYTHON

def range_overlap(ranges):
pass

Here are three test statements for range_overlap:

### PYTHON

assert range_overlap([ (0.0, 1.0) ]) == (0.0, 1.0)
assert range_overlap([ (2.0, 3.0), (2.0, 4.0) ]) == (2.0, 3.0)
assert range_overlap([ (0.0, 1.0), (0.0, 2.0), (-1.0, 1.0) ]) == (0.0, 1.0)

### ERROR

---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
<ipython-input-25-d8be150fbef6> in <module>()
----> 1 assert range_overlap([ (0.0, 1.0) ]) == (0.0, 1.0)
2 assert range_overlap([ (2.0, 3.0), (2.0, 4.0) ]) == (2.0, 3.0)
3 assert range_overlap([ (0.0, 1.0), (0.0, 2.0), (-1.0, 1.0) ]) == (0.0, 1.0)

AssertionError:

The error is actually reassuring: we haven’t implemented any logic into range_overlap yet, so if the tests passed, it would indicate that we’ve written an entirely ineffective test.

And as a bonus of writing these tests, we’ve implicitly defined what our input and output look like: we expect a list of pairs as input, and produce a single pair as output.

Something important is missing, though. We don’t have any tests for the case where the ranges don’t overlap at all:

### PYTHON

assert range_overlap([ (0.0, 1.0), (5.0, 6.0) ]) == ???

What should range_overlap do in this case: fail with an error message, produce a special value like (0.0, 0.0) to signal that there’s no overlap, or something else? Any actual implementation of the function will do one of these things; writing the tests first helps us figure out which is best before we’re emotionally invested in whatever we happened to write before we realized there was an issue.

### PYTHON

assert range_overlap([ (0.0, 1.0), (1.0, 2.0) ]) == ???

Do two segments that touch at their endpoints overlap or not? Mathematicians usually say “yes”, but engineers usually say “no”. The best answer is “whatever is most useful in the rest of our program”, but again, any actual implementation of range_overlap is going to do something, and whatever it is ought to be consistent with what it does when there’s no overlap at all.

Since we’re planning to use the range this function returns as the X axis in a time series chart, we decide that:

1. every overlap has to have non-zero width, and
2. we will return the special value None when there’s no overlap.

None is built into Python, and means “nothing here”. (Other languages often call the equivalent value null or nil). With that decision made, we can finish writing our last two tests:

### PYTHON

assert range_overlap([ (0.0, 1.0), (5.0, 6.0) ]) == None
assert range_overlap([ (0.0, 1.0), (1.0, 2.0) ]) == None

### ERROR

---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
<ipython-input-26-d877ef460ba2> in <module>()
----> 1 assert range_overlap([ (0.0, 1.0), (5.0, 6.0) ]) == None
2 assert range_overlap([ (0.0, 1.0), (1.0, 2.0) ]) == None

AssertionError:

Again, we get an error because we haven’t written our function, but we’re now ready to do so:

### PYTHON

def range_overlap(ranges):
"""Return common overlap among a set of [left, right] ranges."""
max_left = 0.0
min_right = 1.0
for (left, right) in ranges:
max_left = max(max_left, left)
min_right = min(min_right, right)
return (max_left, min_right)

Take a moment to think about why we calculate the left endpoint of the overlap as the maximum of the input left endpoints, and the overlap right endpoint as the minimum of the input right endpoints. We’d now like to re-run our tests, but they’re scattered across three different cells. To make running them easier, let’s put them all in a function:

### PYTHON

def test_range_overlap():
assert range_overlap([ (0.0, 1.0), (5.0, 6.0) ]) == None
assert range_overlap([ (0.0, 1.0), (1.0, 2.0) ]) == None
assert range_overlap([ (0.0, 1.0) ]) == (0.0, 1.0)
assert range_overlap([ (2.0, 3.0), (2.0, 4.0) ]) == (2.0, 3.0)
assert range_overlap([ (0.0, 1.0), (0.0, 2.0), (-1.0, 1.0) ]) == (0.0, 1.0)
assert range_overlap([]) == None

We can now test range_overlap with a single function call:

### PYTHON

test_range_overlap()

### ERROR

---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
<ipython-input-29-cf9215c96457> in <module>()
----> 1 test_range_overlap()

<ipython-input-28-5d4cd6fd41d9> in test_range_overlap()
1 def test_range_overlap():
----> 2     assert range_overlap([ (0.0, 1.0), (5.0, 6.0) ]) == None
3     assert range_overlap([ (0.0, 1.0), (1.0, 2.0) ]) == None
4     assert range_overlap([ (0.0, 1.0) ]) == (0.0, 1.0)
5     assert range_overlap([ (2.0, 3.0), (2.0, 4.0) ]) == (2.0, 3.0)

AssertionError:

The first test that was supposed to produce None fails, so we know something is wrong with our function. We don’t know whether the other tests passed or failed because Python halted the program as soon as it spotted the first error. Still, some information is better than none, and if we trace the behavior of the function with that input, we realize that we’re initializing max_left and min_right to 0.0 and 1.0 respectively, regardless of the input values. This violates another important rule of programming: always initialize from data.

### Pre- and Post-Conditions

Suppose you are writing a function called average that calculates the average of the numbers in a NumPy array. What pre-conditions and post-conditions would you write for it? Compare your answer to your neighbor’s: can you think of a function that will pass your tests but not his/hers or vice versa?

### PYTHON

# a possible pre-condition:
assert len(input_array) > 0, 'Array length must be non-zero'
# a possible post-condition:
assert numpy.amin(input_array) <= average <= numpy.amax(input_array),
'Average should be between min and max of input values (inclusive)'

### Testing Assertions

Given a sequence of a number of cars, the function get_total_cars returns the total number of cars.

### PYTHON

get_total_cars([1, 2, 3, 4])

### OUTPUT

10

### PYTHON

get_total_cars(['a', 'b', 'c'])

### OUTPUT

ValueError: invalid literal for int() with base 10: 'a'

Explain in words what the assertions in this function check, and for each one, give an example of input that will make that assertion fail.

### PYTHON

def get_total_cars(values):
assert len(values) > 0
for element in values:
assert int(element)
values = [int(element) for element in values]
total = sum(values)
assert total > 0
return total
• The first assertion checks that the input sequence values is not empty. An empty sequence such as [] will make it fail.
• The second assertion checks that each value in the list can be turned into an integer. Input such as [1, 2, 'c', 3] will make it fail.
• The third assertion checks that the total of the list is greater than 0. Input such as [-10, 2, 3] will make it fail.

### Key Points

• Program defensively, i.e., assume that errors are going to arise, and write code to detect them when they do.
• Put assertions in programs to check their state as they run, and to help readers understand how those programs are supposed to work.
• Use preconditions to check that the inputs to a function are safe to use.
• Use postconditions to check that the output from a function is safe to use.
• Write tests before writing code in order to help determine exactly what that code is supposed to do.

Content from Debugging

## Overview

### Questions

• How can I debug my program?

### Objectives

• Debug code containing an error systematically.
• Identify ways of making code less error-prone and more easily tested.

Once testing has uncovered problems, the next step is to fix them. Many novices do this by making more-or-less random changes to their code until it seems to produce the right answer, but that’s very inefficient (and the result is usually only correct for the one case they’re testing). The more experienced a programmer is, the more systematically they debug, and most follow some variation on the rules explained below.

## Know What It’s Supposed to Do

The first step in debugging something is to know what it’s supposed to do. “My program doesn’t work” isn’t good enough: in order to diagnose and fix problems, we need to be able to tell correct output from incorrect. If we can write a test case for the failing case — i.e., if we can assert that with these inputs, the function should produce that result — then we’re ready to start debugging. If we can’t, then we need to figure out how we’re going to know when we’ve fixed things.

But writing test cases for scientific software is frequently harder than writing test cases for commercial applications, because if we knew what the output of the scientific code was supposed to be, we wouldn’t be running the software: we’d be writing up our results and moving on to the next program. In practice, scientists tend to do the following:

1. Test with simplified data. Before doing statistics on a real data set, we should try calculating statistics for a single record, for two identical records, for two records whose values are one step apart, or for some other case where we can calculate the right answer by hand.

2. Test a simplified case. If our program is supposed to simulate magnetic eddies in rapidly-rotating blobs of supercooled helium, our first test should be a blob of helium that isn’t rotating, and isn’t being subjected to any external electromagnetic fields. Similarly, if we’re looking at the effects of climate change on speciation, our first test should hold temperature, precipitation, and other factors constant.

3. Compare to an oracle. A test oracle is something whose results are trusted, such as experimental data, an older program, or a human expert. We use test oracles to determine if our new program produces the correct results. If we have a test oracle, we should store its output for particular cases so that we can compare it with our new results as often as we like without re-running that program.

4. Check conservation laws. Mass, energy, and other quantities are conserved in physical systems, so they should be in programs as well. Similarly, if we are analyzing patient data, the number of records should either stay the same or decrease as we move from one analysis to the next (since we might throw away outliers or records with missing values). If “new” patients start appearing out of nowhere as we move through our pipeline, it’s probably a sign that something is wrong.

5. Visualize. Data analysts frequently use simple visualizations to check both the science they’re doing and the correctness of their code (just as we did in the opening lesson of this tutorial). This should only be used for debugging as a last resort, though, since it’s very hard to compare two visualizations automatically.

## Make It Fail Every Time

We can only debug something when it fails, so the second step is always to find a test case that makes it fail every time. The “every time” part is important because few things are more frustrating than debugging an intermittent problem: if we have to call a function a dozen times to get a single failure, the odds are good that we’ll scroll past the failure when it actually occurs.

As part of this, it’s always important to check that our code is “plugged in”, i.e., that we’re actually exercising the problem that we think we are. Every programmer has spent hours chasing a bug, only to realize that they were actually calling their code on the wrong data set or with the wrong configuration parameters, or are using the wrong version of the software entirely. Mistakes like these are particularly likely to happen when we’re tired, frustrated, and up against a deadline, which is one of the reasons late-night (or overnight) coding sessions are almost never worthwhile.

## Make It Fail Fast

If it takes 20 minutes for the bug to surface, we can only do three experiments an hour. This means that we’ll get less data in more time and that we’re more likely to be distracted by other things as we wait for our program to fail, which means the time we are spending on the problem is less focused. It’s therefore critical to make it fail fast.

As well as making the program fail fast in time, we want to make it fail fast in space, i.e., we want to localize the failure to the smallest possible region of code:

1. The smaller the gap between cause and effect, the easier the connection is to find. Many programmers therefore use a divide and conquer strategy to find bugs, i.e., if the output of a function is wrong, they check whether things are OK in the middle, then concentrate on either the first or second half, and so on.

2. N things can interact in N! different ways, so every line of code that isn’t run as part of a test means more than one thing we don’t need to worry about.

## Change One Thing at a Time, For a Reason

Replacing random chunks of code is unlikely to do much good. (After all, if you got it wrong the first time, you’ll probably get it wrong the second and third as well.) Good programmers therefore change one thing at a time, for a reason. They are either trying to gather more information (“is the bug still there if we change the order of the loops?”) or test a fix (“can we make the bug go away by sorting our data before processing it?”).

Every time we make a change, however small, we should re-run our tests immediately, because the more things we change at once, the harder it is to know what’s responsible for what (those N! interactions again). And we should re-run all of our tests: more than half of fixes made to code introduce (or re-introduce) bugs, so re-running all of our tests tells us whether we have regressed.

## Keep Track of What You’ve Done

Good scientists keep track of what they’ve done so that they can reproduce their work, and so that they don’t waste time repeating the same experiments or running ones whose results won’t be interesting. Similarly, debugging works best when we keep track of what we’ve done and how well it worked. If we find ourselves asking, “Did left followed by right with an odd number of lines cause the crash? Or was it right followed by left? Or was I using an even number of lines?” then it’s time to step away from the computer, take a deep breath, and start working more systematically.

Records are particularly useful when the time comes to ask for help. People are more likely to listen to us when we can explain clearly what we did, and we’re better able to give them the information they need to be useful.

### Version Control Revisited

Version control is often used to reset software to a known state during debugging, and to explore recent changes to code that might be responsible for bugs. In particular, most version control systems (e.g. git, Mercurial) have:

1. a blame command that shows who last changed each line of a file;
2. a bisect command that helps with finding the commit that introduced an issue.

## Be Humble

And speaking of help: if we can’t find a bug in 10 minutes, we should be humble and ask for help. Explaining the problem to someone else is often useful, since hearing what we’re thinking helps us spot inconsistencies and hidden assumptions. If you don’t have someone nearby to share your problem description with, get a rubber duck!

Asking for help also helps alleviate confirmation bias. If we have just spent an hour writing a complicated program, we want it to work, so we’re likely to keep telling ourselves why it should, rather than searching for the reason it doesn’t. People who aren’t emotionally invested in the code can be more objective, which is why they’re often able to spot the simple mistakes we have overlooked.

Part of being humble is learning from our mistakes. Programmers tend to get the same things wrong over and over: either they don’t understand the language and libraries they’re working with, or their model of how things work is wrong. In either case, taking note of why the error occurred and checking for it next time quickly turns into not making the mistake at all.

And that is what makes us most productive in the long run. As the saying goes, A week of hard work can sometimes save you an hour of thought. If we train ourselves to avoid making some kinds of mistakes, to break our code into modular, testable chunks, and to turn every assumption (or mistake) into an assertion, it will actually take us less time to produce working programs, not more.

### Debug With a Neighbor

Take a function that you have written today, and introduce a tricky bug. Your function should still run, but will give the wrong output. Switch seats with your neighbor and attempt to debug the bug that they introduced into their function. Which of the principles discussed above did you find helpful?

### Not Supposed to be the Same

You are assisting a researcher with Python code that computes the Body Mass Index (BMI) of patients. The researcher is concerned because all patients seemingly have unusual and identical BMIs, despite having different physiques. BMI is calculated as weight in kilograms divided by the square of height in metres.

Use the debugging principles in this exercise and locate problems with the code. What suggestions would you give the researcher for ensuring any later changes they make work correctly? What bugs do you spot?

### PYTHON

patients = [[70, 1.8], [80, 1.9], [150, 1.7]]

def calculate_bmi(weight, height):
return weight / (height ** 2)

for patient in patients:
weight, height = patients[0]
bmi = calculate_bmi(height, weight)
print("Patient's BMI is:", bmi)

### OUTPUT

Patient's BMI is: 0.000367
Patient's BMI is: 0.000367
Patient's BMI is: 0.000367

### Suggestions for debugging

• Add printing statement in the calculate_bmi function, like print('weight:', weight, 'height:', height), to make clear that what the BMI is based on.
• Change print("Patient's BMI is: %f" % bmi) to print("Patient's BMI (weight: %f, height: %f) is: %f" % (weight, height, bmi)), in order to be able to distinguish bugs in the function from bugs in the loop.

### Bugs found

• The loop is not being utilised correctly. height and weight are always set as the first patient’s data during each iteration of the loop.

• The height/weight variables are reversed in the function call to calculate_bmi(...), the correct BMIs are 21.604938, 22.160665 and 51.903114.

### Key Points

• Know what code is supposed to do before trying to debug it.
• Make it fail every time.
• Make it fail fast.
• Change one thing at a time, and for a reason.
• Keep track of what you’ve done.
• Be humble.

Content from Command-Line Programs

## Overview

### Questions

• How can I write Python programs that will work like Unix command-line tools?

### Objectives

• Use the values of command-line arguments in a program.
• Handle flags and files separately in a command-line program.
• Read data from standard input in a program so that it can be used in a pipeline.

The Jupyter Notebook and other interactive tools are great for prototyping code and exploring data, but sooner or later we will want to use our program in a pipeline or run it in a shell script to process thousands of data files. In order to do that in an efficient way, we need to make our programs work like other Unix command-line tools. For example, we may want a program that reads a dataset and prints the average inflammation per patient.

### OUTPUT

5.45
5.425
6.1
...
6.4
7.05
5.9

We might also want to look at the minimum of the first four lines

$head -4 inflammation-01.csv | python ../code/readings_06.py --min or the maximum inflammations in several files one after another: ### BASH $ python ../code/readings_04.py --max inflammation-*.csv

Our scripts should do the following:

1. If no filename is given on the command line, read data from standard input.
2. If one or more filenames are given, read data from them and report statistics for each file separately.
3. Use the --min, --mean, or --max flag to determine what statistic to print.

To make this work, we need to know how to handle command-line arguments in a program, and understand how to handle standard input. We’ll tackle these questions in turn below.

## Command-Line Arguments

We are going to create a file with our python code in, then use the bash shell to run the code. Using the text editor of your choice, save the following in a text file called sys_version.py:

### PYTHON

import sys
print('version is', sys.version)

The first line imports a library called sys, which is short for “system”. It defines values such as sys.version, which describes which version of Python we are running. We can run this script from the command line like this:

### OUTPUT

sys.argv is ['argv_list.py']

the only thing in the list is the full path to our script, which is always sys.argv[0]. If we run it with a few arguments, however:

### PYTHON

import sys
import numpy

def main():
script = sys.argv[0]
filename = sys.argv[1]
for row_mean in numpy.mean(data, axis=1):
print(row_mean)

This function gets the name of the script from sys.argv[0], because that’s where it’s always put, and the name of the file to process from sys.argv[1]. Here’s a simple test:

### PYTHON

import sys
import numpy

def main():
script = sys.argv[0]
filename = sys.argv[1]
for row_mean in numpy.mean(data, axis=1):
print(row_mean)

if __name__ == '__main__':
main()

and run that:

### OUTPUT

small-01.csv small-02.csv small-03.csv

### OUTPUT

0.333333333333
1.0

Using small data files as input also allows us to check our results more easily: here, for example, we can see that our program is calculating the mean correctly for each line, whereas we were really taking it on faith before. This is yet another rule of programming: test the simple things first.

We want our program to process each file separately, so we need a loop that executes once for each filename. If we specify the files on the command line, the filenames will be in sys.argv, but we need to be careful: sys.argv[0] will always be the name of our script, rather than the name of a file. We also need to handle an unknown number of filenames, since our program could be run for any number of files.

The solution to both problems is to loop over the contents of sys.argv[1:]. The ‘1’ tells Python to start the slice at location 1, so the program’s name isn’t included; since we’ve left off the upper bound, the slice runs to the end of the list, and includes all the filenames. Here’s our changed program readings_03.py:

### OUTPUT

0.333333333333
1.0
13.6666666667
11.0

### The Right Way to Do It

At this point, we have created three versions of our script called readings_01.py, readings_02.py, and readings_03.py. We wouldn’t do this in real life: instead, we would have one file called readings.py that we committed to version control every time we got an enhancement working. For teaching, though, we need all the successive versions side by side.

## Handling Command-Line Flags

The next step is to teach our program to pay attention to the --min, --mean, and --max flags. These always appear before the names of the files, so we could do this:

### OUTPUT

1.0
2.0

but there are several things wrong with it:

1. main is too large to read comfortably.

2. If we do not specify at least two additional arguments on the command-line, one for the flag and one for the filename, but only one, the program will not throw an exception but will run. It assumes that the file list is empty, as sys.argv[1] will be considered the action, even if it is a filename. Silent failures like this are always hard to debug.

3. The program should check if the submitted action is one of the three recognized flags.

This version pulls the processing of each file out of the loop into a function of its own. It also checks that action is one of the allowed flags before doing any processing, so that the program fails fast:

### PYTHON

import sys

count = 0
for line in sys.stdin:
count += 1

print(count, 'lines in standard input')

This little program reads lines from a special “file” called sys.stdin, which is automatically connected to the program’s standard input. We don’t have to open it — Python and the operating system take care of that when the program starts up — but we can do almost anything with it that we could do to a regular file. Let’s try running it as if it were a regular command-line program:

$python ../code/count_stdin.py < small-01.csv ### OUTPUT 2 lines in standard input A common mistake is to try to run something that reads from standard input like this: ### BASH $ python ../code/count_stdin.py small-01.csv

i.e., to forget the < character that redirects the file to standard input. In this case, there’s nothing in standard input, so the program waits at the start of the loop for someone to type something on the keyboard. Since there’s no way for us to do this, our program is stuck, and we have to halt it using the Interrupt option from the Kernel menu in the Notebook.

We now need to rewrite the program so that it loads data from sys.stdin if no filenames are provided. Luckily, numpy.loadtxt can handle either a filename or an open file as its first parameter, so we don’t actually need to change process. Only main changes:

### OUTPUT

0.333333333333
1.0

That’s better. In fact, that’s done: the program now does everything we set out to do.

### Arithmetic on the Command Line

Write a Python program that adds, subtracts, multiplies, or divides two numbers provided on the command line:

### OUTPUT

-1.0

### PYTHON

import sys

def main():
assert len(sys.argv) == 4, 'Need exactly 3 arguments'

operator = sys.argv[1]
assert operator in ['--add', '--subtract', '--multiply', '--divide'], \
'Operator is not one of --add, --subtract, --multiply, or --divide: bailing out'
try:
operand1, operand2 = float(sys.argv[2]), float(sys.argv[3])
except ValueError:
print('cannot convert input to a number: bailing out')
return

do_arithmetic(operand1, operator, operand2)

def do_arithmetic(operand1, operator, operand2):

value = operand1 + operand2
elif operator == 'subtract':
value = operand1 - operand2
elif operator == 'multiply':
value = operand1 * operand2
elif operator == 'divide':
value = operand1 / operand2
print(value)

main()

### Finding Particular Files

Using the glob module introduced earlier, write a simple version of ls that shows files in the current directory with a particular suffix. A call to this script should look like this:

### OUTPUT

usage: python check_argument.py filename.txt

### BASH

\$ python check_arguments.py filename.txt

### OUTPUT

Thanks for specifying arguments!

### Key Points

• The sys library connects a Python program to the system it is running on.
• The list sys.argv contains the command-line arguments that a program was run with.
• Avoid silent failures.
• The pseudo-file sys.stdin connects to a program’s standard input.