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1
Matlab Basic
programs. fortanor C with interact to ability
:GUI program nApplicatio 5.
computing. advanced
to elementary from ranging function in-built
Library Function alMathematic Matlab The4.
ionvisualizat D-3 & D-2 commands & function
:Graphics Handle 3.
workspace manage to Facility
:tEnvironmen Working 2.
language gprogrammin level High
:language Matlab The1.
:parts 5 has system Matlab
GUI. including ntdevelopeme napplicatio & analysis
,simulation & modelling n,computatiofor used Today
oratory.Lab rixMatfor dstans Matlab
⇒
⇒
2
MATLAB Basic
3
s
2 1 s
instance,For key. Returnor Enter the press next and command a
type nscomputatio simple a perform Tokey. Returnor Enter
the press next and clc type Window Command theclear To
window. command in programs short simple write can We
(propmt) by followed shown be will logo the pause short
aer window.Aft sterm the of one in Matlab launch UNIXFor
prompt. command is shown.This be will prompt A
appear. will window Command icon, Matlab on clicking double By
:windowsFor
=
+=>>
>>
⇒
>>
⇒
3
MATLAB Basic (cont.)
matfun help
function matrix on examplefor topic, a on help specificFor
....
.transformsFourier and analysis Data - datafun\matlab
algebra.linear numerical - functions Matrix - matfun\matlab
functions. math dSpecialize - specfun\matlab
functions. math Elementary - elfun\matlab
on.manipulati matrix and matrices Elementary - elmat\matlab
.constructs language gProgrammin - lang\matlab
.characters special and Operators - ops\matlab
commands. purpose General - general\matlab
help
:topics HELP
topics. of list a genrate will prompt.It command at help Type
:help line Command
>>
>>
⇒
4
MATLAB Basic (cont.)
matrices matlab demo
matrices matlabfor examplefor option, demo specific aFor
demo.for window new a open will
demo
demo. type feature, MATLAB on iondemonstratFor
:Demo
... ... ...
division. %Matrix :slash.m
multiply. Matrix *% :mtimes.m
divide. matrix rightor Slash %/ :mrdivide.m
power. Matrix %^ :mpower.m
divide. matrix leftor Backslash \% :mldivide.m
matrixlookfor
keyword thefor files all.M searches lookfor
:lookfor
>>
>>
⇒
>>
⇒
5
MATLAB Basic (cont.)
5)(3/4)(2
.expression the writingfor practice good is () Using
5.7500
= ans
5*3/4+2
right) to left (working nSubtractio & Addition 4.
right) to left (working Division & tionMultiplica 3.
power 2.
brackets 1.
:expression matlab in operaions oforder the
:calculator a as Matlab
++>>
→
>>
⇒
6
MATLAB Basic (cont.)
3.0000i + 2.0000
= ans
i*3+2
j.or i byeither denoted is 1- unit imaginary Theform.
r rectangula in drepresente are MATLAB in numbers Complex
numbers complex 3.
point) decimal with (Numbers numbers real 2.
point. decimal the without enterd are Integers
integers 1.
:MATLAB in used numbers of kinds three are There
:Numbers
>>
→
→
⇒
7
Matlab Basic (cont.)
. - or 0.0/0.0 as such operations undefined
allymathematic the of result a as obtained is andnumber -a-not
thefor stands NaN Thezero. by dividing of operation the byor
overflow by generated is Infinity ly.respective infinity, positive
and negative thefor tionsrepresenta the are Inf and Inf– The
NaN 3.
Inf 2.
Inf-1.
:nonnumbers the ngrepresenti variables three has
MATLAB above, mentioned numbers of classes to addition In
∞∞
⇒
8
Matlab Basic (cont.)
ned.predetermi are valuestheir as
variables as etc, naninf,eps,pi, use tDon' :names Special
z'.' variableor function Undefined ???
5+z=y
18
= y
5+x=y
13;=x
statement. assignment an of side
right on used is it before value a assigned be must variable Each
name. variable a of
characters 31 first the only recognizes MATLAB s.underscoreor
numbers letters, by followed letter, a with begins name Variable
user. the by chosen
are names whose variables in saved are nscomputatio of Results
:Variables
→
>>
→
→
⇒
9
Matlab Basic (cont.)
Save. onclick next and
.m)(or atfilename.m e.g. file,your for name a Chose
menu. File the from
as Workspace Save select workspace currentyour save To
session.
current in used variables all of list a creates who command
prompt. command from variable acheck also can You
variable. the tab.Choose workspace onClick
Workspace. the
in saved are session MATLAB current the in used variables All
:work reloading & Saving
→
…→
→
→
→
⇒
10
Matlab Basic (cont.)
on grid
grid dotted a add to
,....)data2'',data1'legend('
legend put to
)axis'-yylabel('),axis'-xxlabel('
axes label to
) Title'Figuretitle('
title a put to
,...)b.''y2,x,,r-''y1,plot(x,
,multiplotsfor
axis.-x the along isvector first :Note
)r-''y,plot(x,
codes. matlab from figure creates plot command
:Plotting
>>
→
>>
→
>>
→
>>
→
>>
>>
⇒
11
Matlab Basic (cont.)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1sine & cosine wave
x-axis
y-a
xis
sine
cosine
on; grid
,0);cosine'',sine'legend('
);axis'-yylabel('),axis'-xxlabel('
);wave' cosine & sinetitle('
);ro''z,x,,b*''y,plot(x,
x);*cos(pi=z
x);*sin(pi=y
2;:.01:0=x
:Example
>>
12
Matlab Basic (cont.)
on; grid
,0);cosine'',sine'legend('
);axis'-yylabel('),axis'-xxlabel('
);wave' cosine & sinetitle('
off; hold
);ro''z,plot(x,
on; hold
);b*''y,plot(x,
x);*cos(pi=z
x);*sin(pi=y
2;:.01:0=x
shown. be will plot last only on hold Without
Here figure. same on plots multiple plot to used be also can hold
>>
⇒
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1sine & cosine wave
x-axis
y-a
xis
sine
cosine
13
Matlab Basic (cont.)
on; grid
,0);cosine'legend('
);axis'-yylabel('),axis'-xxlabel('
);wave' cosinetitle('
);ro''z,plot(x,
2,3);subplot(2,
on; grid
,0);sine'legend('
);axis'-yylabel('),axis'-xxlabel('
);wave' cosinetitle('
);b*''y,plot(x,
2,2);subplot(2,
x);*cos(pi=z
x);*sin(pi=y
2;:.01:0=x
graph. moreor one plot can we which into
windows,smaller of array nm in splitted is window Graphical
: Subplot
>>
×
⇒
0 0.5 1 1.5 2-1
-0.5
0
0.5
1cosine wave
x-axis
y-a
xis
0 0.5 1 1.5 2-1
-0.5
0
0.5
1cosine wave
x-axis
y-a
xis
sine
cosine
14
Matlab Basic (cont.)
required. where paste and nsapplicatioother or word to Go
figure. copy choose menu, edit figure From
:nsapplicatioother & word to Copy
menu. Edit figure from modified be
also can properties Axis & properties FigureHowever
→
→
⇒
⇒
15
Vectors & Matrices
3
2
1
b
[1;2;3] b
(matrix))vector in row of end marks (Semicolon :vector 2.Column
3 2 1
a
3] 2 [1 a
element) (matrix)vector diff.mark gapor (Comma :vector Row.1
:vectors column & row Creating
=
=>>
=
=
⇒
16
Vectors & Matrices (Cont.)
same. is operation .' & ' both )matrix( vector real For
2.0000i + 2.0000
1.0000i + 1.0000
= ans
c.'
2.0000i - 2.0000
1.0000i - 1.0000
= ans
c'
i];*2+ 2 i+[1=c
(matrix).vector of transpose the createoperator quote) (dot .' The
3 2 1
= ans
b'
3
2
1
= ans
a'
(matrix).vector of transpose conjugate the createoperator (quote) ' The
:(rows) columns into (columns) rows Transfrom•
>>>>
>>
⇒
>>
>>
⇒
17
Vectors & Matrices (Cont.)
9 4 1
= ans
a.^2
9 4 1
= ans
a*a.
opeartor. dot the follows thatopeartor the of
napplicatio isecomponentwfor used is operator) (dot . The
3
= ans
length(a)
vector. of components of no. the esminerdet:length
>>
>>
⇒
>>
⇒
18
Vectors & Matrices (Cont.)
5 8- 1
= ans
b)cross(a,
[-2,1,2];=b
[1;2;3];=a
3. be mustvector gthlength.Len same of be must B &A
B. and A vectors product cross the returns:cross
6
= ans
b)dot(a,
[-2,1,2];=b
[1;2;3];=a
length. same of be must B &A
B. and A vectors of productscalar the returns:dot
>>
⇒
>>
⇒
19
Vectors & Matrices (Cont.)
value numerical indicares[]
address indicates()
8 7
2 1
= b
)2] [1,3] [1a(=b
:2&1 columns and
3 &1 rows of consisting b submatrix a extract to examplefor
:Submatrix Extracting
9 8 7
6 5 4
3 2 1
= a
9] 8 6;7 5 3;4 2 [1=a
:Matrix Creating
columnsrows
→
→
>>
⇒
>>
⇒
321321
20
Vectors & Matrices (Cont.)
value indicates j][i,
position indicates j)(i,
9 7
6 4
3 1
= a
[]=a(:,2) >>
9]; 8 6;7 5 3;4 2 [1=a
[]operator vector empty use :(column) row a delete To
3] 2 [1order in (columns) rows all indicates :
9 7 8
6 4 5
3 1 2
= d
3]) 1 [2a(:,=d
3 2 1
6 5 4
9 8 7
= c
1],:) 2 a([3=c
:ns)rows(colum einterchang To
→
→
⇒
→
>>>>
⇒
21
Vectors & Matrices (Cont.)
5 7 3
= ans
7):2:a(2
3 4 5 6 7 5 3 1
= a
3]:-1:8,6:2:[1=a
order.regular a in bits extarctor build to used be (colon)can :
8
= ans
a(3,2)
10]; 8 6;7 5 3;4 2 [1=a
.position/s specific a of bit/s extarct to used race)is(bracket/b ()
:(matrix)vector of bits gExatractin
>>
>>
⇒
>>
⇒
22
Vectors & Matrices (Cont.)
1 4 9
9 4 1
= ans
a*a.
1]; 2 3;3 2 [1=a
matices.for works alsooperator .(dot) the
9 7
8 5
6 4
3 1
= a
a(3,:)]8]; a(2,:);[5[a(1,:);=a
9]; 6;7 3;4 [1=a
9 8 7
6 5 4
3 2 1
= a
a(:,2)] 8]' 5 [2 [a(:,1)=a
9]; 6;7 3;4 [1=a
:(column) row new a Inserting
>>
⇒
>>
>>
⇒
23
Vectors & Matrices (Cont.)
1 2 4
4- 2- 3
8 1 0
= c
b] [a=c
[8;-4;1];=b
2]; 2;4- 1;3 [0=a
matrices.smaller from from build be can matrix Large
:ionConcatenat Matrix
columns ofnumber
indicates second while rows, of
number indicatesinteger first
matrix. 3-by -3 a its
3 3
= ans
size(a) >>
10]; 8 6;7 5 3;4 2 [1=a
matrix) the of (dimension size the get size
:Matrix a of Size
>>
⇒
⇒
24
Vectors & Matrices (Cont.)
1 0 0
0 1 0
0 0 1
= I
eye(3)=I
matrix identity mm an gives eye(m)
0 0 0
0 0 0
0 0 0
= b
zeros(3,3)=b
s0' of matrix nm gives n)zeros(m,
1 1 1
1 1 1
= a
ones(2,3)=a
s1' of matrix nm an gives n)ones(m,
:Matrices Special
>>
×
>>
×
×
⇒
25
Vectors & Matrices (Cont.)
37 21
47 23
= ans
b*a
9]; 3 8; 4;6 [2=b
1]; 2 3;3 2 [1=a
B in rows of no. to equal be must A of columns of no.
agree. must dimensions matrixInner
* ==> usingError ???
b*a
8]; 4;6 [2=b
1]; 2 3;3 2 [1=a
:tionMultiplica Matrix
>>
→
>>
⇒
26
Vectors & Matrices (Cont.)
9
5
1
= b
diag(a)=b
9]; 8 7 6; 5 4 3; 2 [1=a
matrix. that ofvector diagonal main creates diag matrix a given
:matrix a of diagonal Main
3 0 0
0 2 0
0 0 1
= b
diag(a)=b
3]; 2 [1=a
diagonal. main asvector that with matrix a creates diagvector a given
:matrix Diagonal
>>
⇒
>>
⇒
27
Vectors & Matrices (Cont.)
12
11
10
2
= i
4)==find(a=i
4]; 7 6 4;5 6 5 4;4 3 2 [1=a
condition. given a satisfying matrixor vector
a of (indices) positions the of list a returns find function
:Matrices & Vectorsfor Find
>>
⇒
28
Solving System of Linear Equations
0.0491
0.5849
= x
b\a=x
ones(3,1);=b
2]; 10;1 1;1- [2=a
)solution Square Least(
system edminerdetOver
nm :2 case
0.0000
1.0000
1.0000-
= x
b\a=x
ones(3,1);=b
10]; 8 6;7 5 3;4 2 [1=a
solution) (Exact
nm :1 case
vector. column ldimensiona m is b & nm size of is A
where b,ax symtemlinear solve to have weConsider
division. left as
known .Also opearator) backslash (\ the :solve to way one
>>
>
>>
=
×
=
⇒
29
Solving System of Linear Equations (Cont.)
inv(b)*ac means a/bc
b*inv(a)c means b\ac
matrixfor :Note
0.5000
0
0.5000-
= x
b\a=x
ones(2,1);=b
6]; 5 3;4 2 [1=a
)consistent is system the if solutionr (particula
system minedunderdeter
nm:3 case
==
==
→
>>
<
30
Solving System of Linear Equations (Cont.)
column pivotted zero-non of indices the holds case, second in array c
3
= ans
length(c)
3 2 1
= c
0 1 0 0
1 0 1 0
1- 0 0 1
= x
b]) rref([a=c] [x
ones(3,1);=b
10]; 8 6;7 5 3;4 2 [1=a
0
1
1-
= x
x(:,4)=x
0 1 0 0
1 0 1 0
1- 0 0 1
= x
b]) rref([a=x
ones(3,1);=b
10]; 8 6;7 5 3;4 2 [1=a
b.ax system solve to
want we previous, As etc. ncalculatiorank matrix system,linear of solution as such
nsapplicatio manyfor used be can:)form echelon row reduced( rref Function
→
>>>>
=
⇒
31
Inverse of a Matrix
matrix. a of inverse find to used be also can rref Function
1.0000 2.0000- 1.0000
2.0000- 3.6667 0.6667-
1.0000 1.3333- 0.6667-
= ans
inv(a)
10]; 8 6;7 5 3;4 2 [1=a
matrix given a of inverse the calculates :inv
⇒
>>
⇒
32
Inverse of a Matrix (Cont.)
1.0000 2.0000- 1.0000
2.0000- 3.6667 0.6667-
1.0000 1.3333- 0.6667-
= b
6):b(:,4=b
1.0000 2.0000- 1.0000 1.0000 0 0
2.0000- 3.6667 0.6667- 0 1.0000 0
1.0000 1.3333- 0.6667- 0 0 1.0000
= b
))])eye(size(a rref([a=b
10]; 8 6;7 5 3;4 2 [1=a
))]);eye(size(a rref([a=b
10]; 8 6;7 5 3;4 2 [1=a
:rref function using matrix a of Inverse⇒
33
Determinants
3-
= ans
det(a)
10]; 8 6;7 5 3;4 2 [1=a
ts.determinan gcalculatinfor designed is det Function
>>
⇒
34
Eigenvalues & Eigenvectors
{ {
seigenvalue are These
0.2599
1.3510-
17.0911
= ans
diag(d)
0.2599 0 0
0 1.3510- 0
0 0 17.0911
= d
0.3158 0.4557 0.8252-
0.8128- 0.1245 0.4978-
0.4895 0.8814- 0.2670-
= v
eig(a)=]d,v[ >>
10]; 8 7 6; 5 4 4; 2 [1=a
matrix. given a of rseigenvecto &
eigenvalus computingfor designed is eig function
vector eigenan is
column each
values eigen as elements
diagonalwith matrix
vectorseigen
of matrix
>>
⇒
43421
35
Programming in Matlab
arguments. output return &
arguments take may files function Thearguments. output
the returnor arguments input take not do files Script
files Function 2.
files Script 1.
files. .m of type two in contained are codes Matlab
file-M Select
New Choose
window command from menu file to Go
file .m new a open To
files (mat) .m The
→
→
→
⇒
36
Programming in Matlab (Cont.)
grid
y);plot(x,
sin(x)./x;=y
pi;*10:pi/100:pi/100=x
:file script of Example
>>
⇒
0 5 10 15 20 25 30 35-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
37
Programming in Matlab (Cont.)
size same of not are matrix
dotprod ==> usingError ???
b)dotprod(a,
5]; [4=b
3]; 2 [1=a
18 10 4
= ans
b)dotprod(a,
[4;5;6];=b
3]; 2 [1=a
function, the access To
end
);size' same of not are matrixerror('
else
q;*p.dp
,length(q))(length(p) if
q)dotprod(p, dp function
:file Function of Example
>>>>
=
==
=>>
⇒
38
Programming in Matlab (Cont.)
{
body Functuion
end
);size' same of not are matrixerror('
else
q;*p.dp
,length(q))(length(p) if
ndeclaratio Function q)(p,dotprod dp function
variable. return of value return the create to
arguments input the on works funtrion how Deines
:body Function 2.
alue.variable/v ) (returnor
ouput & arguments input name, function icludes
ndeclaratio Function 1.
:parts two has Function
:function a create to How
umentsarginput
namefunction
iablevaroutputkeyword
=
==
=
⇒
3214342143421
39
Programming in Matlab (Cont.)
dotprod.m
as saved be must file example previous in : examplefor
function. the of name the be must file
the of name the file, M . into function a saving When
folder. same the in be must files
function required the all and files function the accessing
files program the file, .M separate a is file function each
where files function multiple of needs program a If
n.descriptio
bodytheir their before declared be must Function
line. ndeclaratio of end the at coloncomma/semi No
:onconstructi function about something Note
→
→
→
→
⇒
40
Programming in Matlab (Cont.)
10
= ans
f(6,8) »
y^2)+sqrt(x^2 = y)f(x,
:function Inline
= f
)y'',x'',y^2)'sqrt(x^2'( inline=f
functions. inline use to handy is it
session, Matlab currentfor only function a use to have we If
:Functions Inline
quote between
arguments
quote between expression function
keyword321
444 8444 76
321 +>>
⇒
41
Programming in Matlab (cont.)
5050
= sum
sum »
end
i;+sum=sum
100,:1:0=ifor
0;=sum
:Example
end
commands
arraykfor
Structure
:loopsfor 1.
statementsbreak 5.
onsconstructi case-switch 4.
onsconstructi end-else-if 3.
loops while 2.
loopsfor 1.
.statements control 5 have we matlab, In
:Flow Control
>>
→
=
→
⇒
42
Programming in Matlab (cont.)
s(k)sin(k)'*co=a
10;:1:1=k
:ionvectorizat By
end
end
cos(j);*sin(i)=j)a(i,
10:1:1=jfor
10:1:1=ifor
loops for nested By
).jcos()isin(a where matrix 1010 a create we
cases. gprogrammin the
of most in loopsfor of instead used be can which ionvectorizat
called feature a has Matlab ).efficiency time of (because
apply. not do methodsother when used be should loopFor
nested. be also can loopsFor
ij
>>
>>
=×→
→
→
43
Programming in Matlab (cont.)
0.0061
= q
q »
end
;q/2=q
0.01>q while »
pi;=q
end
statements
expression while
Structure
.beforehand
known not is iteration ofnumber when used is loop This
:loops While 2.
statements
expression
43421
48476
→
44
Programming in Matlab (cont.)
end;
);failed'disp('
else
1; = pass
60)) >= rage(grade_ave & 0.90) >= ce((attendan if
end
else
statements
expression if else
statements
expression if
end
statements
else
statements
expression if
end
statements
expression if
:Structure
:onsconstructi endelseIf .3
end-else-elseif-if
end-else- if
end-if
>>
→
−−
M
44 844 76
44 844 76
44 844 76
K
45
Programming in Matlab (cont.)
}
{
end
);Failed'disp('
otherwise
);C' Gradedisp('
case(2)
);B' Gradedisp('
case(3)
);A' Gradedisp('
(4)case
gpa switch
rand);*ceil(4=gpa
:Example
end
statements
otherwise
statements
2 value case
statements
value1 case
expression switch
:Structure
.statements associate the exucutes it found is match the Once
value. case each to expression input the compares Switch
:onconstructi caseSwitch.4
value
expression
>>
→
→
−
M
46
Programming in Matlab (cont.)
required.
not are statementsbreak So, execute. not do statements
caseother the true, is statement case first the If through.
fall not does switch Matlab statement, C Unlike :Note
disp(s)
end
line);strvcat(s, = s
end
break,
ne),isempty(li if
;fgetl(fid) = line
feof(fid)~ while
;'' = s
);r'',fft.m'fopen(' = fid
:example
loop. innnermost the from only exitbreak loops, nested of
case In loop. whileor for from exit early lets statement break
:staements break.5
→
>>
→
47
Programming in Matlab (cont.)
4 4 4
= ans
a(ind) >>
0 1 1 0 1 0 0
= ind
4)==(a=ind
1]; 4 4 3 4 1 [0=a
false'.' if 0 and true'' are
they when 1 returns and variables
two compares operators These
to) equal (Not ~
to) (Equal
to) equalor (Greater
(Greater)
to) equalor than (Less
than) Less (
operators following the with performed are MATLAB in sComparison
:Operator Logical & Relations
>>
=
==
>=
>
<=
<
⇒
48
Programming in Matlab (cont.)
isempty[]. :like
functions. logical in-built several are there Matlab In
2.5000 2.0000 1.0000
= ans
a(ind) >>
1 0 0 0 1 1 0 0
= ind
3)<(a&1)>=(a=ind
2.5]; 3 4 3.5 2 1 0.5 [0=a
(not) ~
(and) &
(or) |
MATLAB. in available operators logical three are There
:operator Logical
→
>>
⇒
49
Programming in Matlab (cont.)
48 48
24 through 23 Columns
51 50 45 69 69 32 102 111 32 115 115
22 through 12 Columns
97 108 99 32 101 109 111 99 108 101 87
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Programming in Matlab (Cont.)
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