matlab lecture notes

Bi ging Tin ng dng 2 Matlab 7

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I HC THY LIB MN QUN L TNG HP BIN VI B

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MATLABTIN HC NG DNG HC PHN II

(Ti liu tham kho & Bi tp cho sinh vin K thut Bin K45)

Nguyn B TuynNguyn Quang Chin

H Ni, thng 08 nm 2007


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MC LC

1. CHNG I: MATLAB CN BN .......................................................................41.1. Matlab ngn ng ca tnh ton k thut.........................................................41.2. Kh nng v nhng ng dng ca Matlab ........................................................ 41.3. c im ca Matlab .......................................................................................61.4. Cit v khi ng Matlab 7.0.......................................................................71.5. Qun l khng gian lm vic ca Matlab..........................................................81.6. Ghi & phc hi d liu...................................................................................111.7. S dng Help .................................................................................................121.8. History & Editing...........................................................................................13

2. CHNG II: TNH TON TRONG MATLAB .................................................. 152.1. Matlab - mt my tnh c nhn .......................................................................152.2. Bin trong Matlab ..........................................................................................162.3. Cc kiu d liu -nh dng kt qu.............................................................. 172.4. Cc kiu d liu s & s phc........................................................................182.5. Cc k t, Chui v Vn bn..........................................................................192.6. Cc hng s dng sn.....................................................................................202.7. Cc hm dng sn ..........................................................................................202.8. Cc php ton quan h...................................................................................232.9. Cc php ton logic........................................................................................ 242.10. Kt hp nhiu lnh trn mt dng; n kt qu tnh. ....................................26

3. CHNG III: VECT........................................................................................ 273.1. Gii thiu .......................................................................................................273.2. Vcthng..................................................................................................... 283.3. Vectct .......................................................................................................293.4. Ton t hai chm ( : ) .....................................................................................293.5. Lm vic vi vect& ma trn (mng) ............................................................303.6. X l d liu vi cc hm dng sn cho vect& ma trn............................... 32

4. CHNG IV: MA TRN I S & TUYN TNH..........................................344.1. nh ngha v khi to ma trn ...................................................................... 344.2. Mt s ma trn c bit.................................................................................. 344.3. Cc php ton vi tng phn t trong ma trn ................................................ 354.4. Cc php ton vi ma trn .............................................................................. 354.5. Gii phng trnhi s................................................................................. 354.6. Gii h phng trnhi s tuyn tnh............................................................354.7. Tm nghim ca a thc................................................................................. 354.8. Gii phng trnh phi tuyn ...........................................................................354.9. Gii phng trnh vi phn .............................................................................. 354.10. Cc lnh hu ch khc ................................................................................ 35


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5. CHNG V: SCRIPTS V FUNCTIONS (M-FILES)........................................375.1. Gii thiu M-file............................................................................................ 375.2. Bin son v thc thi M-file...........................................................................375.3. Ch thch (comments)....................................................................................385.4. Cc hm m-file (function m-files) ..................................................................395.5. Cu lnh r nhnh (if v switch) ..................................................................... 415.6. Vng lp (for v while).................................................................................. 425.7. c d liu t file v ghi ra file...................................................................... 43

6. CHNG VI: TH DNG NG .............................................................446.1. Biu din ng qu trnh.............................................................................. 446.2. La chn mu v, nt v................................................................................ 466.3. To cc ch thch, ch gii trn hnh v..........................................................486.4. Xang biu , lu biu ..................................................................... 506.5. th Logarit ................................................................................................ 506.6. Dy biu ....................................................................................................52

7. CHNG VII: TH KHNG GIAN .............................................................557.1. Cc dng cbn .............................................................................................557.2. Ch nh cc v tr trong khng gian 2 chiu ...................................................587.3. Mt ct a hnh ............................................................................................. 587.4. Trng vct.................................................................................................59

8. PHN BI TP ..................................................................................................61Bi tp s1:.............................................................................................................. 61Bi tp s2............................................................................................................... 62Bi tp s3............................................................................................................... 62Bi tp s4:.............................................................................................................. 63

LI GII ...................................................................................................................... 63Bi tp s1:.............................................................................................................. 63Bi tp s2:.............................................................................................................. 64Bi tp s3:.............................................................................................................. 64Bi tp s4:.............................................................................................................. 64

9. TI LIU THAM KHO: ...................................................................................66


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1. CHNG I: MATLAB CN BN

1.1. Matlab ngn ng ca tnh ton k thut- MATLAB l mt ngn ng bc cao v mi trng tng tc cho php bn tin hnh cc nhim v tnh ton c cng ln nhanh hn vi cc ngn ng lp trnh nhC, C++ v Fortran.- MATLAB vit tt cho "Matrix Laboratory" - Phng th nghim ma trn. Ban u Matlab c thit k bi Cleve Moler vo nhng nm 1970 s dng nhmt cng c dy hc. T n nay n c pht trin thnh mt b phn mm thng mi rt thnh cng.- Hin nay MATLAB R14 l mt b phn mm cho cng vic tnh ton trong cc ngnh k thut, trong khoa hc v trong lnh vc ton hc ng dng. Matlab cho ta mt ngn ng lp trnh mnh, giao din ha xut sc, v mt phm vi rt rng cc kin thc chuyn mn. Matlab l mt thng hiu c thng mi ha ca tp on MathWorks, Massachusetts, USA (hin l nh cung cp hngu th gii cho cc phn mm tnh ton k thut v thit k da trn m hnh).

1.2. Kh nng v nhng ng dng ca Matlab- Mt trong nhng tnh nng tuyt vi nht ca Matlab nhn t gc nhng nhkhoa hc tnh ton l thvin dng sn to ln rt phong ph cc chu trnh tnhton v cc cng c hin th ha. - Matlab cho php ngi dng tin hnh rt nhiu cc nhim v thng thng linquan ti vic gii quyt cc vn mt cch s hc. N cho php chng ta dnhnhiu thi gian hn cho vic suy ngh, khuyn khch chng ta th nghim.

- Matlab ng dng nhng thut ton ht sc c trn trng v vy chng ta c th tin tng vo kt qu thu c.- Cc tnh ton rt mnh c th c thc hin ch vi mt hoc hai cu lnh.- Bn c th xy dng ring cho mnh nhng hm ton hc cho nhng ng dng c bit.- Matlab cung cp giao din ha tuyt ho, cc hnh t Matlab c th em chnvo LATEX v cc ti liu Word.- Ti liu hng dn ny ch em n mt ci nhn thong qua v sc mnh v s linh hot ca h thng Matlab. c c nhng hiu bit su sc v chi tit hn,xin tham kho cc gio trnh Matlab chuyn dng khc hin c trn th trng.


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VD: Hy cng tham kho cc demo ca Matlab xem ta c th lmc nhng g ch vi mt vi dng lnh n gin:

>> colormap(hsv(64))>> z = cplxgrid(30); % min khng gian s phc n v z>> cplxmap(z,z^3) % v th hm x = z^3 hinh1>> cplxroot(3) % v th hm y = z^(1/3) hinh2

Hnh 1: th hm x = z3 trong khng gian s phc

Hnh 2: th hm 3 zy trong khng gian s phc


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1.3. c im ca MatlabLp trnh theo ngha thng thng, l nhp vo my nhng cu lnh r rng, theomt th t nht nh sao cho khi my thc hin theo ng th t th s cho ta kt qu mong mun. Mt khi nim nm na tng t nhvy thng thy trong cc kha hc lp trnh cc ngn ng C, Pascal... Khi khi u vi MatLab ta hy hiu theo ngha rng hn: lp trnh cn c ccbc biu din bi ton di dng cc hm v my tnh qua vic thc hin cc hm ny cho ta kt qu. Phng php ny c mc tru tng cao hn so vi cc cu lnh ch dn n thun.

minh ha iu ny, ta xt mt v d rt n gin: so snh php cng hai vcttrong ngn ng lp trnh Pascal v MatLab.- Pascal biu din mt vctdi dng mng (array), chng hn c 3 vec-tA, B,C v A + B = C:

varA: array[1..5] of integer = (3, 7, 4, 2, 0);B: array[1..5] of integer = (-2, 4, 8, 5, 1);C: array[1..5] of integer;i: integer;

beginfor i := 1 to 5 dobeginC[i] := A[i] + B[i]

endend.

- Cch lm trong MatLab n gin hn nhiu:A = [3 7 4 2 0];B = [-2 4 8 5 1];C = A + B;

- Cc s n gin ni trn l nh MatLab xy dng sn khi nim ma trn.Du cng trong dng lnh MatLab biu th php cng ma trn. Pascal khng c nhvy; mng ch l s biu din c th t ca cc bin. Khng c php cng ma trn, ch c php cng hai s v vy chng trnh Pascal di hn rt nhiu.- Mt c im na l tt c cc bin trong chng trnh Pascal trnu phi c khai bo. Trong MatLab cc bin s t ng hnh thnh trong mi cu lnh gn.

Trong nhng nm gn y, bn cnh cc ngn ng lp trnh truyn thng (C / C++ / Fortran), cc ngn ng vn lnh (scripting languages) c s dng ph bin hn trong lnh vc nghin cu tnh ton. MatLab l mt trong cc ngn ng nhvy. L mt ngn ng bc cao, mi dng lnh MatLab thng c tc dng tngng vi khong 10 dng lnh ca C / C++. Ngi lp trnh s tn t thi gian gcu lnh v tp trung hn vo ni dung chng trnh.


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Tuy vy cc ngn ng lp trnh bin dch nhC / Fortran cho php chng trnhtnh ton rt nhanh v tc cng l mt yu cu rt quan trng trong cc chngtrnh tnh ln. Do mt cch kt hp thng minh l phn li tnh ton c th c vit bng ngn ng bin dch, v cc thao tc nhp xut, x l, hin th s liu c vit bi ngn ng vn lnh nhMatLab.

1.4. Cit v khi ng Matlab 7.01.4.1. Cit Matlab 7.0

- Yu cu v cu hnh my tnh:+ B vi x l Pentium hoc Pentium Pro+ Windows 95 hoc NT (WinXP home, XPprofessional u c)+ B iu phi ha 8 bit v card mn hnh ti thiu 256 mu+ Dung lng cng 25Mb cho ti hn 1Gb (ty thuc vo cch cu hnha cng, phn vnga, s hp phn ca Matlab c ci t), v ti 2,1Gb nu cit Matlab cng vi Simulink.

+ B nh ng (RAM) ti thiu 16Mb (nn c b nh ti thiu 128Mb)+ Cc khuyn ngh khc: B nh b sung, card ha b sung, card m

thanh, my in, MS-Word 7.0 hoc hn, trnh bin dch C, Borlean, Mcosoft (xy dng file MEX), trnh duyt internet ( chy Matlab Helpdesk online).

- Qu trnh cit Matlab 7.0 cho WindowsXP (b gm 2 a CD): +aa CD vo c. Nu chng trnh SETUP khng t ng chy th

nhn p vo biu tng setup.exe bt u qu trnh cit.+ Accept (chp nhn) nhng tha thun v bn quyn. sau click Next.+ Nu bn ci theo kiu mc nh (hay cn gi l Typical setup - kiu ph

bin), Matlab trn my tnh ca bn s c cc hp phn cbn nht lm vic theo cc hng dn trong ti liu ny. Theo cc hng dn trn mn hnh. ChoaCD th 2 vo khic yu cu.

+ Nu bn cit theo kiu ty chn c nhn (Manual setup) th nhn vocc hp thnh phn du 'v' nu bn mun c ty chn . Nhn tip nu bn khng c nh (c th thm vo sau ny nu mun).

+ Trn mn hnh hin th 'C:\MATLAB7' l thmc mc nh ca qu trnhcit. Nu bn mun cit voa ch khc, hoc i tn thmc, th bn la chn 'Browse'.


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+ Chi tit hng dn cit xin xem file install_guide.pdf trong a CD1 (bn ting Anh).1.4.2. Khi ng Matlab (H iu hnh Windows)

- T HH Windows, khi ng Matlab n gin bng cch nhy p vo biu tng MATLAB trn mn hnh, hoc bng cch chn MATLAB t Menu Start.- Qu trnh khi ng a ngi dngn Ca s lnh, ni ccdng lnh c biu th bng '>>'.

>>_

y l du hiu cho thy Matlab ang ch bn nh mt (cu) lnh. Khi hot ng trong ch my tnh cm tay, tt c cc lnh ca Matlab c nhp vo dnglnh t bn phm.- Matlab c th c s dng theo nhiu ch v nhiu cch khc nhau;

+ Nhmt my tnh cm tay cao cp trong ch my tnh cm tay+ Nhmt ngn ng lp trnh bc cao + Nhmt chu trnh con gi t chng trnh C

Trong ti liu ny chng ta s i nghin cu chi tit 2 ch u tin.

1.5. Qun l khng gian lm vic ca Matlab- V cbn, khng gian lm vic ca Matlab gm c cc phn sau:

+ Ca s tr gip (Help window)+ Nt Start

+ Ca s nhp lnh (Command window)+ Ca s khng gian lm vic (Workspace window)+ Ca s qu trnh lnh (Command History window - lch s)+ Ca s bin tp mng, vect, ma trn (Array editor window)+ Ca s a ch thmc hin thi (Current directory window)

- Nt x gc trn bn phi mi ca s dng ng chng. Hin th li ca s bng cch tch vo tn ca s tng ng trong menu Desktop.- Nt mi tn cong bn cnh nt x dng tch cc ca s lm vic trong ca s chnh MATLAB thnh ca s con c lp. n nt ny mt ln na s nhp mt ca s c lp v ca s chnh ca MATLAB.- Ca s Help, History s c gii thiu c th trong mc 1.7 v mc 1.8. Sauy cc ca s lm vic cn li s c gii thiu vn tt.


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Hnh 1.1: Giao din ca Matlab 7.0* Nt Start: gc di bn tri ca mn hnh Matlab, cho php ta chy cc ng dng mu (demos), cc cng c v ca s cha hin th khi khi ng Matlab. Bng cch nh lnh 'demo' bn c th tip cn vi mt tp hp su rng nhng file trnh din gi tr rt cao, v l biu hin cho nhng kh nng ca Matlab.V d: Th chy Start -> Matlab -> Demos v chy mt ng dng mu trong ca s Demo(s).Ghi ch: Lnh ny s xa tt c gi tr ca cc bin hin c.

* Ca s lnh:c cp mc 1.4.2. (Khi ng Matlab). - Cc din gii v cu (mnh ) ca Matlab c nh gi khi bn g vo 'Ca s lnh', v cc kt qu tnh ton cng c th hin ti y. Khng ging nhFortran v cc ngn ng tnh ton cn bin dch khc, Matlab l mt mi trng tng tc bn a ra mt cu lnh, v Matlab c gng thc thi n ngay lp tc trc khi i hi 1 lnh tip theo.- Cc din gii v cu cng c s dng trong cc M-file (s c trnh by chitit chng V). Chng thng c cu trc:

>> bin = din gii hoc n gin l >> din gii - Cc din gii thng c son bng cc ton t, cc hm, v tn cc bin, vc hin th trn mn hnh sau khi n Enter. Cc cu lnh c dng tn bin =


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din giith din gii s c gn cho bin s dng sau ny. Khi tn binv du =c b i th kt qu ca din gii s c t ng gn cho bin c tn ans (hay answer cu tr li) v hin th trn mn hnh.

- Mt cu (lnh) thng thng s kt thc cui dng. Tuy nhin c th tip tc mt cu bng ba du chm cui dng.- C th t mt vi cu lnh trn cng mt hng, ngn cch bi du phy , hoc chm phy ;- Nu mt cu lnh kt thc bng du chm phy cui cu th kt qu ca lnh s khng c hin th, tuy nhin yu cu tnh vn c thc hin (php tnh hay php gn vn c thc hin, kt qu c trong workspace).iu ny l thit yu trong vic n i cc kt qu trung gian khng mong mun (VD nhkhi thc hin mt lot php tnh, hay tnh ton vi cc ma trn ln).- Bn c th xa trng ton b ca s lnh bng lnh

>> clc % (clear command window)hoc vo menu Edit -> Clear Command Window. Khi thc hin lnh ny, tonb gi tr ca cc bin hin c khng thay i hay mt i.

* Ca s khng gian lm vic(workspace):

Cc bin v d liu m bn nhp vohoc tnh ton ra s c Matlab lutrong mt phn gi l 'khng gian lmvic'. Tt c cc bin, ngoi tr nhng bin cc b thuc v mt M-file, s c th hin trong khng gian lmvic- Lnh 'who' hoc 'whos' lit k cc bin hin c trong khng gian lm vic. VD:nh lnh 'whos' vo ca s lnh, bn s thy mt danh sch cc bin hin c cng kiu loi v kch c ca chng. - bit gi tr hin ti ca mt bin, bn nh vo tn bin ti du nhc ca ca s lnh v Enter.- xa mt hm hoc bin khi khng gian lm vic, ta s dng lnh 'clear':

>> clear tn_bin Bn thn lnh 'clear' s xa tt c cc bin hin c (tngng vi 'clear all')


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* Ca s bin tp mng (ma trn ni chung): Khi ta c mt mng, ta c th chnh sa, bin tp li n bng Array Editor. Cng c ny lm vic nhmt bng tnh (spreadsheet) cho ma trn. V d: C ma trn M, hy th click v thayi n, thay i cc phn t, hay kch thc ma trn. Quay tr li Ca s lnh v g 'M' ri Enter, xem ma trn M ca chng ta sau khi thayi.

+ Bn cng c th bin tp li ma trn M bng cch nh lnh

>> openvar ('C')

* Ca s a ch thmc hin thi: Thmc hin thi l ni chng trnhMatlab s tm cc M-file, v cc file khng gian lm vic (.mat files) m bn Load v Save.

1.6. Ghi & phc hi d liu1.6.1. Lu v phc hi d liu

- nh cc bin, Matlab c th ghi v gi li d liu t file trong my tnh ca bn. Mc Save Workplace as... trong bng chn File s m hp hi thoi ghi tt c cc bin hin ti. - Tng t, mc Load Workplace trong bng chn File s m hp hi thoi gi li tt c cc bin m ta ghi li t khng gian lm vic trc. Ghi ch: vic Load khng lm mt cc bin hin c trong khng gian lamg vic hin ti. Khi ta gi li cc bin m chng trng tn vi cc bin trong khng gian lm vic ca Matlab, n s thay i gi tr ca cc bin theo gi tr ca cc bin gi ra t file. - Ngoi cc bng chn, Matlab cn cung cp hai lnh Save v Load, n thc hin mt cch mm do hn. Lnh save cho php bn ghi mt hoc nhiu hn mt bin ty theo s la chn. V d:

>> save - lu tt c cc bin trong Matlab theo kiu nh phn trong file matlab.mat

>> save dulieu - lu tt c cc bin trong Matlab theo kiu nh phn trong file dulieu.mat

>> save dulieu A B C D -ascii - lu cc bin A, B, C, D theo dng m ASCII trong file dulieu.mat

1.6.2. Lu mt b d liu (record)


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1.6.3. Lu mt phin (session)

Khi lm bi tp, vic lu tt c cc thng s u vo vu ra ca phin lm vic vi Matlab hin ti ca bn cho vic in n sau ny l rt hu ch. Lnh 'diary' s dng cho mc ch ny, s lu tt c nhng thng s u vo vu ra gia hai lnh 'diary' v 'diary off'. T du nhc dng lnh, bn nh:

>> diary('diary_file_name') >> ........ (cc cu lnh ca bn y) >> diary off

1.7. S dng Help - Tr gip v thng tin v cc lnh ca Matlab c th c tm thy theo nhiu cch:

+ T dng lnh bng cch nh lnh 'help ch ' (xem di y)+ T ca s Help ring bit xut pht Menu Help+ T helpdesk ca Matlab lu tr trna hoc CD-rom, hoc+ T mng Internet

- T dng lnh, n gin nht hynh lnh 'help' v Enter!Kt qu: Matlab cho ta mt bn tm tt v h thng tr gip.Mt vi dngu tinca kt qu s nhsau:

HELP topics: (Cc ch tr gip)matlab/general - Cc lnh vi mc ch tng qut.matlab/ops - (operators) Cc ton t v cc k t c bit...matlab/lang - (language) Ngn ng lp trnh...matlab/elmat - (elementary) Ma trn cn bn...matlab/elfun - (elementary functions) Cc hm ton cn bn.matlab/specfun - (specialized functions) Cc hm tonc bit.

- Thng thng bn s thy ca s text khng ln cha tt c thng tin t mt lnh Matlab. Do bn c th s dng chc nng 'more on' xem thng tintheo tng trang mn hnh, sau duyt tng trang mt bng cch nhn phm bt k.nh 'more off' vo ca s lnh s a Matlab tr v cch cx thng thng, khng duyt tng trang.- Thng thng bn c th khng nh chnh xc tn ca mt lnh Matlab, trongtrng hp bn c th s dng lnh 'lookfor' (tm kim) nhmt s tr gip.


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V d, nu bn nh vo dng lnh 'lookfor logarithm', Matlab s lit k tt c cc hm tng bit ca Matlab c lin quan ti Logarit.

Hnh 1. : Giao din ca s Help ca Matlab 7.01.8. History & Editing

- Trong giao din mc nh ca Matlab, ca s 'Command History' (lch s cc lnh) nm gc phn tbn di, pha tri. Trong ca s ny, cc lnh s dng trong cc ln khi ng Matlab gn y u c lu li. Mi ln khi ng Matlab, ton b cc lnh s dng trong ln s c lu li di dng mt nhm c th ng m bng nt biu tng '+' (expand)hoc '-' (collapse) u dng(dng ghi mc thi gian gia hai du ch thch '%'):VD: (+) %-- 8/14/07 3:21 PM --%

(-) %-- 8/14/07 3:21 PM --%

- gi li lnh t ca s 'Command History', bn tmn lnh bng cc thanh cun, ri nhy p vo tn lnh.- gi li cc lnh bn s dng t du nhc ca ca s lnh, Matlab dng ccphm mi tn () trn bn phm.- V d, gi li lnh bn g vo lc gn nht, bn nhn phm mi tn ln ().Tip tc nhn phm ny, n s gi tip lnh trc . Phm mi tn xung gi li lnh theo th tngc li.


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- Cc phm mi tn v c th dng thay i v tr con tr trong dng lnh ti du nhc ca Matlab, nhvy chng ta c th sa dng lnh. Thm na, c th dng chut cng vi b nh m ct, copy, dn v sa vn bn ti du nhc ca dng lnh.


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2. CHNG II: TNH TON TRONG MATLAB

2.1. Matlab - mt my tnh c nhn

* Gii thiu cc ton ts hc:- Cc ton t s hc ca Matlab hot ng theo mt c php rt ging vi c php ca cc ngn ng khc m bn c th quen thuc nhTurbo Pascal, C, C++,Fortran, Java...

- Cc ton t cbn gm c + - * / ^ = v chngc dng kt hp vi ngoc n: ( ). Ton t '=' l ton t gn. Ton t ^ c dng cho ly tha:2^4=16. Vi nhng ton t ny ta c th dng Matlab nhmt my tnh c nhn n gin.* V d: Bn c th nh cc lnh di y vo sau du nhc lnh: >>_.

>> A = 2 + 3/4*5A =

5.7500>> B = 2^5 - 3*AB =

14.7500>> A + Bans =

20.5000

Khi khng c ton t gn, Matlab tr kt qu ca php tnh gn nht vo bin 'ans= ...' (answer). Xem thm mc 2.2.* Th t u tin tnh ton:Trong v d trn, Matlab tnh nhth no, 2 + 3/(4*5) hay 2 + (3/4)*5?Matlab lm vic theo th t u tin sau:

1. cci lng trong ngoc n,

2. ly tha 2 + 3^2 2 + 9 = 11,3. * /, lm vic t tri qua phi (3*4/5 = 12/5),4. + -, lm vic t tri qua phi (3+4-5=7-5),

V vy php tnh trn s theo th t u tin 3.* B cc ton t ca Matlab: (Xem thm Help/Arithmetic operators)

Ton t M t+ Cng - Tr


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.* Nhn mng cng kch thc (nhn phn t vi phn t)

./ Chia mng cng kch thc (chia phn t vi phn t)

.\ Chia mng tri: Ton t Hai chm.^ Ly tha mng, ly tha tng phn t vi phn t.' Chuyn v mng' Chuyn v ma trn - ma trn lin hp (MTLH phc)* Nhn (ma trn). i s tuyn tnh.

/ Chia (ma trn), B/A B*inv(A), chnh xc hn B/A=(A'\B')\ Chia (ma trn) tri. A\B ~ inv(A)*B^ Ly tha ma trn

2.2. Bin trong Matlab* V d:

>> 2^3-3ans =

5>> ans*6ans =

30

- Kt qu ca php tnh th nht c Matlab gn cho bin 'ans ', bin nyc s dng cho php tnh th hai, qua gi tr ca n c thay i (c gn li). - Chng ta c th s dng tn ring do tat lu cc gi tr s

>> x = 2^3-3x =

5>> y = x*6y =

30

t 'x' c gi tr bng 5 v 'y' bng 30. Chng c th c s dng cho nhng tnh ton tip theo. -y l cc v d v v cu lnh gn: cc gi trc gn cho cc bin. Cn phi gn mt gi tr cho mi bin trc khi s dng bin trong cu lnh tip theo.

* Quy tc t tn bin:- Tn bin hp l cu to bi cc ch v s, bt u bng ch. Nn t tn bin phn nh gi tr m ni din cho. Cc tn sau hp l:


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Hsig, Let2try, Dhaluu, T1, V2, z25c5

Cc tn sau khng hp l:chu-ky, 2P, %x, @wru

- Chiu di tn bin: Mc d tn bin c th c di ty , nhng Matlab s ch s dng N k t u tin ca tn, v vy cc bin khc nhau khng c c N k t u tinu ging nhau.

N = namelengthmax N =

63

- Bn c th s dng hm 'isvarname ' kim tra tnh hp l ca tn bin. Hm tr v gi tr 1 nu tn hp l v 0 nu tn khng hp l.

isvarname 8th_column ans =

0 % Not valid - begins with a number

- Thng thng, tn bin khng ph thuc vo ch hoa - ch thng. V th 'xyz's ging nh'xYz'.

- Trnh t tn bin trng vi tn cc hm chun, hoc cc t kha ca Matlab. Vnhvy thng thng bn s khng th s dng cc hm, t kha ca Matlab na. VD: Nu bn gn cho 1 bin tn l 'sqrt' mt gi tr, th bn s khng th s dng hm cn bc hai (sqrt) na! - Matlabng k trc rt nhiu t kha (xem bng lnh 'iskeyword'):

'break' 'case' 'catch' 'continue' 'else' 'elseif' 'end' 'for' 'function''global' 'if' 'otherwise' 'persistent' 'return' 'switch' 'try' 'while'

v cc hm, xem danh sch trong Help/Functions/Categorical List); v cc hng s. Mt s hng s v hm thng dng c th xem mc 2.5 v 2.6.

2.3. Cc kiu d liu -nh dng kt qu* Tng qut v cc kiu d liu:- Matlab s dng 15 kiu (loi) d liu chnh. Mi mt kiu d liu ny u dng ca mt ma trn hoc mng. Cc mng hoc ma trn ny c kch c ti thiu l 0-nhn-0 v c th pht trin ti mng n-chiu vi kch c ty .- Ngoi ra cn c cc kiu d liu do ngi dng nh ngha (thit lp), kiu hng i tng, v kiu d liu lin quan ti Java.


- 18 -

Hnh 2.1. Cc kiu d liu ca Matlab*nh dng kt qu:- S dng lnh 'format' cng ccnh dng. Lnh ny ch lm thayi cch m kt qu c hin th trn mn hnh, khng lm thay i chnh xc ca s hoc php tnh. Hu ht cc php tnh s hc ca Matlab c thc hin vi chnh xc Double, ngha l chnh xc 16 ch s sau du phy thp phn.- thc hin lnh, t du nhc ca ca s lnh nh mt trong cc lnh sau:

format short : du phy thp phn c nh, 5 ch sformat long : du phy c nh, 15 ch sformat short e : k hiu khoa hc, 5 ch sformat long e : k hiu khoa hc, 15 ch sformat short g : du phy c nh hoc di ng, 5 ch sformat long g : du phy c nh hoc di ng, 15 ch sformat hex : format dng Hexa (h 16)

format '+' : dng (+), m (-), v k t trng (blank) ng vi 0format bank : Dollars v cents

format rat : t l xp x integer- Thng thng, 'format short' l dng mc nh. Khi c gi ln, mt dng format s c hiu lc ti khi n c thay i.

2.4. Cc kiu d liu s & s phc- Integer: v d nh-5 hay 9888.


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- Double precision reals: Trong Matlab, tt c cc s thc c lu vi chnh xc double, khng ging cc ngn ng lp trnh khc nhC hay Fortran khi ch c mt loi ring bit float hay real*8 cho cc s thc vi chnh xc single.- Mt dng ngn cc k hiu qu cho vic nhp cc s rt ln hoc rt b l dng k hiu 'e'. Chng hn -1.23456e-7 l dng ngn ca -1.23456 x 10-7; v 8.76e+12l dng vit ngn ca 8.76 x 1012. V d:

>> 1.23e-2 ans =

0.0123>> 5e6 ans =

5000000

- S phc: c nhp vo di dng 3+2*i hoc 3+2*sqrt(-1).- Chui: l mt mng tp hp ca cc k t, c nhp vo di dng 'abc' hoc 'vi du day la mot chuoi'.

Trny l nhng kiu d liu cbn m bn s rt thng dng trong kha hc ny. bit danh sch y hn, bn c th dng lnh 'help datatypes' t ca s nhp lnh.

2.5. Cc k t, Chui v Vn bn- Kh nng x l vn bn trong tnh ton rt hu ch cho vic nhp/xut kt qu t/ti mn hnh v file lu trna. c th qun l vn bn, mt loi d liu l'character' c a vo Matlab. Mt mnh ca vn bn n gin l mt chui(vect) hay mt mng cc k t.VD: >> t1='A'

s gn gi tr A cho mt mng k t tn 't1', kch thc 1 x 1.>> t2='BCDE'

s gn gi tr BCDE cho mt mng k t tn 't2', kch thc 1 x 4.- Cc chui c th c cng vi nhau bng cch s dng cc ton t thao tc trong mng.VD: >> t3=[t1, t2]

s gn gi tr ABCDE cho mt mng k t tn 't3', kch thc 1 x 5.>> t4=[t3, ' la 5 ky tu dau tien ';...'trong bang chu cai latinh.']

s gn gi tr 'ABCDE la 5 ky tu dau tien ' ''trong bang chu cai latinh.'

cho mt mng k t tn 't4', kch thc 2 x 26.


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- Cn ch rng s cc k t hai dng phi bng nhau, nu khng vic thc thi cu lnh trn s dn ti mt li:

??? Error using ==> vertcatAll rows in the bracketed expression must have the samenumber of columns.

- Du ba chm '...' th hin rng cu lnh cn tip tc dng sau.* Chuyn i gia chui v s-i khi chng ta cn chuyn mt chui thnh mt s tng ng, hoc ngc li. Cc cng vic chuyn i nyc thc hin bi lnh:

- 'str2num': chuyn mt chui thnh s tng ngv hai lnh:

- 'num2str': chuyn mt s thc thnh chui tng ng- 'int2str': chuyn mt chui thnh s tng ng

- Nhng lnh ny rt hu ch trong vic to ra cc nhn v tiu mt cch t ng, chng hn nh

2.6. Cc hng s dng snMatlabnh ngha sn nhiu hm s rt hu ch, bao gm:

pi,= 3.141592654... i v j, c hai u bng phn o ca s phc, = sqrt(-1) inf, 'infinity' hay 'v cng' NaN, 'not-a-number' hay 'khng phi l mt s' ans, lunc gn cho kt qu ca lnh tnh trc ...

Bn nn trnh gn li gi tr khc cho cc hng s nu trn nu c th. Ch c mt ngoi l l i v j, v c hai thng c s dng nhcc ch s ca vng lp. Vic gn li gi tr khc cho cc hng s ny l chp nhn c v s phc lun c th thuc bng cch s dng sqrt(-1).

2.7. Cc hm dng sn - Cng nhnhng ngn ng bc cao khc, Matlab thc thi cc 'function' (hm)nhiu hn 'procedure ' (chng trnh con). Cc hm ny bao gm cn bc hai


- 21 -

(sqrt), ly tha (exp), logarit (log, log10, log2), gi tr tuyt i (abs), v cc hmlng gic (sin, cos, tan, atan,...). V d:

>> sin(45) ans =

0.8509

tr kt qu bng sin ca 45 radians... m thc ra nh ca bn l tnh sin ca 450,

s bng 45180

radians:

>> sin(45/180*pi) ans =

0.7071

v kim tra li xem bn c thuc 22

nhnh khng

>> sqrt(2)/2 ans =

0.7071

- Ch rng tt c cc tnh ton ca Matlab u c li lm trn, mi khi bn li thy mt cch khng mong i. V d, bn khng nn ngc nhin khi thy

>> tan(pi) ans =

-1.2246e-016

Nn nh rng li lm trn c mt khp ni, v chng ta nnn gin tip nhn kt qu ny nhtan()=0.* Danh mc cc hm dng sn ph bin:Cc hm lng gic:

sin - hm sin.

sind - sin ca argument tnh theo.sinh - sin hypecbolic.

asin - arcsin, hay hm nghch o ca hm sin.asind - hm nghch o ca hm sin, kt qu theo .asinh - hm nghch o ca hm sin hyperbolic.cos - hm cos.

cosd - cos ca argument tnh theo .cosh - cos hyperbolic.

acos - hm nghch o ca hm cos.acosd - hm nghch o ca hm cos, kt qu theo .acosh - hm nghch o ca hm cos hyperbolic.


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tan - hm tang.

tand - tang ca argument tnh theo .tanh - tang hyperbolic.

atan - hm nghch o ca hm tang.atand - hm nghch o ca hm tang, kt qu theo .atan2 - hm nghch o ca hm tang 4 gc phn t.atanh - hm nghch o ca hm tang hyperbolic.cot - hm ctang.

cotd - ctang ca argument tnh theo ..coth - ctang hyperbolic.

acot - hm nghch o ca hm ctang.acotd - hm nghch o ca hm ctang, kt qu theo .acoth - hm nghch o ca hm ctang hyperbolic.

Cc hm ly tha:exp - hm m.expm1 - tnh chnh xc exp(x)-1.

log - logarit cs t nhin.log1p - tnh chnh xc log(1+x).

log10 - logarit cs 10.reallog - loga cs t nhin ca s thc.realsqrt - cn bc hai ca mt s >= 0.sqrt - cn bc hai.nthroot - nghim thc bc n ca cc s thc.

Cc hm lin quann s phc:abs - gi tr tuyt i.angle - gc pha.

complex - xy dng d liu v s phc t cc phn thc v o.conj - lin hp ca phc.imag - phn o ca phc.real - phn thc ca phc.isreal - hm logic, tr v gi tr 'true' vi mng s thc.


- 23 -

cplxpair - sp xp cc s v cc cp lin hp phc.Cc hm lm trn v phn d:

fix - lm trn v pha 0.floor - lm trn v pha m v cng.ceil - lm trn v pha dng v cng.round - lm trn v pha s nguyn gn nht.mod - mun (ly phn dca php chia).rem - ly phn dca php chia (tng t mod)sign - hm ly du ca mt bin, tr v +1, 0, -1 (+, 0, -).

V d:mod([1 2 3 4 5 6 7],3) ans =

1 2 0 1 2 0 1

2.8. Cc php ton quan h

* Cc ton t quan h(so snh):Ton t C php M t< A < B Nh hn B Ln hn>= A >= B Ln hn hoc bng== A == B Bng~= A ~=B Khng bng

* M t:- Cc ton t quan hthc hin s so snh tng phn t vi phn t gia hai mng. N cho kt qu l mt mng logic c cng kch c, vi cc phn t ca mng l ng (1) nu quan h l ng, v phn t ca mng l sai (0) nu khngng.- Cc ton t, = ch s dng phn thc ca cc ton hng cho phpso snh. Cc ton t== v ~= kim tra c phn thc v phn o. V d:

>> X = 5*ones(3,3) X =

5 5 5


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5 5 5

5 5 5

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

1 2 3

4 5 6

7 8 9

>> X >= Y ans =

1 1 1

1 1 0

0 0 0

Kt qu c tr v di dng mt ma trn c cng kch thc vi ma trn X vY. Trong mi phn t c gi tr 1 (ng - true) hoc 0 (sai - false) ty thuc vos logic ca php so snh X>=Y.

2.9. Cc php ton logic

- Matlab biu din ng v sai bi cc s nguyn t 1 v 0:ng = 1, sai = 0 (true = 1, false = 0)

- V d trong qu trnh tnh ton, bin x (x l mt i lng v hng) nhn mt gi tr bt k, chng ta c th tin hnh cc php kim tra logic cho n:

x = = 2 xem x c bng 2 khng?x ~= 2 xem x c khc 2 khng?

x > 2 xem x c ln hn 2 khng?x < 2 xem x c nh hn 2 khng?x >= 2 xem x c ln hn hoc bng 2 khng?x > x = pi x =

3.1416>> x ~= 3 ans =

1>> x ~= pi


- 25 -

ans =0

- Khi X l mt vc thay ma trn, cc php kim tra ny s c tin hnh chotng phn t ca X. V d mc trc (2.8), php kim tra xem X c ln hn hoc bng Y hay khng cho ta kt qu:

>> X >= Y ans =

1 1 1

1 1 0

0 0 0

- Chng ta c th phi hp cc php kim tra logic, v d 4 Y6>> Y>=4 & Y5) ngha l x khng ln hn 5, nu x=4 th php

kim tra ny s cho kt qu ng (true), hay = 1- Mt ng dng khc na ca cc php kim tra logic l ta c th xa (hay b qua) cc phn t nht nh ca mt ma trn:

khi tnh phn b lu tc theo chiu su (tnh t y knh), ta c th b qua lp bin vi chiu su nc z tha mniu kin z N.

VD:>> H = [4.7506 1.1557 3.0342 2.4299 4.4565... (shift + )

3.8105 2.2823 0.0925 4.1070 2.2235]; >> N = 3; >> kiemtra = H > N kiemtra =


- 26 -

1 0 1 0 1 1 0 0 1 0>> H = H.* kiemtra H =

4.7506 0 3.0342 0 4.4565 3.8105 0 0 4.1070 0

Nh vctH by gi ch cn cha cc s liu sng c chiu cao ln hnngng 3m.

2.10. Kt hp nhiu lnh trn mt dng; n kt qu tnh.Du phy (,) v du chm phy (;) l nhng k t c ngha c bit trong Matlab, v s chng t l rt hu ch.

* Kt hp nhiu lnh trn mt dng:Ton t phy (,)c dng nhm nhiu lnh trn mt dng, v d:

>> x=3.5, y=-5.0, x 3 y x =

3.5000

y =

-5

ans =

47.8750

* n kt qu tnh (Surpessing output)- Thng thng, chng ta khng mun theo di tt c cc tnh ton trung gian, hay ta mun n i mt cu lnh, mt din gii. Khi ta dng du chm phy (;). Vd:

>> x=3.5; y=-5.0; x 3 y ans =

47.8750

Trong v d trn, kt qu ca hai lnh gn u tin c n i.


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3. CHNG III: VECT

3.1. Gii thiu-i s tuyn tnh l tri tim v l phn hn ca Matlab. Trong thc t th banu Matlab l t vit tt ca matrix laboratory. V vy hn bt k ngn ng nokhc, Matlab khuyn khch v trngi bn tn dng mi kh nng ca cc mng,vctv ma trn.

* Mt vi thut ng trong chng III (Vct) v IV (Ma trn):- Mng l mt tp hp cc s, c gi l cc phn t hay cc u s, c bit n vi mt hoc nhiu ch s chy sut cc tp hp ch s. Trong Matlab, cc tp hp ch s lun l chui s nguyn t bt u bng 1. - S chiu ca mt mng l s cc ch s cn thit nh ngha mt phn t trong mng. Chng hn mng 2 chiu s cn 2 ch s i v j c trng cho mt phn t ca mng. - Kch thc ca mng l mt danh sch cc kch thc ca cc tp hp ch s, vd:

>> r = [1 2 3; -1 -2 -7]r =

1 2 3-1 -2 -7

>> size(r)ans =

2 3

Ngha l kch thc ca mng r s l 2x3 (2 hng, 3 ct).- Ma trn l mt mng hai chiu (kch thc m x n vi cc quy lut t bit cho php cng, nhn v cc tnh ton khc. N c trng cho mt s bin i tuyn tnh v ton hc. Hai chiu ca ma trn l hng v ct (m hng v n ct).- Vctl mt ma trn m mt chiu ch c ch s =1. C th, mt vcthng lmt ma trn ch c mt hng (kch thc 1 x n), cn mt vctct l mt ma trn ch c mt ct (kch thc m x 1).

- Mc d khi nim mng tng qut hn v t tnh cht ton hc hn mt ma trn,nhng hai thut ng ny vn thng c dng ln vi nhau. Hn na, Matlab i khi khng c mt s phn bit chnh thc no, thm ch l gia mt i lng v hng v mt ma trn kch thc 1x1.- Cc lnh c th c sp xp theo s phn bit gia mng/ma trn, nhngMatlab thng cho php bn s dng chng ln ln mt cch thoi mi. tng


- 28 -

y (v bt c ch no khc) l Matlab mun gi cho ngn ng ca mnhn gin v t nhin, bn c th t mnh trnh khi cc rc ri. - Cc phn t n l trong ma trn c th c tip cn v sa i bng cch s dng ch s phn t (subscripting). Trong Matlab, phn t th i ca vctVc biu din bng k hiu V(i), ch s c vit trong ngoc n. V d:

>> V = [10 20 30] V =

10 20 30>> V(2) ans =

20>> V(2)=50 V =

10 50 30

- Sau y chng ta s xem xt ln lt hai loi vctchnh trong Matlab: vcthng v vctct.

3.2. VcthngVcthng l chui cc s c phn cch bi du phy hoc khong trng. S lng cc u s c gi l chiu di ca vct, v mi u s thng c nhc n nhphn t, hoc hp phn ca vct. C php cbn nhp 1 vctl mt chui cc gi tr c bao trong cp ngoc vung [ ]. V d:

>> v = [ 1 3 sqrt(5)] v =

1.0000 3.0000 2.2361>> length(v) ans =

3

hoc cch khai bo khc cho kt qu tng t, s dng cc du phy ( , )>> v = [1, 3, sqrt(5)] v =

1.0000 3.0000 2.2361

- Trong v d u tin, cc khong trng c dng phn cch cc phn t ca vct. Khong trng (space) rt quan trng trong khi khai bo vct, iu ny cth minh ha bng s khc bit nh gia hai dng lnh di y:

>> v2 = [3+ 4 5] v2 =

7 5>> v3 = [3 +4 5] v3 =

3 4 5

- Nh cp trn, chng ta c th xem hoc thay i gi tr ca nhng phn t ring bit ca vct:


- 29 -

>> w(2) = -2, w(3)w =

1 -2 3ans =

3

3.3. VectctVctct c cu to tng t nhvcthng. Khinh ngha vctct, cc phn t c phn cch nhau bi k t ; hoc bi newlines. V d:

>> c = [ 1; 3; sqrt(5)] c =

1.00003.00002.2361

>> c2 = [3 (shift + )4 (shift + )5] c2 =

345

>> c3 = 2*c - 3*c2 c3 =

-7.0000-6.0000-10.5279

V d trn cho thy cc vctct c th c cng hoc tr vi nhau nu chng c cng chiu di.3.4. Ton t hai chm ( : )- Ton t ny dng to ra vc thng mt cch nhanh chng:

>> x = 1:4 x =

1 2 3 4>> y = 3:7 y =

3 4 5 6 7>> z = 1:-1 z =

Empty matrix: 1-by-0

- Mt cch tng qut th a : b : cs to ra mt vc tvi cc phn t bt u t gi tr ca a, tng dn vi bc tng bng gi tr ca b, cho ti khi t ti gi tr ca c (s khng to ra mt gi tr vt qu c).iu ny gii thch v sao 1:-1 to ramt vctrng [ ].

>> 0.32:0.1:0.6 ans =

0.3200 0.4200 0.5200>> -1.4:-0.3:-2 ans =


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-1.4000 -1.7000 -2.0000

- Ton t : cnc dng trch xut mt phn ca vct. Gi thit chng ta c vc t

>> r = [1:2:6, -1:-2:-7] r =

1 3 5 -1 -3 -5 -7

th trch ra cc phn t t th 3 n th 6 ta c th dng lnh:>> r(3:6) ans =

5 -1 -3 -5

hoc trch cc phn t theo mt quy lut, chng hn:>> r(1:2:7) ans =

1 5 -3 -7

Hy xem r(1:2:7) cho ta kt qu nhth no?

3.5. Lm vic vi vect& ma trn (mng)

* Cc php ton s hc:- Chng ta c th tin hnh mt s php ton s hc nht nh (cng, tr) vi cc vctc cng chiu di. Matlab s bo li khi ta thc hin cc php ton ny vi cc vctc kch thc (chiu di) khc nhau. V d:

v1 = [1 2 3]v2 = [4 5 6]>> v1+v2 ans =

5 7 9>> v3=3*v1 v3 =

3 6 9>> v4=2*v1-3*v2 v4 =

-10 -11 -12>> v5=[10 11 12 13]; >> v4+v5??? Error using ==> plusMatrix dimensions must agree.

- Mt vc tcng c th nhn dc vi mt i lng v hng (mt s), thao tcc Matlab tin hnh vi tng phn t.- tin hnh cc tnh ton cng loi (tnh ton vi tng phn t): nhn, chia vly tha, Matlaba ra cc ton t .*, ./ v .^. V d:

>> v1.*v2 ans =

4 10 18


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>> v2./v1 ans =

4.0000 2.5000 2.0000

Ton t ly tha c th c s dng theo hai cch, vi ly tha s v hng hoc ly tha vct:

>> v2.^2 ans =

16 25 36>> v2.^v1 ans =

4 25 216

L do Matlab cn cc ton t . ny s c lm r hn trong chng 5.- .* thc ra c ngha ca mt php nhn ma trn, tng ng vi .* cho cc vct.Tt c cc hm s hc dng sn ca Matlab c thit k hot ng vi cc vct(v ma trn), v vy chng ta c th xy dng cc din gii i s hot ng vi tng phn t ca vct.

VD: on m lnh di y tnh ton gi tr biu thc ).cos(2 3 yxyx

x

theo-tng-phn-t. Tnh vi mi mt phn t trong vctx v y:>> x = [1 2 3]; y = [4 5 6]; >> s = 2*sqrt(x) + x./y - x.^3.*cos(pi*y) s =

1.2500 11.2284 -23.0359

Lu cc php tnh ca cc i lng v hng trn cc vctkhc nhth novi cch lm vic phn t vi phn t, v d: 2 * sqrt(x) r rng l nhn s v hng vi vct, trong khi x/y th khc, v vy y ta cn phi s dng x./y

Ch : Cc php cng v tr phn t vi phn t l ra cng phi s dng .+ v .-, tuy nhin trong v d ny th khng cn thit. * Ghp cc vct:- C th to ra mt vctt nhng vctc trc nu nhkch thc ca chng tng thch vi nhau, v d:

>> w = [1 2 3], z = [8 9] >> cd = [2*z,-w], sort(cd) w =

1 2 3z =

8 9cd =

16 18 -1 -2 -3ans =

-3 -2 -1 16 18


- 32 -

Lu rng cu lnh cui cng (sort) sp xp cc phn t ca vcttheo chiu tng dn. Ta cng c th s dng cc lnh cat, vertcat, horzcat ghp ni cc vct(xem thm help).

* Cc lnh cho thng tin v ma trn (vc t):size - kch thc theo mi chiulength - kch thc ca chiu di nht (c bit l cho vct)ndims - s chiufind - cc ch s ca cc phn t khc 0 * Chuyn v ma trn:Ta c th chuyn i mt vcthng thnh mt vctct (v ngc li) bng mt qu trnh gi l chuyn v k hiu bng k t . Hy xem cc v d sau:

>> w, w', c, c' w =

1 -2 3ans =

1-23

c =1.00003.00002.2361

ans =1.0000 3.0000 2.2361

>> t = w + 2*c' t =

3.0000 4.0000 7.4721>> T = 5*w'-2*c T =

3.0000-16.000010.5279

3.6. X l d liu vi cc hm dng sn cho vect& ma trn

(Xem thm Help v bi ging trn lp)* Sp xp d liu: sort

* Tm gi tr ln nht: max

* Tm gi tr nh nht: min


- 33 -

* Tnh tng: sum

* Tm gi tr trung bnh: mean

* Tm lch qun phng: std


- 34 -

4. CHNG IV: MA TRN I S & TUYN TNH

4.1. nh ngha v khi to ma trn- Ma trn l dng cu trc d liu cbn ca Matlab. V nh cp chngtrc, cc vctchng qua l nhng dng c bit ca ma trn c kch thc (1 x n) hoc (m x 1). - T du nhc ca ca s nhp lnh, nh lnh help elmat v help matfun c mt danh sch cc lnh v hm lm vic vi ma trn trong Matlab. - C php ca vic nh ngha v khi to ma trn rt ging vi nhng g bn thy vi vct: cc khong trng (hoc du phy) phn cch cc phn t trong mt hng, v cc du chm phy l k hiu cho bit bt u mt hng mi sau .V d khi bn nh:

>> A = [2 -1 0 0; 1 1 2 3; -1 4 0 5 ]

Matlab s a ra kt quA =

2 -1 0 0

1 1 2 3

-1 4 0 5

V bin A by gi cha mt ma trn 3x 4.

- Cc phn t n l ca mt ma trn c th c tip cn v chnh sa theo cngmt cch nhvi cc vct, l cung cp cc ch s hng v ct. V d lnh

A(3,2) = 0 s thay th gi tr phn t ct 2 hng cui cng ca ma trn A thnh 0.- C nhiu lnh khi to mt s dng ma trn c bit, v d

zeros(n,m) - to ma trn vi tt c cc phn t = 0ones(n,m) - to ma trn vi tt c cc phn t = 1eye(n) - to ma trn n v kch thc n x n.

- khi to mt ma trn vung c bit, bn c th s dng dng ngn zeros(n),lnh ny ngm nh rng s hng v s ct ca ma trn l bng nhau.

4.2. Mt s ma trn c bit* Cc lnh dng xy dng ma trn v mng:

eye - ma trn n v


- 35 -

zeros - ma trn vi tt c cc phn t = 0ones - ma trn vi tt c cc phn t = 1diag - ma trn ng cho (hoc chch xut mt ng cho)toeplitz - ma trn vi mi ng cho bng 1 hng striu - ma trn tam gic trntril - ma trn tam gic dirand - ma trn vi cc phn t ngu nhin (t -1n 1)linspace - ma trn vi cc phn t cch u nhaucat - mc ni cc ma trn vi nhau theo mt chiu nhrepmat - xy dng ma trn mi bng cch lp mt vc ttheo 1 chiu

(hoc nhiu chiu) nhXem help c hng dn chi tit hn v cch s dng cc hm ny.

4.3. Cc php ton vi tng phn t trong ma trn

4.4. Cc php ton vi ma trn

4.5. Gii phng trnhi s

4.6. Gii h phng trnhi s tuyn tnh

4.7. Tm nghim ca a thc

4.8. Gii phng trnh phi tuyn

4.9. Gii phng trnh vi phn

4.10. Cc lnh hu ch khc

inv(A), the matrix inverse,

det(A), the determinant of a matrix,


- 36 -

trace(A), the trace,

cond(A), the condition number,

norm(A), the matrix norm.

eig(A), _nds the eigenvalues and eigenvectors.

(Tng t nhphn vct- Xem thm Help v bi ging trn lp)


- 37 -

5. CHNG V: SCRIPTS V FUNCTIONS (M-FILES)

5.1. Gii thiu M-file- Cc M-file l cc file ASCII (file text) bnh thng cha cc (cu) lnh Matlab. Mt iu thit yu l cc file c phn m rng l '.m' (VD: baitap2.m) v v ldo ny, chng thng c bit n di ci tn cc m-files.- C hai loi m-file: Script v Function. Cc Script v Function files cng hot ng gn nhcc Procedures v Functions trong cc ngn ng lp trnh thngdng khc. - V cbn ni dung ca mt script file c hiu ging ht nhkhi ni dung c g vo ti du nhc ca s nhp lnh. Hiu n gin th n ch thc hin mt chui cc cu lnh ca Matlab. Tuy nhin trong thc t nhiu ngi dnga thchs dng Matlab bng cch nh tt c cc lnh vo script file v chy (cc) file . uim ca phng php s dng script l:

To ra v xem xt, chnh sa mt chui nhiu dng lnh (thng l 4, 5dng tr ln). C th d dng xem li hoc thc hin li cng vic ca bn sau ny. Chy cc tnh ton (cng vic) i hi cng cao ca CPU trn nn, x l kt qu v lu li t ng, cho php bn log-off (lin quan ti UNIX).

5.2. Bin son v thc thi M-file- Bin son: Matlab cung cp cho ta mt cng c bin son cc m-file kh tt, l Matlab editor. Tuy nhin bn c th t do s dng cc ng dng son tho khc cho file text ca Windows nhNotepad, Textpad...

- Bn c th khi ng Matlab Editor bng nhiu cch: T menu File/New/M-file,hoc nhn t hp phm tt Ctrl N, hay cch nhn vo nt New Doccumenttrn thanh cng c, cch nh vo ca s nhp lnh edit v tn file (nu file chatn ti trong thmc hin thi, Matlab s hi bn khng nh rng bn mun to ra mt file mi vi tn nhvy)- Son tho cc cu lnh ca bn v Save.- bit trong thmc hin ti (current directory) c nhng m-file no, bn cth s dng lnh

>> what


- 38 -

- xem ni dung ca mt m-file, bn nhy p vo file m n ra hoc nh lnh

>> type tn_file

- Thc thi: c th thc thi mt m-file, n cn phi tn ti trong thmc hin thi (xem ca s Current Directory). Bn c th di chuyn gia cc thmc trong cng gn ging nhvi trnh duyt Exprorer ca Windows, hoc dng lnh editpath (path lng dn n thmc m Matlab s tm kim file ). - Bin dch: khng cn thit bin dch c hai loi M-file ca Matlab. Mun thc hin cc lnh cha trong file ny rt n gin, bn ch cn nh tn file (khng cn phn m rng '.m') t du nhc ca s lnh . Cc chnh sa tin hnh vi file vghi li vo a s c thc thi khi bn gi function hay script ln sau. V d gi thc thi cc lnh c trong file baitap2.m nhsau:

>> baitap2

Ch c cc thng s u ra s c th hin trn mn hnh, ch khng phi bn thn cc cu lnh. - c th xem cc cu lnh c trong file cng lc vi cc thng s u ra, bn nh lnh

>> echo on

v lnh 'echo off' s tt chc nng ny.

5.3. Ch thch (comments)

- Mt dng cu quan trng trong M-file l cu ch thch,c bt u bng k t phn trm (%). Bt c phn text no sau k t '%' trn mt dng lnh s c Matlab b qua khng thc hin (tr trng hp k t % l mt phn ca chui k t gia hai du nhy ).- Mc ch chnh ca tnh nng ny l cho php b sung cc cu ch thch(comments) vo script file, m t r rng hn mc ch, tnh nng cc lnh, on, vng lp, bin...- Hn na, khi cc cu ch thch u tin trong mt M-file s hot ng nhmt hng dn s dng m-file ca bn, v s hin ra ca s nhp lnh khi bn s dng lnh help + tn_m-file.V d: gi s trong file baitap2.m ca bn c ni dung sau:

% script nay giai quyet cac bai tap ve nha

% lien quan toi kien thuc chuyen nganh ky thuat bien

%

z= rand(1); % muc nuoc bien


- 39 -

a=omega*t*sin(2*pi); % bien do song...

Th khi mt ngi dng khc ngi vo my tnh ca bn, mun bit nhng thng tin cbn nht xem file baitap2.m vit v vn g, h c th nh vo ca s lnh:

help baitap2

v kt qu nhn c s lscript nay giai quyet cac bai tap ve nha

lien quan toi kien thuc chuyen nganh ky thuat bien

5.4. Cc hm m-file (function m-files)- Trc tin chng ta cn phn bit cc hm m-file v cc hm s dng sn, hmtrong mt dng.

Hm dng sn, VD nhsqrt( ), log( ), exp( ), sin( )... Hm trong 1 dng (inline function): l cch n gin nht m ngi

dng c th nh ngha mt hm, VD: Dng lnh di y s khai bo hm 2)sin(.)( xxxf v tnh gi tr hm ti x=5 bng cch chuyn hm ny cho lnh inline ca Matlab trong mt cp du nhy :

>> f = inline('x*sin(x)+2'), f(5)f =

Inline function:f(x) = x*sin(x)+2

ans =-2.7946

Hm vi m-file: Dng cho cc hm phc tp hn, chng hn nhccha cc vng lp, cu iu kin... bn cn dng m-file khai bo cc hm.

- Sau na chng ta cn phn bit cc hm m-file v cc script-file: Script m-file, nh cp phn trc, khng phi l mt hm. N

khng c cc tham s u vo cng nhu ra, vn gin n ch thc hin mt chui cc cu lnh ca Matlab, vi cc bin c nh ngha trong khong gian lm vic. Hm m-file khc vi script m-file ch n c mt dng nh ngha

hm, qua lin h gia cc tham s u vo vu ra. Hm l cch ch yu pht huy kh nng ca Matlab. So vi cc script, cc hmc kh nng phn chia nhim v tt hn nhiu.

Mt v d v hm trong Matlab c th tham kho bi tp 4 (tnh din tch tam gic), chng 8 trong gio trnh ny.


- 40 -

* Cc bc chnh cn tun theo khi khai bo mt hm trong Matlab l:- t tm cho hm, lu rng tn khngc xung t vi cc tnc Matlab dnh trc. Trong v d ny tn hm l dientich v vy cc nh ngha ca n s c lu trong mt file tn l dientich.m- Dngu tin ca file ny cn c dng thc nhsau:

function[cc outputs] = tn_hm(cc inputs)

Ly v d trong bi ton ca chng ta, bin u ra S (din tch) l mt hms ca cc bin u vo a, b, c (l chiu di ca ba cnh). Do dng u tin ca m-file hm dientich s l:

function [S] = area(a,b,c)

- Son tho hng dn s dng cho hm (khng bt buc, xem thm phn ch thch - Comments). M t ngn gn mc ich ca hm v lm th no s dng n. Cc dng ny cn bt u bng k t %, hay chnh l ccdng ch thch m ta cp, v Matlab s b qua n khi thc thi hm.- Cui cng v cng l quan trng nht: son tho m lnh thc thi ni dung ca hm. i cng vi ni dung ta cng cn y cc cu ch thch ngi dng khc c th hiu c qu trnh taang lm.

Mt m-file hm hon chnh c th trng nhsau (theo v d trn ca chng ta)function [A] = dientich(a,b,c)% Tinh dien tich cua mot tam giac% khi biet chieu dai 3 canh la a, b va c.% Dau vao:% a,b,c: Chieu dai cua cac canh% Dau ra:% A: Dien tich tam giac% Cach su dung (cu phap):% Dientichcantinh = dientich(2,3,4);% Nguoi viet: Ng.Ba.Tuyen, 2007.

s = (a+b+c)/2;A = sqrt(s*(s-a)*(s-b)*(s-c));

%%%%%%%%% ket thuc dientich %%%%%%%%%%%

Ta thy rng ch thch y kh y , v ngi dng sau c th d dng hiu c ni dung cng nhcch s dng hm dientich bng cch nh lnh helpdientich t ca s nhp lnh, hng dn thu c s nhsau:

>> help dientich Tinh dien tich cua mot tam giackhi biet chieu dai 3 canh la a, b va c.Dau vao:a,b,c: Chieu dai cua cac canhDau ra:A: Dien tich tam giacCach su dung (cu phap):Dientichcantinh = dientich(2,3,4);Nguoi viet: Ng.Ba.Tuyen, 2007.

Th s dng hm va lp tnh din tch mt tam gic khc:


- 41 -

>> dientich(4, 5, 7)ans =

9.7980

Nhvy chng ta i qua cc bc cbn t khai bo mt hm bng m-file,son tho ni dung, m lnh, v s dng hm. Hy s dng help c hiu bit su hn v hm trong Matlab.* Mt kha cnh quan trng khc ca hm M-file l hu ht cc hm xy dng trong Matlab (tr nhng hm li ton hc) u l cc M-file m bn c th c vcopy.y l mt cch rt tt hc hi, luyn tp lp trnh v cng l mt mo.

5.5. Cu lnh r nhnh (if v switch)- Thng thng mt hm cn r nhnh ty theo cc iu kin thc thi. Matlabcung cp cho ta cc cng c lm vic ny cng nhhu ht cc ngn ng lp trnh khc.

* Cu lnh if...elseif...else...end- V d sau minh ha hu ht cc tnh nng ca if

if isinf(x) | isreal(x)disp(So lieu dau vao xau!)y = NaN;

elseif (x == round(x)) && (x > 0)y = prod(1:x-1);

elsey = gamma(x);

end

- Ta thy cc iu kin cho cu lnh if c th lin quan ti cc ton t quan h cp chng 2, cng c th lin quan ti cc hm cho ta gi tr logc (isinf, ~isreal... kim tra xem x c phi l s v cng, hay x khng phi l s thc... ).

* Cu lnh switch...case...case... case...otherwe...end- B cu lnh if/elseif ch hu ch trong trng hp ch c mt vi la chn. Cnkhi c mt s lng ln cc la chn kh d, thng thng ta dng switch thayth. V d:

switch donvicase Chieudai

disp(met)case The tich

disp(lit)case Thoi gian

disp(giay)otherwise

disp(Toi chiu thua)end


- 42 -

- Din gii ca lnh switch c th l mt chui hoc mt s. Trng hp u tinph hp vi case th cc lnh ca n s c thc thi.- C th s dng otherwise hoc khng. Trong trng hp c s dng, th Matlabthc thi cc lnh sau otherwise nu khng c trng hp no ph hp vi cccase.

5.6. Vng lp (for v while)* Vng lp for...end-c s dng khi ta mun lp mt on m lnh cho mt s ln ty (thc ra ta s t dng n n trong Matlab hn l trong cc ngn gn lp trnh khc, bi vMatlab cung cp cho ta ton t :)

- V d, v th sin(n..x) trong khong -1x1 vi cc gi tr khc nhau ca n = 1, 2, ...8.

- Thc thi: Chng ta c th a ra 8 lnh v ring r, nhng s d dng hn nhiu nu ta s dng mt vng lp. Dng n gin nht ca n s l

>> x = -1:.05:1; >> for n = 1:8 (shift + )subplot(4,2,n), plot(x,sin(n*pi*x)) (shift + )end

Tt c cc lnh gia hai dng bt u bng for v kt thc bng endu c lp i lp li vi n=1 ln th nht, n=2 ln th 2... cho ti khi n=8. Lnh subplot to ra mt mng 4x2 ca s th con trong mt th chnh. ln lp th n, mt hnh s c v ln ca s th con th n.

Hnh v: Minh ha cho vng lp for...end

* Vng lp while...end


- 43 -

- c s dng khi bn mun thc hin lp i lp li mt on m lnh ca Matlab cho ti khi mt iu kin (logic) no c tha mn, nhng ta khngth ni trc n s cn lp bao nhiu ln. Khi chng ta c th s dng vng lp ny.

- V d, tm gi tr ln nht ca n sao cho tng di y vn nh hn 100?2222 ...321 n

- M lnh cho Matlab thc thi nhim v trn:>> S = 1; n = 1; >> while S+ (n+1)^2 < 100 (shift + )

n = n+1; S = S + n^2; (shift + )end

>> [n, S] ans =

6 91

- V d khc: Tm gi tr gn ng ca nghim phng trnh x=cos(x) ?

5.7. c d liu t file v ghi ra file

(SV 45B khng hc/cha hc phn ny)- Nhp d liu trc tip t bn phm s tr nn khng th (khng thc t) khi

Lng d liu qu ln D liu c dng cho phn tch nhiu ln

Trong nhng trng hp ny th ngi s dng Matlab s chn cch nhp/xut d liu vi file d liu.- Hai lnh save v load m ta hc chng 2 cng c chc nng ghi vc gi tr ca cc bin vo/t a. - Khi lm vic vi file d liu, mt iu ct yu cn lu lnh dng ca d liu phi ng. nh dng d liu l cha kha quyt nh vic bin dch d liu. C hai dng file d liu: formatted v unformatted (c nh dng v khng nh dng).

File d liu c nh dng s dng cch nh dng chui khai bo chnh xc xem d liu c lu v tr no v nhth no. File d liu khng nh dng th khc, n ch nh rnh dng ca s.

Cchn gin nht hc cch lm vic vi file d liu l thng qua v d sau:Gi s d liu dng s c lu trong file c tn table.dat trong thmc hin hnh, d liu nhsau

100 2256


- 44 -

200 4564300 3653400 6798500 6432

3 lnh sau>> fid = fopen('table.dat','r');>> a = fscanf(fid,'%3d%4d');>> fclose(fid);

s ln lt lm cc nhim v: M mt file c, vic nyc ch nh bng chui r, (r l vit tt

ca read). Bin fid c gn cho mt gi tr bng 1 s nguyn t duy nht, c trng cho file s s dng (s ny cn gi l s ch th ca file). Sau ny mi khi nhc n file ny chng ta s s dng s ch th fid. c vo b nh tng cp s t file (file c s ch th l fid), mt s c 3

ch s v mt s c 4 ch s. ng file (file c s ch th l fid).

Qu trnh ny to ra mt vc tct cha cc phn t 100 2256 200 4564 ...5006432. Vctny c th c chuyn i v ma trn 5x2 bng lnh:

A = reshape(2,2,5)';

.......... (lc bt) .............. (xem thm Help nu cn thit) ....................

6. CHNG VI: THDNG NG

6.1. Biu din ng qu trnhTrng hp n gin nht l biu din s bin thin tng gim s liu trong mt dy. Chng hn vi dy s liu mc nc z o c ta c th biu din di dng ng qu trnh nhsau:z = [-0.05 0.18 0.28 0.33 0.19 0 -0.26 -0.35 -0.31 -0.22 0.05 0.14 0.310.38 0.18 0.09 -0.11 -0.20 -0.36 -0.11 0.08];1

plot(z)

Lnh plot(z) s v biu dng ng vi s liu cho bi vec-tz. Trng hp ny trc honh s nh s th t ln lt 1, 2,... iu ny khng gip ch g trongtrng hp thng thng khi trc honh cn biu th khong cch khng gian hoc

1 Ch rng y xung dng do hn chbngang ca ti liu. Khi lp trnh khng n Enter v my shiu nhm z thnh mt ma trn.


- 45 -

thi gian. Chng hn, nu s liu z v d trn l mc nc o c ti cc thi im 0 s, 10 s, 20 s... (cch nhau 10 giy) th ta c th b sung m lnh nhsau:figure;

t = 0:10:200;

plot(t, z);

y lnh figure c tc dng to ra mt hnh mi.Ch : Cc vec-tcn v thng c rt nhiu phn t, v do ta cn dng du ; cui cu lnh ngn khng cho my hin li ni dung ca ton b vec-t.

Tm li v biu dng ng ni chung ta theo 3 bc sau:1) Pht sinh mt vec-tcha cc ta x ca cc im2) Pht sinh mt vec-tcha cc ta y, c th l t s liu sn c, hoc l mt hm tnh t cc gi tr tng ng ca x. Trong trng hp sau cn lu php tnhcn c p dng cho tng phn t mt.3) Thc hin lnh v plot(x, y)

Trong cc biu ta phi ghi tiu ca biu v in cc i lng vn v ln cc trc (x, y). C th thc hin vic ny bng cch:title('Tiu biu ')xlabel('Tiu trc x')ylabel('Tiu trc y')

Chng hn vi v d v mu quan trc mc nc theo thi gian nhtrn ta c th vit:title('Qua trinh muc nuoc thuc do')

xlabel('t (s)')

ylabel('z (m)')2

Kt qu biu thu c nhtrn Hnh 1. MatLab t ng cn chnh phm vi ca trc tung v trc honh sao cho c th hin th ton b s liu cn v. Tuy vy trong mt s trng hp ta cn th hin tng phn ca biu , hoc v tnh thm m m c th chnh sa phm vi ca cc trc. Cu lnh nhsau:

2 Vy nu mun c V(m3) th sao? Hy thV(m^3) xem!


axis([xmin xmax ymin ymax])

trong:xmin, xmax ln lt l gii hn tri v phi ca trc honhymin, ymax ln lt l gii hn di v trn ca trc tung.

Ta cn nhp c 4 gi tr ni trn ca vec-tphm vi trc. Chng hn khi mun biu th mc nc ch trong khong thi gian t t = 100 s n t = 150 s, v hn ch cao mt nc t 0 n 0.4 m, ta g lnh:axis([100 150 0 0.4])

c

6Tvp

Tmv

V

0

0.2

0.4Qua trinh muc nuoc thuc do

(m)

0.3

0.4Qua trinh muc nuoc thuc do xa ton b th hin thi, ta g lnh:

0 50 100 150 200-0.4

-0.2

t (s)

z

Hnh 1: V dvbiudngng- 46 -

lf

.2. La chn mu v, nt v rng hp c nhiu ng nt vkhc nhau mu nt vkhc nhau. Nhng la chn ny clot(x, y, 'la chn')

rong, la chn l mt chui k tc 3 phd--

i m l mt k tchmu v, thng l chd l k hiu nh du cc im nt-- l mt hay hai k tthhin kiu nt v

d:100 110 120 130 140 1500

0.1

0.2

t (s)

z(m

)

Hnh 2: Biudngng sau khi chnh liphm vi cc trc, ta nn phn bit bng nhng kiu ngay trong cu lnh plot.

n quinh nhsau:

u ca tting Anh tng ng


- 47 -

plot(x, y, 'r') vthnt vmu(red). Khng c la chn kiu nt vcth,do my svkiu nt lin (mcnh).

plot(x, y, 'g--') vthnt vxanh lc (green). Nt vc chn l kiu ntt(--).

plot(x, y, 'b*-') vthnt vxanh lam (blue). Nt vc chn l kiu nt linvi ccim du sao (*-).

Nhvy c ththp cc kiu mu v nt vkhc nhau, theo bng sauy3:

Mu v Nt v im ntr red, - nt lin * du saog green, xanh lc -- ntt + du cngb blue, xanh lam : nt chm s hnh vungk black,en .- nt chm gch ^ tam gic

3 Thc ra ta c thla chn kiu v nt vtrc tip trn biuca MatLab bng cch chn Edit Plot

(hoc nttrn thanh cng c) ri nhy phi chut vo ng cn chnh v la chn Line Style (kiung), LineWidth (brng) hoc Marker (kiuim nt) (xem Hnh 3).

Hnh 3: Kiu nt vcng cc thuc tnh khc c thla chntrc tip sau khi chn chEdit Plot v nhy phi chut

vo ng biu


Theo mc nh, khi c mt ng mi c v ra thng c s bin mt. v nhiu ng trn cng mt biu ta cn g lnh:hold ontrc khi v cc ng tip theo.

Chng hn ta c th thm mt ng nt t nm ngang biu th mc nc bng 0 theo cch sau:hold on; plot([0 200],[0 0],':');

Bn thn trnng mc nc c th thm ccim du *: plot(t,z,'*-');

Nbg

N bg

6Mbb

-0.2

0

0.2


z(m

)

0 50 100 150 200-0.4

-0.2

0

0.2


z(m

)u mun ng khung th v to cc ngox onrid on

gc li, xa cc ng ng khung vox off

0 50 100 150 200-0.4

t (s)

Hnh 4: Biudngng vi hai nt vckiu khc nhau- 48 -

rid off

.3. To cc ch thch, ch gii trn ht biumc d mang nhiu thng tin nh

ng nhng ch thch (thng l nhng nt vng ch). Chng hn, vi v dtrn ta munt cc i (nhHnh 6). Cch lm c ththeo

Vo menu Insert Ellipse, vmt vng ttrnh dng ta ln lt g vo cc lnh:

ng dng, ch cn g:

t (s)

Hnh 5: Biuc khung vng dngnh vngi khi ta vn mun lm r thmn gin bng tay v ch thchchra trn biu vtr mc nccc bc sau:rn vo vtr nh ca ng qu


- 49 -

Vo menu Insert Text Box, vch ra mt khung chnht v g vo z max4 Vo menu Insert Arrow, vch mi tn chtkhung chvo vng trnMun xa cc ch thch, chcn chni tng cn xa, n Delete.

* Ch gii (legend):Khi c nhiung biutrn mtth, cn c ch gii (legend)phn bitchng. Giscng trnthqu trnh mc nc trn, ta bsung thm mtng mc nc tnh tonc tm hnh:z2 =[0.05 0.2 0.34 0.38 0.28 0.08 -0.21 -0.35 -0.23 -0.18 0.11 0.22 0.40.45 0.2 0.13 -0.02 -0.11 -0.32 -0.02 0.09];hold on; plot(t,z2,'-o');title('Qua trinh muc nuoc tai N23');

Trn thanh cng c, n nt (hoc menu Insert Legend). Sau hy nhy pphn ch gii mi xut hin, g vo tn ch gii cnt (Hnh 7).

4 Mun c zmax, hy thg z_{max}. G z_max cc khng, ti sao?

0 50 100 150 200-0.4

-0.2

0

0.2


t (s)

z(m

)

z max

Hnh 6: Biuvi cc ch thch


- 50 -

6.4. Xang biu , lu biu - Nu vsai mtng biuno ta c thxa bng cch chn menu Tools Edit Plot; chnng biu, n Delete hoc chn Delete trong danh mc khinhy phi chut trn Hnh 3.

- MatLab c thlu li biu chng ta to ra, di dng nhiu dng file nhchun hin nay: *.gif, *.png, *.jpeg, *.emf, *.eps v.v... Bn cnh , MatLab cnc mt dng file ring gi l *.fig, trong lu ton bthng tin ca cc ng,nt, im... trn biu. Do vy m file fig chi tit hnng thi thng c kchthc file ln.-lu biutrong MatLab ta chn Menu File Save, sau nhp tn cho filehnh m ta mun lu. Cng c thnhn vo biu tng Save ( ) trn thanh cngc. Ch chn kiu file hnh (Save as type) thch hp.

6.5. th LogaritTrong mt strng hp, cc thlogarit cn c sdng, chng hn biung cp phi ht. Munt thang logarit vi trc honh ta chcn thay tn lnhplot bng semilogx.

Chng hn ta cn vng cp phi ht vi mu bn ct sau:

ng knh (mm)

Khi lng (mg)

Hnh 7: Chnh sa tn ch gii tng ng vi ccng qu trnh


- 51 -

d < 0.15 9000.15 < d < 0.21 29000.21 < d < 0.30 160000.30 < d < 0.42 201000.42 < d < 0.60 89000.60 < d 1200(Ton b) 50000

Trc khi vthhy tnh tlbn ct tng ng vi mi khongng knh vtlcng dn:KhoiLuong = [900 2900 16000 20100 8900 1200];TiLe = KhoiLuong / 50000;

Hm cumsum gip ta tnh cng dn, chng hn:>> cumsum(TiLe)ans =0.0180 0.0760 0.3960 0.7980 0.9760 1.0000

Ta cn tnh tlP theo phn trm, cho nn:P = cumsum(TiLe) * 100;

ng knh (mm)

Khi lng (mg)

T l (%)

T l cng dn

P (%)

ng knh d (mm)

d < 0.15 900 1.8 1.8 0.150.15 < d < 0.21 2900 4.8 7.6 0.210.21 < d < 0.30 16000 32.0 39.6 0.300.30 < d < 0.42 20100 40.2 79.8 0.420.42 < d < 0.60 8900 17.8 97.6 0.600.60 < d 1200 2.4 100 1(Ton b) 50000 100

Sliu dngvthl hai ct sau cng: tlcng dn (P) vng knh (d).C P (%) khi lng bn ct mn hn d (mm). y githit rngng knhln nht bng 1 mm nhl gii hn trn ca biu.

d = [0.15 0.21 0.30 0.42 0.60 1];title('Bieu do duong cap phoi hat');xlabel('d (mm)');ylabel('P (%)');semilogx(d,P,'*-');grid on; box on;


Cc ngtv

6.6.Bng y,nhiu lc ta mun c mt dy (hoc bng) cc biuxp ktip nhau, c kchthc bng nhau tin vic so snh. MatLab htrhthng subplot (biu nh) vi cu lnh c dng chung nhsau:subplot(m,n,k);

100Bieu do duong cap phoi hatHnh 9: Vtr cc biutrong dy to bng lnh subplotthvi thang logarit trn trc y v trn c2 trc cngc thc hin ti cc cu lnh ln lt l semilogy v loglog.

Dy biu lnh figure ta c thto ra nhiu hnh vc lp trn nhiu ca s. Tuy v

100

0

20

40

60

80

d (mm)

P(%

)

Hnh 8: V dvi biuc trc theo thang logarit- 52 -


- 53 -

Sto ra mt bng gm (m n) biunh(m hng v n ct). Tip hnh thk(tnh ttrn xung di, tri qua phi) sc kch hot v chun bc v.

Chng hn, sau khi thc hin lnhsubplot(2,3,4);tac kt qunhHnh 8.

Gn hn na ta c thvit (trong trng hp m, n, k < 10):subplot 234

Xt mt v dn gin: ta cn vng qu trnh mc nc (z) v vn tc dngchy (v) theo thi gian (t), nhng trn hai biukhc nhau. c si chiuvthi gian gia hai biuta nn xp chng theo mt ct dc. Nhvy m = 2 vn = 1.

t = 0:5:100;z = [-0.14 -0.08 -0.05 -0.04 0.01 0.07 0.15 0.23 0.25 0.37 0.4 0.45 0.550.6 0.66 0.76 0.82 0.91 1 1.03 1.14];v = [0.84 0.89 0.91 0.89 0.91 0.88 0.92 0.97 0.97 0.97 0.99

1.02 0.96 1.03 0.98 1.04 1.04 1.11 1.04 1.12 1.16];

subplot 211plot(t, z); xlabel('t (phut)'); ylabel('z (m)');title('Duong qua trinh muc nuoc tai diem A1');

subplot 212plot(t, v, 'g'); xlabel('t (phut)'); ylabel('v (m/s)');title('Duong qua trinh luu toc tai diem A1');Kt qunhtrn Hnh 7.5

5 MatLab cn c lnh plotyy cho php hai trc tung vi haii lng khc nhau (chng hn z v v) trncng mt biu.


0 20 40 60 80 100-0.5

0

0.5

1

1.5

t (s)

z(m

)

Duong qua trinh muc nuoc tai diem A1

0 20 40 60 80 1000.8

1

1.2

1.4

t (s)

v(m

/s)

Duong qua trinh luu toc tai diem A1

Hnh 10: Haing qu trnh trn hai subplot- 54 -


- 55 -

7. CHNG VII: TH KHNG GIAN

Trong kthut rt cn cc biu khng gian. Thng gp nht l cc bnh (bn a hnh ca mt khu vc nh). Bn cnh , biukhng gian cn cthc dngbiu dinsua hnh hay mt trng khng gian ni chung(nhit , kh p ...). Trong tt ccc trng hp ni trn, lun c mt bin (z)c biu din theo hai bin khng gian trn mtt (x, y).

7.1. Cc dng cbn

Cc dng cbnMatLab htrnhiu phng php biu din sliu; trong ti liu ny ta lm quenvi mt sloi cbn, l: Mng mu (color patch) ngng mc (contour) Bmt 3 chiu (surface)

Hy bt u vi mt v dn gin l m phng a hnhy bin ca mt khuvc gitng c cho trong ma trn z. y bin ny c dng tng tnhmtct ngang cn bng (Dean) theo phng trnh:

z = - 0.1 y2/3

Vi trc x dc theo bi bin v trc y hng ra khi. Ta xt li ta trn mtbng, cc im nt li c phm vi 0 < x < 200, 0 < y < 200. Khong cch giaccim nt li theo phng x l x = 10, theo phng y l y = 4. Ngha l taca tt cccim nt li c dng:

x i , y i=[ 0,0 10,0 200,00,4 10,4 200,4 0,200 10,200 200,200]Lnh meshgrid sgip ta lmiu:[x, y] = meshgrid(0:10:200, 0:4:200);

(Mt ln na cn ch du ; cui cu lnh, nu khng rt nhiu con sscin ra mn hnh!)

Lnh meshgrid ly hai thng s: thng svec-tthnht l cc ta trn trc x,thng svec-tthhai l cc ta trn trc y. Kt qutac mt ma trn cc


- 56 -

im trn mt vng hnh chnht (51 21) c cc ta tng ng dng tccvec-ttrn6. Sau mng z sc tnh tmng y theo cng thc Dean:z = -0.1 * y .^ (2/3);

Trong cn ch php tnh ly tha cho tng phn t.

Cu lnhn gin nhthin thmngmu biu thz l:pcolor(x, y, z)

Bng mu mcnhc dng c tn ljet.7 Ta c ththay bng mu ny bngmt sbng mu khc, chng hn:colormap(gray); pcolor(x, y, z);

Cn hin tn cc trc x v y theo cchtng tnhta lm vi biu dngng:xlabel('x(m)'); ylabel('y(m)');

C thhin ththanh ch thch bn cnhbng mu bng lnh:colorbar

Vit thm dng chz(m) bn cnh thanh chdn mu ny bng cch Insert Text Box. Xa bng bao ca hnh chnht bng cch nhy phi chut LineStyle None.

Ch rng khi hin cc bn a hnh / bn vmt bng, trong hu ht cctrng hp ta munt nhng tlbng nhau trn hai trc x v y. Khi ta dnglnh:axis equal;

6 x v yu l ma trn 2 chiu. Do ccim trn li xp theo hng nn ta nhn thy cc phn tgingnhau trn mi ct ca x (ccim c cng tax); v tng ti vi y.

x= [0 10 2000 10 200 0 10 200] v y=[0 0 04 4 4

200 200 200]7 Bng mu jet mc d rc rnhng khng hiu qukhi in trngen, thay vo nn dng bng mu

gray.

Hnh 11: Bng mu biu tha hnhy bin vimt ct ngang cn bng theo Dean


- 57 -

Tip theo ta c khung cathli cho va vi bng mu8:axis tight;

Bn cnh cch dng biu mng mu, cnc thbiu thdi dng ng ng mc.Cch ny thng c dng vi cc bn inln giy:[C,h] = contour(x,y,z);9

Cc ng ng mc ca y bin xuthin song song vi trc x, nhng cn phi cgi trstrnngng mc:clabel(C,h);

V cng nhi vi mng mu, ta c thcnchnh cc trc mt cch hp l:axis equal tight;xlabel('x(m)'); ylabel('y(m)');

Ta cng c thbiu din a hnh di dng khng gian (3 chiu) sdng lnhsurf hoc mesh:figure; surf(x, y, z);figure; mesh(x, y, z);Sau hy sdng cng cxoay hnh bng cch n nt Rotate 3D trn thanhcng c( ).

8 Hai lnh trn c thc gp li thnh mt lnh axis equa9 Cch vit ny c vkhc vi cu lnh thng thng, tuy nhi

di dng hm. Chng hn, hy g thlnh zzz = plot(t,clabel(contour(x,y,z)); ?

-3 -3 -3

-2.5 -2.5 -2.5

-2 -2 -2

-1.5 -1.5 -1.5

-1 -1 -1

-0.5 -0.5 -0.50 0 0 0

x (m)

y(m

)

0 50 100 150 2000

20

40

60

80

100

120

140

160

Hnh 12:ngng mc biu dinahnhy bin vi mt ct theo Deanl tightn theo MatLab, cc lnh vu c thvitz). Mt khc, c g khc nu ta g lnh


- 58 -

7.2. Ch nh cc v tr trong khng giaKhi th hin d liu khng gian bng mng mch ra nhng v tr tha mn mt iu kin nochng bng nhng im ring.

Chng hn, hy chra cc vtr c z < -3trong v dtrn. C hai bc nhsau: Tm cc chs(i,j) trong ma trn c gi

trtha mn z(i,j) < -3 Chm cc im xc nh bi x(i,j), y(i,j)

ln mng mu

ind = find(z < -3);hold on;plot(x(ind), y(ind), ... 'k.');

7.3. Mt ct a hnhTrong nhiu trng hp cn biu din mt mV tng qut hn, c thl phn bsu nbinc trng no dc theo mt tuyn xcnh

S liu ca mt ct c ly t 1 ct (hoc Chng hn, mt ct c x = 100 m (tng ng vma trn z):

Hnh 13: Biu din mt ct Dean di dngmt 3 chiu Hnh 14: Biu din mt ct Dean di dng li

3 chiu

Hnh 15: nh du trn mng mu 2 chiut ct a hnh tbiu hai chiu.c, p sut, mn, hay bt k mttrn mt bng.

hng) t mng 2 chiu tng ng. i ct th 11 (trong s 21 ct) trong n 2 chiuu, trong mt s trng hp ta phi

. Cchn gin nht lnh du


- 59 -

ymc1 = y(11,:);zmc1 = z(11,:);plot(ymc1, zmc1, '*-');xlabel('y (m)'); ylabel('z (m)');

7.4. Trng vctTrong cc bi ton kthut thyng lc thng yu cu m phng trng dngchy. Biu din dng chy trong khng gian 2 chiu c htrrt tt trongMatLab bng cu lnh:quiver(x, y, u, v)

trong x, y l hai ma trn cha ta ca tt ccc im theo phng ngang(thng c pht sinh bng lnh meshgrid); u v v l hai ma trn cha thnhphn lu tc ca tt ccc im (u l lu tc theo phng x, v l lu tc theophng y).

Gistrong thmc hin thi c file data_u.txt v data_v.txt, mi file chamt ma trn gi tru v v. Khi , hai ma trn nycc nhsau:u = dlmread('data_u.txt');v = dlmread('data_v.txt');

Gisu v vc c kch thc ging nhau = sim trn trc x sim trntrc y:[sizex, sizey] = size(u);

Ta mun biu din ln hnh vi, chng hn, x = 10 m v y = 5 m:dx = 10; dy = 5;[x, y] = meshgrid(0:dx:(sizex 1)*dx, 0:dy:(sizey -1) * dy);figure;quiver(x, y, u, v);xlabel('X(m)'); ylabel('Y(m)');axis equal tight;


0 20 40 60 800

10

20

30

40

50

X(m)

Y(m

)

Hnh 16: Biu din trng vec-t- 60 -


- 61 -

8. PHN BI TP

Bi tp s1:Tnh ton sng theo s liu sau:

T = 8 s, Ho= 2 m,

o= 30

o

.

Ggi tr cho 3 bin T, Ho, alpha0.Th Co.Th L

o

M 1 file disperse.m bng cch g>> edit disperseVi file mi m hy g vo ni dung sau:function [L] = disperse(h, Lo) L = Lo;err = Inf;while err > 0.1;Ltry = Lo * tanh(2*pi*h / L);err = abs(Ltry - L);L = Ltry;end;Ta thit lp c hm tnh L t cc gi tr h v Lo cho trc

Hy thit lp mt vec-th cha su khc nhau: 3 m, 3.2 m, ..., 4 m. Tnh L ti cc su cho bi h.Th C tng ng vi LTnh sin_alpha theo cng thcsin= sin

o* C / Co(ch n v !)

Th alpha (dg lnh asin)

Th Kr = sqrt(coso/ cos)

Th Ksh theo cg thc Ksh =

Tnh H = Ho Ksh Kr

Ghi li c gi tr ca H


- 62 -

Vit kt qu ra file ketqua.txt

Bi tp s2

Quan h gia vn chuyn bn ct S v lu tc u c quan h dng: S = aub. xc nh cc h s a v b ngi ta tin hnh th nghim v thuc kt qu sau:u (m/s) 0.2 0.35 0.57 0.68 0.81 0.96 1.12

S(m3/s.m)

0.0002 0.0018 0.0159 0.0282 0.0609 0.1258 0.2858

1) Hy nhp cc gi tr u v S vo hai vec-t, sau tnh X v Y l logarit tngng ca u v S.2) V th im ca X v Y.3) Hai h s a v b c xc nh bng cch da vo quan h: log S = log a + b log u, hay Y = b X + log a.

S dng hm polyval tnh b v log a trong phng trnh trn nhsau:p = polyval(X, Y, 1)

Phn t u ca vec-tp chnh l b; phn t th 2 ca p bng log a.Hy tnh a.

4) V th ng thng: Y = b X + log a ln cng h trc vi cc im chm cu 2).

Bi tp s3

1) Mt chui s liuoc vn tc dng chy c pht sinh bi:t = 0:0.5:48;N l dy s ngu nhin c chiu di bng length(t) u = 0.4 + 0.12 sin(2t / 24) + 0.05 N

2) Tnh ng sut tip ti ven b, bitC = 60 m0.5/s = g u2 / C2Thit lp subplot 3 hng 1 ct. Hai vng trn v hai th u ~ t, ~ t.

3) Nu b c thnh phn t st vi ng sut tip ti hn c = 0.65 N/m2, hy ch ra xem c bao nhiu thi im xut hin >c .


- 63 -

4) Cng thc xi l ng b c xc nh bi:

Hy tnh khong cch xi l E.

E = 10 (c) nu >c= 0 trng hp cn li

V E ~ t ln vng th di cng to bi subplot.

Bi tp s4:Cho vctX = [10 20 30] v Y = [10 40 30].1. Tnh din tch tam gic to bi 3 nh c ta X(1)Y(1), X(2)Y(2), X(3)Y(3).2. Tng qut hn, tnh din tch a gic n cnh (trn mt phng 2 chiu) vi ta xi v yi ca nh th i cho bi phn t th i ca vctX v Y tng ng (do X v Y l 2 vctc cng chiu di = n).

LI GII

Bi tp s1:Hng dn: to mt script file c tn baitap1.m, son tho ni dung di y, vghi li. Sau chy file ny, ta s thu c kt qu.

% baitap1% Inputs: T, H0, alpha0% Outputs: C0, L0, L%-------------------------------------------------------------

clear all;

g=9.81;T=8;H0=2;alpha0=30;%-------------------------------------------------------------

L0=g*T^2/(2*pi)C0 = L0/T;h=[3:0.2:4]

% n=length(h);% for i = 1:n


- 64 -

% L(i)=disperse(h(i), L0);% end;

L = disperse(h,L0); % Wave length

C=L/T % Wave celeritysin_alpha=sin(alpha0)/C0*Calpha = asin(sin_alpha) % arcsinKr=sqrt(cos(alpha0)./cos(alpha)) % Refraction coefficientk=2*pi./L % Wave numberKsh=sqrt(1./tanh(k.*h)/(1+2*k.*h/sinh(2*k.*h))) % Shoaling coefficientH=H0*Ksh.*Kr % Wave height


(Bi ny lm theo cc bc nhtrn lp: tnh log(u), log(S), v ln trc ta thng (khng v ln trc loga v y ta tnh gi tr ca loga ri), v xcnh cc h s a, b ca ng thng mt cch gn ng trn th).


clear all;t=0:0.5:48N=rand(1,length(t));u=0.4+0.12*sin(2*pi*t/24)+0.05*Nplot(N);hold on;plot(u,'+');C=60;Rho = 1000;g=9.81;To = Rho*g/C^2*u.^2plot(t,To)hold ongrid onToc = 0.6510 * (To - Toc) .* (To > Toc) + 0 .* (To


- 65 -

function Sdagiac = dientich(x,y);% Tinh dien tich da giac

n = length (x);m = length (y);if m ~=n

'Error: 2 vecto X va Y can co chieu dai bang nhau!'else

Sdagiac = 0;for i = 1:(n-1)

Sdagiac = Sdagiac + 0.5*(y(i)+y(i+1))*(x(i+1)-x(i));endSdagiac = Sdagiac + 0.5*(y(n)+y(1))*(x(1)-x(n));

end2. Va ri ta to ra mt hm mi trong Matlab, vi tn l hm dientich. S dng hm ny ta c th d dng tnh c din tch a gic ni chung v tam gicni ring bng cch gi hm tca s nhp lnh

>> dientich(X,Y) Lu rng hm tnh din tch ngm nh rng 2 vc tX, Y y cha s liu cho trc v ta cc nh ca a gic theo nhquy c. Hn na, khi nhp ta ta nh s cc nh t 1 n n theo chiu kim ng h.

* tnh din tch tam gic S vi chiu di 3 cnh cho trc l a, b, c, bn c th th thut ton khc nhsau:

))()(( cpbpappS vi p=(a+b+c)/2 l mt na chu vi.


- 66 -

9. TI LIU THAM KHO:

1. Matlab R14 - Helps & Demos, The Mathworks, Inc., 2004

2. David F. Griffths, An introduction to Matlab, Department of Mathematics-The University of Dundee Sweden, 1996

3. John M. Stockie, A Whirlwind Tour of MATLAB for Students of CS 3113,Department of Mathematics and Statistics, University of New Brunswick -Canada, 2003

4. Bill Mason, Introduction to Matlab, Northeastern University - College ofComputer and Information Science USA, 2003.

5. Tobin A. Driscoll, Crash course in MATLAB, Department of MathematicalSciences - University of Delaware USA, 2006

6. Nguyn Hong Hi & Nguyn Vit Anh, Lp trnh Matlab v ng dng,NXB Khoa hc v K thut H Ni, 2005

7. Nguyn Phng Quang, Matlab & Simulink dnh cho k siu khin t ng, NXB Khoa hc & K thut H Ni, 2006

8. Nguyn Phng Tho, Programming in Matlab, handouts, 20079. H. Thy Li, Matlab version 7.0 cbn, Kha tin hc nng cao cho cn

b ging dy ca d n 95 b NN&PTNT, handouts, 200710. Knight A., Basics of MatLab and beyond, CRC Press, 2000

11. Timothy A. Davis & Kermit Sigmon, Matlab Primer, Chapman &Hall/CRC

12. R. J. Braun, Beginning Matlab Exercises, Department of MathematicalSciences University of Delaware USA.

matlab lecture notes

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