MATLAB
Basics
1
MATLAB Documentation
http://www.mathworks.com/access/helpdesk
/help/techdoc/
Matrix Algebra
http://www.sosmath.com/matrix/matrix.html
2
What is MATLAB?
MATLAB (Matrix laboratory) is an
interactive software system. It
integrates mathematical
computing, visualization, and a
powerful language to provide a
flexible environment for technical
computing. Typical uses include
• Math and computation
•
•
•
Algorithm development
•
Data analysis, exploration, and
visualization
•
•
Scientific and engineering graphics
Data acquisition
Modeling, simulation, and
prototyping
Application development, including
graphical user interface building
3
The MATLAB Product Family
The MathWorks offers a set of integrated products for data analysis,
visualization, application development, simulation, design, and code
generation. MATLAB is the foundation for all the MathWorks products.
Demos: http://www.mathworks.com/products/matlab/demos.html
4
Using MATLAB in CUHK
• With Windows Version
• With Unix Version
• 200 concurrent licenses using throughout
the Departments in CUHK
• Licenses controlled by a License Server
• Used by more than 10 Departments in
Engineering and Science Faculties
5
Starting MATLAB
• Windows
double-click the MATLAB shortcut icon on your
Windows desktop.
• UNIX
type matlab at the operating system prompt.
• After starting MATLAB, the MATLAB
desktop opens.
6
Quitting MATLAB
• select Exit MATLAB from the File menu in the
desktop, or type quit in the Command Window.
7
MATLAB Desktop
8
Command Window
9
Command History
10
Current Directory Browser
11
Workspace Browser
Command line
variables saved in
MATLAB workspace
»workspace
12
Window Preferences
13
Getting help
• MATLAB Documentation
•
>> helpdesk or doc
– Online Reference (HTML / PDF)
– Solution Search Engine
– Link to The MathWorks (www.mathworks.com)
•
•
FTP site & latest documentation
Submit Questions, Bugs & Requests
• MATLAB access - MATLAB Digest / Download upgrades
14
Using Help
• The help command
• The help window
• The lookfor command
>> help
>> helpwin
>> lookfor
»
lookfor example
DDEX1 Example 1 for DDE23.
DDEX1DE Example of delay differential equations for solving with DDE23.
DDEX2 Example 2 for DDE23.
ODEEXAMPLES Browse ODE/DAE/BVP/PDE examples.
....
»
help lookfor
LOOKFOR Search all M-files for keyword.
LOOKFOR XYZ looks for the string XYZ in the first comment line
(the H1 line) of the HELP text in all M-files found on MATLABPATH.
For all files in which a match occurs, LOOKFOR displays the H1 line.
....
15
Calculations at the Command Line
MATLAB as a calculator
»
-5/(4.8+5.32)^2
ans =
-0.0488
» (3+4i)*(3-4i)
ans =
25
» cos(pi/2)
ans =
6.1230e-017
» exp(acos(0.3))
ans =
3.5470
Assigning Variables
» a = 2;
» b = 5;
» a^b
ans =
32
» x = 5/2*pi;
» y = sin(x)
Semicolon
suppresses
screen output
Results
assigned to
“ans” if name
not specified
y =
1
» z = asin(y)
z =
() parentheses for
function inputs
1.5708
Numbers stored in double-precision
floating point format
16
Simple Mathematics
>>
>>
>>
>>
>>
>>
>>
2 +3
2 *3
1/2
2 ^3
0/1
1/0
0/0
(
5
)
(
6
)
(
0.5000 )
(
8
)
(
0
)
( Warning: Divide by zero. Inf )
(
NaN
)
Up/Down arrow to recall previous commands
Or use Ctrl+C and Ctrl+V to reuse commands
17
Some Common Functions
cos(x), sin(x), tan(x), asinh(x), atan(x), atanh(x), …
ceil(x): smallest integer which exceeds x, e.g. ceil(-3.9) returns -3
floor(x): largest integer not exceeding x, e.g. floor(3.8) returns 3
date, exp(x), log(x), log10(x), sqrt(x), abs(x)
max(x): maximum element of vector x
min(x): minimum element of vector x
mean(x): mean value of elements of vector x
sum(x): sum of elements of vector x
size(a): number of rows and columns of matrix a
18
Some Common Functions
rand: random number in the interval [0, 1)
realmax: largest positive floating point number
realmin: smallest positive floating point number
rem(x, y): remainder when x is divided by y, e.g. rem(19,5)
returns 4
sign(x): returns -1, 0 or 1 depending on whether x is
negative, zero or positive
sort(x): sort elements of vector x into ascending order (by
column if x is a matrix)
19
The M-file
A Matlab program can be edited and saved
(using Notepad) to a file with .m extension. It
is also called a M-file, a script file or simply
a script.
When the name of the file is entered in >>,
Matlab (or right-click and then run) carries
out each statement in the file as if it were
entered at the prompt. You are encouraged to
use this method.
20
21
22
Basic Concepts
a = 2;
b = 7;
c = a + b;
disp(c)
Variables such as a, b and c
are called scalars; they are
single-valued.
MATLAB also handles
vectors and matrices, which
are the key to many powerful
features of the language.
23
Vectors
A vector is a special type of matrix, having only one row, or one column.
x = [1 3 0 -1 5]
a = [5, 6, 8]
y = 1:10
(elements are the integers 1, 2, …, 10)
z = 1:0.5:4
(elements are the values 1, 1.5, …, 4 in increments of 0.5)
x’ is the transpose of x. Or you can do it directly: [1 3 0 -1 5]’.
24
Working with Matrices
MATLAB == MATrix LABoratory
25
The Matrix in MATLAB
Columns
(n)
2
3
4
1
A=
1
2
4
1
8
2
5
6
1
11
6
16
1.2 7
9
12
4
17
25 22
10
2
21
A (2,4)
7.2 3
5
8
7
13
1
18
11 23
A (17)
4
0
4
0.5 9
4
14
5
19
56 24
Rectangular Matrix:
5
23
5
83 10 13 15
0
20
10 25
Scalar: 1-by-1 array
Vector: m-by-1 array
1-by-n array
Matrix: m-by-n array
Rows (m) 3
where m, n can be 1, 2, 3, 4, …
26
Entering Numeric Arrays
Row separator:
semicolon (;)
Column separator:
space / comma (,)
» a=[1 2;3 4]
Use square
brackets [ ]
a =
1
2
3
4
» b=[-2.8, sqrt(-7), (3+5+6)*3/4]
b =
-2.8000
0 + 2.6458i
10.5000
» b(2,5) = 23
Matrices must
be rectangular.
(Set undefined
elements to zero)
b =
-2.8000
0 + 2.6458i
10.5000
0
0
0
0
0
0
23.0000
Any MATLAB expression can
be entered as a matrix element
27
Entering Numeric Arrays - cont.
Scalar expansion
Creating sequences:
colon operator (:)
» w=[1 2;3 4] + 5
w =
6
7
8
9
» x = 1:5
x =
1
2
» y = 2:-0.5:0
Utility functions for
creating matrices.
(Ref: Utility Commands)
y =
2.0000
1.5000
» z = rand(2,4)
3
4
5
1.0000
0.5000
0.8913
0.7621
0.4565
0.0185
0
z =
0.9501
0.2311
0.6068
0.4860
28
Numerical Array Concatenation - [ ]
Use [ ] to combine
existing arrays as
matrix “elements”
Row separator:
semicolon (;)
Column separator:
space / comma (,)
The resulting
matrix must
be rectangular.
» a=[1 2;3 4]
Use square
brackets [ ]
a =
1
2
3
4
» cat_a=[a, 2*a; 3*a,
cat_a =
1
2
2
3
4
6
3
6
4
9
12
12
5
10
6
15
20
18
4*a; 5*a, 6*a]
4
8
8
16
12
24
4*a
>> size(cat_a)
ans =
6
4
29
Array Subscripting / Indexing
1
A=
A(3,1)
A(3)
•
•
•
•
4
1
2
2
8
3
7.2
3
4
0
4
5
23
5
1
2
3
4
6
1
11
6
16
1.2 7
9
12
4
17
10
5
2
21
25 22
8
7
13
1
18
11 23
0.5 9
4
14
5
19
56 24
83 10 13 15
0
20
10 25
5
A(1:5,5) A(1:end,end)
A(:,5)
A(:,end)
A(21:25) A(21:end)’
A(4:5,2:3)
A([9 14;10 15])
Use () parentheses to specify index
colon operator (:) specifies range / ALL
[ ] to create matrix of index subscripts
‘end’ specifies maximum index value
30
Matrix Multiplication
•
•
•
Inner dimensions must be equal
Dimension of resulting matrix = outermost
dimensions of multiplied matrices
Resulting elements = dot product of the
rows of the 1st matrix with the columns of
the 2nd matrix
» a = [1 2 3 4; 5 6 7 8];
[2x4]
» b = ones(4,3);
[4x3]
» c = a*b
[2x4]*[4x3]
[2x3]
c =
10
26
10
26
10
26
a(2nd row).b(3rd column)
31
Array Multiplication
•
•
•
Matrices must have the same dimensions
Dimensions of resulting matrix =
dimensions of multiplied matrices
Resulting elements = product of
corresponding elements from the original
matrices
» a = [1 2 3 4; 5 6 7 8];
» b = [1:4; 1:4];
» c = a.*b
c =
1
5
4
12
9
21
16
32
c(2,4) = a(2,4)*b(2,4)
Same rules apply for other array operations
32
Deciding with if
bal = 15000 * rand;
if bal < 5000
rate = 0.09;
elseif bal < 10000
rate = 0.12;
else
rate = 0.15;
end
newbal = bal + rate + bal;
disp(’New balance is: ’)
disp(newbal)
33
Repeating with for
for index = j:k
statements
end
for index = j:m:k
statements
end
(m is the increment)
34
Square rooting with Newton Method
Create a program in newton.m file to
calculate the square root of 2
%NEWTON Newton Method example
a = 2;
x = a/2;
for i = 1:6
x = (x+a/x)/2;
disp (x)
end
35
Running newton.m
>> newton
1.5000
1.4167
1.4142
1.4142
1.4142
1.4142
>> format long
>> newton
1.50000000000000
1.41666666666667
1.41421568627451
1.41421356237469
1.41421356237309
1.41421356237309
36
Input / Output
fprintf formats the output as specified by a
format string.
fprintf ('format string', list of variables)
fprintf ('filename', 'format string' , list of variables)
balance = 123.45678901;
fprintf('New balance: %8.3f', balance)
%8.3f means fixed point over 8 columns altogether (including the decimal point and
a possible minus sign), with 3 decimal places (spaces are filled in from the left if
necessary).
37
Input / Output Examples
fprintf example (io_1.m)
balance = 12345;
rate = 0.09;
interest = rate * balance;
balance = balance + interest;
fprintf('Interest rate: %6.3f
%8.2f\n', rate, balance);
>> io_1
Interest rate:
0.090
New balance:
New balance: 13456.05
>>
38
Input / Output
The input statement gives the user the prompt in the text string and
then waits for input from the keyboard. It provides a more flexible
way of getting data into a program than by assignment statements
which need to be edited each time the data must be changed. It
allows you to enter data while a script is running.
The general form of the input statement is:
variable = input(’prompt’);
39
Input / Output Examples
Interactive Input (io_2.m)
balance = input('Enter bank balance: ');
rate = input('Enter interest rate: ');
interest = rate * balance;
balance = balance + interest;
fprintf('New balance: %8.2f\n', balance);
>> io_2
Enter bank balance: 2000
Enter interest rate: 0.08
New balance: 2160.00
>>
40
2-D Plotting
• Specify x-data and/or y-data
• Specify color, line style and marker symbol
(clm), default values used if ‘clm’ not specified)
• Syntax:
– Plotting single line:
plot(xdata, ydata, 'clm')
– Plotting multiple lines:
plot(x1, y1, 'clm1', x2, y2, 'clm2', ...)
41
2-D Plot – Examples
x = 0 : 10
y=2*x
plot (x, y)
plot (x, sin(x))
x = 0 : 0.1 :10;
pause
plot (x, sin(x))
plot (x, sin(x)), grid
42
2-D Plot – Labels
Graphs may be labelled with the following
statements:
gtext(’text’): writes a string in the graph window
grid: add/removes grid lines to/from the current graph
text(x, y, ’text’): writes the text at the point specified by x and y
title(’text’): writes the text as a title on top of the graph
xlabel(’text’): labels the x-axis
ylabel(’text’): labels the y-axis
43
3D Plot - Examples
The function plot3 is the 3-D version of plot. The command plot3(x,y,z)
draws a 2-D projection of a line in 3-D through the points whose coordinates are the elements of the vectors x, y and z.
plot3(rand(1,10), rand(1,10), rand(1,10))
The above command generates 10 random points in 3-D space, and joins
them with lines.
44
MATLAB
Exercise
45