Programming Matlab

Chng 3: Lp trnh Matlab

Trn Minh Ton (1)

Vin Ton ng dng v Tin hc, HBK H Ni

H Ni, thng 1 nm 2012

(1)Email: [email protected]. Ton (SAMI-HUST) Lp trnh Matlab 1/87H Ni, thng 1 nm 2012 1 / 87

M u

Ni dung

1 M u

2 Cc th tc

3 Cc hm m-file

4 Nhp, xut d liu

5 iu khin lung

6 Vector ha (Vectorization)

7 Qun l cc bin Input, Output

8 Tnh gi tr hm mt cch gin tip

9 Ch thch

10 G li

11 Mt s kinh nghim trong lp trnh Matlab

T.M. Ton (SAMI-HUST) Lp trnh Matlab 2/87H Ni, thng 1 nm 2012 2 / 87

M u

M uTip cn lp trnh Matlab

Mt th tc chun ca vic s dng lp trnh MatLab cho vic gii quyt mt bi tonk thut bao gm cc bc:

1 Phn tch bi ton v xc nh thut gii (trn giy)

2 Phc tho cc cng thc tnh ton (trn giy)

3 Vit chng trnh MatLab (M-file) s dng MATLAB Editor/Debugger

4 Kim nghim v sa li

5 Gii bi ton


M u

M u

Cc chng trnh MatLab c cha trong cc m-files

L cc file vn bn thng thng, khng phi file nh phn Cc file phi c ui .m

Cc m-file phi c t trong ng dn hin thi trong ca s Command

Window

MatLab qun l ng dn trong ca n ng dn l mt danh sch cc th mc m MatLab s tm kim

mt m-file thc thi Mt chng trnh c th tn ti v khng c li nhng c th vn

khng chy nu MatLab khng tm thy n C th thay i ng dn bng cch dng cc lnh path, addpath

v rmpath.


Cc th tc

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1 M u

2 Cc th tc

3 Cc hm m-file

4 Nhp, xut d liu

5 iu khin lung




9 Ch thch

10 G li



Cc th tc

Cc th tc (Script Files)

Khng thc s l cc chng trnh

Khng c cc d liu input/output Cc bin th tc l mt phn ca khng gian lm vic

Hu ch cho cc cng vic c nh

Hu ch nh l mt cng c khi to cc ti liu cho cc bi tp nh

Li khuyn

Cc hm (functions) c rt nhiu tin ch so vi cc th tc (scripts)= Lun lun s dng hm thay cho th tc.


Cc th tc

Cc th tc (Script Files)Tc dng ph ca cc th tc

Tt c cc bin c to ra trong th tc s c thm vo khng gian lm vic. iuny s c nh hng ng k bi v

Cc bin tn ti trong khng gian lm vic c th b vit chng ln

S thc thi ca cc th tc c th b nh hng bi trng thi ca cc bin trongkhng gian lm vic.

V d 1

Th tc easyplot

% Load

D=load(xy.dat); % D is a matrix with two columns

x=D(:,1); y=D(:,2); % x is the first column, y is second one

plot(x,y) % Generate the plot and label it

xlabel(x axis)

ylabel(y axis)

title(Plot of generic x-y data set)


Cc th tc


Th tc easyplot tc ng ln khng gian lm vic bng cch to ra ba bin:

>> clear

>> who

(khng c bin no)

>> easyplot

>> who

Your variables are:

D x y


Cc th tc


Ni chung, cc tc dng ph:

Din ra khi mt chng trnh thay i cc bin ngoi tr input/output

C th gy cc li m rt kh pht hin ra

Khng phi lc no cng trnh c

Cc tc dng ph ca th tc

To ra v thay i cc bin trong khng gian lm vic

Khng a ra khuyn co rng cc bin trong khng gian lm vic b thay i.

Bi v cc th tc c cc tc dng ph, tt hn l gi gn tt c trong hm m-file.


Cc hm m-file

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1 M u

2 Cc th tc

3 Cc hm m-file

4 Nhp, xut d liu

5 iu khin lung




9 Ch thch

10 G li



Cc hm m-file

Cc hm m-file

Trong MatLab th tn hm phi trng vi tn ca file c ui .m

Hm l cc chng trnh con:

Cc hm s dng cc tham s u vo/ra kt hp chng vi cchm khc v cc lnh window

Cc hm s dng cc bin a phng (local variables) m ch tn tikhi hm ang thc thi. Cc bin a phng c phn bit vi ccbin trng tn trong khng gian lm vic hoc ca cc hm khc.

Cc d liu u vo cho php cng mt th tc tnh ton (cng thut ton) pdng vi cc d liu khc nhau. Do , cc hm m-file c th dng li nhiu ln.

Cc hm c th gi cc hm khc

Cc th tc ring c th gi vo trong mt hm. Cc tip cn ny cho php phttrin li gii cu trc ca cc bi ton phc tp.


Cc hm m-file

Cc hm m-file

C php

Dng u tin ca hm m-file c dng

function [outArgs]=funName(inArgs)

trong outArgs l danh sch cc bin u ra, c t trong [ ]

Cc bin trong outArgs c cch nhau bi du ,

[ ] l ty chn nu ch c 1 tham s u ra

Hm m khng c outArgs vn l hp l

v danh sch cc bin u vo inArgs c t trong ( )

Cc bin trong inArgs c cch nhau bi du ,

Hm m khng c inArgs vn l hp l

C th kim tra tnh hp l ca tn hm bng cch dng lnh

>> isvarname funName


Cc hm m-file

Cc hm m-fileInput v Output

twosum.m: two inputs, no output

function twosum(x,y)

% twosum Add two matrices and print the result

% two inputs, no output

x+y

threesum.m: three inputs, one output

function s=threesum(x,y,z)

% threesum Add three matrices and return the result

% three inputs, one output

s=x+y+z;

addmult.m: two inputs, two outputs

function [s,p]=addmult(x,y)

% addmult Compute sum and product of two matrices

% two inputs, two outputs

s=x+y;

p=x*y;T.M. Ton (SAMI-HUST) Lp trnh Matlab 13/87H Ni, thng 1 nm 2012 13 / 87

Cc hm m-file


V d 2

Xt hm twosum

>> twosum(2,2)

ans =

4

>> x=[1 2]; y=[3 4];

>> twosum(x,y)

ans =

4 6

>> A = [1 2; 3 4]; B = [5 6; 7 8];

>> twosum(A,B);

ans =

6 8

10 12


Cc hm m-file


V d 3

>> clear

>> x = 4; y = -2;

>> twosum(1,2)

ans =

3

>> x+y

ans =

2

>> disp([x y])

4 -2

>> who

Your variables are:

ans x y

Trong v d cc bin x v y c nh ngha trong khng gian lm vic l khc vi ccbin x, y c xc nh trong hm twosum. Cc bin x, y trong twosum l cc bin aphng trong hm ny.


Cc hm m-file

Cc hm m-fileTm tt v cc tham s Input v Output

Cc gi tr c kt hp thng qua cc d liu input v output

Cc bin c nh ngha trong mt hm l bin a phng. Cc hm khc vmi trng ca s lnh s khng nhn c chng.

S lng cc bin tr v nn trng vi s lng cc bin output trong hm.


Nhp, xut d liu

Ni dung

1 M u

2 Cc th tc

3 Cc hm m-file

4 Nhp, xut d liu

5 iu khin lung




9 Ch thch

10 G li



Nhp, xut d liu

Nhp, xut d liu

Cc hm nhp d liu

Hm input c th c s dng nhp d liu t bn phm.

Cc tham s u vo ca cc hm c a dng hn.

Cc hm xut d liu

Hm disp c th c s dng cho cc kt qu n gin

Dng hm fprintf cho cc d liu nh dng trc.


Nhp, xut d liu

Nhp, xut d liuXut d liu vi disp v fprintf

Xut d liu trong ca s lnh c thc hin vi hm disp hoc fprintf. Nu munghi d liu vo file bt buc phi dng hm fprintf.

disp

S dng rt n gin. Tuy nhin vic iu khin nh dng ca cc output l rt hn ch.

fprintf

Tng i phc tp hn disp. Cung cp ton b cc cch iu khin nh dng ca ccoutput.


Nhp, xut d liu

Nhp, xut d liuHm disp

C php

disp(outMatrix)

trong outMatrix c th l ma trn s hoc xu.

V d 4

>> disp(5)

5

>> x = 1:3; disp(x)

1 2 3

>> y = 3-x; disp([x; y])

1 2 3

2 1 0

>> disp([x y])

1 2 3 2 1 0

>> disp([x y])

??? Error using ==> horzcat

CAT arguments dimensions are not consistent.


Nhp, xut d liu


V d 5

>> disp(Hello World!)

Hello World!

>> s=Have a nice day; disp(s)

Have a nice day

>> t=You are using Matlab 7.10.0;

>> disp([s;t])

??? Error using ==> vertcat


>> disp(char(s,t))

Have a nice day

You are using Matlab 7.10.0


Nhp, xut d liu


Ch 4.1

Lnh disp([s;t]) xut hin li bi v s c t k t hn t. Hm char to mt ma trnxu bng cch t mi input trn mt dng ring v chn thm cc khong trng nucn.

>> S=char(s,t);

>> length(s), length(t), length(S(1,:))

ans =

15

ans =

27

ans =

27


Nhp, xut d liu

Nhp, xut d liuHm num2str

Hm num2str thng c dng vi hm disp to ra d liu u ra c gn nhnca mt gi tr s

C php

stringValue=num2str(numericValue)

chuyn numericValue thnh mt xu biu din gi tr s .

V d 6

>> num2str(pi)

ans =

3.1416


Nhp, xut d liu

Nhp, xut d liuHm num2str

>> A=eye(3)

A =

1 0 0

0 1 0

0 0 1

>> S=num2str(A)

S =

1 0 0

0 1 0

0 0 1

Mc d A v S c v cha cng cc gi tr, chng khng tng ng. A l mt ma trns cn S l ma trn xu.

>> A-S

??? Error using ==> minus

Matrix dimensions must agree.


Nhp, xut d liu

Nhp, xut d liuS dng num2str vi disp

>> x=sqrt(2);

>> outString=[x=,num2str(x)];

>> disp(outString)

x=1.4142

hoc

>> disp([x=,num2str(x)])

x=1.4142


Nhp, xut d liu


Ch

Cu trc

disp([x=,num2str(x)])

ch lm vic khi x l mt ma trn hng cn vi ma trn ct th khng

>> y=1:4;

>> z=y;

>> disp([z=,num2str(z)])

??? Error using ==> horzcat



Nhp, xut d liu


Thay vo , s dng hai lnh disp hin th ct ca cc vector hay ma trn

>> disp(z=); disp(z)

z=

1

2

3

4

hoc n gin l nhp vo tn ca bin m khng c du ; cui dng

>> z

z =

1

2

3

4


Nhp, xut d liu

Nhp, xut d liuHm format

Hm format iu chnh chnh xc ca d liu in ra.

>> format short

>> disp(pi)

3.1416

>> format long

>> disp(pi)

3.141592653589793

Ngoi ra, thng s th hai ca hm num2str cng c th dng vi mc ch trn

>> disp([pi=,num2str(pi,2)])

pi=3.1


pi=3.142


pi=3.1415927


Nhp, xut d liu

Nhp, xut d liuHm fprintf

C php

fprintf(outFormat, outVariables)

fprintf(filehandle, outFormat, outVariables)

s dng outFormat chuyn outVariables thnh cc xu c in ra. Trong dng utin, kt qu s hin th trong ca s lnh. Trong dng th hai, kt qu s c lu vofile c tham chiu bi fileHandle.

V d 7

>> x=3;

>> fprintf(Square root of %g is %8.6f\n,x,sqrt(x))

Square root of 3 is 1.732051


Nhp, xut d liu


Thnh phn outFormat nh r cch cc outVariables c chuyn thnh v hin th.Xu outFormat c th cha bt k mt k t no. N cng phi cha mt m chuyni cho mi outVariables. Cc m chuyn i c bn c cho di bng sau:

M Dng%s dng xu

%d dng s nguyn

%f dng du chm ng

%e dng du chm ng trong k hiu khoa hc

%g dng gn nht ca %f hoc %e

\n chn mt dng mi sau xu kt qu

\t chn mt tab sau xu kt qu


Nhp, xut d liu


Ta c th ch nh thm rng v chnh xc ca kt qu bng cc c php:

% wd

% w.pf

% w.pe

trong w l s k t trong rng ca kt qu cui cng v p l s ch s sau duphy s c hin th. Mt s v d

Gi tr %8.4f %12.3e %10g %8d

2 2.0000 2.000e+00 2 2sqrt(2) 1.4142 1.414e+00 1.41421 1.414214e+00sqrt(2e-11) 0.0000 4.472e-06 4.47214e-06 4.472136e-06sqrt(2e11) 447213.5955 4.472e+05 447214 4.472136e+05


Nhp, xut d liu


C th dng fprintf in vector hoc ma trn di dng ngn gn. iu ny c thdn ti cc kt qu khng nh mong mun. V d

>> x=1:4; y=sqrt(x);

>> fprintf(%9.4f\n,y)

1.0000

1.4142

1.7321

2.0000

y, nh dng %9.4f c s dng li cho mi thnh phn ca y. iu ny c th skhng cho kt qu nh mong mun:

>> fprintf(y=%9.4f\n,y)

y= 1.0000

y= 1.4142

y= 1.7321

y= 2.0000


Nhp, xut d liu


Hm fprintf duyt cc outVariables theo cc ct. iu ny cng c th dn n cckt qu khng nh mong mun

>> A=[1 2 3; 4 5 6; 7 8 9]

A =

1 2 3

4 5 6

7 8 9

>> fprintf(%8.2f %8.2f % 8.2f \n, A )

1.00 4.00 7.00

2.00 5.00 8.00

3.00 6.00 9.00


Nhp, xut d liu


Xut d liu ra file

ghi d liu ra file cn phi to ra mt fileHandle vi lnh fopen. Tt c tc dngca cc nh dng cng nh vector ha u c th p dng.

V d 8

Lu cc thnh phn ca mt vector vo mt file

x=1:10;

fout=fopen(out.dat,wt);

fprintf(fout, k x(k)\n);

for k=1:length(x)

fprintf(fout,%4d % 5.2f\n,k,x(k));

end

fclose(fout)


iu khin lung

Ni dung

1 M u

2 Cc th tc

3 Cc hm m-file

4 Nhp, xut d liu

5 iu khin lung




9 Ch thch

10 G li



iu khin lung

iu khin lung

c th thc thi mt thut ton, mt ngn ng lp trnh cn c cc cu trc iukhin

Cc cu trc lp (Looping or Iteration)

Cc cu trc iu kin: r nhnh (Branching)

So snh (Comparison)

So snh

S so snh c th hin qua cc ton t quan h (Relational Operators). Cc ton tny c dng kim tra hai gi tr bng nhau, nh hn, ln hn.

Ton t ngha< < >>= == =~= 6=


iu khin lung

iu khin lung

So snh (tip)

Khi p dng cc ton t quan h th kt qu s l mt gi tr logic, tc l Truehoc False.

Trong MatLab , cc gi tr khc 0, bao gm c mt xu khc rng l tngng vi True. Ch c gi tr 0 l tng ng vi False.

Ch 5.1

Trong cc ton t quan h = v ~= th k hiu "=" phi ng sau. iu ny cngha = v =~ l khng hp l.


iu khin lung

iu khin lungCc ton t quan h

V d 9

Kt qu ca mt php ton quan h l True (1) hoc False (0)

>> a=3; b=5;

>> aIsSmaller=a> bisSmaller=b> x=1:5; y=5:-1:1;

>> z=x>y

z =

0 0 0 1 1


iu khin lung

iu khin lungCc ton t logic (Logical Operators)

Cc ton t logic c s dng kt hp cc biu thc logic (vi and v or) hocthay i gi tr logic vi not.

Ton t ngha&& and|| or~ not


iu khin lung

iu khin lungCc ton t logic (Logical Operators)

V d 10

>> a=3; b=5;

>> aIsSmaller=a bothTrue=aIsSmaller && bIsSmaller

bothTrue =

0

>> eitherTrue=aIsSmaller || bIsSmaller

eitherTrue =

1

>> ~eitherTrue

ans =

0


iu khin lung

iu khin lungCc ton t logic v quan h

Tm tt

Cc ton t quan h lin quan n cc php so snh ca hai gi tr.

Kt qu ca mt php ton quan h l mt gi tr logic (True (1)/ False (0)).

Cc ton t logic kt hp (hoc ph nh) cc gi tr logic to ra cc gi tr logicmi.

Lun c nhiu hn mt cch th hin cng mt php so snh.

Li khuyn

bt u, tp trung vo cc so snh n gin. ng s biu thc logic qu di (nhiuphp so snh).


iu khin lung

iu khin lungCu trc iu kin hoc r nhnh

Da vo kt qu ca mt php so snh, hoc ca php kim tra logic, cc khi mchng trnh chn s c thc thi hoc b qua.

Cc cu trc iu kin bao gm: if, if...else v if...elseif, hoc cu trcswitch.

C 3 dng ca cu trc if

1 if

2 if...else

3 if...elseif


iu khin lung

iu khin lungCu trc if

C php

if expression

block of statements

end

Khi block of statements ch c thc thi nu expression nhn gi tr True.

V d 11

if a

iu khin lung

iu khin lungCu trc if...else v if...elseif

if x0

disp(x is positive);

elseif x

iu khin lung

iu khin lungCu trc switch

Cu lnh switch rt hu dng khi tp gi tr ca cc bin kim tra l ri rc (c th ls nguyn hay xu k t)

C php

switch expression

case value1

block of statements

case value2

block of statements

...

otherwise

block of statements

end


iu khin lung

iu khin lungCu trc switch

V d 12

color=input(Enter your favorite color: ,s); % color is a string

switch color

case red

disp(Your color is red);

case blue

disp(Your color is blue);

case green

disp(Your color is green);

otherwise

disp(Your color is not red, blue or green);

end


iu khin lung

iu khin lungCu trc lp for

C php

for index=expression

block of statements

end

V d 13

Tnh tng cc thnh phn ca mt vector

x=1:5; % create a row vector

sumx=0; % initialize the sum

for k=1:length(x)

sumx=sumx+x(k);

end


iu khin lung


V d 14

Vng lp for vi ch s tng theo mc 2 n v

for k=1:2:n

block of statements

end

V d 15

Vng lp for vi ch s gim dn

for k=n:-1:1

block of statements

end


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V d 16

Vng lp for vi ch s khng phi l s nguyn

for x=0:pi/15:pi

fprintf(%8.2f %8.5f\n,x,sin(x));

end

Ch 5.2

Trong v d trn, x l mt i lng v hng trong vng lp. Mi ln lp, x c gnvi 1 trong cc ct ca 0:pi/15:pi.


iu khin lung

iu khin lungCu trc lp while

C php

while expression

block of statements

end

Khi lnh block of statements c thc thi nu iu kin expression vn l True.

trnh tnh trng lp v hn, nn t gii hn trn cho s ln lp.


iu khin lung


V d 17

Gii phng trnh f(x) = 0 trn khong phn ly nghim [a, b] bng phng php chia i

n=0;

while abs(b-a)>=err && n

iu khin lung


Cc cu lnh break v return l cc cch khc nhau thot khi mt cu trclp. C hai lnh ny u c th dng cho cu trc for v while.

break c s dng thot khi phm vi ca vng lp hin thi for hocwhile, chng trnh s tip tc sau .

return c dng thot khi mt hm hin thi. iu ny s nh hng nvic thot khi mt vng lp. Bt k mt cu lnh no tip theo vng lp tronghm u b b qua.


Vector ha (Vectorization)

Ni dung

1 M u

2 Cc th tc

3 Cc hm m-file

4 Nhp, xut d liu

5 iu khin lung




9 Ch thch

10 G li




Vector ha

Vector ha l vic s dng cc php ton vector x l ton b cc phn t ca mtvector hay ma trn. Tht ra cc biu thc vector ha l tng ng vi php lp trncc phn t ca ma trn hay vector. Biu thc vector ha s ngn gn v thc thinhanh hn cc biu thc lp thng thng.

S dng cc php ton vector thay cho vng lp khi c th

Tin cp pht b nh cho cc vector hay ma trn

S dng vic nh ch mc vector ha v cc hm logic

M khng s dng vector ha gi l m v hng (scalar code) bi v cc phpton c thc hin trn cc phn t v hng ca vector hay ma trn thay vton b.

Li khuyn

Chng trnh tuy chm m chnh xc cn hn chng trnh nhanh m khng chnh xc.= Bt u vi cc m v hng, sau vector ha nu cn



Vector haThay th vng lp bi cc php ton vector

M v hng

x=...

for k=1:length(x)

y(k)=sin(x(k));

end

M vector ha tng ng

x=...

y=sin(x);



Vector haTin cp pht b nh

Vng lp sau s tng chiu ca s sau miln lp

y=[4 -1 9 0];

for j=1:length(y)

if y(j)>0

s(j)=sqrt(y(j));

else

s(j)=0;

end

end

Tin cp pht cho s trc khi gn ccgi tr cho cc thnh phn

y=[4 -1 9 0];

s=zeros(size(y));

for j=1:length(y)

if y(j)>0

s(j)=sqrt(y(j));

end

end



Vector hanh ch mc vector ha v cc hm logic

Vic vector ha m hon ton i hi vic s dng vic nh ch s mng (arrayindexing) v nh ch s logic (logical indexing).

nh ch s mng

>> x=sqrt(0:4:20)

x =

0 2.0000 2.8284 3.4641 4.0000 4.4721

>> i=[1 2 5];

>> y=x(i)

y =

0 2 4

Biu thc y=x(i) tng ng vi on m

k=0;

for i=[1 2 5], k=k+1; y(k)=x(i); end




nh ch s logic

>> x=sqrt(0:4:20)

x =

0 2.0000 2.8284 3.4641 4.0000 4.4721

>> j=find(rem(x,2)==0)

j =

1 2 5

>> z=x(j)

z =

0 2 4




V d 18

Vector ha m v hngXt on m

y=. . .

s=zeros(size(y));

for j=1:length(y)

if y(j)>0

s(j)=sqrt(y(j));

end

end

Thc ra, c th thay th ton b vng lp bng cch s dng nh ch s logic hocnh ch s mng.




V d (tip)

y=. . .

s=zeros(size(y));

i=find(y>0);

s(y>0)=sqrt(y(y>0));

hoc gn hn

y=. . .

s=zeros(size(y));

s(y>0)=sqrt(y(y>0));



Vector haVector ha cc php sao chp

Sao chp ton b cc ct (hng)

M v hng

[m,n]=size(A); % Gi s rng A v B c cng s hng (ct)

for i=1:m

B(i,1)=A(i,1);

end

M vector ha

B(:,1)=A(:,1);



Vector haVector ha cc php sao chp

Sao chp v chuyn v cc ma trn con

M v hng

for j=2:3

B(1,j)=A(j,3);

end

M vector ha

B(1,2:3)=A(2:3,3);



Vector haMt s v d khc

Xa cc thnh phn ca mt mng

xa cc thnh phn khng phi l s (NaN) hoc gi tr v cng (inf) ca mt mngx ta c th dng on m s dng nh ch s mng

i=find(isnan(x) | isinf(x)); % Find bad elements

x(i)=[]; % and delete them

hay mt cch khc

i=find(~isnan(x) & ~isinf(x)); % Find elements that are are not NaN and not infinite

x=x(i); % Keep those elements

Ta c th thay i cc on m trn bng cch s dng ch s logic

x(isnan(x) | isinf(x))=[]; % Delete bad elements

hoc

x=x(~isnan(x) & ~isinf(x)); % Keep good elements




Hm tng khc (Piecewise functions)

Hm sinc c nh ngha bi sinc(x) =

{sin(x)/x, x 6= 01, x = 0.

So snh on m s dng lnh find

function y=sinc(x)

y=ones(size(x)); % Set y to all ones, sinc(0)=1;

i=find(x~=0); % Find nonzero x values

y(i)=sin(x(i))./x(i); % Compute sinc when x ~=0

end

v mt cch vit th v khc:

y=(sin(x)+(x==0))./(x+(x==0));




Ni suy a thc

Cho n mc ni suy x1, x2, . . . , xn v cc gi tr hm tng ng y1, y2, . . . , yn. Khi ,cc h s c0, c1, . . . , cn1 ca a thc ni suy bc n 1 c th c tnh bng cch giih

xn11 xn21 x21 x1 1

xn12 xn22 x22 x2 1

......

xn1n xn2n x2n xn 1

cn1cn2...c0

=y1y2...yn

hay Ac = y.

H trn c nh thc Vandermond |A| =n

1i



Ni suy a thc

function c=polyinterp(x,y)

x = x(:); y=y(:); % Make sure that x and y are both column vectors

n = length(x); % n= Number of points

%%% Compute the left-hand side matrix %%%

xMatrix = repmat(x,1,n); % Make an nxn matrix with x on every column

powMatrix = repmat(n-1:-1:0,n,1); % Make another nxn matrix of exponents

A = xMatrix .^ powMatrix; % Compute the powers

c=A\y; % Solve the matrix equation for coefficients

end




Ni suy a thc

Trong chng trnh trn, xy dng ma trn v tri A, trc ht to ra 2 ma trnn n ca c s v ly tha, sau s dng ton t ly tha tng t .^. Hm repmat("replicate matrix") c s dng to ma trn c s xMatrix v ma trn ly thapowMatrix:

xMatrix =

x(1) x(1) x(1)x(2) x(2) x(2)...

...x(n) x(n) x(n)

; powMatrix =n 1 n 2 0n 1 n 2 0

......

n 1 n 2 0

Ma trn xMatrix c to bng cch lp li vector ct x n ln.

Ma trn powMatrix c to bi mt vector hng vi cc thnh phnn 1, n 2, . . . , 0 lp li n ln.y ch l mt v d, c th s dng hm chun ca MatLab polyfit cho mtlot cc a thc ni suy (c thm help tm hiu thm).


Qun l cc bin Input, Output

Ni dung

1 M u

2 Cc th tc

3 Cc hm m-file

4 Nhp, xut d liu

5 iu khin lung




9 Ch thch

10 G li





Mi hm c cc bin ni ti bao gm nargin (number of input arguments) vnargout (number of output arguments).

S dng gi tr nargin trong phn u ca hm xc nh c bao nhiu binu vo s c s dng.

S dng gi tr nargout trong phn cui ca hm xc nh s bin u ramong mun.

Li ch

Cho php mt chng trnh n c th thc hin nhiu cng vic lin quan.

Cho php cc hm gi thit cc gi tr mc nh ca mt s bin u vo, do lm n gin vic s dng hm trong mt s trng hp.




V d 19

Xt hm plot

nargin nargout

plot(x,y) 2 0plot(x,y,s) 3 0plot(x,y,s--) 3 0plot(x1,y1,s,x2,y2,o) 6 0h=plot(x,y) 2 1

Cc gi tr ca nargin v nargout c xc nh khi hm plot c gi ra.


Tnh gi tr hm mt cch gin tip

Ni dung

1 M u

2 Cc th tc

3 Cc hm m-file

4 Nhp, xut d liu

5 iu khin lung




9 Ch thch

10 G li




Tnh gi tr hm mt cch gin tipS dng hm feval

Li ch

Cho php cc th tc c vit x l mt hm f(x) bt k.

Chia nh mt thut ton phc tp bng cch s dng cc on m ring.

V d 20

function s=fsum(fun,a,b,n)

x=linspace(a,b,n);

y=feval(fun,x);

s=sum(y);

end

>> fsum(sin,0,pi,5)

ans =

2.4142

>> fsum(cos,0,pi,5)

ans =

0T.M. Ton (SAMI-HUST) Lp trnh Matlab 72/87H Ni, thng 1 nm 2012 72 / 87


Cc hm inline

MatLab gii thiu cc m rng ca lp trnh hng i tng (object-orientedprogramming - OOP). Hm inline rt n gin v gip chng trnh linh hot hn. Cth, ta khng cn vit cc hm m-files tnh gi tr mt s hm c cng thc n ginv vn dng c hm feval.Thay v

function y=myFun(x)

y=x.^2-log(x);

ta dng

myFun=inline(x.^2-log(x));

C hai dng khai bo trn ca myFun cho php cc biu thc dng

z=myFun(3);

s=linspace(1,5);

t=myFun(s);


Ch thch

Ni dung

1 M u

2 Cc th tc

3 Cc hm m-file

4 Nhp, xut d liu

5 iu khin lung




9 Ch thch

10 G li



Ch thch

Ch thch

C php : % Matlab comment line

Cc ch thch c bit

Cc khi comment lin nhau trong m-file chnh l phn help cam-file :

>> help filename

= Khi vit mt hm m-file, c gng thm cc ch thch: m tmc ch ca hm, yu cu v cc bin input v nh dng ca ccbin output.

M "cells" c phn nh bi %% Cell title

Trnh son tho Matlab Editor c nhng kh nng c bit lm

vic vi cc "cells"S dng publish(file.m) thc thi file.m v to ra cc ouput dnhn.

% publish all m-files in current directory

files=dir(*.m);

cellfun(@(x) publish(x,struct(evalCode,false)),...

{files.name},UniformOutput,false);


G li

Ni dung

1 M u

2 Cc th tc

3 Cc hm m-file

4 Nhp, xut d liu

5 iu khin lung




9 Ch thch

10 G li



G li

G li

MatLab h tr mt trnh g li tng tc

Cc lnh type v dbtype hin th ton b ni dung ca mt m-file

Lnh error hin th mt li nhn trn mn hnh v dng hn chng trnh.

Hm warning hin th mt li nhn ln mn hnh tuy nhin khng dng chngtrnh

Cc lnh pause hoc keyboard c th dng tm dng chng trnh. thotkhi ch g li (debug-mode) v tip tc chng trnh dng mt trong cc lnhreturn, dbcont, dbquit.


G li

G liS dng lnh keyboard

function r = quadroot(a,b,c)

% quadroot Roots of quadratic equation and demo of keyboard command

%

% Synopsis: r = quadroot(a,b,c)

%

% Input: a,b,c = coefficients of a*x^2 + b*x + c = 0

%

% Output: r = column vector containing the real or complex roots

d = b^2 - 4*a*c;

if d

Mt s kinh nghim trong lp trnh Matlab

Ni dung

1 M u

2 Cc th tc

3 Cc hm m-file

4 Nhp, xut d liu

5 iu khin lung




9 Ch thch

10 G li




(The Profiler)

MatLab phin bn 5.0 hoc mi hn cung cp mt cng c gi l "profiler" h tr vicxc nh cc on tc nghn (bottlenecks) trong chng trnh. Xt chng trnh

function result=example1(Count)

for k=1:Count

result(k)=sin(k/50);

if result(k) < -0.9

result(k)=gammaln(k);

end

end

end

phn tch chng trnh, trc ht dng cc lnh sau khi ng "profiler" v xatt c cc d liu c

>> profile on

>> profile clear



(The Profiler)

By gi, chy th chng trnh

>> example1(50000);

Sau , nhp vo lnh

>> profile report

Profiler to mt thng bo dng HTML v chng trnh v khi to mt ca s trnhduyt. Ty theo tng h thng my tnh m cc kt qu c th hin th cc dng khcnhau.



Tin cp pht b nh cho mng

Cc bin ma trn trong MatLab c kh nng iu chnh s hng v s ct mt cchlinh ng. V d

>> a=2

a =

2

>> a(4,4)=1

a =

2 0 0 0

0 0 0 0

0 0 0 0

0 0 0 1

MatLab t ng iu chnh kch c ca ma trn. Do , b nh dnh cho d liu matrn cn phi c tin cp pht vi c ln.




V d 21

Xt on m

a(1)=1;

b(1)=0;

for k=2:8000

a(k)=0.99803 * a(k-1) - 0.06279 * b(k-1);

b(k)=0.06729 * a(k-1) + 0.99803 * b(k-1);

end

Thi gian thc thi on m trn l 0.147 giy.




Sau khi vng lp for kt thc kch thc ca hai mng a,b u l 10000. Do , tin cp pht b nh, to ra hai vector hng a,b vi 10000 phn t 0:

a = zeros(1,10000);

b = zeros(1,10000);

a(1) = 1;

b(1) = 0;

for k = 2:10000

a(k) = 0.99803 * a(k-1) - 0.06279 * b(k-1);

b(k) = 0.06729 * a(k-1) + 0.99803 * b(k-1);

end

Vi s thay i ny, thi gian thc thi ch cn l 0.005 giy (nhanh hn gn 3 ln).



Gii hn mt gi tr m khng dng cu trc if

gii hn mt gi tr trong mt khong cho trc, mt cch trc tip lp trnh l

if x < lowerBound

x = lowerBound;

elseif x > upperBound

x = upperBound;

end

Tuy nhin, cch ny thc thi rt chm. Mt phng php nhanh hn l dng cchm min v max

x = max(x,lowerBound); % Clip elements from below, x >= lowerBound

x = min(x,upperBound); % Clip elements from above, x


Chuyn mt mng bt k thnh vector ct

Trong nhiu trng hp ta s phi chuyn mt mng bt k thnh mt ma trn ct, vd khi yu cu i vi d liu u vo ca mt hm phi l mt vector ct. Cu lnhsau s chuyn mt mng bt k bao gm mt vector hng, mt ma trn hay mt vectorct thnh mt vector ct

x = x(:); % convert x to a column vector

Bng cch dng lnh trn cng vi php chuyn v ., ta c th chuyn mt mng btk v mt vector hng.



Chun ha vector

chun ha mt vector v, ta c th s dng lnh

v = v/norm(v)

Tuy nhin, chun ha mt tp cc vector v(:,1), v(:,2),... i hi phi tnhv(:,k)/norm(v(:,k)) trong mt vng lp for hoc on m vector ha

vMag = sqrt(sum(v.^2));

v = v./vMag(ones(1,size(v,1)),:);

Tc thc hin ca on m vector ha nhanh hn ng k so vi vic dng vng lpfor. V d, vi vi ngn vector c di 3, cch tip cn vector ha nhanh hn khong10 ln.


M uCc thu tucCc hm m-fileNhp, xut d liuiu khin lungVector ha (Vectorization)Quan l cc bin Input, OutputTnh gi tri hm mt cch gin tipCh thchG liMt s kinh nghim trong lp trnh Matlab

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Programming Matlab