How can I fit a curve where integration of a function is involved?

My function is like f1 = integral(@(x1)fun(x1,A,B),0,1000); where "fun" has a exponential term and a "ln" term. A,B are constants which would come out after fitting the curve Is there any way to put this equation in matlab curve fitting tools? If it is possible then how can i call the function "fun"?

[Star Strider]

What precisely are you doing?

What are your independent and dependent variables with respect to ‘f1’?

Are you fitting ‘A’ and ‘B’?

[SWAGATA BHUNIA]

f1(m)=integral(@(x1)fun(x1,A,B),0,1000); where fun=(x1,m,A,B); like fun=exp(-A*x^2*ln(B+x))*cos(m*x). I am fitting f1(m) with respect to m. After the fitting the A and B value would come out.

Answer 1

[Torsten]

function fitting
xdata = [...];
ydata = [...];
fun=@(x,xdata,A,B)exp(-A*x.^2.*log(B+x)).*cos(xdata*x);
fun2=@(y)integral(@(x)fun(x,xdata,y(1),y(2)),0,1000,'ArrayValued',true);
y0=[1 1];
y = lsqcurvefit(fun2,y0,xdata,ydata)

Best wishes

Torsten.

Answer 2

[SWAGATA BHUNIA]

I am not getting the plot. It is showing that lsqcurvefit stopped because the final change in the sum of squares relative to its initial value is less than the default value of the function tolerance. I have written the plot command as

times = linspace(xdata(1),xdata(end),1000); plot(xdata,ydata,'ko',times,fun2(y,times),'b-')

How can I remove this problem? I am changing the y0 value but it is showing same.

Answer 3

[Torsten]

Add the lines

ydata_sim = fun2(y);
plot(xdata,ydata,xdata,ydata_sim)

at the end of the code.

Best wishes

Torsten.