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

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

[Dyuman Joshi]

The equation you are solving does not have a solution.

BaseRD = 15;
BaseRD = BaseRD*10^-6;

c = 299792458; %speed of light in m/s

CavityLength = 0.725;

syms x
fun(x) = ((pi*sqrt(x))./(1-x))/(c/(2*CavityLength)) - BaseRD;

%Check the limit
limit(fun, x, Inf)

ans = 

fplot(fun, [0 1e18])

[Ben van Zon]

I am getting the solution for Reflectivity that I need, it is about 0.998988.

However, my problem was getting answers as multiples of pi.

[Dyuman Joshi]

I am aware that your problem was with the symbolic notation of pi.

But I was making another point, which I noticed for the given set of data.

Maybe you got that answer for a different set of data, but for the values noted above, there is no solution.

[Ben van Zon]

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]

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.

Answer 1

[Walter Roberson]

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)

[Ben van Zon]

You were a minute before me finding sym(pi 'd'), thank you!

Answer 2

[John D'Errico]

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