Fitting data to integral2 function

Hello everybody,

I need to fit my datas which are (xdata,ydata) by the following equation :

B is the independant variable (corresponding to xdata), M is the dependant variable (corresponding to ydata),

Msat, NmB/kT and Ea/kT are the fitting parameters (called x(1), x(2) and x(3) in the following)

I managed to fit manualy my data with the function by choosing manually x(1), x(2) and x(3), using the following code :

x=[0.23,5.5,10.5];

fun=@(xdata)arrayfun(@(xdata)x(1).*integral2(@(th,ph)sin(th).*cos(th).*exp(x(2).*xdata.*cos(th)+x(3).*(sin(th0).*sin(th).*cos(ph)+cos(th0).*cos(th)).^2),0,pi,0,2*pi)./integral2(@(th,ph)sin(th).*exp(x(2).*xdata.*cos(th)+x(3).*(sin(th0).*sin(th).*cos(ph)+cos(th0).*cos(th)).^2),0,pi,0,2*pi),xdata)

ydatafit=fun(xdata);

plot(xdata,ydatafit,'-r')

this gives :

My question is how can I fit automatically ?

I tried this code :

fun=@(x,xdata)arrayfun(@(xdata)x(1).*integral2(@(th,ph)sin(th).*cos(th).*exp(x(2).*xdata.*cos(th)+x(3).*(sin(th0).*sin(th).*cos(ph)+cos(th0).*cos(th)).^2),0,pi,0,2*pi)./integral2(@(th,ph)sin(th).*exp(x(2).*xdata.*cos(th)+x(3).*(sin(th0).*sin(th).*cos(ph)+cos(th0).*cos(th)).^2),0,pi,0,2*pi),xdata)

x0 = [0.23,5.5,10.5];

x = lsqcurvefit(fun,x0,xdata,ydata)

plot(xdata,ydata,'ko',xdata,fun(x,xdata),'b-')

And I get these errors :

warning: quad2d: Maximum number of sub-tiles reached without convergence

warning: called from

quad2d at line 329 column 7

integral2 at line 230 column 12

@<anonymous> at line 9 column 168

@<anonymous> at line 9 column 15

nonlin_curvefit>@<anonymous> at line 84 column 14

__nonlin_residmin__ at line 585 column 9

nonlin_curvefit at line 83 column 18

lsqcurvefit at line 231 column 19

error: dimensions of observations and values of model function must match

error: called from

__nonlin_residmin__ at line 590 column 7

nonlin_curvefit at line 83 column 18

lsqcurvefit at line 231 column 19

>> plot(xdata,ydata,'ko',xdata,fun(x,xdata),'b-')

error: 'x' undefined near line 1 column 33

Thank you in advance for your answer !!!

[Torsten]

Write a function in which you calculate M. Then it's easier for you to debug what your problem is.

[rom3413]

That's what I have done, the M function is called fun in my code.

I can plot it as a function of xdata by fixing manually paremeters x(1), x(2) and x(3).

But I didn't manage to obtain x(1), x(2) and x(3) by fitting fun to my datas

Answer 1

[Torsten]

x0 = [0.23,5.5,10.5];
th0 = ...;
x = lsqcurvefit(@(x,xdata)fun(x,xdata,th0),x0,xdata,ydata)

function res = fun(x,xdata,th0)
  for i = 1:numel(xdata)
    xdata_actual = xdata(i);
    numerator = x(1)*integral2(@(th,ph)sin(th).*cos(th).*exp(x(2).*xdata_actual.*cos(th)+x(3).*(sin(th0).*sin(th).*cos(ph)+cos(th0).*cos(th)).^2),0,pi,0,2*pi);
    denominator = integral2(@(th,ph)sin(th).*exp(x(2).*xdata_actual.*cos(th)+x(3).*(sin(th0).*sin(th).*cos(ph)+cos(th0).*cos(th)).^2),0,pi,0,2*pi);
    res(i) = numerator/denominator;
  end
end  

[rom3413]

It returns the same error...

warning: quad2d: Maximum number of sub-tiles reached without convergence

warning: called from

quad2d at line 329 column 7

integral2 at line 230 column 12

fun at line 4 column 15

@<anonymous> at line 1 column 27

nonlin_curvefit>@<anonymous> at line 84 column 14

__nonlin_residmin__ at line 585 column 9

nonlin_curvefit at line 83 column 18

lsqcurvefit at line 231 column 19

error: dimensions of observations and values of model function must match

error: called from

__nonlin_residmin__ at line 590 column 7

nonlin_curvefit at line 83 column 18

lsqcurvefit at line 231 column 19

Maybe you can reproduce the error, thus here attached is the ydata file (MH60.txt)

I add an offset of 0.012 to have roughly ydata (-inf)=-ydata(+inf)

ydata=MH60(:,1)+0.012;

xdata=linspace(-6.4,6.4,129);

[rom3413]

you also need th0

th0=70*pi/180