An Introduction to Matlab

Brien Alkire

Last Revised:  2:26PM, Jan 10, 2000

Contents:

          Starting Matlab and Entering Data

          Saving And Restoring Workspace

          Getting Help

          Visualization

          Programming and M-Files

          Debugging M-Files

 

Starting Matlab and Entering Data

We will use Matlab extensively in this course to learn how to pose and solve engineering problems with a computer.  Matlab is an interactive environment that allows us to easily enter data, numerically solve problems and it provides graphing capabilities so we can visualize the results.

To start Matlab on a Windows machine, click Start\Programs\Matlab\Matlab or click on the Matlab icon on your desktop.  To start Matlab from a UNIX machine, type ‘matlab’ at a command prompt.  The Matlab command window and command line should appear similar to that shown in Figure 1.

 


 


Figure 1 - The Matlab command line as viewed on a Windows machine.

From the Matlab command line, we may enter numbers directly.  Let’s compute 23 using Matlab:

» 2^3

 

ans =

 

     8

 

Observe that Matlab uses the variable ans to store the results of the last operation.  You can type the name of a variable at the command line and Matlab will respond with its numerical value:

» ans

 

ans =

 

     8

We can enter our own variables as well.  For instance,

» x=1+3i

 

x =

 

                          1 +                     3i

creates the variable x that represents a complex number with real part equal to one and an imaginary part equal to three.  We can also create variables that represent vectors and matrices.  Let’s create a variable A to represent a matrix with three rows and four columns containing the numbers 1 through 12 (row-wise).  We indicate the beginning of the matrix with the character ‘[‘ and the end with the character ‘]’.  We separate elements across a row using a blank space or a comma.  We separate elements down a column using a semicolon.

» A=[1 2 3 4;5 6 6 8;9 10 11 12]

 

A =

 

     1     2     3     4

     5     6     6    8

     9    10    11    12

Observe that a mistake was made, the element at row 2, column 3 is a 6.  It should be a 7.  Fortunately we don’t have to retype the entire matrix.  We may simply change the element using its row and column indices.

» A(2,3)=7

 

A =

 

     1     2     3     4

     5     6     7     8

     9    10    11    12

There are other ways to fix the mistake too, observe that hitting the up arrow key cycles the Matlab command line through prior commands.  We can simply find the original line we used to enter A and modify it to correct the error. 

» A=[1 2 3 4;5 6 7 8;9 10 11 12]

Perhaps we wish to obtain the transpose of the matrix, that is, perhaps we wish to swap the rows and columns of the matrix.  The single quotation mark can be used to generate the transpose:

» A'

 

ans =

 

     1     5     9

     2     6    10

     3     7    11

     4     8    12

We can perform arithmetic with vectors and matrices the same way as we did with scalars.  For instance, we can compute the product of A with its transpose and assign the result to a new variable B.

» B=A*A'

 

B =

 

    30    70   110

    70   174   278

   110   278   446

Note that we get an error if we forget the transpose operator and try to multiply A with itself.  Why?

Saving and Restoring Workspace

At this point you may be bored with our little tutorial and wish to spend a few hours with your friends in the village.  If you leave your computer unattended you run the risk of someone (an evil roommate perhaps) closing Matlab in which case you might loose the data you tediously entered.  Fortunately we may save the Matlab workspace to disk for retrieval at a later time.  First let’s obtain a summary of the variables we have so far, use the ‘whos’ command.

» whos

  Name      Size         Bytes  Class

 

  A         3x4             96  double array

  B         3x3             72  double array

  ans       3x3             96  double array

  x         1x1             16  double array (complex)

To save the workspace we can type

» save practicedata

which saves the data in the file ‘practicedata.mat’ in the current directory.  To verify that the file is there, we can actually execute shell commands from Matlab.  On a Windows machine we can type ‘dir’ to get a directory listing.  On a UNIX machine we can type ‘ls’ to get a directory listing.  We must precede the shell command with an exclamation point (actually, some commands work without it).

 » !dir

 Volume in drive C is Applications1

 Volume Serial Number is 40ED-0A50

 

 Directory of C:\MATLABR11\work

 

01/07/00  09:58p        <DIR>          .

01/07/00  09:58p        <DIR>          ..

01/07/00  09:55p                   416 practicedata.mat

               3 File(s)            416 bytes

                            582,668,800 bytes free

Now our data is stored safely on disk.  Let’s clear out the variables in our workspace so it’s as if we’ve closed Matlab and reopened it.  We use the ‘clear’ command to remove all variables and then obtain another summary.

» clear

» whos

Matlab doesn’t list any variables after the ‘whos’ command which verifies that all variables have been cleared.  We may now restore the workspace using the ‘load’ command.

» load practicedata

» whos

  Name      Size         Bytes  Class

 

  A         3x4             96  double array

  B         3x3             72  double array

  ans       3x3             96  double array

  x         1x1             16  double array (complex)

 

Grand total is 34 elements using 280 bytes

Suppose we only want to save a few variables instead of all of them, how do you think we’d accomplish that?  Try typing ‘help save’ to obtain more information.

On a Windows machine we may alternately using the menu items File\Save Workspace and File\Load Workspace to save and restore the workspace respectively.

Getting Help

Help information for a command may be obtained by typing ‘help’ followed by the name of the command.  For instance, type ‘help save’ to get information about saving workspace.  If we need more general information we simply type ‘help’.

» help

 

HELP topics:

 

matlab\general       -  General purpose commands.

matlab\ops           -  Operators and special characters.

matlab\lang          -  Programming language constructs.

matlab\elmat         -  Elementary matrices and matrix manipulation.

matlab\elfun         -  Elementary math functions.

matlab\specfun       -  Specialized math functions.

matlab\matfun        -  Matrix functions - numerical linear algebra.

matlab\datafun       -  Data analysis and Fourier transforms.

matlab\polyfun       -  Interpolation and polynomials.

matlab\funfun        -  Function functions and ODE solvers.

matlab\sparfun       -  Sparse matrices.

matlab\graph2d       -  Two dimensional graphs.

matlab\graph3d       -  Three dimensional graphs.

matlab\specgraph     -  Specialized graphs.

matlab\graphics      -  Handle Graphics.

matlab\uitools       -  Graphical user interface tools.

matlab\strfun        -  Character strings.

matlab\iofun         -  File input/output.

matlab\timefun       -  Time and dates.

matlab\datatypes     -  Data types and structures.

matlab\winfun        -  Windows Operating System Interface Files (DDE/ActiveX)

matlab\demos         -  Examples and demonstrations.

signal\signal        -  Signal Processing Toolbox.

signal\siggui        -  Signal Processing Toolbox GUI

signal\sigdemos      -  Signal Processing Toolbox Demonstrations

toolbox\tour         -  MATLAB Tour

MATLABR11\work       -  (No table of contents file)

toolbox\local        -  Preferences.

 

For more help on directory/topic, type "help topic".

You can obtain the same information in a separate window by typing ‘helpwin’.  This produces a list of help topics.  Then for instance, we can type ‘help elfun’ to obtain information about elementary math functions.

» help elfun

 

  Elementary math functions.

 

  Trigonometric.

    sin         - Sine.

    sinh        - Hyperbolic sine.

    asin        - Inverse sine.

    asinh       - Inverse hyperbolic sine.

    cos         - Cosine.

    cosh        - Hyperbolic cosine.

    acos        - Inverse cosine.

    acosh       - Inverse hyperbolic cosine.

    tan         - Tangent.

    tanh        - Hyperbolic tangent.

    atan        - Inverse tangent.

    atan2       - Four quadrant inverse tangent.

    atanh       - Inverse hyperbolic tangent.

    sec         - Secant.

    sech        - Hyperbolic secant.

    asec        - Inverse secant.

    asech       - Inverse hyperbolic secant.

    csc         - Cosecant.

    csch        - Hyperbolic cosecant.

    acsc        - Inverse cosecant.

    acsch       - Inverse hyperbolic cosecant.

    cot         - Cotangent.

    coth        - Hyperbolic cotangent.

    acot        - Inverse cotangent.

    acoth       - Inverse hyperbolic cotangent.

 

  Exponential.

    exp         - Exponential.

    log         - Natural logarithm.

    log10       - Common (base 10) logarithm.

    log2        - Base 2 logarithm and dissect floating point number.

    pow2        - Base 2 power and scale floating point number.

    sqrt        - Square root.

    nextpow2    - Next higher power of 2.

 

  Complex.

    abs         - Absolute value.

    angle       - Phase angle.

    complex     - Construct complex data from real and imaginary parts.

    conj        - Complex conjugate.

    imag        - Complex imaginary part.

    real        - Complex real part.

    unwrap      - Unwrap phase angle.

    isreal      - True for real array.

    cplxpair    - Sort numbers into complex conjugate pairs.

 

  Rounding and remainder.

    fix         - Round towards zero.

    floor       - Round towards minus infinity.

    ceil        - Round towards plus infinity.

    round       - Round towards nearest integer.

    mod         - Modulus (signed remainder after division).

    rem         - Remainder after division.

    sign        - Signum.

Typing ‘helpdesk’ will start your web browser and open an HTML based help system.

What do you think we’d get if we sought help on the help command?  Try it and see.

Visualization

Matlab has many features that allow us to visual data.  Let’s generate a vector of sine wave samples and plot the results.  First we will create a length 100 vector represented by the variable x containing all zeros using the ‘zeros’ function.  Then we will use a for-loop to fill the vector with sine wave samples.  Note that in the following example, we place a semicolon at the end of the line ‘x(k)=sin(k*2*pi/100);’, this prevents the value of ‘x(k)’ from being displayed during each iteration of the loop.

» x=zeros(100,1);

» for k=1:100

x(k)=sin(k*2*pi/100);

end

To plot the results we simply use the ‘plot’ command.  We follow this command with the ‘xlabel’, ‘ylabel’ and ‘title’ commands to label the plot, these commands are completely optional.

» plot(x)

» xlabel('sample index');

» ylabel('sample value');

» title('Sine wave');

A plot should appear in a separate window.  It should be similar to that shown in Figure 2. 


 


Figure 2 – Sine wave plot.

Next, let’s superimpose a second plot.  For the second plot we’ll use a sine wave of twice the frequency.  It is important to point out that for-loops are very inefficient in Matlab.  In time critical applications we should find ways to eliminate the use of for-loops.  For generating a sine wave it is simple and we will show how by example.  We’ll create a length 100 vector represented by the variable z containing the samples of our second sine wave. 

» z=sin( (1:2:200)*2*pi/100 );

The statement ‘(1:2:200)’ generates a sequence of numbers from 1 to 200 in increments of 2 (actually, from 1 to 199).  That is, it creates the vector [1 3 5 … 199].  Do not use ‘plot(z)’ at this juncture for it will overwrite the existing plot.  Since we wish to superimpose the plots, we use the ‘hold’ command.

» hold on;

Since we wish to differentiate x from z, we plot z in the color red and using a dotted line using a slightly different version of the ‘plot’ command.

» plot(z,'red.')

The plot should appear similar to that shown in Figure 3.  If we then use the command ‘hold off’, future plot commands will overwrite the existing plot. 


 


Figure 3 – Superimposed sine wave plots.

What if we wanted a legend to accompany our plot?  Much more sophisticated plots are possible.  Try using the help system to obtain more information about plots and related topics.

Programming and M-Files

So far we have done all of our work using the Matlab command line.  We used functions like ‘sin’ for generating data.  M-files provide a way for us to write our own functions.  An m-file is a script that allows us to sequence commands.  Any command that can be used from the command line can be used in an m-file.

Let’s write an m-file to generate the two vectors x and z from the previous example.  The function prototype should look like this:

[x,z]=generatesinewaves( n );

where n is the length of the vectors.  The m-file should plot the vectors and return them.  We use a text editor to create m-files. 

On a UNIX machine for instance we can use a text editor such as emacs or vi.  Create a text file with the filename ‘generatesinewave.m’ (for example, type ‘vi generatesinewave.m’ at a command line in the same directory that you used for starting Matlab). 

On a Windows machine, we can also use any text editor such as notepad, but there’s a built-in editor called ‘MEdit’ that has some useful debugging utilities.  To start MEdit, click File\New\M-File from the Matlab menu.

The first line of the m-file must contain the keyword ‘function’ followed by the function prototype.

function [x,z]=generatesinewaves( n );

Enter this line now.  With MEdit, click File\Save now and it will automatically generate the correct filename.  The lines following the first will contain the help information that can be displayed from the Matlab command line by typing ‘help generatesinewaves’.  Each line of the help information must begin with the ‘%’ character, this character indicates that the line is a comment.  The first comment line should be the function prototype.  Enter the help information now, the m-file so far should appear as follows:

function [x,z]=generatesinewaves( n );

% [x,z]=generatesinewaves(n);

% Input:

% n - the number of samples

% Output:

% x - a vector containing n samples of a single cycle of a sine wave

% z - a vector containing n samples of two cycles of a sine wave

%

% Plots of the sine waves are generated automatically.

Now we are ready to list the commands needed to generate the vectors and plot the results.  The complete m-file is shown below, notice that we have used additional comments in the code to make it more readable.

function [x,z]=generatesinewaves( n );

% [x,z]=generatesinewaves(n);

% Input:

% n - the number of samples

% Output:

% x - a vector containing n samples of a single cycle of a sine wave

% z - a vector containing n samples of two cycles of a sine wave

%

% Plots of the sine waves are generated automatically.

 

% Generate the vectors x and z

x=sin( (1:1:n)*2*pi/n );

z=sin( (1:2:n)*2*pi/n );

 

% Plot the results

plot(x);

xlabel('sample index');

ylabel('sample value');

title('Sine waves');

hold on;

plot(z,'red.');

Save the file when you’ve finished entering it.  Note:  you should save the m-file in the current directory in which Matlab is running or else Matlab may not be able to find the m-file.  To determine what directory Matlab is running in you can type ‘pwd’ from the Matlab command line. 

Now we are ready to test the m-file.  Type ‘help generatesinewaves’ at the Matlab command line and ensure that the help information is displayed properly.

» help generatesinewaves

 

  [x,z]=generatesinewaves(n);

  Input:

  n - the number of samples

  Output:

  x - a vector containing n samples of a single cycle of a sine wave

  z - a vector containing n samples of two cycles of a sine wave

 

  Plots of the sine waves are generated automatically.

Now test the by typing

  [x,z]=generatesinewaves(100);

at the command line.  If everything was entered correctly you should obtain a plot of the sine waves and the variables x and z should contain the samples.  If there’s a syntax error, you will get a detailed error message.  For instance, suppose we misspelled the command ‘sin’ as ‘sine’:

x=sine( (1:1:n)*2*pi/n );

The following error message is displayed in response to this syntax error

» [x,z]=generatesinewaves(100);

??? Undefined function or variable 'sine'.

 

Error in ==> C:\MATLABR11\work\generatesinewaves.m

On line 12  ==> x=sine( (1:1:n)*2*pi/n );

which suggests that you should inspect line 12 and that you should check the validity of the call to ‘sine’.  The next section covers some debugging fundamentals.

What happens if we call ‘generatesinewave’ and forget to pass in the size n?  What if n has a fractional part (say n=1.2) or is negative?  Check the help information for the functions ‘ceil’ and ‘floor’ and see if you can add code to verify that n is a positive and has no fractional part.  Also, check the ‘error’ function for a way of reporting errors detected in your m-files.

Debugging M-Files

As discussed in the last section, syntax errors will prevent a function from being invoked.  A detailed error message will be generated.  But logic errors are more difficult to find, they may allow a function to run until the logic error is encountered.  There are several debug commands available to help you in debugging your m-file.  Type ‘help debug’ at the command line now to get a listing of available debugging commands.

Perhaps the most useful debugging tool is the ‘keyboard’ command.  This allows us to stop execution of an m-file at a particular location in a file and return control to the keyboard for inspecting the values of variables and for using the debug commands to step through the code.

As an example insert the ‘keyboard’ command in your m-file as shown below.

function [x,z]=generatesinewaves( n );

% [x,z]=generatesinewaves(n);

% Input:

% n - the number of samples

% Output:

% x - a vector containing n samples of a single cycle of a sine wave

% z - a vector containing n samples of two cycles of a sine wave

%

% Plots of the sine waves are generated automatically.

 

% Generate the vectors x and z

x=sin( (1:1:n)*2*pi/n );

z=sin( (1:2:n)*2*pi/n );

 

% Plot the results

keyboard;

plot(x);

xlabel('sample index');

ylabel('sample value');

title('Sine waves');

hold on;

plot(z,'red');

Remember to save the m-file after modifying it or your changes will not be instantiated.  Now execute the function by typing ‘[x,z]=generatesinewaves(100)’ at the command line.  When execution gets to the ‘keyboard’ command, the Matlab command line should return the prompt

K»

Execution is suspended before the ‘plot’ function.  You can use the command line to inspect the values of x and z.  You can use the ‘dbstep’ command to execute the next line in the m-file.  Experiment with the debug commands.  The ‘dbquit’ will stop the debugger.

If you are using MEdit then debugging is even easier.  You don’t need to use ‘keyboard’ or the debug commands at all.  Simply set your cursor next to the ‘plot’ function.  Then click the Debug\Set/Clear Breakpoint menu item from the MEdit menu.  Then run the m-file by typing ‘[x,z]=generatesinewaves(100)’ at the Matlab command line.  Execution will stop at the ‘plot’ function.  You can inspect the values of variables by placing the cursor over the variables in the m-file.  If you return to the Matlab command line, you will see that you can also use the command line to inspect the values of variables.  Use the “Debug” menu of MEdit to step through lines of code.  See Figure 4.

 


 


Figure 4 – An m-edit debugging session.  Execution has halted at the breakpoint before the ‘plot’ command.  The cursor is placed over the variable x which causes its contents to be displayed.