Matlab tutorial
Da-Chuan Cheng
20.10.2006
Münster (Westf.)
Matlab is a commercial "Matrix Laboratory" package which
operates as an interactive programming environment. It is a
mainstay of the Mathematics Department software lineup and
is also available for PC's and Macintoshes and may be found
on the CIRCA VAXes. Matlab is well adapted to numerical
experiments since the underlying algorithms for Matlab's
builtin functions and supplied m-files are based on the
standard libraries LINPACK and EISPACK.
Matlab program and script files always have filenames
ending with ".m"; the programming language is exceptionally
straightforward since almost every data object is assumed
to be an array. Graphical output is available to supplement
numerical results.
How to use “help” command:
help help
Use help to see available commands/toolboxes
help
help fft
helpdesk
doc fft2
What version do I use?
‘ver’ to see the complete version information, whereas ‘version’ the short one.
ver
version
Know what workspace is, how to see variables in the current workspace:
a=10
% If you don’t define it, then matlab assumes it as a double.
whos
% List current variables, long form.
who
% Lists the variables in the current workspace.
clear
% clear variables in the workspace./Clear function in the memory.
clear a*
% clear all variables starting with “a”.
help .
% Operators and special characters.
help punct
% Punctuation / Zeichensetzung
.
Decimal point. 325/100, 3.25 and .325e1 are all the same.
.
Array operations. Element-by-element operations.
.
Field access.
.. Parent directory. ex: cd ..
... Continuation. ex:
p=3.1415926535897932384626433832795...
+2;
is equal to:
p=3.1415926535897932384626433832795+2;
,
% Comma. The comma is used to separate matrix subscripts
% and arguments to functions.
% ex:
A=rand(2,3);
function m=myfun(a,b,c);
;
% Semicolon: to suppress printing and to separate rows;
% ex:
a=3;
a=[1 2 3;4 5 6]
%
Percent: comments.
!
% Exclamation point: to execute operating system commands.
% ex:
!copy file1 file2
’
% Transpose and string quoting.
a=[1:5]
a’
b=’b is a string’
= % Assigment / Zuweisung
^ % Power / Potenz
% ex:
2^3
2^0.5
% is equal to
sqrt(2)
Data types:
Help-> Matlab-> Programming-> Data type-> Overview
or
>>doc datatypes
15 data types.
a=20;
% a is assigned automatically as a ‘double’.
a=int16(a); % convert a to 16-bit integer.
a=cell(1);
% build a cell.
% build a structure: ‘field name’,field value.
s = struct('type',{'big','little'},'color','red','x',{3 4})
ans
% result saved always in.
Normally, the variable will be defined automatically as a local variable.
If you want to define a global variable, use “global”:
global a1 a2;
a1=10;
whos
To see the (extended) ASCII code:
int8(‘abc’) % or int8 abc
int16 €
char(8364)
The usage of ‘;’
p=30; -- The result will be shown in the workspace.
p=30 -- The result will not be shown in the workspace but be saved in ‘ans’.
‘:’
a=[1:5]
% construct a row vector, overwrite the previous
definition.
%or
a=(1:5)
a=[1:5]’
% construct a column vector. (transpose)
b=a(:)
% convert vector “a” to a column vector.
a=zeros(5,6); % build a matrix with all elements as 0.
b=ones(6,3); % build a “one” matrix.
c=rand(3,2); % build a random matrix.
d=rand(5,6,2);
% build a 3D matrix.
e=rand(M,N,P,...); % build a multi-dimensional matrix.
Inner product: (scalar product)
a=[2 4 6];
b=[3 5 7];
a*b’
Outer product:
a’*b
vector product:
cross(a,b) or cross(b,a)
Matrix index:
The first term indicates row number and the second one indicates the column
number.
c(1,2)
Any vector or matrix indication starts from 1, not 0.
c(0,0)
% Error example
Select one column vector from a matrix:
c=d(:,2,1)
Select one sub-matrix from a matrix:
c=d(1:3,2:4,2)
[ ] Brackets are used in forming vectors and matrices.
a=[];
for i=1:10,
a=[a i];
end;
How to find the index of a certain value in an array/a matrix?
A=randn(5);
[i,j]=find(A>0);
Vector and matrix computation:
Any variable can be directly used without definition if it is NOT defined
before.
If it is defined before, and if you want to change its size or data type, then
you have to clear it or redefine it before you use it.
for i=1:5,
for j=1:6,
d(i,j)=i*j;
end;
end;
Inverse a matrix:
inv(A)
Without definition:
for i=1:10; d(i)=i; end;
If d is defined, and if you want to change the data type, you have to clear it
firstly.
clear d;
for i=1:10; d{i}=’s’;end;
real and imaginary (FFT)
“i” is reserved for imaginary if you do not define it as others.
clear i;
a=3+7i;
real(a)
imag(a)
% obtain the real part from a
% obtain the imaginary part from a.
a=[1:5]; b=[6:10];
a+b
% vector addition
a*b’
% inner product
a.*b
% Array multiply
a./b
% left array divide
a.\b
% right array divide
Array multiply has two ways:
for i=1:5,
c(i)=a(i)*b(i);
end;
c=a.*b
% this one is quicker and more efficient.
Important: One has to write the programs (in Matlab) as many as possible to use
array/matrix computation instead of “for” loop. “for” loop is used only when it
cannot be programmed as array/matrix computation, this is because for loop or
if statement will influence the computing efficiency.
“for” and “while”
for i=1:5,
for j=1:5,
A(i,j)=i+j;
end;
end;
p=1;
while p<5,
p=p+1
end;
“if”, “else”, and “elseif”
IF expression
statements
ELSEIF expression
statements
ELSE
statements
END
The expression is usually of the form expr rop expr, where rop is ==, <, >, <=,
>=, or ~=.
expr: expression.
rop: relational operator.
Ex:
for i=1:5,
for j=1:5,
if i==j,
A(i,j)=i*j;
elseif i>j,
A(i,j)=i;
else
A(i,j)=-j;
end;
end;
end;
Relational operators and logical operators see: help relop
How to create and handle a figure?
Create a figure window:
figure;
% you let the system give a figure number automatically.
or figure(1); % you can give a figure number in the parenthesis.
h=figure(2); % you get a figure handle number and save it in h.
Close a figure by command:
close;
% close current figure.
close(1)
% close figure 1.
close all
% close all figures.
Get the current figure handle:
h1=gcf
% Get Current Figure. (gcf)
Get Object (figures, axes, …) properties:
get(h1)
Set Object properties:
pos=get(h1,'position')
Note: pos= [x y width height] where (x,y) is the coordinate of the figure
(left-bottom corner) on the screen.
pos(3)=100;
set(h1,'position',pos);
How to prevent a figure closed unintentionally?
set(h1,'closerequestfcn','');
Recover it by:
set(h1,'closerequestfcn','closereq');
Show an array in a figure:
t=[0:0.01:2*pi];
p=sin(t);
figure; plot(p);
Use “subplot”:
q=cos(t);
figure; subplot(2,1,1); plot(p); subplot(212); plot(q);
Use “hold”:
figure; plot(p); hold on; plot(q,’r’);
Text display
format long g
pi*1000
Show a matrix/image in a figure:
for i=1:30,
for j=1:30,
A(i,j)=sin(i/15*pi)* cos(j/15*pi);
end;
end;
figure; mesh(A);
figure; imshow(A,[]);
Show two images (with different colormaps) in a figure:
load trees
‘load’ command will then return the image to ‘X’ and the colormap to ‘map’
automatically. (However, this is a special case!) Or you can give it by
yourself:
[X1,map1]=imread(‘trees.tif’);
Question: What is ‘trees’? Where can I find it?
In matlab there are some existed image files that one can use them.
Some are saved in Matlabm_main_path\toolbox\images\imdemos\
Or, if you know the filename, you can use ‘which’ to find them out:
which trees.tif
Now you have another image which has different colormap:
[X2,map2]=imread(‘kids.tif’);
You want to put them together:
figure; subplot(121); imshow(X1,map1); subplot(122); imshow(X2,map2);
You will find that the colormap can not be used in the same figure.
The ‘subimage’ can convert them to true color for display purposes:
figure; subplot(121); subimage(X1,map1); subplot(122); subimage(X2,map2);
How to read and write an image file and show it in a figure:
R=imread(‘file1.bmp’,’bmp’);
figure; imshow(R);
If the matrix “R” has RGB-channel, then you can read only red channel by
Red=R(:,:,1);
If the matrix is in “char”, then you can show the matrix directly.
imshow(R);
If the matrix is in “double”, then you can show it by
imshow(Red,[]);
More see: help imshow.
imwrite(A,’file2.bmp’,’bmp’);
Frequently, we got an error in writing an image file.
ex:
A=[0:255];
A=repmat(A,50,1);
imwrite(A,’file1.bmp’,’bmp’);
R=imread(‘file1.bmp’);
figure; imshow(R);
Then we got an empty image in R. Why?
The reason is that “A” is in double precision. We have to convert “A” to
“char”:
A=uint8(A);
Then write “A” into a file.
Load image from internet:
A=imread(‘http://cvpr.unimuenster.de/teaching/ws06/bildverarbeitungWS06/download/Eisberg.jpg’);
How to write a matlab *.m program. Use editor:
function m=myfun(n);
for j=1:5,
m=j*n;
end;
Some frequently used computing commands:
sum, prod, max, min, mean, std, mean2, std2,
Range images
R=double(imread(‘Tiefenbild1.gif’));
% anzeigen
Obj=surf(R); colorbar;
set(Obj,’Linestyle’,’none’); % to delete the meshgrids
mesh(R); colorbar;
Practices: Write your own functions and compare your results with the ones from
matlab functions.
1. Write a program to synthesize a 1D and 2D Gaussian function by given
values (mean=0, std=2, and the range=[-7,7]). Plot it in a figure. (Do
not call gaussmf or other matlab functions)
2. Write a program to implement the function defined after and plot it on
the figure. y=x^2+50*sin(x) for x=[-10:10], step of x is 0.1.