Need help fitting nonlinear model to data

Hi,

I have a set of data that I would like to fit to the logistical function 1/(A+B*exp(-C*x)). I attempted to to do this by using the function NonLinearModel.fit but for some reason it is not workking.

CODE:

Data = ...

   [0.0000    0.1700
    1.0000    0.2000
    1.5000    0.9900
    1.6000    1.5600
    1.8000    3.5500
    2.0000    4.5200
    2.2500   11.1400
    2.3000   13.2700
    2.4000   16.0000
    2.5500   22.6500
    2.6100   25.3000
    2.7000   29.5700
    2.7500   31.6500
    2.8000   33.9100
    2.9000   39.1300
    2.9400   40.6000
    3.0000   42.5500
    3.1000   45.1200
    3.1500   46.3100
    3.2000   47.1800
    3.3000   48.6300
    3.4500   50.0400
    3.5000   50.3400
    3.5500   50.5500
    3.6000   50.7200
    3.7000   50.9300
    3.8000   51.0400
    3.8800   51.1000
    3.9600   51.1300
    4.0000   51.1400
    4.1000   51.1600
    4.3000   51.1700
    4.6000   51.1800
    5.0000   51.1800];
xData = Data(:,1);
yData = Data(:,2);
x1 = xData';
LF = @(b,xData)(1/(b(1)+b(2)*exp(-b(3)*x1)));
IPP = [0.0185 360 3.5]';
Lmodel = NonLinearModel.fit(xData,yData,LF,IPP);

Here are the errors that are displayed in the command window after running the code:

Error using nlinfit (line 142)

Error evaluating model function '@(b,xData)(1/(b(1)+b(2)*exp(-b(3)*x1)))'.

Error in NonLinearModel/fitter (line 1121)

[model.Coefs,~,J_r,model.CoefficientCovariance,model.MSE,model.ErrorModelInfo,~] = ...

Error in classreg.regr.FitObject/doFit (line 219) model = fitter(model);

Error in NonLinearModel.fit (line 1484) model = doFit(model);

Error in Model (line 48) Lmodel = NonLinearModel.fit(xData,yData,LF,IPP);

_Caused by:

    Error using  / 

    Matrix dimensions must agree._

Any help would be greatly appreciated.

Answer 1

[Alan Weiss]

I think you forgot a dot and a ':

 LF = @(b,xData)(1./(b(1)+b(2)*exp(-b(3)*x1)))';

You need a dot after the 1 because you don't want matrix division, you want elementwise division. You need a ' at the end to make the answer a column.

Alan Weiss

MATLAB mathematical toolbox documentation