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syms f

l=0.1008;

T=0.005;

Dh=0.01;

D1=0.04;

D2=0.16;

x=20*(T*pi*Dh^2/4)/(0.1008*pi*D1^2/4);

c_0=619;

k=2*pi*f/c_0;

t=(0.006+1i*k*(T+0.75*Dh))/x;

Ka=(k^2)-((1i*4*k)/(D1*t));

Kb=(k^2)-((1i*4*k*D1)/((D2^2-D1^2)*t));

Delta=[-1 0 0 0; 0 -1 0 0; 0 0 Ka^2 Ka^2-k^2; 0 0 Kb^2-k^2 Kb^2]

g=eig(Delta);

ee=vpa(g,3)

C1=[1 1 1 1];

C2=[-((g(1,1)^2+Ka^2)/(Ka^2-k^2)) -((g(2,1)^2+Ka^2)/(Ka^2-k^2)) -((g(3,1)^2+Ka^2)/(Ka^2-k^2)) -((g(4,1)^2+Ka^2)/(Ka^2-k^2))];

C3=[1/g(1,1) 1/g(2,1) 1/g(3,1) 1/g(4,1)];

C4=[C2(1,1)/g(1,1) C2(1,2)/g(2,1) C2(1,3)/g(3,1) C2(1,4)/g(4,1)];

A1=[C3(1,1)*exp(g(1,1)*l) C3(1,2)*exp(g(2,1)*l) C3(1,3)*exp(g(3,1)*l) C3(1,4)*exp(g(4,1)*l)];

A2=[C4(1,1)*exp(g(1,1)*l) C4(1,2)*exp(g(2,1)*l) C4(1,3)*exp(g(3,1)*l) C4(1,4)*exp(g(4,1)*l)];

A3=[-exp(g(1,1)*l)/(i*k) -exp(g(2,1)*l)/(i*k) -exp(g(3,1)*l)/(i*k) -exp(g(4,1)*l)/(i*k)];

A4=[-(exp(g(1,1)*l)*C2(1,1))/(i*k) -(exp(g(1,1)*l)*C2(1,2))/(i*k) -(exp(g(1,1)*l)*C2(1,3))/(i*k) -(exp(g(1,1)*l)*C2(1,4))/(i*k)];

E1=[C3(1,1) C3(1,2) C3(1,3) C3(1,4)];

E2=[C4(1,1) C4(1,2) C4(1,3) C4(1,4)];

E3=[1/(i*k) 1/(i*k) 1/(i*k) 1/(i*k)];

E4=[-C2(1,1)/(i*k) -C2(1,2)/(i*k) -C2(1,3)/(i*k) -C2(1,4)/(i*k)]

A=[A1; A2; A3; A4]

I=eye(4);

invA=A\I;

E=[E1; E2; E3; E4];

PP=E*invA;

vpa(PP,3)

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