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

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Ben van Zon
Ben van Zon 2023-11-30
评论： Dyuman Joshi 2023-11-30
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
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Ben van Zon
Ben van Zon 2023-11-30
编辑：Ben van Zon 2023-11-30
Ran in:
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 2023-11-30
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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采纳的回答

Walter Roberson
Walter Roberson 2023-11-30
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)

更多回答（1 个）

John D'Errico
John D'Errico 2023-11-30
Ran in:
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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