plot piecewise 3d function

Hey, my code is

if
clear
hbar = 6.582119e-01; % Planck constant (meV ps)
clf reset;
Delta = 1.0;
tau = 0.5;
o = 3./hbar;
A = 1;
[omega,d] = meshgrid(0:0.25:7,0:0.25:7);
syms k(omega) l_1(omega) l_2(omega) 
k_0 = (omega-2.*Delta)./(omega+2.*Delta);
k(omega) = piecewise(2.*Delta<= omega, k_0, 0);                % the 0 is just random to stay inside the definition interval of the elliptic functions; later I cut them off by the heaviside function
l_1_0 = (o-omega-2.*Delta)./(-omega+o+2.*Delta);
l_1(omega) = piecewise(o-2.*Delta<= omega, l_1_0, 0);
l_2_0 = (omega-o-2.*Delta)./(omega-o+2.*Delta);
l_2(omega) = piecewise(o+2.*Delta<= omega, l_2_0, 0);
[K,E] = ellipke(k(omega));
[L_1,F_1] = ellipke(l_1(omega));
[L_2,F_2] = ellipke(l_2(omega));
Resi_0 = pi./8.*((1+2.*Delta./omega).*E-(4.*Delta./omega).*K).*heaviside(omega-2.*Delta);
Resi_l_1 = -2.*pi./8.*A.*(((1+2.*Delta./(o-omega)).*L_1-(4.*Delta./(o-omega).*F_1).*heaviside(o-omega-2.*Delta)).*sin(o.*d));
Resi_l_2 = 2.*pi./8.*A.*(((1+2.*Delta./(omega-o).*L_2-4.*Delta./(omega-o).*F_2).*heaviside(omega-o-2.*Delta)).*sin(o.*d));
Resigma = Resi_0 + Resi_l_1 + Resi_l_2; 
plot3(d,omega,Resigma); % I tried plot3 and fplot3, both with the same error
hold on
view(-35,45)
axis([-.5 10.5 -.5 10.5 0 1.5])
hold off
end

I really don't understand why matlab doesn't want to do what I want it to do...the error I get is:

if true
  Error using plot3
Data must be numeric, datetime, duration or an array convertible to double.
Error in gamma (line 30)
plot3(d,omega,Resigma);
end

I would really appreciate any kind of help...

Answer 1

[Jason Whitfield]

In your code, the following line will overwrite your "omega" variable with a symbolic variable.

syms k(omega) l_1(omega) l_2(omega)

You can fix this issue by replacing the "omega" variable in your symbolic functions with some unused name.

[Rebecca Müller]

Thanks, I did so (I just called k(omega) k, l_1(omega) l_1,..), but now I get the error:

if
  Undefined function 'piecewise' for input arguments of type 'double'.
Error in gamma (line 14)
k = piecewise(2.*Delta<= omega, k_0, 0);
end

[Jason Whitfield]

Your symbolic functions still need to have a parameter, it just can't be called "omega." You could call it "x" instead. Then, the first function would look something like this:

syms k(x) l_1(x) l_2(x) 

k_0 = (x-2.*Delta)./(x+2.*Delta);
k(x) = piecewise(2.*Delta<= x, k_0, 0);

[K,E] = ellipke(k(omega));

[Rebecca Müller]

with the replacement you suggested before editing your first answer:

if 
   k_0 = (omega-2.*Delta)./(omega+2.*Delta );
k(omega) = piecewise(2.*Delta<= omega, k_0, 0 );
[K,E] = ellipke(k(omega));

Would become this:

k = (omega-2.*Delta)./(omega+2.*Delta ); k(2.*Delta > omega) = 0 ; [K,E] = ellipke(k); end it worked!!! Thank you very much!!