Fitting data with integral function

I want to fit an ensemble (t,Y) of data by a function defined as an integral

$$

f(x)=\int{\frac{A}{1+A*x*y}dy,0,10}

$$

where A is a parameter to be fitted on the data.

I tried something as follows

% t and y are previously defined as two array of numbers
syms z
f = @(x,xdata,z) x(1)/(1+x(1)*xdata*z);
fit = @(x,xdata) int(f(x,xdata,z),[0, 10]);
x0 = [1];
[x,resnorm,~,exitflag,output] = lsqcurvefit(fit,x0,t,y);

Unfortunately, the software available in my university is in Japanese, and I can't understand the error message. From my understanding, at least two things are problematic

• I don't know if "int" can be used this way. For instance, I don't understand how to declare the variable on which the integral should be performed. I copied the MWE from https://fr.mathworks.com/help/symbolic/int.html
• I don't know if "fit" can indeed be used as a fitting function.

Thank you for your help

Answer 1

[Torsten]

Try

f = @(x,xdata,z) x(1)./(1+x(1)*xdata*z);
fit = @(x,xdata) integral(@(z)f(x,xdata,z),0,10,'ArrayValued',true);
x0 = 1;
[x,resnorm,~,exitflag,output] = lsqcurvefit(fit,x0,t,y);

Don't use z as symbolic variable now since you use integral instead of int.

Best wishes

Torsten.

[Daniel Suchet]

Thank you for your answer.

I tried your proposal and received the following code (I found a way to get error messages in english eventually)

??? Undefined function or method 'integral' for input arguments of type
'function_handle'.
Error in ==> @(x,xdata)integral(@(z)f(x,xdata,z),0,10,'ArrayValued',true)
Error in ==> lsqcurvefit at 209
            initVals.F = feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:});
Error in ==> NDRfit at 73
[x,resnorm,~,exitflag,output] = lsqcurvefit(fit,x0,y,t);
Caused by:
    Failure in initial user-supplied objective function evaluation. LSQCURVEFIT cannot
    continue.

[Walter Roberson]

It sounds as if you might be using a version before R2012a. For versions before that you should see quadgk() or quadl() or quad()