Error "Arrays have incompatible sizes for this operation" when try to integrate

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Hello. This is my entire code, but the relevant part is at the end:
syms kb hbar T c l p k d n m xi q d;
T=300;
hbar=1.054571817*10^(-34);
kb=1.380649*10^(-23);
c=300000000;
d1=1e-7;
N=10;
M=300;
a=load('SiO2Tourne.dat');
w1=a(:,1);
ep1=a(:,2);
eprot1=@(omega) interp1(w1,ep1,omega); %% DIELECTRIC FUNCTION %%
xi_k=@(k) 2.*pi.*kb.*T.*k./hbar;
z=d1./N;
q0=@(xi,q) sqrt(xi.^2./c.^2+q.^2);
q1=@(xi,q) sqrt(xi.^2./c.^2.*eprot1(xi)+q.^2);
q0te=@(xi,q) q0(xi,q);
q1te=@(xi,q) q1(xi,q);
q0tm=@(xi,q) q0(xi,q);
q1tm=@(xi,q) q1(xi,q)./eprot1(xi);
ste0=@(xi,q) 1./[q1te(xi,q)+q0te(xi,q)].*...
[1.*(q0te(xi,q)-q1te(xi,q)) 2.*q1te(xi,q); 2.*q0te(xi,q) q1te(xi,q)-q0te(xi,q)];
ste=@(n,xi,q) 1./[2*q1te(xi,q)].*...
[0 2*exp(-q1(xi,q).*z).*q1te(xi,q); 2*exp(-q1(xi,q).*z).*q1te(xi,q) 0];
steN=@(xi,q) 1./[q0te(xi,q)+q1te(xi,q)].*...
[exp(-2*q1(xi,q).*z).*(q1te(xi,q)-q0te(xi,q)) 2*exp(-q1(xi,q).*z).*q0te(xi,q); 2*exp(-q1(xi,q).*z).*q1te(xi,q) q0te(xi,q)-q1te(xi,q)];
stm0=@(xi,q) 1./[q0tm(xi,q)+q1tm(xi,q)].*...
[q0tm(xi,q)-q1tm(xi,q) 2*q1tm(xi,q); 2*q0tm(xi,q) -q0tm(xi,q)+q1tm(xi,q)];
stm=@(n,xi,q) 1./[2*q1tm(xi,q)].*...
[0 2*exp(-q1(xi,q).*z).*q1tm(xi,q); 2*exp(-q1(xi,q).*z).*q1tm(xi,q) 0];
stmN=@(xi,q) 1./[q0tm(xi,q)+q1tm(xi,q)].*...
[exp(-2*q1(xi,q).*z).*(q1tm(xi,q)-q0tm(xi,q)) 2*exp(-q1(xi,q).*z).*q0tm(xi,q); 2*exp(-q1(xi,q).*z).*q1tm(xi,q) q0tm(xi,q)-q1tm(xi,q)];
f11=@(x,y) x(1,1)+x(1,2)./[1-y.*x(2,2)].*y.*x(2,1);
for m=0:M-1
temp_te=@(q) 1./(q0te(xi_k(m),q)+q1te(xi_k(m),q)).*(exp(-2*q1(xi_k(m),q).*z).*(q1te(xi_k(m),q)-q0te(xi_k(m),q)));
temp_tm=@(q) 1./(q0tm(xi_k(m),q)+q1tm(xi_k(m),q)).*(exp(-2*q1(xi_k(m),q).*z).*(q1tm(xi_k(m),q)-q0tm(xi_k(m),q)));
for n=N-1:-1:1
S11te=@(q) f11(ste(n,xi_k(m),q),temp_te(q));
temp_te=@(q) S11te(q);
S11tm=@(q) f11(stm(n,xi_k(m),q),temp_tm(q));
temp_tm=@(q) S11tm(q);
end
S11te=@(q) f11(ste0(xi_k(m),q),temp_te(q));
temp_te=@(q) S11te(q);
S11tm=@(q) f11(stm0(xi_k(m),q),temp_tm(q));
temp_tm=@(q) S11tm(q);
rte{m+1}=temp_te;
rtm{m+1}=temp_tm;
end
g=@(k,q,d) q.*q0(xi_k(k),q).*((exp(2.*q0(xi_k(k),q).*d)./(rte{k+1}(q).^2)-1).^(-1)+...
(exp(2.*q0(xi_k(k),q).*d)./(rtm{k+1}(q).^2)-1).^(-1));
add=@(k,d) quadgk(@(q) g(k,q,d),0,Inf);
Now, when I try to evaluate the function "add" for some specific values I get the following error message:
Arrays have incompatible sizes for this operation.
Error in
untitled>@(xi,q)1./[q1te(xi,q)+q0te(xi,q)].*[1.*(q0te(xi,q)-q1te(xi,q)),2.*q1te(xi,q);2.*q0te(xi,q),q1te(xi,q)-q0te(xi,q)]
(line 38)
ste0=@(xi,q) 1./[q1te(xi,q)+q0te(xi,q)].*...
Error in untitled>@(q)f11(ste0(xi_k(m),q),temp_te(q)) (line 78)
S11te=@(q) f11(ste0(xi_k(m),q),temp_te(q));
Error in untitled>@(q)S11te(q) (line 79)
temp_te=@(q) S11te(q);
Error in
untitled>@(k,q,d)q.*q0(xi_k(k),q).*((exp(2.*q0(xi_k(k),q).*d)./(rte{k+1}(q).^2)-1).^(-1)+(exp(2.*q0(xi_k(k),q).*d)./(rtm{k+1}(q).^2)-1).^(-1))
(line 95)
g=@(k,q,d) q.*q0(xi_k(k),q).*((exp(2.*q0(xi_k(k),q).*d)./(rte{k+1}(q).^2)-1).^(-1)+...
Error in @(q)g(k,q,d)
Error in quadgk/evalFun (line 330)
fx = FUN(x);
Error in quadgk/f2 (line 361)
[y,too_close] = evalFun(t2t);
Error in quadgk/vadapt (line 249)
[fx,too_close] = f(x);
Error in quadgk (line 196)
[q,errbnd] = vadapt(@f2,interval);
Error in @(k,d)quadgk(@(q)g(k,q,d),0,Inf)
Related documentation
The same thing happens using "integral" instead of "quadgk". I partly solved the issue using the "integral" function and putting the optional inputs "'arrayvalue',true". In such a way the code works but it is too slow for the next computations, so I would like to solve the problem more efficiently.

Accepted Answer

Walter Roberson
Walter Roberson on 6 Jul 2022
quadgk and integral pass in vectors for the first parameter.
@(xi,q)1./[q1te(xi,q)+q0te(xi,q)].*[1.*(q0te(xi,q)-q1te(xi,q)),2.*q1te(xi,q);2.*q0te(xi,q),q1te(xi,q)-q0te(xi,q)]
Because q is a vector, q1te and q0te are vectors so the left [] calculates a vector. The right [] thinks that it is building a 2x2 array but because q is a vector it is building something that is larger than 2x2... something that is not compatible for .* purposes with the left []
You need to use arrayvalued, or you need to reorganize your logic. For example perhaps you could build the right [] in the third dimension
  4 Comments
Walter Roberson
Walter Roberson on 6 Jul 2022
Remember that MATLAB itself does not have type declarations. When you assign to an unindexed variable, the variable becomes whatever the type of the right hand side is.

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