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Practice 2 — Functions & Conditionals

Skills: 0, 1, 2​

Reading: the Notes sections of Class 3, Class 4, and Class 5​

Calculating Distance -- Test First​

  • Have each student or group select two landmarks (using Google Maps) that are approximately 1 mile apart according to "measure distance" function (right/ctrl click to use it). They should record the latitude and longitude for each point.
  • Students define their chosen points. For example: 
    POINT_A_LAT = 42.3505
    POINT_A_LON = -71.1054

    POINT_B_LAT = 42.3430
    POINT_B_LON = -71.1020
    (Students should use the coordinates they find.)

Write a Helper Function: deg_to_rad**​

  • The FCC approximation formula we will use to calculate distance use trigonometric functions, and Python's (from the math library) require angles to be in radians, whereas latitude & longitude are in degrees.
  • Have students write a function to convert from degrees to radians. Remember, 2 PI is the same as 360 degrees. The constant math.pi comes from Python's math library (so put import math at the top of your file).

Developing FCC Constants​

Building the Distance Function​

  • Given the following function header: 
    def dist(lat1: float, lat2: float, lon1: float, lon2: float) -> float:
        """Calculates the distance between two coordinates using FCC approximation"""
    define a function to calculate the distance. The key is that north-south distance is the difference of latitudes multiplied by KPDLAT and the east-west distance is the difference in longitudes multiplied by KPDLON, and then the pythagorean theorem can get the actual distance.

Writing a Test Case​

  • At the beginning, we found two points that we chose to be 1 mile apart -- let's write a test using those points: 
    import pytest

    def dist(lat1: float, lat2: float, lon1: float, lon2: float) -> float:
        """Calculates the distance between two coordinates using FCC approximation"""
        ...

    def test_dist():
        assert dist(POINT_A_LAT, POINT_B_LAT, POINT_A_LON, POINT_B_LON) == pytest.approx(1, abs=0.1)
  • Numeric calculations using decimal numbers will often have small inaccuracies, so tests will work better if they test that the output is not equal, but rather, within a certain bound of the expected value. pytest.approx can be given a bound, as pytest.approx(expected, abs=N), where N is some number. This checks that the output is 1 +- 0.1, i.e., that it is greater than 0.9 and less than 1.1.
  • Run the test -- what do you see?

Discovering the Bug​

  • If our FCC formulas produce a result based on our constants, why might the computed value be different from 1?
  • If tests fail, either the code is wrong or the tests are wrong. Which is the case here?
  • What is the value that is produced? (Approximately 1.609). What is the relationship between 1.609 and 1?
  • Once you figure out the bug, go back and fix the issue in the code! Re-run to confirm that the bug has been fixed.

Wrap-Up​

  • Breaking the problem into parts (helper function, constants, raw computation) helped manage complexity.
  • Test cases (e.g., using real-world data -- two points chosen to be 1 mile apart) revealed the a bug (unit mismatch).
  • In 1999, a space probe was lost because of failure to correctly convert between units! https://en.wikipedia.org/wiki/Mars_Climate_Orbiter