Output of MATLAB Curve Fitting Toolbox does not match generated function

Question

A similar question has been answered in the past, but my part of their question was not answered ( Matlab curve fitting tool, cftool, generate code function does not give the same fit ).

I have a set of data points that are meant to show the "ideal" curve for the mechanism I am studying.

When I ask the Curve Fitting Toolbox in Matlab to find a 2-term exponential, I get a great fit (R-square: 0.9998, Adjusted R-square: 0.9997). However, when I generate code for this fit, it changes the coefficients a, b, c and d.

In the toolbox, it displays:

General model Exp2:

  f(x) = a*exp(b*x) + c*exp(d*x) 

Coefficients (with 95% confidence bounds):

  a = 4.698e+04 (-1.477e+13, 1.477e+13) b = 0.4381 (-1200, 1201) c = -4.698e+04 (-1.477e+13, 1.477e+13) d = 0.4381 (-1200, 1201) 

Goodness of fit:

SSE: 0.002979

R-square: 0.9998

Adjusted R-square: 0.9997

RMSE: 0.006823

Function generated by the curve-fitting toolbox:

function [fitresult, gof] = createFit1(bgSt, testSt)
%CREATEFIT1(BGST,TESTST)
%  Create a fit.
%
%  Data for 'standard mechanism' fit:
%      X Input : bgSt
%      Y Output: testSt
%  Output:
%      fitresult : a fit object representing the fit.
%      gof : structure with goodness-of fit info.
%
%  See also FIT, CFIT, SFIT.

%  Auto-generated by MATLAB on 29-Apr-2015 15:54:07


%% Fit: 'standard mechanism'.
[xData, yData] = prepareCurveData( bgSt, testSt );

% Set up fittype and options.
ft = fittype( 'exp2' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.935605768794225 0.667093185616236 0 0.667093185616236];

% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );

% Plot fit with data.
figure( 'Name', 'standard mechanism' );
h = plot( fitresult, xData, yData );
legend( h, 'testSt vs. bgSt', 'standard mechanism', 'Location', 'NorthEast' );
% Label axes
xlabel bgSt
ylabel testSt
grid on

Notice that the coefficients are completely different, as are the curves generated.

Notice also that for coefficients displayed in the curve-fitting toolbox, c = -a and d = b, so that y should equal zero for any value of x, which is ludicrous.

But when I edit the generated function to replace the function's coefficients with the coefficients from the toolbox, I get a good curve.

Edited code:

function [fitresult, gof] = standardFit(bgSt, testSt)
%STANDARDFIT(BGST,TESTST)
%  Create a fit.
%
%  Data for 'standard mechanism' fit:
%      X Input : bgSt
%      Y Output: testSt
%  Output:
%      fitresult : a fit object representing the fit.
%      gof : structure with goodness-of fit info.
%
%  See also FIT, CFIT, SFIT.

%  Auto-generated by MATLAB on 29-Apr-2015 15:54:07

%FROM CURVE FITTING TOOLBOX:
%General model Exp2:
%     f(x) = a*exp(b*x) + c*exp(d*x)
%Coefficients (with 95% confidence bounds):
%       a =   4.698e+04  (-1.477e+13, 1.477e+13)
%       b =      0.4381  (-1200, 1201)
%       c =  -4.698e+04  (-1.477e+13, 1.477e+13)
%       d =      0.4381  (-1200, 1201)

%Goodness of fit:
%  SSE: 0.002979
%  R-square: 0.9998
%  Adjusted R-square: 0.9997
%  RMSE: 0.006823


%% Fit: 'standard mechanism'.
[xData, yData] = prepareCurveData( bgSt, testSt );

% Set up fittype and options.
ft = fittype( 'exp2' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [4.698e+04 0.4381 -4.698e+04 0.4381];

% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );

% Plot fit with data.
figure( 'Name', 'standard mechanism' );
h = plot( fitresult, xData, yData );
legend( h, 'testSt vs. bgSt', 'standard mechanism', 'Location', 'NorthEast' );
% Label axes
xlabel bgSt
ylabel testSt
grid on

I don't have enough reputation to post images of the curves, but in the toolbox it looks perfect and the one from the function looks awful - translated in the same way as the linked poster.

Here's variable bgSt:

-2.85 -2.8 -2.75 -2.7 -2.65 -2.6 -2.55 -2.5 -2.45 -2.4 -2.35 -2.3 -2.25 -2.2 -2.15 -2.1 -2.05 -2 -1.95 -1.9 -1.85 -1.8 -1.75 -1.7 -1.65 -1.6 -1.55 -1.5 -1.45 -1.4 -1.35 -1.3 -1.25 -1.2 -1.15 -1.1 -1.05 -1 -0.95 -0.9 -0.85 -0.8 -0.75 -0.7 -0.65 -0.6 -0.55
-0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Here's variable testSt:

0 0.01 0.01 0.02 0.02 0.02 0.03 0.04 0.04 0.05 0.06 0.06 0.07 0.08 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.2 0.21 0.23 0.24 0.26 0.28 0.3 0.31 0.33 0.35 0.37 0.39 0.41 0.43 0.45 0.48 0.5 0.52 0.55 0.57 0.6 0.63 0.66 0.68 0.72 0.74 0.78
0.81 0.85 0.88 0.92 0.96 1 1.04 1.08 1.12 1.17 1.21 1.26 1.3 1.35 1.39 1.44

Edit: I now have enough reputation to add images.

Figure generated by curve fitting toolbox:

Figure generated by automatically-generated function:

Answer 1

I ran into a similar problem using the exponential fit due to how the coefficients were bounded. It's possible that they're bounded in the dialogue, but I don't see where they'd be bounded in the generated code.