i need to find the optimize values of R for a values in an interval but R values are in form of the root of the equation; how to solve this sir? for simple equation it was ok.
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syms R a
%t=solve(100*a^16-R^8==0,R)
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==0,R)
%a=(.1:.001:5);
a1=1;a2=5;
for i=1:1:8 %because t is representing 8 different R roots of given equation.
n=matlabFunction(t(i,1))
m=fminbnd(n,a1,a2) % finding minimum of every R value
end
0 Comments
Accepted Answer
Torsten
on 30 Jul 2022
Edited: Torsten
on 30 Jul 2022
I think this is the safest way:
syms R a
p = 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;
alow = 1.0;
ahigh = 10.0;
A = alow:0.01:ahigh;
minimum = Inf;
I = 0;
for i = 1:numel(A)
aa = A(i);
pp = subs(p,a,aa);
pp_num = sym2poly(pp);
r = roots(pp_num);
r = r(abs(imag(r)) < 1e-10);
rmin = min(real(r));
RR(i) = rmin;
if rmin < minimum
minimum = rmin;
I = i;
end
end
minimum
A(I)
plot(A,RR)
More Answers (1)
Torsten
on 30 Jul 2022
Edited: Torsten
on 30 Jul 2022
Try "fmincon" for the problem
min: R
s.c.
f(R,a) = 0 (f is the complete expression between "t=solve(" and "==0,R))
a_left <= a <= a_right
f can be prescribed in function "nonlcon".
The unknowns are R and a.
So no need to solve directly for R as a function of a.
5 Comments
Torsten
on 30 Jul 2022
Edited: Torsten
on 30 Jul 2022
sorry R value is 5488.547380 at a=4.44580555360928
Doesn't seem to be correct: R = 5819.0523324 at a = 4.44580555360928.
Maybe there is an error in your "long formula" or there is a problem with the precision of the root calculation.
Yes, the latter will be the case. It's impossible to get reliable roots because the polynomial coefficients in R are of the order 1e-101 !!!!
syms R a
p = 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;
aa = 4.44580555360928;
pp = subs(p,a,aa);
format long
r = double(vpa(root(pp,R)))
pp_num = sym2poly(pp).'
roots(pp_num)
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