lab01 : FtoC and CtoF with test cases

num ready? description assigned due
lab01 true FtoC and CtoF with test cases Wed 10/02 12:00AM Wed 10/16 08:59AM

In this lab, you’ll practice:

Step 0: Install pytest for your account (or on your machine)

This lab is one that you may find you need to do on the CSIL machines. It’s important to differentiate between the Python shell >>> vs the terminal $.

It is probably the case that pytest is not installed for your version of Python3. You can check by typing python3 at the Terminal prompt to get to the Python Shell Prompt >>>, and then typing import pytest.

If you get an error message like the one shown below, then pytest is not installed. However, if you do not get an error message, skip to Step 1.

[cgaucho@csil-12 ~]$ python3
Python 3.4.3 (default, Aug 9 2016, 15:36:17) [GCC 5.3.1 20160406 (Red Hat 5.3.1-6)] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import pytest
Traceback (most recent call last):
File "", line 1, in ImportError: No module named 'pytest'
>>> exit()
[cgaucho@csil-12 ~]$ pip3 install --user pytest

In order to exit the python shell in terminal press Ctrl+D or type exit() in order to return to the normal terminal.

To install pytest, type this command into the terminal session (the Unix Terminal prompt) to install pytest for your CSIL account:

pip3 install --user pytest

To install pytest on Windows, see this tutorial

You can also try this command on Mac. It might work, or it might not. If it does—great, then you can do this lab on your own machine. If not, then you’ll need to do it on CSIL.

The output should look something like this:

[cgaucho@csil-12 ~]$ pip3 install --user pytest
You are using pip version 7.1.0, however version 9.0.1 is available.
You should consider upgrading via the 'pip install --upgrade pip' command.
Collecting pytest
  Downloading pytest-3.2.1-py2.py3-none-any.whl (186kB) 100% 188kB 1.5MB/s
Collecting py>=1.4.33 (from pytest)
  Downloading py-1.4.34-py2.py3-none-any.whl (84kB) 100% 86kB 2.0MB/s
Requirement already satisfied (use --upgrade to upgrade): setuptools in /usr/lib/python3.4/site-packages (from pytest)
Installing collected packages: py, pytest
Successfully installed py pytest
[cgaucho@csil-12 ~]$

To tell whether it worked or not, try the import pytest command again:

[cgaucho@csil-12 ~]$ python3
Python 3.4.3 (default, Aug 9 2016, 15:36:17) [GCC 5.3.1 20160406 (Red Hat 5.3.1-6)] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import pytest
>>>

The lack of an error message (just another >>> prompt) means “it worked!”. We are going to use the Python prompt in the next step anyway, so just stay at the Python prompt. (Or if you need to get out of Python, use CTRL-D to return to the Unix shell prompt.)

Step 1: Warmup–experiencing floating point inaccuracy

If you are not already at the Python prompt, bring up a terminal window, and just type python3. This should give you the Python Shell Prompt (>>>) where you can type in some expressions and see the resulting values.

Type in the import math, followed by math.sqrt(2). It should look like this:

>>> import math
>>> math.sqrt(2)
1.4142135623730951
>>>

Note that the import statement gives us access to math.sqrt(). The name that comes after the key word import is called a library (here we are importing the math library). This allows the program to use other code like math.sqrt() that we didn’t write ourselves (someone else wrote it for us). There are a lot of libraries that come with programming language (such as math), and some libraries that can be downloaded and imported into your program (see Section 1.2 in Perkovic). In either case, using libraries helps developers focus on solving their problems and manage their code without having to re-implement certain functionality (like making a sqrt function from scratch).

The value we get back is the square root of 2, which is an irrational number—its decimal representation goes on forever. Unfortunately, real world computing devices typically store numbers with a finite number of decimal places†. So, the representation we see for the square root of two is an approximation.

(† Technically, "binary places", or "binary digits" rather than "decimal places". For purposes of this discussion it amounts to the same thing. Also, some computer systems do work with "symbolic" representations of numeric quantities, e.g., retaining √2 or π as symbolic values rather than as numerical approximations. On those systems, you can get exact results, without losing precision, at the expense of speed. We won't discuss that kind of software in this course.)

We can see this if we multiply math.sqrt(2) by itself. Try it:

>>> math.sqrt(2) * math.sqrt(2)
2.0000000000000004
>>>

See that pesky 4 digit in the ten quadrillionths place? My goodness, we are really, really close to 2.0, but if we ask whether the values are equal, Python says no:

>>> math.sqrt(2) * math.sqrt(2)== 2.0
False

In fact, Python is very clear about the difference between 2.0 and math.sqrt(2) * math.sqrt(2), and can even tell us how big that difference is. The 4 digit is only the tip of the very, very, very small iceberg:

>>> math.sqrt(2) * math.sqrt(2)- 2.0
4.440892098500626e-16
>>>

We can deal with this in our code by subtracting the expected value from the result, taking its absolute value, and finally checking if it is less than some tolerance. This might come in handy in your future coding experiences, but for now we’ll leave it here.

>>> a = 5
>>> b = 5.00001
>>> a == b
False
>>> abs(a - b) < .001
True

We should plan to program with the knowledge that some mathematics operations are approximations (especially irrational numbers). When we test software involving floating point numbers, we must allow for some inaccuracy. This “allowable inaccuracy” is sometimes called the tolerance, and it might be a small value such as 0.001 (1x10-3, or 0.000001 (1x10-6).

In Python, we can write 0.001 as 1e-03, and 0.000001 as 1e-06. (The lowercase e is the way that Python represents scientific notation.)

You can see that Python, by default, formats numbers in this notation once the fifth decimal place is reached:

>>> 0.01
0.01
>>> 0.0001
0.0001
>>> 0.00001
1e-05
>>> 0.000001
1e-06
>>>

We’ll come back to that idea later in this lab.

As a reminder, CTRL-D gets you out of the Python Shell Prompt (>>>) and returns you to the Unix shell prompt.

Step 2: Make a ~/cs8/lab01 folder

In the previous lab, you should already have created the ~/cs8/lab00. You are now going to create a folder ~/cs8/lab01 for the files for this lab.

In general, it’s probably a good idea to keep your work for this class under ~/cs8, in folders called lab00, lab01, lab02, etc.

This isn’t exactly required (no-one is going to check), but it’s probably a good habit to develop. Here’s why: all the rest of the instructions will be written based on the assumption that you did things this way. And if you continue to take CS courses at UCSB, you’ll often find that’s the case from one course to the next. Plus, it helps you organize your files from different labs.

So, we strongly encourage you to do it.

As a reminder:

With that information, you should be able to determine how to create a ~/cs8/lab01 directory, and make that directory your current working directory (the one that comes up when you type pwd.) Do that now. (Remember that creating and navigating directories happens using the terminal shell prompt, also known as the Unix command line, marked by $.)

Then, you are ready for the next step.

Step 3: Create a file called convert.py in your ~/cs8/lab01 directory

The contents of convert.py should be as shown below: it should contain two Python function definitions that, at the moment are incorrect.

Choose “File => New File” in IDLE to bring up an “untitled” window, then copy and paste this code into that window.

Note that the formulas for converting between Celsius and Fahrenheit are incorrect. That’s deliberate, so just go with it for now. We’ll fix those at a later step.

def fToC(fTemp):
    return fTemp - 32  # TODO: Fix this line of code

def cToF(cTemp):
    return cTemp + 32 # TODO: Fix this line of code

The code above is how we define functions in python. We will work on defining our own functions throughout the course.

On a very high level, the def fToC(fTemp) and def cToF(cTemp) is what we call a function signature.

Step 4: Test your code by hand

To test this code, we’ll first do what many programmers do: test the code by hand.

That is, we’ll run the file in IDLE, and then “call the function” (i.e. enter some function calls in the Python shell) to see what results we get. These two functions are supposed to convert between Fahrenheit where water freezes at 32 degrees, and Celsius where it freezes at 0 degrees. Let’s see if they work properly.

Use the Run Module command to run the code: doing so will definte the functions (i.e., make Python aware that they exist and what they are supposed to do according to the provided function definitions). You can then try entering these function calls at the Python Shell prompt. You should see output similar to what is shown below:

>>> fToC(32)
0
>>> cToF(0)
32
>>>

As you can see, for those two particular values, the function appears to return the correct answer: 32 degrees fahrenheit is indeed 0 degrees celsius, and 0 degrees celsius is indeed 32 degrees fahrenheit.

So clearly, testing with a single value is not enough. Indeed, if we test with another well known value, 212 Fahrenheit and 100 Celsius (the boiling point of water), we see that the output is incorrect:

>>> fToC(212)
180
>>> cToF(100)
132
>>>

One of the problems with testing by hand is that it is tedious, and folks have a tendency to skip it. So, experienced programmers have learned that it’s generally a better idea to automate the process of testing. We’ll learn how to do that next. We’ll see that when we set up these four tests, two of them will pass, and two of them will fail.

Step 5: Setting up automated tests

Add this line at the top of your convert.py file:

import pytest

Then, add the following code to your convert.py file after the function definitions for ftoC and cToF that defines four automated tests:

def test_fToC_freezing():
   assert fToC(32.0)==pytest.approx(0.0) 

def test_cToF_freezing():
   assert cToF(0.0)==pytest.approx(32.0) 

def test_fToC_boiling():
   assert fToC(212.0)==pytest.approx(100.0) 

def test_cToF_boiling():
   assert cToF(100.0)==pytest.approx(212.0)

These are automated tests that use a module(library) known as pytest. When defining tests using the pytest library, we typically define functions that:

If the expresssion after assert is true, the test passes, otherwise it fails, and gives us an error message which explains what went wrong.

We are using pytest.approx() here because any time you are testing with floating point numbers, we have to be aware that there may be some inaccuracy, as we discussed earlier. Using pytest.approx() is a cleaner way of subtracting the expected value from the actual value, taking the absolute value, and checking if it is les than some tolerance which we touched on in Step 1. Using pytest.approx() allows for a tolerance of 1.0e-04.

(Recall our discussion of what happens when you multiply math.sqrt(2.0) by itself. Here, it’s probably overkill since we aren’t using any irrational numbers, but it is still safer to always use some way of approximating equality when dealing with floating point.)

You can click the plus to open a dropdown showing what your entire file should look like at this point:

Contents of convert.py so far

import pytest

def fToC(fTemp):
    return fTemp - 32

def cToF(cTemp):
    return cTemp + 32
    
def test_fToC_freezing():
   assert fToC(32.0)==pytest.approx(0.0) 

def test_cToF_freezing():
   assert cToF(0.0)==pytest.approx(32.0) 

def test_fToC_boiling():
   assert fToC(212.0)==pytest.approx(100.0) 

def test_cToF_boiling():
   assert cToF(100.0)==pytest.approx(212.0)

After entering this, save the file and use “Run Module” to make sure there are no error messages (error messages are discplayed as red output in the Python Shell Window). If there are any, make sure to fix them before running the next step.

Step 6: Running the test cases

Running the test cases requires us to go outside of IDLE back to the terminal shell prompt. Make sure to use quit() or Ctrl-D to exit the python interpreter (>>>). Once you are back on the command line prompt ($) continue on.

Your current directory needs to be the same one that your convert.py file is stored in. That should be ~/cs8/lab01, but if it isn’t, then fix things so that the convert.py file is in that directory, and your current working directory is set to that directory. If you need help, ask for assistance.

You should be able to type the ls command (or on Windows, dir) at the terminal shell prompt and see the convert.py file listed:

your-prompt-here $ ls
convert.py
your-prompt-here $

When that’s the case, copy and then paste this command after the $ in your terminal window:

python3 -m pytest convert.py

You should see output like what’s shown below. It may be a little overwhelming at first. Once you know what you are looking for, it is very easy to read. After the output, there is a guide to understanding it.

169-231-175-204:lab01 cgaucho$ python3 -m pytest convert.py
==================================== test session starts ====================================
platform darwin -- Python 3.6.2, pytest-3.2.1, py-1.4.34, pluggy-0.4.0
rootdir: /Users/cgaucho/github/ucsb-cs8/Lecture5_0816/lab01, inifile:
collected 4 items                                                                            

convert.py ..FF

========================================= FAILURES ==========================================
_____________________________________ test_fToC_boiling _____________________________________

    def test_fToC_boiling():
>      assert fToC(212.0)==pytest.approx(100.0)
E      assert 180.0 == 100.0 ± 1.0e-04
E       +  where 180.0 = fToC(212.0)
E       +  and   100.0 ± 1.0e-04 = <function approx at 0x1026c40d0>(100.0)
E       +    where <function approx at 0x1026c40d0> = pytest.approx

convert.py:16: AssertionError
_____________________________________ test_cToF_boiling _____________________________________

    def test_cToF_boiling():
>      assert cToF(100.0)==pytest.approx(212.0)
E      assert 132.0 == 212.0 ± 2.1e-04
E       +  where 132.0 = cToF(100.0)
E       +  and   212.0 ± 2.1e-04 = <function approx at 0x1026c40d0>(212.0)
E       +    where <function approx at 0x1026c40d0> = pytest.approx

convert.py:19: AssertionError
============================ 2 failed, 2 passed in 0.03 seconds =============================
169-231-175-204:lab01 cgaucho$

Ok, let’s now break down this output.

Step 7: Understanding the output of pytest

Here’s how to understand pytest output.

  1. Get the big picture first from the convert.py ..FF line.

    Look for a line near the beginning that has the name of your file, followed by a list of either dots, letter E or letter F characters, like this one:

    convert.py ..FF

    In this case, the . characters are tests that passed. If you have four tests, then ideally, you’d want to see four dots, like this convert.py …., which means that four tests for convert.py all successfully passed.

    Instead, here, we see ..FF, which means we had two tests that succeeded and two tests that failed. Later in the output, we’ll see more detail about each of those failures.

  2. Understand the overall structure of the output.

    The rest of the output will be divided into sections, one for each failure. Here is what it look like with the details taken out so that you can see the big picture more easily:

    ==================================== test session starts ====================================
(blah blah here that you can ignore)
   
convert.py ..FF
========================================= FAILURES ==========================================
_____________________________________ test_fToC_boiling _____________________________________

...
(details about the first test case failure are here)
...
   
_____________________________________ test_cToF_boiling _____________________________________

...
(details about the second test case failure are here)
...
   
========================= 2 failed, 2 passed in 0.03 seconds =============================

    Note that the last line gives us a nice summary: 2 failed, 2 passed in 0.03 seconds. We now know that we need to focus on the two failures. And the headers tell us which test cases failed, namely test_fToC_boiling and test_cToF_boiling. So let’s focus on those next, by first looking in detail at the first one:

  3. Focus in on the first test case failure.

    Let’s focus just on the detailed output for the first test case failure, test_fToC_boiling. What does all of the detailed output mean?

    In general, its a breakdown of why the assertion turned out to be false, showing every step in the calculation. Let’s break it down one line at a time:

    line of output meaning
    def test_fToC_boiling(): first line of the failing test case
    E assert 180.0 == 100.0 ± 1.0e-04 This is the assertion that turned out not to be true
    E + where 180.0 = fToC(212.0) This tells us why 180.0 was on the left hand side of the ==. It was the result of computing ftoC(212.0)
    E + and 100.0 ± 1.0e-04 = <function approx at 0x1026c40d0>(100.0) This tells us why 100.0 ± 1.0e-04 was on the right hand side of the ==. It shows the expected value (100.0) and the tolerance ( ± 1.0e-04).
    E + where <function approx at 0x1026c40d0> = pytest.approx This tells us that pytest.approx was used to calculate the tolerance.
       
    convert.py:16: AssertionError This shows which line in the file convert.py had the failed assertion, namely, line 16. That helps us find the error faster if we are dealing with a large file of code.

    If we look at this, we can see that amidst all of the clutter is the crucial fact that fToC(212.0) returned 180.0 when what we were expecting was 100.0, with a tolerance of ± 1.0e-04.

Step 8: Fixing the code

So, if you have failing test cases, the thing to do is fix the code so that the test cases pass.

To do that you’ll need to correct the forumla.

Keep in mind that in Python:

Also, the order of operations in Python is that multiplication and division are done before addition and subtraction. Some examples:

When you replace return ftemp - 32.0 with the correct formula for converting a Fahrenheit temperature to Celsius, you should remove the comment that says # TODO: Fix this line of code .

You’ll also want to replace the similar line in the cToF function.

When you have the test cases passing, try running the pytest command again (shown below)—remembering that:

python3 -m pytest convert.py

When you see four passing tests, your output will look like this. Also, the last line will be a pleasant shade of green instead of an angry looking red.

169-231-175-204:lab01 cgaucho$ python3 -m pytest convert.py
======================== test session starts =========================
platform darwin -- Python 3.6.2, pytest-3.2.1, py-1.4.34, pluggy-0.4.0
rootdir: /Users/cgaucho/github/ucsb-cs8/Lecture5_0816/lab01, inifile:
collected 4 items                                                     

convert.py ....

====================== 4 passed in 0.01 seconds ======================
169-231-175-204:lab01 cgaucho$

At that point, you are ready to submit your work to Gradescope.

Step 9: Submit your convert.py file to Gradescope

Navigate to the Lab assignment “Lab01” and upload your convert.py, similar to how you submitted hello.py for Lab00. Gradescope will check if your fToC(fTemp) and cToF(cTemp) functions are correct. If your tests do not pass, go back to these functions and double-check your conversion formulas and function syntax.

Final Step: Log Out

Actually, this is the final step of every lab.

In fact, you should do this every time you walk away from a lab computer, either in Phelps 3525 or CSIL.

Here’s how: