How to enter a sigmoidal equation for a curve fit with lsqfitting

Question

Wilfredo 2023-12-9

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https://ww2.mathworks.cn/matlabcentral/answers/2058529-how-to-enter-a-sigmoidal-equation-for-a-curve-fit-with-lsqfitting

评论： Wilfredo 2023-12-11

he tratado de ingresar esta ecuación sigmoidal para un ajunste de curva lsqcurvefit con esta ecuación

y=1/(1+exp(4a(b-X)+2))
fun=@(x,xdata)1./(1+exp(4.*x(1).*(x(2) - xdata)+2)) 
x=lsqcurvefit(fun,x0,xdata,ydata)

he podido leer los datos aunque no he podido hacer los ajustes, al parecer reconoce al exponecial pero no los ajuste con X(1) y x(2).

alquien me podra ayudar con este tema

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Matt J 2023-12-10

You haven't provided the data we would need to run the code. Most likely, though, the problem is your x0 has been chosen randomly (and therefore, poorly).

Wilfredo 2023-12-10

Gracias Matt J, x0= [0 5900] puede ser que aqui este el error entonces.

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Answer 1

Image Analyst 2023-12-9

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https://ww2.mathworks.cn/matlabcentral/answers/2058529-how-to-enter-a-sigmoidal-equation-for-a-curve-fit-with-lsqfitting#answer_1368679

See my attached demo where I fit data to the rate equation (a sigmoid type of formula).

Adapt as needed, like using a different sigmoid formula. If you have problems, write back and attach your data and m-file.

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Image Analyst 2023-12-10

在 MATLAB Online 中打开

OK, I adjusted the formula slightly to make some of your constants variables and now the fit is pretty good.

% Demo by Image Analyst.

clc; % Clear the command window.

close all; % Close all figures (except those of imtool.)

clear; % Erase all existing variables. Or clearvars if you want.

workspace; % Make sure the workspace panel is showing.

format short g;

format compact;

fontSize = 15;

markerSize = 6;

X = ...

[0 270 450 720 990 1170 1440 1710 1890 2520 3150 3690 4320 4950 5850 6750 7650 8550 10350 12150];

Y = ...

[0.00115 0.00115 0.00115 0.00115 0.00115 0.00115 0.00115 0.00115 0.00115 0.00115 0.000865 0.00202 0.00317 0.00533 0.0098 0.01326 0.01571 0.01744 0.02032 0.02104];

plot(X, Y, 'b.-', 'MarkerSize', 30);

grid on;

xlabel('X', 'FontSize', fontSize);

ylabel('Y', 'FontSize', fontSize);

title('Data to fit exponential to', 'FontSize', fontSize);

% Maximize the figure.

hFig2.WindowState = 'maximized';

drawnow;

% Convert X and Y into a table, which is the form fitnlm() likes the input data to be in. Use (:) to reshape data into column vectors.

tableXY = table(X(:), Y(:));

%-----------------------------------------------------------------------------------------------------------------------------------

% y = c1 / (c2 + exp(c3*(c4 + c5*X))))

% Make a model. B are the coefficients

modelFunction = @(b, tbl) b(1) ./ (b(2) + exp(b(3) .* (b(4) - b(5) .* tbl(:, 1))));

beta0 = [.021, 1, .0004, 11000, 2]; % Guess values to start with. Just make your best guess.

% Once you get close and see what the coefficients are, you can set beta0 to those values and

% Make another run to get better coefficients.

% Now the next line is where the actual model computation is done.

model1 = fitnlm(tableXY, modelFunction, beta0);

Warning: The Jacobian at the solution is ill-conditioned, and some model parameters may not be estimated well (they are not identifiable). Use caution in making predictions.

% Now the model creation is done and the coefficients have been determined.

% YAY!!!!

coefficients1 = model1.Coefficients{:, 'Estimate'}

coefficients1 = 5×1

1.0e+00 * 0.020835 0.98745 0.00041504 11474 1.8483

% Create smoothed/regressed data using the model:

yFitted = coefficients1(1) ./ (coefficients1(2) + exp(coefficients1(3) .* (coefficients1(4) - coefficients1(5) .* X)));

% Now we're done and we can plot the smooth model as a red line going through the noisy blue markers.

hold on;

plot(X, yFitted, 'r-', 'LineWidth', 2);

grid on;

title('Fitting Noisy Data to the Equation', 'FontSize', fontSize);

drawnow;

Is there a theoretical basis for why you chose this particular sigmoid formula? Like it models well the physics of your experiment, or is it just one that you heard of?

Wilfredo 2023-12-11

Hello friend, thank you very much for your help, it helps me a lot, for the values I expect are for A=0.000186865 and B=3524.

Wilfredo 2023-12-11

throws up the following error.

Warning: The Jacobian at the solution is ill-conditioned, and some model parameters may not be estimated well (they are not

identifiable). Use caution in making predictions.

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How to enter a sigmoidal equation for a curve fit with lsqfitting

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