1. Project:Introduction to MATLAB

1.1. Introduction

In this project, you will be familiar with MATLAB. Each of the computers in the HELC has Matlab installed, so you can go there to work on projects. To get started with this project, you will need to download the starter code and unzip its contents to the directory where you wish to complete the project.

Files included in this project

• project1.m - MATLAB script that steps you through the project.

• checkMyAnswer.m - Script that checks your code.

• checkMyAnswer.mat - Data set.

• data.mat - Data set.

• * f.m - Functions in MATLAB.

• * matrix.m - Matrix operations in MATLAB.

• * piecef.m - Use if statement to give a piecewise function.

• * sumUp.m - Use for loop to calculate a Sigma sum.

• * ftl.m - Use while loop to calculate a factorial.

You need to complete the files with *.

Throughout the project, you will be using the script project1.m. This script set up all dataset for the problem and make calls to functions that you will write. Do not modify it. You are only required to modify functions in * files, following the instructions in this project.

Where to get help

At the MATLAB command line, typing help followed by a function name displays documentation for a built-in function. For example, help plot will bring up help information for plotting.

1.2. Assignments

Part 1 - Function in MATLAB

The first part of project1.m gives you practice with MATLAB syntax. In the file f.m, you will find the outline of a MATLAB function. Modify it to return the function

\[ y=6-4x^2+\frac{3}{x+2}-e^{2x}+\sin x^2 \]

Hint

• This function should work for both scalar \(x\) and vector \(\mathbf{x}\). Check your code and use the proper element-by-element operators.

• Use the built-in exp() to calculate the natural exponential function.

• Use the built-in sin() to calculate the sine function.

• Use semicolon ; to suppress the output.

Solution

y = 6 - 4*x.^2 + 3./(x+2) - exp(2*x) + sin(x.^2);

Once complete, run project1.m (assuming you are in the correct directory, type project1 in the command window of MATLAB). You should see output similar to the following:

Part 2 - Matrix operations in MATLAB

In this part of project, you will implement matrix operations to evaluate a matrix function. Modify the file matrix.m to return a matrix \(A\) as follows

\[ A=2B-C\times D^T \]

Hint

• Matlab is case sensitive.

• These are matrix arithmetic operations. Do not use element-by-element operators.

• Use single quote ' to calculate the transpose of a matrix.

Solution

A = 2*B - C*D';

Once complete, run project1.m. You should see output

A=
    -34   -32     0
    -12   -18    -4
    -68   -67   -25

Part 3 - Use if statement for a piecewise function

In this part, you will use if statement to express a piecewise function. Modify the file piecef.m to return the following function

\[\begin{split} y = \begin{cases} x+1, & x<0 \\ x^2-3x+1, & 0\le x\le 2 \\ -\frac{2}{x}, & x>2 \end{cases} \end{split}\]

Hint

• When you write the code for the second piece, note that MATLAB does not accept the expression like 0<=x<=2, it should be x>=0 && x<=2. However, if the code runs into the second piece, it means \(x\) is not less than 0, so x>=0 is automatically true. In a nutshell, the condition expression for the seconde piece is just x<=2.

• When you write the code for the last piece, i.e. the else piece, note that there is no condition expression behind else.

Solution

if x < 0
  y = x + 1;
elseif x <= 2
  y = x.^2 - 3*x + 1;
else
  y = -2./x;
end

Once complete, run project1.m. You should see output similar to the following:

Part 4 - Use for loop to calculate a Sigma sum

In this part, you will use for loop to express a sum. Modify the file sumUp.m to return the following sum

\[ s=\sum_{i=1}^n x_i \]

Hint

• Use x(i) to get the i-th component of the vector x.

• Use the built-in function length() to obtain the length of a vector.

Solution

for i = 1:length(x)
  s = s + x(i);
end

Once complete, run project1.m. You should see output like:

1+2+...+9+10 =  55

See also

This is a simple practice to use for loop. MATLAB does have a built-in sum function to calculate the sum of array elements. Check out here

Part 5 - Use while loop to calculate a factorial

In this part, you will use while loop to evaluate a factorial. Modify the file ftl.m to return \(n!\), the factorial of \(n\).

Hint

• You can reduce n in each loop until it gets 1. So the condition expression can be set as while n>0.

• Note that the initial value of y is 1 while in last section the initial value of s is 0.

Solution

while n > 0
    y = y*n;
    n = n - 1;
end

Once complete, run project1.m. You should see output like:

10! =3628800

1.3. Submit your code

This is the last step. You should submit your code files to WTClass. After clicking Browse My Computer, you should select all files listed in Introduction to upload. Failure to do so will affect your grade.

1. Click Browse My Computer:

2. Select all files listed in Introduction to upload