Assignment 4 New Matrices

Assignment 4

New Matrices
1. (30 points) Write a function called makemat that will receive two column vectors
as input arguments, and from them create and return a matrix with two columns (n
x 2). If either of both of the vectors passed in are row vectors, transpose them into
column vectors. If either input is a matrix, your program should throw a unique
error (create your own error message.) You may not assume that the length of the
vectors is known. Also, the vectors may be of two different lengths. If that is the
case, add 0’s to the end of one vector first to make it as long as the other (this is
often referred to as padding the matrix with 0s - do not use any built-in functions
such as padarray()). Some examples of calling the function and the result you
should see:
makemat([2;8;7],[9;0;3])
ans =
2 9
8 0
7 3
makemat([2 8 7],[9 0 3 4 3])
ans =
2 9
8 0
7 3
0 4
0 3
makemat([4 8;3 6],[4 9 0])
Error using makemat (line 17)
Can’t process a matrix, try again. Undefined for
matrix input arguments.
Smallest number adjacent to a zero
2. (40 points) Write a function named smallest that will receive one vector vec as
input argument. The elements of vec are of type double, and they can be positive or
negative numbers. The function will return the smallest element of vec that comes
before an element with the value 0(zero).
If the input argument vector is empty, or if there is no element with the value
zero (hence, no element adjacent to a zero), then the function should return an
empty vector.
You are NOT allowed to use the following built-in Matlab
functions: imdilate, unique, diff (or any other exotic built-in functions not covered
in lecture or recitation). You are allowed to use the find and min built-in Matlab
functions. The function should return the desired output regardless of the input
vector size.
Some examples of calling the function:
vec = [1 5 3 0 2 7 0 8 9 1 0];
% Here the elements that come before 0 are [3 7 1] and
hence % the smallest number among these elements is 1
smallest(vec)
ans =
1
smallest([1 2 3 2 4])
ans =
[]
smallest([])
ans =
[]
smallest([11])
ans =
[]
smallest([0, 0])
ans =
0
smallest([3 -4 0 0 -6])
% Here the elements adjacent to 0 are [-4 0 ] and hence
% the smallest number among these elements is -4
ans =
-4
Adding Noise to Data
3. (30 points) Write a script noisify.m where you first create a vector x that has 20
linearly spaced elements with values ranging from 1 to 20. Second, set a vector y
equal to √x . Plot this curve with x on the horizontal axis and y on the vertical axis.
Finally, create a new vector, call it y2, and add random noise of amplitude between
-0.05 and 0.05 (i.e. -0.05<noise<0.05 ) to the original vector y. (Hint: y2 is of the
same length as y. Each element of y2 is either larger or smaller than the
corresponding element of y.) Plot the original curve y and the noisy-y (using red dot
for the noisy data points). Give appropriate axis labels, title, and legend (use
legend() function). The resulting plot should look similar to this:
Submitting the assignment:
Make sure all your .m files are well commented and they include a comment block
with your name, student ID, course number, assignment number and recitation
section. Zip all the files together and submit the resulting .zip file through Moodle as
Assignment 4 by due date.