Description

Question 1

It’s time to put all of your Python skills to work. This time we are giving you a non-trivial problem and a method to solve it, but giving you very little guidance on how to use python solve it. You are allowed to use any of the Python language features and problem solving methods that we have discussed in class or used on assignments or in labs in order to solve the problem. You will be graded not only for correctness, but also for making good choices about how you store data, how your organize your program, how well you document (comment) your program, and how well you test your program.

Problem Description

In order to determine the feasibility of growing weeds as a cash crop in Saskatchewan, samples have been taken from wild weeds in various locations. In each sample the amount of vitiamin C, and the amount of gamma-linolenic acid (GLA) has been measured. The samples with low levels of nutrients or samples containing toxins are discarded, so in the data only samples from edible weeds remain. The next step is to understand how many species of edible weeds are present at a each location.

Your task for this assignment is to write a program to display the different species of weed present at a given location, based only on the given data. It is unknown how many species may be involved at any one location , but the number is believed to be between two and four. At a particular location, the samples from one particular species will have similar levels of nutrients and determining the species present is a matter of grouping the data so samples in a given group belong to the same species. This grouping process is called clustering. Given a file of pairs of integers, giving the levels of Vitamin C and GLA, your task to to plot the data with each species given a different color, and to produce a representative for each species at that location. The representative of a species will have the average amounts of nutrients of the members of the species.

Problem Details

Input Data

A given input file is associated with a particular area of the province. Each line of the file contains the infomation for a particular sample and the Vitamin C and GLA measures for a sample is separated by a

comma. For example

40,40

10,10

200,200

230,231

40,43

15,45 220,190

is the contents of the file backyard.txt giving information on seven samples, and the last sample has vitamin C level 220 and GLA level 190.

Species Identification

Since the number of species at a location is not known, we will need to consider the possibility that there are s species present, where s can vary from 2 to 4.

Given s and a data file we need to cluster the data into s groups and determine what the nutrient levels of an representative of a group would be. Note that the representative for a group will generally not be an actual member of the group, but a “fake” member having the “average” nutrients of the members in the group.

To do this as a first cut, we first grab the first s samples, and use the nutrient levels of these samples as those of the representatives (reps) of the s species. Keep track of the reps for each species separately from the data on the samples, as although they start off as having the same nutrient levels as individual samples, later they will be “fake” members and have different nutrient levels then real actual samples do.

A sample will assumed to belong to the same species as one of the reps when it is closer to that rep than to any other rep. We measure closeness by the usual Euclidean distance, ie. the distance from sample

(u,v) to rep (x,y) is ^p(u−x)²+(v−y)². We now label all the samples as to which of the s reps they are closest to. This process is called labelling.

We next find new reps for each of the s groups. The new rep for a group will have a Vitamin C level which is the average of the Vitamin C levels of the samples in the group, and likewise it will have a GLA level which is the average of the GLA levels of the group members. This process is called selecting representatives.

Now since the nutrient levels of the reps have changed, we relabel all the samples so they again are labeled like the closest rep and we again update the nutrient levels of the reps since the group members have changed. This process of labelling and updating is repeated over and over until there are no more changes in the group memberships.

To recap, we iterate over the following two steps until the there are no more changes.

• Select representatives
• Use the representtives to label the samples

Display Results

For a given file and number of species s, plot the samples so that the samples from the same species have the same color, but samples from different species have different colors. Also plot the reps for each species.

For the backyard.txt input file with s equal to two, the plot should look like this:

We are providing you with four input files for four different locations. For each location submit the plot for the s which best seems to match the data at that location. Although there are some algorithmic methods to decide which s to use, here we will assume there is a human in the loop (“you”) to decide which s to use for the plot you submit.

For example, for location file locationA.txt select best plot and save it in the file a9-locationA.png.

Testing

Because you do not have the answers in advance for most of the input files, you will have to employ your testing skills to ensure the correctness of your program. Therefore, you should create a set of tests and a matching test driver for each function that you write as part of solving the main problem. In a separate file from your main program, hand in any test drivers that you write.

Hints

• Divide up the work you need to do to solve this problem into subtasks and determine the best order in which to solve them. Use your lab sections during the next week to plan your approach!
• Make sure the code for each sub-task is working before you proceed to the next one (using testing).

What to Hand In

• Submit your solution to the main problem in a file called a9q1.py
• Submit your test drivers in a file called a9q1_tests.py
• Submit four output files .png files, one for each input location file. You save the plot for the s which best seems to match the data at a given location. For example, for location file locationA.txt select the best plot and submit it in the file a9-locationA.png. To save a plot in pycharm right click (control click on a Mac) on the thumbnail of the plot and a menu will pop up allowing you to save the plot as a .png file.
• You do not have to submit the provided input files themselves.

Evaluation Criteria

A detailed grading rubric is found at the end of this document. Evaluation criteria include:

• Appropriate organization of the program using functions and/or modules.
• Use of appropriate data types.
• Good use of commenting and docstrings.
• Evidence of thorough testing (test cases and test drivers).
• Correctness of program.