How to do integration over an internal variable in fitfunc?

Integrate1D is used to perform definite integration of a function.

DisplayHelpTopic "Integrate1D"

Are you integrating with respect to the independent variable? If so, you will also want to use an all-at-once fitting function:

DisplayHelpTopic "All-At-Once Fitting Functions"

Thank you. I successfully write the fitting code using Integrate1D but how to determine integration range? What I want to do is integrating from -inf to inf. But when I take large values as integration boundary it is very slow. Codes are attached below:

function PINEMnewfit(w,x): FitFunc
   wave w
   variable x
    //w[0] : coupling
    //w[1] : multii 
    //w[2]:thetaE
    //w[3]:thetaL
    //w[4]:thetae
    //w[5]:chirp
    //w[6]:time0
    //w[7]: time
   variable/g a=w[0],b=w[1],c=w[2],d=w[3],f=w[4],g=w[5],h=w[6],k=w[7]
   variable ii,y=0
   for(ii=-7;ii<8;ii++)
      y=y+kernel1(ii,x)
   endfor     
   return y
End
 
function kernel0(inj)
variable inj
NVAR a,b,c,d,f,g,h,k
NVAR ini,inx
return  b/pi/c/f*exp(-((k-h)-inj+g*(inx-2.40747*ini))^2/f^2)*(besselj(abs(ini),abs(2*a*exp(-inj^2/d^2))))^2*exp(-(inx-2.40747*ini)^2/c^2)
end
 
function kernel1(ii,xx)
variable ii,xx
variable/g ini,inx
ini=ii
inx=xx
return Integrate1D(kernel0,-10,10,1)
end

I have compared the results of integrating from -10 to 10 and from -20 to 20, they are basically the same. So I determine to use the range -10 to 10. I still want to know is there any way to speed up the code?

Possibly the best strategy is to integrate from 0 to <largish positive number> and from 0 to <largish negative number>. Be sure the options are correct to get the adaptive integration. Presumably your integrand is large near zero and approaches zero at +-<largish number>. By starting at zero and working outward, the adaptive integration will not spend time trying to add up very small numbers that later turn out to be useless.

Also- if you use the optional parameters, you can pass a coefficient wave to the integrand function rather than messing with global variables. The optional coefficient wave is a relatively new feature.

Thank you!