THMMY.gr

clear; 
t=[0 : 10^-8 : 9*10^-6]; 
u=26*(exp(-t*(10^5)/3.09)-exp(-t*(10^6)/0.3))*(1-exp(-t*(10^8)/2.17)); 
plot(t,u);

??? Error using ==> mtimes
Inner matrix dimensions must agree.

y = [1.0; 1.2; 0.8; 0.6];

c4=load('c4.mat')
for j=1:numel(c4)
    figure(4)
    stem(c4)
end

lx=length(x);
ly=length(y);
x1(1:2:lx*2-1)=x;
x1(2:2:lx*2)=x+1;
y1(2:2:ly*2)=y;
y1(1:2:ly*2-1)=y;
plot(x1, y1);

lx=length(x);
ly=length(y);
x1(1:2:lx*2-1)=x;
xt=x(2:lx);
xt(lx)=2*x(lx)-x(lx-1);
x1(2:2:lx*2)=xt;
y1(2:2:ly*2)=y;
y1(1:2:ly*2-1)=y;
plot(x1, y1);

phi=0:pi/60:2*pi;
x=repmat([0;5],1,legth(phi));
y=repmat(cos(phi),2,1);
z=repmat(sin(phi),2,1);

tri=delaunay(x,y,z);
trisurf(tri,x,y,z);
axis equal;

R = 42;
phi = 0:pi/60:2*pi;
x = R*cos(phi);
y = R*sin(phi);
plot(x,y);

for i=1:length(u)
        for j=1:length(v)
              Out(u(i),v(j)) = In(I(i),J(j));
        end
    end

Zo=50;
f0=1;
Yo=1/Zo;
R=100;
C=2*10^(-3);
N=201;
GL=1/R;
for f=0:(4*f0/N):(4*f0)
    BL=C*2*pi*f;
    yL=GL/Yo+1i*BL/Yo;
    y1in=Yo*((yL+1i*Yo*tan(2*pi*0.2))/(Yo+1i*yL*tan(2*pi*0.2)));
    y2=Yo*1i*tan(2*pi*0.13);
    y2in=y1in+y2;
    y3in=Yo*((y2in+1i*Yo*tan(2*pi*0.1))/(Yo+1i*y2in*tan(2*pi*0.1)));
    B2=2.7*10^(-3)*2*pi*f;
    b2=B2/Yo;
    yin=y3in+1i*b2;
    G(f)=(Yo-yin)/(Yo+yin);
end

Zo=50;
f0=1;
Yo=1/Zo;
R=100;
C=2*10^(-3);
N=201;
GL=1/R;
j=1;
for f=0:(4*f0/N):(4*f0)
    F(j)=f;
    BL=C*2*pi*f;
    yL=GL/Yo+1i*BL/Yo;
    y1in=Yo*((yL+1i*Yo*tan(2*pi*0.2))/(Yo+1i*yL*tan(2*pi*0.2)));
    y2=Yo*1i*tan(2*pi*0.13);
    y2in=y1in+y2;
    y3in=Yo*((y2in+1i*Yo*tan(2*pi*0.1))/(Yo+1i*y2in*tan(2*pi*0.1)));
    B2=2.7*10^(-3)*2*pi*f;
    b2=B2/Yo;
    yin=y3in+1i*b2;
    G(j)=10*log((Yo-yin)/(Yo+yin));
    if (G(j)<-40)
        G(j)=-40;
    end
    j=j+1;
end

sqrt((real(x)).^2+(imag(x)).^2)

syms theta;
phi=pi/6;
for h=[0 0.1 0.2 0.5 1 2 5]
        y=(sin(theta))^2+ 2*h*cos(theta-phi);
        y1 = sin(theta)*cos(theta)+h*sin(theta-phi);
        y2 = cos(2*theta)+h*cos(theta-phi);
        ezplot(y,[0 2*pi]);

//κάπου εδω θέλω να βρω της ριζες της y1.

        %ezplot(y1,[0 2*pi]);
        %ezplot(y2,[0 2*pi]);
        %hold all;
end

syms theta;
phi=pi/6;
h = 0.1; %paradeigma

        y=(sin(theta))^2+ 2*h*cos(theta-phi);
        y1 = sin(theta)*cos(theta)+h*sin(theta-phi);
        y2 = cos(2*theta)+h*cos(theta-phi);
        ezplot(y,[0 2*pi]);
>> 
>> 
>> 
>> solve(y1,theta)
 
ans =
 
0.046027347431528771078536140575958 + 1.8436655436388304855647095976386e-34*i
 
>> solve(y2,theta)
 
ans =
 
-0.7977431803860713605522195021279
 
>> solve(y,theta)
 
ans =
 
- 0.049895392467347344096156514398011 - 0.41934903901100004962886897809882*i
 
>> 

yy =@(theta) sin(theta).^2+ 2*h*cos(theta-phi);

fsolve(yy,[2 4])

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.

<stopping criteria details>


ans =

    2.7782    3.6048

function [ A ,B] = dixotomos2( func,a,b,l,e)
z=1;
A(z)=a;
A(z)=b;

while (b-a)>l
    x1=(a+b)/2 -e;
    x2=(a+b)/2 +e;
    if func(x1)<func(x2)
        A(z+1)=a;
        B(z+1)=x2;
    else
        A(z+1)=x1;
        B(z+1)=b;
    end
 z=z+1;  
    
end

end

function [ak,bk] = dichotomy_method( l,e,a )

a1=0;
b1=4;

if(a==1)
    while(b1-a1>=l)
        x1=(a1+b1)*0.5-e;
        x2=(a1+b1)*0.5+e;
        if((x1-1)^2+cos(x1)<(x2-1)^2+cos(x2))
            b1=x2;
        else
            a1=x1;
        end;
    end;
            ak=a1;
            bk=b1;
else if(a==2)
    while(b1-a1>=l)
        x1=(a1+b1)*0.5-e;
        x2=(a1+b1)*0.5+e;
        if((x1+4)^0.5+(x1^2-6)*ln(x1+1)<(x2+4)^0.5+(x2^2-6)*ln(x2+1))
            b1=x2;
        else
            a1=x1;
        end;
    end;
ak=a1;
bk=b1;
    end;
end

function X = newton_stathero( x0,y0,e,gk,df,d2f )
%Είσοδος:(x0,y0)το αρχικό σημείο
%e->η σταθερά τερματισμού ε
%το βήμα γκ->εδώ σταθερό
%df->to grad tis f pou thelo na elaxistopoihso->apo cmw
%d2f->o essianos tis f os jacobian(df,v) opou v=[x,y]

k=1;
syms x y;
grad=subs(df,{x,y},{x0,y0});
%ypologismos arxikis timis gia na ksekinisei o algorithmos
%df diastaseis 1x2
%d2f diastaseis 2x2



while norm(grad)>e
    disp(norm(grad));
    grad=subs(df,{x,y},{x0,y0});%se kathe bima
    ess=subs(d2f,{x,y},{x0,y0});% 2x2
    i=inv(ess);%2x2
    dk=-i.*[grad(1);grad(2)];%(2x2)*(2x1)=(2x1)
    x0=x0+gk.*dk(1);
    y0=y0+gk.*dk(2);
    k=k+1;
end;
X(1)=x0;
X(2)=y0;
X(3)=k;


end

function m = LevenbergMarquart( f,x0,y0 )

xk=[x0, y0];
gk=0.5;
e=0.01;
k=1;

gradf=jacobian(f);
hessianf=jacobian(gradf);
gradf=matlabFunction(gradf);
d=eig(hessianf);
a=inv(hessianf);
hessianf=matlabFunction(hessianf);
a=matlabFunction(a);
d=matlabFunction(d);


while norm(gradf(xk(1),xk(2)),2)>=e
    
    
    mk=max(d(xk(1),xk(2)))+10*e;
    syms x y;
    dk=[x ; y];
    sol=(hessianf(xk(1),xk(2))+mk*eye(2))*dk+gradf(xk(1),xk(2))';
    [dx ,dy]=solve(sol(1),sol(2));
    
    
    xk=xk+gk*[dx dy]
    
    
    k=k+1;
    
    
    
end

m=xk;

end