MATLAB: Problem with for loop plotting a graph

for loop

Hi I'm really new to Matlab so you'll have to bare with me. I'm trying to plot a graph using the for function but to no avail.
I'm using the following code:
>> for a=2.0:-0.02:0.0
p=[f(a),g(a),h(a),r(a),t(a)] (where f,g,h,r,t are complicated functions of a I don't fancy writing down.)
R=roots(p)
C=imag(R)
c=C(1,1)
….
end
I'm looking to plot the complex part of the first root of each polynomial against each value of a or if its possible plotting the complex part of every root against a for every a on the same graph with different colours representing each root.
Thanks, sorry if the problem is ill described.

Best Answer

The Symbolic Math Toolbox is inefficient for this sort of problem.
Try this: 
U = 1;
B = 0.1;
H = 0.5;
pfcn = @(a) [2*exp(2*a*(1-H)).*(1 - tanh(a*H)), -6*U*(1 + tanh(a*H)).*exp(2*a*(1 - H)) + 2*U*(1 - tanh(a*H)),(7*U^2 *(1 + tanh(a*H)) - 2*B^2 *tanh(a*H)).*exp(2*a*(1 - H)) - 5*U^2 *(1 - tanh(a*H)), exp(2*a*(1 - H)).*(2*U*B^2 *tanh(a*H) - 4*U^3 *(1 + tanh(a*H))) - (2*U*B^2 *tanh(a*H) - 4*U^3 *(1 + tanh(a*H))), U^2 *(U^2 *(1 + tanh(a*H)) - B^2 *tanh(a*H)).*exp(2*a*(1 - H)) - U^2 *(U^2 *(1 - tanh(a*H)) - B^2 *tanh(a*H))];
a=2.0:-0.02:0.0;
for k1 = 1:numel(a)
    p = pfcn(a);
    R = roots(p);
    C(:,k1) = imag(R);
end
figure
plot(a, C, '.')
grid
figure
meshc(C)
grid on
That should tell you all you need to know about the imaginary roots of your function at each ‘a’ value.
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