Improving chose of guesses in my fit

Question

Yohay 2024-5-30

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编辑： Matt J 2024-6-2

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Hi everyone,

I do some fit on my data, and my guesses is no good enough.

Here an example of plotting my data:

And this is the code of the function that fit my data:

%fit function
function [Xmax,beta] = fit_function(x,y,peaks,t_peaks,peak_num,check_fit)
% ymax calculated analytically with Wolfram Mathematica
ymax = @(b) (2-b(2)/b(1))*(2*b(1)/b(2)-1)^(-b(2)/2/b(1));
modelfun = @(b,x) b(3)/ymax(b)*exp((x-b(4))*(b(1)-b(2))).*sech(b(1)*(x-b(4)));
bguess=[60, 15, peaks(peak_num), x(t_peaks(peak_num))];
%bguesses is [alpha, beta, amplitude, x offset]
%alpha and beta controlling of the slope of the peak, each one of them control in one slope side.
beta = nlinfit(x, y, modelfun, bguess);
Xmax=(log(-1+(2*beta(1)/beta(2)))/(2*beta(1)))+beta(4);
%check fit:
if check_fit==1
    fittedCurve = modelfun(beta, x);
    hold on;
    plot(x, fittedCurve, 'm');
    legend('Original Data','Fitted Curve');
else
end
end

In this fit, I have 4 guesses. The first two of them(call alpha and beta), chosing as a constant number, according to my attempts to see what would be suitable. The other two of them is depend on the data and according to the data, the code chose the appropriate guesses. (actually is the amplitude and x offset)

So, if you look on the code, you see that 60 and 15 is the constant guesses, and the "peaks(peak_num)" and "x(t_peaks(peak_num))", is the guesses that variable according to the maximum point of the data.

The problem is that in some cases,alpha and beta, the two that are constant, sometimes suitable and sometime unsuitable.

I want to insert guesses, that will be change according to the data, exactlly like the last two guesses of the amplitude and x offset. I thinking about derivative of the peaks or something like this, but I managed to mess with it..

do you have idae for good variable guesses or how to do something that will be appropriate to any try of fitting my data?

thank you all (:

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Answer 1

Matt J 2024-5-30

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https://ww2.mathworks.cn/matlabcentral/answers/2123916-improving-chose-of-guesses-in-my-fit#answer_1465341

编辑：Matt J 2024-5-30

It appears from the plot that you are giving nlinfit the data for all peaks simultaneously. You should not be doing that. Rather, you should be extracting the x,y data local to the peak you are currently fitting. Doing so would likely make the fit more robust to the choice of initial guess
The model appears to try fitting both the left and right side of the peak. It seems more prudent to fit the right side of the peak only, which looks like it would follow a much simpler model, e.g., a two-parameter exponential. The left side of the peak looks like a simple jump discontinuity or a linear slope, which needn't be fit explicitly.
If you insist on using your current model, an exhaustive search over alpha and beta should be very tractable. It's only two unknown parameters, and your model function is abundantly vectorizable in alpha and beta.

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Yohay 2024-6-2

@Matt J

Thanks for the advice!

I'm actually begginer in MATLAB, so I'd appreciate some more detailed guidance. I have no problem changing the model of the fit I did, it's just what I was able to do.

In the comment above I explained why I even need the fit, maybe it will help you understand more what I'm trying to do.

1. Are you actually saying cut my data to only the segment of the specific pik at a time? I'm a bit confused about how to do this in the sense of writing the code...

2. I haven't really been able to find a model function to fit these peaks other than this one, if you have an idea how to write it better with fewer variables that would be great.

finally, i need the locations of the picks so I can do error correction with their data, that's all (:

Thank you!

Matt J 2024-6-2

编辑：Matt J 2024-6-2

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You can use findpeaks for peak detection. Then you can extract the i-th inter-peak data by doing,

I=peaks(i):peaks(i+1)-5;
xi=x(I);
yi=y(I);

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Answer 2

Sarthak 2024-5-30

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移动：Image Analyst 2024-5-31

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You can try to determine the values of the constant guesses based on the data and use a peak detection algorithm to identify the peaks in the data and then calculate the derivatives at those peak points. The values of alpha and beta can then be set based on the properties of the peaks and their derivatives.

Here's an example of how you can modify your code:

function [Xmax, beta] = fit_function(x, y, peaks, t_peaks, peak_num, check_fit)
    % Calculate the derivatives of the data
    dy = diff(y);
    dx = diff(x);
    derivatives = dy ./ dx;
    % Find the peaks in the data
    [~, peak_indices] = findpeaks(y);
    % Calculate the average derivative at the peak points
    avg_derivative = mean(derivatives(peak_indices));
    % Calculate the values of alpha and beta based on the average derivative
    alpha = avg_derivative / 2;
    beta = 2 * alpha;
    % Use the calculated values of alpha and beta in the model function
    ymax = @(b) (2 - b(2) / b(1)) * (2 * b(1) / b(2) - 1)^(-b(2) / 2 / b(1));
    modelfun = @(b, x) b(3) / ymax(b) * exp((x - b(4)) * (b(1) - b(2))) .* sech(b(1) * (x - b(4)));
    bguess = [alpha, beta, peaks(peak_num), x(t_peaks(peak_num))];
    % Fit the data using the modified guesses
    beta = nlinfit(x, y, modelfun, bguess);
    Xmax = (log(-1 + (2 * beta(1) / beta(2))) / (2 * beta(1))) + beta(4);
    % Plot the fitted curve if check_fit is true
    if check_fit == 1
        fittedCurve = modelfun(beta, x);
        hold on;
        plot(x, fittedCurve, 'm');
        legend('Original Data', 'Fitted Curve');
    end
end