CSE 200, Day 1, Matlab Intro

1. http://www.cyclismo.org/tutorial/matlab/
2. http://amath.colorado.edu/computing/Matlab/Tutorial/
3. http://www.math.utah.edu/lab/ms/matlab/matlab.html#tutorial
4. http://www.engin.umich.edu/group/ctm/basic/basic.html

Today, my goal is to motivate why we use MATLAB in this class (and why, in my biased opinion, it is probably the only programing language you need to know) by showing how much you can do with just a few commands. This is a 6 part demonstration.

1. Getting started. Run matlab. It often takes 1-2 minutes to get started. There may be a window with a graph on it that shows on the screen then disappears. When it finally starts up, you will be in the "matlab workspace" which has 3 windows, two small ones on the left, and one filling the right side. On the right side window, the command window, type 2+2, then press (enter). Don't go on to the next step until you see a 4. You can seek advice from/ help your neighbor to get to this point.
2. First exercise. A visualization of the Nyquist-Shannon sampling theorem (wiki). This theorem says that you can't see very high frequency signals if you don't have samples that are close together. Our plan here is to define a function: y = sin(x), and then look at that function with example "x" values with different spacings. Try typing the following into the command window:

   
    sin(0)         %(then press enter)
    sin(180)       %(then press enter)
    sin(3.14159)   %(then press enter)
   

   Note: the "%" character is a comment (like // in java). Matlab won't pay attention to any part of a line after a %. Tthe number Pi comes up all the time in math, wouldn't it be nice if there was a way to use "Pi" without typing all the digits? try typing

   
   sin(pi)
   sin(Pi)
   

   Pop quiz.
   • (Circle T or F) MATLAB is case sensitive. That is, does matlab care about the capitalization of what you type?
   • (Circle the correct answer) MATLAB interprets arguments to the "sin" function as degrees or radians?
3. It is difficult to understand a function by looking at one value at a time, so we want to look at the function for many values of x. If you've done programming in the past, you might be thinking something like, "how can I do a for loop in matlab?" This is not the Tao of Matlab. Instead, let's specify the values of x we are interested in as a vector. In the command window, try each of the following:

   
   1:100
   sin(1:100)
   plot(sin(1:100))
   

   The quick explanation of what you see is:
   • 1:100 is matlab syntax for make a vector (a list) starting at 1 and going to 100.
   • sin(1:100) is matlab syntax for compute the sin of a list of numbers starting at 1 and going to 100.
   • plot(sin(1:100)) is matlab syntax for plot the values that you get when you take the sin of a list of numbers starting at 1 and going to 100.
   Thank goodness that we have programming languages, because writing out these instructions in english gets unwieldy.
4. This is a useful time to introduce variables. They help make what you are doing more understandable, even if you don't strictly need them. The better way to write the above lines would be:

   
   x = 1:100
   y = sin(x)
   plot(y)
   

   This assigns the vector [1 2 3 ... 100] to the variable x, Then assigns sin(x) to the variable y, then plots that variable. Matlab has the pleasant feature that when you assign something to a variable, it also prints the value (or vector, or matrix) to the command window. if you add a semi-colon to the end of the line, it does not print this out. Notice the difference between:

   
   x = 1:100             % and...
   x = 1:100;
   

5. Now, suppose we want to sample our function more densely. we can use:

   
   xDense = 1:.1:100;    % this make a list [1 1.1 1.2 1.3 1.4 ... 100]
   yDense = sin(xDense);
   plot(yDense);
   

   and then try the "zoom in" tool (the magnifying glass with a "+", to zoom in to the figure and see how smooth it is. If we want to sample our function less densely. we can use:

   
   xSparse = 1:13:100;    % this make a list [1 14 27 40 ... ~100]
   ySparse = sin(xSparse);
   plot(ySparse);
   

   Now, the best part of matlab is that it makes it easy to plot things. To compare y, yDense, and ySparse, we can use the following commands:

   
   clf;                       % this clears the figure.
   plot(y);                   % plot the original y values
   hold on;                   % tell matlab not to clear the figure
   plot(ySparse,'r');         % plot the ySparse values, in red.
   

   With luck, you see a blue sin curve, and the start of a different sin curve in red. Is that what you expected? We were trying to plot the same function, just sampled at different frequencies... the range of our function should have been the same. This is a good chance to introduce the "help" function. type:

   
   help plot
   

   You may have to scroll up to see the beginning of this help function. Take a few minutes to see if you can figure out what happened. See if you can fix the problem...

   
   seriously, try to figure it out on your own.
   

   You can use "help command" for any command in matlab. So far the only two matlab commands you've seen are "sin" and "plot". The tutorials at the top of this page introduce you to a large number of useful commands.

   ok, ok, so the problem is we asked matlab to plot a list of y-values, without telling if what the x-values should be. Matlab tries to be helpful... if you only give it a list of y values, it assumes the x-values are 1,2,3,4 etc... So, to fix this, we can try the following:

   
   clf;                       % this clears the figure.
   plot(x,y);                 % plot the original y values
   hold on;                   % tell matlab not to clear the figure
   plot(xSparse,ySparse,'r'); % plot the ySparse values, in red.
   plot(xDense,yDense,'g');   % plot the ySparse values, in green.
   

   What you are seeing here is our function, y = sin(x). When sampled with a spacing of 0.1 (shown in green), it gives a relatively smooth sin curve. When sampled with a spacing of 1 (shown in blue), it gives an approximation to the sin curve. When sampled with a spacing of 13, it gives a completely different frequency. This is because sampling this function every 13 points is "below the Nyquist limit", it cannot capture the frequency of the function.
   • Pop Assignment. What is the Nyquist limit for this function? That is, try a collection of different definitions of xSparse, then compute ySparse = sin(xSparse), and plot them. At what spacing does the sparse sampling start to miss the original sin curve?
     
     
     
     
6. So plotting curves in matlab is part of what matlab is good at. But i think more motivation is in order. You can copy the below lines into matlab chunk by chunk to see some of the power of what it can simply do.

   
   clf;                       % this clears the figure.
   
                              % grab current wash U webcam image.
   cameraURL = 'http://166.211.74.92/jpg/image.jpg'
   % cameraURL = 'http://210.236.173.198/axis-cgi/jpg/image.cgi'
   im = imread(cameraURL);  
   image(im);                 % display the image
   
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   % so we can read and display an image.  not so exciting.  try this:
   
   for n = 1:30               % loop 30 times.
                              % grab and display image
     im = imread(cameraURL);
     image(im);               
   
     drawnow;                 % force matlab to draw the figure right now.
     pause(0.5);              % pause .5 seconds
   end                        % end of loop
   
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   % so we can read and display a live movie.  a little exciting?  try this:
   
   
   colormap gray;                   % color is over-rated.  lets show only grays.
   imA = imread(cameraURL);  
   imA = double(rgb2gray(imA));     % make it a double so we can do math with it.
   for n = 1:300                    % loop 30 times.
                                    % grab new image
     imB = imread(cameraURL);  
     imB = double(rgb2gray(imB));   % make it a double so we can do math with it.
   
     imDiff = imB-imA;              % make a difference image
   
     subplot(1,2,1);                % Seperate the figure into 2 parts,
                                    % and get ready to plot in the first one.
     imagesc(imA);                  % show the image
   
   
     % show where things have changed.
     subplot(1,2,2);                % Seperate the figure into 2 parts,
                                    % and get ready to plot in the second one.
     imagesc(imDiff,[-80 80]);      % show the difference image 
   
     drawnow;                       % force matlab to draw the figure right now.
     pause(0.5);                    % pause .5 seconds
   
     imA = imB;                     % keep the newest image around for the next iteration.
   end                             %end the foor loop
   
   

   A little bit of commentary on this function. This was intended as a brief introduction to what matlab can do with just a few commands. However, this short program illustrates a few of the things we've talked about. First, why the semi-colons? Languages like C and Java require semi-colons. In matlab they are optional, but you almost always use them when you are programming in matlab; usually you want to assign data values to a variable, rather then printing out numbers on a screen. For instance, type the last line above (imA = imB) without the semi-colon (and press enter). "blechh!", especially when dealing with images, we really don't want to have to have all our data printed on the screen.