CS101 - Lab Activity 3

Name: ____________________ NetID: ______________ Section#: ______ (e.g. AYA, AYB, ...)

Name: ____________________ NetID: ______________ Section#: ______

Name: ____________________ NetID: ______________ Section#: ______

Part 1: Standard MATLAB Functions 

Section I. Polynomials

1. Fill in the blank below to find the roots of the polynomial f(x) = x³ - 3x²+ 2x .  
   . 
   

   >> f = ______ [ 1   -3    2    0] _______________________;
   >result = roots(f)

2. Write the result you get (the roots).
   
       0.0000
       2.0000
       1.0000
   
   
   result = ___________above may be written vertically or horizontally for full credit and 2.0000 may be written as 2_________________

3. Use the polyval function to check your that you really have found the roots.



 >> check = polyval( _____ f _______, __________ result ____________)




4. Write the results you get (the value of check).
   
   
       0
       0
       0
   
   
   check = ____________________________
   


Its easy to create a polynomial if you know all the roots. Use the Matlab function named poly to create a the coefficients of a polynomial that
has  -1, 1, 2 and 3 as its only roots.

>> p = poly([-1, 1, 2, 3])



5. Write the results you obtained ( the value of p ).
   
   p = _______[   1    -5     5     5    -6 ]___________________________________
   

6. Write the single MATLAB command to find all the roots of -x + x¹⁰⁰ . (Don't write the roots, just write the MATLAB command that gives the roots.)

   >> p = _____  [  1, linspace(0,0,98),   -1,  0 ]  ______or ________   [ 1, zeros(1,98), -1, 0]  ________(commas not necessary)___________ 
   >> roots(p)

   Hint: x¹⁰⁰ - x   = x¹⁰⁰ + 0*x^{99 +} 0*x⁹⁸+ ... + 0*x³ + 0*x² - 1*x + 0 . Create a vector, p [ 1  (followed by 98 0's)  -1  0]. Use linspace or zeros function to create the 98 0's.





7. Use the polyval function to compute the value of x⁴ + 2x² + 3 at x= -2 . Don't write the solution, just write the MATLAB command that gives you the solution.)

   
   ____________  polyval( [ 1 ,0 , 2, 0, 3], -2)  _______________________________________________________
   
   
   

   Section II. Miscellaneous functions
   

8. Use the Matlab sum function and : and .^ operators to compute 20^-20+18^-18+16^-16+ ...+2^-2
   
   total = ____________  sum(   (20:-2:2) .^ -(20:-2:2)    )  OR  sum(   (20:-2:2) .^ (-20:2:-2)    )   ______________(both pairs of inner parenthesis are necessary)____________________
   
   

9. Use the Matlab factorial function ( 4! in our notation below is written as factorial(4) in Matlab) to compute the following sum.
   total = 1 + x + x²/2! + x³/3! + x⁴/4! + x⁵/5! + x⁶/6!  where x is a row vector.
   
   total = polyval( ____   1./ factorial(6:-1:0) ____________(./ is necessary)________________________ , x)
               Hint: Use 6:-1:0 and remember that factorial(0) equals 1.
   
   
10. Use the Matlab factorial function to compute the following sum.
    total = x - x³/3! + x⁵/5! - x⁷/7! + x⁹/9! - x¹¹/11!  where x is a row vector.
    
    total = polyval( _____  repmat([-1, 0, 1, 0], 1, 3)./factorial(11:-1:0) ______(./ is necessary)______ , x)
              Hint: Use 11:-1:0 and repmat([-1,0,1,0],1,3) (see lecture 4-9).




Fill in the blank with the result that MATLAB gives when you type the following commands.

11. 
    >> x = [ 5.9 -5.1 -1 0 4.99 -0.99 ];
    >> floor(x)
    ans =
    
    _______________   5     -6    -1     0     4    -1  ______________________________________
    

12. 
    >> ceil(x)
    ans =
    
    
    ______________   6     -5    -1     0     5     0 _______________________________________
    

13. 
    >> z = [8  7  5  2  1];
    >> cumsum(z) % note how this differs from the sum function
    ans =
    
    ______________   8  15   20   22  23    _______________________________________
    
    

14. 
    >> w = 1:2:7;
    >> cumprod(w) % note how this differs from the prod function
    ans =
    
    ________________   1     3    15   105   _____________________________________
    







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Part 2: Scripts and Functions





Section A. Scripts are just lists of commands




15. What variables are listed in your workspace after you run the clear command?

__________________  none i.e no variables _______________________________________




16. What variables are listed in your workspace after running the script?

_________________a, b, c ________________________________________







17. Are variables that are created within a script accessible to you in the workspace? Y / N  _____ Y_________
    
    

18. Can workspace variables be overwritten(changed) by running a script? Y / N    ______ Y _______
    
    
    

    Section B. Functions are different from scripts
    
    
    

19. What is returned when you call the rolldice function?


ans =

          1 or 2 or 3 or 4 or 5 or 6
________________________________________________________



20. What is the value of b after calling the rolldice function?
    
    _____________ b = 1234 _________________________________________
    
    
21. What did you get when you executed r = dieroll ?
    
    ??? Attempt to execute SCRIPT dieroll as a function:
    \\dcshome.cs.illinois.edu\gambill\My Documents\MATLAB\dieroll.m
    
    ________________or   ERROR ______________________________________
    
    

22. What do you get after running help rolldice the second time?
    
     function c = rolldice()
      rolldice: simulate the roll of a six sided die.
      returns a random integer between 1 and 6 inclusive.
    
    ______________  or  the comments in the function are displayed ________________________________________
    




Section D. Passing parameters to functions




23. What do you get after running rolldice(5) ?
    
    ans =
    
         3     1     6     1     5
    _________________or  any five integers with values between 1 and 6 inclusive since they occur at random _________________
    


24. What happens if you forget the argument to rolldice ?
    
    ??? Input argument "n" is undefined.
    
    Error in ==> rolldice at 5
     a = rand(1,n);
    __________________or  ERROR ____________________________________
    
    

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Part 3: Kinetic Energy of a particle




25. What value did Matlab return when you typed energy(m,0)?

>> energy( m , 0)


_________________ 0 _____________________________








26. What value did Matlab return when you typed energy(m, [0 , .5*c])?

    >> energy( m , [ 0 , .5*c ])
    
       ans =
    
                       0   1.26655050546144e-14
    ______________________________________________




27. What value did Matlab return when you typed energy(m,c)?
    >> energy(m, c)
    
    ________________ Inf ______________________________
    
    

28. Fill in the blanks to create a vector v that has 200 equally spaced values from 0 to .99*c.

    >> v = linspace( _____ 0 ______ , ____ .99*c ___________ , 200);
    
    
    
    

29. Write your code for the function energy in the blanks given. You may not need all the lines.

______________ function ke = energy(m,v) ________________________________

_______________ c = 299792458; _______________________________

_______________ ke = ( 1./sqrt(1 - v.^2 ./ c.^2) - 1) .* m .* c.^2; _______________________________




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Part 4: Writing your own function: finding the farthest points to the origin.

30. Write the function definition line (i.e. the first line) for the function farthest. Use the variables x, y for input parameters and  xfarthest, yfarthest. as output variables.
    
    Don't write the entire function, just the function definition (first line of code).
    
    ___________________function [xfarthest, yfarthest] = farthest(x,y)________________________________________________
    
    


31. For two vectors x and y write a single Matlab expression that returns a vector of the distances from the points to the orign.
    
    
      distances = ______________sqrt(x.^2 + y.^2); ( ^ not valid, must use .^)__or________(x.^2 + y.^2) .^ 0.5;________
    



32. Write the results of running your function as shown above.
    
    xfarthest =
    
         -8     8
    
    
    yfarthest =
    
         8     8
    
                  
    



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Part 5: if statement and multi-valued function



33. Complete the function definition line for the function named info. Use the variables named name and age contain the results that the function returns.
    
    function [name, age] = ______________ info() ______________________________________ 



34. Complete the code that traps an error.
    
    name = input('What is your name?');
    
    if   ischar(name)
         error = 0;   % 0 means false in Matlab
    else
         error =  ___________ 1; _____________________
    end



35. Complete the code that traps an error.

  error = 1; % no correct name obtained yet so error is true
       
  while error == ______ 1 ___________


36. Type at the Matlab prompt,
    
    >> [name, age] = info()
    
    And enter Bob and not 'Bob' when asked for your name. What error message do you get?
    
    
    ??? Error using ==> input
    Undefined function or variable 'Bob'.
    
    Error in ==> info at 7
    name = input('What is your name?');
     
    What is your name?
    _____________________or  ERROR _______________________