Matlab Short 152

MATLAB Language of Technical Computing and

Visualization

Presented by

Dr. M. Nuruzzaman

Electrical Engineering Department, KFUPM

Office: 59-0077, Email: [email protected], Ph: 2830

Under the auspice of ETS sem 152

Overview

What is MATLAB?

What can be conducted in MATLAB?

What are MATLAB Toolboxes?

Where to start in MATLAB?

prompt - history - mfile

Prep. by: Dr. M. Nuruzzaman

Matrix entering row, column, and rectangular

Enter row matrix [2 3 4 -2 0] into MATLAB

>>R=[2 3 4 -2 0]

111087

Enter

231901131257620

Enter

Space gap

between

elements,

semicolon

between rows,

and housed in

third bracket

>>C=[7 8 10 -11]' or

>>C=[7;8;10;-11]

A=[20 6 7;5 12 -3;1 -1 0;19 3 2]


Vector generation row and column by colon operator

Syntax - start : increment: last value

A=1:4 R=1:3:10 C=[0:2: 10]'

linspace (first element, last element, number of points from

first to last)

Functional codes


Logical & Comparative Operators:

Table D.4 Basic logical operations on matrix elements

for NOT(A) operation,

>>A=[0 0;0 1];

>>~A

ans =

1 1

1 0

for A OR B,

>>A=[1 1;0 1];

>>B=[0 1;1 1];

>>A|B

ans =

1 1

1 1

for A AND B,

>>A&B

ans =

0 1

0 1

for A XOR B,

>>xor(A,B)

ans =

1 0

1 0


Matrix of ones, zeroes, and constants

>>O=ones(3,1) >>z=zeros(3,1)

>>C=3*ones(3,2)

Syntax: ones(row

number,column number)


A=[0 2 3]

B=[-1 4 5]

A/5

1./A

3./A

A+5

A.^2

A./B

A^2

1/A

Matrix arithmetic

200

120

512

21

41

21

89

41

21

00

0

>>A=sym([2 1 5;0 2 1;0 0 2]);

>>B=inv(A)

1yx

yx

xyxy

x

xyxy

yx

xyxy

y

xyxy

22

22

1

>>syms x y

>>A=[x y;x+y 1]; B=inv(A); pretty(B)

Matrix inverse


A=[2 4 3 -10 0 9 73 29 -31 50];

Indexing and coloning of arrays

B=A([2 3 9]) C=A(3:8)

E=A([4 1])

2982873724547140729216645627648

A=[8 64 27 56;-64 216 729 40;1 47 45 72;3 87 82 29];

Array indexing starts from 1 rather from 0

Changing one element

A(2,3)=0

Column delete

A(:,3)=[ ]

Syntax: Array(required row,required column)

Particular colm division

A(:,1)=A(:,1)/2

Two row multiplication

A(:,1)=A(:,1).*A(:,2)/4

Column selection

A(:,4)

Row selection

A(3,:)

Submatrix selection

A([3 4],[1 2])

Consecutive element selection

A(2:4,2:4)

Appending rows

874

059

862

531

862

531[9 5 0] [4 7 8]

B=[1 3 5;2 6 8]

B =

1 3 5

2 6 8

B=[B;[9 5 0]]

B =

1 3 5

2 6 8

9 5 0

A=[B;[4 7 8]]

A =

1 3 5

2 6 8

9 5 0

4 7 8


059

862

531

913

109

Appending columns

91059

10862

39531

D=[1 3 5;2 6 8;9 5 0]

D =

1 3 5

2 6 8

9 5 0

D=[D [9 0 1]']

D =

1 3 5 9

2 6 8 0

9 5 0 1

C=[D [3 1 9]']

C =

1 3 5 9 3

2 6 8 0 1

9 5 0 1 9

for counter = starting value:increment or decrement of the counter value : final value

Executable MATLAB command(s)

end

For-loop syntax

for k=10:10:70

y(k/10)=cosd(k);

end

Or, as a one line: for k=10:10:70, y(k/10)=cosd(k); end

Data accumulation by using the two appending techniques

f=[ ]; k=2; f=[f;k] f=[f k]


for the right shifting,

>>f=[ ]; for k=1:3 f=[f k^2]; end

>>f

f =

1 4 9

for the left shifting,

>>f=[ ]; for k=1:3 f=[k^2 f]; end

>>f

f =

9 4 1

minimum/maximum/sum

/product/sort of data

max

min

sum

sort

prod

Row or column matrix

one function

Rectangular matrix two

functions >>B=[1 3 5;2 6 8]

>>max(max(B))

>>B=[1 3 7 5 -8]

>>max(B)

Index returning

>>B=[1 3 7 5 -8]

>>[M,I]=max(B)


Scalar code for functional computing

)59)(1412( 34 xxxy

)59)(1412( 34 xxxy

Compute

for x=[0 1 2] and y=[3 -2 1]

x=[0 1 2]

y=(12*x.^4-4*x+1).*(9*x.^3-5)

21 x 5.0xCompute

x=-1:0.5:2;

y=(12*x.^4-4*x+1).*(9*x.^3-5)

)59)(112(),( 34 yxyxyxfCompute

x=[0 1 2]; y=[3 -2 1]

f=(12*x.^4-x.*y+1).*(9*y.^3-5)


Rectangular Matrix based computing for 2D function

)59)(112(),( 34 yxyxyxf 21 x 84 y

1x 2y

[x,y]=meshgrid(-1:1:2,4:2:8)

x =

-1 0 1 2

-1 0 1 2

-1 0 1 2

y =

4 4 4 4

6 6 6 6

8 8 8 8

f=(12*x.^4-x.*y+1).*(9*y.^3-5)

f =

9707 571 5139 105635

36841 1939 13573 350959

96663 4603 23015 814731

Symbolic differentiation

xxdxd cos)(sin

2

1

1

1)(cot

xx

dxd

)]59)(1412[( 34 xxxdx

d

>>syms x

>>y=diff(sin(x))

>>syms x

>>y=diff(acot(x))

>>syms x

>>y=diff((12*x^4-4*x+1)*(9*x^3-5))


)]59)(1412[( 343

3

xxxdx

d>>syms x

>>y=(12*x^4-4*x+1)*(9*x^3-5)

>>yn=diff(y,3)

use pretty for math

readable form,

expand for

expansion

Indefinite symbolic integration

xxdx cossin

dxxx

22 )1(

1

dxx

x

4)(ln

>>syms x

>>y=int(sin(x))

>>syms x

>>y=int(1/x/(x^2+1)^2)

>>syms x

>>y=int(log(x)^4/x)


Definite symbolic

integration

xdxsin20

3

222 )1(

1x

x

dxxx

>>syms x

>>y=int(sin(x),0,pi/2)

>>syms x

>>y=int(1/x/(x^2+1)^2,2,3)

dxx

x

x

5

3

4)(ln >>syms x

>>y=int(log(x)^4/x,3,5)

use pretty for math

readable form

Simple if

if logical expression


end

x=2;

if x>=1

y=sin(x);

end

If-else

if logical expression


else


end

x=1;

if x==1

y=sin(x*pi/2);

else

y=cos(x*pi/2);

end

Nested-if if logical expression


elseif logical expression


elseif logical expression


else Executable MATLAB command(s)

end

N=77;

if N>=90

g='A';

elseif (N=80)

g='B';

elseif (N=70)

g='C';

elseif (N=60)

g='D';

elseif (N=50)

g='E';

else

g='F';

end



Switch-case-otherwise syntax

While-end syntax

General syntax:

while logical expression

Executable command(s)

end

where while and end are the reserve words

Example: A positive integer

greater than 1 will be asked

from the user. The sum of the

squares from 1 to that integer

is required to compute.

Executable M-file:

I=input('Enter integer > 1: ');

k=0; s=0;

while ~(k>I)

s=s+k^2; k=k+1;

end

User input during the run time of an M-file

>>A=input('Enter any integer from 1 to 10: ');

>>Enter any integer from 1 to 10: 5

>>A=input('Enter your name: ','s');

>>Enter your name: mohammad


5898

yxyx

Algebraic equation solving solve(eqn 1, eqn 2, eqn 3, so on,var 1,var 2, so on)

>>e1='x-y=-8';

>>e2='9*x+8*y=5';

>>s=solve(e1,e2)

>>[s.x s.y]

242

8222

xzxy

zyx >>e1='x^2-y^2-z^2=-8'; >>e2='2*y+x=4';

>>e3='z-x=2';

>>s=solve(e1,e2,e3)

>>[s.x s.y s.z]

2sin2cos3 xx

>>e='3*cos(x)+2*sin(x)=2';

>>s=solve(e)

double for decimal

pretty for math readable

form

For structure array

array.member for any

element


Fourier transform forward

fourier(function in string form, independent variable, transform variable)

t

t

tj dttfe )(

)(F


Fourier transform inverse

ifourier(function in string form, independent variable, transform variable)

dteF ti)(2

1

)(tf

Laplace transform forward

laplace(function in string form, independent variable, transform variable)


dtetft

t

st

0

)(

)(sF


Laplace transform inverse

ilaplace(function in string form, independent variable, transform variable)

ics

ics

st dssFei

)(2

1

)(tf


Z transform forward

ztrans(function in string form, independent variable, transform variable)

Z transform inverse

n

n

nznf0

][)(zF

C

n dzzzFi

1)(2

1

][nf

Z transform inverse

iztrans(function in string form, independent variable,

transform variable)



)2( 211

2

xxx

For loop conversion

For loop computation: Vector form computation:

S=0; x=-2:11;

for x=-2:11 S=sum(x.^2+2*x);

S=S+x^2+2*x;

end

partial fraction symbolic and linear decimal

)1(3

2

)1(3

12

xx

x

x

1

13x

>>syms x

>>f=1/(x^3+1);

>>R=maple('convert',f,'parfrac',x);

>>pretty(R)

maple('convert',f,'parfrac',x)

866.05.0

2887.01667.0

866.05.0

2887.01667.0

1

3333.0

jx

j

jx

j

x

1

13x

>>syms x

>>N=1;

>>D=sym2poly(x^3+1);

>>[R P K]=residue(N,D)

R =

-0.1667 - 0.2887i

-0.1667 + 0.2887i

0.3333

P =

0.5000 + 0.8660i

0.5000 - 0.8660i

-1.0000

K =

[ ]

residue(Numerator coefficient,Denominator coefficient)


Polynomial roots

013 x

roots(polynomial as a row matrix)

>> r=roots([1 0 0 1])

r =

-1.0000

0.5000 + 0.8660i

0.5000 - 0.8660i

Polynomial multiplication

)3)(1( 23 xxx

syms x

y=(x^3-x+1)*(x^2-3)

pretty(expand(y))

Numerator denominator

separation

7

5

4

12

xx

syms x

y=1/(x^2+4)+5/(x-7);

[N,D]=numden(y)

pretty(N)

pretty(D)

Use expand if

necessary

Algebraic substitution

R

VVsCVV oi

11)( 1AVVo ?

i

o

V

V

maple('algsubs', variable to be eliminated as

an equation but left side of the equation must

be the variable itself, expression from which

the variable is to be eliminated)

syms s R C V1 Vo Vi

e1=(Vi-V1)*s*C-(V1-Vo)/R;

e2='V1=-Vo/A';

O1=maple('algsubs',e2,e1)

O2=solve(O1,Vo)

Vi=1;

subs(O2)

1

ARCs

sRCA


Single input single output function file

Multiple inputs single output function file

Function file for three input and two output

arguments

),,( 321 xxxf2

321

2

1 2 xxxx 8)(2 xxxf

2

321

2

11 2 xxxxp 3212 xxxp

Creating function file:

File starts with function

= is a must for return

Input argument separated

by comma

Output argument

separated by comma

Input argument under first

brace

Output argument under

third brace


yx

y

dx

dyx 42

2

xC

xy

22

ODE without boundary condition

dsolve(ODE code,indpendent variable)

S=dsolve('2*x*Dy=y^2/x+4*y','x');

pretty(S)

01522

2

ydt

dy

dt

yd)(ty tt eCeC 32

5

1

=

S=dsolve('D2y-2*Dy-15*y=0');

pretty(S)

02'''' yyy xeCxy 1)(

2

7sin

2

7cos 32

2x

Cx

Cex

>>S=dsolve('D3y+Dy-2*y=0','x');

pretty(S)

first derivative Dy

Second derivative D2y

Third derivative D3y


ODE with boundary conditions

dsolve(ODE code, initial conditions separated by comma but as a

single string under quote, independent variable)

System of ODE with boundary conditions

dsolve(ODE 1 code, ODE 2 code, and so on, initial conditions separated by

comma but as a single string under quote, independent variable)

21

2

21

1

22

25

yydt

dy

yydt

dy

2)0(

1)0(

2

1

y

y

tt

tt

ee

ee

6

6

5

4

5

65

8

5

3

2

1

yy



y=f(x) versus x graph

From expression

From data

ezplot(function,interval

as a row matrix)

532 2 xxy

33 x

y='2*x^2-3*x+5';

ezplot(y,[-3,3])

plot(x data,y data)

Tabular data Command to plot y vs x:

X -6 -4 0 4 5 7 >>x=[-6 -4 0 4 5 7];

>>y=[9 3 -3 -5 2 0];

>>plot(x,y) y 9 3 -3 -5 2 0

hold

ezplot(x+4',[-3,3]) ezplot(sin(x)',[-3,3])

X -6 -4 0 4 5 7

y1 9 3 -3 -5 2 0

y2 0 -2 1 0 5 7.7

y3 -1 2 8 1 0 -3

plot(x,y1,x,y2,x,y3)

Multiple y

Multiple y

Surface plot

)(8 22 yx ),( yxf

ezsurf('-8*(x^2+y^2)')

from expression from data

Use surf or mesh ezsurf(function code,[x min x max y min ymax])

default surf(functional data as a

retangular matrix,x

variation as a row matrix, y

variation as a row matrix)

Needs computing or

sample generation


2,2 yx

22 x 40 y

22),( yxyxyxf

x=-2:0.2:2;

y=0:0.2:4;

[X,Y]=meshgrid(x,y);

f=X.^2+X.*Y+Y.^2;

surf(x,y,f)

tx cos2 ty sin 20 t

Parametric equation

x='2*cos(t)'; y='sin(t)';

ezplot(x,y,[0,2*pi])

21 1)1ln(ln yyxyy

Implicit function 1.55.2 x 23 y

E='1/y-log(y)+log(-1+y+x)+y^2-1';

D=[-2.5 5.1 -3 2];

ezplot(E,D)

Surface plot

Contour plot for

),( yxf

Syntax: ezcontour(code of f(x,y )under quote, x interval bounds as two

element row matrix, y interval bounds as two element row matrix)

2423

2

1),( yxeyxyxf

2.12.1 x 11 y

Subplot for window splitting

Treat graphs as matrix elements

Syntax: subplot(m-row directed graph number, n-column directed graph

number, particular number from mxn)

All are integers

Suppose m=2, n=2, particular number is 1, 2, 3, 4 consecutively

rowwise


Discrete plot by stem, bar, bar3,


Random numbers

Generation of a single random

number X between 4 and 5,

X=unifrnd(-4,5)

Decimal random numbers:

unifrnd(lower bound,upper bound,row number,column number)

Generation of a rectangular matrix X of order 23 in

which every element is inbetween -4 and 5,

X=unifrnd(-4,5,2,3)

Generation of a single random integer X between -3 and 5,

X=randint(1,1,[-3 5])

Integer random numbers:

unifrnd(row number,column number, [lower bound upper bound])

Generation of a rectangular matrix X of order 33 in which each element is in

between -3 and 5,

X=randint(3,3,[-3,5])

Excel file reading

f=xlsread(book1.xls')

Data statistics

datastats(y)

Matlab Short 152

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