BC U LM VIC VI MATLAB Gii thiu MATLAB l mt b chng trnh phn mm ln
dnh cho tnh tan k thut. ta c th dng MATLAB : Tnh tan. Pht trin thut
tan. Thu thp d liu. M hnh v m phng. Phn tch d liu. V th. Giao din
ha. MATLAB l tn vit tt t MATrix LABoratory. Nh tn ca phn mm cho
thy, phn ct li ca phn mm l d liu c lu di dng array (ma trn) v cc
php tnh tan ma trn, gip vic tnh tan trong MATLAB nhanh v thun tin
hn so vi lp trnh trong C hay FORTRAN. c bit, kh nng tnh tan ca
MATLAB c th d dng c m rng thng qua cc b toolbox. Toolbox l tp hp cc
hm MATLAB (M-file) gip gii quyt mt bi tan c th. MATLAB gm 5 phn
chnh: Development Environment: l mt b cc cng c gip ta s dng cc hm v
tp tin ca MATLAB. N bao gm: MATLAB desktop, Command Window, a
command history, an editor, debugger, browsers for viewing help,
the workspace, files, the search path. MATLAB Mathematical Function
Library: tp hp cc hm tan hc nh sum, sine, s hc, v.v. MATLAB
Language (scritp): ngn ng lp trnh bc cao. Graphics: cc cng c gip
hin th d liu di dng th. Ngai ra n cn cho php xy dng giao din ha.
MATLAB Application Program Interface (API): b th vin cho php ta s
dng cc hc nng tnh tan ca MATLAB trong chng trnh C hay FORTRAN. Giao
din Command Window: y l ca s lm vic chnh ca MATLAB. Ti y ta thc hin
tan b vic nhp d liu v xut kt qu tnh tan. Du nhy >> bo hiu
chng trnh sn sng cho vic nhp d liu. Ta kt thc vic nhp d liu bng cch
nhn phm Enter. MATLAB s thc thi dng lnh m ta nhp vo Command Window
v tr kt qu trong Command Window. Command History: Lu li tt c cc lnh
m ta nhp vo trong Command Window. Ta c th xem li tt c cc lnh bng
cch dng scroll bar, hay thc hin li lnh bng cch nhp kp ln dng lnh.
Ngai ra ta cn c th cut, paste, delete cc lnh. Workspace browser:
trong MATLAB cc d liu c lu trong bin. Workspace browser lit k tt c
cc bin m ta ang s dng trong MATLAB. N cung cp thng tin v kch thc,
loi d liu. Ta c th truy cp trc tip vo d liu bng cch nhn kp vo bin
hin th Array editor. Launch pad: cho php ngi dng truy cp nhanh vo
cc b Toolbox, phn Help. Editor: dng san tho v debug cc M-file ca
MATLAB.
Matlab introduction
1/21
Current Directory Browser: xem cc file trong th mc hin hnh.
Hnh 1. MATLAB desktop
Hnh 2. MATLAB preference dialogMatlab introduction 2/21
Hnh 3. m-file editor Mt s thao tc c bn trong MATLAB Trong
MATLAB, thanh trnh n thay i ty theo ca s m ta la chn. Tuy vy cc
trnh n File, Desktop, Window, Help c mt hu ht trong cc thanh trnh
n. Trnh n File: New: to mt i tng mi (bin, m-file, figure, model,
GUI). Open: m mt file theo nh dng ca MATLAB (*.m, *.mat, *.mdl)
Import data: nhp d liu t cc file khc vo MATLAB. Save workspace: lu
cc bin trong MATLAB vo file *.mat. Set path: khai bo cc ng dn ca cc
th mc cha cc m-file. Preferences: thay i cc nh dng v font, font
size, color cng nh cc ty chn cho Editor, Command Window v.v. Page
Setup: nh dng trang in. Print: in. Trnh n Desktop: Desktop layout:
sp xp cc ca s trong giao din. Save layout: lu cch sp xp ca s. Trnh
n Window dng kch hat (activate) ca s. Nt Start cung cp shortcut ti
cc cng c trong MATLABMatlab introduction 3/21
Bin Tn ca bin: c th cha ti 31 k t. phn bit ch hoa v thng. c th
cha gch thp _ bt u bng ch ci. MATLAB khng yu cu ta phi khai bo kch
thc ca bin. to mt bin mi ta ch cn g tn bin, du bng v gi tr gn cho
bin. Nu bin tn ti trong MATLAB, gi tr ca n s c thay i. V d:
>> variable_1=25; Nu ta ch nhp tn bin, gi tr ca bin s hin th
trong Command Window V d: >>variable_1 25 >> Lu rng
trong MATLAB nu ta kt thc cu lnh bng du ; th Command Window s khng
hin th kt qu tnh tan ra mn hnh. V d: >> variable_1; >>
hin th cc cu lnh nhp trc vo Command Window ta c th dng phm Arrow.
Mt s tn bin c dnh ring cho MATLAB: pi: s pi. i, j: s o. inf: v cng.
NaN: khng phi l s. Tan t Cc tan t c bn : + : cng. - : tr. * : nhn.
/ : chia. \ :chia bn tri (dng cho ma trn). ^ : ly tha. : han v. ( )
(du ngoc): th t u tin tnh tan. Hm Chng trnh MATLAB cung cp mt tp hp
rt ln cc hm tan hc :Matlab introduction 4/21
Hm tan s cp (elemetary functions): nh sin, cos, tan, atan, log,
log10, exp, sqrt, round, ceil, floor, sum,min, max, mean, abs. Hm
tan chuyn dng: nh besselj (Bessel function of the first kind),
bessely (Bessel function of the second kind), beta (Beta
function),erf (Error function),gamma (Gamma function), primes
(Generate list of prime numbers), cart2sph (Transform Cartesian to
spherical coordinates) v.v. Hm chuyn dng cho ma trn.
Lu : xem cc danh sch cc hm m MATLAB cung cp ta dng lnh: help
elfun, help specfun, help elmat. bit cch s dng mt hm ta dng lnh
help theo sau bi tn ca hm. V d: >> help sine Biu thc Biu thc
trong MATLAB bao gm bin, du =, cc tan t v hm V d: >>
variable_2=sine(5)+(4+variable_1)*exp(2); Kim sat ch nhp xut d liu
cho Command Window Hm format: Hm format kim sat nh dng xut ra mn
hnh ca cc gi tr. Hm ny ch kim sat nh dng xut ra m khng nh hng ti nh
dng ca d liu c lu tr. V d: >> x = [4/3 1.2345e-6]; >>
format short 1.3333 0.0000 >> format short e 1.3333e+000
1.2345e-006 >>format short g 1.3333 1.2345e-006
>>format long 1.33333333333333 0.00000123450000
>>format long e 1.333333333333333e+000 1.234500000000000e-006
>>format long g 1.33333333333333 1.2345e-006 >>format
bank 1.33 0.00 >>format rat 4/3 1/810045 >>format hex
3ff5555555555555 3eb4b6231abfd271 Dng ch mc Preferences/ Command
Window thay i nh dng ca Command Window Khng xut kt qu ra mn
hnh:Matlab introduction 5/21
Dng du ; cui cu lnh Command Window khng xut kt qu ra mn hnh. Cu
lnh qu di Nu cu lnh qu di ta dng du 3 chm thng bo cu lnh c tip tc
dng tip theo. V d: >>s = 1 -1/2 + 1/3 -1/4 + 1/5 - 1/6 + 1/7
... -1/8 + 1/9 - 1/10 + 1/11 - 1/12; Ma trn Trong MATLAB ma trn l
mt array cha cc d liu. nhp mt ma trn vo MATLAB ta c th dng cc cch
sau: Nhp trc tip vo Command Window. Nhp t cc file d liu. Dng cc hm
trong MATLAB. Nhp trc tip vo Command Window: V d: >>
my_vector = [1 2 3] my_vector = 1 2 3 >> my_matrix = [1 2 3;
4 5 6; 7 8 9] my_matrix = 1 2 3 4 5 6 7 8 9 >> my_matrix = [1
2 3 456 7 8 9] my_matrix = 1 2 3 4 5 6 7 8 9 Nhp t cc file d liu:
Dng menu File/ Import Data chn file d liu m ta mun nhp vo MATLAB.
Dng cc hm trong MATLAB: Hm ones(r,c) to mt ma trn c r hng v c ct vi
cc gi 1. Hm zeros(r,c) to mt ma trn c r hng v c ct vi cc gi 0. Hm
eye(r) to mt ma trn c r hng v r ct vi cc gi 1 ti ng cho v gi tr 0
ti cc phn t cn li. rand(r,c) to mt ma trn c r hng v c ct vi cc gi
tr ngu nhin t 0 ti 1 theo phn b uniform. randn(r,c) to mt ma trn c
r hng v c ct vi cc gi tr ngu nhin theo phn b Normal n v. Ch s ca ma
trn truy cp ti cc gi tr trong ma trn ta dng ch s.Matlab
introduction 6/21
V d: >> A=[1 2 3; 4 5 6; 7 8 9]; >> A(1,2) ans = 2
>>A(end,end) 9 Tan t : (2 chm) y l mt tan t c bit ca MATLAB.
V d: >>1:5 ans = 1 2 3 4 5 >>1:2:10 ans = 1 3 5 7 9
>>10:-3:1 ans = 10 7 4 1 >> A=[1 2 3; 4 5 6; 7 8 9];
>>A(2,1:3) ans= 4 5 6 Thay i kch thc ca ma trn Concatenation-
kt hp cc ma trn V d: >>a=[1 2 3]; >>b=[4 5 6];
>>ab=[a ; b] ab= 1 2 3 4 5 6 >>ab=[a b] ab= 1 2 3 4 5 6
Xa mt hng hay ct ca ma trn V d: >>a=[ 1 2 3 456 7 8 9];
>> a(2,:)=[] a= 1 2 3 7 8 9 >>a=[ 1 2 3 456 7 8
9];Matlab introduction 7/21
>> a(:,2)=[] a= 1 3 4 6 7 9 >>>>a=[ 1 2 3 456
7 8 9]; >> a(1:2,:)=[] a= 7 8 9 Cc tan t cho ma trn A+B : cng
ma trn A v B (2 ma trn cng kch thuc) A - B : tr ma trn A v B (2 ma
trn cng kch thuc) A*B : nhn ma trn (s ct ca A bng s hng ca B) A.*B
: nhn tng phn t ca A v B (A, B cng kch thc) inv(A) : nghch o A B/A=
(A'\B')' hay xp x B*inv(A) B./A: chia tng phn t ca B cho A (A, B
cng kch thc). A\B: nu A l ma trn vung, A\B xp x inv(A)*B. Nu A l ma
trn nxn v B l vector ct vi n phn t th X = A\B l li gii cho h ng thc
AX = B. A.^B: ly tha tng phn t ca A vi tng phn t ca B.
Structure thun tin cho vic qun l v s dng, ta c th tp hp nhiu bin
li trong mt structure. Mt structure c tao nh sau: struct(name_1,
value_1,name_2, value_2,) trong name_* l tn ca field l thnh phn ca
mt structure v value_* l gi tr m ta cn gn cho field. >>
myst=struct(data, [1 2 3], name,John Down) myst = data: [1 2 3]
name: 'John Down' truy cp d liu trong structure ta dng du .
>>myst.data(1)+1 ans = 2 Optimization toolbox B cng c ti u ha
cho php: Ti thiu phi tuyn khng rng buc (Unconstrained nonlinear
minimization) Ti thiu phi tuyn c rng buc (Constrained nonlinear
minimization) Quy hach tuyn tnh v tan phng (Quadratic and linear
programming) Nonlinear least squares and curve-fitting
Matlab introduction
8/21
Hm bintprog(f, A, b, Aeq, beq, x0) Dng gii bi tan quy hach ngyn
(binary integer programming)min f Tx
st
Aeq x beq
A x b
V d: min -9x1 -5x2 -6x3 -4x4 st 6x1+3x2+5x3+3x2 9 x3+ x4 1 -x1
+x3 0 -x2 +x4 0 x1,x2,x3,x4 l nh phn >> f=[-9 ; -5 ; -6 ; -4]
; >>A=[6 3 5 2 ; 0 0 1 1 ; -1 0 1 0 ; 0 -1 0 1] ;
>>b=[9 ; 1 ;0 ; 0] ; >>x=bintprog(f,A,b) x= 1 1 0 0 Hm
linprog(f,A,b,Aeq,beq,lb,ub) Dng gii bi tan quy hach tuyn tnhmin
fT
x
st A x b
Aeq x beq
lb x ub
V d: min -5x1 -4x2 -6x3 st x1 x2 + x3 20 3x1 + 2x2 + 4x3 42 3x1
+ 2x2 30 0 x1, 0 x2, 0 x3 >>f=[-5 ; -4 ; -6] >>A=[1 -1
1 ; 3 2 4 ; 3 2 0] ; >>b=[20 ; 42 ; 30] ;
>>lb=zeros(3,1) ; >>x=linprog(f,A,b,[],[],lb) x= 0.0
15.0 3.0
Matlab introduction
9/21
Hm x = fminbnd(fun,x1,x2) Tm cc tiu ca hm fun(x) vi x1 x x2 V d:
Tm cc tiu hm 0.5x3-x2-x+exp(0.1x) >>
f1=inline('0.5*x^3-x^2-x+exp(0.1*x)','x') f1 = Inline function:
f1(x) = 0.5*x^3-x^2-x+exp(0.1*x) >> [x,fval]=fminbnd(f1,0, 3)
x= 1.6827 fval = -0.9487 Hm fiminunc(fun,x0) Tm cc tiu ca hm a bin
fun (x l vector) V d:
>>f2=inline('2*x(1)^4+x(2)^4-2*x(1)^2-2*x(2)^2+4*sin(x(1)*x(2))','x')
f2 = Inline function: f2(x) =
2*x(1)^4+x(2)^4-2*x(1)^2-2*x(2)^2+4*sin(x(1)*x(2)) >>
[x,fval]=fminunc(f2,[1 -1]) x= 0.9039 -1.1732 fval = -4.6476 Hm
fmincon(fun,x0,A,b,Aeq,beq,lb,ub) min hm phi tuyn fun(x) st A x
bAeq x beq
lb x ub
V d: min f(x)= -x1*x2*x3 -x1-2*x2-2*x3 0 x1+2*x2+2*x3 72
>> f3=inline('-x(1)*x(2)*x(3)','x') f3 = Inline function:
f3(x) = -x(1)*x(2)*x(3) >> A=[-1 -2 -2; 1 2 2]; >>
b=[0; 72]; >> [x,fval]=fimcon(f3,[10;10;10],A,b) x=
24.0000Matlab introduction 10/21
12.0000 12.0000 fval = -3.4560e+003 Statistics toolbox B cng c
vi hn 200 hm h tr tnh tan trong: Probability Distributions: h tr 20
phn b xc sut khc nhau, cung cp cc hm phn b, mt , tch ly, nghch o, b
to s ngu nhin. Ngai ra n cn cho php xc nh phn b cho d liu.
Descriptive Statistics: cung cp cc hm cho thng k m t. Linear
Models: h tr one-way, two-way, and n-way analysis of variance
(ANOVA), analysis of covariance (ANOCOVA), hi quy (regression).
Hypothesis Tests: hm cho cc kim nh. Statistical Plots: h tr v cc th
thng k. Design of Experiments (DOE): h tr vic thit k thc nghim.
Probability Distributions normpdf(X,MU,SIGMA) tnh gi tr ca hm mt ti
X cho phn b Normal c tham s MU v SIGMA. R = normrnd(MU,SIGMA,m,n)
to mt ma trn R(m,n) cha cc gi tr ngu nhin c phn b Normal vi tham s
MU v SIGMA. norminv(P,MU,SIGMA) tnh gi tr nghch o ca xc sut p ca hm
phn b Normal tch ly vi tham s MU v SIGMA.
[muhat,sigmahat,muci,sigmaci] = normfit(DATA, alpha) c lng tham MU
v SIGMA vi tin cy100(1 - alpha) % cho d liu DATA theo phn b Normal.
V d: X l bin ngu nhin nh thc vi n=50, p=0,3. Tm P(X>
p=binocdf(17,50,0.3) p= 0.7822 V d: Tm tham s =1/ cho d liu c phn b
hm s m vi tin cy l 99% >>data = exprnd(3, 100, 1);
>>[parmhat, parmci] = expfit(data, 0.01) parmhat = 2.7292
parmci = 2.1384 3.5854 Descriptive Statistics mean(x) tnh trung bnh
cho mi ct d liu trong X. var(X) tnh phng sai cho mi ct d liu trong
X. prctile(X,p) tnh s phn v p% ca d liu X. p trong khang [0 100]
skewness(X), kurtosis(X) tm skewness v kurtosis cho mi ct d liu ca
X.Matlab introduction 11/21
V d: >> x=[2 3 4 5]; >> var(x) ans = 1.6667
Statistical plotting boxplot(X) to th box- whisker cho mi ct d liu
trong X. normplot(X) v th phn b Normal cho mi ct d liu trong X.
hist(X) v th histogram cho d liu X. pareto(X) v th Pareto cho d liu
X V d: >> boxplot(x)
Hnh 4. boxplot Linear model p = anova1(X) tnh bng one-way ANOVA
so snh trung bnh ca 2 hay nhiu ct d liu trong ma trn mxn X, trong
cc ct cha mu c m quan sat c lp. Hm tr li gi tr p gi thuyt H0. p =
anova2(X,reps) tnh two-way ANOVA so snh trung bnh ca 2 hay nhiu ct
v 2 hay nhiu hng cc quan st trong ma trn X. D liu trong cc ct tng
ng vi cc thay i trong yu t A, d liu trong hng tng ng vi thay i
trong yu t B. Nu c hn mt quan st trong mt t hp ta dng reps. V d:
>>X = meshgrid(1:5); >>X = X + normrnd(0,1,5,5)
>>X = -0.0741 2.7782 2.2129 1.2018 1.9937 3.7520 1.7629
2.5245 2.8331 -0.2882 3.3643 2.1838 0.0470 2.4820 5.0941 >>p
= anova1(X) p=Matlab introduction
4.0802 5.7902 3.0627 5.1053 4.6357 4.8414 5.6820 5.8709 4.5936
4.8052
12/21
4.0889e-007 V d: C 2 yu t A v B. A c 3 cp v B c 2 cp. D liu A c
xp theo ct v B theo hng. >>pop =[ 5.5000 4.5000 3.5000 5.5000
4.5000 4.0000 6.0000 4.0000 3.0000 6.5000 5.0000 4.0000 7.0000
5.5000 5.0000 7.0000 5.0000 4.5000]; >> p = anova2(pop,3) p=
0.0000 0.0001 0.7462 Php so snh a = =b (eq(a,b))- so snh bng: so
snh cc phn t ca ma trn a v b. Php so snh n tr v mt ma trn c gi tr 1
nu a(i,j)=b(i,j). a~ =b (ne(a,b))- khc a=b (ge(a,b))- ln hn hoc
bng. Php tnh logic ~a (not(a)) cho mt ma trn vi phn t l 1 nu phn t
tng ng ca a l 0 v 0 nu phn t tng ng ca khc 0. a&b (and(a,b))
cho mt ma trn c phn t l 1 nu phn t tng ng ca a v b khc 0 v bng 0 nu
mt trong 2 phn t tng ng ca a,b bng 0. a|b (or(a,b) cho mt ma trn c
phn t l 1 nu mt trong 2 phn t tng ng ca a v b khc 0 v bng 0 nu c 2
phn t tng ng ca a,b bng 0. xor(a,b) cho mt ma trn c phn t l 1 nu ch
mt trong 2 phn t tng ng ca a v b khc 0 v bng 0 nu c 2 phn t tng ng
ca a,b bng 0 hay khc khng. Script Lnh if C php: if expression
statements end ngha: MATLAB nh gi expression, nu expression cho gi
tr true hay khc khng, MATLAB s thc hin statement C php: if
expression1 statements1Matlab introduction 13/21elseif expression2
statements2 else statements3 end ngha: MATLAB nh gi expression1, nu
expression1 cho gi tr true hay khc khng, MATLAB s thc hin
statement1. Nu expression1 cho gi tr false v expression2 cho gi tr
true s thc hin statement2. Lnh switch C php: switch switch_expr
case case_expr statement,...,statement case
{case_expr1,case_expr2,case_expr3,...} statement,...,statement ...
otherwise statement end Loop for C php: for varname=x:y:z statement
statement end for varname=[a b c ...] statement statement end trong
varname phi l tn bin. x, y, z c th l s thc hay biu thc Loop while C
php while expression statements end ngha: lp li statement khi no
expression c tt c phn t khc khng. Lnh continueMatlab introduction
14/21chuyn sang bc lp tip theo Lnh break ngng v thot ra vng lp. Lnh
return tr v chng trnh gi hm hay script. Symbolic Math toolbox B cng
c b sung kh nng gii tan vi cc k hiu tan hc cho MATLAB. Li ca b cng
c ny c pht trin bi Maple. N cho php thc hin cc php tan sau:
Calculus: o hm, tch phn, gii hn, chui. i s tuyn tnh: nghch o, nh
thc, gi tr eigen, Inverses, determinants, eigenvalues, singular
value decomposition, and canonical forms of symbolic matrices. Rt
gn: dng rt gn biu thc. Gii phng trnh: i s v vi phn Cc hm c bit:
cung cp cc hm cd bit nh beta, bessel, gamma. Transforms: Fourier,
Laplace, z-transform. Symbolic object dng c b cng c ta phi nh ngha
mt lai d liu c bit khc vi cc lai d liu khc trong MATLAB- l symbolic
(k hiu). Symbolic l mt cu trc d liu lu li chui k t i din cho k hiu
tan hc m ta ang x l. ta dng symbolic biu hin mt bin, biu thc hay ma
trn. V d: >> sqrt(2) ans = 1.4142 >>= sqrt(sym(2)) ans=
2^(1/2) khai bo mt symbolic trong MATLAB, ta c th dng lnh sym. Lnh
syms dng khai bo nhiu symbolic trong mt dng lnh. V d: >>
x=sym('x') x= x >>syms a b >> f=sin(a*x) f= sin(a*x)
>> diff(f) ans = cos(a*x)*aMatlab introduction 15/21 xc nh c
bao nhiu bin symbolic trong mt biu thc ta dng lnh findsym V d:
>> findsym(f) ans = a, x thay th gi tr vo mt mt bin symbolic
ta dng lnh subs V d: >> subs(f,a,2) ans = sin(2*x) >>
subs(f,{x,a},{2,5}) ans = -0.5440 Calculus Cc hm cho gii tch diff:
o hm. int: tch phn. jacobian: ma trn Jacobian limit: gii hn symsum:
tng ca mt chui. taylor: khai trin chui Taylor. V d: >> int(f)
ans = -1/a*cos(a*x) >> taylor(f) ans =
a*x-1/6*a^3*x^3+1/120*a^5*x^5 Rt gn biu thc: collect(f,v): gom a
thc theo bin v. expand: khai trin a thc. factor: phn tch a thc thnh
cc nhn t. horner: phn tch a thc thnh mt biu thc dn Horner. numden:
phn tch biu thc thnh dng hu t. simple: n gin ti a biu thc.
simplify: rt gn biu thc. V d: >> t=(x-2)^2+(x-2)^3+2 t=
(x-2)^2+(x-2)^3+2 >> collect(t,x) ans =
-2+x^3-5*x^2+8*xMatlab introduction 16/21>> expand(t) ans =
-2+x^3-5*x^2+8*x >> t=x^2 +2*a*x +a^2 ; >> factor(t)
ans = (a+x)^2 th th 2D plot(X,Y) v cc im trong vector Y theo vector
X V d: >>x=[1:0.2:20]; >> y=sin(x); >>
plot(x,y)Hnh. th to ra bi plot(x,y) Trong MATLAB th c to trong mt
window gi l figure. Khi ta dng mt lnh v th, nu trong MATLAB khng c
sn mt figure, mt figure mi s c to ra. Nu c mt hay nhiu figure, th
th mi s thay th th c trong figure hin hu. trnh iu ny ta c th to nn
mt figure (empty) bng lnh figure V d: >> figureMatlab
introduction17/21Hnh. Empty figure v chng th (thay v thay th) ln mt
th c sn trong figure ta dng lnh hold on. b ch v chng, ta dng tip
lnh hold off. V d: >>z=cos(x); >>hold on
>>plot(x,z)Hnh. Dng lnh hold v chng th Lnh subplot(m,n,p) hay
subplot(mnp) dng chia Figure window thnh mxn th v chn th th p lm
hin hnh. c xp th t theo hng trn xung di , t tri sang phi. V d:
>> figure >> subplot(1,2,1) >>plot(x,y) >>
subplot(1,2,2) >> plot(x,z)Matlab introduction18/21Hnh.
Subplot bar(x,y) v th ct vi d liu trong y theo x. Nu y l ma trn mxn
th bar s v m nhm. Mi nhm c n ct. v ct nm ngang ta dng barh. v ct
trong 3D dng bar3 hay bar3h. V d: >> x=[1 3 6]; >> y=[5
12; 8 10 ; 12 5]; >> bar(x,y)Hnh. th bar hist(y,m) dng v th
histogram vi d liu trong y v m l s khang chia. errorbar(x,y,e) v th
x,y vi dung sai [-e,+e]. V d: >> x=[1:0.1:2]; >>
y=x.^3-2*x.^2; >> e=rand(1,length(x)); >>
error(x,y,e)Matlab introduction19/21Hnh. errorbar pie(x) dng v th
hnh bnh v d: >> x=[10 25 45]; >> pie(x)Hnh. th pie
ezplot(f,[a,b]) v biu thc f trong khang [a,b] V d: >>
ezplot('sin(x)/x',[-5,5]) Ty bin th MATLAB cho php ta thay i nh dng
ca th nh: font ch, kch thc ch, kch thc ng, mu sc, trc th v.v. thay
i nh dng th ta c th: Dng menu File/Edit, chn Figure properties thay
i nh dng cho figure window, Axis properties thay i nh dng cho trc,
Current Object properties thay i nh dng cho i tng hin hnh. Chn i
tng m ta mun thay nh dng v nhn chut phi hin ln menu la chn.Matlab
introduction 20/21 thm cc i tng nh nhn, vn bn, ghi ch, tiu v.v. ta
c th dng menu Insert. xut th ra cc dng hnh nh nh jpg, gif, ta dng
menu File/Export As th 3D Ta c v th 3 chiu dng cc lnh sau: plot3:
tng t nh plot nh c thm trc z. mesh: to th 3D di dng li (mesh).
surf: to b mt 3D.Matlab introduction21/21
