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MATLAB Basics

Start MATLAB on your machine. You get a prompt like this:

>>

Here are some things you can do.

>> diary on   % Causes Matlab to save a record of the session in a
              % file named diary.  Later you can edit this file,
              % print it out, turn it in as homework, or whatever.
              % For more information about diary, type ``help diary''

>> a = [1 2 ; 3 4]

a =

     1     2
     3     4

>> x = ones(2,1)

x =

     1
     1

>> b = a*x

b =

     3
     7

>> y = a\b    % Solves system Ay=b for y.

y =

    1.0000
    1.0000
>> c = a'        % transpose

c =

     1     3
     2     4

>> H = a'*a

H =

    10    14
    14    20

>> chol(H)     % upper triangular Cholesky factor

ans =          % The default variable name is ans.

    3.1623    4.4272
         0    0.6325

>> m = ans

m =

    3.1623    4.4272
         0    0.6325

>> A = a^2; % exponentiation.  Semicolon suppresses printing of result.
>> A        % To have a variable printed out, just type its name.

A =         % Matlab is case sensitive:  A and a are different.

     7    10
    15    22

>> A(1,1) = A(1,1) + 13

A =

    20    10
    15    22

>> [L U] = lu(A)   % LU decomposition (with pivoting if necessary)

L =

    1.0000         0
    0.7500    1.0000


U =

   20.0000   10.0000
         0   14.5000

>> AI = inv(A)

AI =

    0.0759   -0.0345
   -0.0517    0.0690

>> p = A*AI

p =

    1.0000         0
         0    1.0000

>> format long               % some alternative formats
>> p

p =

   1.00000000000000                  0
                  0   1.00000000000000

>> format short e
>> p

p =

   1.0000e+00            0
            0   1.0000e+00

>> format                     % The default format is called `short'.
>> p 

p =

    1.0000         0
         0    1.0000

>> a = hilb(3)       % 3 by 3 Hilbert matrix

a =

    1.0000    0.5000    0.3333
    0.5000    0.3333    0.2500
    0.3333    0.2500    0.2000

>> b = 1:3      

b =

     1     2     3

>> b=b'

b =

     1
     2
     3

>> x=a\b

x =

   27.0000
 -192.0000
  210.0000

>> r=b-a*x
r =

   1.0e-14 *       % scale factor for the array

         0
   -0.7105
         0

>> n = norm(r)

n =

   7.1054e-15

>> cond(a)

ans =

  524.0568

>> a = zeros(4,4)

a =

     0     0     0     0
     0     0     0     0
     0     0     0     0
     0     0     0     0

>> for i=1:3
     a(i+1,i)=1;      % a simple loop
     a(i,i)=2;        % The whole thing could have gone on one line.
     a(i,i+1)=3;
   end
>> a(4,4)=2;
>> a

a =

     2     3     0     0
     1     2     3     0
     0     1     2     3
     0     0     1     2

>> quit                 % Quit MATLAB

% Some other useful commands are:

>> intro

>> demo

>> help 

>> help help 

>> help elmat

>> help eig 

>> help plot 

>> help sparse

>> help [name your favorite topic]

% Other commands are less useful:

>> why

% Chances are, you are running a recent version of MATLAB with
% a GUI interface.  In this case you can do lots of things using 
% the pulldown menus and push buttons.  There is also a built-in 
% editor.





2004-01-15