Lab (1) - Introduction to Data Analysis in MATLAB

Objectives

• To learn some basics in MATLAB
• To learn to manipulate data in MATLAB
• To learn to import data from other applications, for example Excel
Preparation
MATLAB is an interactive system for numerical computations. It is widely used in universities and industry, and has many advantages over languages such as C, Fortran and Java, including:
• It is very easy to write MATLAB code to solve complex problems in mathematics, sciences and engineering.
• Data structures in MATLAB require minimal attention. Arrays, for example, do not need to be declared.
• MATLAB has high quality graphics and visualization tools that can be used to analyze computational results.
• MATLAB provides additional toolboxes that are designed to solve specific classes of problems. For example, there are toolboxes for statistics, image processing, signal processing, differential equations, splines and optimization.
Because MATLAB is an “interpretive” language codes written in C, C++ and Fortran can be more efficient for very large problems. However, MATLAB is excellent for developing algorithms and problem solving environments.

MATLAB is very useful for solving problems involving many numbers at the same time. These numbers can be stored as matrices or vectors and computations can be performed on all of them at once rather than one-by-one. We explore some of these basics operations
through a series of examples.

Starting MATLAB
We will use MATLAB in this lab.  To start MATLAB, double click on MATLAB icon on your PC.  You will get a screen that looks like this:

In this lab manual every time that we show >> we are referring to the MATLAB command prompt where you can type a MATLAB command.  Then you have to press Enter to execute that command. MathWorks provides an excellent online introductory tutorial, click here to bring that page up.

Manipulating data in MATLAB
MATLAB gets its name from Matrix laboratory. A matrix is a 2 dimensional array of numbers, with a certain number of rows and columns. For example:

is a matrix with 3 rows and 4 columns. We often say A is a 3 × 4 matrix.

then we say x is a column vector of length 5, and y is a row vector of length 4. MATLAB is very useful for solving problems involving matrices and vectors. We explore some of these basics through a series of examples.

>> x = [1, 2, 3, 4]
This creates a row of 4 values and store them all in x. Thus x is 1-by-4 or 1 × 4 matrix.
>> y = [1; 2; 3; 4]
This one creates a column of 4 values and store them all in y. Thus y is a 4-by-1 or 4 × 1
matrix.
>> y = [1
2
3
4]

This will do the same thing.

Initialization refers to the process of creating a matrix and having some values stored in them right at the beginning.

Initializing Vectors. We can create row and/or column vectors in MATLAB as follows:

>> x = [1 2 3 4]
>> x = [1, 2, 3, 4]
>> x = [1; 2; 3; 4]

Note that the first two produce 1 × 4 matrices and the third is a 4 × 1 matrix.  It is very important that you pay careful attention to ";" as that is the separator of rows when you use it.  If you do not use that, then you have to use Line-Break to separate the rows.

Initializing Matrices. In general, we can create matrices with more than one row and column just as we did above. Here are some examples:
Here is an example in which we use Line-Break to separate the rows:
>> A = [1 2 3 4
5 6 7 8
9 10 11 12]

In this one which is the same we will use ";" to separate the rows:
>> A = [1 2 3 4; 5 6 7 8; 9 10 11 12]

Array Operations. MATLAB supports certain array operations that can be very useful in scientific computing applications. Some of these operations are:
.* ,  ./    and .ˆ

The dot indicates that the operation is to act on the matrices in an element by element way. That is,

Now let's do this in MATLAB:
>> A = [1 ; 2; 3; 4]
>> B = [5 6 7 8]’

Note the (single quote) ’ at the end of the line where B is defined. That is actually a very handy thing that turns a matrix around (transpose). The command

>> B = [5 6 7 8] will create one row of 4 data points. But we really want B to be one column with 4 rows, so if we add the single quote (’) at the end, it will convert that matrix to a column.

Now try
>> A .* B

Note that if these two were not the same type, we couldn't do this operation. In cases such as this one, we say that matrices must be compatible.

Lab Activity (1)
What do you get for each of the following?

>> A .^ 3
>> A ./ B

Initializing Vectors with Many Entries
. Suppose we want to create a vector, x, containing the values 1, 2, . . . , 100. We could do this using the colon operator:

>>  x = 1:100

Another useful MATLAB command is linspace. In general, linspace(a, b, n) generates a vector of n equally space points between a and b. So, if we want 100 equally spaced points between 0 and 1, you would type the following:

>>  n = 100;
>>  x = linspace(0, 1, n);

Lab Activity (2)
Create the following two matrix and vector in MATLAB:

Explain what the following commands do and try them to confirm that you were correct.  If you have a question feel free to ask:
>> A(1,2)
>> A(:,2)
>> A(1:3,1:3)
>> A(2,:)
>> min(A)
>> max(A)
>> mean(b)
>> max(b)
>> [m,i] = max(b)
>> median(b)
>> help max
>> sum(b)

Creating a simple two column data set.
Suppose you want to create a line graph for a set of x and y data points. There are two simple ways to create the two column data sets (matrix). In the first approach, you can create two single column data set, one for x and another for y and then put these two tgether side-by-side and in the other approach is to create the two column data as you go. Here is an example:
Date set x = {0 2 4 6 8 10}
y = {5 9 13 17 21 25}

Approach 1: Creating two single arrays and putting them together You have learned to create arrays, so you can do the same thing here:
x = [0 2 4 6 8 10]' % this is array x as a single column
y = [5 9 13 17 21 25]' % this is array y as a single column
z = [x y]
Now you have z with two columns.

Just to see something interesting:
Type: plot(z) % What do you produce?
Try this one: plot(x,y) % now what do you produce?

What is the difference ebtween these two plots?
Importing Excel file to MATLAB

There are a couple ways to import an Excel file to MATLAB. We will demonstrate this using the command xlsread with a sample excel spreadsheet called AprilWeatherBoone.xls. Before we can proceed with this lab activity we need to save the weather file on our PC.  To do this right click on AprilWeatherBoone.xls and use the Save Target As option to save it under Desktop directory.  Once you saved the file then at the MATLAB prompt, type:

Type whos at the command line to learn about the imported date. You should get:
num 30x10 2400 double array

which tells us that the variable num is a 30 × 10 matrix (double array). To see what the values are, just type num at the command line. Here is what you should get for the first 5 columns and first 12 rows (we left off some of the rows and columns due to space). To view the data type::

>> num

num =
63.9000     NaN     52.3000     NaN     7.0000
71.9000     NaN     43.9000     NaN     6.0000
66.8000     NaN     40.8000     NaN     12.0000
49.7000     NaN     31.6000     NaN     24.0000
56.9000     NaN     37.0000     NaN     18.0000
58.0000     NaN     39.9000     NaN     14.0000
75.9000     NaN     51.7000     NaN     4.0000
58.6000     NaN     34.6000     NaN     15.0000
55.7000     NaN     28.2000     NaN     24.0000
61.0000     NaN     28.6000     NaN     18.0000
66.6000     NaN     34.6000     NaN     12.0000
65.4000     NaN     43.5000     NaN     10.0000

If you'd like to read in just part of the spreadsheet, you could type: