Learning Goals #
- Understand the advantages of programming compared to spreadsheet operators.
- Conduct simple calculations in MATLAB.
- Work with variables and matrixes.
1. Introduction to MATLAB #
1.1. Why programming? #
A question frequently asked to us is why we would use programming instead of a tool such as Excel. This is of course a very valid question. Excel is an excellent, established and accessible tool that can be found on most computers. For the average analytical scientists it is very likely that the person is familiar with this program. We also use such programs for some of our work.
However, for analytical chemistry there are a number of reasons why it is worthwhile to invest in cultivating some programming skills. Programming languages offer tons of advantages.
- Data size: Tables of considerable size are manageable for Excel, but things get quickly tricky once we try to load one or several LC-MS datasets. Programming languages can easily handle large datasets.
- Compatibility: Excel works with most formatted data such as .CSV, but cannot process data formats frequently encountered in analytical chemistry, such as .mzXML and .netCDF. Most programming languages offer extensive support for all kinds of formats.
- Scalability: Sure it is possible to program some interesting functionality into a spreadsheet, but a programming language offers endless possibilities to automate and scale your computations.
1.2. Overview of MATLAB #
Let’s move on to the MATLAB interface. After you have downloaded and installed MATLAB, you will see the following window (Figure 2). This window will comprise of several components that may be displayed differently in your case.
First, there is the Current Folder window (A), which is used to show the folder in which you are working as well as other folders located in this folder. Generally, MATLAB will exclusively be able to work with files located in your Current Folder. It therefore makes sense to assign a dedicated folder on your computer.
2. Variables & Operations #
2.1. Operations #
Let’s start with working with the program and practice some simple commands. First, enter the following code and press Enter to execute it.
a = 1
Upon executing the above code, MATLAB will return the following
a =
1
We can see that MATLAB has assigned the value 1 to the variable that we have named “a”. In essence, we can store any information in a variable, and we can make as many variables as we want.
Now, also execute the following:
b = 2
c = a + b
We can see that – without us having assigned the value to it – MATLAB returns 3 as value for c. As you can see, you can name any variable as you wish.
| Operation | Expression |
|---|---|
|
Addition |
x + y |
|
Subtraction |
x – y |
|
Multiplication |
x * y |
|
Division |
x / y |
|
Inverse division |
x \ y (equivalent to y/x) |
|
Power |
x ^ y |
|
Square root |
sqrt(x) |
2.2. Vectors and matrices #
It happens continuously that we want to store several values in a single variable. For example, maybe we have a series (or array) of measurement results, or simple the entire chromatogram. We therefore need to talk about the terminology here and introduce some new concepts. Our variables can have different dimensionalities, or tensor orders, as is also shown by Figure 3.
Single values are zero-order tensors, whereas one-dimensional series of values are first-order tensors. Such a series is also known as a vector. A second-order tensor is a matrix, and third-order tensors are blocks.
Important for us is that a vector can be expressed in different ways. This is illustrated in Figure 4. A row vector is a horizontal 1 x m array
row_vector = [1 2 3]
yielding
row_vector =
1 2 3
Note how we use brackets to indicate that we are designing a vector. In contrast, a column vector is a vertical n x 1 array.
column_vector = [1; 2; 3]
resulting in
column_vector =
1
2
3
Here, we use the semicolon to indicate that the next value belongs to the new row.
When you have more data, a matrix will likely be a better expression for your data. An n x m matrix has n rows and m columns.
example_matrix = [1 2 3 4; 5 6 7 8; 9 10 11 12]
example_matrix =
1 2 3 4
5 6 7 8
9 10 11 12
Placing all these values was a lot of work, huh? Don’t worry, we’ll learn how to load files with large amounts of data into MATLAB in future tutorials.
2.3. Indexing #
We have now entered our first matrix into MATLAB! But how do we access the information stored in this matrix? This is done by indexing. Indexing refers to selecting specific values in a variable. Let’s take a fictive 3×4 matrix as shown in Figure 5A. This matrix features 3 rows and 4 columns. We now need to select 2 different values, which are indicated in pink.
For example, we can select a value in a matrix through
result = example_matrix(2,3)
result = example_matrix(:,3);
Subtract all values of Lab C from Lab D, and divide the 9th value of the result vector through the 5th value of Lab A. If needed, round your answer to 1 decimal.
Got it! This is the correct answer!
Oops! Almost? Try again!
3. Functions #
3.1. Using functions #
Now that we know how to enter and work with vectors and matrices, as well as can access information stored in them, let’s see if we can use this to our advantage.
MATLAB had a lot of built-in features, such as functions. These functions can be regarded as tools in a toolkit that can be used to perform various mathematical actions. Think about simple operations such as computing the mean of a vector, processing a signal from a chromatogram, but also imagine running an ANOVA with just a few lines of code.
Let’s start simple: a general function is composed of an output, the function name and input variables (often referred to as input arguments) which are needed to run the function. To apply this, make the following exercise.
To help you
matrix_mean = mean(example_matrix(:,3))
The mean() function is just one of the more simple functions. There are also function which offer the user to specify further optional input, such as the dimension of a matrix over which the mean should be calculated. These optional inputs are called kwargs (KeyWord Arguments).
3.2. Getting help #
Of course, it is difficult to guess the input arguments or kwargs of a function that we did not use before. MATLAB therefore offers the help and doc functions to help you.
To use the help function, you write “help function name”. For example
help mean
yields
mean Average or mean value.
S = mean(X) is the mean value of the elements in X if X is a vector.
For matrices, S is a row vector containing the mean value of each
column.
For N-D arrays, S is the mean value of the elements along the first
array dimension whose size does not equal 1.
mean(X,"all") is the mean of all elements in X.
mean(X,DIM) takes the mean along the dimension DIM of X.
mean(X,VECDIM) operates on the dimensions specified in the vector
VECDIM. For example, mean(X,[1 2]) operates on the elements contained
in the first and second dimensions of X.
S = mean(...,OUTTYPE) specifies the type in which the mean is performed,
and the type of S. Available options are:
"double" - S has class double for any input X
"native" - S has the same class as X
"default" - If X is floating point, that is double or single,
S has the same class as X. If X is not floating point,
S has class double.
Example:
X = [1 2 3; 3 3 6; 4 6 8; 4 7 7]
mean(X,1)
mean(X,2)
This was only a selection, but you can already see that there is an extensive information package.
MATLAB also offers an extensive documentation repository, which you can access by writing “doc function_name”. For example:
doc mean
This will prompt a window with extensive information along with a range of examples with example data. Aside from the additional examples, the information is also laid out in a structured way.
4. Troubleshooting #
We have done some basic MATLAB exercises, and began our MATLAB journey. However, at some point you will encounter errors and weird outputs. Perhaps you made a typo, or you used a function wrong.
For example, if we use our above example_matrix by indexing a number that didn’t exist, then we obtain:
example_matrix(6,:)
Index in position 1 exceeds array bounds.
Index must not exceed 3.
Or if we used a variable that did not exist yet:
apples
Unrecognized function or variable 'apples'.
4.1. General advice for coding #
- Frequently check if the outcome is meeting your expectations. For example, whether your calculation yields the expected output and dimensions.
- Google is your friend! When you do not know how to do something, Google it: “MATLAB how to calculate mean of each row of a matrix”. Every programmer does it.
- MATLAB is designed in a way that most of the errors will give you advice on how to solve them. Therefore, when you encounter an error, read the important part, and if you still do not understand: use the advice above!
For more information also look at the MATLAB website. Here you can find even more information about how to work with everything from matrices to different functions, and so much more.
Concluding remarks #
We have made huge steps already in these first hours of using MATLAB. From here on, it will only get easier. Now that we know how to use the program, we can start exploring what other powerful tools exist in the toolkit. This, as well as learning about other concepts, will be topics of further tutorials.
