Rules of Debugging
- Fail early, fail often.
- Always initialize from data.
- Know what it’s supposed to do.
- Make it fail every time.
- Make it fail fast.
- Change one thing at a time, for a reason.
- Keep track of what we’ve done.
- Be humble.
- 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
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
Python doesn’t create the variable
temp right away.
it creates something called a stack frame
to keep track of the variables defined by
this stack frame only holds the value of
When we call
Python creates another stack frame to hold
It does this because there are now two variables in play called
the parameter to
and the parameter to
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
to hold the temperature in Kelvin:
It then calls
which means it creates a stack frame to hold that function’s variables:
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 is done,
Python throws away its stack frame
and puts its result in a new variable called
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?
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.max(a) - numpy.min(a) return diff data = numpy.loadtxt(fname='inflammation-01.csv', delimiter=',') print('span of data:', span(data))
span of data: 20.0
span assigns a value to a variable called
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
as it does in the main body of our program.
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
outer. Draw a diagram showing how the call stack changes when we run the following:
Let’s start by creating some simple heat maps of our own
using a library called
The first step is to create our own “image”:
from ipythonblocks import ImageGrid
import statements we have seen earlier,
this one doesn’t load the entire
it just loads
ImageGrid from that library,
since that’s the only thing we need (for now).
Once we have
we can use it to create a very simple grid of colored cells:
grid = ImageGrid(5, 3) grid.show()
Just like a NumPy array,
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)
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 = 40 print('first element of color after change:', color)
--------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-11-9c3dd30a4e52> in <module>() ----> 1 color = 40 2 print('first element of color after change:', color) 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
To help us,
ipythonblocks provides a function called
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 do computers use red, green, and blue as their primary colors?
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?