Numeerinen analyysi 2012, Matlab-muistiinpanot, harjoitus 1 % %-merkki kertoo Matlabille, että rivillä ei ole suoritettavia komentoja %näin voit kommentoida juttuja ilman, että Matlab tekee mitään %Tein näin: tein muistitikulleni kansion, jonka nimesin kuvaavasti NumMatlabiksi. Näin muistan, että siihen tulevat Numeerisen analyysin Matlab-jutut. %Asetin kansion työkansioksi. Työkansio lukee näkymässä ylhäällä laatikossa "Current Folder:". %Laitoin päälle päiväkirjan, joka kerää komentohistorian talteen. Näin muistan myös jatkossa, mitä olen tehnyt. Komentohistorian "Command history" löytää myös työkalupalkista kohdasta Desktop->Command history tai Matlabin työnäkymän oikeasta alakulmasta. Näin on, kun työtila=Desktop on perustilassa. Voit asettaa sen perustilaan valitsemalla työkalupalkista Desktop->Desktop layout->Default. %Siis päiväkirjalla tai "Command historyllä" saa talteen käytetyt komennot. % %Päiväkirjan käyttö: %tee työkansioosi .txt-tiedosto, johon haluat päiväkirjan. Sen jälkeen käytä Matlabiin komentoa % %diary muistiinpanoja.txt % %Nyt Matlab on valmiina kirjoittamaan päiväkirjan tiedostooni muistiinpanoja.txt %Laitan vielä päiväkirjan päälle kirjoittamalla % %diary on % %Tämän jälkeen kaikki kirjoittettu tallentuu tiedostooni. %Kun haluan lukea jo kirjoitetut asiat, katkaisen päiväkirjan kirjoittamisen komennolla % %diary off % %Nyt jo kirjoitetut asiat löytyvät muistiinpanoja.txt-tiedostosta %Tarkasteltuani muistiinpanoja.txt-tiedostoa ja halutessani palata Matlabiin, suljen tiedoston ja laitan päiväkirjan taas päälle komennolla "diary on" %Esimerkkejä Matlabin käytöstä: 1+2 ans = 3 pi ans = 3.1416 format long pi ans = 3.141592653589793 format short pi ans = 3.1416 exp(1) ans = 2.7183 A=[1 2; 3 4] A = 1 2 3 4 inv(A) ans = -2.0000 1.0000 1.5000 -0.5000 det(A) ans = -2 x=-1 x = -1 x=-1; %<- puolipiste ";" estää luvun tulostumisen x x = -1 %kirjoittamalla muuttujan nimen sen arvon saa näkyviin A A = 1 2 3 4 %jos muuttuja on iso, niin koko komentoikkuna "Command Window" täyttyy muuttujasta A=rand(2) A = 0.8147 0.1270 0.9058 0.9134 A=rand(2,3) A = 0.6324 0.2785 0.9575 0.0975 0.5469 0.9649 %jos nyt annettaisiin komento A=rand(100), niin komentoikkuna olisi täynnä satunnaislukuja %Kuvion piirtäminen x=[1 2] x = 1 2 x*x {Error using * Inner matrix dimensions must agree. } x.* x.* | {Error: Expression or statement is incomplete or incorrect. } x.*x ans = 1 4 2*3 ans = 6 %* on kertomerkki, + on plusmerkkki ja .* antaa vektorien alkioittaisen tulon [2 3].*[5 4] ans = 10 12 %Halutaan piirtää funktion x^2 kuvaaja. Tehdään näin x=-1:0.01:1 %x on vektori, jossa ensimmäinen luku on -1 ja viimeisin 1. Arvojen etäisyys toisistaan on 0.01 x = Columns 1 through 8 -1.0000 -0.9900 -0.9800 -0.9700 -0.9600 -0.9500 -0.9400 -0.9300 Columns 9 through 16 -0.9200 -0.9100 -0.9000 -0.8900 -0.8800 -0.8700 -0.8600 -0.8500 Columns 17 through 24 -0.8400 -0.8300 -0.8200 -0.8100 -0.8000 -0.7900 -0.7800 -0.7700 Columns 25 through 32 -0.7600 -0.7500 -0.7400 -0.7300 -0.7200 -0.7100 -0.7000 -0.6900 Columns 33 through 40 -0.6800 -0.6700 -0.6600 -0.6500 -0.6400 -0.6300 -0.6200 -0.6100 Columns 41 through 48 -0.6000 -0.5900 -0.5800 -0.5700 -0.5600 -0.5500 -0.5400 -0.5300 Columns 49 through 56 -0.5200 -0.5100 -0.5000 -0.4900 -0.4800 -0.4700 -0.4600 -0.4500 Columns 57 through 64 -0.4400 -0.4300 -0.4200 -0.4100 -0.4000 -0.3900 -0.3800 -0.3700 Columns 65 through 72 -0.3600 -0.3500 -0.3400 -0.3300 -0.3200 -0.3100 -0.3000 -0.2900 Columns 73 through 80 -0.2800 -0.2700 -0.2600 -0.2500 -0.2400 -0.2300 -0.2200 -0.2100 Columns 81 through 88 -0.2000 -0.1900 -0.1800 -0.1700 -0.1600 -0.1500 -0.1400 -0.1300 Columns 89 through 96 -0.1200 -0.1100 -0.1000 -0.0900 -0.0800 -0.0700 -0.0600 -0.0500 Columns 97 through 104 -0.0400 -0.0300 -0.0200 -0.0100 0 0.0100 0.0200 0.0300 Columns 105 through 112 0.0400 0.0500 0.0600 0.0700 0.0800 0.0900 0.1000 0.1100 Columns 113 through 120 0.1200 0.1300 0.1400 0.1500 0.1600 0.1700 0.1800 0.1900 Columns 121 through 128 0.2000 0.2100 0.2200 0.2300 0.2400 0.2500 0.2600 0.2700 Columns 129 through 136 0.2800 0.2900 0.3000 0.3100 0.3200 0.3300 0.3400 0.3500 Columns 137 through 144 0.3600 0.3700 0.3800 0.3900 0.4000 0.4100 0.4200 0.4300 Columns 145 through 152 0.4400 0.4500 0.4600 0.4700 0.4800 0.4900 0.5000 0.5100 Columns 153 through 160 0.5200 0.5300 0.5400 0.5500 0.5600 0.5700 0.5800 0.5900 Columns 161 through 168 0.6000 0.6100 0.6200 0.6300 0.6400 0.6500 0.6600 0.6700 Columns 169 through 176 0.6800 0.6900 0.7000 0.7100 0.7200 0.7300 0.7400 0.7500 Columns 177 through 184 0.7600 0.7700 0.7800 0.7900 0.8000 0.8100 0.8200 0.8300 Columns 185 through 192 0.8400 0.8500 0.8600 0.8700 0.8800 0.8900 0.9000 0.9100 Columns 193 through 200 0.9200 0.9300 0.9400 0.9500 0.9600 0.9700 0.9800 0.9900 Column 201 1.0000 %; unohtui x=-1:0.01:1; y=x.^2; plot(x,y) %Nyt kuvaaja aukesi uuteen ikkunaan %kuvaajaa voi muokata hiirellä ja erilaisilla komennoilla print -djpeg 'kuva.jpg' %tallensin juuri kuvan nimellä kuva.jpg %Laskuharjoitus 1 %teht.2 etsitään sopiva alkuarvo graafisesti % %ollaan ratkaisemassa yhtälöä f(x)=x-e^(-x)=0 <=> x=e^(-x), joten piirretään kuvaajat y=x ja y=e^(-x) 0-exp(-0) ans = -1 1-exp(-1) ans = 0.6321 %koska f on jatkuva, niin f:llä on nollakohta välillä ]0,1[ x=0:0.1:1; y=x; z=exp(-x); plot(x,y) hold on %laitetaan kuva pitoon, että kuvaaja y=x ei häviä plot(x,z) %voidaan lukea, että kuvaajat leikkaavat likimain x-akselin kohdassa x=0.6 %luetaan arvo vielä hiirellä painamalla, käyttäen komentoa [a,b] = ginput %annetaan komento "[a,b] = ginput" ja sitten klikataan hiirellä leikkauskohtaa kuvasta. hiiren osoitin muuttuu tähtäimeksi [a,b] = ginput a = 0.5657 b = 0.5658 %kun hiirellä on painettu, pitää vielä painaa Enter-näppäintä [a,b] = ginput a = 0.7961 b = 0.0804 %nyt luku a=0.5657 on graafisesti saatu likimääräinen ratkaisu yhtälölle f(x)=x-e^(-x)=0 <=> x=e^(-x) %Tehtäväpaperin iteraatioista suppenee x_(k+1)=e^(-x_k). Käytetään tätä iteraatiota seuraavaksi. % %Poistetaan tähänastiset luvut sotkemasta komennolla clear clear %muistetaan kuitenkin tarvittava alkuarvo a=0.5657 a=0.5657 a = 0.5657 %asetetaan alkuarvoksi tämä luku x(1)=0.5657 x = 0.5657 %iteroidaan 10 kierrosta for-silmukalla for i=1:10 x(i+1)=exp(-x(i)); % pannaan ;, jotta arvot eivät tulostu sotkemaan näkymää end %nyt x(11) on jonkinlainen likiarvo ratkaisulle x(11) ans = 0.5671 x x = Columns 1 through 8 0.5657 0.5680 0.5667 0.5674 0.5670 0.5672 0.5671 0.5672 Columns 9 through 11 0.5671 0.5672 0.5671 x(11)-exp(-x(11)) ans = -7.7909e-06 %siis likiarvon virhe on enää 0.000008 %piirretään kuvaaja iteroinnista y=1:11; z=1:2 z = 1 2 k=[x(11) x(11)]; close %suljin kuvaikkunan z=[1 11]; plot(z,k, 'r') hold on plot(y,x) %nyt kuvaajasta nähdään, että iterointi suppeni oskilloimalla oikean arvon kummallakin puolella print -djpeg 'h1t2.jpg' %tallennettiin kuva %kokeillaan malliksi myös toista iterointia, joka ei suppene clear x x(1)=0.5657 x = 0.5657 %poistettiin vanha tulos x for i=1:10 x(i+1)=exp(-x(i)); end %käytetyt komennot saa näkyviin painamalla nuolinäppäimiä x(11) ans = 0.5671 plot(z,k, 'r') close plot(z,k, 'r') plot(y,x) close clear x x(1)=0.5657 x = 0.5657 for i=1:10 x(i+1)=log(-x(i)); end x(11) ans = 0.7246 - 1.9281i %saatiin jotain kompleksista, ratkaisussa ei ole tolkkua x x = Columns 1 through 4 0.5657 -0.5697 + 3.1416i 1.1609 - 1.3914i 0.5945 + 2.2661i Columns 5 through 8 0.8514 - 1.8274i 0.7011 + 2.0068i 0.7541 - 1.9069i 0.7181 + 1.9474i Columns 9 through 11 0.7302 - 1.9241i 0.7217 + 1.9335i 0.7246 - 1.9281i %kaava meni väärin clear x x(1)=0.5657 x = 0.5657 for i=1:10 x(i+1)=-log(x(i)); end x(11) ans = 0.1904 x x = Columns 1 through 8 0.5657 0.5697 0.5627 0.5751 0.5532 0.5919 0.5243 0.6456 Columns 9 through 11 0.4375 0.8266 0.1904 plot(z,k, 'r') plot(y,x) hold on plot(z,k, 'r') %nyt kuvasta nähdään, että iteraatit loittonevat oikeasta ratkaisusta, jonka lähellä alkuarvaus x(1)=0.5657 jo oli %teht.1 clear a=0.5; x(1)=2/3; x(1)^2 ans = 0.4444 %hyvä alkuarvaus for i=1:10 x(i+1)=a+x(i)-x(i)^2; end x(11) ans = 0.7071 x(11)^2 ans = 0.5000 format long x(11)^2 ans = 0.499992136611991 sqrt(2) ans = 1.414213562373095 sqrt(0.5) ans = 0.707106781186548 x(11) ans = 0.707101220909702 sqrt(0.5)-x(11) ans = 5.560276845839596e-06 %saatiin hyvä likiarvo clear a=2; x(1)=3/2 x = 1.500000000000000 format short for i=1:10 x(i+1)=1+x(i)-x(i)^2/2; end x(11) ans = 1.4142 format long x(11) ans = 1.414227144925212 sqrt(2) ans = 1.414213562373095 sqrt(2)-x(11) ans = -1.358255211658666e-05 %saatiin hyvä likiarvo z=[1 11]; y=1:11; k=[x(11) x(11)]; plot(z,k, 'r') hold on plot(y,x) clear z=[1 11]; y=1:11; k=[x(11) x(11)]; {Undefined function 'x' for input arguments of type 'double'. } close %onnistuin tuhoamaan lasketut arvot laittamalla sekaan vahingossa clear-komennon %teht.4 %esim. a=3 a=3 a = 3 x(1)=3/2; clear a=3 a = 3 x=-10:0.1:10; for i=1:10 x=x+(a-x.^4).*x.^(-3) y=-10:0.1:10; plot(y,x) F(i) = getframe; end x = 1.0e+03 * Columns 1 through 4 -0.000003000000000 -0.000003091830456 -0.000003187447407 -0.000003287048045 Columns 5 through 8 -0.000003390842014 -0.000003499052340 -0.000003611916435 -0.000003729687191 Columns 9 through 12 -0.000003852634174 -0.000003981044918 -0.000004115226337 -0.000004255506270 Columns 13 through 16 -0.000004402235162 -0.000004555787901 -0.000004716565837 -0.000004884998982 Columns 17 through 20 -0.000005061548429 -0.000005246709002 -0.000005441012173 -0.000005645029269 Columns 21 through 24 -0.000005859375000 -0.000006084711351 -0.000006321751884 -0.000006571266480 Columns 25 through 28 -0.000006834086602 -0.000007111111111 -0.000007403312736 -0.000007711745245 Columns 29 through 32 -0.000008037551440 -0.000008381972055 -0.000008746355685 -0.000009132169895 Columns 33 through 36 -0.000009541013637 -0.000009974631188 -0.000010434927790 -0.000010923987255 Columns 37 through 40 -0.000011444091797 -0.000011997744424 -0.000012587694270 -0.000013216965297 Columns 41 through 44 -0.000013888888889 -0.000014607140944 -0.000015375784165 -0.000016199316389 Columns 45 through 48 -0.000017082725948 -0.000018031555222 -0.000019051973784 -0.000020150862793 Columns 49 through 52 -0.000021335912608 -0.000022615736029 -0.000024000000000 -0.000025499579257 Columns 53 through 56 -0.000027126736111 -0.000028895331478 -0.000030821073395 -0.000032921810700 Columns 57 through 60 -0.000035217881292 -0.000037732526696 -0.000040492387431 -0.000043528097387 Columns 61 through 64 -0.000046875000000 -0.000050574015071 -0.000054672692812 -0.000059226501885 Columns 65 through 68 -0.000064300411523 -0.000069970845481 -0.000076328109098 -0.000083479422322 Columns 69 through 72 -0.000091552734375 -0.000100701554161 -0.000111111111111 -0.000123006273320 Columns 73 through 76 -0.000136661807580 -0.000152415790276 -0.000170687300865 -0.000192000000000 Columns 77 through 80 -0.000217013888889 -0.000246568587162 -0.000281743050338 -0.000323939099449 Columns 81 through 84 -0.000375000000000 -0.000437381542499 -0.000514403292181 -0.000610624872786 Columns 85 through 88 -0.000732421875000 -0.000888888888889 -0.001093294460641 -0.001365498406919 Columns 89 through 92 -0.001736111111111 -0.002253944402705 -0.003000000000000 -0.004115226337449 Columns 93 through 96 -0.005859375000000 -0.008746355685131 -0.013888888888889 -0.024000000000000 Columns 97 through 100 -0.046875000000001 -0.111111111111112 -0.375000000000004 -3.000000000000032 Columns 101 through 104 Inf 3.000000000000032 0.375000000000004 0.111111111111112 Columns 105 through 108 0.046875000000001 0.024000000000000 0.013888888888889 0.008746355685131 Columns 109 through 112 0.005859375000000 0.004115226337449 0.003000000000000 0.002253944402705 Columns 113 through 116 0.001736111111111 0.001365498406919 0.001093294460641 0.000888888888889 Columns 117 through 120 0.000732421875000 0.000610624872786 0.000514403292181 0.000437381542499 Columns 121 through 124 0.000375000000000 0.000323939099449 0.000281743050338 0.000246568587162 Columns 125 through 128 0.000217013888889 0.000192000000000 0.000170687300865 0.000152415790276 Columns 129 through 132 0.000136661807580 0.000123006273320 0.000111111111111 0.000100701554161 Columns 133 through 136 0.000091552734375 0.000083479422322 0.000076328109098 0.000069970845481 Columns 137 through 140 0.000064300411523 0.000059226501885 0.000054672692812 0.000050574015071 Columns 141 through 144 0.000046875000000 0.000043528097387 0.000040492387431 0.000037732526696 Columns 145 through 148 0.000035217881292 0.000032921810700 0.000030821073395 0.000028895331478 Columns 149 through 152 0.000027126736111 0.000025499579257 0.000024000000000 0.000022615736029 Columns 153 through 156 0.000021335912608 0.000020150862793 0.000019051973784 0.000018031555222 Columns 157 through 160 0.000017082725948 0.000016199316389 0.000015375784165 0.000014607140944 Columns 161 through 164 0.000013888888889 0.000013216965297 0.000012587694270 0.000011997744424 Columns 165 through 168 0.000011444091797 0.000010923987255 0.000010434927790 0.000009974631188 Columns 169 through 172 0.000009541013637 0.000009132169895 0.000008746355685 0.000008381972055 Columns 173 through 176 0.000008037551440 0.000007711745245 0.000007403312736 0.000007111111111 Columns 177 through 180 0.000006834086602 0.000006571266480 0.000006321751884 0.000006084711351 Columns 181 through 184 0.000005859375000 0.000005645029269 0.000005441012173 0.000005246709002 Columns 185 through 188 0.000005061548429 0.000004884998982 0.000004716565837 0.000004555787901 Columns 189 through 192 0.000004402235162 0.000004255506270 0.000004115226337 0.000003981044918 Columns 193 through 196 0.000003852634174 0.000003729687191 0.000003611916435 0.000003499052340 Columns 197 through 200 0.000003390842014 0.000003287048045 0.000003187447407 0.000003091830456 Column 201 0.000003000000000 x = 1.0e+08 * Columns 1 through 4 -1.111111111110985 -1.015019163871731 -0.926386402366581 -0.844701176282166 Columns 5 through 8 -0.769482217582487 -0.700277121916028 -0.636660891364947 -0.578234536654428 Columns 9 through 12 -0.524623736985291 -0.475477555699337 -0.430467210000459 -0.389284893008608 Columns 13 through 16 -0.351642646476724 -0.317271282492296 -0.285919352568515 -0.257352162536996 Columns 17 through 20 -0.231350831700878 -0.207711394741809 -0.186243944899607 -0.166771816996648 Columns 21 through 24 -0.149130808888889 -0.133168439980719 -0.118743245459155 -0.105724104943504 Columns 25 through 28 -0.093989604273991 -0.083427429199205 -0.073933789750090 -0.065412874120305 Columns 29 through 32 -0.057776330904669 -0.050942778576052 -0.044837341111107 -0.039391208706210 Columns 33 through 36 -0.034541222551585 -0.030229482662550 -0.026402977793111 -0.023013236486548 Columns 37 through 40 -0.020015998343869 -0.017370904618725 -0.015041207273624 -0.012993495658704 Columns 41 through 44 -0.011197439999999 -0.009625550909618 -0.008252954155163 -0.007057179950426 Columns 45 through 48 -0.006017966053494 -0.005117073982205 -0.004338117680348 -0.003666403990891 Columns 49 through 52 -0.003088784315151 -0.002593516858989 -0.002170138888889 -0.001809348442123 Columns 53 through 56 -0.001502894956216 -0.001243478303448 -0.001024655736299 -0.000840756269531 Columns 57 through 60 -0.000686802043899 -0.000558436235485 -0.000451857093166 -0.000363757704882 Columns 61 through 64 -0.000291271111111 -0.000231920401288 -0.000183573445848 -0.000144401933106 Columns 65 through 68 -0.000112844396298 -0.000087572931858 -0.000067463325296 -0.000051568316002 Columns 69 through 72 -0.000039093746765 -0.000029377357956 -0.000021870000000 -0.000016119051084 Columns 73 through 76 -0.000011753839948 -0.000008472886094 -0.000006032781866 -0.000004238552517 Columns 77 through 80 -0.000002935341711 -0.000002001280735 -0.000001341410242 -0.000000882533385 Columns 81 through 84 -0.000000568888889 -0.000000358541886 -0.000000220399212 -0.000000131764307 Columns 85 through 88 -0.000000076354974 -0.000000042714844 -0.000000022956719 -0.000000011782777 Columns 89 through 92 -0.000000005733089 -0.000000002619942 -0.000000001111111 -0.000000000430467 Columns 93 through 96 -0.000000000149131 -0.000000000044837 -0.000000000011197 -0.000000000002170 Columns 97 through 100 -0.000000000000291 -0.000000000000022 -0.000000000000001 -0.000000000000000 Columns 101 through 104 NaN 0.000000000000000 0.000000000000001 0.000000000000022 Columns 105 through 108 0.000000000000291 0.000000000002170 0.000000000011197 0.000000000044837 Columns 109 through 112 0.000000000149131 0.000000000430467 0.000000001111111 0.000000002619942 Columns 113 through 116 0.000000005733089 0.000000011782777 0.000000022956719 0.000000042714844 Columns 117 through 120 0.000000076354974 0.000000131764307 0.000000220399212 0.000000358541886 Columns 121 through 124 0.000000568888889 0.000000882533385 0.000001341410242 0.000002001280735 Columns 125 through 128 0.000002935341711 0.000004238552517 0.000006032781866 0.000008472886094 Columns 129 through 132 0.000011753839948 0.000016119051084 0.000021870000000 0.000029377357956 Columns 133 through 136 0.000039093746765 0.000051568316002 0.000067463325296 0.000087572931858 Columns 137 through 140 0.000112844396298 0.000144401933106 0.000183573445848 0.000231920401288 Columns 141 through 144 0.000291271111111 0.000363757704882 0.000451857093166 0.000558436235485 Columns 145 through 148 0.000686802043899 0.000840756269531 0.001024655736299 0.001243478303448 Columns 149 through 152 0.001502894956216 0.001809348442123 0.002170138888889 0.002593516858989 Columns 153 through 156 0.003088784315151 0.003666403990891 0.004338117680348 0.005117073982205 Columns 157 through 160 0.006017966053494 0.007057179950426 0.008252954155163 0.009625550909618 Columns 161 through 164 0.011197439999999 0.012993495658704 0.015041207273624 0.017370904618725 Columns 165 through 168 0.020015998343869 0.023013236486548 0.026402977793111 0.030229482662550 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NaN NaN NaN NaN Columns 14 through 26 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 27 through 39 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 40 through 52 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 53 through 65 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 66 through 78 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 79 through 91 NaN NaN 0 NaN NaN NaN NaN NaN NaN Inf NaN NaN NaN Columns 92 through 104 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 105 through 117 NaN NaN NaN NaN NaN NaN NaN NaN NaN Inf NaN NaN NaN Columns 118 through 130 NaN NaN NaN 0 NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 131 through 143 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 144 through 156 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 157 through 169 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 170 through 182 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 183 through 195 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 196 through 201 NaN NaN NaN NaN NaN NaN x = Columns 1 through 13 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 14 through 26 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 27 through 39 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 40 through 52 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 53 through 65 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 66 through 78 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 79 through 91 NaN NaN Inf NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 92 through 104 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 105 through 117 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 118 through 130 NaN NaN NaN Inf NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 131 through 143 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 144 through 156 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 157 through 169 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 170 through 182 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 183 through 195 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN Columns 196 through 201 NaN NaN NaN NaN NaN NaN movie F {Error using hgMovie Invalid movie: expected a structure Error in movie (line 41) builtin('hgMovie',varargin{:}); } movie(F,1,1) clear x=-10:0.1:10; y=-10:0.1:10; for i=1:10 x=x+(a-x.^4).*(4*x).^(-3) plot(y,x) F(i) = getframe; end {Undefined function or variable 'a'. } a=3 a = 3 x=-10:0.1:10; y=-10:0.1:10; for i=1:10 x=x+(a-x.^4).*(4*x).^(-3) plot(y,x) F(i) = getframe; end x = Columns 1 through 4 -9.843796875000001 -9.745360809850881 -9.646924803865737 -9.548488860125696 Columns 5 through 8 -9.450052981906467 -9.351617172692812 -9.253181436194293 -9.154745776362363 Columns 9 through 12 -9.056310197408974 -8.957874703826846 -8.859439300411523 -8.761003992285477 Columns 13 through 16 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-46.239477991318907 Columns 101 through 104 NaN 46.239477991318907 5.961832116800924 2.005274264783915 Columns 105 through 108 1.141394583457460 0.925516732859909 0.883998959917200 0.896082301183569 Columns 109 through 112 0.934325067035889 0.990022081963001 1.057878182979068 1.134102500920349 Columns 113 through 116 1.216062341775098 1.301980524146041 1.390666964267305 1.481320627084349 Columns 117 through 120 1.573395872286023 1.666515416495015 1.760414178626452 1.854902914727193 Columns 121 through 124 1.949844426686129 2.045137789129923 2.140707739031366 2.236497431617460 Columns 125 through 128 2.332463421934008 2.428572139049149 2.524797375530649 2.621118477028373 Columns 129 through 132 2.717519021018072 2.813985841625990 2.910508302228936 3.007077747451362 Columns 133 through 136 3.103687086436485 3.200330473144189 3.297003059044340 3.393700800311692 Columns 137 through 140 3.490420306399154 3.587158720277906 3.683913623095982 3.780682957801450 Columns 141 through 144 3.877464967594829 3.974258146052143 4.071061196489340 4.167872998687232 Columns 145 through 148 4.264692581511578 4.361519100279802 4.458351817968874 4.555190089546755 Columns 149 through 152 4.652033348855535 4.748881097588396 4.845732895991930 4.942588354995972 Columns 153 through 156 5.039447129529161 5.136308912823020 5.233173431543187 5.330040441615087 Columns 157 through 160 5.426909724634640 5.523781084773348 5.620654346102500 5.717529350273709 Columns 161 through 164 5.814405954503301 5.911284029816479 6.008163459514243 6.105044137831743 Columns 165 through 168 6.201925968761606 6.298808865019767 6.395692747134682 6.492577542643598 Columns 169 through 172 6.589463185381947 6.686349614853884 6.783236775673704 6.880124617069297 Columns 173 through 176 6.977013092439952 7.073902158961974 7.170791777236310 7.267681910973275 Columns 177 through 180 7.364572526709998 7.461463593556839 7.558355082969469 7.655246968543739 Columns 181 through 184 7.752139225830786 7.849031832170190 7.945924766539184 8.042818009416234 Columns 185 through 188 8.139711542657434 8.236605349384430 8.333499413882610 8.430393721508560 Columns 189 through 192 8.527288258605848 8.624183012428265 8.721077971069832 8.817973123400893 Columns 193 through 196 8.914868459009686 9.011763968148904 9.108659641686735 9.205555471062009 Columns 197 through 200 9.302451448243014 9.399347565689689 9.496243816318872 9.593140193472316 Column 201 9.690036690887254 x = Columns 1 through 4 -9.538681386306443 -9.443300473595045 -9.347919744283757 -9.252539207923066 Columns 5 through 8 -9.157158874666513 -9.061778755315592 -8.966398861368505 -8.871019205073157 Columns 9 through 12 -8.775639799484798 -8.680260658528820 -8.584881797069135 -8.489503230982846 Columns 13 through 16 -8.394124977241702 -8.298747054001192 -8.203369480697978 -8.107992278156612 Columns 17 through 20 -8.012615468706557 -7.917239076310579 -7.821863126705848 -7.726487647559130 Columns 21 through 24 -7.631112668637665 -7.535738221997590 -7.440364342191908 -7.344991066500343 Columns 25 through 28 -7.249618435183686 -7.154246491765625 -7.058875283345433 -6.963504860945369 Columns 29 through 32 -6.868135279897199 -6.772766600272851 -6.677398887364931 -6.582032212223755 Columns 33 through 36 -6.486666652258402 -6.391302291910577 -6.295939223411291 -6.200577547632027 Columns 37 through 40 -6.105217375043858 -6.009858826800153 -5.914502035961095 -5.819147148881209 Columns 41 through 44 -5.723794326784754 -5.628443747558054 -5.533095607792956 -5.437750125121647 Columns 45 through 48 -5.342407540890456 -5.247068123228931 -5.151732170581151 -5.056400015779041 Columns 49 through 52 -4.961072030753038 -4.865748631994419 -4.770430286906882 -4.675117521213442 Columns 53 through 56 -4.579810927619884 -4.484511175979520 -4.389219025258036 -4.293935337664688 Columns 57 through 60 -4.198661095400699 -4.103397420582217 -4.008145599029960 -3.912907108789237 Columns 61 through 64 -3.817683654463156 -3.722477208723813 -3.627290062730587 -3.532124887658760 Columns 65 through 68 -3.436984810161957 -3.341873505409025 -3.246795312419460 -3.151755377868422 Columns 69 through 72 -3.056759836478681 -2.961816038755132 -2.866932840421922 -2.772120972887626 Columns 73 through 76 -2.677393520962459 -2.582766543720930 -2.488259888079561 -2.393898264181932 Columns 77 through 80 -2.299712679811576 -2.205742371954441 -2.112037433633695 -2.018662422870830 Columns 81 through 84 -1.925701372715102 -1.833264818723791 -1.741499755339383 -1.650603870147046 Columns 85 through 88 -1.560846039890695 -1.472595948882193 -1.386366768747764 -1.302875772918886 Columns 89 through 92 -1.223127329909290 -1.148517597159034 -1.080943284937875 -1.022859605301975 Columns 93 through 96 -0.977197042630052 -0.947228489371803 -0.938042126730445 -0.970182889463867 Columns 97 through 100 -1.155083751609332 -1.979755116976463 -5.868899698599707 -45.516986621840090 Columns 101 through 104 NaN 45.516986621840090 5.868899698599707 1.979755116976463 Columns 105 through 108 1.155083751609332 0.970182889463867 0.938042126730445 0.947228489371803 Columns 109 through 112 0.977197042630052 1.022859605301975 1.080943284937875 1.148517597159034 Columns 113 through 116 1.223127329909290 1.302875772918886 1.386366768747764 1.472595948882193 Columns 117 through 120 1.560846039890695 1.650603870147046 1.741499755339383 1.833264818723791 Columns 121 through 124 1.925701372715102 2.018662422870830 2.112037433633695 2.205742371954441 Columns 125 through 128 2.299712679811576 2.393898264181932 2.488259888079561 2.582766543720930 Columns 129 through 132 2.677393520962459 2.772120972887626 2.866932840421922 2.961816038755132 Columns 133 through 136 3.056759836478681 3.151755377868422 3.246795312419460 3.341873505409025 Columns 137 through 140 3.436984810161957 3.532124887658760 3.627290062730587 3.722477208723813 Columns 141 through 144 3.817683654463156 3.912907108789237 4.008145599029960 4.103397420582217 Columns 145 through 148 4.198661095400699 4.293935337664688 4.389219025258036 4.484511175979520 Columns 149 through 152 4.579810927619884 4.675117521213442 4.770430286906882 4.865748631994419 Columns 153 through 156 4.961072030753038 5.056400015779041 5.151732170581151 5.247068123228931 Columns 157 through 160 5.342407540890456 5.437750125121647 5.533095607792956 5.628443747558054 Columns 161 through 164 5.723794326784754 5.819147148881209 5.914502035961095 6.009858826800153 Columns 165 through 168 6.105217375043858 6.200577547632027 6.295939223411291 6.391302291910577 Columns 169 through 172 6.486666652258402 6.582032212223755 6.677398887364931 6.772766600272851 Columns 173 through 176 6.868135279897199 6.963504860945369 7.058875283345433 7.154246491765625 Columns 177 through 180 7.249618435183686 7.344991066500343 7.440364342191908 7.535738221997590 Columns 181 through 184 7.631112668637665 7.726487647559130 7.821863126705848 7.917239076310579 Columns 185 through 188 8.012615468706557 8.107992278156612 8.203369480697978 8.298747054001192 Columns 189 through 192 8.394124977241702 8.489503230982846 8.584881797069135 8.680260658528820 Columns 193 through 196 8.775639799484798 8.871019205073157 8.966398861368505 9.061778755315592 Columns 197 through 200 9.157158874666513 9.252539207923066 9.347919744283757 9.443300473595045 Column 201 9.538681386306443 x = Columns 1 through 4 -9.389693499903538 -9.295804567111119 -9.201915883011004 -9.108027460553302 Columns 5 through 8 -9.014139313505801 -8.920251456514839 -8.826363905171403 -8.732476676082980 Columns 9 through 12 -8.638589786951707 -8.544703256659501 -8.450817105360773 -8.356931354583638 Columns 13 through 16 -8.263046027340369 -8.169161148248159 -8.075276743661224 -7.981392841815453 Columns 17 through 20 -7.887509472987060 -7.793626669666629 -7.699744466750379 -7.605862901750538 Columns 21 through 24 -7.511982015026983 -7.418101850042630 -7.324222453645341 -7.230343876379475 Columns 25 through 28 -7.136466172830629 -7.042589402007626 -6.948713627766307 -6.854838919280367 Columns 29 through 32 -6.760965351565186 -6.667093006061452 -6.573221971286346 -6.479352343561269 Columns 33 through 36 -6.385484227826307 -6.291617738553306 -6.197753000771119 -6.103890151218820 Columns 37 through 40 -6.010029339645099 -5.916170730275011 -5.822314503468728 -5.728460857600981 Columns 41 through 44 -5.634610011194814 -5.540762205348958 -5.446917706505068 -5.353076809609232 Columns 45 through 48 -5.259239841732089 -5.165407166223665 -5.071579187493381 -4.977756356522964 Columns 49 through 52 -4.883939177241037 -4.790128213913665 -4.696324099736547 -4.602527546852837 Columns 53 through 56 -4.508739358067926 -4.414960440591022 -4.321191822205981 -4.227434670364437 Columns 57 through 60 -4.133690314807743 -4.039960274467028 -3.946246289571055 -3.852550360121018 Columns 61 through 64 -3.758874792183999 -3.665222253832826 -3.571595843045039 -3.477999170503495 Columns 65 through 68 -3.384436461063450 -3.290912678731421 -3.197433681429786 -3.104006413722679 Columns 69 through 72 -3.010639148226944 -2.917341789870988 -2.824126261838766 -2.731006998437011 Columns 73 through 76 -2.638001578953930 -2.545131548850638 -2.452423491811151 -2.359910440410312 Columns 77 through 80 -2.267633747558965 -2.175645589994321 -2.084012345481090 -1.992819186471459 Columns 81 through 84 -1.902176377765247 -1.812227971218504 -1.723163876136436 -1.635236663862958 Columns 85 through 88 -1.548784925089953 -1.464265434589496 -1.382296449554559 -1.303713282090988 Columns 89 through 92 -1.229632847504400 -1.161512580380569 -1.101167101176964 -1.050679348973723 Columns 93 through 96 -1.012162001967728 -0.987582045619931 -0.980175530259778 -1.006354867250263 Columns 97 through 100 -1.167451480935779 -1.954862415768160 -5.777430025041539 -44.805784202947521 Columns 101 through 104 NaN 44.805784202947521 5.777430025041539 1.954862415768160 Columns 105 through 108 1.167451480935779 1.006354867250263 0.980175530259778 0.987582045619931 Columns 109 through 112 1.012162001967728 1.050679348973723 1.101167101176964 1.161512580380569 Columns 113 through 116 1.229632847504400 1.303713282090988 1.382296449554559 1.464265434589496 Columns 117 through 120 1.548784925089953 1.635236663862958 1.723163876136436 1.812227971218504 Columns 121 through 124 1.902176377765247 1.992819186471459 2.084012345481090 2.175645589994321 Columns 125 through 128 2.267633747558965 2.359910440410312 2.452423491811151 2.545131548850638 Columns 129 through 132 2.638001578953930 2.731006998437011 2.824126261838766 2.917341789870988 Columns 133 through 136 3.010639148226944 3.104006413722679 3.197433681429786 3.290912678731421 Columns 137 through 140 3.384436461063450 3.477999170503495 3.571595843045039 3.665222253832826 Columns 141 through 144 3.758874792183999 3.852550360121018 3.946246289571055 4.039960274467028 Columns 145 through 148 4.133690314807743 4.227434670364437 4.321191822205981 4.414960440591022 Columns 149 through 152 4.508739358067926 4.602527546852837 4.696324099736547 4.790128213913665 Columns 153 through 156 4.883939177241037 4.977756356522964 5.071579187493381 5.165407166223665 Columns 157 through 160 5.259239841732089 5.353076809609232 5.446917706505068 5.540762205348958 Columns 161 through 164 5.634610011194814 5.728460857600981 5.822314503468728 5.916170730275011 Columns 165 through 168 6.010029339645099 6.103890151218820 6.197753000771119 6.291617738553306 Columns 169 through 172 6.385484227826307 6.479352343561269 6.573221971286346 6.667093006061452 Columns 173 through 176 6.760965351565186 6.854838919280367 6.948713627766307 7.042589402007626 Columns 177 through 180 7.136466172830629 7.230343876379475 7.324222453645341 7.418101850042630 Columns 181 through 184 7.511982015026983 7.605862901750538 7.699744466750379 7.793626669666629 Columns 185 through 188 7.887509472987060 7.981392841815453 8.075276743661224 8.169161148248159 Columns 189 through 192 8.263046027340369 8.356931354583638 8.450817105360773 8.544703256659501 Columns 193 through 196 8.638589786951707 8.732476676082980 8.826363905171403 8.920251456514839 Columns 197 through 200 9.014139313505801 9.108027460553302 9.201915883011004 9.295804567111119 Column 201 9.389693499903538 x = Columns 1 through 4 -9.243036161205716 -9.150615976052798 -9.058196107155593 -8.965776570981831 Columns 5 through 8 -8.873357385038968 -8.780938567951580 -8.688520139545405 -8.596102120938696 Columns 9 through 12 -8.503684534641582 -8.411267404664304 -8.318850756635090 -8.226434617928829 Columns 13 through 16 -8.134019017807500 -8.041603987573701 -7.949189560738588 -7.856775773205785 Columns 17 through 20 -7.764362663473060 -7.671950272853588 -7.579538645719099 -7.487127829767298 Columns 21 through 24 -7.394717876316332 -7.302308840629433 -7.209900782273257 -7.117493765513898 Columns 25 through 28 -7.025087859755078 -6.932683140023668 -6.840279687508335 -6.747877590157944 Columns 29 through 32 -6.655476943347313 -6.563077850618923 -6.470680424510459 -6.378284787479585 Columns 33 through 36 -6.285891072938910 -6.193499426416174 -6.101110006856940 -6.008722988089779 Columns 37 through 40 -5.916338560477076 -5.823956932778366 -5.731578334257401 -5.639203017069419 Columns 41 through 44 -5.546831258971197 -5.454463366403769 -5.362099678006440 -5.269740568631063 Columns 45 through 48 -5.177386453938109 -5.085037795670988 -4.992695107723180 -4.900358963134634 Columns 49 through 52 -4.808030002180412 -4.715708941746890 -4.623396586230357 -4.531093840241306 Columns 53 through 56 -4.438801723457317 -4.346521388041267 -4.254254139132963 -4.162001459036388 Columns 57 through 60 -4.069765035867295 -3.977546797605299 -3.885348952720858 -3.793174038834965 Columns 61 through 64 -3.701024981235471 -3.608905163543500 -3.516818513428108 -3.424769607050779 Columns 65 through 68 -3.332763796942024 -3.240807369349649 -3.148907738861158 -3.057073690440798 Columns 69 through 72 -2.965315682141966 -2.873646225946451 -2.782080369846239 -2.690636311988569 Columns 73 through 76 -2.599336188250985 -2.508207089133859 -2.417282381960148 -2.326603442329870 Columns 77 through 80 -2.236221937788310 -2.146202861170800 -2.056628587086737 -1.967604330228326 Columns 81 through 84 -1.879265527603869 -1.791787856309406 -1.705400834039628 -1.620406205709778 Columns 85 through 88 -1.537202504588592 -1.456317044921905 -1.378445588710533 -1.304496884339181 Columns 89 through 92 -1.235632276284229 -1.173277604489635 -1.119067385337695 -1.074676377564897 Columns 93 through 96 -1.041552461930256 -1.020816635947525 -1.014637401433261 -1.036623158175370 Columns 97 through 100 -1.178669510029758 -1.930592386524777 -5.687400754167437 -44.105694345898016 Columns 101 through 104 NaN 44.105694345898016 5.687400754167437 1.930592386524777 Columns 105 through 108 1.178669510029758 1.036623158175370 1.014637401433261 1.020816635947525 Columns 109 through 112 1.041552461930256 1.074676377564897 1.119067385337695 1.173277604489635 Columns 113 through 116 1.235632276284229 1.304496884339181 1.378445588710533 1.456317044921905 Columns 117 through 120 1.537202504588592 1.620406205709778 1.705400834039628 1.791787856309406 Columns 121 through 124 1.879265527603869 1.967604330228326 2.056628587086737 2.146202861170800 Columns 125 through 128 2.236221937788310 2.326603442329870 2.417282381960148 2.508207089133859 Columns 129 through 132 2.599336188250985 2.690636311988569 2.782080369846239 2.873646225946451 Columns 133 through 136 2.965315682141966 3.057073690440798 3.148907738861158 3.240807369349649 Columns 137 through 140 3.332763796942024 3.424769607050779 3.516818513428108 3.608905163543500 Columns 141 through 144 3.701024981235471 3.793174038834965 3.885348952720858 3.977546797605299 Columns 145 through 148 4.069765035867295 4.162001459036388 4.254254139132963 4.346521388041267 Columns 149 through 152 4.438801723457317 4.531093840241306 4.623396586230357 4.715708941746890 Columns 153 through 156 4.808030002180412 4.900358963134634 4.992695107723180 5.085037795670988 Columns 157 through 160 5.177386453938109 5.269740568631063 5.362099678006440 5.454463366403769 Columns 161 through 164 5.546831258971197 5.639203017069419 5.731578334257401 5.823956932778366 Columns 165 through 168 5.916338560477076 6.008722988089779 6.101110006856940 6.193499426416174 Columns 169 through 172 6.285891072938910 6.378284787479585 6.470680424510459 6.563077850618923 Columns 173 through 176 6.655476943347313 6.747877590157944 6.840279687508335 6.932683140023668 Columns 177 through 180 7.025087859755078 7.117493765513898 7.209900782273257 7.302308840629433 Columns 181 through 184 7.394717876316332 7.487127829767298 7.579538645719099 7.671950272853588 Columns 185 through 188 7.764362663473060 7.856775773205785 7.949189560738588 8.041603987573701 Columns 189 through 192 8.134019017807500 8.226434617928829 8.318850756635090 8.411267404664304 Columns 193 through 196 8.503684534641582 8.596102120938696 8.688520139545405 8.780938567951580 Columns 197 through 200 8.873357385038968 8.965776570981831 9.058196107155593 9.150615976052798 Column 201 9.243036161205716 x = Columns 1 through 4 -9.098673081655985 -9.007698778724965 -8.916724862007332 -8.825751351612800 Columns 5 through 8 -8.734778268920685 -8.643805636674387 -8.552833479084013 -8.461861821937912 Columns 9 through 12 -8.370890692723991 -8.279920120761858 -8.188950137346746 -8.097980775906601 Columns 13 through 16 -8.007012072173536 -7.916044064371271 -7.825076793420149 -7.734110303161674 Columns 17 through 20 -7.643144640604705 -7.552179856195578 -7.461216004114930 -7.370253142604147 Columns 21 through 24 -7.279291334324826 -7.188330646755059 -7.097371152626841 -7.006412930409455 Columns 25 through 28 -6.915456064844321 -6.824500647537603 -6.733546777617632 -6.642594562465250 Columns 29 through 32 -6.551644118526311 -6.460695572216850 -6.369749060932981 -6.278804734179367 Columns 33 through 36 -6.187862754832119 -6.096923300554427 -6.005986565385959 -5.915052761530443 Columns 37 through 40 -5.824122121369578 -5.733194899736059 -5.642271376483750 -5.551351859399409 Columns 41 through 44 -5.460436687507833 -5.369526234831148 -5.278620914673636 -5.187721184516017 Columns 45 through 48 -5.096827551618420 -5.005940579449351 -4.915060895080018 -4.824189197709875 Columns 49 through 52 -4.733326268521501 -4.642472982102081 -4.551630319716690 -4.460799384777270 Columns 53 through 56 -4.369981420923360 -4.279177833219895 -4.188390213087866 -4.097620367721385 Columns 57 through 60 -4.006870354916656 -3.916142524454511 -3.825439567450541 -3.734764575432175 Columns 61 through 64 -3.644121111341469 -3.553513295224724 -3.462945908092992 -3.372424518371972 Columns 65 through 68 -3.281955636574102 -3.191546905412033 -3.101207334656759 -3.010947592797089 Columns 69 through 72 -2.920780371215010 -2.830720841478539 -2.740787232918167 -2.651001566517279 Columns 73 through 76 -2.561390593173730 -2.471987000775267 -2.382830976924546 -2.293972244800306 Columns 77 through 80 -2.205472731560801 -2.117410085770102 -2.029882337240432 -1.943014094278613 Columns 81 through 84 -1.856964802603174 -1.771939743182886 -1.688204600099232 -1.606104516991551 Columns 85 through 88 -1.526088418953069 -1.448738655979718 -1.374804053264346 -1.305230144292473 Columns 89 through 92 -1.241172498421328 -1.183967917116185 -1.135030143076851 -1.095651183855676 Columns 93 through 96 -1.066763848244772 -1.048931811216585 -1.043659127836105 -1.062506195470517 Columns 97 through 100 -1.188879093302472 -1.906941206857295 -5.598789917596750 -43.416543418076181 Columns 101 through 104 NaN 43.416543418076181 5.598789917596750 1.906941206857295 Columns 105 through 108 1.188879093302472 1.062506195470517 1.043659127836105 1.048931811216585 Columns 109 through 112 1.066763848244772 1.095651183855676 1.135030143076851 1.183967917116185 Columns 113 through 116 1.241172498421328 1.305230144292473 1.374804053264346 1.448738655979718 Columns 117 through 120 1.526088418953069 1.606104516991551 1.688204600099232 1.771939743182886 Columns 121 through 124 1.856964802603174 1.943014094278613 2.029882337240432 2.117410085770102 Columns 125 through 128 2.205472731560801 2.293972244800306 2.382830976924546 2.471987000775267 Columns 129 through 132 2.561390593173730 2.651001566517279 2.740787232918167 2.830720841478539 Columns 133 through 136 2.920780371215010 3.010947592797089 3.101207334656759 3.191546905412033 Columns 137 through 140 3.281955636574102 3.372424518371972 3.462945908092992 3.553513295224724 Columns 141 through 144 3.644121111341469 3.734764575432175 3.825439567450541 3.916142524454511 Columns 145 through 148 4.006870354916656 4.097620367721385 4.188390213087866 4.279177833219895 Columns 149 through 152 4.369981420923360 4.460799384777270 4.551630319716690 4.642472982102081 Columns 153 through 156 4.733326268521501 4.824189197709875 4.915060895080018 5.005940579449351 Columns 157 through 160 5.096827551618420 5.187721184516017 5.278620914673636 5.369526234831148 Columns 161 through 164 5.460436687507833 5.551351859399409 5.642271376483750 5.733194899736059 Columns 165 through 168 5.824122121369578 5.915052761530443 6.005986565385959 6.096923300554427 Columns 169 through 172 6.187862754832119 6.278804734179367 6.369749060932981 6.460695572216850 Columns 173 through 176 6.551644118526311 6.642594562465250 6.733546777617632 6.824500647537603 Columns 177 through 180 6.915456064844321 7.006412930409455 7.097371152626841 7.188330646755059 Columns 181 through 184 7.279291334324826 7.370253142604147 7.461216004114930 7.552179856195578 Columns 185 through 188 7.643144640604705 7.734110303161674 7.825076793420149 7.916044064371271 Columns 189 through 192 8.007012072173536 8.097980775906601 8.188950137346746 8.279920120761858 Columns 193 through 196 8.370890692723991 8.461861821937912 8.552833479084013 8.643805636674387 Columns 197 through 200 8.734778268920685 8.825751351612800 8.916724862007332 9.007698778724965 Column 201 9.098673081655985 x = Columns 1 through 4 -8.956568545800684 -8.867017620989270 -8.777467154871896 -8.687917171331291 Columns 5 through 8 -8.598367695757883 -8.508818755162007 -8.419270378295758 -8.329722595785428 Columns 9 through 12 -8.240175440275557 -8.150628946585828 -8.061083151881977 -7.971538095862297 Columns 13 through 16 -7.881993820961213 -7.792450372571835 -7.702907799289373 -7.613366153177725 Columns 17 through 20 -7.523825490061772 -7.434285869848080 -7.344747356877281 -7.255210020311643 Columns 21 through 24 -7.165673934561793 -7.076139179757167 -6.986605842265252 -6.897074015265398 Columns 25 through 28 -6.807543799383699 -6.718015303396413 -6.628488645010299 -6.538963951729468 Columns 29 through 32 -6.449441361819718 -6.359921025382804 -6.270403105554961 -6.180887779846072 Columns 33 through 36 -6.091375241638300 -6.001865701865857 -5.912359390900881 -5.822856560674305 Columns 37 through 40 -5.733357487065115 -5.643862472596814 -5.554371849486152 -5.464885983096727 Columns 41 through 44 -5.375405275858852 -5.285930171727611 -5.196461161263586 -5.106998787435590 Columns 45 through 48 -5.017543652262781 -4.928096424434945 -4.838657848075679 -4.749228752844609 Columns 49 through 52 -4.659810065612644 -4.570402823990603 -4.481008192047891 -4.391627478627041 Columns 53 through 56 -4.302262158744877 -4.212913898675935 -4.123584585443576 -4.034276361605849 Columns 57 through 60 -3.944991666424749 -3.855733284760583 -3.766504405351614 -3.677308690542342 Columns 61 through 64 -3.588150360035901 -3.499034291900271 -3.409966144897199 -3.320952507284826 Columns 65 through 68 -3.232001078647245 -3.143120893130297 -3.054322594853105 -2.965618779409213 Columns 69 through 72 -2.877024419527809 -2.788557398486715 -2.700239182234364 -2.612095671042866 Columns 73 through 76 -2.524158284767558 -2.436465353629631 -2.349063910462502 -2.262012012639312 Columns 77 through 80 -2.175381764997522 -2.089263271923320 -2.003769820074652 -1.919044684005042 Columns 81 through 84 -1.835270050904668 -1.752678660453380 -1.671568805153273 -1.592323230195304 Columns 85 through 88 -1.515431993519124 -1.441518094391340 -1.371362006204580 -1.305916378991858 Columns 89 through 92 -1.246294909203697 -1.193712111158957 -1.149352017906867 -1.114170538436978 Columns 93 through 96 -1.088708918070870 -1.073158472437693 -1.068586883174787 -1.084983844402657 Columns 97 through 100 -1.198197975982753 -1.883904980824320 -5.511575915833617 -42.738160499932519 Columns 101 through 104 NaN 42.738160499932519 5.511575915833617 1.883904980824320 Columns 105 through 108 1.198197975982753 1.084983844402657 1.068586883174787 1.073158472437693 Columns 109 through 112 1.088708918070870 1.114170538436978 1.149352017906867 1.193712111158957 Columns 113 through 116 1.246294909203697 1.305916378991858 1.371362006204580 1.441518094391340 Columns 117 through 120 1.515431993519124 1.592323230195304 1.671568805153273 1.752678660453380 Columns 121 through 124 1.835270050904668 1.919044684005042 2.003769820074652 2.089263271923320 Columns 125 through 128 2.175381764997522 2.262012012639312 2.349063910462502 2.436465353629631 Columns 129 through 132 2.524158284767558 2.612095671042866 2.700239182234364 2.788557398486715 Columns 133 through 136 2.877024419527809 2.965618779409213 3.054322594853105 3.143120893130297 Columns 137 through 140 3.232001078647245 3.320952507284826 3.409966144897199 3.499034291900271 Columns 141 through 144 3.588150360035901 3.677308690542342 3.766504405351614 3.855733284760583 Columns 145 through 148 3.944991666424749 4.034276361605849 4.123584585443576 4.212913898675935 Columns 149 through 152 4.302262158744877 4.391627478627041 4.481008192047891 4.570402823990603 Columns 153 through 156 4.659810065612644 4.749228752844609 4.838657848075679 4.928096424434945 Columns 157 through 160 5.017543652262781 5.106998787435590 5.196461161263586 5.285930171727611 Columns 161 through 164 5.375405275858852 5.464885983096727 5.554371849486152 5.643862472596814 Columns 165 through 168 5.733357487065115 5.822856560674305 5.912359390900881 6.001865701865857 Columns 169 through 172 6.091375241638300 6.180887779846072 6.270403105554961 6.359921025382804 Columns 173 through 176 6.449441361819718 6.538963951729468 6.628488645010299 6.718015303396413 Columns 177 through 180 6.807543799383699 6.897074015265398 6.986605842265252 7.076139179757167 Columns 181 through 184 7.165673934561793 7.255210020311643 7.344747356877281 7.434285869848080 Columns 185 through 188 7.523825490061772 7.613366153177725 7.702907799289373 7.792450372571835 Columns 189 through 192 7.881993820961213 7.971538095862297 8.061083151881977 8.150628946585828 Columns 193 through 196 8.240175440275557 8.329722595785428 8.419270378295758 8.508818755162007 Columns 197 through 200 8.598367695757883 8.687917171331291 8.777467154871896 8.867017620989270 Column 201 8.956568545800684 x = Columns 1 through 4 -8.816687402628043 -8.728537707698230 -8.640388546600745 -8.552239947129309 Columns 5 through 8 -8.464091938832123 -8.375944553142430 -8.287797823520293 -8.199651785606696 Columns 9 through 12 -8.111506477391142 -8.023361939394212 -7.935218214866416 -7.847075350005175 Columns 13 through 16 -7.758933394191691 -7.670792400249851 -7.582652424729441 -7.494513528216285 Columns 17 through 20 -7.406375775672298 -7.318239236808569 -7.230103986495305 -7.141970105212682 Columns 21 through 24 -7.053837679547253 -6.965706802739184 -6.877577575286255 -6.789450105611292 Columns 25 through 28 -6.701324510800637 -6.613200917422294 -6.525079462433506 -6.436960294188930 Columns 29 through 32 -6.348843573562124 -6.260729475194848 -6.172618188890781 -6.084509921172738 Columns 33 through 36 -5.996404897025188 -5.908303361847317 -5.820205583645558 -5.732111855499197 Columns 37 through 40 -5.644022498337775 -5.555937864075373 -5.467858339154070 -5.379784348557605 Columns 41 through 44 -5.291716360366494 -5.203654890938009 -5.115600510808984 -5.027553851436643 Columns 45 through 48 -4.939515612913453 -4.851486572816850 -4.763467596384640 -4.675459648243180 Columns 49 through 52 -4.587463805959211 -4.499481275739665 -4.411513410668832 -4.323561731951942 Columns 53 through 56 -4.235627953732109 -4.147714012168303 -4.059822099611315 -3.971954704900351 Columns 57 through 60 -3.884114661034247 -3.796305201761342 -3.708530028996507 -3.620793393434531 Columns 61 through 64 -3.533100191313177 -3.445456081023866 -3.357867624220925 -3.270342457305933 Columns 65 through 68 -3.182889500747002 -3.095519215747678 -3.008243920458840 -2.921078181434626 Columns 69 through 72 -2.834039300644928 -2.747147924443125 -2.660428808945231 -2.573911786969581 Columns 73 through 76 -2.487632995892790 -2.401636444641455 -2.315976023005908 -2.230718089271762 Columns 77 through 80 -2.145944814709860 -2.061758517353923 -1.978287282966591 -1.895692244608652 Columns 81 through 84 -1.814176961458241 -1.733999371536408 -1.655486724090935 -1.579053590562385 Columns 85 through 88 -1.505222262323680 -1.434643172227367 -1.368109915199178 -1.306558676575037 Columns 89 through 92 -1.251036235899758 -1.202618028475142 -1.162266624364581 -1.130652770956307 Columns 93 through 96 -1.108022867698292 -1.094317477257688 -1.090306179616451 -1.104731428327443 Columns 97 through 100 -1.206725444249756 -1.861479712545492 -5.425737513697371 -42.070377342594512 Columns 101 through 104 NaN 42.070377342594512 5.425737513697371 1.861479712545492 Columns 105 through 108 1.206725444249756 1.104731428327443 1.090306179616451 1.094317477257688 Columns 109 through 112 1.108022867698292 1.130652770956307 1.162266624364581 1.202618028475142 Columns 113 through 116 1.251036235899758 1.306558676575037 1.368109915199178 1.434643172227367 Columns 117 through 120 1.505222262323680 1.579053590562385 1.655486724090935 1.733999371536408 Columns 121 through 124 1.814176961458241 1.895692244608652 1.978287282966591 2.061758517353923 Columns 125 through 128 2.145944814709860 2.230718089271762 2.315976023005908 2.401636444641455 Columns 129 through 132 2.487632995892790 2.573911786969581 2.660428808945231 2.747147924443125 Columns 133 through 136 2.834039300644928 2.921078181434626 3.008243920458840 3.095519215747678 Columns 137 through 140 3.182889500747002 3.270342457305933 3.357867624220925 3.445456081023866 Columns 141 through 144 3.533100191313177 3.620793393434531 3.708530028996507 3.796305201761342 Columns 145 through 148 3.884114661034247 3.971954704900351 4.059822099611315 4.147714012168303 Columns 149 through 152 4.235627953732109 4.323561731951942 4.411513410668832 4.499481275739665 Columns 153 through 156 4.587463805959211 4.675459648243180 4.763467596384640 4.851486572816850 Columns 157 through 160 4.939515612913453 5.027553851436643 5.115600510808984 5.203654890938009 Columns 161 through 164 5.291716360366494 5.379784348557605 5.467858339154070 5.555937864075373 Columns 165 through 168 5.644022498337775 5.732111855499197 5.820205583645558 5.908303361847317 Columns 169 through 172 5.996404897025188 6.084509921172738 6.172618188890781 6.260729475194848 Columns 173 through 176 6.348843573562124 6.436960294188930 6.525079462433506 6.613200917422294 Columns 177 through 180 6.701324510800637 6.789450105611292 6.877577575286255 6.965706802739184 Columns 181 through 184 7.053837679547253 7.141970105212682 7.230103986495305 7.318239236808569 Columns 185 through 188 7.406375775672298 7.494513528216285 7.582652424729441 7.670792400249851 Columns 189 through 192 7.758933394191691 7.847075350005175 7.935218214866416 8.023361939394212 Columns 193 through 196 8.111506477391142 8.199651785606696 8.287797823520293 8.375944553142430 Columns 197 through 200 8.464091938832123 8.552239947129309 8.640388546600745 8.728537707698230 Column 201 8.816687402628043 x = Columns 1 through 4 -8.678995057056099 -8.592224794277604 -8.505455143268222 -8.418686135877927 Columns 5 through 8 -8.331917805967091 -8.245150189556050 -8.158383324987561 -8.071617253103353 Columns 9 through 12 -7.984852017436143 -7.898087664418784 -7.811324243612093 -7.724561807953424 Columns 13 through 16 -7.637800414028041 -7.551040122365717 -7.464280997765179 -7.377523109649400 Columns 17 through 20 -7.290766532455126 -7.204011346060273 -7.117257636253497 -7.030505495250630 Columns 21 through 24 -6.943755022263287 -6.857006324125671 -6.770259515986370 -6.683514722072803 Columns 25 through 28 -6.596772076536972 -6.510031724392456 -6.423293822553782 -6.336558540990948 Columns 29 through 32 -6.249826064013663 -6.163096591701880 -6.076370341501613 -5.989647550007867 Columns 33 through 36 -5.902928474959641 -5.816213397475800 -5.729502624564985 -5.642796491947873 Columns 37 through 40 -5.556095367236148 -5.469399653519623 -5.382709793421317 -5.296026273690197 Columns 41 through 44 -5.209349630412937 -5.122680454939982 -5.036019400637721 -4.949367190598268 Columns 45 through 48 -4.862724626462010 -4.776092598536414 -4.689472097428637 -4.602864227450805 Columns 49 through 52 -4.516270222106588 -4.429691462028411 -4.343129495808548 -4.256586064257708 Columns 53 through 56 -4.170063128735739 -4.083562904335794 -3.997087898872245 -3.910640958832503 Columns 57 through 60 -3.824225323714086 -3.737844690495250 -3.651503290397756 -3.565205980617994 Columns 61 through 64 -3.478958354357792 -3.392766873319404 -3.306639027892928 -3.220583531628371 Columns 65 through 68 -3.134610558340984 -3.048732032469240 -2.962961986252076 -2.877317001131486 Columns 69 through 72 -2.791816755804008 -2.706484709919373 -2.621348961054725 -2.536443323927715 Columns 73 through 76 -2.451808695680696 -2.367494790499392 -2.283562352028342 -2.200085984280414 Columns 77 through 80 -2.117157782016436 -2.034891989886114 -1.953430973343747 -1.872952835002971 Columns 81 through 84 -1.793681037187206 -1.715896351376458 -1.639951262907576 -1.566286461349892 Columns 85 through 88 -1.495447994765877 -1.428101721310527 -1.365038559259352 -1.307159913366087 Columns 89 through 92 -1.255429206349451 -1.210777083367276 -1.173961683027861 -1.145416812596272 Columns 93 through 96 -1.125168410543019 -1.112988135324442 -1.109435760999745 -1.122237314779773 Columns 97 through 100 -1.214546061999914 -1.839661279420259 -5.341253835876853 -41.413028326140136 Columns 101 through 104 NaN 41.413028326140136 5.341253835876853 1.839661279420259 Columns 105 through 108 1.214546061999914 1.122237314779773 1.109435760999745 1.112988135324442 Columns 109 through 112 1.125168410543019 1.145416812596272 1.173961683027861 1.210777083367276 Columns 113 through 116 1.255429206349451 1.307159913366087 1.365038559259352 1.428101721310527 Columns 117 through 120 1.495447994765877 1.566286461349892 1.639951262907576 1.715896351376458 Columns 121 through 124 1.793681037187206 1.872952835002971 1.953430973343747 2.034891989886114 Columns 125 through 128 2.117157782016436 2.200085984280414 2.283562352028342 2.367494790499392 Columns 129 through 132 2.451808695680696 2.536443323927715 2.621348961054725 2.706484709919373 Columns 133 through 136 2.791816755804008 2.877317001131486 2.962961986252076 3.048732032469240 Columns 137 through 140 3.134610558340984 3.220583531628371 3.306639027892928 3.392766873319404 Columns 141 through 144 3.478958354357792 3.565205980617994 3.651503290397756 3.737844690495250 Columns 145 through 148 3.824225323714086 3.910640958832503 3.997087898872245 4.083562904335794 Columns 149 through 152 4.170063128735739 4.256586064257708 4.343129495808548 4.429691462028411 Columns 153 through 156 4.516270222106588 4.602864227450805 4.689472097428637 4.776092598536414 Columns 157 through 160 4.862724626462010 4.949367190598268 5.036019400637721 5.122680454939982 Columns 161 through 164 5.209349630412937 5.296026273690197 5.382709793421317 5.469399653519623 Columns 165 through 168 5.556095367236148 5.642796491947873 5.729502624564985 5.816213397475800 Columns 169 through 172 5.902928474959641 5.989647550007867 6.076370341501613 6.163096591701880 Columns 173 through 176 6.249826064013663 6.336558540990948 6.423293822553782 6.510031724392456 Columns 177 through 180 6.596772076536972 6.683514722072803 6.770259515986370 6.857006324125671 Columns 181 through 184 6.943755022263287 7.030505495250630 7.117257636253497 7.204011346060273 Columns 185 through 188 7.290766532455126 7.377523109649400 7.464280997765179 7.551040122365717 Columns 189 through 192 7.637800414028041 7.724561807953424 7.811324243612093 7.898087664418784 Columns 193 through 196 7.984852017436143 8.071617253103353 8.158383324987561 8.245150189556050 Columns 197 through 200 8.331917805967091 8.418686135877927 8.505455143268222 8.592224794277604 Column 201 8.678995057056099 x = Columns 1 through 4 -8.543457461568279 -8.458045178455384 -8.372633587994264 -8.287222726244018 Columns 5 through 8 -8.201812631539660 -8.116403344661409 -8.030994909018585 -7.945587370849436 Columns 9 through 12 -7.860180779438504 -7.774775187353328 -7.689370650702334 -7.603967229416174 Columns 13 through 16 -7.518564987554873 -7.433163993643517 -7.347764321039460 -7.262366048334424 Columns 17 through 20 -7.176969259795345 -7.091574045848059 -7.006180503608702 -6.920788737468143 Columns 21 through 24 -6.835398859735424 -6.750010991347050 -6.664625262649794 -6.579241814265673 Columns 25 through 28 -6.493860798048903 -6.408482378146044 -6.323106732171929 -6.237734052515826 Columns 29 through 32 -6.152364547794282 -6.066998444469393 -5.981635988653946 -5.896277448128122 Columns 33 through 36 -5.810923114595918 -5.725573306213869 -5.640228370429475 -5.554888687172646 Columns 37 through 40 -5.469554672450217 -5.384226782401625 -5.298905517883239 -5.213591429659988 Columns 41 through 44 -5.128285124296109 -5.042987270852450 -4.957698608516417 -4.872419955312804 Columns 45 through 48 -4.787152218070367 -4.701896403850839 -4.616653633085407 -4.531425154710021 Columns 49 through 52 -4.446212363646848 -4.361016821047221 -4.275840277794357 -4.190684701865306 Columns 53 through 56 -4.105552310275858 -4.020445606485011 -3.935367424324315 -3.850320979751524 Columns 57 through 60 -3.765309932019013 -3.680338456211148 -3.595411329560471 -3.510534034526398 Columns 61 through 64 -3.425712882344779 -3.340955161676197 -3.256269318151484 -3.171665172109448 Columns 65 through 68 -3.087154183741781 -3.002749777332177 -2.918467739469657 -2.834326710252269 Columns 69 through 72 -2.750348791866348 -2.666560305906047 -2.582992739871382 -2.499683935060367 Columns 73 through 76 -2.416679583294502 -2.334035119441960 -2.251818121407246 -2.170111359810152 Columns 77 through 80 -2.089016675924432 -2.008659906736820 -1.929197114484046 -1.850822401210093 Columns 81 through 84 -1.773777568553350 -1.698363764856158 -1.624954948811235 -1.554012332789386 Columns 85 through 88 -1.486097724660898 -1.421881626574953 -1.362139033442453 -1.307722769528734 Columns 89 through 92 -1.259503099711134 -1.218267493630168 -1.184590600951573 -1.158712206257002 Columns 93 through 96 -1.140494684239971 -1.129596972307249 -1.126427744155438 -1.137867903817770 Columns 97 through 100 -1.221732488781876 -1.818445405172947 -5.258104362608647 -40.765950418523495 Columns 101 through 104 NaN 40.765950418523495 5.258104362608647 1.818445405172947 Columns 105 through 108 1.221732488781876 1.137867903817770 1.126427744155438 1.129596972307249 Columns 109 through 112 1.140494684239971 1.158712206257002 1.184590600951573 1.218267493630168 Columns 113 through 116 1.259503099711134 1.307722769528734 1.362139033442453 1.421881626574953 Columns 117 through 120 1.486097724660898 1.554012332789386 1.624954948811235 1.698363764856158 Columns 121 through 124 1.773777568553350 1.850822401210093 1.929197114484046 2.008659906736820 Columns 125 through 128 2.089016675924432 2.170111359810152 2.251818121407246 2.334035119441960 Columns 129 through 132 2.416679583294502 2.499683935060367 2.582992739871382 2.666560305906047 Columns 133 through 136 2.750348791866348 2.834326710252269 2.918467739469657 3.002749777332177 Columns 137 through 140 3.087154183741781 3.171665172109448 3.256269318151484 3.340955161676197 Columns 141 through 144 3.425712882344779 3.510534034526398 3.595411329560471 3.680338456211148 Columns 145 through 148 3.765309932019013 3.850320979751524 3.935367424324315 4.020445606485011 Columns 149 through 152 4.105552310275858 4.190684701865306 4.275840277794357 4.361016821047221 Columns 153 through 156 4.446212363646848 4.531425154710021 4.616653633085407 4.701896403850839 Columns 157 through 160 4.787152218070367 4.872419955312804 4.957698608516417 5.042987270852450 Columns 161 through 164 5.128285124296109 5.213591429659988 5.298905517883239 5.384226782401625 Columns 165 through 168 5.469554672450217 5.554888687172646 5.640228370429475 5.725573306213869 Columns 169 through 172 5.810923114595918 5.896277448128122 5.981635988653946 6.066998444469393 Columns 173 through 176 6.152364547794282 6.237734052515826 6.323106732171929 6.408482378146044 Columns 177 through 180 6.493860798048903 6.579241814265673 6.664625262649794 6.750010991347050 Columns 181 through 184 6.835398859735424 6.920788737468143 7.006180503608702 7.091574045848059 Columns 185 through 188 7.176969259795345 7.262366048334424 7.347764321039460 7.433163993643517 Columns 189 through 192 7.518564987554873 7.603967229416174 7.689370650702334 7.774775187353328 Columns 193 through 196 7.860180779438504 7.945587370849436 8.030994909018585 8.116403344661409 Columns 197 through 200 8.201812631539660 8.287222726244018 8.372633587994264 8.458045178455384 Column 201 8.543457461568279 x=-10:0.1:10; y=-10:0.1:10; for i=1:10 x=x+(a-x.^4).*(4*x).^(-3); plot(y,x) F(i) = getframe; end movie(F,1,1) movie(F,10,10) x=-100:1:100; y=x; for i=1:10 x=x+(a-x.^4).*(4*x).^(-3); plot(y,x) F(i) = getframe; end movie(F,10,10) x=-20:0.1:20; y=x; for i=1:100 x=x+(a-x.^4).*(4*x).^(-3); plot(y,x) F(i) = getframe; end movie(F,10,10) x=-20:1:20; y=x; for i=1:1000 x=x+(a-x.^4).*(4*x).^(-3); plot(y,x) F(i) = getframe; end {Error using capturescreen Figure destroyed during getframe Error in getframe (line 103) x=builtin('capturescreen', varargin{:}); } figure %akselit pitää kiinnittää, jotta saadaan video axis([xmin xmax ymin ymax]) x=-20:1:20; y=x; for i=1:1 x=x+(a-x.^4).*(4*x).^(-3); plot(y,x) F(i) = getframe; end axis[-20 20 -20 20] axis[-20 20 -20 20] | {Error: Unbalanced or unexpected parenthesis or bracket. } axis([-20 20 -20 20]) x=-20:1:20; y=x; for i=1:1000 x=x+(a-x.^4).*(4*x).^(-3); plot(y,x) F(i) = getframe; end {Error using capturescreen Figure destroyed during getframe Error in getframe (line 103) x=builtin('capturescreen', varargin{:}); } axis([-20 20 -20 20]) axis tight %akselit kiinni x=-20:1:20; y=x; for i=1:1000 x=x+(a-x.^4).*(4*x).^(-3); plot(y,x) F(i) = getframe; end {Error using capturescreen Figure destroyed during getframe Error in getframe (line 103) x=builtin('capturescreen', varargin{:}); } axis([-20 20 -20 20]) axis tight %akselit kiinni x=-20:1:20; y=x; for i=1:1000 x=x+(a-x.^4).*(4*x).^(-3); axis tight plot(y,x) F(i) = getframe; end {Error using capturescreen Figure destroyed during getframe Error in getframe (line 103) x=builtin('capturescreen', varargin{:}); } x=-20:1:20; y=x; for i=1:1000 x=x+(a-x.^4).*(4*x).^(-3); plot(y,x), axis([-20 20 -20 20]) F(i) = getframe; end {Error using capturescreen Figure destroyed during getframe Error in getframe (line 103) x=builtin('capturescreen', varargin{:}); } x=-20:1:20; y=x; for i=1:100 x=x+(a-x.^4).*(4*x).^(-3); plot(y,x), axis([-20 20 -20 20]) F(i) = getframe; end x=-20:1:20; y=x; for i=1:200 x=x+(a-x.^4).*(4*x).^(-3); plot(y,x), axis([-20 20 -20 20]) F(i) = getframe; end %Toimiva videokomento: x=-20:1:20; y=x; for i=1:200 x=x+(a-x.^4).*(4*x).^(-3); plot(y,x), axis([-20 20 -20 20]) F(i) = getframe; end movie(F,24,1) movie(F,1,24) %näyttää siltä, että iteraatio suppenee kaikilla alkuarvoilla x0>0 %teht.5 clear x(1)=1.5; for i=1:20 x(i+1)=x(i)*(x(i)-1)^2; end x(20) ans = 0.022827564814187 clear x(1)=1.1 x = 1.100000000000000 format short for i=1:20 x(i+1)=x(i)*(x(i)-1)^2; end x(20) ans = 0.0078 x x = Columns 1 through 8 1.1000 0.0110 0.0108 0.0105 0.0103 0.0101 0.0099 0.0097 Columns 9 through 16 0.0095 0.0093 0.0092 0.0090 0.0088 0.0087 0.0085 0.0084 Columns 17 through 21 0.0082 0.0081 0.0080 0.0078 0.0077 clear x(1)=3; for i=1:20 x(i+1)=x(i)*(x(i)-1)^2; end x(20) ans = Inf x(1)=2; for i=1:20 x(i+1)=x(i)*(x(i)-1)^2; end x(20) ans = 2 x x = Columns 1 through 13 2 2 2 2 2 2 2 2 2 2 2 2 2 Columns 14 through 21 2 2 2 2 2 2 2 2 x(1)=.5; for i=1:20 x(i+1)=x(i)*(x(i)-1)^2; end x(20) ans = 0.0214 x x = Columns 1 through 8 0.5000 0.1250 0.0957 0.0783 0.0665 0.0579 0.0514 0.0463 Columns 9 through 16 0.0421 0.0386 0.0357 0.0332 0.0310 0.0291 0.0275 0.0260 Columns 17 through 21 0.0246 0.0234 0.0224 0.0214 0.0205 x(1)=1.12312; for i=1:20 x(i+1)=x(i)*(x(i)-1)^2; end x(20) ans = 0.0105 x x = Columns 1 through 8 1.1231 0.0170 0.0165 0.0159 0.0154 0.0149 0.0145 0.0141 Columns 9 through 16 0.0137 0.0133 0.0130 0.0126 0.0123 0.0120 0.0117 0.0114 Columns 17 through 21 0.0112 0.0109 0.0107 0.0105 0.0103 x(1)=3; for i=1:20 x(i+1)=x(i)-x(i)*(x(i)-1)^2; %nyt kaava meni oikein! end x(20) ans = NaN x x = 1.0e+238 * Columns 1 through 8 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 8.1987 -Inf Columns 9 through 16 NaN NaN NaN NaN NaN NaN NaN NaN Columns 17 through 21 NaN NaN NaN NaN NaN x(1)=1.1; for i=1:20 x(i+1)=x(i)-x(i)*(x(i)-1)^2; %nyt kaava meni oikein! end x(20) ans = 1.0320 x x = Columns 1 through 8 1.1000 1.0890 1.0804 1.0734 1.0676 1.0627 1.0585 1.0549 Columns 9 through 16 1.0517 1.0489 1.0464 1.0442 1.0421 1.0403 1.0386 1.0370 Columns 17 through 21 1.0356 1.0343 1.0331 1.0320 1.0309 x(1)=3; for i=1:200 x(i+1)=x(i)-x(i)*(x(i)-1)^2; %nyt kaava meni oikein! end x(20) ans = NaN x(1)=1.1; for i=1:200 x(i+1)=x(i)-x(i)*(x(i)-1)^2; %nyt kaava meni oikein! end x(20) ans = 1.0320 x x = Columns 1 through 8 1.1000 1.0890 1.0804 1.0734 1.0676 1.0627 1.0585 1.0549 Columns 9 through 16 1.0517 1.0489 1.0464 1.0442 1.0421 1.0403 1.0386 1.0370 Columns 17 through 24 1.0356 1.0343 1.0331 1.0320 1.0309 1.0299 1.0290 1.0281 Columns 25 through 32 1.0273 1.0266 1.0258 1.0251 1.0245 1.0239 1.0233 1.0227 Columns 33 through 40 1.0222 1.0217 1.0212 1.0208 1.0203 1.0199 1.0195 1.0191 Columns 41 through 48 1.0187 1.0184 1.0180 1.0177 1.0174 1.0171 1.0168 1.0165 Columns 49 through 56 1.0162 1.0160 1.0157 1.0154 1.0152 1.0150 1.0147 1.0145 Columns 57 through 64 1.0143 1.0141 1.0139 1.0137 1.0135 1.0133 1.0131 1.0130 Columns 65 through 72 1.0128 1.0126 1.0125 1.0123 1.0122 1.0120 1.0119 1.0117 Columns 73 through 80 1.0116 1.0114 1.0113 1.0112 1.0111 1.0109 1.0108 1.0107 Columns 81 through 88 1.0106 1.0105 1.0104 1.0102 1.0101 1.0100 1.0099 1.0098 Columns 89 through 96 1.0097 1.0096 1.0096 1.0095 1.0094 1.0093 1.0092 1.0091 Columns 97 through 104 1.0090 1.0089 1.0089 1.0088 1.0087 1.0086 1.0086 1.0085 Columns 105 through 112 1.0084 1.0083 1.0083 1.0082 1.0081 1.0081 1.0080 1.0079 Columns 113 through 120 1.0079 1.0078 1.0077 1.0077 1.0076 1.0076 1.0075 1.0075 Columns 121 through 128 1.0074 1.0073 1.0073 1.0072 1.0072 1.0071 1.0071 1.0070 Columns 129 through 136 1.0070 1.0069 1.0069 1.0068 1.0068 1.0067 1.0067 1.0066 Columns 137 through 144 1.0066 1.0066 1.0065 1.0065 1.0064 1.0064 1.0063 1.0063 Columns 145 through 152 1.0063 1.0062 1.0062 1.0062 1.0061 1.0061 1.0060 1.0060 Columns 153 through 160 1.0060 1.0059 1.0059 1.0059 1.0058 1.0058 1.0058 1.0057 Columns 161 through 168 1.0057 1.0057 1.0056 1.0056 1.0056 1.0055 1.0055 1.0055 Columns 169 through 176 1.0054 1.0054 1.0054 1.0054 1.0053 1.0053 1.0053 1.0052 Columns 177 through 184 1.0052 1.0052 1.0052 1.0051 1.0051 1.0051 1.0051 1.0050 Columns 185 through 192 1.0050 1.0050 1.0049 1.0049 1.0049 1.0049 1.0049 1.0048 Columns 193 through 200 1.0048 1.0048 1.0048 1.0047 1.0047 1.0047 1.0047 1.0046 Column 201 1.0046 length(x) ans = 201 y=1:201; plot(y,x) print -djpeg 'h1t5.jpg' diary off %jos tulee päättymätön silmukka, niin sen saa katkaistua komennolla Ctrl+c diary off