Discussion

Rules of Debugging

1. Fail early, fail often.
2. Always initialize from data.
3. Know what it’s supposed to do.
4. Make it fail every time.
5. Make it fail fast.
6. Change one thing at a time, for a reason.
7. Keep track of what we’ve done.
8. Be humble.
9. Test the simple things first.

And remember, a week of hard work can sometimes save you an hour of thought.

The Call Stack

Let’s take a closer look at what happens when we call fahr_to_celsius(32.0). To make things clearer, we’ll start by putting the initial value 32.0 in a variable and store the final result in one as well:

original = 32.0
final = fahr_to_celsius(original)

The diagram below shows what memory looks like after the first line has been executed:

When we call fahr_to_celsius, Python doesn’t create the variable temp right away. Instead, it creates something called a stack frame to keep track of the variables defined by fahr_to_kelvin. Initially, this stack frame only holds the value of temp:

When we call fahr_to_kelvin inside fahr_to_celsius, Python creates another stack frame to hold fahr_to_kelvin’s variables:

It does this because there are now two variables in play called temp: the parameter to fahr_to_celsius, and the parameter to fahr_to_kelvin. Having two variables with the same name in the same part of the program would be ambiguous, so Python (and every other modern programming language) creates a new stack frame for each function call to keep that function’s variables separate from those defined by other functions.

When the call to fahr_to_kelvin returns a value, Python throws away fahr_to_kelvin’s stack frame and creates a new variable in the stack frame for fahr_to_celsius to hold the temperature in Kelvin:

It then calls kelvin_to_celsius, which means it creates a stack frame to hold that function’s variables:

Once again, Python throws away that stack frame when kelvin_to_celsius is done and creates the variable result in the stack frame for fahr_to_celsius:

Finally, when fahr_to_celsius is done, Python throws away its stack frame and puts its result in a new variable called final that lives in the stack frame we started with:

This final stack frame is always there; it holds the variables we defined outside the functions in our code. What it doesn’t hold is the variables that were in the various stack frames. If we try to get the value of temp after our functions have finished running, Python tells us that there’s no such thing:

print('final value of temp after all function calls:', temp)

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-12-ffd9b4dbd5f1> in <module>()
----> 1 print('final value of temp after all function calls:', temp)

NameError: name 'temp' is not defined

final value of temp after all function calls:

Why go to all this trouble? Well, here’s a function called span that calculates the difference between the minimum and maximum values in an array:

import numpy

def span(a):
    diff = numpy.amax(a) - numpy.amin(a)
    return diff

data = numpy.loadtxt(fname='inflammation-01.csv', delimiter=',')
print('span of data:', span(data))

span of data: 20.0

Notice that span assigns a value to a variable called diff. We might very well use a variable with the same name to hold data:

diff = numpy.loadtxt(fname='inflammation-01.csv', delimiter=',')
print('span of data:', span(diff))

span of data: 20.0

We don’t expect diff to have the value 20.0 after this function call, so the name diff cannot refer to the same thing inside span as it does in the main body of our program. And yes, we could probably choose a different name than diff in our main program in this case, but we don’t want to have to read every line of NumPy to see what variable names its functions use before calling any of those functions, just in case they change the values of our variables.

The big idea here is encapsulation, and it’s the key to writing correct, comprehensible programs. A function’s job is to turn several operations into one so that we can think about a single function call instead of a dozen or a hundred statements each time we want to do something. That only works if functions don’t interfere with each other; if they do, we have to pay attention to the details once again, which quickly overloads our short-term memory.

Following the Call Stack

We previously wrote functions called fence and outer. Draw a diagram showing how the call stack changes when we run the following:

print(outer(fence('carbon', '+')))

Image Grids

Let’s start by creating some simple heat maps of our own using a library called ipythonblocks. The first step is to create our own “image”:

from ipythonblocks import ImageGrid

Unlike the import statements we have seen earlier, this one doesn’t load the entire ipythonblocks library. Instead, it just loads ImageGrid from that library, since that’s the only thing we need (for now).

Once we have ImageGrid loaded, we can use it to create a very simple grid of colored cells:

grid = ImageGrid(5, 3)
grid.show()

Just like a NumPy array, an ImageGrid has some properties that hold information about it:

print('grid width:', grid.width)
print('grid height:', grid.height)
print('grid lines on:', grid.lines_on)

grid width: 5
grid height: 3
grid lines on: True

The obvious thing to do with a grid like this is color in its cells, but in order to do that, we need to know how computers represent color. The most common schemes are RGB, which is short for “red, green, blue”. RGB is an additive color model: every shade is some combination of red, green, and blue intensities. We can think of these three values as being the axes in a cube:

An RGB color is an example of a multi-part value: like a Cartesian coordinate, it is one thing with several parts. We can represent such a value in Python using a tuple, which we write using parentheses instead of the square brackets used for a list:

position = (12.3, 45.6)
print('position is:', position)
color = (10, 20, 30)
print('color is:', color)

position is: (12.3, 45.6)
color is: (10, 20, 30)

We can select elements from tuples using indexing, just as we do with lists and arrays:

print('first element of color is:', color[0])

first element of color is: 10

Unlike lists and arrays, though, tuples cannot be changed after they are created — in technical terms, they are immutable:

color[0] = 40
print('first element of color after change:', color[0])

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-11-9c3dd30a4e52> in <module>()
----> 1 color[0] = 40
2 print('first element of color after change:', color[0])

TypeError: 'tuple' object does not support item assignment

If a tuple represents an RGB color, its red, green, and blue components can take on values between 0 and 255. The upper bound may seem odd, but it’s the largest number that can be represented in an 8-bit byte (i.e., 2⁸-1). This makes it easy for computers to manipulate colors, while providing fine enough gradations to fool most human eyes, most of the time.

Let’s see what a few RGB colors actually look like:

row = ImageGrid(8, 1)
row[0, 0] = (0, 0, 0)   # no color => black
row[1, 0] = (255, 255, 255) # all colors => white
row[2, 0] = (255, 0, 0) # all red
row[3, 0] = (0, 255, 0) # all green
row[4, 0] = (0, 0, 255) # all blue
row[5, 0] = (255, 255, 0) # red and green
row[6, 0] = (255, 0, 255) # red and blue
row[7, 0] = (0, 255, 255) # green and blue
row.show()

Simple color values like (0,255,0) are easy enough to decipher with a bit of practice, but what color is (214,90,127)? To help us, ipythonblocks provides a function called show_color:

from ipythonblocks import show_color
show_color(214, 90, 127)

It also provides a table of standard colors:

from ipythonblocks import colors
c = ImageGrid(3, 2)
c[0, 0] = colors['Fuchsia']
c[0, 1] = colors['Salmon']
c[1, 0] = colors['Orchid']
c[1, 1] = colors['Lavender']
c[2, 0] = colors['LimeGreen']
c[2, 1] = colors['HotPink']
c.show()

Making a Colorbar

Fill in the ____ in the code below to create a bar that changes color from dark blue to black.

bar = ImageGrid(10, 1)
for x in range(10):
    bar[x, 0] = (0, 0, ____)
bar.show()

Why RGB?

Why do computers use red, green, and blue as their primary colors?

Nested Loops

Will changing the nesting of the loops in the code above — i.e., wrapping the Y-axis loop around the X-axis loop — change the final image? Why or why not?

Where to Change Data

Why did we transpose our data outside our heat map function? Why not have the function perform the transpose?

Return Versus Display

Why does the heat map function return the grid rather than displaying it immediately? Do you think this is a good or bad design choice?

Generative AI

ImportantGenerative AI: Concept

The section on generative AI is intended to be concise but Instructors may choose to devote more time to the topic in a workshop. Depending on your own level of experience and comfort with talking about and using these tools, you could choose to do any of the following:

• Explain how large language models work and are trained, and/or the difference between generative AI, other forms of AI that currently exist, and the limits of what LLMs can do (e.g., they can’t “reason”).
• Demonstrate how you recommend that learners use generative AI.
• Discuss the ethical concerns listed below, as well as others that you are aware of, to help learners make an informed choice about whether or not to use generative AI tools.

This is a fast-moving technology. If you are preparing to teach this section and you feel it has become outdated, please open an issue on the lesson repository to let the Maintainers know and/or a pull request to suggest updates and improvements.

Generative AI: Concept B

It is increasingly common for people to use generative AI chatbots such as ChatGPT to get help while coding. You will probably receive some useful guidance by presenting your error message to the chatbot and asking it what went wrong. However, the way this help is provided by the chatbot is different. Answers on StackOverflow have (probably) been given by a human as a direct response to the question asked. But generative AI chatbots, which are based on an advanced statistical model, respond by generating the most likely sequence of text that would follow the prompt they are given.

While responses from generative AI tools can often be helpful, they are not always reliable. These tools sometimes generate plausible but incorrect or misleading information, so (just as with an answer found on the internet) it is essential to verify their accuracy. You need the knowledge and skills to be able to understand these responses, to judge whether or not they are accurate, and to fix any errors in the code it offers you.

💡 Treat AI suggestions as drafts: verify correctness, safety, and relevance.

Generative AI: Concept C

In addition to asking for help, programmers can use generative AI tools to generate code from scratch; extend, improve and reorganise existing code; translate code between programming languages; figure out what terms to use in a search of the internet; and more. However, there are drawbacks that you should be aware of.

The models used by these tools have been “trained” on very large volumes of data, much of it taken from the internet, and the responses they produce reflect that training data, and may recapitulate its inaccuracies or biases. The environmental costs (energy and water use) of LLMs are a lot higher than other technologies, both during development (known as training) and when an individual user uses one (also called inference). For more information see the AI Environmental Impact Primer developed by researchers at HuggingFace, an AI hosting platform. Concerns also exist about the way the data for this training was obtained, with questions raised about whether the people developing the LLMs had permission to use it. Other ethical concerns have also been raised, such as reports that workers were exploited during the training process.

We recommend that you avoid getting help from generative AI during the workshop for several reasons:

Generative AI: Worked Solution

1. For most problems you will encounter at this stage, help and answers can be found among the first results returned by searching the internet.
2. The foundational knowledge and skills you will learn in this lesson by writing and fixing your own programs are essential to be able to evaluate the correctness and safety of any code you receive from online help or a generative AI chatbot. If you choose to use these tools in the future, the expertise you gain from learning and practising these fundamentals on your own will help you use them more effectively.
3. As you start out with programming, the mistakes you make will be the kinds that have also been made – and overcome! – by everybody else who learned to program before you. Since these mistakes and the questions you are likely to have at this stage are common, they are also better represented than other, more specialised problems and tasks in the data that was used to train generative AI tools. This means that a generative AI chatbot is more likely to produce accurate responses to questions that novices ask, which could give you a false impression of how reliable they will be when you are ready to do things that are more advanced.