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matlab [2026/04/20 19:35] – ARCHIVED asimonsmatlab [2026/09/06 00:19] (current) – removed lnor
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-<html> +
-<p><div align="center">   +
-<h1> ARCHIVED MATERIAL</h1>               +
-<h1>A Beginning MATLAB Tutorial for&nbsp;</h1></p> +
-<p><h1>the UC Davis Department of Mathematics</h1></p> +
-<p>by Sarah Williams<br> +
-                <br> +
-                updated 9/15/2003<br> +
-                </div></p> +
-<p><hr>  <font size="+1">Introduction and Overview</font><br></p> +
-<p><ul> +
-            <li>What is MATLAB?</li> +
-            <li>Why use MATLAB? Why not?</li> +
-              <!-- <li>What to expect from this workshop and beyond </li> --></p> +
-<p></ul> +
-           <font size="+1">Command-Line MATLAB</font><br></p> +
-<p><ul> +
-           <li>Launch MATLAB</li> +
-           <li>Generate matrices</li> +
-           <li>Implement functions</li> +
-           <li>Write a small program that generates a plot</li></p> +
-<p></ul> +
-           <font size="+1">M-File MATLAB</font><br></p> +
-<p><ul> +
-           <li>Directory Structure (where will you save your file?)</li> +
-           <li>Put your small program into an m-file, and run it</li> +
-           <li>Scripts vs. Functions: write a function m-file</li> +
-  <li>Get your Scripts and Functions Talking</li> +
-  <li>Add More Features and Get More Help<br><p>  </li></p> +
-</p> +
-<p></ul> +
-           <font size="+1"></font> +
-<ul></p> +
-<p></ul></p> +
-<p><hr width="100%" size="2"><font size="+1">Introduction and Overview</font><br> +
-          <br></p> +
-<p>Please note that MatLAB can be accessed both on the department computers and from home via SSH.  From home, one can even combine SSH with X Windows to use the graphical version of MatLAB.</p> +
-<h2><h3><a name="IntroA"></a>What is MATLAB?</h3></h2> +
-<p>          MATLAB is both a programming language and a software package. &nbsp;"MATLAB" +
-     stands for "Matrix Laboratory." &nbsp;Accordingly, many features exploit  +
-    matrices, and assume you are working with matrices. &nbsp;MATLAB  +
-generally solves  +
-  problems numerically, not symbolically (compared to Mathematica).<br> +
-          <br></p> +
-<p><h3><a name="IntroB"></a>Why use MATLAB? Why not?</h3> +
-          Pros:<br></p> +
-<p><ul> +
-            <li>It's easy to start using MATLAB, with or without prior programming +
-     experience.</li><p>            <li>MATLAB has a lot of built-in mathematical knowledge; e.g.  +
-MATLAB    has  a function to find the 1-, 2-, or max-norm of a vector -- you +
-don't   have to program this yourself.<br> +
-            </li> +
-            <li>MATLAB has a lot of very powerful "toolboxes" to work in +
-specific     areas of math (optimization, wavelets, etc.)</li> +
-            <li>It's easy to produce nice graphs.</li></p> +
-</p> +
-<p></ul> +
-Cons:<br> +
-<ul> +
-  <li>MATLAB has a lot of "overhead," like graphics and notation that make +
-it easy to use. &nbsp;This can slow it down compared to more bare-bones programming +
-languages (like C, FORTRAN). MATLAB may be too slow to solve some  +
-large problems.</li><p>  <li>MATLAB is not free - although we have good access at school (and you +
-can run the school's version remotely), if you happen to want your own private +
-copy, it costs $100 for students, and more for each toolbox.</li> +
-</ul></p> +
-</p> +
-<p><!--                                   +
-<h3>What to expect from this workshop and beyond</h3> +
-          After this workshop, you will be able to:<br></p> +
-<p><ul> +
-            <li>complete a practice MATLAB homework assignment (based  +
-on mat228a)</li> +
-            <li>write a program, save it, run it, edit it, and run it again</li><p>            <li>save subroutines in different files and call them from the +
- main   program<br> +
-            </li> +
-            <li>make simple graphs</li> +
-            <li>look for more help in the MATLAB documentation</li></p> +
-</p> +
-<p></ul> +
-          After working with MATLAB this quarter, you can expect to:<br></p> +
-<p><ul> +
-            <li>be familiar with a lot of useful functions built into MATLAB</li> +
-            <li>recognize common error messages and how to fix them</li> +
-            <li>make more complex graphs<br> +
-            </li></p> +
-<p></ul> +
---></p> +
-<p><hr width="100%" size="2">           +
-<ul></p> +
-<p></ul> +
-           <font size="+1">Command-Line MATLAB</font><br></p> +
-<p><h3>Launch MATLAB</h3></p> +
-<p><ul> +
-            <li>Click (once) on the MATLAB icon. (Enter your password  +
- when   prompted.)</li> +
-<li>OR from the terminal window type "ssh sine" (enter) and then  +
-"matlab"</li></p> +
-<p></ul></p> +
-<p><h3>Generate matrices</h3></p> +
-<p><ul> +
-            <li>Find the panel called the Command Window. &nbsp;This is where  +
-  we  will  be working.</li> +
-            <li>Type the following commands:</li><p>  <ul> +
-             <li>In what follows, the&nbsp;<font +
- face="Courier New, Courier">&gt;&gt;</font>    symbol is meant to represent  +
- the MATLAB prompt (i.e., don't type this yourself).</li><p>             <li>Hit the return key at the end of each line; observe the +
-result    and  try to understand the cause-and-effect of your commands.  +
-   </li></p> +
-</p> +
-<p>  </ul> +
-           <br> +
-                <font face="Courier New, Courier">&gt;&gt; A = [1 2 3; 4 5  6]<br> +
-          &gt;&gt; B = [7; 8; 9] <br> +
-          &gt;&gt; C = A*B<br><p>             <br> +
-             </font>    <li>Now try a slightly different version of the same +
-  thing:<br> +
-             <br> +
-              <font face="Courier New, Courier">&gt;&gt; clear<br> +
-                                            &gt;&gt; A = [1 2 3; 4 5 6];</font>  +
-   (note  the semicolon at the end)<br><p>              <font face="Courier New, Courier">&gt;&gt; B = [7 8 9]'; </font> +
-   (note   the apostrophe)<br> +
-              <font face="Courier New, Courier">&gt;&gt; C = A*B; <br> +
-                                            &gt;&gt; C<br> +
-                                            &gt;&gt; C'<br></p> +
-</p> +
-<p>             <br> +
-             </font></li> +
-            <li>Accessing matrix entries (vector components):<br> +
-             <br> +
-              <font face="Courier New, Courier">                         +
-         &gt;&gt;</font>&nbsp;A<br> +
-             <font face="Courier New, Courier">                          +
-        &gt;&gt;</font>&nbsp;A(1,1)<br><p>              <font face="Courier New, Courier">                         +
-         &gt;&gt;</font>&nbsp;A(1,2)<br> +
-              <font face="Courier New, Courier">                         +
-         &gt;&gt;</font>&nbsp;A(2,1)<br> +
-              <font face="Courier New, Courier">                         +
-             </font><font face="Courier New, Courier">                   +
-               &gt;&gt;</font>&nbsp;B<br> +
-             <font face="Courier New, Courier">&gt;&gt;</font>&nbsp;B(1,1)<br> +
-              <font face="Courier New, Courier">                         +
-         &gt;&gt;</font>&nbsp;B(1)<br></p> +
-<p>              <font face="Courier New, Courier">                         +
-         &gt;&gt;</font>&nbsp;B(3)<br> +
-             <br> +
-           </li> +
-            <li>A very handy way of making uniformly spaced "grids" in MATLAB:<br> +
-            <br> +
-                <font face="Courier New, Courier">&gt;&gt; clear<br></p> +
-<p>          &gt;&gt; X = 1:5 <br> +
-          &gt;&gt; Y = 3:0.3:5 <br> +
-                                                  &gt;&gt; Z = [0:(pi/4):(2*pi)]'<br> +
-            <br> +
-            </font></li> +
-            <li>To  review:</li></p> +
-</p> +
-</p> +
-<p>  <ul> +
-              <li>Put square brackets [] around matrices.</li> +
-              <li>You will get a single row if you just type numbers in the  +
- brackets.    &nbsp;To go to the next row, type a semicolon.</li> +
-              <li>Use * for matrix multiplication (works for regular multiplication, +
-     too).</li> +
-              <li>MATLAB repeats what you just typed. &nbsp;To suppress this,  +
-  put   a semicolon ; at the end of the line.</li> +
-              <li>To see the value of a matrix (or other variable) you've  +
-entered,     just type its name and hit return.<br><p>              </li> +
-              <li>An apostrophe gives you the transpose (the complex conjugate +
-   transpose,   in fact) of the matrix.<br> +
-              </li> +
-              <li>To refer to the component of matrix A in the mth row down  +
- and   nth  column over, type A(m,n). &nbsp;If A is a row or column vector,  +
- you  can just  type A(j) to see the jth component. &nbsp;<br> +
-              </li> +
-              <li>The colon : notation gives you uniformly spaced grids (row +
-  or  column  vectors). &nbsp;The first number is the left endpoint of the +
- grid.  &nbsp;If  you include a middle number, it's the grid spacing (delta +
- x); if  you don't  state a value here, MATLAB assumes you want a value of +
- 1. &nbsp;The  last number is the maximum right endpoint of the grid.</li></p> +
-<p>              <li>The command "clear" erases all the variable values you've  +
- assigned    so you can start fresh. &nbsp;Use this often -- MATLAB has a  +
-bad habit of   leaving remnants of old variables lying around unless you explicitly +
-clear   them out.&nbsp; &nbsp;<br> +
-              </li></p> +
-</p> +
-<p>  </ul></p> +
-</p> +
-<p></ul></p> +
-<p><h3>Implement functions</h3></p> +
-<p><ul> +
-            <li>Type the following commands:<br><p>            <br> +
-                <font face="Courier New, Courier">&gt;&gt; clear <br> +
-                                                  &gt;&gt; c = -pi/2; <br> +
-                                                  &gt;&gt; X = [0:0.1:1]'; +
-     <br> +
-           <br> +
-                                                  &gt;&gt; sin(c)<br></p> +
-<p>        </font><br> +
-                                                    Now, type the "up" arrow.  +
-   MATLAB   will display the last thing you typed.                        +
-             (Type "up" again and you can move backwards through your command +
-   history.)                                            Use the arrow keys +
- to  edit the last  line to read:<br> +
-           <br> +
-               <font face="Courier New, Courier"> &gt;&gt; sin(X) <br> +
-              <br> +
-                                                  &gt;&gt; sqrt(c) </font></p> +
-<p> (Note    the  imaginary value.)<br> +
-               <font face="Courier New, Courier"> &gt;&gt; sqrt(abs(c))<br> +
-              <br> +
-                                                  &gt;&gt; Y = exp(X)<br> +
-                                                  &gt;&gt; Z = log(Y)<br><p>                                                  </font></li></p> +
-</p> +
-</p> +
-<p></ul></p> +
-<p><h3>Write a small program that generates a plot</h3></p> +
-<p><ul> +
-            <li>Type the following commands to plot a semi-circle:<br> +
-       (Note: <font face="Courier New,Courier">.^</font> gives the component-wise +
-     square, i.e., it raises each entry of X to the power of 2.) <br><p>                <font face="Courier New, Courier"><br> +
-       &gt;&gt; clear <br> +
-                                                  &gt;&gt; X = -2:0.1:2; +
-    <br> +
-                                                  &gt;&gt; Y = sqrt(4-(X.^2));</font><br> +
-                <font face="Courier New, Courier">&gt;&gt; plot(X,Y) <br><p>                                  </font></li></p> +
-</p> +
-</p> +
-<p></ul></p> +
-<p><hr width="100%" size="2"><br> +
-          <font size="+1">M-File MATLAB</font><br> +
-          Typing commands directly to MATLAB is well and good, and you will  +
- want   to  experiment at the command line frequently. &nbsp;However, for  +
-homework   assignments  and other distinct problems, you will want to keep  +
-your program   in a file,  so that you can edit it and run it again. &nbsp;You  +
-will also   want to make  files that call each other -- for example, you could +
-have a  plotting routine  that uses the format you like, and each of your +
-programs   could call this routine when it comes time to make a graph.<br></p> +
-<h2><h3>Directory Structure (where will you save your file?)</h3></h2> +
-<p>          Now is the time when we talk about Linux. &nbsp;If you already +
-know   which   directory you will save your program files in, skip to the +
-next section.<br></p> +
-<p><ul> +
-            <li>Put MATLAB aside for a moment. &nbsp;(Minimize the window  +
-if  you   like.)</li> +
-            <li>Click on the "Localhost" icon to get a new terminal window.</li> +
-            <li>Initially, you are "sitting" at your "home" directory.</li> +
-            <li>Type ls to list the subdirectories.</li><p>            <li>Do you have a subdirectory where you put your coursework?  +
-&nbsp;Would     you like one?</li> +
-            <li>To create a subdirectory called Courses, type mkdir Courses  +
- (you   can  change Courses to any other name you prefer)</li> +
-            <li>Now type cd Courses (cd means change directory)</li> +
-            <li>Now you are sitting at your Courses directory.</li> +
-            <li>Type ls to list what's here. &nbsp;Nothing, right? &nbsp;Let's +
-   put   something here.</li></p> +
-<p>            <li>Type mkdir Math228a to make a directory for numerics.</li> +
-            <li>Now type ls. &nbsp;Can you see your new folder? &nbsp;This +
- is  a  good  place to store your MATLAB programs.</li> +
-            <li>You can exit the terminal window now (type exit) and bring +
- your   MATLAB  window back.<br> +
-            </li></p> +
-</p> +
-<p></ul></p> +
-<p><h3>Put your small program into an m-file, and run it</h3></p> +
-<p><ul> +
-            <li>At the top left of the MATLAB window, there is an icon that  +
- looks    like a "new document" button. &nbsp;Click (once) on this.</li> +
-                 <li>A blank editor window will open. &nbsp;This is where  +
-you   type  your  program. &nbsp;Type:<br> +
-      (Note: in my experience, trying to copy and paste text into the MATLAB +
-  editor  crashes the whole thing. &nbsp;You can try it, but you'll learn +
-more  if you  type the text yourself anyway.)<font +
- face="Courier New, Courier">      <br> +
-              <br><p>          % My Name<br> +
-              </font><font face="Courier New, Courier">% The Date<br> +
-          % The purpose of this program is to plot a semi-circle on [-2,2].<br> +
-           </font><font face="Courier New, Courier">   X&nbsp;= -2:0.1:2;<br> +
-          Y = sqrt(4-(X.^2));<br></p> +
-<p>          plot(X,Y)</font><font face="Courier New, Courier"><br> +
-              <br> +
-              </font></li> +
-            <li>The percent signs % indicate comments. &nbsp;You can put +
-these    anywhere   in a program, to explain your code. &nbsp;Use comments +
-as often    as possible;   otherwise, you will not remember why you did what +
-you did.<br> +
-              </li> +
-            <li>Click on the File menu, and choose "Save As."</li></p> +
-<p>  <ul> +
-           <li>You want the top field to contain the right directory (the  +
-one   you   created in the last step). &nbsp;</li> +
-           <li>In the bottom field, type the name of the program. &nbsp;Call +
-  it   circle1.m</li></p> +
-<p>  </ul> +
-         <li>If your semi-circle figure is still open from before, close +
-it.</li> +
-         <li>Click on the command window.</li><p>         <li>Take a look at the top of the window. &nbsp;There is a field  +
-labeled     "Current Directory." &nbsp;Is it looking in the right place for  +
-your program?</li></p> +
-<p>  <ul> +
-                                   <li>If not, you can type "cd" and "ls'  +
-in  MATLAB  just like you can in  the terminal window. &nbsp;You might need +
- to  type something  like<br> +
-             <font face="Courier New, Courier, monospace">&gt;&gt; cd Courses/Math228a</font></li></p> +
-<h2>  </ul></h2> +
-<p>       <li>                                                        type ls +
- to  see  if your program is there. To run your program, type its name, e.g.<br> +
-          <font face="Courier New, Courier, monospace">&gt;&gt;circle1</font><br> +
-            </li></p> +
-</p> +
-</p> +
-<p></ul></p> +
-<p><h3>Scripts vs. Functions: write a function m-file</h3></p> +
-<p><ul> +
-            <li>The program you just wrote, circle.m, is called a "script" +
- -  it  runs straight from beginning to end, like a script to a play.</li><p>        <li>In   MATLAB, you can also write a program that is a function.</li></p> +
-<p>  <ul> +
-              <li>A function usually takes input and returns output.</li></p> +
-<p>  </ul></p> +
-<p>  <ul> +
-              <li>A function file must start with a "function declaration."  +
- &nbsp;We  will see an example below.</li></p> +
-<h2>  </ul></h2> +
-<p>            <li>Open a blank program file. &nbsp;Type:<br> +
-              <br> +
-               <font face="Courier New, Courier">% My Name<br> +
-            % The Date<br> +
-            % The purpose of this program is to plot a semi-circle of a<br> +
-            % given radius.<br><p>              <br> +
-            function Y = circle2(radius)<br> +
-            X = -radius:0.1:radius;<br> +
-            Y = sqrt(radius^2-(X.^2));<br> +
-            plot(X,Y)<br> +
-              <br> +
-              </font></li></p> +
-</p> +
-<p>            <li>The line&nbsp;<font face="Courier New, Courier">function +
-Y  =  circle2(radius)</font>    is the function declaration. &nbsp;Note:</li></p> +
-<p>  <ul> +
-              <li>The word "function" must be the first (non-comment) word +
- of  the   program.</li> +
-              <li>"Y" is the value that this function returns, or calculates,  +
-  a.k.a. the output.</li> +
-          <li>"radius" is the name of the variable taken as input.</li><p>          <li>"circle2" should be both the name of the function and the name +
-  that  you use to save the file.</li></p> +
-<p>  </ul> +
-        <li>To run your program for different radii, type:<br> +
-          <font face="Courier New, Courier, monospace"><br> +
-      &gt;&gt;circle2(2)<br> +
-          </font><font face="Courier New, Courier, monospace">&gt;&gt;circle2(4)</font>;<br><p>          <font face="Courier New, Courier, monospace">&gt;&gt;circle2(1);<br> +
-          <br> +
-          </font></li> +
-        <li>Note that the figure is replaced each time you call the function,  +
-  and that MATLAB automatically chooses the size of the x- and y-axes.<br> +
-          </li></p> +
-</p> +
-</p> +
-</p> +
-<p></ul> +
-          <br></p> +
-<p><h3>Get your scripts and functions talking</h3></p> +
-<p><ul> +
-       <li>Open a blank program file. &nbsp;Type:<br> +
-         <br> +
-         <font face="Courier New, Courier">% My Name<br> +
-            % The Date<br> +
-            % The purpose of this program is to plot semi-circles      <br><p>     % with radius = 1,2,3, and 4.<br> +
-         <br> +
-     for j = 1:4<br> +
-     &nbsp; &nbsp; circle2(j);<br> +
-     end<br> +
-        <br><p>        </font></li> +
-      <li>Save the file (in the same directory as circle2.m) as makecircles.m</li> +
-    <li>makecircles.m is a script. &nbsp;It is "calling" circle2.m, which  +
-is a function. &nbsp;They're talking to each other. &nbsp;(Who is saying what?)<br> +
-    </li> +
-     <li>Close any plots that are still open.</li> +
-     <li>To run the program, type:<br></p> +
-<p>       <br> +
-       <font face="Courier New, Courier, monospace">&gt;&gt; clear<br> +
-   &gt;&gt; makecircles</font><br> +
-       <br> +
-     </li> +
-     <li>Did you get what you expected? &nbsp;To make the program produce  +
-4  different plots without overwriting, we need to make a small edit:</li></p> +
-<p>  <ul> +
-       <li>open your circle2.m file (probably it is still open in the editor  +
- window and you just need to click on its tab at the bottom of the window)</li> +
-       <li>insert a line that says "<font +
- face="Courier New, Courier, monospace">figure</font>" right above <font +
- face="Courier New, Courier, monospace">plot(X,Y)</font>. &nbsp;This means  +
- "create a new figure (don't overwrite the last one)."</li> +
-       <li>Now your program should read as follows:<br> +
-         <br><p>         <font face="Courier New, Courier">% My Name<br> +
-            % The Date<br> +
-            % The purpose of this program is to plot a semi-circle of a<br> +
-            % given radius.<br> +
-              <br> +
-            function Y = circle2(radius)<br><p>            X = -radius:0.1:radius;<br> +
-            Y = sqrt(radius^2-(X.^2));<br> +
-         <font face="Courier New, Courier, monospace">figure</font><br> +
-            plot(X,Y)</font><br> +
-         <br> +
-       </li></p> +
-<h2>  </ul></h2> +
-<p>     <li>Save circle2.m, close any figures that are open, and run makecircles  +
-again.<br> +
-      <br> +
-    </li> +
-    <li>A different option: make the program produce one plot showing all  +
-4 circles</li></p> +
-<p>  <ul> +
-      <li>open your circle2.m file</li> +
-      <li>"comment out" the "<font +
- face="Courier New, Courier, monospace">figure</font>"  &nbsp;line. &nbsp;That +
-is, put a <font face="Courier New, Courier, monospace">%</font> in front +
-of it.</li><p>    <ul> +
-        <li>MATLAB will not read your comments</li> +
-        <li>"commenting out" can be better than deleting, because you can  +
-easily go back if you change your mind. (by erasing the <font +
- face="Courier New, Courier, monospace">%</font> mark)</li></p> +
-<p>    </ul> +
-      <li>above <font face="Courier New, Courier, monospace">plot(X,Y)</font>, +
- add a line that says "<font face="Courier New, Courier, monospace">hold +
-on</font>."</li><p>      <li>Now your program should read as follows:<br> +
-        <br> +
-        <font face="Courier New, Courier">% My Name<br> +
-            % The Date<br> +
-            % The purpose of this program is to plot a semi-circle of a<br> +
-            % given radius.<br><p>              <br> +
-            function Y = circle2(radius)<br> +
-            X = -radius:0.1:radius;<br> +
-            Y = sqrt(radius^2-(X.^2));<br> +
-         <font face="Courier New, Courier, monospace">%figure<br> +
-        </font>hold on<br></p> +
-</p> +
-</p> +
-<p>            plot(X,Y)</font><br> +
-      <br> +
-    </li> +
-  </ul> +
-  <li>Save cirlce2.m, close any figures that are open, and run makecircles +
-again.</li> +
-  <li>To save your plot:</li> +
-  <ul></p> +
-<p>    <li>At the top of the plot window, click on File</li> +
-    <li>click on Export</li> +
-    <li>Verify that it's going in the right directory, give it a name in +
-place of where it now says *, (try cplot1), and choose a format (eps or color +
-eps is good)<br> +
-      <br> +
-    </li> +
-  </ul> +
-  <ul></p> +
-<p>  </ul></p> +
-</p> +
-</p> +
-</p> +
-</p> +
-</p> +
-<p></ul></p> +
-<p><h3>Add More Features and Get More Help<br> +
-</h3> +
-<ul> +
-  <li>Plots should have titles. &nbsp;How do you add a title?</li> +
-  <ul> +
-    <li>In the MATLAB window, click on the Help menu item. &nbsp;From the +
-list that drops down, choose "MATLAB Help."</li><p>    <li>You'll get a new window full of help. &nbsp;</li> +
-    <li>In the left-hand pane, there are 4 tabs: Contents, Index, Search, +
-and Favorites. &nbsp;Click on Search.</li> +
-    <li>In the blank box, type "title" (and hit return)</li> +
-    <li>double-click on the first "hit" -- the one that simply says "title."</li> +
-    <li>Read the help in the right-hand pane, and see if you can add a line +
-to your program so that your plot will have a title.<br> +
-      <br></p> +
-<p>    </li> +
-  </ul> +
-  <li>Maybe you'd rather change the x-axis of your plot, so that it shows +
-[-5,5].</li> +
-  <ul> +
-    <li>Back in the help window, search for "axis"</li> +
-    <li>double-click on the "hit" that looks the best</li> +
-    <li>go to it!<br></p> +
-<p>    </li> +
-  </ul> +
-</ul> +
-<br> +
-</p> +
-</p> +
-</html>+