MATLAB Minicourse:
Lecture 1


David S. Touretzky


March 2001
What Is Matlab?

·	Product of The Mathworks, Inc.

     http://www.mathworks.com

·	Runs on Unix, LINUX, Windows, and Macs.

·	Strong on matrix manipulation and graphics.

·	Full programming language.

·	Interfaces with C.

·	Latest release is version 6.0.
Variable Creation

a = 5


a = 5;


b = 'penguins love herring'


who


whos
Matrix Creation

x = [1  2  3;  9 8 7]


zeros(3,5)
zeros(5)
zeros(5,1)

ones, rand, randn, eye



The colon operator creates row vectors:
    1:5
    1:3:15
    10:-1:0

    pts = 0 : pi/20 : 2*pi;
Size of a Matrix

whos pts


size(pts)


length(pts)
Subscripting

V = [10 20 30 40 50];

V(3)




M = [1 2 3; 4 5 6; 7 8 9];


M(2,2)

M(2)       % access in column-major order
Matrix Slices

V(2:4)


V(2:end)


M(1:2,2:3)


M(:)


M(:,:)
Expanding a Matrix
a = [1 2 3]


a = [a 4]


a(7) = 5


a(end+1) = 6


b = [a; a.^2]


Efficiency tip:  Use ZEROS to preallocate space instead of expanding dynamically.
Reshaping a Matrix

M = reshape(1:15, 5, 3)


M'


M''


Exercise: how can you recreate the following matrix using just the operators above?

     1     2     3
     4     5     6
     7     8     9
   10   11   12
   13   14   15
Adding Rows vs. Columns

M = [ 1 2 ;  3 4]

M = [M ; 5 6]




V = [10 20 30]'

whos M V

M = [M V]




M = [M [99 98 97]']
Deleting Rows or Columns

M(:,3) = [ ]


M(2,:) = [ ]


size([ ])

Command Line Editing
Basic editing:
  Forward/back char	^F / ^B
  Left/right word		^L / ^R
  Beginning/end of line	^A / ^E
  Delete forward/back char	^D / ^H
  Clear line		^U
  Kill to end of line	^K
  Toggle insert mode	^T

Interrupt execution:		^C

History:
  Next/previous line	^N / ^P
Keyed history:
     foo^P

help cedit

Command/function completion:
     cle<tab><tab>
Editing in Emacs

Current buffer is foo.m


Put "3+5"  in the file (without the quotes.)

On a new line, put "magic(5)" in the file.

Save the file.


Type foo to Matlab
Basic Plotting

pts = 0 : pi/20 : 4*pi;


plot(sin(pts))


plot(pts, sin(pts))


whitebg(gcf, [ 0 0 0 ])


grid on/off

box on/off

axis on/off

clf
Plot Labeling


xlabel('Input value')


ylabel('y = sin(\theta)')


title('The Sine Function')


Multiple Plots

clf

hold on


plot(pts, sin(pts))

plot(pts, cos(pts), 'm')

plot(pts, cos(pts), 'go')


legend('sin','cos','pts')

Use the mouse to position the legend.
Summary of Plot Options
Color:
  r,g,b,w	red, green, blue, white
  c,m,y,k	cyan, magenta, yellow
	  black  

Symbol:
  . o x 	dot, circle, cross, 
  + *	plus, star
  s d	square, diamond
  etc. (there are more)


Line type:
  -	solid
  --	dashed
  ..	dotted
  -.	dash-dot


help plot
Printing


On the File pulldown menu, select Print.


Or type ^P in the figure window.



print -depsc -r300 myfig.ps

print -dtiff  myfig.tiff

print -djpg  myfig.jpg


help print
Plotting with Error Bars

clf


y = sin(pts);


e = rand(1,length(y)) * 0.4;


errorbar(pts,y,e)
Multiple Figures


figure


figure(5)


delete(2)


Or type ^W in the figure window.
Histograms

dat = randn(10000,1);


hist(dat)


hist(dat,50)


b = hist(dat,6)


bar(b)
Writing Functions
In Emacs, create the file parabola.m



parabola(5)


clf, plot(parabola(-10:10))


help parabola
Scripts vs. Functions

Scripts take no input arguments and return no values.

Scripts operate in the workspace of their caller (i.e., the "base" workspace if called from the command line.)



Functions can take zero or more arguments and return zero or more values.

Functions operate in their own local
workspace.  

Variables created inside a function are local to that function; they disappear when the function returns.
Logical Operations

Operators:  ==    ~=    <    >    <=   >=

Binary values are true/false


The IF statement:

Short form (all on one line):
Boolean Subscripting
V = [1 2 3 4 5];

V(logical([1 0 1 1 0]))


a = V >= 3; 

whos a


V(V>=3)

V(V>=3) = 0


S = 'banana cabana'

S(S == 'a') = [ ]
Control Structure
for i = 1:5
   [i  i^2]
end


clf, hold on
for x = pts
   plot(x,cos(x),'gd')
   pause(1)
end



x = 0; i = 0;
while x < 5
    i = i + 1;
    x = x + rand(1);
end
i, x
Matrix Arithmetic

Element-wise operators:  +   -   .*   ./   .^


M = rand(5,3)

M + 100

M * 5

M .* M

M ./ M

M .^ 2

Matrix Multiplication

m1 = rand(5,3)

m2 = rand(3, 5)


m1 * m2

m2 * m1

m1 * m1       -- error! --


m1'/m2


pinv(m1)
Exercise:  Rotation in 2D

Rotation Exercise (cont.)

Test your function:

			rot(30)



Now try this:

for i = 0 : 10 : 90
   rot(i), pause
end



Hit the space key to continue from the pause.
Reduction Operators

M = rand(5,3)


sum(M)

sum(M,2)


sum, prod, min, max, mean, var


min(min(M))

min(M(:))
Expanding with REPMAT

The REPMAT function is often used to expand a vector to fit the shape of a matrix.

Example:  adjusting a dataset to have zero means.

M = rand(5,3)

avg = mean(M);

ma = repmat(avg,5,1);

mz = M - ma

sum(mz)
Exercise

Suppose we want the rows of M to sum to zero, instead of the columns.


How would you do this, without using 
transpose?
MATLAB Documentation

help cos


doc cos


help


which peaks


lookfor rotate


The Matlab Helpdesk:
     helpdesk
Hint: Starting Matlab

Matlab version 6 includes an elaborate "desktop" feature built in Java.  

The desktop is slow and buggy.


To disable the entire Java Virtual Machine:
     % matlab -nojvm


To disable just the desktop:
     % matlab -nodesktop


In case of OpenGL lossage, do:
      opengl neverselect

Can put this in your startup.m file.

M = 
           1    2    3
           4    5    6
           7    8     9

function y = parabola(x)

% y = PARABOLA(x)
%    computes a quadratic

  y = x .^ 2;

if  x  > 3
   y = x;
else
   y = x - 3;
end

if x>3, y=x; else y=x-3; end

function rot(theta)
  % ROT(theta) prints a rotated sine wave

  rads = theta/360*2*pi;

  rotmat = [cos(rads) sin(rads); ...
                 -sin(rads) cos(rads)];

  pts = 0:pi/20:4*pi;

  data = rotmat * [pts/(4*pi); cos(pts)];
 
  plot(data(1,:), data(2,:))
  axis([-1.5 1.5 -1.5 1.5])