how to find x from a fixed y, when using a sigmoidal fit

HI there

sure this is super simple - but it's making my head hurt

I have a sigmoidal fit - which finds y for any x

But i want to fix y and find x (let's say y = 0.5)

a similar question is asked here https://uk.mathworks.com/matlabcentral/answers/416633-predict-y-values-from-x-values?s_tid=answers_rc1-1_p1_Topic

and one answer does it with fsolve(), but not sure how to make it work with my sigmoidal

fsigm = @(param,xval) param(1)+(param(2)-param(1))./(1+10.^((param(3)-xval)*param(4))); 
param=[0 1 5 1];  % "min", "max", "x50", "slope"
x=0:0.1:10;
y=fsigm(param,x) + 0.1*randn(size(x));

plot(x, y)

%% --------i'm sure i should use something like---------
% x = fsolve(@(x)coeffs(1)*x+coeffs(2)-y_val,0)

Answer 1

[cgenes]

Oh yes I was being dim

of course you just rearrage the formula to solve for x

%-- rearrange the formula
syms param1 param2 param3 param4 x y 
eqn =  (y == param1+(param2-param1)./(1+10.^((param3-x)*param4)));
solx = solve(eqn, x)

%---- vreat function to solve for x 
fsigm_for_x = @(param,y) param(3) - log(-(param(2) - y)/(param(1) - y))/(param(4)*log(10)); 
param=[0 1 5 1];  % "min", "max", "x50", "slope"

x = fsigm_for_x(param, 0.5)