i want to write equation in matlab

   % ampiltude
    function[sign]=amplitude(t,x,y)
    
        sign = 2*A(x^2+y^2)*exp(-0.5*((r/p)^2+(t/T)^2));
    end
    
    
% function
% theta
Theta = @(x,y)atan(y/x);
K=1;
U_txy = Amp(t+T/2,x,y)*exp(iS*Theta)*exp(i*K*t)+Amp(t-T/2,x,y)*exp(iS*Theta)*exp(-i*K*t);

i want to write the above eqautions in matlab.that is my atempt. code wont run. doubt its ok. the function is suspose to be the amplitude, sign.

Answer 1

[Walter Roberson]

format long g
x = randn, y = randn, t = 1.2;

x = 
         0.377605597049117

y = 
         -1.54538132450563

U(x,y,t)

ans = 
      -1.62600857320088e-05 -   3.8121853905296e-06i       7.54974455191625e-06 -  1.31539198710771e-06i

function U_txy = U(x,y,t)     %need this in order to have shared constants

    K = 1;
    A = 7;
    rho = 0.3;
    t0 = 0.81;
    tau = 1.28;
    S = -2.16;
    
    Theta = @(x,y)atan2(y,x);
    r = reshape(sqrt(x.^2+y.^2), [], 1);
    th = reshape(Theta(x,y), [], 1);
    U_txy = amplitude(r,t+t0/2).*exp(1i.*S.*th).*exp(1i*K*t) + ...
            amplitude(r,t-t0/2).*exp(1i.*S.*th).*exp(-1i*K*t).*exp(1i.*th.*[-1 1]);

   % amplitude
    function sign = amplitude(r,t)
         sign = A .* r.^abs(S) .*exp(-0.5*((r./rho).^2 + (t./tau).^2));
    end

end