HW2: Analysis of Temperature Data

1. Introduction
In this assignment you will write a Matlab program to perform some analytical
calculations on a vector of numbers. The numbers are a collection of temperature
readings from an airport in Birmingham AL in 2003. You will create a graph of the
data in order to visualize the data.
2. Value
This program is worth a maximum of 20 points. See the grading rubric at the end for
a breakdown of the values of different parts of this project.
3. Due date
This project is due by 11:59PM on Sunday, September 16
4. Objectives
The purpose of this assignment is to have you improve your skills in these areas:
• Creating and running a Matlab program file.
• Using vectors.
• Using simple built-in Matlab functions.
• Visualizing data on a graph.
5. Background
The information you need for this and future projects is mostly in chapter 3 in the
book. The data analysis functions that you will need are in section 3.4. However, the
find() function is not located in chapter 3. You will need to locate this information on
your own and do your best to figure out how to use it. Real world problems never
follow the sequence of topics in a book.
6. Assignment
Read through all of this document before you start to make sure you understand how
you must proceed with the assignment. For this assignment you will create a program
that generates output in the console window and also displays a graph. Then you
will collect your program, data, and graph into a brief report.
6.1. Create a new project folder
In your CSE1010 folder in Matlab create a new folder called HW02 or Project 2 or
Assignment 2: something to distinguish it from all the other assignments you will do
this semester.
If you do not have a CSE1010 folder in Matlab, now is the time to make one. DO
NOT place all your programs in one single folder.
To make a new folder in Matlab, right click in the Current Folder window and select
New folder.
NOT place all your programs in one single folder.
To make a new folder in Matlab, right click in the Current Folder window and select
New folder.
6.2. Create allTemps function
Create a new script file.
Even though you're creating a new function, choose File → New → Script. In the edit
window that pops up, type the function shown below and save it as allTemps.m in
the current folder (be sure to capitalize it like that: small a, big T). This is the function:
function T = allTemps
T = [59 57 57 57 57 57 56 55 55 55 55 54 54 54 54 54 54 54 54 52 50 50 50 ...
50 50 50 49 48 49 48 48 48 47 47 47 46 46 46 46 46 46 46 46 46 46 46 ...
46 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 ...
45 46 46 47 48 48 48 49 49 49 48 50 48 49 48 46 45 45 43 43 42 42 39 ...
38 37 36 35 35 34 34 34 34 34 34 34 34 34 34 33 34 34 34 34 35 34 34 ...
33 33 34 32 31 29 29 28 28 26 27 26 25 25 28 31 35 38 40 44 45 48 48 ...
46 44 44 43 42 43 43 43 44 45 46 46 44 42 40 45 46 49 52 55 58 60 60 ...
59 55 54 51 46 43 41 40 39 37 36 36 36 34 32 32 35 40 43 43 43 43 43 ...
42 42 42 41 38 38 35 34 34 33 31 31 29 30 28 25 27 23 28 31 34 38 41 ...
45 47 47 47 45 42 41 40 38 37 37 36 36 35 34 35 35 33 35 37 40 44 48 ...
52 57 60 60 60 57 56 54 52 53 52 51 49 48 49 49 48 48 48 48 49 53 57 ...
59 62 66 68 67 63 62 62 59 58 55 55 55 55 54 54 54 54 53 54 52 51 50 ...
50 48 45 43 38 37 38 40 42 43 45 47 48 48 47 45 43 41 38 37 34 32 31 ...
30 28 28 27 27 27 25 28 29 31 35 37 39 40 39 38 37 35 35 35 34 34 32 ...
31 29 30 30 28 27 27 26 27 28 29 30 32 33 34 34 34 33 32 32 31 28 29 ...
29 29 29 29 30 30 30 30 30 31 32 34 37 38 42 45 47 47 43 40 35 33 33 ...
30 30 29 29 27 29 27 27 27 27 31 37 42 46 49 53 54 54 54 51 48 41 38 ...
37 37 36 34 33 32 29 28 26 26 26 24 28 31 35 38 40 43 44 45 45 40 40 ...
38 31 33 32 34 34 34 35 31 32 29 34 37 38 40 41 40 39 40 39 41 41 41 ...
41 NaN 41 NaN 43 44 45 45 45 44 45 43 40 37 37 37 35 34 32 31 30 29 29 ...
29 28 28 27 27 27 28 28 28 28 28 28 30 31 32 34 35 36 35 33 31 30 27 ...
23 23 22 20 19 18 17 17 17 14 15 18 21 25 27 30 33 35 36 36 37 35 36 ...
36 36 35 31 29 27 26 25 27 25 25 22 28 30 34 37 39 43 45 47 46 45 41 ...
41 41 41 43 44 44 44 42 42 41 40 41 41 43 42 43 45 48 53 56 57 57 58 ...
59 60 60 58 58 58 58 58 58 58 57 57 57 57 56 55 55 55 56 55 55 56 57 ...
58 60 61 61 63 63 64 64 63 55 54 52 48 47 46 46 45 45 45 45 45 43 43 ...
43 43 43 43 42 42 41 39 40 39 39 37 38 37 37 36 36 36 35 35 36 40 43 ...
46 49 50 51 50 45 41 38 36 34 32 31 29 28 26 25 23 21 21 19 18 16 17 ...
18 17 19 21 23 23 24 23 23 20 19 18 17 16 15 14 12 11 10 9 8 7 7 7 9 ...
13 18 21 24 26 29 32 32 30 27 25 24 25 24 24 23 24 25 24 21 22 23 23 ...
23 27 30 33 34 36 37 38 37 37 36 36 36 36 35 35 35 34 34 34 34 34 34 ...
34 34 35 37 40 44 46 48 49 48 47 44 43 42 39 37 32 30 28 28 26 25 22 ...
21 20 19 18 21 26 29 33 36 39 41 43 43 43 41 38 29 32 30 30 33 33 30 ...
28 31 34 36 38 40 41 44 47 50 53 55 56 56 55 55 54 55 53 55 56 55 53 ...
53 53 53 53 53 53 53 54 55 55 55 55 56 56 57 56 55 55 55 55 55 55 55 ...
55 55 55 56 55 56 56 55 55 56 56 55 NaN 55 NaN 55 NaN 52 51 48 48 46 46 ...
47 45 45 45 44 45 43 43 42 41 39 40 39 40 39 40 40 41 41 42 43 42 43 ...
43 40 39 39 39 39 39 38 38 38 37 37 39 39 38 38 38 38 38 39 40 39 43 ...
43 47 50 53 55 55 52 49];
end
jk lol. I hope you didn't actually type all that. Copy and paste the function shown
above into that file, then save the file and close it. Don't worry about how functions
work just yet. We'll get to that in a few weeks.
Another way to do it is to type edit allTemps.m in the command window, paste the
function, save the file.
Close the edit window when you're done with it.
If copy & paste isn't working for you, go to the Google web site for this course and
find the file to download for this assignment. Send me e-mail if you don't see it.
If copy & paste isn't working for you, go to the Google web site for this course and
find the file to download for this assignment. Send me e-mail if you don't see it.
6.3. Create a main.m script file
Create a new file in your project folder. It should be a script file called main.m. Place
a comment block in the file that contains this information:
% Analysis of Temperature Readings
% Project 2, CSE1010 Fall 2012
% today's date (replace this line with the date)
% your name (replace this line with your name)
% your section number (replace this line with your section number)
% the name of your TA (replace this line with the name of your TA)
% Instructor: Jeffrey A. Meunier
clc % clear command window
clear % clear all variables
The rest of the statements for this program will be typed in this file below the clear all
variables line.
6.4. Store temperatures in a variable
When you call the allTemps function, it returns a vector that you can store into a
variable (type allTemps at the command prompt to see what I mean). Type this line
into your Matlab program:
Temps = allTemps;
Now when you need to work with the vector of temperatures, you will use the vector
stored in the Temps variable rather than calling the allTemps function.
Now write two statements in the main.m file to tell the user how many temperature
readings there are:
1. Use the disp() function to display a message. In my program I wrote this:
disp('Number of readings')
2. Display the length of the Temps vector. If you call the length() function on Temps
and leave off the semicolon, it will do what you need. Type those statements now at
the command prompt to see how they works, then enter them into your program file.
When I run the My output looks like this:
Number of readings
ans =
884
Actually there are blank lines between those lines of output, but I don't show them
here because it takes up too much space. It really looks like this:
Number of readings
ans =
884
6.5. Repair the temperatures vector
The vector contains the value NaN in some locations. In Matlab this means not a
number. This could happen if the temperature reading was not available at that time,
perhaps because the thermometer was malfunctioning. Scientifically speaking, this is
the correct way to proceed: you must not use a number if no number is available.
However, Matlab refuses to do certain calculations on a vector if it contains NaN in
any location, so we will replace each occurrence of NaN with a most likely expected
value, which is just the average of the two temperature readings on either side of the
NaN. For example, if a vector contains [40 NaN 50], you would replace the NaN
with 45, making the vector [40 45 50].
value, which is just the average of the two temperature readings on either side of the
NaN. For example, if a vector contains [40 NaN 50], you would replace the NaN
with 45, making the vector [40 45 50].
Try to follow along with what I explain here. At the end of the section I'll tell you what
to type into your Matlab program.
Type this into Matlab:
Nans = find(isnan(Temps))
This tells you all the vector locations that contain NaN instead of an actual number. It
also stores those locations into the vector stored in the Nans variable. It should look
like this:
EDU Nans
Nans =
439 441 820 822 824
This means that the NaN entries are at index locations 439, 441, 820, 822, and 824.
We'll just have to trust it, because there are just too many numbers to count.
Now the vector elements in those locations must be changed to actual numbers. It's
simplest just to replace each NaN with the average of the two numbers to either side
of the NaN value.
For example, the first two NaNs occur in this series:
.. 41 NaN 41 NaN 43 ...
Thus, the first NaN should be replaced by (41 + 41)/2 = 41, and the second should
be replaced by (41 + 43)/2 = 42.
There are several NaNs in the temperatures vector, and it would be nice if you didn't
have to locate and correct each one manually. It is possible to assign values to all
those locations at once using a single assignment statement like this:
Temps(Nans) = ...some calculation...
but what's on the right hand side of that assignment statement must have exactly the
right number of values (it must have the same number of values as Nans has). You
must create a vector of averages instead of just a single average. Each of those
averages will be stored in Temps at its respective location.
Another useful function is the mean() function. It will calculate the mean (or average)
of several numbers, or calculate a vector of means of two vectors of numbers
arranged into two rows of a vector:
EDU mean([1 2 3])
ans =
2
EDU mean([1 2 3 ; 5 6 7])
ans =
3 4 5
This means that the mean of 1 & 5 is 3, 2 & 6 is 4, and 3 & 7 is 5.
Now observe:
EDU Temps(Nans)
ans =
NaN NaN NaN NaN NaN
Recall: Nans contains the index locations where Temps is equal to NaN. Thus,
Temps(Nans) gives you the values in the Temps vector at all those locations.
Now observe:
EDU Nans-1
ans =
438 440 819 821 823
EDU Temps(Nans-1)
ans =
41 41 55 55 55
Nans - 1 is an expression that subtracts 1 from each element in Nans, which then is a
EDU Temps(Nans-1)
ans =
41 41 55 55 55
Nans - 1 is an expression that subtracts 1 from each element in Nans, which then is a
vector of all the locations before (or to the left of) the NaN entries, and those
temperatures are 41, 41, 55, 55 and 55. You can do the same with Nans + 1. Those
are all the locations after (or to the right of) the NaN entries. Now if you just average
the values of the befores & afters, you have the new values that need to be stored in
place of the NaN values.
EDU Means = mean([Temps(Nans-1); Temps(Nans+1)])
Means =
41.0000 42.0000 55.0000 55.0000 53.5000
EDU Temps(Nans) = Means;
EDU Temps(Nans)
ans =
41.0000 42.0000 55.0000 55.0000 53.5000
Now all the NaN values have been replaced by actual temperatures!
I will summarize what you must type into the main.m script file. Type statements to
do this:
• Store the result of calling allTemps into the Temps variable. Use this statement:
Temps = allTemps;
• Calculate the Nans vector (it's just what you did in the explanation above).
• Calculate the Means vector.
• Store the Means vector back into the Temps vector at the locations in Nans. This
statement appears above. There are actually a few statements above ;) so you need to
know what I'm talking about here in order to choose the right statement.
• Go back and place semicolons after all the assignment statements.
6.6 Calculate max, min, mean
Add these statements to your main.m script file, just below the statements you wrote
previously.
• Show the maximum value of the Temps vector. Use the max() function. If you
omit the semicolon it will display the value for you automatically. This is sufficient for
this project.
• Show the minimum value of the Temps vector. Use the min() function.
• Show the mean value of the Temps vector. Use mean().
Before each of those values, use the disp() function to display a message indicating
whether the value is the maximum, minimum, or mean. Mine looks like this:
Maximum temperature:
ans =
68
Minimum temperature:
ans =
7
Mean temperature:
ans =
39.9338
6.7. Locate temperatures below freezing
Create a variable called Freezing that contains the locations where the Temps vector
is less than freezing (use 32 as the freezing temperature since the vector temperatures
are in Fahrenheit). Use a semicolon because you do not need to show the values in
this vector.
Use the find() function to find these values.
Use the length() function to calculate and display the number of values in the
Freezing vector. Display a message first to make your output more readable.
Number of readings below freezing:
Use the length() function to calculate and display the number of values in the
Freezing vector. Display a message first to make your output more readable.
Number of readings below freezing:
ans =
208
6.8. Longest duration between freezes
The Freezing vector tells you the locations in the Temps vector where the
temperature is at or below freezing.
The first 16 columns of the Freezing vector look like this:
120 121 122 123 124 125 126 127 128 129 130 131 195 196
197 198
This means that readings 120 through 131 were all below freezing, then notice that
the temperature went above freezing until reading number 195 when it went below
freezing again. The number of readings between 195 and 131 is 195 - 131 - 1 = 63,
so there was a duration of 63 readings when the temperature was above freezing.
Calculate the longest duration between freezing temperatures in the vector.
To do this you must subtract each element in the Freezing vector from the element
that comes after it:
121 - 120 - 1 = 0
122 - 121 - 1 = 0
...
130 - 129 - 1 = 0
131 - 130 - 1 = 0
195 - 131 - 1 = 63
196 - 195 - 1 = 0
...
All those differences must be stored in a new vector that will look like this:
0 0 0 0 0 0 0 0 0 0 0 63 0 0 0 ...
The way to construct that vector is to use two vector ranges. After you have created
the Freezing vector, observe what happens when you type this into Matlab:
EDU Freezing(2:end)
ans =
Columns 1 through 10
121 122 123 124 125 126 127 128 129 130
Columns 11 through 20
...
Columns 201 through 207
745 755 757 758 761 762 763
The Freezing vector has 208 elements, but that vector (the answer that Matlab just
showed you) has only 207 elements. Likewise, the following vector also has 207
elements:
EDU Freezing(1:end-1)
ans =
Columns 1 through 10
120 121 122 123 124 125 126 127 128 129
Columns 11 through 20
...
Columns 201 through 207
744 745 755 757 758 761 762
If you subtract those two vectors, then subtract 1 from that vector, you will end up
with a vector that shows how many readings were above freezing:
ans =
Columns 1 through 10
0 0 0 0 0 0 0 0 0 0
Columns 11 through 20
0 63 0 0 0 0 0 0 0 0
Columns 21 through 30
Columns 1 through 10
0 0 0 0 0 0 0 0 0 0
Columns 11 through 20
0 63 0 0 0 0 0 0 0 0
Columns 21 through 30
0 94 0 0 0 0 0 0 0 0
Columns 31 through 40
0 0 13 0 0 0 0 0 0 0
Columns 41 through 50
...
Columns 201 through 207
0 9 1 0 2 0 0
You can see that in the 12th column there is the number 63. That means that at that
point in the temperature readings, there were 63 consecutive readings above
freezing.
Find the maximum number of consecutive readings that were above freezing and
display the number with a message before it, like this:
Maximum consecutive readings above freezing:
ans =
112
6.9. Determine mean number of consecutive readings above freezing
Find the mean value of the vector you created in the previous step. Do not include
any zeros in this calculation. Create a new vector of only the non-zero values from
that vector. It should start like this:
63 94 13 8 13 18 10 ...
This is not as hard as it sounds. Consider how the find() function works. It's designed
to do something just like this. The problem is that find() tells you locations, whereas
you want the values at those locations. So after you find the locations where that
vector is not zero, you need to get the values at those locations. It turns out that you
already know how to get the value of a vector at a location, or a bunch of values at a
bunch of locations.
Then display the mean of that vector with a message:
Mean consecutive readings above freezing:
ans =
24.2222
6.10. Plot the temperatures
Plot the values in the Temps vector. Do this by typing this statement into the Matlab
command prompt. It does not have to be in your program.
plot(Temps)
Save the plot to a file so that you can use it to write your document. You do not need
to label the plot in any way.
To save the plot, click the blue Save Figure icon shaped like a floppy disk in the plot
window.
Save the plot as type Portable Network Graphics (PNG), not as the default FIG.
Microsoft Word does not know how to import FIG files.
7. Deliverables
Create a Microsoft Word or OpenOffice Word file (or some other format that your
TA agrees on -- ask him or her if you are not sure). Save the file with the name
Project2 with a .doc or .docx format.
At
TA agrees on le with the name
Project2 with a .doc or .docx format.
At the beginning of the document include this information:
Analysis of Temperature Data
CSE1010 Project 2, Fall 2011
Your name goes here
The current date goes here
TA: Your TA's name goes here
Section: Your section number goes here
Instructor: Jeffrey A. Meunier
Be sure to replace the parts that are underlined above.
Now create the following five sections in your document.
1. Introduction
In this section copy & paste the text from the introduction section of this assignment.
(It's not plagiarism if you have permission to copy something. I give you permission.)
2. Data
Copy & paste the allTemps function and write one sentence before it describing what
the data represents.
3. Output
Run your program and copy & paste the output from the command window here.
You do not need to write anything.
4. Graphs
Insert the plot in this section. To do this, you can drag & drop the file from wherever
you saved it right into MS Word. Just indicate in the MS Word document that it is a
plot of the temperature data. Do not submit the plot image, but don't delete it until
after your assignment has been graded. Actually, don't delete any file that you create
for this course. Not ever, except maybe after you graduate.
5. Source code
Copy & paste the contents of your main.m file here. You do not need to write
anything.
8. Notes
• This is not a long program, but you will need to do some thinking and
experimenting in Matlab. Use the book and your notes.
• Make sure your program displays these 6 values:
1. Maximum temperature
2. Minimum temperature
3. Mean temperature
4. Number of readings below freezing
5. Maximum consecutive readings above freezing
6. Mean consecutive readings above freezing
9. Submission
Submit two things on HuskyCT:
1. Your main.m file.
2. Your Project2 MS Word document.