MATLAB –––––––––––––––––––––––––––––––––––––––––––– Yaudl_ogbq_kdbo\uqbke_gbc _ckl\bl_evgh dZ`^uc klhe[_pbf__l h^...
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MATLAB –––––––––––––––––––––––––––––––––––––––––––– Yaudl_ogbq_kdbo\uqbke_gbc
Getting Started with MATLAB GZqZehjZ[hlukMATLAB
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I_j_f_ggu_ ............................................................................................................ 14 QbkeZ........................................................................................................................ 14 Hi_jZlhju............................................................................................................... 15 Nmgdpbb .................................................................................................................. 15
JZ[hlZkfZljbpZfb..............................................................................17 =_g_jbjh\Zgb_fZljbp........................................................................................... 17 AZ]jmadZfZljbp...................................................................................................... 17 FnZceu.................................................................................................................. 18 H[t_^bg_gb_........................................................................................................... 18 M^Ze_gb_kljhdbklhe[ph\ ................................................................................... 19
DhfZg^gh_hdgh.....................................................................................20 DhfZg^ZIRUPDW ....................................................................................................... 20 KhdjZs_gb_\uoh^guo^Zgguo ............................................................................ 21 >ebggu_dhfZg^gu_kljhdb.................................................................................. 21 J_^ZdlhjdhfZg^ghckljhdb .................................................................................. 21
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Kha^Zgb_]jZnbdZ................................................................................................... 23 HdgZbah[jZ`_gbc.................................................................................................. 24 >h[Z\e_gb_djb\uogZkms_kl\mxsbc]jZnbd................................................... 25 Ih^]jZnbdb............................................................................................................. 25 Fgbfu_bdhfie_dkgu_^Zggu_........................................................................... 26 MijZ\e_gb_hkyfb .................................................................................................. 27 Ih^ibkbdhkyfbaZ]heh\db.................................................................................. 28 NmgdpbbPHVKbVXUIDFH ......................................................................................... 28
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GZqZeh jZ[hlu k MATLAB K\yavk0DWK:RUNV ................................................................................................. 33
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Ih^jh[g__hfZljbpZobfZkkb\Zo.....................................................37 Ebg_cgZyZe]_[jZ ................................................................................................... 37 FZkkb\u .................................................................................................................. 40 Fgh]hf_jgu_^Zggu_ ............................................................................................ 41 KdZeyjgh_jZkrbj_gb_ .......................................................................................... 42 Eh]bq_kdZybg^_dkZpby.......................................................................................... 42 NmgdpbyILQG ........................................................................................................... 43
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>jm]b_kljmdlmju^Zgguo ..................................................................49 Fgh]hf_jgu_fZkkb\u .......................................................................................... 49 FZkkb\uyq__d ........................................................................................................ 50 Kbf\heubl_dkl..................................................................................................... 51 Kljmdlmju ............................................................................................................... 54
Kp_gZjbbbnmgdpbb............................................................................56 Kp_gZjbb ................................................................................................................. 56 Nmgdpbb .................................................................................................................. 57 =eh[Zevgu_i_j_f_ggu_........................................................................................ 58 DhfZg^ghnmgdpbhgZevgZy^\hckl\_gghklv...................................................... 59 NmgdpbyHYDO........................................................................................................... 60 <_dlhjbaZpby .......................................................................................................... 60 Ij_^\Zjbl_evgh_\u^_e_gb_................................................................................. 61 Nmgdpbyhlnmgdpbc.............................................................................................. 61
MijZ\ey_fZy]jZnbdZ .........................................................................63 =jZnbq_kdb_h[t_dlu ............................................................................................ 63 MijZ\e_gb_h[t_dlZfb .......................................................................................... 63 Nmgdpbbkha^Zgbyh[t_dlh\ ................................................................................. 64 K\hckl\Zh[t_dlZ.................................................................................................... 65 VHWbJHW .................................................................................................................... 65 =jZnbq_kdbcIhevah\Zl_evkdbcBgl_jn_ck *8, ............................................ 66 :gbfZpby ................................................................................................................ 67 Movie ....................................................................................................................... 68
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8
FZljbpu b fZ]bq_kdb_ d\Z^jZlu Ohjhrbc ijbf_j fZljbpu dhlhjZy bkihevam_lky \h \k_c wlhc dgb]_ fh`gh gZclb gZ ]jZ\xj_ \j_f_g J_g_kkZgkZ om^h`gbdZ b ex[bl_eyfZl_fZlbdb:ev[j_olZ >xj_jZ Wlh bah[jZ`_gb_ kh^_j`bl fgh]h fZl_fZlbq_kdbo kbf\heh\ b _keb ohjhrh ijbkfhlj_lvkylh\\_jog_fijZ\hf m]em fh`gh aZf_lblv d\Z^jZlgmx fZljbpm Wlh fZljbpZ ba\_klgZdZdfZ]bq_kdbcd\Z^jZlb \h \j_f_gZ >xj_jZ kqblZehkv qlh hgZ h[eZ^Z_l fZ]bq_kdbfb k\hckl\ZfbHgZbgZkZfhf^_e_ h[eZ^Z_l aZf_qZl_evgufb k\hckl\Zfbklhysbfbbamq_gby
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xj_jZdZdkibkdZwe_f_glh\xj_jZijhklhgZibrbl_ A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1]
MATLABhlh[jZablfZljbpmdhlhjmxfu\\_eb A = 16 5 9 4
3 10 6 15
2 11 7 14
13 8 12 1
Wlhlhqghkhhl\_lkl\m_lqbkeZfgZ]jZ\xj_?kebfu\\_ebfZljbpmlhhgZZ\lhfZlbq_kdb aZihfbgZ_lky kj_^hc MATLAB B fu fh`_f d g_c e_]dh h[jZlblvky dZd d : K_cqZk dh]^Z fu bf__f : \ jZ[hq_f ijhkljZgkl\_ MATLAB,
9
GZqZeh jZ[hlu k MATLAB ihkfhljbf qlh ^_eZ_l _z lZdhc bgl_j_kghc Ihq_fm hgZ gZau\Z_lky fZ]bq_kdhc"
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Z\Zcl_ijh\_jbf wlhbkihevamyMATLABI_j\h_ml\_j`^_gb_dhlhjh_fuijh\_jbf± sum(A)
MATLAB\u^Zklhl\_l ans = 34
34
34
34
Dh]^Z \uoh^gZy i_j_f_ggZy g_ hij_^_e_gZ MATLAB bkihevam_l i_j_f_ggmx ansdhjhldhhlanswer – hl\_l^eyojZg_gbyj_amevlZlh\\uqbke_gbyFuih^kqblZeb \_dlhjkljhdm kh^_j`Zsmx kmffm we_f_glh\ klhe[ph\ fZljbpu : >_ckl\bl_evgh dZ`^uc klhe[_pbf__l h^bgZdh\mx kmffm fZ]bq_kdmx kmffm jZ\gmx : dZd gZkq_l kmff \ kljhdZo" 0$7/$% ij_^ihqblZ_l jZ[hlZlv kh klhe[pZfb fZljbpulZdbfh[jZahfemqrbckihkh[ihemqblvkmffm\kljhdZo±wlhljZgkihgbjh\ZlvgZrmfZljbpmih^kqblZlvkmffm\klhe[pZoZihlhfljZgkihgbjh\Zlvj_amevlZlHi_jZpbyljZgkihgbjh\Zgbyh[hagZqZ_lkyZihkljhnhfbebh^bgZjghc dZ\uqdhc HgZ a_jdZevgh hlh[jZ`Z_l fZljbpm hlghkbl_evgh ]eZ\ghc ^bZ]hgZebbf_gy_lkljhdbgZklhe[puLZdbfh[jZahf A'
\uau\Z_l ans = 16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
:\ujZ`_gb_ sum(A')'
\uau\Z_lj_amevlZl\_dlhjklhe[_pkh^_j`Zsbckmffu\kljhdZo ans = 34 34 34 34
10
FZljbpu b fZ]bq_kdb_ d\Z^jZlu Kmffmwe_f_glh\gZ]eZ\ghc^bZ]hgZebfh`ghe_]dhihemqblvkihfhsvx nmgdpbbdiagdhlhjZy\u[bjZ_lwlm^bZ]hgZev diag(A) ans = 16 10 7 1
:nmgdpby sum(diag(A))
\uau\Z_l ans = 34
>jm]Zy ^bZ]hgZev gZau\Z_fZy Zglb^bZ]hgZevx g_ lZd \Z`gZ fZl_fZlbq_kdb ihwlhfmMATLAB g_bf__lki_pbZevghcnmgdpbb^eyg_zGhnmgdpbydhlhjZy \gZqZe_ ij_^iheZ]ZeZkv ^ey bkihevah\Zgby \ ]jZnbd_ fliplr a_jdZevgh hlh[jZ`Z_lfZljbpmke_\ZgZijZ\h sum(diag(fliplr(A))) ans = 34
LZdbfh[jZahffuijh\_jbebqlhfZljbpZgZ]jZ\xj_ >xj_jZ ^_ckl\bl_evgh fZ]bq_kdZy b gZmqbebkv bkihevah\Zlv g_dhlhju_ fZljbqgu_ hi_jZpbb MATLAB. < ihke_^mxsbo jZa^_eZo fu ijh^he`bf bkihevah\Zlv wlm fZljbpm ^ey^_fhgkljZpbb^hihegbl_evguo\hafh`ghkl_cMATLAB.
Bg^_dku
We_f_gl\kljhd_i bklhe[p_j fZljbpu:h[hagZqZ_lkyA(i,j). GZijbf_jA(4,2) ±wlhqbkeh\q_l\_jlhckljhd_b\lhjhfklhe[p_>eygZr_]hfZ]bq_kdh]hd\Z^jZlZA(4,2) LZdbfh[jZahffh`gh \uqbkeblv kmffm we_f_glh\ \ q_l\_jlhfklhe[p_fZljbpu:gZ[jZ\ A(1,4) + A(2,4) + A(3,4) + A(4,4)
ihemqbf 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
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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
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
14
Hi_jZlhju
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. 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
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
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\
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_ lhqdmkaZiylhcMATLABijh\_^_l\uqbke_gbyghg_hlh[jZablboWlhqZklh [u\Z_lgm`ghijbkha^Zgbb[hevrbofZljbpGZijbf_j A = magic(100);
>ebggu_dhfZg^gu_kljhdb
?keb\ujZ`_gb_g_mf_sZ_lkygZh^ghckljhd_bkihevamcl_ljh_lhqb_ZaZgbf 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
J_^ZdlhjdhfZg^ghckljhdb
JZaebqgu_ klj_edb b mijZ\eyxsb_ deZ\brb gZ \Zr_c deZ\bZlmj_ iha\heyxl \Zf\uau\Zlvj_^Zdlbjh\Zlvbfgh]hdjZlghbkihevah\ZlvdhfZg^ugZ[jZggu_ jZg__GZijbf_jij_^iheh`bfqlh\u^himklbebhrb[dmijb\\h^_ rho = (1 + sqt(5))/2
21
GZqZeh jZ[hlu k MATLAB ^mxsbo deZ\br ^hklmigu gZ \Zr_c fZrbg_ Fgh]b_ ba wlbo deZ\br [m^ml agZdhfuihevah\Zl_eyfj_^ZdlhjZEMACS.) ↑ ↓ ← → ctrl-→ ctrl-← home end esc del backspace
ctrl-p ctrl-n ctrl-b ctrl-f ctrl-r ctrl-l ctrl-a ctrl-e ctrl-u ctrl-d ctrl-h ctrl-k
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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
Kha^Zgb_]jZnbdZ
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 ]jZnbdaZ\bkbfhklby hlx. GZijbf_j^eyihkljh_gby]jZnbdZagZq_gbcnmgdpbbsin hlgmey^hπk^_eZ_fke_^mxs__ t = 0:pi/100:2*pi; y = sin(t); plot(t,y)
23
GZqZeh jZ[hlu k MATLAB
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
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27
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28
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DhfZg^Zhelp ±wlhkZfuchkgh\ghckihkh[hij_^_e_gbykbglZdkbkZbih\_^_gby hl^_evguo nmgdpbc BgnhjfZpby hlh[jZ`Z_lky ijyfh \ dhfZg^ghf hdg_ GZijbf_j help magic
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31
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32
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34
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35
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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
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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 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^
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 jZaguokemqZy Qg_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_
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
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 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!
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]
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
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 =
83¼æ,/©¤2
°±1¶·z}ª0~
:;<=>?@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.'
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
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\ZxlkyFnZceZfbeywlh]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
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
=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
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;
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 WlZkbkl_fZgZau\Z_lkymijZ\ey_fZy]jZnbdZ Handle Graphics®).
=jZnbq_kdb_h[t_dlu
=jZnbq_kdb_h[t_dlu±wlh[Zabkgu_we_f_glukbkl_fumijZ\ey_fhc]jZnbdb\ MATLABHgbknhjfbjh\Zgu\^_j_\hkljmdlmjghcb_jZjobbWlbfhljZ`Z_lky k\yav ]jZnbq_kdbo h[t_dlh\ GZijbf_j h[t_dlu Line (ebgby) gm`^Zxlky \ h[t_dlZoAxes (hkb)dZd\kbkl_f_hlkq_lZ<k\hxhq_j_^vh[t_dluAxes kms_kl\mxllhevdhkh[t_dlZfbFigure. ?klvh^bggZ^pZlv\b^h\h[t_dlh\mijZ\ey_fhc]jZnbdb • H[t_dlu Root y\eyxlky \_jrbghc b_jZjobb Hgb khhl\_lkl\mxl wdjZgm dhfivxl_jZMATLABZ\lhfZlbq_kdbbokha^Z_l\gZqZe_k_ZgkZjZ[hlu • H[t_dluFigure±wlhhdgZgZwdjZg_djhf_dhfZg^gh]hhdgZ • H[t_dluUicontrol ±wlhihevah\Zl_evkdh_mijZ\e_gb_bgl_jn_ckhfDh]^Z ihevah\Zl_ev Zdlb\bjm_l h[t_dl \uau\Z_lky khhl\_lkl\mxsZy nmgdpby Hgb \dexqZxl\k_[ypushbutton, radio button bslider. • H[t_dlu Axes hij_^_eyxl h[eZklv \ hdg_ Figure b hjb_glZpbx ^hq_jgbo h[t_dlh\\wlhch[eZklb • H[t_dlu Uimenu ij_^klZ\eyxl kh[hc f_gx ihevah\Zl_evkdh]h bgl_jn_ckZdhlhjh_jZkiheh`_gh\\_jog_cqZklbhdgZFigure. • H[t_dluImage – wlh^\mf_jgu_h[t_dludhlhju_\u\h^blMATLAB, bkihevamywe_f_gluijyfhm]hevgh]hfZkkb\ZdZdbg^_dku\iZeblj_ • H[t_dluLine y\eyxlkyhkgh\gufb]jZnbq_kdbfb[Zabkgufbwe_f_glZfb ^ey[hevrbgkl\Z^\mf_jguo]jZnbdh\ • H[t_dlu Surface ± wlh lj_of_jgh_ ij_^klZ\e_gb_ ^Zgguo fZljbpu kha^Zggh_iml_f]jZnbq_kdh]hhlh[jZ`_gby^ZgguodZd\ukhlgZ^iehkdhklvxxy. • H[t_dluText – wlhkljhdbkbf\heh\ • H[t_dluLight hij_^_eyxlbklhqgbdk\_lZ^_ckl\mxsbcgZ\k_h[t_dlu\ ij_^_eZoAxes.
MijZ\e_gb_h[t_dlZfb
DZ`^uc hl^_evguc ]jZnbq_kdbc h[t_dl bf__l k\hc mgbdZevguc b^_glbnbdZlhjgZau\Z_fuchandle fZgbimeylhj dhlhjucMATLAB ijbk\Zb\Z_lh[t_dlm ijb kha^Zgbb G_dhlhju_ ]jZnbdb gZijbf_j k g_kdhevdbfb djb\ufb khklhyl ba fgh]bo h[t_dlh\dZ`^uc ba dhlhjuo bf__l k\hc kh[kl\_gguc b^_glbnbdZlhj handle Q_fiulZlvkyijhqblZlvbokwdjZgZbih\lhjgh\\h^blv\um\b^bl_qlh\k_]^Zemqr_ojZgblvagZq_gb_\i_j_f_gghcbbkihevah\Zlv_]hihg_h[oh^bfhklb B^_glbnbdZlhjh[t_dlZroot \k_]^ZgmevB^_glbnbdZlhjfigure ±wlhp_eh_qbkeh dhlhjh_ ih mfheqZgbx hlh[jZ`Z_lky \ aZ]heh\d_ hdgZ B^_glbnbdZlhju ^jm]bo h[t_dlh\ y\eyxlky qbkeZ k ieZ\Zxs_c lhqdhc dhlhju_ kh^_j`Zl bg-
63
GZqZeh jZ[hlu k MATLAB nhjfZpbxbkihevam_fmxMATLABGZijbf_j_kebA –wlhfZ]bq_kdbcd\Z^jZl>xj_jZlh h = plot(A)
kha^Zklebg_cguc]jZnbdkq_lujvfyebgbyfb^eydZ`^h]hklhe[pZ:ZlZd`_ \ha\jZlbl\_dlhjb^_glbnbdZlhjlZdhcdZd h = 3.0022 1.0038 4.0020 5.0016
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K\hckl\Z h[t_dlZ aZ^Zxlky h[jZs_gb_f d g_fm ihke_ _]h kha^Zgby >ey wlh]h bkihevamcl_b^_glbnbdZlhj\ha\jZsZ_fuckha^Z\Z_fhcnmgdpb_c Nmgdpby set iha\hey_l mklZgZ\eb\Zlv k\hckl\Z h[t_dlh\ mdZaZgb_f b^_glbnbdZlhjZh[t_dlZbkh\hdmighklbiZjgZa\Zgb_k\hckl\ZagZq_gb_<dZq_kl\_mijZ`g_gbybaf_gbfp\_lbrbjbgmebgbbbaij_^u^ms_]hijbf_jZ set( h , 'Color' , [0 .8 .8] , 'LineWidth' , 3)
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GZqZeh jZ[hlu k MATLAB
set(h) Color EraseMode: [ {normal} | background | xor | none ] LineStyle: [ {-} | -- | : | -. | none ] LineWidth Marker: [ + | o | * | . | x | square | diamond | v | ^ | > | < | pentagram | hexagram | {none} ] MarkerSize . . . XData YData Zdata . . . .
Qlh[u\u\_klbkibkhd\k_ol_dmsbomklZgh\e_gguok\hckl\aZ^Zggh]hh[t_dlZ \uah\_l_get kb^_glbnbdZlhjhfh[t_dlZ 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 = [] . . .
>eyaZijhkZagZq_gbyhl^_evgh]hk\hckl\Zbkihevamcl_get kbf_g_fk\hckl\Z get(h , 'Color') ans = 0
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MATLAB ij_^hklZ\ey_l g_kdhevdh kihkh[h\ ^ey kha^Zgby ^\b]Zxs_cky ZgbfZpbhgghc ]jZnbdb Bkihevah\Zgb_ k\hckl\Z EraseMode ij_^gZagZq_gh ^ey ^ebgghcihke_^h\Zl_evghklbijhkluo]jZnbdh\]^_baf_g_gb_hldZ^jZddZ^jm fbgbfZevghGb`_ij_^klZ\e_gijbf_jfh^_ebjmxsbc[jhmgh\kdh_^\b`_gb_ Hij_^_ebfdhebq_kl\hlhq_d n = 20;
L_fi_jZlmjmbebkdhjhklvdZd s = .02;
Emqrb_ agZq_gby wlbo iZjZf_ljh\ aZ\bkyl hl kdhjhklb \Zr_c fZrbgu K]_g_jbjm_fn kemqZcguolhq_dkdhhj^bgZlZfb(x,y) f_`^m½ b½. x = rand(n,1)-0.5; y = rand(n,1)-0.5;
Hlh[jZabf lhqdb \ d\Z^jZl_ kh klhjhgZfb \ ij_^_eZo hl ± ^h KhojZgbf b^_glbnbdZlhj^ey\_dlhjZlhq_dbmklZgh\bfk\hckl\hEraseMode jZ\gufxor. WlhmdZ`_l]jZnbq_kdhckbkl_f_MATLABg_i_j_jbkh\u\Zlv\_kv]jZnbddh]^Zbaf_gy_lkydhhj^bgZlZh^ghclhqdbZ\hkklZgZ\eb\Zlvp\_lnhgZ\hdj_klghklblhqdbbkihevamyhi_jZpbxbkdexqZxs_]hBEB 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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>hiheg_gb_ Qlh[u m\b^_lv ^hihegbl_evgu_ ijbf_ju MATLAB \u[_jbl_ Examples and Demos baf_gxbebgZ[_jbl_ demo \dhfZg^ghc kljhd_ MATLAB ey[he__^_lZevgh]hh[tykg_gbyhl^_evguol_faZljhgmluo\wlhcdgb]_h[jZsZcl_kvdke_^mxs_cebl_jZlmj_ MATLAB Installation Guide hibku\Z_l dZd mklZgh\blv MATLAB gZ \Zrm ieZlnhjfm Using MATLABij_^klZ\ey_l[he__]em[hdbcfZl_jbZeihyaudmMATLAB, jZ[hq_ckj_^_bfZl_fZlbq_kdbfl_fZf Using MATLAB Graphicshibku\Z_lbkihevah\Zgb_]jZnbdbbbgkljmf_glh\^ey\bamZebaZpbbMATLAB. MATLAB Application Program Interface Guide h[tykgy_l dZd ibkZlv ijh]jZffugZKbbNhjljZg_dhlhju_\aZbfh^_ckl\mxlkMATLAB. MATLAB 5.1 New Features Guide ij_^hklZ\ey_lihe_agmxbgnhjfZpbx^ey i_j_oh^ZhlMATLABodMATLAB 5.1. MATLAB Toolboxes ±wlh]jmiiuFnZceh\dhlhju_jZkrbjyxl\hafh`ghklb MATLAB\jZaebqguol_ogbq_kdboh[eZklyo>hklmiguhl^_evgu_jmdh\h^kl\Z ihdZ`^hcbagbo
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