CS 112 Assignment 5

Due: Thursday, March 15, at 5:00pm

You can turn in your assignment up until 5:00pm on 3/15/12 without penalty, but it is best to hand in the assignment at the beginning of class. Your hardcopy submission should include a cover sheet and printouts of five code files: makeThumbs.m, getFavorites.m, supplyDemand.m, loadData.m, and computeEQ.m. Your electronic submission is described in the section Uploading your saved work

Reading

The following material in the fourth edition of the text is especially useful to review for this assignment: 190-200 and 219-229 (third edition: pages 155-165, 204-205 and 208-218). You should also review notes and examples from Lectures #7, 8, 10 and 11, and Labs #6 and 7.

Getting Started: Download assign5_programs from cs112d

Use Fetch or WinSCP to connect to the CS server using the cs112d account and download a copy of the assign5_programs folder from the cs112d directory onto your Desktop. Rename the folder to be yours, e.g. sohie_assign5_programs. Set the MATLAB's Current Directory appropriately.

The assign5_programs folder contains two data files, mathworks.mat and widget.xls, and one code file, displayCurves.m, to be used for Problem 2. It also contains a folder named images that contains some class photos for Problem 1. For both problems, you will be writing MATLAB functions or scripts from scratch.

Uploading your saved work

Use Fetch or WinSCP again to upload your saved work, but this time you should connect to the CS file server using your personal user account name and password. After logging in to your account:

• Browse through your directory and find the drop/assign05 folder
• Upload your assign5_programs folder into your drop/assign05 folder
• When done uploading, be sure to delete your renamed assign5_programs folder from the Desktop by dragging it to the trash can, and then empty the trash (Finder--> Empty Trash).
• Be sure to Exit out of MATLAB when you are done

When you are done with this assignment, you should have all the code files stored in your assign5_programs folder that you wrote in addition to the files that we supplied for you. After creating thumbnail versions of the images in Problem 1, you may want to remove the images folder from the version of assign5_programs that you upload to your personal directory.

Problem 1: Image processing in batches

Scientists often need to process a collection of images in a batch. It can be cumbersome to handle each photo individually. For this problem, you'll use a set of 17 digital photos taken during CS112 lecture this semester (to save space, the photos have been converted to grayscale). The set of photos are in the assign5_programs folder in a subfolder called images. In this exercise, you'll write two MATLAB functions to process the set of photos.

Step 1. Creating a set of thumbnails

Smaller versions of a photo are often called thumbnails. Write a function named makeThumbs that creates a thumbnail version of each image in the images folder and stores the new set of thumbnail images in a folder called thumbnails. The thumbnails folder should be created at the same level as the images folder.

In order to write this function, you'll need to be able to keep track of filenames. Some built-in MATLAB functions that will come in handy: filesep, mkdir, pwd, and dir. The functions imread and imwrite can be used to read images from files and write new images to files.

Requirements of makeThumbs.m

• makeThumbs should assume that there is a folder called images that contains the set of images for processing.
• makeThumbs should have one input parameter, called sample, that indicates how often the original image should be sampled. For example, makeThumbs(4) would sample every 4th pixel of the original image in the horizontal and vertical directions to create a thumbnail that is one-quarter the original size.
• Assume that you do not know in advance how many images are in the images folder, nor the exact filename of the images. You may, however, assume that all image files in the images folder end in '.jpg'
• makeThumbs should create a new folder called thumbnails to store the thumbnail versions of the originals. The thumbnail images should have the same filename as the original images, but with the prefix thumb added in front, as shown for the Harry Potter image below. For example, suppose the original images are named: imagea.jpg, imageb.jpg, etc. After running your function, there should be a new folder called thumbnails that contains a set of images named thumbimagea.jpg, thumbimageb.jpg, etc.
• Click here for a more detailed description of the folders/files your function should generate.

original image imagea.jpg	thumbnail image thumbimage.jpg

After successfully generating your set of thumbnails, delete the original set of images (delete the entire images folder). The next function you'll write (described below) works on the thumbnail images.

Step 2. Pick out your favorite images

For this part, write a function called getFavorites that allows the user to step through the set of thumbnails, indicating the user's top three favorites. The user may step through the set of images multiple times before selecting her three favorites. Your function must display the three chosen images together, and also write the three favorite images to a new folder called favorites. In the favorites folder, the images should maintain the same filename. For example, if the original thumbnail image is named thumbPICTURE0001.JPG, then the favorite image (in the favorites folder, which should be at the same level as the images folder) should also be called thumbPICTURE0001.JPG.

Here is an example of the display of the three favorite images:

And here is a sample run of getFavorites. Note that this is just an example. Please add your own personal flavor to your function:

>> getFavorites
Please select your three favorite images
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> f
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> f
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> f
Thanks!  Your 3 favorite image(s) are now stored in the favorites folder.
>> 

>> getFavorites
Warning: Directory already exists/
> in getFavorites at 14
Please select your three favorite images
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> f
  Type n for next image, f to add favorite, q to quit ==> n
  Type n for next image, f to add favorite, q to quit ==> q
Thanks!  Your 1 favorite image(s) are now stored in the favorites folder.

Notes:

1. In the first run of getFavorites above, the user cycled through the set of 10 pictures more than one time in the selection process
2. When the user picked her third favorite picture, the program ended and the three images were display together
3. MATLAB displays a warning when a folder already exists (it's ok for your program to generate this warning)
4. At the end of the code execution above, there are four images in the favorites folder (three from the first run, and one additional image from the second run).

What to turn in

Your assign5_programs folder should contain the functions makeThumbs.m and getFavorites.m as well as the thumbnails and favorites folders (the original images folder should be deleted).

Problem 2: ECON 101 - Supply and Demand

A competitive market has many buyers and sellers of the same goods or services, and is described well by the supply and demand model. In this model, the quantity of a good supplied by a producer and the quantity demanded by the consumer both depend on the price of the good. The law of supply says that the higher the price, the more the producer will supply, while the law of demand says that the higher the price, the less the consumer will demand. The diagram below shows simple supply and demand curves that capture these relationships between the price of a good and the quantity that is supplied by the producer or demanded by the consumer. The law of supply and demand says that the market price of the product will settle at the intersection of the supply and demand curves, called the equilibrium point. If the price is too low, then consumers will demand more than the producer is willing to supply, leading to a shortage of the good and willingness of consumers to pay more, driving the price up. On the other hand, if the price is too high, producers may produce more than consumers will buy, leading producers to lower the price. At the equilibrium point, the price of the product is set so that producers sell exactly the same quantity of goods that consumers will buy.

Changes in the overall demand for, or supply of a product can shift the equilibrium point. In the picture below, demand increases from the curve D1 to the curve D2, while the supply curve remains the same. This leads to an increase in the equilibrium price, from P1 to P2.

In this problem, you will create a program that allows the user to explore the interaction between supply and demand for two small markets. The first is the market for a new student version of MATLAB supplied by Mathworks, Inc., and the second is the market for a new widget supplied by J. J. Widget Co. This problem will also give you practice with creating a larger program that integrates multiple code files that implement different aspects of the task. There are four subtasks in this case: (1) loading the data for the supply and demand curves, (2) computing the equilibrium point, (3) displaying the results and (4) controlling the overall process. Task (3) has already been completed for you. Your goal is to write functions to implement tasks (1) and (2) and a script to complete task (4). The functions for tasks (1) and (2) can be written and tested independently.

When designing a large program, a good way to start is to draw a picture of the main components of the program. Write comments in English to describe the information needed for, or supplied by, each component, and the main actions that need to be performed within each component. The picture below illustrates this information for the supply and demand program:

Each arrow links a step where a function should be called to the function description. Some of the comments will translate into a single line of code, while others may require multiple lines of code to implement. The next four sections describe each part of the program in more detail.

(1) Loading the data

Write a function named loadData that loads in the supply and demand data from a file and returns the data in four output vectors that store the prices and quantities for the supply and demand curves. This function should prompt the user to select the source of data that they would like to analyze. There are two sources of data for this problem, stored in the files mathworks.mat and widget.xls. For the first source, imagine that Mathworks, Inc. is planning to launch a new student version of MATLAB and conducts a market survey to determine a reasonable price for this new product. The survey data, shown below, indicates the expected quantities of MATLAB that students will demand at a set of prices shown in the first column, for six broad areas of the US. The numerical data in the table is stored in a variable matlabDemand in the file mathworks.mat in the assign5_programs folder.

        area1   area2   area3   area4   area5   area6
$175     500     540     460     525     575     475
$150     600     650     550     620     660     580
$125     800     845     740     820     880     760
$100    1100    1160    1050    1130    1170    1070
$75     1500    1550    1445    1525    1585    1480
$50     2000    2055    1955    2030    2080    1985

For this data, the total quantity that students will purchase at each price is the sum of the quantities for the six areas. The variable matlabSupply in the mathworks.mat file stores the data in the following table, which indicates the quantity that Mathworks, Inc. is willing to supply for each of the same prices:

       quantity
$175     7250
$150     6750
$125     6000
$100     5000
$75      3500
$50      1000

Data related to the sale of widgets is stored in the widget.xls file. You can use the xlsread function to load the spreadsheet into a matrix, which will have three columns. The quantities of widgets for both supply and demand are listed in the first column of this matrix. The demand prices are listed in the second column and supply prices are contained in the third column.

(2) Computing the equilibrium point

Write a function named computeEQ that computes and returns the equilibrium price and quantity, given six inputs. The first four inputs should be required: prices for the supply curve, prices for the demand curve, quantities for the supply curve and quantities for the demand curve. The last two inputs should be optional: change in supply quantities and change in demand quantities. Consider developing this function in two steps, where the first step determines the equilibrium point without allowing a change in supply or demand. One strategy for finding the intersection of the supply and demand curves is to fit each set of data with a smooth curve such as a quadratic function, and then determine where these two functions cross each other. Suppose you want to approximate the supply and demand curves with a quadratic function of the form:

y = ax² + bx + c

where x represents quantity and y represents price. The built-in function polyfit calculates the coefficients of a polynomial function of degree n that best fits a given set of points, and returns a vector of these coefficients. This function has three inputs corresponding to the x and y coordinates of the points and the degree of the polynomial. The companion function polyval calculates the values of a polynomial function given a vector of its coefficients and a vector of x values. In the following script, polyfit is used to derive the coefficients of a quadratic function that best fits a set of points whose coordinates are given in the vectors x and y. These coefficients are then used by polyval to calculate values of this polynomial for an evenly spaced set of x coordinates from 1 to 13. The resulting plot is shown below.

% script to test polyfit and polyval
x = [1  3  7  11  13];
y = [10  4  0  1  2];
coeffs = polyfit(x, y, 2);
x2 = 1:13;
y2 = polyval(coeffs, x2);
plot(x, y, 'b', 'Linewidth', 2)
hold on
plot(x2, y2, 'r', 'Linewidth', 2)
axis([0 14 0 11])
axis equal

You can use polyfit to compute the coefficients of quadratic functions that approximate the supply and demand curves, and use polyval to construct a set of at least 100 samples of each of these curves over the range of quantities spanned by the data. The samples of the two curves can then be used to estimate the price and quantity of the equilibrium point. Hints: At the intersection point, the absolute value of the difference between the two curves reaches a minimum, and recall that the min function can return a second output that is the index of the minimum value of a function.

At the end of your computeEQ function, print the computed price and quantity for the equilibrium point and call the displayCurves function (described in the next section) to display the supply and demand curves and the equilibrium point. Note that the computed intersection may be shifted slightly from the apparent intersection, due to the quadratic approximation of the curves.

After you complete this first step, then add the ability to change the overall supply or demand, in order to explore its effect. One way to model an increase in supply or demand is to shift the original supply or demand curves to the right, reflecting an increase in the quantities of the product that people are willing to buy at each price, or an increase in the quantities that the company will sell at each price. Analogously, a decrease in supply or demand can be modelled as a shift to the left of the supply or demand curve. There are different ways that the user could specify the amount of increase or decrease to test. In this problem, the quantities of MATLAB and widgets are on very different scales (roughly 3000-12000 vs. 0-60). One way to specify an amount to change supply or demand is to specify a fraction of the maximum quantity in the data. This fraction can be entered as a number between 0 and 1. For example, the fraction 0.1 (corresponding to 10%), when multiplied by the maximum MATLAB and widget quantities, would yield 1200 and 6, respectively. Thus, specifying a fraction of 0.1 for the change in supply or demand would increase the quantities of MATLAB supplied or demanded at each price by 1200, or increase the quantities of widgets by 6. A factor of -0.1 would decrease these quantities by 1200 or 6. Modify your computeEQ function so that it has two optional inputs for specifying the fractions to use to change supply and demand, and use these fractions to adjust the quantities for the supply and demand curves before computing the equilibrium point. These two inputs can have default values of 0.

(3) Displaying the results

The function displayCurves is provided for you, and displays the supply and demand curves, with the equilibrium point shown as a black dot. A sample figure is shown in the next section. This function has six inputs: supply prices, demand prices, supply quantities, demand quantities, equilibrium price and equilibrium quantity. This function gives the user the option of keeping the current plots on the display, or clearing the current display.

(4) Controlling the overall process

Finally, write a high-level script named supplyDemand that controls the overall flow of the program. This script should print some introductory information to the user about what the program does, call your functions to load the data and compute the equilibrium point, and have a loop that allows the user to specify changes in the supply or demand curves and observe the resulting changes in the equilibrium point. The following interaction illustrates one example of how a user might interact with your program - the user's input is shown in bold:

>> supplyDemand
Welcome to the CS112 Supply and Demand program!
Select a data source, view supply and demand curves,
see the equilibrium price and quantity, and explore
how these values change with supply and demand :)

Select the data to analyze: mathworks (1) or widget (2): 1
Equilibrium price: $116.7817
Equilibrium quantity: $5602.0721

Keep current display? yes (1) no (0): 0

To explore the effects of changes in supply and demand, you can
specify the change in supply or demand as a fraction of the
maximum quantity present in the current supply or demand curves.
Do you want to explore these effects? yes (1) no (0): 1

Change in supply (-0.5 to 0.5): 0.0
Change in demand (-0.5 to 0.5): 0.1
Equilibrium price: $130.3746
Equilibrium quantity: $6066.7372

Keep current display? yes (1) no (0): 1

Explore more changes? yes (1) no(0): 1

Change in supply (-0.5 to 0.5): 0.0
Change in demand (-0.5 to 0.5): -0.1
Equilibrium price: $104.4731
Equilibrium quantity: $5140.041

Keep current display? yes (1) no (0): 1

Explore more changes? yes (1) no(0): 0
>>

You are welcome to modify the text as you'd like, and use a different range of factors for specifying changes in supply and demand. The above interaction resulted in the following display:

Be sure to thoroughly test your code. For your hardcopy submission, hand in the three code files that you wrote, which you can cut and paste into a single file.