The code provided currently fits a quadratic curve using MATLAB’s “nlinfit” function, which is not a sigmoid function. If the intention is to fit a sigmoid curve and also retrieve its inverse (to estimate input values from the output), the approach can be adapted accordingly.
A sigmoid function typically has the form:
y = A / (1 + exp(-k*(x - x0)))
Where:
- A is the maximum value (upper asymptote),
- k determines the steepness of the curve,
- x0 is the midpoint (inflection point).
This function can be fitted using “nlinfit”, and once the parameters are estimated, the inverse can be analytically defined and used as needed. It is important to ensure that the output values passed into the inverse function lie within a valid range to avoid mathematical errors.
Please refer the following MATLAB implementation for the same:
% Sample data (sigmoid shape)
x = linspace(0, 10, 50)';
y = 10 ./ (1 + exp(-1.5*(x - 5))) + 0.5*randn(size(x)); % Sigmoid with noise
% Define sigmoid function
sigmoid = @(F, x) F(1) ./ (1 + exp(-F(2)*(x - F(3))));
% Initial parameter guesses: [Amplitude, Slope, Midpoint]
F0 = [max(y), 1, mean(x)];
% Fit using nlinfit
F_fitted = nlinfit(x, y, sigmoid, F0);
% Define inverse sigmoid function
inverseSigmoid = @(y_val) F_fitted(3) - (1/F_fitted(2)) * log(F_fitted(1)./y_val - 1);
% Plot original fit
figure;
plot(x, y, 'bo'); hold on;
x_fit = linspace(min(x), max(x), 200);
plot(x_fit, sigmoid(F_fitted, x_fit), 'r', 'LineWidth', 2);
legend('Data', 'Sigmoid Fit');
xlabel('x'); ylabel('y'); title('Sigmoid Curve Fit');
% Plot inverse
y_vals = linspace(0.01*F_fitted(1), 0.99*F_fitted(1), 200);
x_est = inverseSigmoid(y_vals);
figure;
plot(y_vals, x_est, 'k', 'LineWidth', 2);
xlabel('y'); ylabel('Estimated x'); title('Inverse of Sigmoid Fit');
Please refer to the below MATLAB documentation to know more about sigmoid function:
I hope this helps you start!
