Custom Fit - Error Functions

Hi All,

So I am trying to fit a series of error functions, and it is not coming up with viable answers. I am using simulated data that I know fits error functions, but the answers it is coming up with are worse fits than linear.

The code I have for the fit is, where N is the number of error functions, and X and Y are the data (Y is normalized). It's not throwing any errors, just the fit is terrible, and it does not seem to be going about it correctly (my initial guesses are better than its result):

    %construct equation string
    expression = '';
    coefficients = {};
    for index = 1:N
        expression = [expression, '(1/2)*(1+erf( (x-mu', num2str(index) ,').^2 / sqrt(2*sigma', num2str(index), '.^2) )) +'];
        coefficients = [coefficients {['mu', num2str(index)]} {['sigma', num2str(index)]}];
    end
    %cut off the last + sign
    expression(end) = [];

    %construct reasonable initial values by dividing the span up evenly
    span = max(X) - min(X);
    mu0 = min(X) + (span/N * (1/2):1:(N-1/2));
    sigma0 = span/(2*N);
    startpoint = zeros(1,2*N); %initial guess
    LB = zeros(1,2*N); %lower bounds
    UB = zeros(1,2*N); %upper bounds
    for index = 1:N
        startpoint(2*index-1) = mu0(index);
        startpoint(2*index) = sigma0;
        LB(2*index-1) = min(X);
        LB(2*index) = span*10^-5;
        UB(2*index-1) = max(X);
        UB(2*index) = 2*span;
    end

    %fit
    f = fittype(expression, 'coefficients', coefficients, 'independent', {'x'}, 'dependent', {'y'});
    [fitobj, gof] = fit(X,Y,f, 'StartPoint', startpoint, 'Lower', LB, 'Upper', UB);

    rmserror = gof.rmse;
    rsquared = gof.rsquare;

    %to debug
    figure;
    plot(X,Y, 'o');
    hold on;
    plot(X,fitobj(cdfx), 'Color', 'red' , 'LineWidth', 1.5)
    hold off

When I use the curve fit toolbox, it also has difficulty with this fit. I have attached some data you can use for X and Y (X is first column, Y is second).

Thanks for any help!

[Erik Schiferle]

Hi,

Any chance you could send your example data to me. And both exponents were supposed to be taken out? I'm trying to do something very similar

Answer 1

[Darin]

Nevermind - I have squared in my expression that shouldn't be there, woops! Sorry! At least this code is helpful if anyone wants to do the same.