Module (1): Introduction to MATLAB
MATLAB: [Matrix] [Laboratory]
1.
MATLAB User Interface
Command Window
The Command
Window is one of the main tools you use to enter data, run MATLAB functions and
other M-files, and display results.
The Command
Window prompt, >>, is where you
enter statements. You can enter a MATLAB function with arguments or assign
values to variables.
For example,
1+2,
ans = 3.
Workspace Window:
Contains any variables generated as the
result of working in the Command window. In this case, the Workspace window
contains a variable named ans that holds a value of 3.
Current folder Window
Contain saved MATLAB files.
Command History window:
Using Up-Down Arrows at your keyboard,
you can show this widow that displays the series of formulas or commands that
you type, along with the date and time you typed them. You can replay a formula
or command in this window. Just select the formula or command that you want to
use from the list to replay it.
2.
Saving the workspace
results in MATLAB
The
workspace is not maintained across sessions of MATLAB®. When you quit MATLAB,
the workspace clears. However, you can save any or all the variables in the
current workspace to a MAT-file (.mat).
You can
then reuse the workspace variables later during the current MATLAB session or
another session by loading the saved MAT file.
There are
several ways to save workspace variables interactively:
1) To save all
workspace variables to a
MAT-file, on the Home tab, in the Variable section, click Save Workspace.
2) To save a subset of
your workspace variables to a
MAT-file, select the variables in the Workspace browser, right-click, and then
select Save As. You also can drag the selected variables from the Workspace
browser to the Current Folder browser.
3) To save variables to a MATLAB script, click the Save
Workspace button or select the Save As option, and in the Save As window, set
the Save as type option to MATLAB Script. Variables that cannot be saved to a
script are saved to a MAT-file with the same name as that of the script.
3.
Saving the Command window
in MATLAB
To save
the contents of your Command Window to PDF. Right-click on the Command
Window bar, and then Print.
Alternatively,
copy and paste the commands into an editable file.
4.
OCTAVE User Interface
If you don’t have
access to MATLAB for practicing, you can download OCTAVE. It is a powerful open-source
(free) and has almost the same platform as MATLAB.
To download it,
please follow this link https://www.gnu.org/software/octave/
5.
Some Useful Commands in MATLAB
help: Display help text in Command Window.
doc: Opens the Help browser if it is not
already running and otherwise brings the Help browser to the top.
clear: Removes
all variables from the workspace.
clear AII: Removes all variables, globals, functions and MEX links.
home: Moves
the cursor to the upper left corner of the window. It also scrolls the visible
text in the window up out of view; you can use the scroll bar to see what was
previously on the screen.
clc: Clear command window.
who: Lists the variables in the current
workspace..
whos: is a
long-form of WHO. It lists all the
variables in the current workspace, together with their size, bytes, class,
etc..
6.
How to work with
mathematics in MATLAB
Basic Arithmetic functions in MATLAB
Practice-1
>>
x=10;
>>
y=2;
>>
z1=x+y
z1 =12
>>
z2=x-y
z2 =8
>>
z3=x*y
z3 =20
>>
z4=x/y
z4 =5
>>
z5=x\y
z5 =0.2000
>>
z6=y-x
z6 =-8
>>
A1=abs(z6)
A1 = 8
Practice-2
>>
x=4.454
x =4.4540
>>
floor(x)
ans =4
>> ceil(x)
ans =5
>>
round(x)
ans =4
>>
round(x,1)
ans = 4.5000
>>
round(x,2)
ans =4.4500
>>
y=315.214
y = 315.2140
>>
round(y,-1)
ans = 320
>>
round(y,-2)
ans = 300
>>sqrt
(x)
ans = 2.1105
7.
Formatting in MATLAB
Format command can be used to set the output format to
the default appropriate for the class of the variable.
format long: Scaled fixed point format with 15
digits.
format short: Scaled fixed point format with 5 digits.
format bank: Fixed format for dollars and cents.
8.
Symbolic and Numeric in MATLAB
In MATLAB, you can construct symbolic numbers using the command (sym), and you can return them to scalar using the command (double).
You can also construct symbolic variables and objects using
command syms x. For more than one
variable, leave a space between them.
You can also use the function pretty to present the
answer in a pretty way.
9.
Vectors and Matrices in MATLAB
Creating Vectors in MATLAB
Vectors can be created horizontally using the
following commands and functions
>> A=[1 2 3 4 5] or A=[1,2,3,4,5]
A =1 2
3 4 5
>> A=[1:5]
A =1 2
3 4 5
>> D=[1:2:5]
D =1 3
5
>> A=linspace(1,5,5)
A =1 2
3 4 5
>> linspace(1,10,3)
ans =1.000000000000000 5.500000000000000 10.000000000000000
>>
A=rand(1,8) %to create 1 raw and 8 columns (0-1) randomly
A =0.4173 0.0497
0.9027 0.9448 0.4909
0.4893 0.3377 0.9001
>>
A=500*rand(1,7)
A =390.1260 194.8694
120.8456 201.9561 48.2273
65.9866 471.0253
>>
A=round(500*rand(1,10))
A =117 177
411 8 22
84 325 366
324 225
Note: if you want to create random numbers between two values,
the following formula can be used: A=round(low +(up-low)*rand(m,n))
[Example: 5 integers from 100-500]
>>
A=round(100+(500-100)*rand(1,5))
A =117 477
411 325 266
Vectors can be created vertically using the
following commands and functions
|
>>
a=[1;2;3;4;5] a = 1 2 3 4 5
|
>>
a= [1:2:10]' a = 1 3 5 7 9
|
MATLAB can reshape an array into a specific size. So,
it can be used to make arrays only verticals or horizontal using
reshape(X,M,N)
•
Where X is the array, M is the number of rows
wanted, and N is the number of columns needed
Example
• Write a
MATLAB syntax that convert (X) horizontal array to a vertical one, and do
nothing for vertical arrays.
•
Here, the column=1, and rows
should be any numbers according to the array size, then the syntax should be: reshape(X,[],1)
>> X=[1:5]
X = 1.00
2.00 3.00 4.00
5.00
>> Y=reshape(X,[],1)
Y =
1.00
2.00
3.00
4.00
5.00
Another functional syntax is Y=x(:)
Example
• Write a
MATLAB syntax that converts (X) vertical array to a horizontal one and does
nothing for horizontal arrays.
•
Here, the rows=1 and columns
should be any numbers according to the array size. Then the syntax should be: reshape(X,1,[])
>>
X=[1:5]’
X =
1.00
2.00
3.00
4.00
5.00
>>
Y=reshape(X,1,[])
Y
= 1.00 2.00 3.00 4.00
5.00
Creating Matrices in MATLAB
Matrices can be created using the following commands
and functions
>> a=[1 2 3 4 5]; b=[2 3 1 4 5];
c=[1 0 3 2 4];
>> d=[a;b;c]
d =
1
2 3 4
5
2
3 1 4
5
1
0 3 2 4
>> A=[1 2 3;4
5 6;7 8 9]
A =
1
2 3
4
5 6
7
8 9
Special matrices can be also created using the
following commands and functions
>> ones(3)
ans =
1 1
1
1
1 1
1
1 1
>> ones(3,2)
ans =
1
1
1
1
1
1
>> zeros(2)
ans =
0
0
0
0
>> eye(3)
ans =
1
0 0
0
1 0
0
0 1
Extracting, Replacing or Eliminating an element or more from Arrays
and Matrices
In
order to extract an element or array from vectors or matrices; the following commands and
functions can be executed A(Row number, Column Number)
>> A=[1 2 3; 4 5 6; 7 8 9]
A =
1
2 3
4
5 6
7
8 9
>> A(2,3)
ans =6
>> A(2)
ans =4
>> A(2,:)
ans = 4 5
6
>> A(:,1)
ans =
1
4
7
>> A(3,1:2)
ans = 7.00 8.00
In
order to extract a small matrix from a larger one, for example to extract [2 3;
5 6]:
>> A=[1 2 3; 4 5 6; 7 8 9]
A =
1
2 3
4
5 6
7
8 9
>> A(1:2,2:3)
ans =
2.00 3.00
5.00 6.00
Changing a vector in MATLAB
If you want to
change a value of a vector in an array or a matrix, you can double click in the
workplace; this will open a window contains all variables, so you can change
the value you want.
In
order to replace an element or array in a vectors or matrix
>> A=[1 2 3; 4 5 6; 7 8 9]
A =
1
2 3
4
5 6
7
8 9
>> A(1:2,2:3)=0
A =
1
0 0
4
0 0
7
8 9
In
order to remove elements from an array, [] can be used as follows
>> A=[1 2 3 4 5]
A = 1.00 2.00 3.00 4.00 5.00
>> A(2)=[]
A = 1.00 3.00
4.00 5.00
10.
Some useful commands in Matrices
and Vectors
Find: To find the location of a vector
A =
1
2 3
4
2 5
2
8 1
>> find(A==2)
ans =
3
4
5
>> find(A==5)
ans =8
Sort: To sort the vectors of each column.
A =
1
2 3
4
2 5
2
8 1
>>
sort(A) %ascending by default
ans =
1
2 1
2
2 3
4
8 5
>> sort(A,'ascend')
ans =
1
2 1
2
2 3
4
8 5
>> sort(A, 'descend')
ans =
4
8 5
2
2 3
1
2 1
numel, length, size: To calculate the number of vectors, length of vectors, and size
of a matrix.
A =
1
2 3
4
2 5
2
8 1
>> numel (A)
ans =9
>> length (A)
ans =3
>> size(A)
ans = 3 3
11.
Some Useful Statistical Commands
A =
1
2 3
4
2 5
2
8 1
To find the min for each
column.
>> min(A)
ans =1 2
1
To find the minimum value in a
matrix
>> min (min(A))
>> min(A(:))
>> min(A, [], 'all') % Starting in R2018b
ans =1
To find the max for each
column.
>> max(A)
ans = 4 8
5
To find the maximum value in a
matrix
>> max (max(A))
>> max(A(:))
>> max(A, [], 'all') % Starting in R2018b
To find the mean in a matrix
>> mean(A)
>> mean(A(:))
To find the median in a matrix
>> median(A)
>> median(A(:))
To find the standard deviation in
a matrix
>> std(A)
>> std(A(:))
To find the variance in a
matrix
>> var(A)
>> var(A(:))
To find the correlation
coefficient in a matrix
>> corrcoef (A)
>> corrcoef (A(:))
12. Mathematical Operations in Arrays/Matrices in MATLAB
The absolute value of the
elements
>>
A=[1 2 3;-4 5 6; 7 8 -9]
A =
1
2 3
-4
5 6
7
8 -9
>>
abs(A)
ans =
1
2 3
4
5 6
7
8 9
Trigonometric functions of the
matrix
>>
cos(A)
ans =
0.54 -0.42 -0.99
-0.65 0.28 0.96
0.75 -0.15 -0.91
>>
sin(A)
ans =
0.84 0.91 0.14
0.76 -0.96 -0.28
0.66 0.99 -0.41
>>
log(A)
ans =
0.00 0.69 1.10
1.39 1.61 1.79
1.95 2.08 2.20
The root of the matrix
A =
4.00 9.00 16.00
8.00 27.00 64.00
>>
sqrt(A)
ans =
2.00 3.00 4.00
2.83
5.20 8.00
>>
nthroot(A,2)
ans =
2.00 3.00 4.00
2.83 5.20 8.00
>>
nthroot(A,3)
ans =
1.59 2.08 2.52
2.00 3.00 4.00
Multiplication of arrays and
matrix
A =
4.00 9.00 16.00
8.00 27.00 64.00
>>
2*A
ans =
8.00 18.00 32.00
16.00 54.00 128.00
>> A/2
ans =
2.00 4.50 8.00
4.00 13.50 32.00
Note the following command
>> A=[1 2 3]; B=[4 5 6];
>> A*B
Error using *
Incorrect dimensions for matrix
multiplication. Check that the number of columns in the first matrix matches
the number of rows in the second matrix. To perform elementwise multiplication,
use '.*'.
The number of columns in
the first matrix should match the number of rows in the second matrix.
Write the following command
>> A=[1 2 3]; B=[4; 5; 6];
>> A*B
ans =32.00
Why??, Because it is (1*4+2*5+3*6)=32
So, in order to perform it,
you run the following commands
>>
A*B' %Transpose
ans =32.00
or
>>
dot(A,B)
ans =32.00
If you want to perform a Cross
Product, run the following commands
>> cross(A,B)
ans = -3.00 6.00 -3.00
If you want one by one
multiplication then.
Write the following commands
>> A=[1 2 3]; B=[4; 5; 6];
>> A.*B
ans =
4.00 8.00 12.00
5.00 10.00 15.00
6.00 12.00 18.00
Write the following commands
>> A=[1 2 3]
A =
1.00 2.00 3.00
>> B= [2 4 6]
B =
2.00 4.00 6.00
>> A.*B
ans =
2.00 8.00 18.00
>> A.^B
ans =
1.00 16.00 729.00
LU: To find the Lower
triangular and upper triangular matrices
for a matrix.
13.
Input/output functions
Input function prompts the user for values directly from the
command window. and its syntax is
n=input(‘promtstring’)
Similarly, the output can be displayed as a value or a string, and
its syntax is
disp(variable)
disp(‘string’)
if you want to combine both string and variable
or value in the same line, you can write the syntax as
disp([‘string’ , num2str(variable)])
Practice
Can you
calculate the area of a circle, where the diameter is an input variable? Properly
display the results.
>>
x=input('Insert the Circle Diameter: ');
Insert the Circle Diameter:
5
>>
A=pi*x^2/4;
>>
disp(['The area is: ' ,num2str( A)])
The area is: 19.635
Another valuable way to display several strings
and values is by using the function fprinf
>> fprintf('The Area of the Circle
is %f cm \n', A)
The Area of the Circle is
19.634954 cm
>> fprintf('The Area of the Circle
is %0.2f cm \n', A)
The Area of the Circle is
19.63 cm
>> fprintf('The Area of the Circle
is %0.0f cm \n', A)
The Area of the Circle is
20 cm
Notes:
%s → print a string
%c
→ print a single character
%d
→ print
a whole number
%f →
print a floating point
number
%0.2f → print a number with two decimal
%0.1f → print a number with one decimal
%0.0f → print a number with no decimal (as Integer)
\n → print a new line (go to the
next line to continue printing)
msgbox
msgbox is a display
tool to display a message in a box
msgbox(‘Good Morning’)
error
error can be used also to display a
massage with a notification sound
error('Good morning')
14.
Plotting
Plot, xlabel, ylabel, title
You can plot X vs Y
and put titles for the axis using these function
You can also change the line style
You can change the line color and style
|
|
|
Subplot
If you want to have
more than one plot in the same page, then the subplot can
be used
subplot(number of rows,
number of columns, location of figure)
Scale limits
To assign limits for
x and y axis, you can use the functions ylim and xlim
ylim([min max])
xlim([min max])
Grid
To add gird to your
plot
grid on
To remove gird from
your plot
grid off
End of This section
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