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Introduction to MATLAB R2012b
What is Matlab?• Matlab is basically a high level language which
has many specialized toolboxes for making things easier for us
• How high?
Assembly
High Level Languages such as
C, Pascal etc.
Matlab
MATLAB R2012 Interface
Command Window
Basic Arithmetic Operations in Command Window
Command Window
Workspace
• Double click on “m” variable (m is a 3x4 matrix)
Command History
Current Folder Tab
• We will not use current folder tab so oftenly, so minimize it for now.
Again, MATLAB R2012b General Interface (without “Current Folder” tab)
MATLAB R2012 Interface: Home, Plots, Apps
MATLAB R2012 Interface:Home
MATLAB R2012 Interface:Home
Introduction to MATLAB R2012b: Editor
Introduction to MATLAB R2012b: Editor
Introduction to MATLAB R2012b
Introduction to MATLAB R2012b: Editor
Introduction to MATLAB R2012b: Functions
Introduction to MATLAB R2012b
Introduction to MATLAB R2012b
Introduction to MATLAB R2012b
Introduction to MATLAB R2012b
Introduction to MATLAB R2012b
Introduction to MATLAB R2012b
Introduction to MATLAB R2012b
Function Usage in MATLAB R2012b
Functions in MATLAB
• You do not need always writing new functions.• There are also embedded functions in MATLAB.• Write “help” command in the command window
and see the list of help topics of MATLAB.• If you would like to get some knowledge for any
function, write “help function_name” in command window. For example, write “help factorial” .
• Now, use factorial function to compute factorial of 5 by using the given knowledge.
Functions in MATLAB
• Another example: Write “help linspace” in command window.
• Can you say what linspace command does ?Write in command window:
t=linspace(0,1,100)
What will the content of “t” be?
• There are lots of other functions in MATLAB.
Introduction to MATLAB R2012bCommand Line
(Series of MATLAB commands)
.mat files(Parameters,
Variables)
.m files (Scripts, Functions)
Introduction to MATLAB R2012b• No need for types. i.e.,
• All variables are created with double precision unless specified and they are matrices.
• After these statements, the variables are 1x1 matrices with double precision
int a;double b;float c;
Example:>>x=5;>>x1=2;
Array, Matrix• a vector x = [1 2 5 1]
x =1 2 5 1
• a matrix x = [1 2 3; 5 1 4; 3 2 -1]
x =1 2 35 1 43 2 -1
• transpose y = x’ y =1251
Long Array, Matrix • t =1:10
t =1 2 3 4 5 6 7 8 9 10
• k =2:-0.5:-1
k =2 1.5 1 0.5 0 -0.5 -1
• B = [1:4; 5:8]
x =1 2 3 45 6 7 8
Matrix Index• The matrix indices begin from 1 (not 0 (as in C))• The matrix indices must be positive integer
Given:
A(-2), A(0)
Error: ??? Subscript indices must either be real positive integers or logicals.
A(4,2)Error: ??? Index exceeds matrix dimensions.
Concatenation of Matrices• x = [1 2], y = [4 5], z=[ 0 0]
A = [ x y]
1 2 4 5
B = [x ; y]
1 2
4 5
C = [x y ;z] Error:??? Error using ==> vertcat CAT arguments dimensions are not consistent.
Operators (arithmetic)+ addition- subtraction* multiplication/ division^ power‘ complex conjugate transpose
Matrices Operations
Given A and B:
Addition Subtraction Product Transpose
Operators (Element by Element)
.*element-by-element multiplication
./ element-by-element division
.^element-by-element power
The use of “.” – “Element” Operation
K= x^2Erorr:??? Error using ==> mpower Matrix must be square.B=x*yErorr:??? Error using ==> mtimes Inner matrix dimensions must agree.
A = [1 2 3; 5 1 4; 3 2 1]A =
1 2 35 1 43 2 -1
y = A(3 ,:)
y= 3 4 -1
b = x .* y
b=3 8 -3
c = x . / y
c= 0.33 0.5 -3
d = x .^2
d= 1 4 9
x = A(1,:)
x=1 2 3
Determinant of a matrix
Power of a matrix
Power of a matrix
=
Ploting in MATLAB
• Create an x-array of 10 samples between 0 and 1.
• Calculate y function which is given as
• Plot the y
>>x=linspace(0,1,10);
>>y=x;
>>plot(x,y)>>grid
Ploting in MATLAB
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ploting in MATLAB
• Now write xlabel('x') ylabel('y') title(‘y=x')
and open the Figure 1 again.
Can you see labels on the axis of plot and title?
Ploting in MATLAB
Ploting in MATLAB
• Write in command window “hold” now.• This command will overwrite the new plot on
to current figure without delete it. • At this step, we will use “stem” command
instead of plot.• Now, write stem(x,y, 'r');• Open Figure 1 again.
Ploting in MATLAB
Open a new figure by using figure comand and do the same plot for 100 points.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1y=x
y
x
Ploting in MATLAB
• There are several properties of plot command.• To learn these properties, remember that
there is a help command in MATLAB.• Learn how to use the commands related to
plot command such as axis, subplot, ...
Operators (relational, logical)
• == Equal to• ~= Not equal to• < Strictly smaller• > Strictly greater• <= Smaller than or equal to• >= Greater than equal to• & And operator• | Or operator
Flow Control
• if • for • while • break
Control Structures • If Statement Syntax
if (Condition_1)Matlab Commands
elseif (Condition_2)Matlab Commands
elseif (Condition_3)Matlab Commands
elseMatlab Commands
end
Some Dummy Examples
if ((a>3) & (b==5))Some Matlab Commands;
end
if (a<3)Some Matlab Commands;
elseif (b~=5) Some Matlab Commands;
end
if (a<3)Some Matlab Commands;
else Some Matlab Commands;
end
Control Structures
• For loop syntax
for i=Index_ArrayMatlab Commands
end
Some Dummy Examples
for i=1:100Some Matlab Commands;
end
for j=1:3:200Some Matlab Commands;
end
for m=13:-0.2:-21Some Matlab Commands;
end
for k=[0.1 0.3 -13 12 7 -9.3]Some Matlab Commands;
end
Control Structures
• While Loop Syntax
while (condition)Matlab Commands
end
Dummy Example
while ((a>3) & (b==5))Some Matlab Commands;
end
If Examplefunction compare(x,y)
if x>y
display('x is greater than y');
else if x<y
display('y is greater than x');
else
display('x is equal to y');
end % Ending for else if
end % Ending for if
If examplefunction compare(x,y)
if x>y
display('x is greater than y');
else if x<y
display('y is greater than x');
else
display('x is equal to y');
end % Ending for else if
end % Ending for if
“For” example
for i=1:100
x(i)=i^2 ;
end
1
2 3
“For” example
Another Examplex=10*randn(1,100);
for i=1:100
if x(i) > 0
y(i)=1;
elseif x(i)<0
y(i)=-1;
else
y(i)=0;
end
end
Another Example
Another Example
Another Example
• Now, get the same result of y by using the MATLAB function “sign(x)”
• Write in command window “help sign”.• Learn how to use sign command and use it for
determining the sign of elements of x.
MATLAB HW#11. Solve the following linear system
equation using Cramer Rule in MATLAB.
MATLAB HW#12. By applying
find the inverse of following matrix in MATLAB
Verify your result by using “inv” command.
MATLAB HW#13. Find a matrix X such that AX=B for the given A
and B matrices below
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