Lab activity #1

CS101 - Lab activity #1

Learning Objectives: This Lab is not to be worked in groups. Each student must work this Lab. By completing this Lab exercise you should be competent in the following learning objectives:

Simple use of the X Window System.
How to enter/exit the Matlab environment.
Use Matlab arithmetic operators on scalars, row vectors, and column vectors.
Use Matlab's built-in editor.
Use of Matlab Help facility.
Symbolics using Matlab
View the course website using Netscape or Mozilla.
Lock your screen to protect your work

Instructions:

Read the instructions below carefully. Each student should perform the following on an individual basis. However, you should be able to get assistance from any student in your lab. If you can't solve it, ask the TA.

Passing of the Lab will require that you answer all the questions on the lab answer sheet and submit your answers to the TA. Your TA should provide you with a printed copy of the answer sheet.

Part 1 Questionnaire

Fill out the Questionnaire (Part 1 on the answer sheet). This information will be used by your TA to set up your Lab groups and Lab activities.

Log onto an ews account and follow the instructions for each of the next five sections.

Part 2 Matlab constants

Using your mouse, left click the Applications menu (located at the top of the screen) then choose EWS Software and finally Matlab.

Wait for the Matlab prompt ">>" to appear and then type the following commands:
(When entering commands, don't include the ">>" symbol.)

Matlab works like a high powered hand calculator. Type the following commands at the Matlab prompt:
>> 1+1
>> 1.0 + 1.0
>> 1.0e0 + 1.0e0

You should see,
1+1

Therefore , Matlab doesn't distinguish between the integer 1 and the decimal representation 1.0 and scientific notation 1.0e0 . The numbers 1 or 1.0 or 1.0e0 are called scalars in Matlab ( so 2, 2.0 and 2.0e0 are the same scalar too and 101.101 and 1.01101e2 are also the same Matlab scalars).

On the answer sheet fill in the blanks with the correct answers for questions 1 - 5.
If the answer gives a Matlab error message, don't write down the entire message, just fill in the blanks with the word ERROR.
Before you type the following make sure to first type

>> format short e

at the Matlab prompt.

1.
>> 1 / 3

2.
>> 1 \ 3

3.
>> 2^5

4.
>> 2.0e0 - 3.0e1 * 5.0e1

5.
>> (2.0e0 - 3.0e1) * 5.0e1

Constants in Matlab are literal 1, 1.0 , 1.0e0 or symbolic , like "pi" . At the Matlab prompt type:
>> pi

Note that your answer is incorrect since the decimal expansion for pi is infinite. This is an important point concerning Matlab---Matlab does not implement inifinite precision arithmetic. The difference between Matlab's value and the correct value of pi is called round-off error
( http://mathworld.wolfram.com/RoundoffError.html ) . However we are not "seeing" the full precision of Matlab. Use the format command to see all the digits of Matlab's internal representation of pi .
>> format long e
>>pi

If you want to know the details of any Matlab command xxx (or function yyy) type help xxx (or help yyy), so type,
>> help format
You can get more detailed Matlab help by Using the Matlab Help Facility, for example, on the Matlab Tile Bar click Help,
Help

Next click on "Matlab Help" in the drop-down list,

and click the Search tab,

and finally type "format" and click Go (or your Enter key on your keyboard).

format

Matlab has other constants, such as i (imaginary , in Matlab you can also use j instead of i) , Inf (infinity) , and Nan (which means Not a number )
On the answer sheet answer questions 6-20.

6.
>> Inf + 1

7.
>> Inf - 1

8.
>> 1 / Inf

9.
>> Inf / Inf

10.
>> 0 * Inf

11.
>> (-1) * Inf

12.
>> Inf - Inf

13.
>> 1 / 0

14.
>> -1 / 0

15.


>> i * i

16.


>> format short

>> 1 + 2*i

17.


>> 1 + 2i

18.


>> (1 + 2i) + (3 + 4i)

19.


>> (1 + 2i) * (3 + 4i)

20.


>> (1 + 2i) / (3 + 4i)

Part 3 Matlab lists (row vectors and column vectors)

To make a list in Matlab use a pair of square brackets [ ] . For example at the Matlab command prompt type,
>> [ ]
Ok that's the empty list,
>> [ 1    2     3     4 ]
>> [ 1 2     3 4    [ 5 6     7     8]]
You can optionally use the comma as a separator rather than a space (blank).
>> [1, 2, 3 ,4]
>> [ [1, 2, 3, 4],[5, 6, 7, 8] ]
or
>> [ 1      2, 3 ,    4]

The lists above are examples of row vectors (row lists). In Matlab you can also make column lists using the semi-colon.
>> [1 ; 2 ; 3 ; 4]

You can change a row vector into a column vector and vice versa using the apostrophe operator.
>> [ 1    2     3 4]'
>> [ 1 ; 2 ; 3 ; 4]'

In the future we will dicuss how you can create tables of values (called matrices) in Matlab. We will also apply commas/blanks and semi-colons to tables.
The general rule for comma/blank (example [xxx , yyy]) and semi-colon [xxx ; yyy ] in Matlab is the following:
the comma or blank means paste the value yyy to the right of xxx whereas a semicolon means paste the value yyy below xxx.
However, the new vector (or table) must be a full rectangle otherwise Matlab will generate an error. For example type,

>> [ 1    2     3     4 ; 5]
Okay it's the future, so lets do a table,
>> [ 1     2     3 ; 4     5     6]

Important: The length of a vector the number of values it holds. The size of a list (vector) or table (matrix) is the number of rows by number of columns.
You can add two vectors if and only if they are of the same size, that is they have the same number of rows and the same number of columns. For example,
>> [ 1     2     3] + [ 4     5     6]

but not,
>> [ 1 2 3] + [ 4 5]

The Matlab colon operator is useful in creating lists,
>> 1 : 4
>> .5 : 2.5
So a : b means create a list by starting at a and keep adding 1 until you get to b. But what if b is not an integer multiple of a? You will stop before you exceed b.
>> 1 : 2.5
1 is the default stepsize for the colon operator, but you can choose your own, for example for a step size of 2 type,
>> 1 : 2 : 7
You can also choose a negative stepsize,
>> 7 : -2 : 1

On the answer sheet answer questions 21-26.
21.


>> [ 1  2  3]'

(that's an apostrophe not one double-quote character on your keyboard)

22.



>> [1; 2; 3] + [4; 5; 6]

23.
>> [1; 2; 3] + [1 2 3]

24.
>> [ [1; 2; 3], [1 2 3]' ]

25.
>> x = -1 : 3

26.
>> x = 1 : -3 : 7

Part 4 Matlab variables

Matlab variables are likened to drawers in your desk. They(the drawers) have a loction and hold stuff. To create a variable, use an assignment statement like,
>> x = [ 1     2     3]
Now to dump the stuff out of your drawer just type,
>> x
Its not the same as emptying your drawer since the the stuff is still there, type again,
>> x
Important: An assignemnt statement works this way, evaluate what's on the right hand side of the equals and then assign the results of the evaluation to the variable on the left hand side of the equals sign. For example type,
>> [ 1 2     3] = x

which doesn't work since the varible must be on the left hand side of the equals.
Evaluation of the right hand side means use the current values of the variables, for instance, if x was assigned [ 1 2 3] then typing,
>> y = x + [ 1 2 3]

means , evaluate [ 1 2     3] + [ 1 2     3] ( which is [ 2 4     6] ) and then assign [ 2 4 6] to the variable y.

As a note, when you type,
>> [ 1     2     3]
since you haven't used an assignment statement (=) Matlab evaluates the expression and assigns the results to the variable ans .
ans =
         1 2 3
You can treat ans as any other variable,
>> ans
1   2   3

On the answer sheet answer questions 27-29.

27.
>> x = [1 1 1]; >> x = x + [1 1 1]

28.
>> x

29.
>> y = [x, 2 3 4]

Part 5 Matlab built-in functions

A Matlab function is a sequence of Matlab statements (the code) . These Matlab statements are evaluated sequentially, using the input values (if any) provided in the call to the function. The function then may return a value or values. Functions differ from scripts in that all function variables are local to the function. That is, the variables in a function can't been seen or modified in the Matlab command window.

The basic Math functions you find on your hand calculator are included in Matlab for example,
>> sin( pi/2)      (formally when we type this and hit the Enter key in programming terminology we say we "call" the sin function)
>> exp (1)     ( e¹)
>> log( exp(1))   (natural log, that is, log base e, standard math notation is ln)
>> log10(10)      ( log base 10)
>> abs(-1)    ( absolute value)
>> sqrt( 4)     (square root)

If you forget or want to get more details as to what these functions do, you can use Matlab Help or type help xxx at the Matlab command window.
Matlab has innumerably many functions. Consider a few we will use later this semester.

On the answer sheet answer questions 30-42 .
30.
>> x = linspace(-1, 1, 4)

31.
>> x = linspace(0, 5, 1000); (don't forget this semi-colon, it means suppress out to screen)
>> min(x)

32.
>> max(x)

33.
>> x = [1 3 5]; >> sum(x)

34.
>> sum([1; 3; 5])

35.
>> z = [1 2 3; 4 5 6]; >> sum(z)

36.
>> x = [1 3 6 12]; >> diff(x)

37.
>> x = [1 2 3]; >> mean([1 2 3])

38.
>> x = [1 2 3]; >> median(x)

39.
>> x = [1 2 3 4]; >> median(x)

40.
>> x = [1 2 3 4]; >> cumsum(x)

41.
>> sqrt(-1)

42.
>> abs(1 + 2i)

Part 6 Matlab Editor

All Matlab programs are either scripts or functions. In this part of Lab 1 we will write a script. In Lab 2 we will write a function and compare the differences between functions and scripts.
A MATLAB script file contains any Matlab command you can enter at the Matlab prompt.
To write a script you first open the Matlab editor using the "edit" command. Then after your type in your code (Matlab statements) you save your file. Script files can have any name you choose but their file extension must be ".m". To execute a script file, while in the Matlab environment, type in the name of the script file.

All the commands (but not comments ) in a script file are executed. The execution starts with the first command at the top of the file and proceeds sequentially downward. A comment is anything (text, numbers, ...) that follows (on the same line) the "%" symbol. Comments are informative messages programmers include to help remind themselves and explain to others what the code is trying to accomplish.

You may choose to comment a script file. A comment is not executable but gives information for the programmer.

Open the Matlab editor by typing (use your last name not "lastname")

   >> edit lastname.m

If you are asked whether to create the file, choose yes.

in the Matlab command window. Type the following Matlab commands into ".m" and click File then select Save or Save AS from the menu.

   % This is a comment.
   % A comment begins with a percent symbol.
   % All text following a percent symbol is ignored when the script is
   % executed.
   clc % Command to clear the Matlab screen.
   r = 4;
   x = [1 2 3] % No semicolon here
   y = sin(x);
   y

scripts

scripts2

On the answer sheet answer questions 43-50 .

43. Before we run the script file, in the Matlab environment, enter the who command, which lists all your variables:

>> who

List the variables: (Write "Nothing" if no variables appear)

44. Now type the following,

>> clear
>> who

List the variables:

45. Next type,

>> r = 1;

>> who

List the variables:

>> r

46.
What is the value of r? _________

Use the "what" system command to make sure that you have correctly saved your lastname.m file.

>> what(this lists the .m and .mat files in your directory)

If you don't see the "lastname" file ask your TA for help before you proceed.

47. Run the script by typing your last name at the prompt.

Write what is displayed on your screen:

48. Type

>>r

What is the value of r? _________

49. So, can running a script alter the value of a workspace variable? Y / N

50. Again, type

>> who

List the variables in your workspace:

Part 7 Symbolics in Matlab

Like Mathematica, Matlab can be used to perform symbolic differentiation, integration and to compute limits. Symbolic operations like differentiation, integration or limits require that we tell Matlab which symbolic variables are in use in our formula. To do this we need to use the syms command (not to be confused with "The Sims").
Example 1: Find the indefinite integral of x² with respect to x
>> syms x ( we tell Matlab that x is a symbolic variable not a variable in the sense discussed above in Part 4)
>> int(x*x,x) ( the first argument in the call to the int function is x*x and the second argument is x)

When there is no ambiguity, you can omit the argument that lists the symbolic variable. Type,
>> int(x*x)

The result is symbolic so you can use the result is the input to another function. For example, type,
>> result = int(x^2,x)
Let's check our answer by differentiating with respect to x
>> diff(result,x,1) ( 1 means first derivative)
or since there is only one symbolic variable in result and there is no ambiguity,
>> diff(result)

Example 2: find the limit of x/x as x goes to 0
>> limit(x/x, x, 0)

Example 3: The formula may contain non-symbolic variables as in,
>> a = 2.5
>> solution = int(a*x,x)

On the answer sheet answer questions 51-53 .

51. Compute the derivative of t³ with respect to t,

>> syms t

Note: When you execute the syms command, you may see a page of red text. If you do, please restart Matlab.

Fill in the blank with Matlab code to call the diff function to compute the second derivative of t³. You must use the diff function.

>> solution = _______________________________ (The solution should be 6t, but you should write the command used to find the solution.)

52. Write the result of executing the following code,
>> syms y >> limit(sin(y) / y, y, 0)

53. Write the result of executing the following code,
>> syms z >> diff(sin(z), z, 4) (this is called the fourth derivative of sin(z) with respect to z)

You can Exit matlab now by typing

  >> exit

at the Matlab prompt ">>" .

Part 8 Get Course Information

On the answer sheet answer questions 54 - 55.

54. Find in the course syllabus: Find the grade range(in points) for an A- grade for CS101:

55. Click the "Staff " hyper-link: What is the email address of your lab TA?

For your reference, the course website is at:
http://www.ews.uiuc.edu/~cs101/

Part 9 Security

Although some lab work is done in groups, the MPs(machine problems) must be worked individually. It is the students responsibility to make sure that his/her code is not copied since this would constitute cheating--- see Lecture 0 of the class notes. When you are working on your MP and have to leave the lab for a brief time, you should choose Lock Screen from the System menu at the top of the screen. When you come back into the lab, click on the computer screen and type your password to unlock the terminal.

To complete the first Lab activity you should Lock Screen and have your TA sign that you have done this correctly in question 56 of your answer sheet.

56. Follow the instructions in Part 9.
Then, obtain the signature of your TA and submit this answer sheet to your lab TA.

Log out: Choose "Log Out" from the System menu. NEVER leave your computer without logging out since someone else entering the lab after you would have access to all your files (MPs).

Congratulations you have just finished Lab #1 !!!

Submit your answer sheet to your lab TA.