fit function breaches the lower option limits

I was trying to do fit with a script generated from cftool. It puts lower limit of 0 on all coefficients and the result returned is still negative. I would like to share the dataset but I am new to this forum and I don't find any option of sharing file. Please help me.

Answer 1

[Amol]

0 votes Edit Delete Amol answered less than a minute ago

ok here is the script

    function [cf_,gof]=myfit(tau,avar,weight)
    %MYFIT    Create plot of datasets and fits
    %   MYFIT(TAU,AVAR,WEIGHT)
    %   Creates a plot, similar to the plot in the main curve fitting
    %   window, using the data that you provide as input.  You can
    %   apply this function to the same data you used with cftool
    %   or with different data.  You may want to edit the function to
    %   customize the code and this help message.
    %
    %   Number of datasets:  1
    %   Number of fits:  1
    % Data from dataset "avar vs. tau with weight":
    %    X = tau:
    %    Y = avar:
    %    Weights = weight:
    %
    % This function was automatically generated on 04-Nov-2009 17:20:51
    % --- Create fit "fit 1"
    fo_ = fitoptions('method','LinearLeastSquares','Lower',[0 0 0 0 0]);
    ok_ = isfinite(tau) & isfinite(avar) & isfinite(weight);
    set(fo_,'Weight',weight(ok_));
    if ~all( ok_ )
        warning( 'GenerateMFile:IgnoringNansAndInfs', ...
            'Ignoring NaNs and Infs in data' );
    end
    ft_ = fittype({'1/(x^2)', '1/x', 'x', 'x^2', '1'},...
         'dependent',{'y'},'independent',{'x'},...
         'coefficients',{'a', 'b', 'd', 'e', 'c'});
    % Fit this model using new data
    [cf_,gof] = fit(tau(ok_),avar(ok_),ft_,fo_);
    % Or use coefficients from the original fit:
    %if 0
    %   cv_ = { 2.8012463154944958529e-09, 4.1224210467149593554e-06, -6.2806159338057854499e-10, 1.1525415994665557154e-11, 5.4419882197796621562e-07};
    %   cf_ = cfit(ft_,cv_{:});
    end

and yes I am sorry for a late response. I seems that i need to turn on some option to get email notification from the forum

[Walter Roberson]

By the way, at present the forum does not generate email notifications. There is some support, though, for RSS feeds.

[Walter Roberson]

What magnitude of data are you passing in to be fitted? Looking at those coefficients in the comment, it does not appear to me that your fit is numerically stable.

[Amol]

the x data spans from 10e-2 to 10e6

y data sans from 10-3 to 10

[Walter Roberson]

(1E6)^2 = 1E12

1/(1E6)^2 = 1E-12

You are thus attempting to form systems with a range of 1E24, which is more than can be worked with in binary floating point numbers -- the maximum range is about 1E16.

Therefore you cannot expect to be able to fit your data without calculations that might take some coefficients negative due to round-off error.

[Amol]

is it true unconditionally?

[Walter Roberson]

It is unconditionally true that IEEE Double Precision Binary Floating Point numbers have 53 bits of precision, which is a dynamic range of about 1E-16.

If you need greater precision, then you need to either use the Symbolic Toolbox, or the Fixed Point Toolbox, or the Matlab File Exchange contribution for Variable Precision calculations, vpi . Note though that the functions you are wanting to use are probably not defined with any of these kinds of numeric representation.

[Amol]

thanks