MATLAB: Error using quad “Error using quad (line 75) The integrand function must return an output vector of the same length as the input vector.”

errorfsolveintegrationMATLAB

I have edited the code according to answers.
Can anyone explain the reason behind the errors and help me correcting the following code:
U = 1;    
e = @(q) 2*(1-cos(2*pi*q));
hq = @(q,n0) ((e(q)).^2+2*U*n0*(e(q))).^0.5;
y = @(q,n0) (((e(q))+(U*n0))/hq(q,n0))-1;
a = -0.5;
b = 0.5;
v = @(n0) quad(@(q) y(q,n0),a,b);
cv =@(n0) n0+(0.5*v(n0))-1;
while U < 20
n0 = 0.1;
options = optimset('Display', 'iter'); 
n = fsolve(cv(n0),n0,0.1,options);
plot(U,n)
hold on 
U = U + 1;
end
Errors:
    Error using quad (line 75)
  The integrand function must return an output vector of the same length as the input vector.
Error in @(n0)quad(@(q)y(q,n0),a,b)
Error in @(n0)n0+(0.5*v(n0))-1
Error in simulv1 (line 12)
n = fsolve(cv(n0),n0,0.1,options);

Best Answer

You forgot to fully vectorise those equations. Change them to:
hq = @(q,n0) ((eq(q)).^2+2*U*n0*(eq(q))).^0.5;
y = @(q,n0) (((eq(q))+(U*n0))./hq(q,n0))-1;
and see if that helps.
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