6 Functions [10 marks]

Some important computational problems rely on performing a circular shift of the elements in a vector. A circular shift of a vector x by n positions produces a new vector where the elements of the vector are formed by shifting the elements of x by n positions to the right. Elements that are shifted past the end of the vector wrap around to the front of the vector. For example, suppose that the vector x has the following values:

1, 2, 3, 4, 5, 6, 7, 8

A circular shift of x by 0 positions returns a new vector that is equal to x.

A circular shift of x by 1 position returns the following vector:

8, 1, 2, 3, 4, 5, 6, 7

Notice that the 8 has wrapped around to the front of the new vector.

A circular shift of x by 2 positions returns the following vector:

7, 8, 1, 2, 3, 4, 5, 6

Notice that the 7 and 8 have wrapped around to the front of the new vector.

A circular shift of x by 7 positions returns the following vector:

2, 3, 4, 5, 6, 7, 8, 1

A circular shift of x by 8 positions returns a new vector that is equal to x because x has 8 elements.

A circular shift of x by 9 positions produces the same result as a circular shift of 1 position (in the case where x has 8 elements).

If n is negative then the elements are shifted to the left instead of to the right. For example, a circular shift of x by -2 positions returns the following vector:

3, 4, 5, 6, 7, 8, 1, 2

Observe that in this case, a shift of -2 positions is equivalent to a shift of 6 positions.

Create a function that computes the circular shift of a row vector x by n positions.

Your function should satisfy the following constraints:

  1. it should be named cshift
  2. it should return one value v (the vector obtained by circularly shifting the input vector x by n positions)
  3. it should have two input values x (a row vector) and n (an integer number of positions to shift x by)

Your function must not use the MATLAB function circshift.

Your function should work for all non-empty row vectors x.

You will receive part marks if your function works correctly only for positive values of n.

6.1 Example usage

x = [2 8 12 15];

% y should equal [15 2 8 12]
y = cshift(x, 1)

% y should equal [12 15 2 8 ]
y = cshift(x, 2)

% y should equal [8 12 15 2]
y = cshift(x, 3)

% y should again equal [8 12 15 2]
y = cshift(x, -1)