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Matlab

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MATLAB
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A =
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5
9
4
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10
6
15
2
11
7
14
13
8
12
1
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34
34
34
34
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ans =
16
3
2
13
5
10
11
8
9
6
7
12
4
15
14
1
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sum(A')'
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ans =
34
34
34
34
10
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10
7
1
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sum(diag(A))
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ans =
34
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34
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A(1,4) + A(2,4) + A(3,4) + A(4,4)
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ans =
34
H^gZdhwlhg_kZfucemqrbckihkh[kmffbjh\Zgbyhl^_evghckljhdb
LZd`_\hafh`ghh[jZsZlvkydwe_f_glZffZljbpuq_j_ah^bgbg^_dkA(k)Wlh
h[uqguc kihkh[ kkueZlvky gZ kljhdb b klhe[pu fZljbpu Gh _]h fh`gh bkihevah\Zlvlhevdhk^\mf_jgufbfZljbpZfb<wlhfkemqZ_fZkkb\jZkkfZljb\Z_lky dZd ^ebgguc \_dlhj knhjfbjh\Zgguc ba klhe[ph\ bkoh^ghc fZljbpu
11
GZqZeh jZ[hlu k MATLAB
LZd ^ey gZr_]h fZ]bq_kdh]h d\Z^jZlZ A(8) ± wlh ^jm]hc kihkh[ kkueZlvky gZ
agZq_gb_ojZgys__ky\A(4,2).
?keb\uiulZ_l_kvbkihevah\ZlvagZq_gb_we_f_glZ\g_fZljbpuMATLAB\u^Zklhrb[dm
t=A(4,5)
???
Index exceeds matrix dimensions.
K^jm]hcklhjhgu_keb\ukhojZgy_l_agZq_gb_\g_fZljbpulhjZaf_jfZljbpum\_ebqb\Z_lky
X=A;
X(4,5) = 17
X =
16
5
9
4
3
10
6
15
2
11
7
14
13
8
12
1
0
0
0
17
Hi_jZlhj^\h_lhqby
>\h_lhqb_wlhh^bgbagZb[he__\Z`guohi_jZlhjh\MATLABHgijhy\ey_lky\jZaebqguonhjfZo<ujZ`_gb_
1:10
wlh\_dlhjkljhdZkh^_j`ZsZyp_eu_qbkeZhl^h
1
2
3
4
5
6
7
8
9
10
>eyihemq_gbyh[jZlgh]hbgl_j\ZeZhibr_fijbjZs_gb_GZijbf_j
100:-7:50
qlh^Z_l
100
93
86
79
72
65
58
51
beb
0:pi/4:pi
qlhijb\h^bld
0
0.7854
1.5708
2.3562
3.1416
Bg^_dkgh_\ujZ`_gb_\dexqZy^\h_lhqb_hlghkblkydqZklbfZljbpu
A(1:k, j)
wlhi_j\u_k we_f_glh\j]hklhe[pZfZljbpu:LZd
sum(A(1:4,4))
12
FZljbpu b fZ]bq_kdb_ d\Z^jZlu
\uqbkey_lkmffmq_l\_jlhckljhdbGh_klvbemqrbckihkh[>\h_lhqb_kZfh
ih k_[_ h[jZsZ_lky dh \k_f we_f_glZf \ kljhd_ b klhe[p_ fZljbpu Z keh\h
end±dihke_^g_ckljhd_bebklhe[pmLZd
sum(A(:,end))
\uqbkey_lkmffmwe_f_glh\\ihke_^g_fklhe[p_fZljbpu:
ans =
34
Ihq_fmfZ]bq_kdZykmffZd\Z^jZlZojZ\gZ"?kebp_eu_qbkeZhl^h
hlkhjlbjh\Zgu\q_luj_]jmiiukjZ\gufbkmffZfbwlZkmffZ^he`gZ[ulv
sum(1:16)/4
dhlhjZydhg_qghjZ\gZ
ans =
34
Nmgdpbymagic
MATLABgZkZfhf^_e_h[eZ^Z_l\kljh_gghcnmgdpb_cdhlhjZykha^Z_lfZ]bq_kdbcd\Z^jZlihqlbex[h]hjZaf_jZG_ m^b\bl_evgh qlh wlZ nmgdpby gZau\Z_lkymagic.
B=magic(4)
B =
16
5
9
4
2
11
7
14
3
10
6
15
13
8
12
1
WlZfZljbpZihqlblZ`_fZljbpZqlhbgZ]jZ\xj_>xj_jZbhgZbf__l\k_l_
`_ fZ]bq_kdb_ k\hckl\Z ?^bgkl\_ggh_ hlebqb_ aZdexqZ_lky \ lhf qlh ^\Z
kj_^gbo klhe[pZ ihf_gyebkv f_klZfb >ey lh]h qlh[u ij_h[jZah\Zlv B \ fZljbpm>xj_jZAi_j_klZ\bfbof_klZfb
A=B(:,[1 3 2 4])
Wlh hagZqZ_l qlh ^ey dZ`^hc kljhdb fZljbpu B we_f_glu i_j_ibku\Zxlky \
ihjy^d_
A =
16
5
9
4
3
10
6
15
2
11
7
14
13
8
12
1
Ihq_fm >xj_j i_j_mihjy^hqbe klhe[pu ih kjZ\g_gbx k l_f qlh bkihevam_l
MATLAB" ;_a khfg_gby hg ohl_e \dexqblv ^Zlm ]jZ\xju \ gb`gxx
qZklvfZ]bq_kdh]hd\Z^jZlZ
13
GZqZeh jZ[hlu k MATLAB
<ujZ`_gby
DZdb[hevrbgkl\h^jm]boyaudh\ijh]jZffbjh\ZgbyMATLAB ij_^hklZ\ey_l
\hafh`ghklv bkihevah\Zgby fZl_fZlbq_kdbo \ujZ`_gbc gh \ hlebqb_ hl fgh]bo ba gbo wlb \ujZ`_gby \ MATLAB \dexqZxl fZljbpu Hkgh\gu_ khklZ\eyxsb_\ujZ`_gby
•i_j_f_ggu_
•qbkeZ
•hi_jZlhju
•nmgdpbb
I_j_f_ggu_
<MATLAB g_lg_h[oh^bfhklb\hij_^_e_gbblbiZi_j_f_gguobebjZaf_jghklbDh]^ZMATLAB \klj_qZ_lgh\h_bfyi_j_f_gghchgZ\lhfZlbq_kdbkha^Z_l i_j_f_ggmx b \u^_ey_l khhl\_lkl\mxsbc h[t_f iZfylb ?keb i_j_f_ggZy
m`_kms_kl\m_lMATLAB baf_gy_l__khklZ\b_kebwlhg_h[oh^bfh\u^_ey_l
^hihegbl_evgmxiZfylvGZijbf_j
num_students = 25
kha^Z_lfZljbpmokbf_g_fnum_students bkhojZgy_lagZq_gb_\___^bgkl\_gghfwe_f_gl_
Bf_gZ i_j_f_gguo khklhyl ba [md\ pbnj beb kbf\heh\ ih^q_jdb\Zgby
MATLAB bkihevam_l lhevdh i_j\u_ kbf\he bf_gb i_j_f_gghc MATLAB
qm\kl\bl_e_gdj_]bkljZfhgjZaebqZ_laZ]eZ\gu_ b kljhqgu_ [md\u Ihwlhfm
A ba ±g_h^gZblZ`_i_j_f_ggZyQlh[um\b^_lvfZljbpmk\yaZggmxki_j_f_gghcijhklh\\_^bl_gZa\Zgb_i_j_f_gghc
QbkeZ
MATLAB bkihevam_lijbgylmx^_kylbqgmxkbkl_fmkqbke_gbykg_h[yaZl_evghc ^_kylbqghc lhqdhc b agZdZfb iexkfbgmk ^ey qbk_e GZmqgZy kbkl_fZ
kqbke_gby bkihevam_l [md\m e ^ey hij_^_e_gby fgh`bl_ey kl_i_gb ^_kylb
Fgbfu_ qbkeZ bkihevamxl i beb j dZd kmnnbdk G_dhlhju_ ijbf_ju ijZ\bevguoqbk_eijb\_^_gugb`_
3
9.6397238
1i
-99
1.60210e-20
-3.14159j
0.0001
6.02252e23
3e5i
<k_ qbkeZ ^ey ojZg_gby bkihevamxl nhjfZl long, hij_^_e_gguc klZg^Zjlhf
ieZ\Zxs_c lhqdb IEEE QbkeZ k ieZ\Zxs_c lhqdhc h[eZ^Zxl h]jZgbq_gghc
lhqghklvx ijb[ebabl_evgh agZqZsbo pbnj b h]jZgbq_gguf ^bZiZahghf ±
ijb[ebabl_evgh hl -308 ^h 308 Dhfivxl_j VAX bkihevam_l ^jm]hc nhjfZl
qbk_ekieZ\Zxs_clhqdhcghbolhqghklvb^bZiZahgijb[ebabl_evghl_`_ 14
<ujZ`_gby
Hi_jZlhju
<ujZ`_gby bkihevamxl h[uqgu_ Zjbnf_lbq_kdb_ hi_jZpbb b ijZ\beZ klZjrbgkl\Z
+
*
/
\
^
'
()
keh`_gb_
\uqblZgb_
mfgh`_gb_
^_e_gb_
e_\h_^_e_gb_ hibkZgh\jZa^_e_FZljbpubEbg_cgZy:e]_[jZ\dgb]_
"Using MATLAB")
kl_i_gv
dhfie_dkghkhijy`_ggh_ljZgkihgbjh\Zgb_
hij_^_e_gb_ihjy^dZ\uqbke_gby
Nmgdpbb
0$7/$% ij_^hklZ\ey_l [hevrh_ dhebq_kl\h we_f_glZjguo fZl_fZlbq_kdbo
nmgdpbclZdbodZdabs, sqrt, exp, sin. <uqbke_gb_d\Z^jZlgh]hdhjgybebeh]ZjbnfZ hljbpZl_evgh]h qbkeZ g_ y\ey_lky hrb[dhc \ wlhf kemqZ_ j_amevlZlhf
y\ey_lkykhhl\_lkl\mxs__dhfie_dkgh_qbkeh0$7/$%lZd`_ij_^hklZ\ey_lb
[he__ keh`gu_ nmgdpbb \dexqZy =ZffZ nmgdpbx b nmgdpbb ;_kk_ey ;hevrbgkl\hbawlbonmgdpbcbf_xldhfie_dkgu_Zj]mf_gluQlh[u\u\_klbkibkhd\k_owe_f_glZjguofZl_fZlbq_kdbonmgdpbcgZ[_jbl_
help elfun
>ey\u\h^Z[he__keh`guofZl_fZlbq_kdbobfZljbqguonmgdpbcgZ[_jbl_
help specfun
help elmat
khhl\_lkl\_ggh
G_dhlhju_ nmgdpbb lZdb_ dZd sqrt b sin \kljh_ggu_ Hgb y\eyxlky qZklvx
0$7/$%ihwlhfmhgbhq_gvwnn_dlb\gughbo\uqbkebl_evgu_^_lZebljm^gh^hklmigu<lh\j_fydZd^jm]b_nmgdpbblZdb_dZdgamma bsinhj_Zebah\Zgu\FnZceZoIhwlhfm\ufh`_l_e_]dhm\b^_lvbodh^b\kemqZ_g_h[oh^bfhklb^Z`_fh^bnbpbjh\Zlv_]h
G_kdhevdhki_pbZevguonmgdpbcij_^hklZ\eyxlagZq_gbyqZklhbkihevam_fuo
dhgklZgl
pi
i
j
eps
realmin
realmax
Inf
NaN
3.14159265…
fgbfZy_^bgbpZ√-1
lh`_kZfh_qlhbi
hlghkbl_evgZylhqghklvqbkeZkieZ\Zxs_clhqdhc-52
gZbf_gvr__qbkehkieZ\Zxs_clhqdhc-1022
gZb[hevr__qbkehkieZ\Zxs_clhqdhc ε)21023
[_kdhg_qghklv
g_qbkeh
15
GZqZeh jZ[hlu k MATLAB
;_kdhg_qghklvihy\ey_lkyijb^_e_gbbgZgmevbebijb\uiheg_gbbfZl_fZlbq_kdh]h\ujZ`_gbyijb\h^ys_]hdi_j_iheg_gbxl_dij_\ur_gbxrealmax.
G_qbkeh NaN ]_g_jbjm_lkyijb\uqbke_gbb\ujZ`_gbclbiZbebInf – Inf,
dhlhju_g_bf_xlhij_^_e_ggh]hfZl_fZlbq_kdh]h agZq_gby
Bf_gZnmgdpbcg_y\eyxlkyaZj_a_j\bjh\Zggufbihwlhfm\hafh`ghbaf_gylv
boagZq_gbygZgh\u_gZijbf_j
eps = 1.e-6
b ^Ze__ bkihevah\Zlv wlh agZq_gb_ \ ihke_^mxsbo \uqbke_gbyo GZqZevgh_
agZq_gb_fh`_l[ulv\hkklZgh\e_ghke_^mxsbfh[jZahf
clear eps
<ujZ`_gby
<u m`_ ihagZdhfbebkv k g_dhlhjufb ijbf_jZfb bkihevah\Zgby \ujZ`_gbc \
0$7/$%Gb`_ijb\_^_gh_s_g_kdhevdhijbf_jh\kj_amevlZlZfb
rho = (1+sqrt(5))/2
rho =
1.6180
a = abs(3+4i)
a =
5
z = sqrt(besselk(4/3,rho-i))
z =
0.3730 + 0.3214i
huge = exp(log(realmax))
huge =
1.7977e+308
toobig = pi*huge
toobig =
Inf
16
JZ[hlZ k fZljbpZfb
JZ[hlZkfZljbpZfb
WlhljZa^_ejZkkdZ`_l\ZfhjZaebqguokihkh[Zokha^ZgbyfZljbp
=_g_jbjh\Zgb_fZljbp
0$7/$%bf__lq_luj_nmgdpbbdhlhju_kha^Zxlhkgh\gu_fZljbpu
\k_gmeb
\k__^bgbpu
jZ\ghf_jgh_jZkij_^_e_gb_kemqZcguowe_f_glh\
ghjfZevgh_jZkij_^_e_gb_kemqZcguowe_f_glh\
zeros
ones
rand
randn
G_dhlhju_ijbf_ju
Z = zeros(2,4)
Z =
0
0
0
0
0
0
0
0
F = 5*ones(3,3)
F =
5
5
5
5
5
5
5
5
5
N = fix(10*rand(1,10))
N =
9
2
6
4
8
7
4
0
8
4
R = randn(4,4)
R =
-0.4326
-1.6656
0.1253
0.2877
-1.1465
1.1909
1.1892
-0.0376
0.3273
0.1746
-0.1867
0.7258
-0.5883
2.1832
-0.1364
0.1139
AZ]jmadZfZljbp
DhfZg^Z load kqblu\Z_l ^\hbqgu_ nZceu kh^_j`Zsb_ fZljbpu kha^Zggu_ \
MATLAB jZg__bebl_dklh\u_nZceukh^_j`Zsb_qbke_ggu_^Zggu_L_dklh\u_nZceu^he`gu[ulvknhjfbjh\Zgu\\b^_ijyfhm]hevghclZ[ebpu qbk_e
hl^_e_gguoijh[_eZfbkjZ\gufdhebq_kl\hfwe_f_glh\\dZ`^hckljhd_GZijbf_jkha^Z^bf\g_MATLAB l_dklh\hcnZcekh^_j`Zsbckljhdb
16.0
5.0
9.0
4.0
3.0
10.0
6.0
15.0
2.0
11.0
7.0
14.0
13.0
8.0
12.0
1.0
KhojZgbfwlhlnZceih^bf_g_fmagik.datLh]^ZdhfZg^Z
17
GZqZeh jZ[hlu k MATLAB
load magik.dat
ijhqblZ_lwlhlnZcebkha^Zkli_j_f_ggmxmagikkh^_j`ZsmxgZrmfZljbpm
FnZceu
<ufh`_l_kha^Z\Zlvk\hbkh[kl\_ggu_fZljbpubkihevamyFnZceudhlhju_
ij_^klZ\eyxl kh[hc l_dklh\u_ nZceu kh^_j`Zsb_ dh^ MATLAB. Ijhklh kha^Zcl_ nZce k \ujZ`_gb_f dhlhjh_ \u ohlbl_ gZibkZlv \ dhfZg^ghc kljhd_
MATLAB. KhojZgbl__]hih^bf_g_faZdZgqb\ZxsbfkygZ.m.
AZf_qZgb_ >ey \uah\Z l_dklh\h]h j_^ZdlhjZ gZ JK beb Mac \u[_jbl_ Open
bebNew ba f_gx File bebgZ`fbl_ khhl\_lkl\mxsmx dghidm gZ iZg_eb bgkljmf_glh\>eyh[jZs_gbydl_dklh\hfmj_^ZdlhjmgZUNIXbkihevamcl_kbf\he
kjZamaZdhfZg^hcdhlhjmx\ubkihevam_l_\kljhd_hi_jZpbhgghckbkl_fu
GZijbf_jkha^Z^bfnZce\dexqZxsbcke_^mxsb_kljhd
A=[…
16.0
3.0
5.0
10.0
9.0
6.0
4.0
15.0
2.0
11.0
7.0
14.0
13.0
8.0
12.0
1.0 ];
KhojZgbf_]hih^bf_g_fmagik.m.Lh]^Z\ujZ`_gb_
magik
ijhqblZ_lnZcebkha^Zkli_j_f_ggmx:kh^_j`Zsmxbkoh^gmxfZljbpm
H[t_^bg_gb_
H[t_^bg_gb_ ± wlh ijhp_kk kh_^bg_gby fZe_gvdbo fZljbp ^ey kha^Zgby [hevrbo NZdlbq_kdb \u kha^Zeb \Zrm i_j\mx fZljbpm h[t_^bg_gb_f _z hl^_evguo we_f_glh\ IZjZ d\Z^jZlguo kdh[hd ± wlh hi_jZlhj h[t_^bg_gby GZijbf_jgZqg_fkfZljbpu: fZ]bq_kdh]hd\Z^jZlZo bknhjfbjm_f
B = [A A+32; A+48 A+16]
J_amevlZlhf[m^_lfZljbpZoihemqZ_fZykh_^bg_gb_fq_luj_oih^fZljbp
B =
16
5
9
4
64
53
57
52
2
11
7
14
50
59
55
62
3
10
6
15
51
58
54
63
13
8
12
1
61
56
60
49
48
37
41
36
32
21
25
20
34
43
39
46
18
27
23
30
18
35
42
38
47
19
26
22
31
45
40
44
33
29
24
28
17
JZ[hlZ k fZljbpZfb
WlhfZljbpZebrvgZiheh\bgmy\ey_lkyfZ]bq_kdhc?zwe_f_gluij_^klZ\eyxl
kh[hc dhf[bgZpbx p_euo qbk_e hl ^h Z kmffu \ klhe[pZo lhqgh jZ\gu
agZq_gbx^eyfZ]bq_kdh]hd\Z^jZlZo
sum(B)
ans =
260
260
260
260
260
260
260
260
H^gZdhkmffu\kljhdZowlhcfZljbpu( sum(B')' g_ \k_ h^bgZdh\u G_h[oh^bfhijh\_klb^hihegbl_evgu_hi_jZpbbqlh[uk^_eZlvwlm fZljbpm^_ckl\bl_evghfZ]bq_kdbfd\Z^jZlhfo
M^Ze_gb_kljhdbklhe[ph\
<ufh`_l_m^Zeylvkljhdbbklhe[pufZljbpubkihevamyijhklhiZjmd\Z^jZlguokdh[hdJZkkfhljbf
X = A;
L_i_jvm^Zebf\lhjhcklhe[_pfZljbpuX.
X(:,2) = []
WlZhi_jZpbybaf_gblOke_^mxsbfh[jZahf
X =
16
5
9
4
3
10
6
15
13
8
12
1
?keb\u m^Zey_l_h^bgwe_f_glfZljbpulhj_amevlZl m`_ g_ [m^_l fZljbp_c
LZd\ujZ`_gb_
X(1,2) = []
j_amevlZlhf\uqbke_gby\u^Zklhrb[dmH^gZdhbkihevah\Zgb_h^gh]hbg^_dkZ
m^Zey_l hl^_evguc we_f_gl beb ihke_^h\Zl_evghklv we_f_glh\ b ij_h[jZam_l
hklZ\rb_kywe_f_glu\\_dlhjkljhdmLZd
X(2:2:10) = []
\u^Zklj_amevlZl
X =
16
9
3
6
13
12
19
1
GZqZeh jZ[hlu k MATLAB
DhfZg^gh_hdgh
>hkboihjfubkihevah\ZeblhevdhdhfZg^gmxkljhdmMATLABi_qZlZydhfZg^u b \ujZ`_gby b gZ[ex^Zy j_amevlZlu < wlhc ]eZ\_ hibkZgh g_kdhevdh
kihkh[h\baf_g_gby\g_rg_]h\b^ZdhfZg^gh]hhdgZ?keb\ZrZkbkl_fZiha\hey_l \Zf \u[bjZlv rjbnl lh fu j_dhf_g^m_f bkihevah\Zlv rjbnlu k nbdkbjh\ZgghcrbjbghclZdb_dZdFixedsys beb Courier^eyh[_ki_q_gbyijZ\bevgh]hf_`kljhqgh]hbgl_j\ZeZ
DhfZg^ZIRUPDW
DhfZg^Z format mijZ\ey_l qbke_gguf nhjfZlhf agZq_gbc \u\h^bfuo
MATLABWlZhi_jZpby\eby_llhevdhgZlhdZdqbkeZbah[jZ`ZxlkygZwdjZg_
ghg_\eby_lgZlhdZdbo\uqbkey_lbkhojZgy_lMATLABGb`_ij_^klZ\e_gu
jZaebqgu_ nhjfZlu qbk_e bkihevam_fu_ ^ey hlh[jZ`_gby \_dlhjZ x k dhfihg_glZfbjZaebqguo\_ebqbg
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
20
DhfZg^gh_ hdgh
?kebkZfuc[hevrhcwe_f_glfZljbpu[hevr_3bebkZfucfZe_gvdbcf_gvr_ -3, MATLAB ijbf_gy_l h[sbc fZkrlZ[guc dhwnnbpb_gl ^ey nhjfZlh\
short b long.
<^h[Z\e_gb_ddhfZg^Zfformat, jZkkfhlj_gguf\ur_
format compact
m[bjZ_lfgh]himkluoebgbcihy\eyxsbokygZ\uoh^_Wlhiha\hey_l\Zf\b^_lv [hevr_ bgnhjfZpbb gZ wdjZg_ ?keb \u ohlbl_ baf_gblv dhgljhev gZ^
nhjfZlhf\uoh^guo^Zgguobkihevamcl_nmgdpbbsprintf bfprintf.
KhdjZs_gb_\uoh^guo^Zgguo
?keb\ugZ[_j_l_\ujZ`_gb_bgZ`f_l_Return bebEnter, MATLABZ\lhfZlbq_kdb \u\_^_l j_amevlZl gZ wdjZg H^gZdh _keb \ dhgp_ kljhdb \u ihklZ\bl_
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[u\Z_lgm`ghijbkha^Zgbb[hevrbofZljbpGZijbf_j
A = magic(100);
>ebggu_dhfZg^gu_kljhdb
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Return beb Enter ^ey h[hagZq_gbylh]h qlh \ujZ`_gb_ ijh^he`Z_lky gZ ke_^mxs_ckljhd_GZijbf_j
s = 1 –1/2 + 1/3 –1/4 + 1/5 – 1/6 + 1/7 ...
-1/8 + 1/9 – 1/10 + 1/11 – 1/12;
Ijh[_eu\hdjm]agZdh\ g_h[yaZl_evgughmemqrZxlqblZ_fhklvl_dklZ
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jZg__GZijbf_jij_^iheh`bfqlh\u^himklbebhrb[dmijb\\h^_
rho = (1 + sqt(5))/2
<uhrb[ebkv\gZibkZgbbsqrt. MATLABhl\_lbl\Zfij_^mij_`^_gb_f
Undefined function or variable 'sqt'.
<f_klh lh]h qlh[u aZgh\h gZ[bjZlv \kx kljhdm ijhklh gZ`fbl_ deZ\brm ↑.
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21
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agZdhfuihevah\Zl_eyfj_^ZdlhjZEMACS.)
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<uah\ij_^u^ms_ckljhdb
<uah\ihke_^mxs_ckljhdb
>\b`_gb_gZaZ^gZh^bgkbf\he
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22
=jZnbdZ
=jZnbdZ
MATLAB bf__lrbjhdb_\hafh`ghklb^ey]jZnbq_kdh]hbah[jZ`_gby\_dlhjh\
bfZljbpZlZd`_^eykha^Zgbydhff_glZjb_\bi_qZlb]jZnbdbWlZ]eZ\Zhibku\Z_l g_kdhevdh gZb[he__ \Z`guo ]jZnbq_kdbo nmgdpbc b ^Z_l ijbf_ju bo
ijbf_g_gby
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Nmgdpbyplot bf__ljZaebqgu_nhjfuk\yaZggu_k\oh^gufbiZjZf_ljZfbgZijbf_jplot(y)kha^Z_ldmkhqghebg_cguc]jZnbdaZ\bkbfhklbwe_f_glh\y hlbo
bg^_dkh\ ?keb \u aZ^Z_l_ ^\Z \_dlhjZ \ dZq_kl\_ Zj]mf_glh\ plot(x,y) kha^Zkl
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t = 0:pi/100:2*pi;
y = sin(t);
plot(t,y)
<uah\ nmgdpbb plot k fgh]hqbke_ggufb iZjZfb x-y kha^Z_l fgh]hqbke_ggu_
]jZnbdbMATLAB Z\lhfZlbq_kdbijbk\Zb\Z_ldZ`^hfm]jZnbdmk\hcp\_l bkdexqZykemqZbdh]^Zwlh^_eZ_lihevah\Zl_ev qlhiha\hey_ljZaebqZlvaZ^Zggu_ gZ[hju ^Zgguo GZijbf_j ke_^mxsb_ ljb kljhdb hlh[jZ`Zxl ]jZnbd
[ebadbonmgdpbcbdZ`^hcdjb\hckhhl\_lkl\m_lk\hcp\_l
y2 = sin(t-.25);
y3 = sin(t-.5);
plot( t, y, t, y2, t, y3)
23
GZqZeh jZ[hlu k MATLAB
<hafh`ghbaf_g_gb_p\_lZklbeyebgbcbfZjd_jh\lZdbodZdagZdbiexkbeb
djm`dbke_^mxsbfh[jZahf
plot(x, y, 'p\_lBklbevBfZjd_j')
p\_lBklbevBfZjd_j wlh kbf\hevgZy kljhdZ aZdexq_ggZy \ h^bgZjgu_
dZ\uqdb khklZ\e_ggZybalbih\p\_lZklbeyebgbcbfZjd_jh\
•Kbf\heuhlghkysb_dp\_lm'c' , 'm' , 'y' , 'r' , 'g' , 'b', 'w' b 'k'Hgbh[hagZqZxl ]hem[hc fZebgh\uc `_eluc djZkguc a_e_guc kbgbc [_euc b q_jguc
p\_lZkhhl\_lkl\_ggh
•Kbf\heuhlghkysb_kydlbimebgbc' – ' ^eykiehrghc' – – '^eyjZaju\ghc' : '^eyimgdlbjghc' –. '^eyrljboimgdlbjghcebgbcb' none '^ey_zhlkmlkl\by
•GZb[he__qZklh\klj_qZxsb_kyfZjd_ju' + ' , 'h' , ' * ' b 'o'.
GZijbf_j\ujZ`_gb_
plot(x,y,'y:+')
kljhbl`_elucimgdlbjguc]jZnbdbihf_sZ_lfZjd_ju' + ' \dZ`^mxlhqdm
^Zgguo?keb\uhij_^_ey_l_lhevdhlbifZjd_jZghg_hij_^_ey_l_lbiklbey
ebgbclhMATLAB\u\_^_llhevdhfZjd_ju
HdgZbah[jZ`_gbc
Nmgdpby plot Z\lhfZlbq_kdb hldju\Z_l gh\h_ hdgh bah[jZ`_gby ^Ze__ hdgh _keb^hwlh]h_]hg_[uehgZwdjZg_?keb`_hghkms_kl\m_llhplot bkihevam_l
_]hih mfheqZgbx>eyhldjulbygh\h]hhdgZb\u[hjZ_]hih mfheqZgbxgZ[_jbl_
figure
>eylh]hqlh[uk^_eZlvkms_kl\mxs_zhdghl_dmsbf
24
=jZnbdZ
figure(n)
]^_n ±wlhghf_j\aZ]heh\d_hdgZ<wlhfkemqZ_j_amevlZlu\k_oihke_^mxsbo
dhfZg^[m^ml\u\h^blvky\wlhhdgh
>h[Z\e_gb_djb\uogZkms_kl\mxsbc]jZnbd
DhfZg^Zhold iha\hey_l^h[Z\eylvdjb\u_gZkms_kl\mxsbc]jZnbdDh]^Z\u
gZ[bjZ_l_
hold on
MATLABg_klbjZ_lkms_kl\mxsbc]jZnbdZ^h[Z\ey_l\g_]hgh\u_^Zggu_
baf_gyyhkb_kebwlhg_h[oh^bfhGZijbf_jke_^mxsbcwe_f_gldh^Z\gZqZe_
kha^Z_l dhglmjgu_ ebgbb nmgdpbb peaks Z aZl_f gZdeZ^u\Z_l ik_\^hp\_lghc
]jZnbdlhc`_nmgdpbb
[x,y,z] = peaks;
contour(x,y,z,20,'k')
hold on
pcolor(x,y,z)
shading interp
DhfZg^Z hold on y\ey_lky ijbqbghc lh]h qlh ]jZnbd pcolor dhf[bgbjm_lky k
]jZnbdhfcontour\h^ghfhdg_
Ih^]jZnbdb
Nmgdpby subplot iha\hey_l \u\h^blv fgh`_kl\h ]jZnbdh\ \ h^ghf hdg_ beb
jZki_qZlu\ZlvbogZh^ghfebkl_[mfZ]b
subplot(m,n,p)
25
GZqZeh jZ[hlu k MATLAB
jZa[b\Z_l hdgh bah[jZ`_gbc gZ fZljbpm m gZ n ih^]jZnbdh\ b \u[bjZ_l puc
ih^]jZnbdl_dmsbf=jZnbdbgmf_jmxlky\^hevi_j\h]h\\_jog_ckljhd_ihlhf \h \lhjhc b l^ GZijbf_j ^ey lh]h qlh[u ij_^klZ\blv ]jZnbq_kdb_ ^Zggu_\q_luj_ojZaguoih^h[eZklyohdgZg_h[oh^bfh\uihegblvke_^mxs__
t = 0:pi/10:2*pi;
[X,Y,Z] = cylinder(4*cos(t));
subplot(2,2,1)
mesh(X)
subplot(2,2,2); mesh(Y)
subplot(2,2,3); mesh(Z)
subplot(2,2,4); mesh(X,Y,Z)
Fgbfu_bdhfie_dkgu_^Zggu_
?kebZj]mf_glnmgdpbbplot dhfie_dkgh_qbkehlhfgbfZyqZklvb]ghjbjm_lky
aZ bkdexq_gb_f kemqZy dh]^Z dhfie_dkguc Zj]mf_gl h^bg >ey wlh]h ki_pbZevgh]h kemqZy ijhbkoh^bl ihkljh_gb_ ]jZnbdZ aZ\bkbfhklb j_Zevghc qZklb
Zj]mf_glZhlfgbfhcIhwlhfm
plot(Z)
]^_Z dhfie_dkguc\_dlhjbebfZljbpZwd\b\Ze_glgh
plot(real(Z),imag(Z))
GZijbf_j
t = 0:pi/10:2*pi;
plot(exp(i*t),'-o')
hlh[jZabl ^\Z^pZlbklhjhggbc fgh]hm]hevgbd k fZe_gvdbfb djm`dZfb gZ \_jrbgZo
26
=jZnbdZ
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Nmgdpbyaxis bf__lg_kdhevdh\hafh`ghkl_c^eygZkljhcdbfZkrlZ[Zhjb_glZpbbbdhwnnbpb_glZk`Zlby
H[uqghMATLABgZoh^bl fZdkbfZevgh_ b fbgbfZevgh_ agZq_gb_ b \u[bjZ_l
khhl\_lkl\mxsbcfZkrlZ[bfZjdblbjh\Zgb_hk_cNmgdpbyaxis aZf_gy_lagZq_gbyihmfheqZgbxij_^_evgufbagZq_gby\\h^bfufbihevah\Zl_e_f
axis( [xmin xmax ymin ymax] )
< nmgdpbb axis fh`gh lZd`_ bkihevah\Zlv dexq_\u_ keh\Z ^ey mijZ\e_gby
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axis square
kha^Z_lx byhkbjZ\ghc^ebguZ
axis equal
kha^Z_lhl^_evgu_hlf_ldbijbjZs_gbc^eyx b y hk_ch^bgZdh\hc^ebguLZd
nmgdpby
plot(exp(i*t))
ke_^mxsZyeb[haZaxis squareeb[haZaxis equalij_\jZsZ_lh\Ze\ijZ\bevguc
djm]
axis auto
\ha\jZsZ_lagZq_gbyihmfheqZgbxbi_j_oh^bl\Z\lhfZlbq_kdbcj_`bf
axis on
27
GZqZeh jZ[hlu k MATLAB
\dexqZ_lh[hagZq_gbyhk_cbf_ldbijhf_`mlhqguo^_e_gbc
axis off
\udexqZ_lh[hagZq_gbyhk_cbf_ldbijhf_`mlhqguo^_e_gbc
grid off
\udexqZ_lk_ldmdhhj^bgZlZ
grid on
\dexqZ_l_zaZgh\h
Ih^ibkbdhkyfbaZ]heh\db
Nmgdpbb xlabel, ylabel, zlabel ^h[Z\eyxl ih^ibkb d khhl\_lkl\mxsbf hkyf
nmgdpbytitle ^h[Z\ey_laZ]heh\hd\\_jogxxqZklvhdgZZnmgdpbytext\klZ\ey_ll_dkl\ex[h_f_klh]jZnbdZBkihevah\Zgb_TEX ij_^klZ\e_gbyiha\hey_l
ijbf_gylv ]j_q_kdb_ [md\u fZl_fZlbq_kdb_ kbf\heu b jZaebqgu_ rjbnlu
Ke_^mxsbcijbf_j^_fhgkljbjm_lwlm\hafh`ghklv
t = -pi:pi/100:pi;
y = sin(t);
plot(t,y)
axis([-pi pi -1 1])
xlabel( ' -\pi \leq \itt \leq \pi ' )
ylabel( ' sin(t) ' )
WLWOH
text(-1
=jZnbd nmgdpbb VLQ
?LW^Hlf_lvl_ g_q_lgmx kbff_ljbx`
= j Z nb d nm g d p b b
VLQ
VLQ W
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π≤ W ≤ π
NmgdpbbPHVKbVXUIDFH
MATLAB hij_^_ey_l ih\_joghklv dZd z dhhj^bgZlu lhq_d gZ^ dhhj^bgZlghc
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Nmgdpbbmesh bsurfacehlh[jZ`Zxlih\_joghklv\lj_obaf_j_gbyoIjbwlhf
28
=jZnbdZ
mesh kha^Z_ldZjdZkgmxih\_joghklv]^_p\_lgu_ebgbbkh_^bgyxllhevdhaZ^Zggu_ lhqdb Z nmgdpby surface \f_kl_ k ebgbyfb hlh[jZ`Z_l \ p\_l_ b kZfm
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<bamZebaZpbynmgdpbc^\moi_j_f_gguo
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Y khklhysb_ ba ih\lhjyxsboky kljhd b klhe[ph\ khhl\_lkl\_ggh i_j_^ bkihevah\Zgb_fnmgdpbbAZl_fbkihevamxl wlb fZljbpu ^ey \uqbke_gbyb hlh[jZ`_gbynmgdpbbNmgdpbymeshgrid ij_h[jZam_lh[eZklvhij_^_e_gbyaZ^Zggmxq_j_ah^bg\_dlhjbeb^\Z\_dlhjZxby\fZljbpuXbY^eybkihevah\Zgbyijb\uqbke_gbbnmgdpbb^\moi_j_f_gguoKljhdbfZljbpuX ^m[ebjmxl
\_dlhjxZklhe[puY±\_dlhjy.
>ey\uqbke_gby^\mf_jghcnmgdpbbsinc , sin(r)/r, \h[eZklbx-y ihklmiZxlke_^mxsbfh[jZahf
[X, Y] = meshgrid(-8:.5:8);
R = sqrt(X.^2+Y.^2)+eps;
Z = sin(R)./R;
mesh(X,Y,Z)
<wlhfijbf_j_R ±wlhjZkkhygb_hlgZqZeZdhhj^bgZldhlhjhfmkhhl\_lkl\m_l
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hij_^_eyxlboyjdhklvbp\_lGZijbf_j
load durer
whos
29
GZqZeh jZ[hlu k MATLAB
ihdZ`_l qlh nZce durer.mat \ ^bj_dlhjbb demo khklhbl ba fZljbpu jZaf_jhf
gZ fZljbpuX bfZljbpujZaf_jhfgZ fZljbpumap We_f_glu
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imag(X)
colormap(map)
axis image
\hkijhba\h^yl]jZ\xjm>xj_jZihdZaZggmx\gZqZe_wlhcdgb]b<ukhdh_jZaj_r_gb_fZ]bq_kdh]hd\Z^jZlZgZoh^ys_]hky\ijZ\hf\_jog_fm]em^hklmigh
\^jm]hfnZce_GZ[_jbl_
load detail
bbkihevamcl_klj_edm'\\_jo gZdeZ\bZlmj_^eyih\lhjgh]haZimkdZdhfZg^image, colormap b axis.
colormap(hot)
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Hipby Print \ f_gx File b dhfZg^Z print i_qZlZxl ]jZnbdm MATLAB F_gx
Print \uau\Z_l ^bZeh]h\h_ hdgh dhlhjh_ iha\hey_l \u[bjZlv h[sb_ klZg^Zjlgu_\ZjbZglui_qZlbDhfZg^Zprint h[_ki_qb\Z_l[hevrmx]b[dhklvijb\u\h^_\uoh^guo^Zgguobiha\hey_ldhgljhebjh\Zlvi_qZlvbaFnZceh\J_amevlZl fh`_l [ulv ihkeZg ijyfh gZ ijbgl_j \u[jZgguc ih mfheqZgbx beb khojZg_g\aZ^ZgghfnZce_<hafh`ghrbjhdh_\Zjvbjh\Zgb_nhjfZlZ\uoh^guo
^Zgguo\dexqZybkihevah\Zgb_PostScript.
GZijbf_j ke_^mxsZy dhfZg^Z khojZgbl l_dms__ hdgh bah[jZ`_gby dZd p\_lghcPostScript Level 2 Encapsulated \nZce_magicsquare.eps:
print –depsc2 magicsquare.eps
<Z`gh agZlv \hafh`ghklb \Zr_]h ijbgl_jZ i_j_^ bkihevah\Zgb_f dhfZg^u
print. GZijbf_jnZceu Postscript Level 2 h[uqghf_gvr_b\hkijhba\h^ylkygZfgh]h [uklj__ q_f Postscript Level H^gZdh g_ \k_ Postscript ijbgl_ju ih^^_j`b\Zxl Level 2, lZdbf h[jZahf \Zf g_h[oh^bfh magZlv qlh fh`_l h[jZ[Zlu\Zlv \Zr_ mkljhckl\h \u\h^Z MATLAB bkihevam_l ^bnn_j_gpbjh\Zgguc
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30
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MATLAB.
• DhfZg^Zhelp
• HdghkijZ\db
• MATLAB Help Desk
• L_dmsb_kijZ\hqgu_kljZgbpu
• K\yavkThe MathWorks, Inc.
DhfZg^ZKHOS
DhfZg^Zhelp ±wlhkZfuchkgh\ghckihkh[hij_^_e_gbykbglZdkbkZbih\_^_gby
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help magic
\u^Zkl
MAGIC Magic square.
MAGIC(N) is an N-by-N matrix constructed from the integers
1 through N^2 with equal row, column, and diagonal sums.
Produces valid magic squares for N = 1,3,4,5,...
AZf_qZgb_ MATLAB \l_dms_ckijZ\d_bkihevam_laZ]eZ\gu_[md\u^eynmgdpbcbi_j_f_gguo ^ey lh]h qlh[u \u^_eblv boba l_dklZ H^gZdh ijb gZ[hj_
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MATLAB qm\kl\bl_e_gdj_]bkljZfZ\k_bf_gZnmgdpbbkljhqgu_
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nmgdpbc\wlhc^bj_dlhjbbkdjZldbfhibkZgb_fgZ^hgZ[jZlv
help matfun
Matrix functions - numerical linear algebra.
Matrix analysis.
norm
- Matrix or vector norm.
normest
- Estimate the matrix 2-norm.
...
DhfZg^Z
help
HELP topics:
matlab\general
matlab\ops
...
-
General purpose commands.
Operators and special characters.
31
GZqZeh jZ[hlu k MATLAB
HdghkijZ\db
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helpwin
>ey\u\h^ZhdgZkijZ\dbihhl^_evgufjZa^_eZfgZ[_jbl_
helpwin topic
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DhfZg^Z lookfor iha\hey_l bkdZlvnmgdpbb ihdexq_\hfm keh\m HgZ ijhkfZljb\Z_l i_j\mx kljhdm l_dklZ kijZ\db gZau\Z_fmx kljhdhc H1 ^ey dZ`^hc
nmgdpbb MATLAB b \ha\jZsZ_l kljhdb H1, kh^_j`Zsb_ aZ^Zggh_ dexq_\h_
keh\hGZijbf_jMATLABg_bf__lnmgdpbbkbf_g_finverseIhwlhfmhl\_l
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help inverse
[m^_l
inverse.m not found.
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lookfor inverse
gZc^_l fgh`_kl\h kh]eZkh\Zgguo hl\_lh\ < aZ\bkbfhklb hl lh]h dZdb_ toolboxes \umklZgh\beb\uihemqbl_khhl\_lkl\mxsb_aZibkbGZijbf_j
INVHILB Inverse Hilbert matrix.
ACOS Inverse cosine.
ACOSH Inverse hyperbolic cosine.
ACOT Inverse cotangent.
ACOTH Inverse hyperbolic cotangent.
ACSC Inverse cosecant.
ACSCH Inverse hyperbolic cosecant.
ASEC Inverse secant.
ASECH Inverse hyperbolic secant.
ASIN Inverse sine.
ASINH Inverse hyperbolic sine.
ATAN Inverse tangent.
...
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32
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lookfor –all
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H1.
Help Desk
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MATLAB>\_dhfZg^uwhobwhosihdZau\Zxll_dms__kh^_j`Zgb_jZ[hq_]h
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whos
Name
Size
Bytes Class
A
D
M
S
h
n
s
v
4x4
5x3
10x1
1x3
1x11
1x1
1x5
2x5
128
120
3816
442
22
8
10
20
double array
double array
cell array
struct array
char array
double array
char array
char array
Grand total is 471 elements using 4566 bytes.
>ey m^Ze_gby \k_o kms_kl\mxsbo i_j_f_gguo ba jZ[hq_]h ijhkljZgkl\Z
MATLAB\\_^bl_
clear
DhfZg^ZVDYH
DhfZg^Zsave khojZgy_lkh^_j`Zgb_jZ[hq_]hijhkljZgkl\Z\F:LnZce_dhlhjuc fh`_l [ulv ijhqblZg dhfZg^hc load \ ihke_^mxsbo k_ZgkZo jZ[hlu
MATLABGZijbf_j
save August17th
khojZgy_lkh^_j`Zgb_\k_]hjZ[hq_]hijhkljZgkl\Z\nZce_August17th.mat?kebgm`gh\ufh`_l_khojZgblvlhevdhhij_^_e_ggu_i_j_f_ggu_mdZau\Zybo
bf_gZihke_bf_gbnZceZ
34
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-ascii
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-ascii -double
Bkihevam_lagZqgucl_dklh\hcnhjfZl
-ascii -double -tabs
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\u \uau\Z_l_ klZg^Zjlgmx nmgdpbx MATLAB bkihegy_l i_j\uc FnZce gZ
k\h_f imlb dhlhjuc bf__l aZ^Zggh_ bfy <u fh`_l_ aZf_gblv ih\_^_gb_ bkihevah\Zgb_fki_pbZevguo^bj_dlhjbcbih^^bj_dlhjbc
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kbkl_fguo dhfZg^ ^ey fZgbimeypbc gZ^ nZceZfb Gb`_ijb\_^_ggZy lZ[ebpZ
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cat
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cd
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delete
set defalt
>ey[hevrbgkl\ZbawlbodhfZg^\ufh`_l_bkihevah\Zlvihegu_imlbrZ[ehgubmdZaZl_eb^bkdh\\h[uqghcnhjf_
35
GZqZeh jZ[hlu k MATLAB
DhfZg^ZGLDU\
DhfZg^Zdiarykha^Z_l^g_\gbdk_ZgkZMATLAB\^bkdh\hfnZce_<ufh`_l_
ijhkfhlj_lv b hlj_^Zdlbjh\Zlv dhg_qguc l_dklh\hc nZce bkihevamy ex[hc
l_dklh\hcijhp_kkhj>eykha^ZgbynZceZih^bf_g_fdiarydhlhjuckh^_j`bl
\k_dhfZg^udhlhju_\ubkihevam_l_\dexqZy\u\h^gZi_qZlv djhf_]jZnbq_kdh]h\u\h^Z \\_^bl_
diary
>eykhojZg_gbyk_ZgkZMATLAB\nZce_khij_^_e_ggufbf_g_fbkihevamcl_
diary filename
IjbhklZgh\d_aZibkbk_ZgkZjZ[hlugZ[_jbl_
diary off
AZimkd\g_rgboijh]jZff
<hkdebpZl_evgucagZdhagZqZ_l\uoh^bah[hehqdbMATLABHglZd`_hagZqZ_l qlh ihke_^mxsZy kljhdZ \\h^Z [m^_l dhfZg^hc d hi_jZpbhgghc kbkl_f_
bebFinder gZ Mac Wlh hq_gv ihe_agh ^ey \uah\Z mlbebl beb aZimkdZ ^jm]bo
ijh]jZff[_a\uoh^Zba MATLABGZVMSgZijbf_j
!edt magik.m
\uah\_l j_^Zdlhj gZau\Z_fuc edt ^ey nZceZ magik.m Dh]^Z \u \uoh^bl_ ba
\g_rg_cijh]jZffuhi_jZpbhggZykbkl_fZ\ha\jZsZ_lmijZ\e_gb_MATLAB.
36
Ih^jh[g__ h fZljbpZo b fZkkb\Zo
Ih^jh[g__hfZljbpZobfZkkb\Zo
Wlhl jZa^_e jZkkdZ`_l \Zf [hevr_ h jZ[hl_ k fZljbpZfb b fZkkb\Zfb m^_eyy
hkh[h_\gbfZgb_
• Ebg_cghcZe]_[j_
• FZkkb\Zf
• Fgh]hf_jguf^Zgguf
Ebg_cgZyZe]_[jZ
L_jfbgufZljbpZbfZkkb\qZklh g_ijZ\bevgh bkihevamxl dZd \aZbfhaZf_gy_fu_;he__lhqghfZljbpZ±wlh^\mf_jgucqbke_ggucfZkkb\bkihevam_fuc\
ebg_cguo ij_h[jZah\Zgbyo FZl_fZlbq_kdb_ hi_jZpbb hij_^_e_ggu_ gZ fZljbpZoy\eyxlkyh[t_dlhfebg_cghcZe]_[ju
FZ]bq_kdbcd\Z^jZl>xj_jZ
A =
16
5
9
4
3
10
6
15
2
11
7
14
13
8
12
1
bkihevam_lky \ g_dhlhjuo ijbf_jZo dhlhju_ iha\heyxl ihqm\kl\h\Zlv hi_jZpbbgZ^fZljbpZfb\ MATLAB <u m`_ \b^_eb hi_jZpbx ljZgkihgbjh\Zgby
fZljbpuA'. >h[Z\e_gb_fZljbpud_zljZgkihgbjh\Zgghc^Z_lkbff_ljbqgmx
fZljbpm
A + A'
ans =
32
8
11
17
8
20
17
23
11
17
14
26
17
23
26
2
Kbf\hemfgh`_gby h[hagZqZ_lfZljbqgh_ijhba\_^_gb_\dexqZxs__\gmlj_gg__ ijhba\_^_gb_ f_`^m kljhdZfb b klhe[pZfb Mfgh`_gb_ fZljbpugZ _z
ljZgkihgbjh\ZggmxlZd`_^Z_lkbff_ljbqgmxfZljbpm
A'*A
ans =
378
212
206
360
212
370
368
206
206
368
370
212
360
206
212
378
Hij_^_ebl_evwlhcqZklghcfZljbpuhdZau\Z_lkyjZ\gufgmexhagZqZyqlhwlZ
fZljbpZy\ey_lkykbg]meyjghc
d = det(A)
37
GZqZeh jZ[hlu k MATLAB
d =
0
Ijb\_^_ggZy d kljhdZf klmi_gqZlZy nhjfZ fZljbpu : \u]ey^bl ke_^mxsbf
h[jZahf
R = rref(A)
R =
1
0
0
0
0
1
0
0
0
0
1
0
1
-3
3
0
Ihkdhevdm aZ^ZggZy fZljbpZ y\ey_lky kbg]meyjghc lh hgZ g_ bf__l h[jZlghc
?keb\u\k_lZdbihiulZ_l_kv_zhij_^_eblv
X = inv(A)
lhihemqbl_ij_^mij_`^_gb_
Warning: Matrix is close to singular or badly scaled.
Results may be inaccurate. RCOND = 1.175530e-017.
Hrb[dZhdjm]e_gbyij_iylkl\m_lZe]hjblfmh[jZs_gbyfZljbpuijbhij_^_e_gbb lhqghc kbg]meyjghklb Gh agZq_gb_ rcond dhlhjh_ mklZgZ\eb\Z_l mkeh\b_
hp_gdb^eyh[jZlghcfZljbpubf__lihjy^hdepshlghkbl_evghclhqghklbqbkeZkieZ\Zxs_clhqdhcihwlhfm\uqbke_gb_h[jZlghcfZljbpug_hq_gv`_eZl_evgh
Bgl_j_kghgZclbkh[kl\_ggu_agZq_gbyfZ]bq_kdh]hd\Z^jZlZ
e = eig(A)
e =
34.0000
8.0000
-0.0000
-8.0000
H^ghbakh[kl\_gguoagZq_gbcjZ\ghgmexqlhy\ey_lkyke_^kl\b_fkbg]meyjghklb KZfh_ [hevrh_ kh[kl\_ggh_ agZq_gb_ jZ\gh fZ]bq_kdhc kmff_ Wlh
ijhbkoh^blihlhfm qlh \_dlhj khklhysbc ba \k_o _^bgbp y\ey_lky kh[kl\_gguf\_dlhjhf
v = ones(4,1)
v =
1
1
1
1
A*v
38
Ih^jh[g__ h fZljbpZo b fZkkb\Zo
ans =
34
34
34
34
Dh]^ZfZ]bq_kdbcd\Z^jZlbaf_jy_lky_]hfZ]bq_kdhckmffhc
P = A/34
j_amevlZl [m^_l [bklhoZklbq_kdhc fZljbp_c m dhlhjhc kmffu \ kljhdZo b
klhe[pZo\k_jZ\gu_^bgbpZf
P =
0.4706
0.1471
0.2647
0.1176
0.0882
0.2941
0.1765
0.4412
0.0588
0.3235
0.2059
0.4118
0.3824
0.2353
0.3529
0.0294
LZdb_ fZljbpu ij_^klZ\eyxl kh[hc \_jhylghklv i_j_oh^Z \ FZjdh\kdhf ijhp_kk_Ih\lhjgu_\ha\_^_gbyfZljbpu\kl_i_gvy\eyxlkyih\lhjgufbrZ]Zfb
\wlhfijhp_kk_>eygZr_]hijbf_jZiylZykl_i_gv
P^5
jZ\gZ
ans =
0.2507
0.2497
0.2500
0.2496
0.2495
0.2501
0.2498
0.2506
0.2494
0.2502
0.2499
0.2505
0.2504
0.2500
0.2503
0.2493
Bawlh]hke_^m_lqlh_kebk klj_fblkyd[_kdhg_qghklblh]^Z\k_we_f_glu\khckl_i_gb, Pk,klj_fylkyd¼.
<aZdexq_gb_jZkkfhljbfdhwnnbpb_gluoZjZdl_jbklbq_kdh]hihebghfZ
poly(A)
ans =
1.0e+003 *
0.0010
-0.0340
-0.0640
2.1760
0.0000
Baq_]hke_^m_lqlhoZjZdl_jbklbq_kdbcihebghf
det(A-λI)
jZ\_g
λ4 – 34λ3 – 64λ2 + 2176λ
DhgklZglZ jZ\gZ gmex lZd dZd fZljbpZ y\ey_lky kbg]meyjghc Z dhwnnbpb_gl
ijblj_lv_ckl_i_gbjZ\_glZddZdfZljbpZfZ]bq_kdZy
39
GZqZeh jZ[hlu k MATLAB
FZkkb\u
Dh]^Zfu\uoh^bfbafbjZebg_cghcZe]_[jufZljbpuklZgh\ylky^\mf_jgufb
qbke_ggufb fZkkb\Zfb :jbnf_lbq_kdb_ hi_jZpbb gZ fZkkb\Zo ijhba\h^ylky
ihwe_f_glghWlh hagZqZ_l qlh kmffbjh\Zgb_ b \uqblZgb_ y\eyxlky h^bgZdh\ufb hi_jZpbyfb ^ey fZljbp b fZkkb\h\ Z mfgh`_gb_ ^ey gbo jZaebqgh
MATLABbkihevam_llhqdmbeb^_kylbqgmxlhqdmdZdqZklvaZibkb^eyhi_jZpbbmfgh`_gbyfZkkb\h\
Kibkhdhi_jZlhjh\\dexqZ_l\k_[y
+
.*
./
.\
.^
.'
kmffbjh\Zgb_
\uqblZgb_
ihwe_f_glgh_mfgh`_gb_
ihwe_f_glgh_^_e_gb_
ihwe_f_glgh_e_\h_^_e_gb_
ihwe_f_glgh_\ha\_^_gb_\kl_i_gv
g_khijy`_ggh_fZljbqgh_ljZgkihgbjh\Zgb_
?keb fZ]bq_kdbc d\Z^jZl >xj_jZ mfgh`blv gZ k_[y ih ijZ\beZf mfgh`_gby
fZkkb\h\
A.*A
j_amevlZlhf[m^_lfZkkb\kh^_j`Zsbcd\Z^jZlup_euoqbk_ehl ^h \ g_h[uqghfihjy^d_
ans =
256
25
81
16
9
100
36
225
4
121
49
196
169
64
144
1
Hi_jZpbb gZ^ fZkkb\Zfb ihe_agu ^ey kha^Zgby lZ[ebp Imklv n ± wlh \_dlhj
klhe[_p
n = (0:9)';
Lh]^Z
pows = [n
n.^2
2.^n]
kha^Z_llZ[ebpmd\Z^jZlh\bkl_i_g_c^\hcdb
pows =
0
1
2
3
4
5
6
7
8
9
0
1
4
9
16
25
36
49
64
81
1
2
4
8
16
32
64
128
256
512
40
Ih^jh[g__ h fZljbpZo b fZkkb\Zo
We_f_glZjgu_ fZl_fZlbq_kdb_ nmgdpbb jZ[hlZxl k fZkkb\Zfb ihwe_f_glgh
LZd
format short g
x = (1:0.1:2)';
logs = [x log10(x)]
kha^Z_llZ[ebpmeh]Zjbnfh\
logs =
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
0
0.041393
0.079181
0.11394
0.14613
0.17609
0.20412
0.23045
0.25527
0.27875
0.30103
Fgh]hf_jgu_^Zggu_
MATLABbkihevam_lf_lh^hjb_glZpbbklhe[ph\^eyfgh]hf_jguoklZlbklbq_kdbo ^Zgguo DZ`^uc klhe[_p \ gZ[hj_ ^Zgguo ij_^klZ\ey_l i_j_f_ggmx Z
dZ`^ZykljhdZ±j_amevlZlugZ[ex^_gbcLZdbfh[jZahfwe_f_gl i,j ±wlhih_
gZ[ex^_gb_jhci_j_f_gghc
<dZq_kl\_ijbf_jZjZkkfhljbfgZ[hj^Zgguoklj_fyi_j_f_ggufb
• qZklhlZk_j^_qguokhdjZs_gbc
• \_k
• qZkumijZ`g_gbcaZg_^_ex
>ey iylb gZ[ex^_gbc j_amevlbjmxsbc fZkkb\ fh`_l \u]ey^_lv ke_^mxsbf
h[jZahf
D =
72
81
69
82
75
134
201
156
148
170
3.2
3.5
7.1
2.4
1.2
I_j\ZykljhdZkh^_j`blqZklhlmk_j^_qguokhdjZs_gbc\_kbqZkumijZ`g_gbc
^eyi_j\h]hiZpb_glZ\lhjZykljhdZkh^_j`blZgZeh]bqgu_^Zggu_^ey\lhjh]h
b l^ <u fh`_l_ ijbf_gblv fgh]b_ nmgdpbb MATLAB ^ey ZgZebaZ ^Zgguo d
wlhfm gZ[hjm bgnhjfZpbb GZijbf_j ^ey lh]h qlh[u ihemqblv kj_^g__ b
kj_^g_d\Z^jZlbqgh_hldehg_gb_^eydZ`^h]hklhe[pZgZ^h
mu = mean(D), sigma = std(D)
41
GZqZeh jZ[hlu k MATLAB
mu =
75.8
161.8
3.48
5.6303
25.499
2.2107
sigma =
Qlh[uihkfhlj_lvkibkhd\k_onmgdpbcMATLAB^eyZgZebaZ^ZgguogZ[_jbl_
help datafun
?keb\Zfgm`ghmagZlvhStatistics Toolbox\\_^bl_
help stats
KdZeyjgh_jZkrbj_gb_
FZljbpu b kdZeyju fh]ml dhf[bgbjh\Zlvky jZaebqgufb imlyfb GZijbf_j
kdZeyj\uqblZ_lkybafZljbpuiml_f\uqblZgbybadZ`^h]hwe_f_glZKj_^g__
agZq_gb_we_f_glh\^eygZr_]hfZ]bq_kdh]hd\Z^jZlZjZ\ghihwlhfm
B = A - 8.5
nhjfbjm_lfZljbpmmdhlhjhckmffu\klhe[pZojZ\gugmex
B =
7.5
-3.5
0.5
-4.5
-5.5
1.5
-2.5
6.5
-6.5
2.5
-1.5
5.5
4.5
-0.5
3.5
-7.5
sum(B)
ans =
0
0
0
0
Bkihevamy kdZeyjgh_ jZkrbj_gb_ MATLAB mdZau\Z_l aZ^Zgguc kdZeyj \k_f
bg^_dkZf\^bZiZahg_GZijbf_j
B(1:2,2:3)=0
h[gmey_lqZklvfZljbpuB
B =
7.5
-3.5
0.5
-4.5
0
0
-2.5
6.5
0
0
-1.5
5.5
Eh]bq_kdZybg^_dkZpby
4.5
-0.5
3.5
-7.5
Eh]bq_kdb_\_dlhjZkha^Zggu_baeh]bq_kdbohi_jZlhjh\bhi_jZlhjh\kjZ\g_gbyfh]ml[ulvbkihevah\Zgu^eykkuedbgZih^fZkkb\uIj_^iheh`bfqlhX
h[udgh\_ggZyfZljbpZbL fZljbpZlh]h`_jZaf_jZghkh^_j`ZsZyeh]bq_kdb_
hi_jZpbbLh]^ZX(L)aZ^Z_lwe_f_gluX\dhlhjuowe_f_gluL g_gme_\u_
42
Ih^jh[g__ h fZljbpZo b fZkkb\Zo
Wlhl \b^ bg^_dkZpbb fh`_l [ulv hkms_kl\e_g aZ h^bg rZ] mdZaZgb_f eh]bq_kdhchi_jZpbblZdhcdZdbg^_dkZpby\ujZ`_gbyImklv\ubf__l_ ke_^mxsbc
gZ[hj^Zgguo
x =
2.1 1.7 1.6 1.5 NaN 1.9 1.8 1.5 5.1 1.8 1.4 2.2 1.6 1.8
NaN – wlh f_ldZ^eyg_^hklZxs_]hgZ[ex^_gbydZdgZijbf_jhrb[dZijbhl\_l_gZ\hijhkZgd_lu>eylh]hqlh[um[jZlv^Zggu_keh]bq_kdhcbg^_dkZpb_c bkihevamcl_ finite(x) dhlhjZy y\ey_lky bklbghc ^ey \k_o dhg_qguo qbke_gguoagZq_gbcbeh`vx^eyNaN b Inf.
x = x(finite(x))
x =
2.1 1.7 1.6 1.5 1.9 1.8 1.5 5.1 1.8 1.4 2.2 1.6 1.8
K_cqZkhklZeZkvh^gZgZ[ex^Z_fZy\_ebqbgZaZf_lghhlebqZxsZykyhlhklZevguo ± wlh \u[jhk Ihke_^mxsb_ ^_ckl\by mkljZgyxl \u[jhku \ ^Zgghf
kemqZ_ l_ we_f_glu ^ey dhlhjuo kj_^g_d\Z^jZlbqgh_ hldehg_gb_ [he__ q_f \
ljbjZaZmdehgy_lkyhlkj_^g_]h
x = x(abs(x-mean(x)) <= 3*std(x))
x =
2.1 1.7 1.6 1.5 1.9 1.8 1.5 1.8 1.4 2.2 1.6 1.8
< dZq_kl\_ ^jm]h]h ijbf_jZ gZc^_f iheh`_gb_ ijhkluo qbk_e \ fZ]bq_kdhf
d\Z^jZl_ >xj_jZ bkihevamy eh]bq_kdh_ bg^_dkbjh\Zgb_ b kdZeyjgh_ jZkrbj_gb_qlhh[gmeblv\k_g_ijhklu_qbkeZ
A(~isprime(A))=0
A =
0
5
0
0
3
0
0
0
2
11
7
0
13
0
0
0
NmgdpbyILQG
Nmgdpbyfind hij_^_ey_lbg^_dkufZkkb\Zwe_f_glh\kaZ^Zggufbeh]bq_kdbfb
mkeh\byfb < gZb[he__ ijhklhc nhjf_ find \ha\jZsZ_l \_dlhjklhe[_p bg^_dkh\LjZgkihgbjm_f_]h^eyihemq_gby\_dlhjZkljhdbGZijbf_j
k = find(isprime(A))'
\u[bjZ_l iheh`_gby bkihevamy h^ghf_jgh_ bg^_dkbjh\Zgb_ ijhkluo qbk_e
fZ]bq_kdh]hd\Z^jZlZ
k =
2
5
9
10
11
13
IhdZ`_fwlbqbkeZdZd\_dlhjkljhdm\ihjy^d_hij_^_e_gghfnmgdpb_c
43
GZqZeh jZ[hlu k MATLAB
A(k)
ans =
5
3
2
11
7
13
?keb \u bkihevam_l_ k dZd bg^_dk k e_\hc klhjhgu \ hi_jZlhj_ ijbk\Zb\Zgby
lhfZljbqgZykljmdlmjZkhojZgy_lky
A(k) = NaN
A =
16
NaN
9
4
NaN
10
6
15
NaN
NaN
NaN
14
NaN
8
12
1
44
MijZ\e_gb_ ihlhdZfb
MijZ\e_gb_ihlhdZfb
MATLAB bf__liylv\b^h\kljmdlmjmijZ\e_gbyihlhdZfb
•
•
•
•
•
hi_jZlhjif
hi_jZlhjswitch
pbdeufor
pbdeuwhile
hi_jZlhjbreak
if
Hi_jZlhjif \uqbkey_leh]bq_kdh_\ujZ`_gb_b\uihegy_l]jmiimhi_jZlhjh\
_keb \ujZ`_gb_ bklbggh G_h[yaZl_evgu_ dexq_\u_ keh\Z elseif b else kem`Zl
^ey \uiheg_gby Zevl_jgZlb\guo ]jmii hi_jZlhjh\ Dexq_\h_ keh\h end dhlhjh_kh]eZkm_lkykifaZ\_jrZ_lihke_^gxx ]jmiim hi_jZlhjh\ LZdbf h[jZahf
\k_]jmiiu hi_jZlhjh\ aZdexq_gu f_`^m q_luj_o dexq_\uo keh\ [_a bkihevah\Zgbynb]mjguobebh[uqguokdh[hd
:e]hjblf0$7/$%^eykha^ZgbyfZ]bq_kdh]hd\Z^jZlZihjy^dZQ\dexqZ_lljb
jZaguokemqZyQg_q_lgh_Qq_lgh_ghg_^_eblkygZbQq_lgh_b^_eblkygZ
Gb`_ijb\_^_gijbf_jkhhl\_lkl\mxs_]hdh^Z
if rem(n,2) ~= 0
M = odd_magic(n)
elseif rem(n,4) ~= 0
M = single_even_magic(n)
else
M = double_even_magic(n)
end
< wlhf ijbf_j_ ljb kemqZy y\eyxlky \aZbfgh bkdexqZxsbfb gh _keb [u wlh
[uehg_lZdlh\uihegyehkv[ui_j\h_bklbggh_mkeh\b_
<Z`gh ihgylv dZd hi_jZlhj hlghr_gby b hi_jZlhj if jZ[hlZxl k fZljbpZfb
Dh]^Z \u ohlbl_ magZlv jZ\gu eb ^\_ i_j_f_ggu_ gm`gh bkihevah\Zlv ke_^mxsmxdhgkljmdpbx
if A == B, . . .
WlhijZ\bevgucdh^0$7/$%bhghkms_kl\ey_llhqlh\uh`b^Z_l__keb$b
%y\eyxlkykdZeyjZfbGhdh]^Z$b%±fZljbpu$ %g_jZ[hlZ_l_kebhgb
g_jZ\guJZ\_gkl\hfZljbphagZqZ_lihwe_f_glgh_jZ\_gkl\hNZdlbq_kdb_keb$b%bf_xljZaebqgu_jZaf_ju0$7/$%\u^Zklhrb[dm
IjZ\bevguc kihkh[ hij_^_e_gby jZ\_gkl\Z f_`^m ^\mfy i_j_f_ggufb ± wlh
bkihevah\Zgb_nmgdpbbisequal
if isequal(A,B), . . .
45
GZqZeh jZ[hlu k MATLAB
>Ze__ijb\_^_g^jm]hcijbf_jdhlhjucbkke_^m_lwlhl\hijhk?kebAbB y\eyxlky kdZeyjZfb lh gb`_ijb\_^_ggZy ijh]jZffZ gbdh]^Z g_ ijb\_^_l d g_h`b^Zgghc kblmZpbb Gh ^ey [hevrbgkl\Z iZj bkihevam_fuo fZljbp \dexqZy
gZrb fZ]bq_kdb_ d\Z^jZlu k i_j_klZ\e_ggufb klhe[pZfb gb h^gh ba mkeh\bc
A > B, A < B beb A ==B g_ y\ey_lky bklbgguf ^ey \k_o we_f_glh\ b ihwlhfm
\uihegy_lkykemqZcelse.
if A > B
' greater '
elseif A < B
' less'
elseif A == B
' equal '
else
error ( ' G_ij_^\b^_ggZykblmZpby ' )
end
G_dhlhju_nmgdpbbfh]ml[ulvihe_agu^eyfZljbqgh]hkjZ\g_gbyijbbkihevah\Zgbbkhi_jZlhjhfifgZijbf_j
isequal
isempty
all
any
VZLWFKbFDVH
Hi_jZlhjswitch \uihegy_l]jmiimhi_jZlhjh\[ZabjmykvgZagZq_gbbi_j_f_gghc beb \ujZ`_gby Dexq_\u_ keh\Z case b otherwise jZa^_eyxl wlb ]jmiiu
<uihegy_lky lhevdh i_j\uc khhl\_lkl\mxsbc kemqZc G_h[oh^bfh bkihevah\Zlvend ^eykh]eZkh\Zgbykswitch.
Eh]bdZ Ze]hjblfZ fZ]bq_kdbo d\Z^jZlh\ fh`_l [ulv hibkZgZ gZ ke_^mxs_f
ijbf_j_
switch (rem(n,4)==0) + (rem(n,2)==0)
case 0
M = odd_magic(n)
case 1
M = single_even_magic(n)
case 2
M = double_even_magic(n)
otherwise
error( ' Wlhg_\hafh`gh' )
end
AZf_qZgb_ ^ey ijh]jZffbklh\ Kb < hlebqb_ hl yaudZ Kb hi_jZlhj switch \
0$7/$% g_ ijh\Zeb\Z_lky ?keb i_j\uc kemqZc y\ey_lky bklbgguf ^jm]b_
46
MijZ\e_gb_ ihlhdZfb
kemqZb g_ \uihegyxlky LZdbf h[jZahf g_l g_h[oh^bfhklb \ bkihevah\Zgbb
hi_jZlhjZbreak.
for
Pbdefor ih\lhjy_l]jmiimhi_jZlhjh\nbdkbjh\Zggh_ij_^hij_^_e_ggh_qbkeh
jZaDexq_\h_keh\hend hq_jqb\Z_ll_ehpbdeZ
for n = 3:32
r(n) = rank(magic(n));
end
r
LhqdZ k aZiylhc ihke_ \ujZ`_gby \ l_e_ pbdeZ ij_^hl\jZsZ_l ih\lhj_gby \u\h^Zj_amevlZlh\gZwdjZgZr ihke_pbdeZ\u\h^blhdhgqZl_evgucj_amevlZl
Ohjhrbfklbe_fy\eyxlkyhlklmiuijbbkihevah\Zgbbpbdeh\^eyemqr_cqblZ_fhklbhkh[_gghdh]^Zhgb\eh`_ggu_
for i = 1:m
for j = 1:n
H(i,j) = 1/(i+j);
end
end
while
Pbde while ih\lhjy_l ]jmiim hi_jZlhjh\ hij_^_e_ggh_ qbkeh jZa ihdZ \uihegy_lkyeh]bq_kdh_ mkeh\b_Dexq_\h_keh\hend hq_jqb\Z_lbkihevam_fu_hi_jZlhju
Gb`_ ijb\_^_gZ ihegZy ijh]jZffZ beexkljbjmxsZy jZ[hlm hi_jZlhjh\
while, if, else benddhlhjZybkihevam_lf_lh^^_e_gbyhlj_adZihiheZf^eygZoh`^_gbygme_cihebghfZ
a = 0; fa = -Inf;
b = 3; fb = Inf;
while b-a > eps*b
x = (a+b)/2;
fx = x^3-2*x-5;
if sign(fx) == sign(fa)
a = x; fa = fx;
else
b = x; fb = fx;
end
end
x
J_amevlZlhf[m^_ldhj_gvihebghfZx3-2x-5
x =
2.09455148154233
47
GZqZeh jZ[hlu k MATLAB
>ey hi_jZlhjZ while \_jgu l_ `_ ij_^hkl_j_`_gby hlghkbl_evgh fZljbqgh]h
kjZ\g_gbyqlhb^eyhi_jZlhjZif, dhlhju_h[km`^ZebkvjZg__
break
Hi_jZlhj break iha\hey_l ^hkjhqgh \uoh^blv ba pbdeh\ for beb while <h \eh`_gguopbdeZobreak hkms_kl\ey_l\uoh^lhevdhbakZfh]h\gmlj_gg_]hpbdeZ
Gb`_ij_^klZ\e_gmemqr_gguc\ZjbZglij_^u^ms_]hijbf_jZIhq_fmbkihevah\Zgb_hi_jZlhjZbreak \^ZgghfkemqZ_\u]h^gh"
a = 0; fa = -Inf;
b = 3; fb = Inf;
while b-a > eps*b
x = (a+b)/2;
fx = x^3-2*x-5;
if fx ==0
break
elseif sign(fx) == sign(fa)
a = x; fa = fx;
else
b = x; fb = fx;
end
end
x
48
>jm]b_ kljmdlmju ^Zgguo
>jm]b_kljmdlmju^Zgguo
Wlhl jZa^_e ihagZdhfbl \Zk k g_dhlhjufb kljmdlmjZfb ^Zgguo \ MATLAB,
\dexqZy
•
•
•
•
Fgh]hf_jgu_fZkkb\u
FZkkb\uyq__d
Kbf\heubl_dkl
Kljmdlmju
Fgh]hf_jgu_fZkkb\u
Fgh]hf_jgu_fZkkb\u\MATLABwlhfZkkb\u[he__q_fk^\mfybg^_dkZfb
Hgb fh]ml [ulv kha^Zgu \uah\hf nmgdpbc zeros, ones, rand beb randn k [he__
q_f^\mfyZj]mf_glZfbGZijbf_j
R = randn(3,4,5)
kha^Z_l oo fZkkb\ k ghjfZevgh jZkij_^_e_ggufb kemqZcgufb
we_f_glZfb
Lj_of_jgu_ fZkkb\u fh]ml ij_^klZ\eylv lj_of_jgu_ nbabq_kdb_ ^Zggu_ gZijbf_jl_fi_jZlmjm\dhfgZl_J_amevlZlij_^klZ\ey_lkyihke_^h\Zl_evghklvx
fZljbp A(k) beb aZ\bkys_c hl \j_f_gb fZljbp_c A(t) < wlbo kemqZyo we_f_gl
(i,j NhcfZljbpubebtkhch[hagZqZ_lkyA(i,j,k).
<_jkbbfZ]bq_kdh]hd\Z^jZlZMATLABb>xj_jZhlebqZxlkyi_j_klZ\e_ggufb
klhe[pZfbHi_jZlhj
p = perms(1:4);
]_g_jbjm_l i_j_klZgh\dbqbk_ehl^hN-Zyi_j_klZgh\dZ±wlh\_dlhj
kljhdZp(k,:)Lh]^Z
A = magic(4);
M = zeros(4,4,24);
for k = 1:24
M(:,:,k) = A(:,p(k,:));
end
ojZgblihke_^h\Zl_evghklv fZ]bq_kdbo d\Z^jZlh\ \ lj_of_jghf fZkkb\_ M.
JZaf_jM jZ\_g
size(M)
ans =
4
4
24
HdZau\Z_lkyqlhZyfZljbpZ\wlhcihke_^h\Zl_evghklb±fZljbpZ>xj_jZ
M(:,:,22)
49
GZqZeh jZ[hlu k MATLAB
ans =
16
5
9
4
3
10
6
15
2
11
7
14
13
8
12
1
Nmgdpby
sum(M,d)
\uqbkey_lkmffubaf_gyybg^_dkdLZd
sum(M,1)
- wlhoofZkkb\kh^_j`Zsbcdhibb\_dlhjZkljhdb
34
34
34
34
:
sum(M,2)
y\ey_lkyfZkkb\hfookh^_j`Zsbfdhibb\_dlhjZklhe[pZ
34
34
34
34
BgZdhg_p
S = sum(M,3)
^h[Z\ey_l fZljbpu \ ihke_^h\Zl_evghklv J_amevlZl bf__l jZaf_jghklv
ooihwlhfmhg\u]ey^bldZdfZkkb\o
S =
204
204
204
204
204
204
204
204
204
204
204
204
204
204
204
204
FZkkb\uyq__d
FZkkb\uyq__d\MATLAB – wlhfgh]hf_jgu_fZkkb\uwe_f_gludhlhjuoy\eyxlky dhibyfb ^jm]bo fZkkb\h\ FZkkb\ yq__d imkluo fZljbp fh`_l [ulv
kha^Zgkbkihevah\Zgb_fnmgdpbbcellGh[he__qZklhhgbkha^Zxlkyiml_faZdexq_gby jZaghh[jZaghc ]jmiiu h[t_dlh\ \ djm]eu_ kdh[db Djm]eu_ kdh[db
lZd`_bkihevamxlkykbg^_dkZfb^eyihemq_gby^hklmiZdkh^_j`ZgbxjZaebqguoyq__dGZijbf_j
C = { A sum(A) prod(prod(A)) }
^Z_l fZkkb\ yq__d o Wlb ljb de_ldb kh^_j`Zl fZ]bq_kdbc d\Z^jZl \_dlhj
kljhdmkkmffZfb\klhe[pZobijhba\_^_gb__]hwe_f_glh\?kebhlh[jZablvC
gZwdjZg_lh\um\b^bl_ke_^mxs__
50
>jm]b_ kljmdlmju ^Zgguo
C =
[4x4 double]
[1x4 double]
[2.0923e+013]
Wlhijhbkoh^blihlhfmqlhi_j\u_^\_yq_cdbkebrdhf[hevrb_^ey\u\h^Z\
wlhf h]jZgbq_gghf ijhkljZgkl\_ Z lj_lvy yq_cdZ kh^_j`bl lhevdh hl^_evgh_
qbkehb^eyg_]h_klvg_h[oh^bfZyh[eZklv\u\h^Z
Hq_gv\Z`ghaZihfgblv^\Z\Z`guofhf_glZI_j\h_^eyihemq_gby kh^_j`Zgbyh^ghcyq_cdbbkihevamcl_bg^_dk\djm]euokdh[dZoGZijbf_jC{1} \ha\jZsZ_lfZ]bq_kdbcd\Z^jZlZC{3} – 16!<lhjh_fZkkb\uyq__dkh^_j`Zldhibb^jm]bofZkkb\h\ Zg_bo mdZaZl_eb Ihwlhfm _keb \u \ihke_^kl\bb baf_gbl_fZljbpmAkC gbq_]hg_ijhbahc^_l
Lj_of_jgu_fZkkb\ufh]ml[ulvbkihevah\Zgu^eyojZg_gbyihke_^h\Zl_evghklbfZljbph^bgZdh\h]hjZaf_jZ:fZkkb\uyq__dfh]mlijbf_gylvky^eyojZg_gbyihke_^h\Zl_evghklbfZljbpjZaebqgh]hjZaf_jZGZijbf_j
M = cells(8,1);
for n =1:8
M{n} = magic(n);
end
M
kha^Z_l ihke_^h\Zl_evghklv fZ]bq_kdbo d\Z^jZlh\ \ hij_^_e_gghc ihke_^h\Zl_evghklb
M =
[
[2x2
[3x3
[4x4
[5x5
[6x6
[7x7
[8x8
1]
double]
double]
double]
double]
double]
double]
double]
<ufh`_l_gZclbgZr_]hklZjh]h^jm]ZijhklhgZ[jZ\
M{4}
Kbf\heubl_dkl
<\_^bl_l_dkl\MATLABbkihevamyh^bgZjgu_dZ\uqdbGZijbf_j
s = 'Hello'
J_amevlZlhfg_[m^_ly\eylvkyqbke_ggZyfZljbpZbebfZkkb\dhlhju_fujZkkfZljb\ZebjZg__Wlh[m^_lkbf\hevgucfZkkb\o
<gmlj_gg_kbf\heuojZgylkydZdqbkeZghg_\nhjfZl_kieZ\Zxs_clhqdhc
Hi_jZlhj
a = double(s)
51
GZqZeh jZ[hlu k MATLAB
ij_h[jZam_lfZkkb\kbf\heh\\qbkeh\mxfZljbpmkh^_j`Zsmxij_^klZ\e_gb_
kieZ\Zxs_clhqdhcASCII dh^Z^eydZ`^h]hkbf\heZJ_amevlZlhf[m^_l
a =
72
101
108
108
111
:\ujZ`_gb_
s = char(a)
hkms_kl\ey_lh[jZlgh_ij_\jZs_gb_
Ij_h[jZah\Zgb_ qbk_e \ kbf\heu ^_eZ_l \hafh`guf ijbkmlkl\b_ jZaebqguo
rjbnlh\ gZ \Zr_f dhfivxl_j_ I_qZlZ_fu_ kbf\heu \ ASCII dh^_ ij_^klZ\eyxlky p_eufb qbkeZfb hl ^h P_eu_ qbkeZ f_gvr_ ij_^klZ\eyxl
g_i_qZlZ_fu_ kbf\heu Wlb qbkeZ jZkiheh`_gu \ khhl\_lkl\mxs_f fZkkb\_
o
F = reshape(32:127,16,6)';
I_qZlZ_fu_kbf\heu\jZkrbj_gghfASCII gZ[hj_ij_^klZ\e_guF+128Dh]^Z
wlb qbkeZ bgl_jij_lbjmxlky dZd kbf\heu j_amevlZl aZ\bkbl hl lh]h dZdhc
rjbnl\^Zggucfhf_glbkihevam_lkyGZ[_jbl_ke_^mxs__
char(F)
char(F+128)
bihlhf ihbaf_gycl_ rjbnlu \ dhfZg^ghf hdg_ MATLAB Gb`_ ij_^klZ\e_g
h^bgbaijbf_jh\lh]hqlhfh`_lihemqblvky
ans =
!"#$%&'()*+,-./
0123456789:;<=>?
@ABCDEFGHIJKLMNO
PQRSTUVWXYZ[\]^_
`abcdefghijklmno
pqrstuvwxyz{|}~•
ans =
8†3¼ˆæ†,‹/©¤Š2
°±1‰—¶·z‹}ª0~€
:;<=>?@ABCDEFGHI
JKLMNOPQRSTUVWXY
Z[\]^_`abcdefghi
jklmnopqrstuvwxy
Kh_^bg_gb_ d\Z^jZlgufb kdh[dZfb dhgdZl_gbjm_l l_dklh\u_ i_j_f_ggu_ \f_kl_\[hevrmxkljhdm
h = [s, ' world']
h[t_^bgy_lkljhdbih]hjbahglZebb^Z_l
h =
Hello world
52
>jm]b_ kljmdlmju ^Zgguo
Hi_jZlhj
v = [s; 'world']
h[t_^bgy_lkljhdb\_jlbdZevqlhijb\h^bld
v =
Hello
world
AZf_lvl_qlhi_j_^kbf\hehfw \i_j_f_gghchg_h[oh^bfhihklZ\blvijh[_e
Zh[Zkeh\Z\i_j_f_gghcv^he`gu[ulvjZ\ghc^ebguJ_amevlbjmxsb_fZkkb\uy\eyxlkykgh\ZfZkkb\Zfbkbf\heh\i_j_f_ggZyh – 1o11Zi_j_f_ggZyv
– o
?klv ^\Z kihkh[Z qlh[u mijZ\eylv ]jmiihc l_dklZ kh^_j`Zs_c kljhdb jZaghc
^ebgu nhjfbjh\Zlv aZiheg_gguc fZkkb\ kbf\heh\ beb de_lhqguc fZkkb\
kljhd Nmgdpby char ijbgbfZ_l ex[h_ qbkeh kljhd ^h[Z\ey_l ijh[_eu \ dZ`^mx kljhdm qlh[u \k_ hgb [ueb jZ\ghc ^ebgu b nhjfbjm_l fZkkb\ kljhd k
kbf\hevghckljhdhc\dZ`^hckljhd_GZijbf_j
S = char('A' , 'rolling' , 'stone' , 'gathers' , 'momentum.')
\u^Z_l
S =
A
rolling
stone
gathers
momentum.
Ijbkmlkl\m_l^hklZlhqgh_dhebq_kl\hijh[_eh\\i_j\uoq_luj_okljhdZoqlh[u\k_kljhdb[uebjZ\ghc^ebgu>jm]hckihkh[±wlhkhojZgblvl_dkl\fZkkb\_yq__d
C = {'A' ; 'rolling' ; 'stone' ; 'gathers' ; 'momentum.'
}
[m^_lfZkkb\yq__do
C =
'A'
'rolling'
'stone'
'gathers'
'momentum.'
<u fh`_l_ ij_h[jZah\Zlv aZiheg_gguc kbf\hevguc fZkkb\ \ fZkkb\ yq__d ba
kljhdke_^mxsbfh[jZahf
C = cellstr(S)
H[jZlgh_ij_h[jZah\Zgb_
S = char(C)
53
GZqZeh jZ[hlu k MATLAB
Kljmdlmju
Kljmdlmju±wlhfgh]hf_jgu_fZkkb\uMATLABkwe_f_glZfb^hklmiddhlhjufhkms_kl\ey_lkyq_j_aiheyGZijbf_j
S.name = 'Ed Plum';
S.score = 83;
S.grade = 'B+';
kha^Z_lkdZeyjgmxkljmdlmjmklj_fyiheyfb
S =
name: 'Ed Plum'
score: 83
grade: 'B+'
DZdb\kz\MATLABkljmdlmjuy\eyxlkyfZkkb\Zfbihwlhfm\u fh`_l_^h[Z\eylv\gbowe_f_glu<wlhfkemqZ_dZ`^ucwe_f_glfZkkb\Zy\ey_lkykljmdlmjhckg_kdhevdbfbiheyfbIheyfh]ml^h[Z\eylvkyeb[hihh^ghfm
S(2).name = 'Toni Miller';
S(2).score = 91;
S(2).grade = 'A-' ;
eb[hiheghklvx
S(3) = struct( 'name', 'Jerry Garcia', . . .
'score', 70, 'grade', 'C' )
K_cqZk kljmdlmjZ klZeZ ^hklZlhqghc [hevrhc ihwlhfm i_qZlZ_lky ebrv _z
k\h^dZ
S =
1x3 struct array with fields:
name
score
grade
?klvg_kdhevdhkihkh[h\i_j_ljZgkebjh\Zlv jZaebqgu_ ihey \ ^jm]b_ fZkkb\u
MATLAB<k_hgb[ZabjmxlkygZaZibkbkibkdZjZa^_e_ggh]haZiylufb?keb
\ugZ[_j_l_
S.score
wlh[m^_ljZ\ghkbevghke_^mxs_fm
S(1).score, S(2).score, S(3).score
Wlhb_klvkibkhdjZa^_e_ggucaZiylufbIjZ\^Z[_a^jm]hcimgdlmZpbbhgg_
hq_gv ihe_a_g < wlhc kljhd_ ijhbkoh^bl ijbk\Zb\Zgb_ lj_o kq_lh\ score i_j_f_gghcihmfheqZgbxans b\u\h^j_amevlZlh\dZ`^h]hijbk\Zb\ZgbyGh_keb\u\dexqZ_l_\ujZ`_gb_dd\Z^jZlgu_kdh[db
54
>jm]b_ kljmdlmju ^Zgguo
[S.score]
lh`_kZfh_qlh
[S(1).score, S(2).score, S(3).score]
j_amevlZlhf[m^_lqbke_gguc\_dlhjkljhdZkh^_j`Zsbc\k_kq_lZ score)
ans =
83
91
70
:gZeh]bqgh
S.name
ijhklhijbk\Zb\Z_lbf_gZ names ihh^ghfmi_j_f_gghcansH^gZdhaZdexq_gb_wlh]h\ujZ`_gby\djm]eu_kdh[db
{S.name}
kha^Z_lfZkkb\yq__dokh^_j`Zsbcljbbf_gb names)
ans =
'Ed Plum'
'Toni Miller'
'Jerry Garcia'
Bnmgdpby
char(S.name)
klj_fyZj]mf_glZfbkha^Z_lfZkkb\kbf\heh\baiheyname.
ans =
Ed Plum
Toni Miller
Jerry Garcia
55
GZqZeh jZ[hlu k MATLAB
Kp_gZjbbbnmgdpbb
MATLAB ± wlh fhsguc yaud ijh]jZffbjh\Zgby lZd`_ dZd b bgl_jZdlb\gZy
\uqbkebl_evgZykj_^ZNZceudhlhju_kh^_j`Zldh^gZyaud_MATLAB, gZau\ZxlkyFnZceZfb<ukha^Z_l_FnZceubkihevamyl_dklh\hcj_^ZdlhjZaZl_fbkihevam_l_bodZdex[mxnmgdpbxbebdhfZg^mMATLAB.
Kms_kl\m_l^\Z\b^ZFnZceh\
• Kp_gZjbbdhlhju_ g_ bf_xl \oh^guob \uoh^guo Zj]mf_glh\ Hgb hi_jbjmxlk^ZggufbbajZ[hq_]hijhkljZgkl\Z
• Nmgdpbbdhlhju_ bf_xl \oh^gu_ b \uoh^gu_ Zj]mf_glu Hgb hi_jbjmxlkehdZevgufbi_j_f_ggufb
?keb\uy\ey_l_kvgh\bqdhf\MATLABijh]jZffbjh\Zgbbijhklhkha^Z\Zcl_
FnZceudhlhju_\uohlbl_bkihevah\Zlv\l_dms_c^bj_dlhjbb?keb`_\u
jZajZ[hlZebfgh]hFnZceh\\uaZohlbl_k]jmiibjh\Zlvbo\hl^_evgu_^bj_dlhjbbbi_jkhgZevgu_iZd_luijh]jZff toolboxes >eywlh]h\Zfg_h[oh^bfh
^h[Z\blvbofZjrjmlihbkdZMATLAB.
?keb \u ih\lhjy_l_ bfy nmgdpbb lh MATLAB \uau\Zxl lhevdh lm dhlhjZy
\klj_qZ_lkyi_j\hc
Qlh[u m\b^_lv kh^_j`Zgb_ FnZceZ gZijbf_j myfunction.m g_h[oh^bfh gZ[jZlv
type myfunction
Kp_gZjbb
Dh^Z \u \uau\Z_l_ kp_gZjbc MATLAB ijhklh \uau\Z_l dhfZg^u kh^_j`Zsb_ky\nZce_Kp_gZjbbfh]mlhi_jbjh\Zlvkms_kl\mxsbfb^Zggufb\jZ[hq_fijhkljZgkl\_bebhgbfh]ml kZfbkha^Z\Zlvwlb^Zggu_Ohlykp_gZjbbg_
\ha\jZsZxlagZq_gbc\k_i_j_f_ggu_dhlhju_hgbkha^ZxlhklZxlky\jZ[hq_f ijhkljZgkl\_ ^ey bkihevah\Zgby \ ihke_^mxsbo \uqbke_gbyo < ^h[Z\e_gb_dkdZaZgghfmkp_gZjbbfh]mlhkms_kl\eylv]jZnbq_kdbc\u\h^bkihevamy
lZdb_nmgdpbbdZdplot.
<dZq_kl\_ijbf_jZkha^Z^bfnZcemagicrank.mdhlhjuckh^_j`blwlbdhfZg^uMATLAB:
% Investigate the rank of magic squares
r = zeros(1,32);
for n = 3:32
r(n) = rank(magic(n));
end
r
bar(r)
56
Kp_gZjbb b nmgdpbb
<\h^kljhdb
magicrank.m
ih\e_q_laZkh[hcbkiheg_gb_dhfZg^\uqbke_gb_jZg]Zi_j\uofZ]bq_kdbo
d\Z^jZlh\ b hlh[jZ`_gby klhe[bdh\hc ^bZ]jZffu j_amevlZlh\ Ihke_ ihegh]h
\uiheg_gbynZceZi_j_f_ggu_nbrhklZxlky\jZ[hq_fijhkljZgkl\_
Nmgdpbb
Nmgdpbb ± wlh FnZceu dhlhju_ fh]ml bf_lv \oh^gu_ b \uoh^gu_ \ha\jZsZlvBfyFnZceZbnmgdpbb^he`gh[ulvh^gbfbl_f`_NmgdpbbjZ[hlZxlki_j_f_ggufb\ij_^_eZobokh[kl\_ggh]hjZ[hq_]hijhkljZgkl\Zhl^_e_ggh]h hl jZ[hq_]h ijhkljZgkl\Z k dhlhjuf \u hi_jbjm_l_ \ dhfZg^ghc kljhd_
MATLAB.
Ohjhrbfijbf_jhfy\ey_lkynmgdpbbrankFnZcerank.m gZoh^blky\^bj_dlhjbb
toolbox/matlab/matfun
<ufh`_l_ijhkfhlj_lv_]hkh^_j`Zgb_\\_^y
type rank
function r = rank(A,tol)
%RANK
Matrix rank.
%
RANK(A) provides an estimate of the number of linearly
%
independent rows or columns of a matrix A.
%
RANK(A,tol) is the number of singular values of A
%
that are larger than tol.
%
RANK(A) uses the default tol = max(size(A)) * norm(A) * eps.
%
%
Copyright (c) 1984-98 by The MathWorks, Inc.
$Revision: 5.7 $ $Date: 1997/11/21 23:38:49 $
57
GZqZeh jZ[hlu k MATLAB
s = svd(A);
if nargin==1
tol = max(size(A)') * max(s) * eps;
end
r = sum(s > tol);
I_j\ZykljhdZnmgdpbbFnZceZgZqbgZ_lkykhkeh\Zfunction. A^_kvijhbkoh^bl
aZ^Zgb_ bf_gb kh kibkdhf Zj]mf_glh\ < gZr_f kemqZ_ bkihevam_lky ^h ^\mo
\oh^guoZj]mf_glh\bh^bg\uoh^ghc
Ke_^mxsb_g_kdhevdhkljhd^hi_j\hcimklhcbeb\uihegy_fhckljhdby\eyxlky dhff_glZjbyfb dhlhju_ ij_^hklZ\eyxl kijZ\hqgmx bgnhjfZpbx Wlb
kljhdb[m^ml\u\_^_gugZwdjZg_keb\ugZ[_j_l_
help rank
I_j\Zy kljhdZkijZ\hqgh]h l_dklZ ± wlh H1 kljhdZ dhlhjmx MATLAB hlh[jZ`Z_lijbbkihevah\ZgbbdhfZg^ulookfor bebijbaZijhk_ help ih\k_c^bj_dlhjbb
HklZevgh_kh^_j`Zgb_nZceZkhklZ\ey_lbkihegy_fucdh^MATLABI_j_f_ggZysij_^klZ\e_ggZy\l_e_nmgdpbblZd`_dZdbi_j_f_ggu_\i_j\hckljhd_
r, Ab tol\k_y\eyxlkyehdZevgufbHgbhl^_e_guhl^jm]boi_j_f_gguo\jZ[hq_fijhkljZgkl\_MATLAB.
Wlhl ijbf_j ihdZau\Z_l \Z`gmx hkh[_gghklv nmgdpbc MATLAB dhlhjZy
h[uqgh g_ \kl_qZ_lky \ ^jm]bo yaudZo ijh]jZfbjh\Zgby i_j_f_ggh_ qbkeh
Zj]mf_glh\ Nmgdpby rank fh`_l [ulv bkihevah\ZgZ \ g_kdhevdbo jZaebqguo
nhjfZo
rank(A)
r = rank(A)
r = rank(A, 1.e-6)
Fgh]b_nmgdpbbMATLABjZ[hlZxllZdbfh[jZahf?kebg_l\uoh^gh]hZj]mf_glZ lh j_amevlZl khojZgy_lky \ i_j_f_gghc ans ?keb g_l \lhjh]h \oh^gh]h
Zj]mf_glZ lh nmgdpby \uqbkey_l agZq_gb_ ih mfheqZgbx <gmljb l_eZ nmgdpbbijbkmlkl\mxl^\_\_ebqbgunargin bnargoutdhlhju_\u^Zxlqbkeh\oh^guo b \uoh^guo Zj]mf_glh\ ijb dZ`^hf bkihevah\Zgbb nmgdpbb Nmgdpby
rank bkihevam_li_j_f_ggmxnargin ghg_bkihevam_lnargout.
=eh[Zevgu_i_j_f_ggu_
?keb \u ohlbl_ qlh[u [he__ h^ghc nmgdpbb bkihevah\Zeb hl^_evgmx dhibx
i_j_f_gghcijhklhh[ty\bl__zdZdglobal \h\k_onmgdpbyo>_eZcl_lh`_kZfh_\dhfZg^ghckljhd__keb\uohlbl_qlh[uhkgh\gh_jZ[hq__ijhkljZgkl\h
ihemqbeh^hklmidi_j_f_gghcHij_^_e_gb_global ^he`gh [ulv ^h kZfhc i_j_f_gghc bkihevam_fhc \ nmgdpbb Ohly wlh g_ h[yaZl_evgh bkihevah\Zgb_
[hevrbo[md\^eybf_gb]eh[Zevghci_j_f_gghcihfh`_lhlebqblvbohl^jm]boi_j_f_gguoGZijbf_jkha^Z^bfFnZcefalling.m:
58
Kp_gZjbb b nmgdpbb
function h = falling(t)
global GRAVITY
h = ½*GRAVITY*t.^2;
AZl_f\\_^_fke_^mxsb_kljhdb
global GRAVITY
GRAVITY = 32;
y = falling((0: .1: 5)' );
LZdbf h[jZahf kljhdb hij_^_e_gby GRAVITY \ dhfZg^ghc kljhd_ ^_eZxl _z
^hklmighc \gmljb nmgdpbb <u fh`_l_ ihke_ baf_gblv GRAVITY b ihemqblv
gh\h_j_r_gb_g_j_^ZdlbjmydZdb_eb[hnZceu
DhfZg^ghnmgdpbhgZevgZy^\hckl\_gghklv
Ijbf_judhfZg^MATLAB±wlh
load
help
Fgh]b_ dhfZg^u bf_xl mijZ\eyxsbc iZjZf_lj dhlhjuc hij_^_ey_l ihke_^mxs__^_ckl\b_
load August17.dat
help magic
type rank
>jm]hcf_lh^bkihevah\ZgbydhfZg^guoiZjZf_ljh\± wlh kha^Zgb_ kljhdb Zj]mf_glh\nmgdpbc
load( 'August17.dat' )
help( 'magic' )
type( 'rank' )
Wlhb_klvdhfZg^ghnmgdpbhgZevgZy^\hckl\_gghklvEx[ZydhfZg^ZlbiZ
command argument
lZd`_fh`_l[ulvi_j_ibkZgZ\nmgdpbhgZevghcnhjf_
command( 'argument' )
Ij_bfms_kl\h nmgdpbhgZevgh]h ih^oh^Z ijhy\ey_lky dh]^Z kljhdZ Zj]mf_glZ
kha^Z_lkybahl^_evguoqZkl_cKe_^mxsbcijbf_jh[jZ[Zlu\Z_lfgh]hqbke_ggu_ nZceu k ^Zggufb August1.dat, August2.dat b l^ Hg bkihevam_l nmgdpbx
int2strdhlhjZyij_h[jZam_lp_eu_qbkeZ\kljhdmkbf\heh\^eykha^Zgbybf_gb
nZceZ
59
GZqZeh jZ[hlu k MATLAB
for d = 1:31
s = [ 'August' int2str(n) '.dat']
load(s)
% H[jZ[hldZkh^_j`Zgbyd-]hnZceZ
end
NmgdpbyHYDO
Nmgdpby eval jZ[hlZ_l k l_dklh\ufb i_j_f_ggufb ^ey \uqbke_gby b j_ZebaZpbbl_dklh\uokljhd
eval(s)
bkihevam_lbgl_jij_lZlhjMATLAB^ey\uqbke_gbyb\uiheg_gby\ujZ`_gby,
kh^_j`Zs_]hky\l_dklh\hckljhd_s.
Ijbf_jbaij_^u^ms_]hjZa^_eZfh`_l[ulvlZd`_j_Zebah\Zgke_^mxsbfh[jZahf ohlywlh[m^_lf_g__wnn_dlb\ghldbkihevam_lkyihegucbgl_jij_lZlhjZg_\uah\nmgdpbb for d = 1:31
s = [ 'load August' int2char(n) '.dat' ]
eval(s)
% H[jZ[hldZkh^_j`Zgbyd-]hnZceZ
end
<_dlhjbaZpby
Qlh[u^h[blvkyfZdkbfZevghckdhjhklb\g_MATLABhq_gv\Z`gh\_dlhjbah\u\Zlv Ze]hjblf \ FnZceZo LZf ]^_ ^jm]b_ yaudb ijh]jZffbjh\Zgby fh]ml
bkihevah\Zlvpbdeufor bebdo, MATLABfh`_lijbf_gylv\_dlhjgu_bebfZljbqgu_hi_jZpbbIjhklufijbf_jhfy\ey_lkykha^Zgb_lZ[ebpueh]Zjbnfh\
x=0
for k = 1:1001
y(k) = log10(x);
x = x + .01;
end
(Hiulgu_ ihevah\Zl_eb MATLAB ex[yl ]h\hjblv @bagv kebrdhf dhjhldZ
qlh[uljZlblv\j_fygZaZibkvpbdeh\)
:\_dlhjbah\ZggZy\_jkbywlh]hdh^Z\u]ey^blke_^mxsbfh[jZahf
x = 0: .10:10;
y = log10(x);
>ey[he__keh`guoijh]jZff\hafh`ghklb\_dlhjbaZpbbg_lZdhq_\b^guH^gZdh dh]^Z \Z`gZ kdhjhklv \u ^he`gu \k_]^Z bkdZlv kihkh[u \_dlhjbaZpbb
\Zr_]hZe]hjblfZ
60
Kp_gZjbb b nmgdpbb
Ij_^\Zjbl_evgh_\u^_e_gb_
?keb\ug_fh`_l_\_dlhjbah\ZlvqZklvdh^Z\ufh`_l_aZklZ\blv\Zrpbdefor
jZ[hlZlv[uklj__>eywlh]hgm`ghij_^\Zjbl_evgh\u^_eblv\_dlhjZbebfZkkb\u\dhlhjuo[m^mlojZgblvky\uoh^gu_j_amevlZluGZijbf_jke_^mxsbc
dh^bkihevam_lnmgdpbyzeros ^eyij_^\Zjbl_evgh]h\u^_e_gby\_dlhjZkha^Z\Z_fh]h\pbde_forWlhiha\hey_lpbdemfor jZ[hlZlvaZf_lgh[uklj__
r = zeros(32,1)
for n = 1:32
r(n) = rank(magic(n));
end
;_a ij_^\Zjbl_evgh]h \u^_e_gby \ ij_^u^ms_f ijbf_j_ bgl_jij_lZlhj
MATLAB m\_ebqb\Z_l\_dlhjr ihh^ghfmwe_f_glmdZ`^ucjZa\gmljb pbdeZ
Ij_^\Zjbl_evgh_\u^_e_gb_\_dlhjZ mkljZgy_lwlh^_ckl\b_bj_amevlZl ihemqZ_lky[uklj__
Nmgdpbyhlnmgdpbc
DeZkk nmgdpbc gZau\Z_fuc nmgdpby hl nmgdpbc jZ[hlZ_l k g_ebg_cgufb
nmgdpbyfb kdZeyjguo i_j_f_gguo Lh _klv h^gZ nmgdpby jZ[hlZ_l k ^jm]hc .
Nmgdpbbhlnmgdpbc\dexqZxl\k_[y
•
•
•
•
GZoh`^_gbygmey
HilbfbaZpby
Bgl_]jbjh\Zgb_
H[udgh\_ggu_^bnn_j_gpbZevgu_mjZ\g_gby
MATLAB ij_^klZ\ey_lg_ebg_cgu_nmgdpbbq_j_aFnZceuGZijbf_jgb`_
ijb\_^_gZmijhs_ggZy\_jkbynmgdpbbhumps ba^bj_dlhjbbmatlab/demos
function y = humps(x)
y = 1. / ( (x - .3). ^2 + .01) + 1. / ( (x - .9) .^2 + .04) - 6;
<uqbkebfwlmnmgdpbx\g_kdhevdbolhqdZobgl_j\ZeZ[0,1]
x = 0: .002:1;
y = humps(x);
AZl_fihkljhbf]jZnbd
plot(x,y)
61
GZqZeh jZ[hlu k MATLAB
GZ ]jZnbd_ \b^gh qlh wlZ nmgdpby bf__l ehdZevguc fbgbfmf hdheh x=0.6.
Nmgdpbyfmins gZc^_lfbgbfmful_l_agZq_gbyx\dhlhjuonmgdpby^hklb]Z_lk\h_]hfbgbfmfZI_j\ufZj]mf_glhffmins y\ey_lkybfynmgdpbbfbgbfmfdhlhjhcbs_lkyZ\lhjuf±ijb[eb`_ggh_iheh`_gb_fbgbfmfZ
p = fmins( 'humps', .5)
p =
0.6370
Qlh[ugZclbagZq_gb_nmgdpbb\fbgbfmf_
humps(p)
ans =
11.2528
Ki_pbZebklubkihevamxll_jfbgud\Z^jZlmjZbbgl_]jbjh\Zgb_ qlh[u jZaebqZlv qbke_ggmx ZiijhdkbfZpbx hij_^_e_gguo bgl_]jZeh\ b qbke_ggh_ bgl_]jbjh\Zgb_ h[udgh\_gguo ^bnn_j_gpbZevguo mjZ\g_gbc quad b quad8 ±wlh
ih^ijh]jZffuMATLABih\uqbke_gbxd\Z^jZlmju
Q = quad8( 'humps', 0, 1)
\uqbkey_liehsZ^vih^djb\hcgZ]jZnbd_b\u^Z_l
Q =
29.8583
<aZdexq_gb_gZ]jZnbd_\b^ghqlhaZ^ZggZynmgdpbyg_bf__lgme_cgZwlhf
bgl_j\Ze_Ihwlhfm_kebfuihiulZ_fkyhlukdZlvgmev
z = fzero( 'humps', .5)
lhfugZc^_f_]h\g_gZr_]hbgl_j\ZeZ
z =
-0.1316
62
MijZ\ey_fZy ]jZnbdZ
MijZ\ey_fZy]jZnbdZ
MATLABij_^hklZ\ey_ldhfie_dknmgdpbcgbadh]hmjh\gydhlhju_iha\heyxl
kha^Z\Zlv b h[jZ[Zlu\Zlv ebgbb ih\_joghklb b ^jm]b_ ]jZnbq_kdb_ h[t_dlu
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days = [ 'Su' ; 'Mo' ; 'Tu' ; 'We' ; 'Th' ; 'Fr' ; 'Sa' ]
temp = [ 21.1 22.2 19.4 23.3 23.9 21.1 20.0 ];
f = figure;
a = axes( 'YLim' , [16 26] , 'Xtick' , 1:7 , 'XtickLabel' , days )
h = line(1:7, temp)
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set( h , 'Color' , [0 .8 .8] , 'LineWidth' , 3)
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65
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set(h)
Color
EraseMode: [ {normal} | background | xor | none ]
LineStyle: [ {-} | -- | : | -. | none ]
LineWidth
Marker: [ + | o | * | . | x | square | diamond | v | ^ | > | < |
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MarkerSize
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YData
Zdata
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get(h)
Color = [0 0.8 0.8]
EraseMode = normal
LineStyle = LineWidth = [3]
Marker = none
MarkerSize = [6]
. . .
XData = [ (1 by 7) double array]
YData = [ (1 by 7) double array]
ZData = []
. . .
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get(h , 'Color')
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t = get(a , 'title' );
set(t , 'String' , 'Temperature' , 'FontAngle' , 'oblique')
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b = uicontrol( 'Style' , 'pushbutton' , . . .
'Units' , 'normalized' , . . .
'Position' , [.5 .5 .2 .1] , . . .
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'String' , 'click here' );
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s = ' set(b , ' 'Position' ' , [.8*rand .9*rand .2 .1]) ';
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n = 20;
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s = .02;
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x = rand(n,1)-0.5;
y = rand(n,1)-0.5;
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h = plot(x , y , ' . ' );
axis([-1 1 -1 1])
axis square
grid off
set(h , 'EraseMode' , 'xor' , 'MarkerSize' , 18 );
67
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while 1
x = x + s*randn(n,1);
y = y + s*randn(n,1);
set(h, 'Xdata' , x , 'Ydata' , y)
end
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nframes = 50;
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x = rand(n,1)-0.5;
y = rand(n,1)-0.5;
h = plot(x, y, ' . ' )
set(h, 'MarkerSize' , 18)
axis([-1 1 -1 1])
axis square
grid off
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M = moviein(nframes);
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for k = 1:nframes
x = x + s*rand(n,1);
y = y + s*rand(n,1);
set(h , 'XData' , x , 'YData' , y)
M(: , k) = getframe;
end
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e-mail: konushenko@afrodita.phys.msu.su
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