Creating a Matrix from a Matrix

3.9 Creating a Matrix from a Matrix
Now that we have covered graph plotting, let’s look how to create a matrix from a matrix before we apply all of what we have learned to the t_z matrix from Example 2.2.

You might be wondering why on Earth one would want to further complicate his/her life by creating a matrix from another one. You’d be surprised to find out that it makes life a lot simpler.
 

3.9.1 Introducing the concept of creating a matrix from a matrix
Let’s first consider what creating a matrix from a matrix actually means. Let’s say you had the coordinates of ten capitals saved in a 10×2 matrix called capital_coordinates. The coordinates are saved such that x-coordinates of the capitals lie in the first column of the matrix and such that the y-coordinates lie in the second column. What if we wanted to create a plot that showed the x-positions of the capitals relative to one another without considering the y-coordinates?

We can do this by considering how matrix indexing works (refer to the matrix indexing section of our MATLAB tutorial series). Applying concept of matrix indexing to extract individual columns from an mxn matrix, you can plot the first column of the capital_coordinates to extract the x-coordinates of each capital. To extract the first column of the matrix, you can use the command: capital_coordinates(:,1). Now, to plot all the x-coordinates to a 1D set of points, you’d need to use the command: plot(capital_coordinates(:,1),0,’x’). Download and run the M-file within the attached zip file to understand what is going on.

Download:

 

Note: Why did the command include a 0 and an ‘x’? Well, we want a 1 dimensional plot so we want all the y-values to be 0. And what about the ‘x’? Well, we would like MATLAB to show the x-coordinates as different coloured crosses (refer back to the section on marker types).

What if we wanted to have a bird’s eye view of the locations of the cities relative to one another? We could plot the x-coordinates of each capital to their y-coordinates using the same concept. The command for that would be: plot(capital_coordinates(:,1),capital_coordinates(:,2),’x’).

I’m sure you’d agree that this is quite a long command and that there must be a better way to do this, and there is! This is where creating a matrix from another matrix comes into play. We can massively simplify the plot command and also the indexing by creating a new variable that directly relates to the x-coordinate column and another one to the y-coordinate column of the main matrix.

We can do this using the following code:

x_capital = capital_coordinates(:,1);
y_capital = capital_coordinates(:,2);
plot(x_capital,y_capital,'x');

 

Much better on the eyes, isn’t it? Download and run the M-file in the attached zip file to see this in action.

Download:

 

Exercise 3.3
Can you add labels to each of the coordinates to identify the coordinates? The list of cities and their coordinates are given in the names_of_capitals.txt file within the attached zip file.

Download:

 

Hint: you can do that by using the TextBox tool in the figure window in the ‘Insert’ menu. You should end up with a graph just like Figure 3.9.

Figure 3.9

Figure 3.9

 

3.9.2 Applying the concept of creating a matrix from a matrix
Here, we will apply the concept introduced to the t_z matrix from Exercise 2.2. For easier reference, the t_z data is again shown below.

Displacement at certain times
t(s) z (m)
0.0   1.000
0.1   0.955
0.2   0.900
…     …
…     …
10.0  0.270

 

Let’s say we wanted to plot z against t. We would first import it into a variable (say called t_z) and we can then do of two things to create the plot. We can either

  • use the indexing t_z(:,1) and t_z(:,2) in the plot function to represent t and z respectively, or
  • create new t and z variables using the indexing and then use the new variables in the plot function.

For the first option, the code would be:

plot(t_z(:,1), t_z(:,2));

 

For the second option, a possible code would be:

t = t_z(:,1);
z = t_z(:,2);

plot(t,z);

 

Which one you choose is up to you. The second option of creating two new variables includes more lines but simplifies massively the plot function.