Harjoitus2


%Tein tehtävää 1 varten funktiosta f matlabfunktion h2t1f.m. Avaamalla funktion voit tutustua siihen, miten se on tehty.

%Nyt voidaan piirtää f:n kuvaaja.

a=-2:0.01:2;
b=h2t1f(a);
plot(a,b)

nolla=0*a;
hold on
plot(a,nolla)

%Luetaan likiarvot nollakohdille Matlabin "kuva-ammunnalla" eli graphical inputilla eli funktiolla ginput

[c,~]=ginput

[d,~]=ginput


h2t1f(c+0.1)
h2t1f(c-0.1)
h2t1f(d-0.1)
h2t1f(d+0.1)

%Näyttää siltä, että c ja d ovat hyvät likiarvot. Käytetään näitä iteroitaessa.

%Tehdään f:n derivaatasta myös matlabfunktio h2t1df. Aloitetaan iterointi.

c(1)=c;
d(1)=d;

for i=1:10
c(i+1)=c(i)-h2t1f(c(i))/h2t1df(c(i));
end

format long

c'
d'

%Voidaan laskea f:n arvo saadussa nollakohdan likiarvossa. Näin voidaan katsoa, onko vastauksessa järkeä.

h2t1f(c)'

%Kokeillaan kumpi juuri saadaan, kun alkuarvo arvotaan satunnaisesti väliltä -2:2

e(1)=4*(rand(1)-0.5); %arvotaan satunnaisluku väliltä -2:2
for i=1:10
e(i+1)=e(i)-h2t1f(e(i))/h2t1df(e(i));
end

e'



%Tehtävä 6
%
%Tehtävässä 1 saatiin
%c=-0.1875;
%d=1.5948;
%Nämä olivat siis graafisesti katsotut nollakohtien likiarvot
%
%Kokeillaan sekanttimenetelmää
%
%Alkuarvot


c=[-0.25 0];
d=[1.5 2];


for k=1:10
c(k+2)=c(k+1)-(c(k+1)-c(k))*h2t1f(c(k+1))/(h2t1f(c(k+1))-h2t1f(c(k)));
end



(ja

for k=1:10
d(k+2)=d(k+1)-(d(k+1)-d(k))*h2t1f(d(k+1))/(h2t1f(d(k+1))-h2t1f(d(k)));
end

)


c'

ans =

   -0.2500
         0
   -0.1847
   -0.1996
   -0.1967
   -0.1968
   -0.1968
   -0.1968
   -0.1968
       NaN
       NaN
       NaN

>> %nyt siis verrattuna tehtäväpaperin kaavaan x_(k+1)=c(k+2),x_k=c(k+1),x_(k-1)=c(k)
>> c(7)-c(6)

ans =

 -1.0874e-007

>> h2t1f(c(7))-h2t1f(c(6))

ans =

  6.8202e-007

>> %muutaman iterointikierroksen jälkeen tulee alivuoto/ylivuoto ja saadaan "Not a Numbereita"=NaN
>> %c(9) lienee hyvä likiarvo
>> c(9)

ans =

   -0.1968

>> format long
>> c(9)

ans =

  -0.196760787015232

>> h2t1f(c(9))

ans =

     0

for k=1:10
d(k+2)=d(k+1)-(d(k+1)-d(k))*h2t1f(d(k+1))/(h2t1f(d(k+1))-h2t1f(d(k)));
end


>> d'

ans =

   1.500000000000000
   2.000000000000000
   1.600077935642649
   1.611913777623435
   1.613425833372391
   1.613418936140604
   1.613418939680558
   1.613418939680566
   1.613418939680567
   1.613418939680567
                 NaN
                 NaN

>> %taas tulee alivuoto/ylivuoto, mutta d(10) on hyvä likiarvo
>> d(10)

ans =

   1.613418939680567

>> h2t1f(d(10))

ans =

    4.440892098500626e-016

>> %siis liki nolla
>> e-016

ans =

  Columns 1 through 5

 -14.376832251697524 -14.386548950704213 -14.386581059967940 -14.386581060319434 -14.386581060319433

  Columns 6 through 10

 -14.386581060319434 -14.386581060319433 -14.386581060319434 -14.386581060319433 -14.386581060319434

  Column 11

 -14.386581060319433

>> h2t1f(d(10)+10^(-5))

ans =

    3.391876581115838e-005

>> h2t1f(d(10)-10^(-5))

ans =

   -3.391853453549309e-005

>> h2t1f(c(9)+10^(-5))

ans =

   -6.271837189641971e-005

>> h2t1f(c(9)-10^(-5))

ans =

    6.271969966364921e-005

>> %ok
>> %



%Tehtävä 4
>> %
>> %arctan on Matlabissa atan
>> N=10;
>> x(1)=0.5; %muutellaan
>> for k=1:N
x(k+1)=x(k)-(1+x(k).^2),*atan(x(k));
??? x(k+1)=x(k)-(1+x(k).^2),*atan(x(k));
                            |
Error: Unexpected MATLAB operator.
 
>> end
??? end
    |
Error: Illegal use of reserved keyword "end".
 
>>  N=10;
x(1)=0.5; %muutellaan
for k=1:N
x(k+1)=x(k)-(1+x(k).^2).*atan(x(k));
end
>> x

x =

  Columns 1 through 5

   0.500000000000000  -0.079559511251008   0.000335302204005  -0.000000000025131                   0

  Columns 6 through 10

                   0                   0                   0                   0                   0

  Column 11

                   0

>> x'

ans =

   0.500000000000000
  -0.079559511251008
   0.000335302204005
  -0.000000000025131
                   0
                   0
                   0
                   0
                   0
                   0
                   0

>> y=1:length(x);
>> y'

ans =

     1
     2
     3
     4
     5
     6
     7
     8
     9
    10
    11

>> plot(y,x)
>>  N=10;
x(1)=0.5; %muutellaan
for k=1:N
x(k+1)=x(k)-(1+x(k).^2).*atan(x(k));
end
>> y=1:length(x);
>> plot(y,x)
>> %Tätä voi käyttää
>>  N=10;
x(1)=1; %muutellaan
for k=1:N
x(k+1)=x(k)-(1+x(k).^2).*atan(x(k));
end
y=1:length(x);
plot(y,x)
>>  N=10;
x(1)=2; %muutellaan
for k=1:N
x(k+1)=x(k)-(1+x(k).^2).*atan(x(k));
end
y=1:length(x);
plot(y,x)
>> axis([1 length(x) -5 5])
>> axis([1 length(x) -100 100])
>> axis([1 length(x) -10000 10000])
>> axis([1 length(x) -1000000 1000000])
>> N=10;
x(1)=1.5; %muutellaan
for k=1:N
x(k+1)=x(k)-(1+x(k).^2).*atan(x(k));
end
y=1:length(x);
plot(y,x)    




                                                                       
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Harjoitus2

>> %Numeerinen analyysi s2012, Laskuharjoitus 2
>> %
>> %Matlabia
>> %
>> %Tein tehtävää 1 varten funktiosta f matlabfunktion h2t1f.m. Avaamalla funktion voit tutustua siihen, miten se on tehty.
>> %
>> %Teko-ohje:
>> %File->New->Function
>> %sopiva koodi:
>> %
>> %function [y] = h2t1f(x)
>> %jne.
>> %
>> %Tämän jälkeen tallenna funktio samalla nimellä, kuin millä sitä koodissa kutsutaan. Tässä tapauksessa siis h2t1f.m.
>> %Nyt funktiota voi kutsua Matlabissa
>> %
>> %Nyt voidaan piirtää f:n kuvaaja.
>> a=-3:0.01:3;
>> b=f(a);
Undefined function 'f' for input arguments of type 'double'.
 
>> b=h2t1f(a);
>> plot(a,b)
>> a=-2:0.01:2;
>> b=h2t1f(a);
>> plot(a,b)
>> A=rand(2,3)

A =

    0.8147    0.1270    0.6324
    0.9058    0.9134    0.0975

>> nolla=0*a;
>> hold on
>> plot(a,nolla)
>> %Tallennetaan kuva nimellä h2t1f.jpg
>> print -djpeg 'h2t1f.jpg'
>> %Luetaan likiarvot nollakohdille Matlabin "kuva-ammunnalla" eli graphical inputilla eli funktiolla ginput
>> [~,c]=ginput

c =

   -0.0676

>> [c,~]=ginput

c =

   -0.1875

>> [d,~]=ginput

d =

    1.5948

>> %komennon jälkeen suurenna kuvaikkuna, klikkaa hiirellä ja paina Enteriä
>> h2t1f(c)

ans =

   -0.0575

>> h2t1f(d)

ans =

   -0.0629

>> h2t1f(c+0.1)

ans =

   -0.6101

>> h2t1f(c-0.1)

ans =

    0.6263

>> h2t1f(d-0.1)

ans =

   -0.3859

>> h2t1f(d+0.1)

ans =

    0.2835

>> %Näyttää siltä, että c ja d ovat hyvät likiarvot
>> c,d

c =

   -0.1875


d =

    1.5948

>> %Tehdään f:n derivaatasta myös matlabfunktio h2t1df
>> a=-2:0.01:2;
>> b=h2t1df(a);
>> plot(a,b)
>> hold on
>> b=h2t1f(a);
>> plot(a,b)
>> %Etsitään nyt nollakohtia iteroimalla
>> c(1)=c;
>> d(1)=d;
>> for i=2:10
end
>> for i=1:10
c(i+1)=c(i)-h2t1f(c(i))/h2t1df(c(i));
end
>> c

c =

  Columns 1 through 8

   -0.1875   -0.1969   -0.1968   -0.1968   -0.1968   -0.1968   -0.1968   -0.1968

  Columns 9 through 11

   -0.1968   -0.1968   -0.1968

>> format long
>> c'

ans =

  -0.187500000000000
  -0.196852528857975
  -0.196760795923276
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232

>> h2t1f(c)

ans =

  Columns 1 through 4

  -0.057515991848934   0.000575451870440   0.000000055870395   0.000000000000001

  Columns 5 through 8

  -0.000000000000000                   0                   0                   0

  Columns 9 through 11

                   0                   0                   0

>> %Nyt siis c(11) on todella tarkka arvo
>> c(11)

ans =

  -0.196760787015232

>> %Sama toiselle nollakohdalle:
>> for i=2:10
end
for i=1:10
d(i+1)=d(i)-h2t1f(d(i))/h2t1df(d(i));
end
>> d'

ans =

   1.594758064516129
   1.613539765211843
   1.613418944657118
   1.613418939680566
   1.613418939680567
   1.613418939680566
   1.613418939680567
   1.613418939680566
   1.613418939680567
   1.613418939680566
   1.613418939680567

>> h2t1f(d)'

ans =

  -0.062891537159646
   0.000409840774171
   0.000000016879790
  -0.000000000000000
   0.000000000000000
  -0.000000000000000
   0.000000000000000
  -0.000000000000000
   0.000000000000000
  -0.000000000000000
   0.000000000000000

>> %Siis d(11) on hyvä likiarvo
>> d(11)

ans =

   1.613418939680567

>> %kokeillaan vielä eri alkuarvoilla
>> e(1)=0;
>> for i=2:10
end
for i=1:10
e(i+1)=e(i)-h2t1f(e(i))/h2t1df(e(i));
end
>> e'

ans =

                   0
  -0.250000000000000
  -0.199592055311246
  -0.196769245001276
  -0.196760787090954
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232

>> %saatiin c(11)
>> e(1)=4*(rand(1)-0.5); %arvotaan satunnaisluku väliltä -2:2
for i=2:10
end
for i=1:10
e(i+1)=e(i)-h2t1f(e(i))/h2t1df(e(i));
end
>> e'

ans =

  -0.886007124531806
  -0.490805919720862
  -0.266208728724747
  -0.201498131697172
  -0.196784415939237
  -0.196760787606206
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232

>> e(1)=4*(rand(1)-0.5); %arvotaan satunnaisluku väliltä -2:2
for i=2:10
end
for i=1:10
e(i+1)=e(i)-h2t1f(e(i))/h2t1df(e(i));
end
>> e'

ans =

   0.187526076819935
  -0.489426251143029
  -0.265633295010951
  -0.201422703713940
  -0.196783671428655
  -0.196760787569552
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232

>>  e(1)=4*(rand(1)-0.5); %arvotaan satunnaisluku väliltä -2:2
for i=2:10
end
for i=1:10
e(i+1)=e(i)-h2t1f(e(i))/h2t1df(e(i));
end
e'

ans =

   1.830027341737190
   1.626763059727360
   1.613478901328828
   1.613418940906263
   1.613418939680566
   1.613418939680567
   1.613418939680566
   1.613418939680567
   1.613418939680566
   1.613418939680567
   1.613418939680566

>>  e(1)=4*(rand(1)-0.5); %arvotaan satunnaisluku väliltä -2:2
for i=2:10
end
for i=1:10
e(i+1)=e(i)-h2t1f(e(i))/h2t1df(e(i));
end
e'

ans =

   1.859554140797106
   1.630275593411184
   1.613514315107829
   1.613418942781513
   1.613418939680566
   1.613418939680567
   1.613418939680566
   1.613418939680567
   1.613418939680566
   1.613418939680567
   1.613418939680566

>>  e(1)=4*(rand(1)-0.5); %arvotaan satunnaisluku väliltä -2:2
for i=2:10
end
for i=1:10
e(i+1)=e(i)-h2t1f(e(i))/h2t1df(e(i));
end
e'

ans =

  -1.369547673289807
  -0.870316781179030
  -0.480061891212526
  -0.261776481162446
  -0.200931721204171
  -0.196779115097216
  -0.196760787370796
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232

>>  e(1)=4*(rand(1)-0.5); %arvotaan satunnaisluku väliltä -2:2
for i=2:10
end
for i=1:10
e(i+1)=e(i)-h2t1f(e(i))/h2t1df(e(i));
end
e'

ans =

   1.882371127042463
   1.633215651220823
   1.613550133120316
   1.613418945547769
   1.613418939680567
   1.613418939680566
   1.613418939680567
   1.613418939680566
   1.613418939680567
   1.613418939680566
   1.613418939680567

>>  e(1)=4*(rand(1)-0.5); %arvotaan satunnaisluku väliltä -2:2
for i=2:10
end
for i=1:10
e(i+1)=e(i)-h2t1f(e(i))/h2t1df(e(i));
end
e'

ans =

   1.828667792971782
   1.626609565218679
   1.613477538080725
   1.613418940851164
   1.613418939680567
   1.613418939680566
   1.613418939680567
   1.613418939680566
   1.613418939680567
   1.613418939680566
   1.613418939680567

>>  e(1)=4*(rand(1)-0.5); %arvotaan satunnaisluku väliltä -2:2
for i=2:10
end
for i=1:10
e(i+1)=e(i)-h2t1f(e(i))/h2t1df(e(i));
end
e'

ans =

  -0.058497405108635
  -0.220853656725267
  -0.197358980198904
  -0.196761165529081
  -0.196760787015384
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232
  -0.196760787015232

>>  e(1)=4*(rand(1)-0.5); %arvotaan satunnaisluku väliltä -2:2
for i=2:10
end
for i=1:10
e(i+1)=e(i)-h2t1f(e(i))/h2t1df(e(i));
end
e'

ans =

   1.201121875555200
   1.708980270767466
   1.616279132561336
   1.613421721275897
   1.613418939683204
   1.613418939680566
   1.613418939680567
   1.613418939680566
   1.613418939680567
   1.613418939680566
   1.613418939680567

>> %Eri alkuarvoilla saadaan eri nollakohta
>> %Tehdään alkuarvoista vektori ja piirretään saatavan nollakohdan kuvaaja alkuarvon funktiona
>> f=[-2:0.01:2]';
>> e=[-2:0.01:2]';
>> for i=2:10
end
for i=1:10
e(i+1)=e(i)-h2t1f(e(i))/h2t1df(e(i));
end
>> plot(e,e(11))
>> plot(e,e(2))
>> for i=2:10
end
for i=1:10
e(i+1,:)=e(i,:)-h2t1f(e(i,:)).*(h2t1df(e(i,:))).^0.5;
end
>> plot(e,e(11))
Warning: Imaginary parts of complex X and/or Y arguments ignored 
>> e=[-2 -1 0 1 2]';
>> e=[-2 -1 0 1 2]'

e =

    -2
    -1
     0
     1
     2

>> h2t1f(e)

ans =

  86.154374428866845
  11.825619755848741
  -1.000000000000000
  -1.600423599106272
   1.476974505942283

>> h2t1df(e)

ans =

   1.0e+02 *

  -1.575306366598724
  -0.276512395116975
  -0.040000000000000
   0.017293294335268
   0.042340392886958

>> e(:,2)=e(:,2)-h2t1f(e(:,2)).*(h2t1df(e(:,2))).^0.5;
Index exceeds matrix dimensions.
 
>> e(:,2)=e(:,1)-h2t1f(e(:,1)).*(h2t1df(e(:,1))).^0.5;
>> e

e =

   1.0e+03 *

 -0.002000000000000                      -0.002000000000000 - 1.081333972312468i
 -0.001000000000000                      -0.001000000000000 - 0.062184366234834i
                  0                       0.000000000000000 + 0.002000000000000i
  0.001000000000000                       0.003104620582390                     
  0.002000000000000                      -0.001039138140168                     

>> 1+(-1).^0.5

ans =

  1.000000000000000 + 1.000000000000000i

>> A=1+(-1).^0.5

A =

  1.000000000000000 + 1.000000000000000i

>> real(A)

ans =

     1

>> imag(A)

ans =

     1

>> e=[-2 -1 0 1 2]'

e =

    -2
    -1
     0
     1
     2

>> e=[-2 -1 0 1 2]';
>> for i=1:10
e(:,i+1)=e(:,i)-h2t1f(e(:,i)).*(h2t1df(e(:,i))).^0.5;
e=real(e);
end
>> e

e =

   1.0e+04 *

  Columns 1 through 4

  -0.000200000000000  -0.000200000000000  -0.000200000000000  -0.000200000000000
  -0.000100000000000  -0.000100000000000  -0.000100000000000  -0.000100000000000
                   0   0.000000000000000   0.000000000000000   0.000000000000000
   0.000100000000000   0.000310462058239  -0.001551177842524  -1.406104740467749
   0.000200000000000  -0.000103913814017  -0.000103913814017  -0.000103913814017

  Columns 5 through 8

  -0.000200000000000  -0.000200000000000  -0.000200000000000  -0.000200000000000
  -0.000100000000000  -0.000100000000000  -0.000100000000000  -0.000100000000000
   0.000000000000000   0.000000000000000   0.000000000000000   0.000000000000000
                -Inf                -Inf                -Inf                -Inf
  -0.000103913814017  -0.000103913814017  -0.000103913814017  -0.000103913814017

  Columns 9 through 11

  -0.000200000000000  -0.000200000000000  -0.000200000000000
  -0.000100000000000  -0.000100000000000  -0.000100000000000
   0.000000000000000   0.000000000000000   0.000000000000000
                -Inf                -Inf                -Inf
  -0.000103913814017  -0.000103913814017  -0.000103913814017

>> %tuli äärettömiä mukaan
>> e'

ans =

   1.0e+04 *

  Columns 1 through 4

  -0.000200000000000  -0.000100000000000                   0   0.000100000000000
  -0.000200000000000  -0.000100000000000   0.000000000000000   0.000310462058239
  -0.000200000000000  -0.000100000000000   0.000000000000000  -0.001551177842524
  -0.000200000000000  -0.000100000000000   0.000000000000000  -1.406104740467749
  -0.000200000000000  -0.000100000000000   0.000000000000000                -Inf
  -0.000200000000000  -0.000100000000000   0.000000000000000                -Inf
  -0.000200000000000  -0.000100000000000   0.000000000000000                -Inf
  -0.000200000000000  -0.000100000000000   0.000000000000000                -Inf
  -0.000200000000000  -0.000100000000000   0.000000000000000                -Inf
  -0.000200000000000  -0.000100000000000   0.000000000000000                -Inf
  -0.000200000000000  -0.000100000000000   0.000000000000000                -Inf

  Column 5

   0.000200000000000
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017

>> isfinite(0)

ans =

     1

>> isfinite(1/0)

ans =

     0

>> isinf(1/0)

ans =

     1

>> isinf(0)

ans =

     0

>> e=isfinite(e).*e;
>> e'

ans =

   1.0e+04 *

  Columns 1 through 4

  -0.000200000000000  -0.000100000000000                   0   0.000100000000000
  -0.000200000000000  -0.000100000000000   0.000000000000000   0.000310462058239
  -0.000200000000000  -0.000100000000000   0.000000000000000  -0.001551177842524
  -0.000200000000000  -0.000100000000000   0.000000000000000  -1.406104740467749
  -0.000200000000000  -0.000100000000000   0.000000000000000                 NaN
  -0.000200000000000  -0.000100000000000   0.000000000000000                 NaN
  -0.000200000000000  -0.000100000000000   0.000000000000000                 NaN
  -0.000200000000000  -0.000100000000000   0.000000000000000                 NaN
  -0.000200000000000  -0.000100000000000   0.000000000000000                 NaN
  -0.000200000000000  -0.000100000000000   0.000000000000000                 NaN
  -0.000200000000000  -0.000100000000000   0.000000000000000                 NaN

  Column 5

   0.000200000000000
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017
  -0.000103913814017

>> e=e(isfinite(e)==1)

e =

   1.0e+04 *

  -0.000200000000000
  -0.000100000000000
                   0
   0.000100000000000
   0.000200000000000
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
   0.000310462058239
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.001551177842524
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -1.406104740467749
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.000103913814017

>> e=e(e~=e+1)

e =

   1.0e+04 *

  -0.000200000000000
  -0.000100000000000
                   0
   0.000100000000000
   0.000200000000000
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
   0.000310462058239
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.001551177842524
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -1.406104740467749
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.000103913814017
  -0.000200000000000
  -0.000100000000000
   0.000000000000000
  -0.000103913814017

>> e=[-2 -1 0 1 2]';
>> for i=1:10
e=e-h2t1f(e).*(h2t1df(e)).^0.5;
e=real(e);
end
>> e'

ans =

  Columns 1 through 4

  -2.000000000000662  -1.000000000000038   0.000000000000001                -Inf

  Column 5

  -1.039138140168365

>> e(isfinite(e)==1)

ans =

  -2.000000000000662
  -1.000000000000038
   0.000000000000001
  -1.039138140168365

>> isfinite(e)

ans =

     1
     1
     1
     0
     1

>> for j=1:length(e)
end
>> E=isfinite(E);
Undefined function or variable 'E'.
 
>> E=isfinite(e);
>> for j=1:length(e)
if E(j)=1, E(j)=e;
 if E(j)=1, E(j)=e;
       |
Error: The expression to the left of the equals sign is not a valid target for an
assignment.
 
>> E=isfinite(e);
for j=1:length(e)
if E(j)=1, E(j)=e;
 if E(j)=1, E(j)=e;
       |
Error: The expression to the left of the equals sign is not a valid target for an
assignment.
 
>> E=isfinite(e);
for j=1:length(e)
if E(j)==1, E(j)=e;
else E(j)=0;
end
end
In an assignment  A(:) = B, the number of elements in A and B
must be the same.
 
>> E=isfinite(e);
for j=1:length(e)
if E(j)==1, E(j)=e(j);
else E(j)=0;
end
end
>> e

e =

  -2.000000000000662
  -1.000000000000038
   0.000000000000001
                -Inf
  -1.039138140168365

>> E

E =

     1
     1
     1
     0
     1

>> E

E =

     1
     1
     1
     0
     1

N=10;
e=[-2:0.01:2]';
for i=1:N
e(:,i+1)=e(:,i)-h2t1f(e(:,i)).*(h2t1df(e(:,i))).^0.5;
e=real(e);
end
>> F=e(:,N+1);
>> G=e(:,1);
>> Ga=G(isfinite(F)==1);
>> Gb=G(isinf(F)==1);
>> Fa=F(isfinite(F)==1);
>> Hb=0.1*sin(100*Gb);
>> plot(Ga,Fa)
hold on
plot(Gb,Hb)