MATLAB Minicourse:
Lecture 2


David S. Touretzky


March 2001
Scientific Functions

Trig:	sin, cos, tan, asin, acos, atan,
		sinh, cosh, tanh, 
	asinh, acosh, atanh

Rounding:	floor, ceil, round, fix

Modular:	rem, mod

Expon.:	exp, log, log2, log10, sqrt

Primes:	factor, primes

Matrix:	det, inv, pinv, eig, svd, fft
	and many more

Polynomials:	   roots, polyfit, polyval

Inf and NaN

3/0    returns   Inf

0/0    returns   NaN

3+Inf

Inf/Inf

-Inf

-NaN
Predicates

isreal(3)

isprime(17)

isnumeric([2 3 5])

isempty([ ])

isinf(Inf)

isnan(NaN)

islogical(1==1)

ischar('a')

isequal('foo','aardvark')


Return Values
Functions can return multiple values.

   A = rand(5,3);

   [r,c] = size(A)



Functions can return values or not, 
depending on whether the user is asking for values.


   plot([1 2 3],[3 1 2])

   h = plot([1 2 3],[3 1 2])

   set(h,'LineStyle','--')

   set(h,'LineWidth',8)
Variable # of Arguments

Some functions take a variable number of arguments.


   peaks

   peaks(50)




  hist(randn(2000,1))

  hist(randn(2000,1), 50)

  b = hist(randn(2000,1), 50)

  [b,c] = hist(randn(2000,1), 50)
nargin and nargout
Inside a function, nargin is the number of input arguments supplied with the call.

nargout is the number of output arguments requested with the call.
Name Spaces

Base workspace:  variables created outside of any function exist in the base workspace.


Each function executes in a separate local workspace holding the arguments, return variables, and any local variables created by the function.


Functions cannot access variables of the base workspace.


Global workspace: variables declared global by a function are accessed in the global workspace.  It's a good idea to also declare
the variable global in the base workspace.
Global Variables

In the base workspace:

       global pts
       pts = 0:pi/20:2*pi;



Inside a function:
Scripts Called by Functions

Scripts do not have their own workspaces.


A script called from the keyboard executes in the base workspace.


A script called from within a function 
executes in the function's workspace.
     Resetting Variables

clear x	removes variable x
	(and undoes global decl.)


clear all	clears everything


clear global	clears global declarations


whos global	show all global vars.
Handle Graphics


clf, plot(rand(5,3))

ax = get(gcf,'Children')
get(ax)

lines = get(ax,'Children')
get(lines(1))
Multiple Axes
clf

subplot(2,2,1)       % uses row-major order
plot(rand(5,5))

subplot(2,2,2)
bar3(rand(5,3))

subplot(2,2,3)
a = rand(15,1);
pie(a, a>0.7)

subplot(2,2,4)
pts = 0:pi/20:2*pi;
polar(pts,cos(2*pts))

set(gca,'Position',[0.32  0.1  0.4  0.4])
Exploring Graphic Objects

propedit(gcf)


Matlab Help Desk:  click on
    "Handle Graphics Property Browser"


set(gca,'Units')

3D Graphics

peaks

rotate3d  on



[x,y,z] = peaks;

surf(x,y,z,z)

surf(x,y,z,x)

surf(x,y,z,rand(length(x)))

Plotting in 3D
function helix

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

  x1 = cos(pts); y1 = sin(pts);
  x2 = cos(pts+pi); y2 = sin(pts+pi);
  z = pts/(2*pi);

  clf, whitebg(gcf,[0 0 0])
  hold on
  plot3(x1,y1,z,'y')
  plot3(x2,y2,z,'w')

  axis([-2 2 -2 2 0 2])
  view(95,9)


  
helix (cont.)
colors = 'rgbm';

for i = 4:4:length(pts)-4

  plot3([x1(i) x2(i)], [y1(i) y2(i)], z([i i]),  ...
       	colors(ceil(rand(1)*length(colors))))

end
helix (cont.)

axis off
set(gcf,'Color','k')

set(gca,'CameraViewAngleMode','manual')

for az =  -180:5:80
  view(az,9)
  drawnow
end
Color Maps

clf
peaks

colorbar

m = colormap;
whos m

colormap(autumn)
brighten(0.5)

colormap(jet)

colormap(bone)

colormap(hot)
2D Data

[x,y] = meshgrid(-2:0.05:2);

z = sin(x).*cos(y);

contour(z,20)

imagesc(z)

imagesc(x(:),y(:),z)

surf(z)

surfc(z)
Surface Objects


 sphere

 [x,y,z]=sphere(30); 

x(15,8)=NaN; 

surf(x,y,z,y)

shading flat



surf(x,y,z,rand(31,31))

shading interp
Data From Files
Create a file temps.dat


load temps.dat

whos te*

plot(temps)
Polynomial Curve Fitting
load /afs/cs/usr/dst/expt1.dat
whos expt1

x = expt1(:, 1); y = expt1(:,2);

clf, hold on, plot(x,y,'o')

c = polyfit(x,y,3)

	example polynomial representation:
	    c = [ 5  -1  4  3]	
	   	    5x3 - x2 + 4x + 3

pts = min(x) : max(x);
plot(pts, polyval(c,pts), 'b')

helpwin polyfit

doc polyfit
Saving Variables

clear all

a = 'aardvark'

[x,y,z] = sphere(5);

save stuff.mat

whos -file stuff.mat



save junk.dat x y -ascii

type junk.dat
General OS Stuff

pwd


cd


dir


ls  *.m


delete stuff.mat


!df
Debugging
Poor man's debugger:  
   Remove semicolons from assignments.

   Add 'quoted strings' in appropriate places.

   Add a call to keyboard.  Use dbcont to
   return from keyboard input mode.

MATLAB Debugger

dbtype helix

dbstop helix 3

helix

dbstep

dbstep 5

whos

dbstep 30

dbquit

dbclear helix

help debug
Formatted Output

for i = 1:10
  fprintf('The square-root of %2d is %f\n', ...
       i, sqrt(i))
end


help fprintf


title(sprintf('f(x) over range %g to %g', ...
                      -3.5,  5.125))

function [x,y,z] = test(p,q,r,s,t)
    % inputs are ignored

    if nargout >= 1
      x = 50;
      if nargout >= 2
        y = 'foo';
        if nargout >= 3
           z = 3:7;
        end
      end
    end
    whos

38	50
42	53
33	57
45	56
44	46
41	40

function y = buggy(vec)

   p = vec > 5
  'got this far'
  keyboard

  z = p*vec
  v = sin(z);


function h = circ(x,y)

 % h = CIRC(x,y) draw circle at (x,y)

 global pts
 hh = plot(x+cos(pts),y+sin(pts));

 if nargout > 0, h = hh; end