How do I get normal numerical answers using solve or vpasolve?

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I'm currently making a function within which I determine a Reflectivity value by solving the equation using solve().
However, the answers given are always values of pi, how do I solve this?
[Result, y] = lorentz(0, 0.725, 15)
function [Result, y] = lorentz(position, CavityLength, BaseRD)
%Enter position, cavity length in m and baserd in microseconds.
c = 299792458; %speed of light in m/s
BaseRD = BaseRD*10^-6;
syms Reflectivity
S = vpasolve(((pi*sqrt(Reflectivity))/(1-Reflectivity))/(c/(2*CavityLength)) == BaseRD, Reflectivity, [0.99 1]);
Result.Reflectivity = S;
Result.Finesse = (pi*sqrt(Result.Reflectivity)/(1-Result.Reflectivity));
Result.FSR = c/(2*CavityLength);
FWHM = Result.FSR./Result.Finesse;
Result.HWHM = FWHM/2;
x = linspace(-1e3,1e3,1e5);
y = (1/pi).*(Result.HWHM./(((x-position).^2)+Result.HWHM.^2));
%y = y.*(height/max(y));
%plot(x,y)
end
Reflectivity: 0.99898752118560808161741982765188
Finesse: 987.1748605317811539461548191278*pi
FSR: 206753419.310345
HWHM: 104719.75511965978378924223514237/pi
  5 Comments
Ben van Zon
Ben van Zon on 30 Nov 2023
Edited: Ben van Zon on 30 Nov 2023
Using this:
c = 299792458;
CavityLength = 0.725;
Pi = sym(pi, 'd');
syms Reflectivity
S = vpasolve(((Pi*sqrt(Reflectivity))/(1-Reflectivity))/(c/(2*CavityLength)) == 14.7E-6, Reflectivity, [0.99 1])
S = 
0.99896686903182896436436014196862
I get the answer I'm looking for.
Dyuman Joshi
Dyuman Joshi on 30 Nov 2023
The BaseRD value is different. And you get your answer.
Also, your comment was marked spam by the Auto Filter, idk how. I have removed the spam notice, and subsequently your flag as well.

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Accepted Answer

Walter Roberson
Walter Roberson on 30 Nov 2023
Use sym(pi,'d') instead of pi
Or...
use sympref to set floating point output on
Or...
Use vpa
Or...
Use double. For example,
structfun(@double, Result, 'uniform', 0)

More Answers (1)

John D'Errico
John D'Errico on 30 Nov 2023
vpa will turn those products involving pi into more normal looking numbers. For example...
x = 17*sym(pi)
x = 
So x has pi in it.
vpa(x)
ans = 
53.407075111026485053864937515752
vpa yields a symbolic high precision floating point number. But double will also work, and create a double as a result.
double(x)
ans = 53.4071

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