MATLAB

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GZqZeh jZ[hlu kMATLAB

4

K\yavk0DWK:RUNV ................................................................................................. 33Kj_^Z0$7/$% .....................................................................................34JZ[hq__ijhkljZgkl\h ............................................................................................ 34DhfZg^ZVDYH ........................................................................................................... 34FZjrjmlihbkdZ ..................................................................................................... 35Hi_jZpbbgZ^^bkdh\ufbnZceZfb...................................................................... 35DhfZg^ZGLDU\.......................................................................................................... 36AZimkd\g_rgboijh]jZff .................................................................................... 36

Ih^jh[g__hfZljbpZobfZkkb\Zo.....................................................37Ebg_cgZyZe]_[jZ ................................................................................................... 37FZkkb\u .................................................................................................................. 40Fgh]hf_jgu_^Zggu_ ............................................................................................ 41KdZeyjgh_jZkrbj_gb_ .......................................................................................... 42Eh]bq_kdZybg^_dkZpby.......................................................................................... 42NmgdpbyILQG ........................................................................................................... 43

MijZ\e_gb_ihlhdZfb..........................................................................45if ............................................................................................................................... 45VZLWFKbFDVH ............................................................................................................ 46for ............................................................................................................................. 47while ......................................................................................................................... 47break ......................................................................................................................... 48

>jm]b_kljmdlmju^Zgguo ..................................................................49Fgh]hf_jgu_fZkkb\u .......................................................................................... 49FZkkb\uyq__d ........................................................................................................ 50Kbf\heubl_dkl..................................................................................................... 51Kljmdlmju ............................................................................................................... 54

Kp_gZjbbbnmgdpbb............................................................................56Kp_gZjbb ................................................................................................................. 56Nmgdpbb .................................................................................................................. 57=eh[Zevgu_i_j_f_ggu_........................................................................................ 58DhfZg^ghnmgdpbhgZevgZy^\hckl\_gghklv ...................................................... 59NmgdpbyHYDO ........................................................................................................... 60hiheg_gb_.............................................................................................70

GZqZeh jZ[hlu kMATLAB

6

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H6LPXOLQN6LPXOLQNkhimlkl\mxsZy0$7/$%ijh]jZffZwlhbgl_jZdlb\gZykbkl_fZ^ey

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^mmijZ\ey_fmxfurvxdhlhjZyiha\hey_lfh^_ebjh\Zlvijhp_kkiml_fi_j_-

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AZimkd MATLAB

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GZqZeh jZ[hlu kMATLAB

8

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jbpZfb

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9

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lhjZybkihevam_lky\h\k_c wlhc

dgb]_ fhgh gZclb gZ ]jZ\xj_

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GZqZeh jZ[hlu kMATLAB

10

ihkfhljbf qlh ^_eZ_l _z lZdhc bgl_j_kghcIhq_fm hgZ gZau\Z_lky fZ]bq_-

kdhc"

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]hgZebaZpbbfZljbpuZ\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^gZyi_j_f_ggZyg_hij_^_e_gZMATLABbkihevam_li_j_f_ggmxansdhjhldhhlanswer hl\_l^eyojZg_gbyj_amevlZlh\\uqbke_gbyFuih^-kqblZeb \_dlhjkljhdm kh^_jZsmx kmffm we_f_glh\ klhe[ph\ fZljbpu :

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jZ\gmx

: dZdgZkq_l kmff \ kljhdZo"0$7/$%ij_^ihqblZ_l jZ[hlZlv kh klhe[pZfb

fZljbpulZdbfh[jZahfemqrbckihkh[ihemqblvkmffm\kljhdZowlhljZgk-

ihgbjh\ZlvgZrmfZljbpmih^kqblZlvkmffm\klhe[pZoZihlhfljZgkihgbjh-

\Zlvj_amevlZlHi_jZpbyljZgkihgbjh\Zgbyh[hagZqZ_lkyZihkljhnhfbebh^b-

gZjghc dZ\uqdhc HgZ a_jdZevgh hlh[jZZ_l fZljbpm hlghkbl_evgh ]eZ\ghc

^bZ]hgZebbf_gy_lkljhdbgZklhe[puLZdbfh[jZahf

A'

\uau\Z_l

ans = 16 5 9 4 3 10 6 15 2 11 7 14 13 8 12 1

:\ujZ_gb_

sum(A')'

\uau\Z_lj_amevlZl\_dlhjklhe[_pkh^_jZsbckmffu\kljhdZo

ans = 34 34 34 34

FZljbpu b fZ]bq_kdb_ d\Z^jZlu

11

Kmffmwe_f_glh\gZ]eZ\ghc^bZ]hgZebfhghe_]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 \ZgZ fZl_fZlbq_kdb

ihwlhfmMATLAB g_bf__lki_pbZevghcnmgdpbb^eyg_zGhnmgdpbydhlhjZy\gZqZe_ij_^iheZ]ZeZkv^eybkihevah\Zgby\]jZnbd_ fliplr a_jdZevghhlh[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.eygZr_]hfZ]bq_kdh]hd\Z^-

jZlZA(4,2) LZdbfh[jZahffhgh\uqbkeblvkmffmwe_f_glh\\q_l\_j-lhfklhe[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_\hafhghh[jZsZlvkydwe_f_glZffZljbpuq_j_ah^bgbg^_dkA(k)Wlhh[uqguc kihkh[ kkueZlvky gZ kljhdb b klhe[pufZljbpuGh _]hfhgh bk-

ihevah\Zlvlhevdhk^\mf_jgufbfZljbpZfb

GZqZeh jZ[hlu kMATLAB

12

LZd^eygZr_]hfZ]bq_kdh]hd\Z^jZlZA(8) wlh^jm]hckihkh[kkueZlvkygZagZq_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_jfZljb-

pum\_ebqb\Z_lky

X=A;X(4,5) = 17

X = 16 3 2 13 0 5 10 11 8 0 9 6 7 12 0 4 15 14 1 17

Hi_jZlhj^\h_lhqby>\h_lhqb_ wlhh^bgbagZb[he__\Zguohi_jZlhjh\MATLABHgijhy\-ey_lky\jZaebqguonhjfZoeyihemq_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))

FZljbpu b fZ]bq_kdb_ d\Z^jZlu

13

\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

enddihke_^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^hegZ[ulv

sum(1:16)/4

dhlhjZydhg_qghjZ\gZ

ans = 34

NmgdpbymagicMATLABgZkZfhf^_e_h[eZ^Z_l\kljh_gghcnmgdpb_cdhlhjZykha^Z_lfZ]b-q_kdbcd\Z^jZlihqlbex[h]hjZaf_jZG_m^b\bl_evghqlhwlZnmgdpbygZau-

\Z_lkymagic.

B=magic(4)

B = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 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_^gboklhe[pZihf_gyebkvf_klZfb>eylh]hqlh[uij_h[jZah\ZlvB\fZl-jbpm>xj_jZAi_j_klZ\bfbof_klZfb

A=B(:,[1 3 2 4])

Wlh hagZqZ_l qlh^ey dZ^hc kljhdbfZljbpuB we_f_glui_j_ibku\Zxlky \ihjy^d_

A = 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1

Ihq_fm>xj_ji_j_mihjy^hqbe klhe[puih kjZ\g_gbx k l_f qlhbkihevam_l

MATLAB";_a khfg_gby hg ohl_e \dexqblv ^Zlm ]jZ\xju \ gbgxxqZklvfZ]bq_kdh]hd\Z^jZlZ

GZqZeh jZ[hlu kMATLAB

14

GZqZeh jZ[hlu kMATLAB

16

;_kdhg_qghklvihy\ey_lkyijb^_e_gbbgZgmevbebijb\uiheg_gbbfZl_fZlb-

q_kdh]h\ujZ_gbyijb\h^ys_]hdi_j_iheg_gbxl_dij_\ur_gbxrealmax.G_qbkehNaN]_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\hafhghbaf_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

JZ[hlZ k fZljbpZfb

17

JZ[hlZkfZljbpZfb

WlhljZa^_ejZkkdZ_l\ZfhjZaebqguokihkh[Zokha^ZgbyfZljbp

=_g_jbjh\Zgb_fZljbp0$7/$%bf__lq_luj_nmgdpbbdhlhju_kha^Zxlhkgh\gu_fZljbpu

zeros \k_gmebones \k__^bgbpurand jZ\ghf_jgh_jZkij_^_e_gb_kemqZcguowe_f_glh\randn ghjfZevgh_jZkij_^_e_gb_kemqZcguowe_f_glh\

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 -1.1465 0.3273 -0.5883 -1.6656 1.1909 0.1746 2.1832 0.1253 1.1892 -0.1867 -0.1364 0.2877 -0.0376 0.7258 0.1139

AZ]jmadZfZljbpDhfZg^Z load kqblu\Z_l ^\hbqgu_nZceu kh^_jZsb_fZljbpu kha^Zggu_ \MATLAB jZg__bebl_dklh\u_nZceukh^_jZsb_qbke_ggu_^Zggu_L_dklh-\u_nZceu^hegu[ulvknhjfbjh\Zgu\\b^_ijyfhm]hevghclZ[ebpuqbk_e

hl^_e_gguoijh[_eZfbkjZ\gufdhebq_kl\hfwe_f_glh\\dZ^hckljhd_GZ-

ijbf_jkha^Z^bf\g_MATLAB l_dklh\hcnZcekh^_jZsbckljhdb

16.0 3.0 2.0 13.0 5.0 10.0 11.0 8.0 9.0 6.0 7.0 12.0 4.0 15.0 14.0 1.0

KhojZgbfwlhlnZceih^bf_g_fmagik.datLh]^ZdhfZg^Z

GZqZeh jZ[hlu kMATLAB

18

load magik.dat

ijhqblZ_lwlhlnZcebkha^Zkli_j_f_ggmxmagikkh^_jZsmxgZrmfZljbpm

FnZceuey\uah\Z l_dklh\h]hj_^ZdlhjZgZJKbebMac\u[_jbl_OpenbebNew baf_gxFilebebgZfbl_khhl\_lkl\mxsmxdghidmgZiZg_ebbgkl-jmf_glh\>eyh[jZs_gbydl_dklh\hfmj_^ZdlhjmgZUNIXbkihevamcl_kbf\hekjZamaZdhfZg^hcdhlhjmx\ubkihevam_l_\kljhd_hi_jZpbhgghckbkl_fu

GZijbf_jkha^Z^bfnZce\dexqZxsbcke_^mxsb_kljhd

A = [ 16.0 3.0 2.0 13.05.0 10.0 11.0 8.09.0 6.0 7.0 12.04.0 15.0 14.0 1.0 ];

KhojZgbf_]hih^bf_g_fmagik.m.Lh]^Z\ujZ_gb_

magik

ijhqblZ_lnZcebkha^Zkli_j_f_ggmx:kh^_jZsmxbkoh^gmxfZljbpm

H[t_^bg_gb_H[t_^bg_gb_ wlhijhp_kk kh_^bg_gbyfZe_gvdbofZljbp^ey kha^Zgby[hev-

rboNZdlbq_kdb\u kha^Zeb \Zrmi_j\mxfZljbpm h[t_^bg_gb_f _z hl^_ev-

guo we_f_glh\IZjZ d\Z^jZlguo kdh[hd wlh hi_jZlhj h[t_^bg_gbyGZijb-

f_jgZqg_fkfZljbpu:fZ]bq_kdh]hd\Z^jZlZobknhjfbjm_f

B = [A A+32; A+48 A+16]

J_amevlZlhf[m^_lfZljbpZoihemqZ_fZykh_^bg_gb_fq_luj_oih^fZljbp

B = 16 2 3 13 48 34 35 45 5 11 10 8 37 43 42 40 9 7 6 12 41 39 38 44 4 14 15 1 36 46 47 33 64 50 51 61 32 18 19 29 53 59 58 56 21 27 26 24 57 55 54 60 25 23 22 28 52 62 63 49 20 30 31 17

JZ[hlZ k fZljbpZfb

19

WlhfZljbpZebrvgZiheh\bgmy\ey_lkyfZ]bq_kdhc?zwe_f_gluij_^klZ\eyxl

kh[hcdhf[bgZpbxp_euoqbk_ehl ^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\uG_h[oh-^bfhijh\_klb^hihegbl_evgu_hi_jZpbbqlh[uk^_eZlvwlmfZljbpm^_ckl\b-

l_evghfZ]bq_kdbfd\Z^jZlhfo

M^Ze_gb_kljhdbklhe[ph\

GZqZeh jZ[hlu kMATLAB

20

DhfZg^gh_hdgh

>hkboihjfubkihevah\ZeblhevdhdhfZg^gmxkljhdmMATLABi_qZlZydh-fZg^ub \ujZ_gbybgZ[ex^Zy j_amevlZlu

DhfZg^gh_ hdgh

21

?kebkZfuc[hevrhcwe_f_glfZljbpu[hevr_3bebkZfucfZe_gvdbcf_gv-

r_ -3

, MATLABijbf_gy_l h[sbcfZkrlZ[guc dhwnnbpb_gl ^eynhjfZlh\short b long.ebggu_dhfZg^gu_kljhdb?keb\ujZ_gb_g_mf_sZ_lkygZh^ghckljhd_bkihevamcl_ljh_lhqb_ZaZgbf

Return bebEnter^eyh[hagZq_gbylh]hqlh\ujZ_gb_ijh^heZ_lkygZke_-^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^ghckljhdbJZaebqgu_ 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_^ihehbfqlh\u^himklbebhrb[dmijb\\h^_

rho = (1 + sqt(5))/2

GZqZeh jZ[hlu kMATLAB

22

^mxsbo deZ\br ^hklmigu gZ \Zr_cfZrbg_ Fgh]b_ ba wlbo deZ\br [m^ml

agZdhfuihevah\Zl_eyfj_^ZdlhjZEMACS.)

ctrl-p \b_gb_\i_j_^gZh^bgkbf\hectrl- ctrl-r >\b_gb_\ijZ\hgZh^ghkeh\hctrl- ctrl-l >\b_gb_\e_\hgZh^ghkeh\hhome ctrl-a I_j_oh^gZgZqZehkljhdbend ctrl-e I_j_oh^gZdhg_pkljhdbesc ctrl-u HqbkldZkljhdbdel ctrl-d M^Ze_gb_kbf\heZaZdmjkhjhfbackspace ctrl-h M^Ze_gb_kbf\heZi_j_^dmjkhjhf

ctrl-k M^Ze_gb_^hdhgpZkljhdb

=jZnbdZ

23

=jZnbdZ

MATLAB bf__lrbjhdb_\hafhghklb^ey]jZnbq_kdh]hbah[jZ_gby\_dlhjh\bfZljbpZlZd_^eykha^Zgbydhff_glZjb_\bi_qZlb]jZnbdbWlZ]eZ\Zhib-

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ijbf_g_gby

Kha^Zgb_]jZnbdZNmgdpbyplot bf__ljZaebqgu_nhjfuk\yaZggu_k\oh^gufbiZjZf_ljZfbgZ-ijbf_jplot(y)kha^Z_ldmkhqghebg_cguc]jZnbdaZ\bkbfhklbwe_f_glh\y hlbobg^_dkh\?keb\uaZ^Z_l_^\Z\_dlhjZ\dZq_kl\_Zj]mf_glh\plot(x,y) kha^Zkl]jZnbdaZ\bkbfhklby hlx.

GZijbf_j^eyihkljh_gby]jZnbdZagZq_gbcnmgdpbbsin hlgmey^hpik^_eZ-_fke_^mxs__

t = 0:pi/100:2*pi; y = sin(t); plot(t,y)

GZqZeh jZ[hlu kMATLAB

24

eyhldjulbygh\h]hhdgZb\u[hjZ_]hihmfheqZgbxgZ-

[_jbl_

figure

>eylh]hqlh[uk^_eZlvkms_kl\mxs_zhdghl_dmsbf

=jZnbdZ

25

figure(n)

]^_n wlhghf_j\aZ]heh\d_hdgZh[Z\e_gb_djb\uogZkms_kl\mxsbc]jZnbdDhfZg^Zhold iha\hey_l^h[Z\eylvdjb\u_gZkms_kl\mxsbc]jZnbdDh]^Z\ugZ[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_ ebgbbnmgdpbb peaks Z aZl_f gZdeZ^u\Z_l ik_\^hp\_lghc]jZnbdlhc_nmgdpbb

[x,y,z] = peaks;contour(x,y,z,20,'k')hold onpcolor(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^]jZnbdbNmgdpby subplot iha\hey_l \u\h^blv fgh_kl\h ]jZnbdh\ \ h^ghf hdg_ bebjZki_qZlu\ZlvbogZh^ghfebkl_[mfZ]b

subplot(m,n,p)

GZqZeh jZ[hlu kMATLAB

26

jZa[b\Z_lhdghbah[jZ_gbcgZfZljbpmm gZn ih^]jZnbdh\b\u[bjZ_lpucih^]jZnbdl_dmsbf=jZnbdbgmf_jmxlky\^hevi_j\h]h\\_jog_ckljhd_ih-

lhf\h\lhjhcbl^GZijbf_j^eylh]hqlh[uij_^klZ\blv]jZnbq_kdb_^Zg-

gu_\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_lkyaZ bkdexq_gb_f kemqZy dh]^Z dhfie_dkguc Zj]mf_gl h^bg>ey wlh]h ki_pb-

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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^pZlbklhjhggbcfgh]hm]hevgbd kfZe_gvdbfbdjmdZfbgZ \_j-

rbgZo

=jZnbdZ

27

MijZ\e_gb_hkyfbNmgdpbyaxis bf__lg_kdhevdh\hafhghkl_c^eygZkljhcdbfZkrlZ[Zhjb_glZ-pbbbdhwnnbpb_glZkZlby

H[uqghMATLABgZoh^blfZdkbfZevgh_bfbgbfZevgh_agZq_gb_b\u[bjZ_lkhhl\_lkl\mxsbcfZkrlZ[bfZjdblbjh\Zgb_hk_cNmgdpbyaxis aZf_gy_lagZ-q_gbyihmfheqZgbxij_^_evgufbagZq_gby\\h^bfufbihevah\Zl_e_f

axis( [xmin xmax ymin ymax] )

GZqZeh jZ[hlu kMATLAB

28

\dexqZ_lh[hagZq_gbyhk_cbf_ldbijhf_mlhqguo^_e_gbc

axis off

\udexqZ_lh[hagZq_gbyhk_cbf_ldbijhf_mlhqguo^_e_gbc

grid off

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grid on

\dexqZ_l_zaZgh\h

Ih^ibkbdhkyfbaZ]heh\dbNmgdpbb xlabel, ylabel, zlabel ^h[Z\eyxl ih^ibkb d khhl\_lkl\mxsbf hkyfnmgdpbytitle ^h[Z\ey_laZ]heh\hd\\_jogxxqZklvhdgZZnmgdpbytext\klZ\-ey_ll_dkl\ex[h_f_klh]jZnbdZBkihevah\Zgb_TEX ij_^klZ\e_gbyiha\hey_lijbf_gylv ]j_q_kdb_ [md\u fZl_fZlbq_kdb_ kbf\heu b jZaebqgu_ rjbnlu

Ke_^mxsbcijbf_j^_fhgkljbjm_lwlm\hafhghklv

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 =jZnbd nmgdpbb VLQ

text(-1 ?LW^Hlf_lvl_ g_q_lgmx kbff_ljbx`

pi W pi

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=jZnbdZ

29

mesh kha^Z_ldZjdZkgmxih\_joghklv]^_p\_lgu_ebgbbkh_^bgyxllhevdhaZ-^Zggu_lhqdbZnmgdpbysurface \f_kl_kebgbyfbhlh[jZZ_l\p\_l_bkZfmih\_joghklv

eyhlh[jZ_gbynmgdpbb^\moi_j_f_gguoz = f (x,y)kha^ZxlkyfZljbpuX bY khklhysb_ ba ih\lhjyxsboky kljhd b klhe[ph\ khhl\_lkl\_ggh i_j_^ bk-ihevah\Zgb_fnmgdpbbAZl_fbkihevamxlwlbfZljbpu^ey\uqbke_gbybhlh-

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>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)

h[Z\e_gb_eps iha\hey_lba[_Zlvg_hij_^_e_gghklb\gZ-qZe_dhhj^bgZl

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hij_^_eyxlboyjdhklvbp\_lGZijbf_j

load durerwhos

GZqZeh jZ[hlu kMATLAB

30

ihdZ_lqlhnZcedurer.mat\^bj_dlhjbbdemo khklhblbafZljbpujZaf_jhfgZfZljbpuXbfZljbpujZaf_jhfgZfZljbpumapWe_f_glufZljbpuX wlhp_eu_qbkeZhl^hdhlhju_kemZlbg^bdZlhjZfb\p\_l-ghfhlh[jZ_gbbPDSKe_^mxsb_kljhdb

imag(X)colormap(map)axis image

\hkijhba\h^yl]jZ\xjm>xj_jZihdZaZggmx\gZqZe_wlhcdgb]b

KijZ\dZ b l_dmsZy ^hdmf_glZpby

31

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MATLAB.

DhfZg^Zhelp HdghkijZ\db

MATLAB Help Desk L_dmsb_kijZ\hqgu_kljZgbpu

K\yavkThe MathWorks, Inc.

DhfZg^ZKHOSDhfZg^Zhelp wlhkZfuchkgh\ghckihkh[hij_^_e_gbykbglZdkbkZbih\_^_gbyhl^_evguonmgdpbcBgnhjfZpbyhlh[jZZ_lkyijyfh\ dhfZg^ghf hdg_GZ-

ijbf_j

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,...

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bf_gnmgdpbc \k_]^Z bkihevamcl_ khhl\_lkl\mxsb_ kljhqgu_ [md\u lZd dZd

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GZqZeh jZ[hlu kMATLAB

32

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DhfZg^ZORRNIRUDhfZg^Z lookfor iha\hey_lbkdZlvnmgdpbbihdexq_\hfmkeh\mHgZijhkfZl-jb\Z_l i_j\mx kljhdm l_dklZ kijZ\db gZau\Z_fmx kljhdhc H1 ^ey dZ^hcnmgdpbbMATLAB b \ha\jZsZ_l kljhdb H1, kh^_jZsb_ aZ^Zggh_ dexq_\h_keh\hGZijbf_jMATLABg_bf__lnmgdpbbkbf_g_finverseIhwlhfmhl\_lgZaZijhk

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34

Kj_^Z0$7/$%

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MATLAB\\_^bl_

clear

DhfZg^ZVDYHDhfZg^Zsave khojZgy_lkh^_jZgb_jZ[hq_]hijhkljZgkl\Z\F:LnZce_dhlh-

juc fh_l [ulv ijhqblZg dhfZg^hc load \ ihke_^mxsbo k_ZgkZo jZ[hluMATLABGZijbf_j

save August17th

khojZgy_lkh^_jZgb_\k_]hjZ[hq_]hijhkljZgkl\Z\nZce_August17th.mat?k-ebgmgh\ufh_l_khojZgblvlhevdhhij_^_e_ggu_i_j_f_ggu_mdZau\Zybo

bf_gZihke_bf_gbnZceZ

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35

H[uqgh i_j_f_ggu_ khojZgyxlky \ ^\hbqghfnhjfZl_ dhlhjucfh_l [ulv

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-ascii Bkihevam_lagZqgucl_dklh\hcnhjfZl

-ascii -double Bkihevam_lagZqgucl_dklh\hcnhjfZl

-ascii -double -tabs JZa^_ey_lwe_f_glufZkkb\ZlZ[meypb_c

-v4 Kha^Z_lnZce^eyMATLAB 4.

-append >h[Z\ey_l^Zggu_\kms_kl\mxsbcMATnZce

Dh]^Z\ukhojZgy_l_kh^_jZgb_jZ[hq_]hijhkljZgkl\Z\l_dklh\hfnZce_\u

^hegukhojZgylvlhevdhh^gmi_j_f_ggmx\^Zggucfhf_gl?keb\ukhojZ-

gy_l_ [he__ h^ghc i_j_f_gghc MATLAB kha^Z_l l_dklh\hc nZce gh \u g_kfh_l_aZ]jmablv_]hh[jZlgh

FZjrjmlihbkdZMATLAB bkihevam_lfZjrjmlihbkdZmihjy^hq_gguckibkhd^bj_dlhjbc^eylh]hqlh[uhij_^_eblvdZd\uihegylvnmgdpbbdhlhju_\u\uau\Z_l_Dh]^Z

\u\uau\Z_l_ klZg^ZjlgmxnmgdpbxMATLAB bkihegy_li_j\ucFnZcegZk\h_fimlbdhlhjucbf__l aZ^Zggh_bfyey[hevrbgkl\ZbawlbodhfZg^\ufh_l_bkihevah\Zlvihegu_imlbrZ[eh-

gubmdZaZl_eb^bkdh\\h[uqghcnhjf_

GZqZeh jZ[hlu kMATLAB

36

DhfZg^ZGLDU\DhfZg^Zdiarykha^Z_l^g_\gbdk_ZgkZMATLAB\^bkdh\hfnZce_eykha^ZgbynZceZih^bf_g_fdiarydhlhjuckh^_jbl\k_dhfZg^udhlhju_\ubkihevam_l_\dexqZy\u\h^gZi_qZlv djhf_]jZnb-

q_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

Ih^jh[g__ h fZljbpZo b fZkkb\Zo

37

Ih^jh[g__hfZljbpZobfZkkb\Zo

WlhljZa^_ejZkkdZ_l\Zf[hevr_hjZ[hl_kfZljbpZfbbfZkkb\Zfbm^_eyy

hkh[h_\gbfZgb_

Ebg_cghcZe]_[j_

FZkkb\Zf

Fgh]hf_jguf^Zgguf

Ebg_cgZyZe]_[jZL_jfbgufZljbpZbfZkkb\qZklhg_ijZ\bevghbkihevamxldZd\aZbfhaZf_gy_-

fu_;he__lhqghfZljbpZwlh^\mf_jgucqbke_ggucfZkkb\bkihevam_fuc\

ebg_cguo ij_h[jZah\ZgbyoFZl_fZlbq_kdb_ hi_jZpbb hij_^_e_ggu_ gZfZl-

jbpZoy\eyxlkyh[t_dlhfebg_cghcZe]_[ju

FZ]bq_kdbcd\Z^jZl>xj_jZ

A = 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1

bkihevam_lky\g_dhlhjuoijbf_jZodhlhju_iha\heyxlihqm\kl\h\Zlvhi_jZ-

pbbgZ^fZljbpZfb\ MATLAB

GZqZeh jZ[hlu kMATLAB

38

d = 0

Ijb\_^_ggZy d kljhdZf klmi_gqZlZy nhjfZ fZljbpu: \u]ey^bl ke_^mxsbf

h[jZahf

R = rref(A)

R = 1 0 0 1 0 1 0 -3 0 0 1 3 0 0 0 0

IhkdhevdmaZ^ZggZyfZljbpZy\ey_lkykbg]meyjghclhhgZg_bf__lh[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_-

gbblhqghckbg]meyjghklbGh agZq_gb_ rconddhlhjh_mklZgZ\eb\Z_lmkeh\b_hp_gdb^eyh[jZlghcfZljbpubf__lihjy^hdepshlghkbl_evghclhqghklbqbk-eZkieZ\Zxs_clhqdhcihwlhfm\uqbke_gb_h[jZlghcfZljbpug_hq_gv_eZ-

l_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]meyj-

ghklbKZfh_[hevrh_kh[kl\_ggh_ agZq_gb_jZ\gh fZ]bq_kdhckmff_Wlh

ijhbkoh^blihlhfmqlh\_dlhjkhklhysbcba\k_o_^bgbpy\ey_lkykh[kl\_g-

guf\_dlhjhf

v = ones(4,1)

v =

1 1 1 1

A*v

Ih^jh[g__ h fZljbpZo b fZkkb\Zo

39

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 0.0882 0.0588 0.3824 0.1471 0.2941 0.3235 0.2353 0.2647 0.1765 0.2059 0.3529 0.1176 0.4412 0.4118 0.0294

LZdb_fZljbpuij_^klZ\eyxl kh[hc \_jhylghklvi_j_oh^Z \FZjdh\kdhfijh-

p_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 0.2495 0.2494 0.2504 0.2497 0.2501 0.2502 0.2500 0.2500 0.2498 0.2499 0.2503 0.2496 0.2506 0.2505 0.2493

Bawlh]hke_^m_lqlh_kebk klj_fblkyd[_kdhg_qghklblh]^Z\k_we_f_glu\k-hckl_i_gb, Pk,klj_fylkyd.

GZqZeh jZ[hlu kMATLAB

40

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qbke_ggufbfZkkb\Zfb:jbnf_lbq_kdb_ hi_jZpbbgZfZkkb\Zo ijhba\h^ylky

ihwe_f_glghWlhhagZqZ_lqlhkmffbjh\Zgb_b\uqblZgb_y\eyxlkyh^bgZdh-

\ufb hi_jZpbyfb ^ey fZljbp b fZkkb\h\ Z mfgh_gb_ ^ey gbo jZaebqgh

MATLABbkihevam_llhqdmbeb^_kylbqgmxlhqdmdZdqZklvaZibkb^eyhi_jZ-pbbmfgh_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_

?kebfZ]bq_kdbc d\Z^jZl>xj_jZ mfghblv gZ k_[y ih ijZ\beZf mfgh_gby

fZkkb\h\

A.*A

j_amevlZlhf[m^_lfZkkb\kh^_jZsbcd\Z^jZlup_euoqbk_ehl^h\g_-

h[uqghfihjy^d_

ans =

256 9 4 169 25 100 121 64 81 36 49 144 16 225 196 1

Hi_jZpbbgZ^fZkkb\Zfbihe_agu^eykha^Zgby lZ[ebpImklvn wlh\_dlhjklhe[_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 0 1 1 1 2 2 4 4 3 9 8 4 16 16 5 25 32 6 36 64 7 49 128 8 64 256 9 81 512

Ih^jh[g__ h fZljbpZo b fZkkb\Zo

41

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 0 1.1 0.041393 1.2 0.079181 1.3 0.11394 1.4 0.14613 1.5 0.17609 1.6 0.20412 1.7 0.23045 1.8 0.25527 1.9 0.27875 2 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^ZykljhdZj_amevlZlugZ[ex^_gbcLZdbfh[jZahfwe_f_gli,jwlhih_gZ[ex^_gb_jhci_j_f_gghc

ey iylb gZ[ex^_gbc j_amevlbjmxsbcfZkkb\fh_l \u]ey^_lv ke_^mxsbf

h[jZahf

D = 72 134 3.2 81 201 3.5 69 156 7.1 82 148 2.4 75 170 1.2

I_j\ZykljhdZkh^_jblqZklhlmk_j^_qguokhdjZs_gbc\_kbqZkumijZg_gbc

^eyi_j\h]hiZpb_glZ\lhjZykljhdZkh^_jblZgZeh]bqgu_^Zggu_^ey\lhjh]h

bl^

GZqZeh jZ[hlu kMATLAB

42

mu =

75.8 161.8 3.48sigma = 5.6303 25.499 2.2107

Qlh[uihkfhlj_lvkibkhd\k_onmgdpbcMATLAB^eyZgZebaZ^ZgguogZ[_jb-l_

help datafun

?keb\ZfgmghmagZlvhStatistics 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 -5.5 -6.5 4.5 -3.5 1.5 2.5 -0.5 0.5 -2.5 -1.5 3.5 -4.5 6.5 5.5 -7.5

sum(B)

ans = 0 0 0 0

Bkihevamy kdZeyjgh_ jZkrbj_gb_MATLAB mdZau\Z_l aZ^Zgguc kdZeyj \k_fbg^_dkZf\^bZiZahg_GZijbf_j

B(1:2,2:3)=0

h[gmey_lqZklvfZljbpuB

B = 7.5 0 0 4.5 -3.5 0 0 -0.5 0.5 -2.5 -1.5 3.5 -4.5 6.5 5.5 -7.5

Eh]bq_kdZybg^_dkZpbyEh]bq_kdb_\_dlhjZkha^Zggu_baeh]bq_kdbohi_jZlhjh\bhi_jZlhjh\kjZ\g_-

gbyfh]ml[ulvbkihevah\Zgu^eykkuedbgZih^fZkkb\uIj_^ihehbfqlhXh[udgh\_ggZyfZljbpZbL fZljbpZlh]h_jZaf_jZghkh^_jZsZyeh]bq_kdb_hi_jZpbbLh]^ZX(L)aZ^Z_lwe_f_gluX\dhlhjuowe_f_gluL g_gme_\u_

Ih^jh[g__ h fZljbpZo b fZkkb\Zo

43

Wlhl\b^bg^_dkZpbbfh_l[ulvhkms_kl\e_gaZh^bgrZ]mdZaZgb_feh]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-

_cbkihevamcl_ finite(x)dhlhjZyy\ey_lkybklbghc^ey\k_odhg_qguoqbke_g-guoagZq_gbcbehvx^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_lghhlebqZxsZykyhlhk-

lZevguo wlh\u[jhkIhke_^mxsb_^_ckl\bymkljZgyxl\u[jhku \^Zgghf

kemqZ_l_we_f_glu^eydhlhjuokj_^g_d\Z^jZlbqgh_hldehg_gb_[he__q_f\

ljbjZaZmdehgy_lkyhlkj_^g_]h

x = x(abs(x-mean(x))

GZqZeh jZ[hlu kMATLAB

44

A(k)

ans = 5 3 2 11 7 13

?keb\ubkihevam_l_k dZdbg^_dkke_\hcklhjhgu\hi_jZlhj_ijbk\Zb\ZgbylhfZljbqgZykljmdlmjZkhojZgy_lky

A(k) = NaN

A = 16 NaN NaN NaN NaN 10 NaN 8 9 6 NaN 12 4 15 14 1

MijZ\e_gb_ ihlhdZfb

45

MijZ\e_gb_ihlhdZfb

MATLAB bf__liylv\b^h\kljmdlmjmijZ\e_gbyihlhdZfb

hi_jZlhjif hi_jZlhjswitch pbdeufor pbdeuwhile hi_jZlhjbreak

ifHi_jZlhjif \uqbkey_leh]bq_kdh_\ujZ_gb_b\uihegy_l]jmiimhi_jZlhjh\_keb\ujZ_gb_bklbgghG_h[yaZl_evgu_dexq_\u_keh\ZelseifbelsekemZl^ey\uiheg_gbyZevl_jgZlb\guo]jmiihi_jZlhjh\Dexq_\h_keh\henddhlh-jh_kh]eZkm_lkyk ifaZ\_jrZ_lihke_^gxx]jmiimhi_jZlhjh\LZdbfh[jZahf\k_]jmiiuhi_jZlhjh\aZdexq_guf_^mq_luj_odexq_\uokeh\[_abkihev-

ah\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) ~= 0M = odd_magic(n)

elseif rem(n,4) ~= 0M = single_even_magic(n)

elseM = double_even_magic(n)

end

GZqZeh jZ[hlu kMATLAB

46

>Ze__ijb\_^_g^jm]hcijbf_jdhlhjucbkke_^m_lwlhl\hijhk?kebAbB y\-eyxlky kdZeyjZfb lhgb_ijb\_^_ggZy ijh]jZffZgbdh]^Zg_ ijb\_^_l dg_-

hb^ZgghckblmZpbbGh^ey[hevrbgkl\ZiZjbkihevam_fuofZljbp\dexqZy

gZrbfZ]bq_kdb_d\Z^jZluki_j_klZ\e_ggufbklhe[pZfbgbh^ghbamkeh\bc

A > B, A < B bebA ==Bg_y\ey_lkybklbgguf^ey\k_owe_f_glh\bihwlhfm\uihegy_lkykemqZcelse.

if A > B' greater '

elseif A < B' less'

elseif A == B' equal '

elseerror ( ' G_ij_^\b^_ggZykblmZpby ' )

end

G_dhlhju_nmgdpbbfh]ml[ulvihe_agu^eyfZljbqgh]hkjZ\g_gbyijbbkihev-

ah\Zgbbkhi_jZlhjhfifgZijbf_j

isequalisemptyallany

VZLWFKbFDVHHi_jZlhjswitch \uihegy_l]jmiimhi_jZlhjh\[ZabjmykvgZagZq_gbbi_j_f_g-ghc beb \ujZ_gbyDexq_\u_ keh\Z case b otherwise jZa^_eyxl wlb ]jmiiu

MijZ\e_gb_ ihlhdZfb

47

kemqZb g_ \uihegyxlkyLZdbf h[jZahf g_l g_h[oh^bfhklb \ bkihevah\Zgbb

hi_jZlhjZbreak.

forPbdefor ih\lhjy_l]jmiimhi_jZlhjh\nbdkbjh\Zggh_ij_^hij_^_e_ggh_qbkehjZaDexq_\h_keh\hend hq_jqb\Z_ll_ehpbdeZ

for n = 3:32r(n) = rank(magic(n));

endr

LhqdZkaZiylhcihke_\ujZ_gby\l_e_pbdeZij_^hl\jZsZ_lih\lhj_gby\u-

\h^Zj_amevlZlh\gZwdjZgZr ihke_pbdeZ\u\h^blhdhgqZl_evgucj_amevlZl

Ohjhrbfklbe_fy\eyxlkyhlklmiuijbbkihevah\Zgbbpbdeh\^eyemqr_cqb-

lZ_fhklbhkh[_gghdh]^Zhgb\eh_ggu_

for i = 1:mfor j = 1:n

H(i,j) = 1/(i+j);end

end

whilePbdewhile ih\lhjy_l]jmiimhi_jZlhjh\hij_^_e_ggh_qbkehjZaihdZ\uihe-gy_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^eygZ-oh^_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

endx

J_amevlZlhf[m^_ldhj_gvihebghfZx3-2x-5

x =

2.09455148154233

GZqZeh jZ[hlu kMATLAB

48

>ey hi_jZlhjZwhile \_jgu l__ ij_^hkl_j__gby hlghkbl_evgh fZljbqgh]hkjZ\g_gbyqlhb^eyhi_jZlhjZif, dhlhju_h[km^ZebkvjZg__

breakHi_jZlhjbreak iha\hey_l^hkjhqgh\uoh^blvbapbdeh\ for bebwhile

>jm]b_ kljmdlmju ^Zgguo

49

>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\uFgh]hf_jgu_fZkkb\u\MATLABwlhfZkkb\u[he__q_fk^\mfybg^_dkZfbHgbfh]ml[ulvkha^Zgu\uah\hfnmgdpbczeros, ones, rand bebrandnk[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\ufh]mlij_^klZ\eylv lj_of_jgu_nbabq_kdb_^Zggu_gZ-

ijbf_jl_fi_jZlmjm\dhfgZl_J_amevlZlij_^klZ\ey_lkyihke_^h\Zl_evghklvx

fZljbpA(k)bebaZ\bkys_chl\j_f_gbfZljbp_cA(t)xj_jZ

M(:,:,22)

GZqZeh jZ[hlu kMATLAB

50

ans =

16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1

Nmgdpby

sum(M,d)

\uqbkey_lkmffubaf_gyybg^_dkdLZd

sum(M,1)

- wlhoofZkkb\kh^_jZsbcdhibb\_dlhjZkljhdb

34 34 34 34

:

sum(M,2)

y\ey_lkyfZkkb\hfookh^_jZsbfdhibb\_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__dFZkkb\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_faZ-dexq_gby jZaghh[jZaghc ]jmiiu h[t_dlh\ \ djm]eu_ kdh[dbDjm]eu_ kdh[db

lZd_bkihevamxlkykbg^_dkZfb^eyihemq_gby^hklmiZdkh^_jZgbxjZaebq-

guoyq__dGZijbf_j

C = { A sum(A) prod(prod(A)) }

^Z_lfZkkb\yq__d oWlb ljbde_ldbkh^_jZlfZ]bq_kdbcd\Z^jZl\_dlhj

kljhdmkkmffZfb\klhe[pZobijhba\_^_gb__]hwe_f_glh\?kebhlh[jZablvCgZwdjZg_lh\um\b^bl_ke_^mxs__

>jm]b_ kljmdlmju ^Zgguo

51

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^_jbl lhevdh hl^_evgh_

qbkehb^eyg_]h_klvg_h[oh^bfZyh[eZklv\u\h^Z

Hq_gv\ZghaZihfgblv^\Z\Zguofhf_glZI_j\h_^eyihemq_gbykh^_jZ-

gbyh^ghcyq_cdbbkihevamcl_bg^_dk\djm]euokdh[dZoGZijbf_jC{1} \ha-\jZsZ_lfZ]bq_kdbcd\Z^jZlZC{3} 16!

GZqZeh jZ[hlu kMATLAB

52

ij_h[jZam_lfZkkb\kbf\heh\\qbkeh\mxfZljbpmkh^_jZsmxij_^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 \hafhguf ijbkmlkl\b_ jZaebqguo

rjbnlh\gZ\Zr_fdhfivxl_j_I_qZlZ_fu_ kbf\heu\ASCII dh^_ij_^klZ\-eyxlkyp_eufbqbkeZfbhl ^h P_eu_qbkeZf_gvr_ ij_^klZ\eyxl

g_i_qZlZ_fu_ kbf\heuWlb qbkeZ jZkiheh_gu \ khhl\_lkl\mxs_ffZkkb\_

o

F = reshape(32:127,16,6)';

I_qZlZ_fu_kbf\heu\jZkrbj_gghfASCII gZ[hj_ij_^klZ\e_guF+128Dh]^Zwlb 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)

bihlhfihbaf_gycl_rjbnlu\dhfZg^ghfhdg_MATLABGb_ij_^klZ\e_gh^bgbaijbf_jh\lh]hqlhfh_lihemqblvky

ans = !"#$%&'()*+,-./0123456789:;?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ans =

83,/2

1z}0~:;?@ABCDEFGHI

JKLMNOPQRSTUVWXY

Z[\]^_`abcdefghi

jklmnopqrstuvwxy

Kh_^bg_gb_d\Z^jZlgufbkdh[dZfbdhgdZl_gbjm_ll_dklh\u_i_j_f_ggu_\f_-

kl_\[hevrmxkljhdm

h = [s, ' world']

h[t_^bgy_lkljhdbih]hjbahglZebb^Z_l

h =Hello world

>jm]b_ kljmdlmju ^Zgguo

53

Hi_jZlhj

v = [s; 'world']

h[t_^bgy_lkljhdb\_jlbdZevqlhijb\h^bld

v =

Helloworld

AZf_lvl_qlhi_j_^kbf\hehfw \i_j_f_gghchg_h[oh^bfhihklZ\blvijh[_eZh[Zkeh\Z\i_j_f_gghcv^hegu[ulvjZ\ghc^ebguJ_amevlbjmxsb_fZk-kb\uy\eyxlkykgh\ZfZkkb\Zfbkbf\heh\i_j_f_ggZyh 1o11Zi_j_f_ggZyv o

?klv^\Zkihkh[Zqlh[umijZ\eylv]jmiihcl_dklZkh^_jZs_ckljhdbjZaghc

^ebgu nhjfbjh\Zlv aZiheg_gguc fZkkb\ kbf\heh\ beb de_lhqguc fZkkb\

kljhdNmgdpbychar ijbgbfZ_lex[h_qbkehkljhd^h[Z\ey_lijh[_eu\dZ-^mx kljhdm qlh[u \k_ hgb [ueb jZ\ghc ^ebgu bnhjfbjm_lfZkkb\ kljhd k

kbf\hevghckljhdhc\dZ^hckljhd_GZijbf_j

S = char('A' , 'rolling' , 'stone' , 'gathers' , 'momentum.')

\u^Z_l

S =Arollingstonegathersmomentum.

Ijbkmlkl\m_l^hklZlhqgh_dhebq_kl\hijh[_eh\\i_j\uoq_luj_okljhdZoqlh-

[u\k_kljhdb[uebjZ\ghc^ebgu>jm]hckihkh[wlhkhojZgblvl_dkl\fZk-

kb\_yq__d

C = {'A' ; 'rolling' ; 'stone' ; 'gathers' ; 'momentum.' }

[m^_lfZkkb\yq__do

C = 'A' 'rolling' 'stone' 'gathers' 'momentum.'

GZqZeh jZ[hlu kMATLAB

54

KljmdlmjuKljmdlmjuwlhfgh]hf_jgu_fZkkb\uMATLABkwe_f_glZfb^hklmiddhlh-jufhkms_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\ufh_l_^h-[Z\eylv\gbowe_f_glu

>jm]b_ kljmdlmju ^Zgguo

55

[S.score]

lh_kZfh_qlh

[S(1).score, S(2).score, S(3).score]

j_amevlZlhf[m^_lqbke_gguc\_dlhjkljhdZkh^_jZsbc\k_kq_lZscore)ans =

83 91 70

:gZeh]bqgh

S.name

ijhklhijbk\Zb\Z_lbf_gZnamesihh^ghfmi_j_f_gghcansH^gZdhaZdex-q_gb_wlh]h\ujZ_gby\djm]eu_kdh[db

{S.name}

kha^Z_lfZkkb\yq__dokh^_jZsbcljbbf_gbnames)ans =

'Ed Plum' 'Toni Miller' 'Jerry Garcia'

Bnmgdpby

char(S.name)

klj_fyZj]mf_glZfbkha^Z_lfZkkb\kbf\heh\baiheyname.

ans =Ed PlumToni MillerJerry Garcia

GZqZeh jZ[hlu kMATLAB

56

Kp_gZjbbbnmgdpbb

MATLAB wlhfhsguc yaud ijh]jZffbjh\Zgby lZd_ dZd bbgl_jZdlb\gZy\uqbkebl_evgZykj_^ZNZceudhlhju_kh^_jZldh^gZyaud_MATLAB, gZau-\ZxlkyFnZceZfbeywlh]h\Zfg_h[oh^bfh^h[Z\blvbofZjrjmlihbkdZMATLAB.

?keb \u ih\lhjy_l_bfynmgdpbb lhMATLAB \uau\Zxl lhevdh lm dhlhjZy\klj_qZ_lkyi_j\hc

Qlh[u m\b^_lv kh^_jZgb_FnZceZ gZijbf_jmyfunction.m g_h[oh^bfhgZ-[jZlv

type myfunction

Kp_gZjbbDh^Z \u \uau\Z_l_ kp_gZjbc MATLAB ijhklh \uau\Z_l dhfZg^u kh^_jZ-sb_ky\nZce_Kp_gZjbbfh]mlhi_jbjh\Zlvkms_kl\mxsbfb^Zggufb\jZ[h-

q_fijhkljZgkl\_bebhgbfh]mlkZfbkha^Z\Zlvwlb^Zggu_Ohlykp_gZjbbg_

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s = svd(A);if nargin==1 tol = max(size(A)') * max(s) * eps;endr = sum(s > tol);

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function h = falling(t)global GRAVITYh = *GRAVITY*t.^2;

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global GRAVITYGRAVITY = 32;y = falling((0: .1: 5)' );

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load( 'August17.dat' )help( 'magic' )type( 'rank' )

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command argument

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command( 'argument' )

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for d = 1:31s = [ 'August' int2str(n) '.dat']load(s)% H[jZ[hldZkh^_jZgbyd-]hnZceZ

end

NmgdpbyHYDONmgdpbyeval jZ[hlZ_lkl_dklh\ufbi_j_f_ggufb^ey\uqbke_gbybj_ZebaZ-pbbl_dklh\uokljhd

eval(s)

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for d = 1:31s = [ 'load August' int2char(n) '.dat' ]eval(s)% H[jZ[hldZkh^_jZgbyd-]hnZceZ

end

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r = zeros(32,1)for n = 1:32

r(n) = rank(magic(n));end

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function y = humps(x)y = 1. / ( (x - .3). ^2 + .01) + 1. / ( (x - .9) .^2 + .04) - 6;

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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_lkybfynmgdpbbfbgb-fmfdhlhjhcbs_lkyZ\lhjufijb[eb_ggh_iheh_gb_fbgbfmfZ

p = fmins( 'humps', .5)

p = 0.6370

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humps(p)

ans =

11.2528

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Q = quad8( 'humps', 0, 1)

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Q = 29.8583

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h = plot(A)

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h = 3.0022 1.0038 4.0020 5.0016

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set(h)

ColorEraseMode: [ {normal} | background | xor | none ]LineStyle: [ {-} | -- | : | -. | none ]LineWidthMarker: [ + | o | * | . | x | square | diamond | v | ^ | > | < |

pentagram | hexagram | {none} ]MarkerSize. . .

XDataYDataZdata. . .

.

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get(h)

Color = [0 0.8 0.8]EraseMode = normalLineStyle = -LineWidth = [3]Marker = noneMarkerSize = [6]. . .

XData = [ (1 by 7) double array]YData = [ (1 by 7) double array]ZData = []. . .

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get(h , 'Color')

ans = 0 0.8000 0.8000

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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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h = plot(x , y , ' . ' );axis([-1 1 -1 1])axis squaregrid offset(h , 'EraseMode' , 'xor' , 'MarkerSize' , 18 );

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while 1x = x + s*randn(n,1);y = y + s*randn(n,1);set(h, 'Xdata' , x , 'Ydata' , y)

end

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