I'm trying to fit some data using lsqcurvefit (Please Help!)

Please Help!!! I know I'm making a really dumb mistake somewhere. I never have problems fitting data with lsqcurvefit except for this function.

I'm trying to fit the function: Jcur = x(3).*exp(-x(2)/T).*exp(-(1/x(1)).*integral(exp(-x(2)/T'),dT', from some constant to T)

so my limits of integration depend on the variable T

I use lsqcurvefit(@tsdcfit,x0,T,J,[],[],options)

and have a separate function file tsdcfit with my fitting variables and T:

function Jcur = tsdcfit(x,T); global k e r;

function fux = fun(x,T) range = 50:0.01:T; ex = exp(-x(2)/(range)); fux = trapz(range,ex); end

Jcur = x(3).*exp(-x(2)/T).*exp(-(1/x(1)).*fun(x,T)); end

Any help would be greatly appreciated! I know there's something wrong with how i call the function fun(x,T), I've played around with it a lot and it's basically only spitting out one value regardless of the range of T

[Russell]

maybe this will make it more simple, i can't get this function file to work, and if I could, I think it would solve my problem:

function fuxc = xint(T)
global k e b;
    ex = exp(-b.*e./(k.*range(T)));
    fuxc = trapz(range(T),ex);
end
function rang = range(T)
    rang = 50:0.01:T;
end

[Russell]

If I put in an array of T values, say T=201:1:210, and then ask for xint(T),

I get one value back, but I'm looking for 10 values...

[Walter Roberson]

Addressed in your duplicate question http://www.mathworks.co.uk/matlabcentral/answers/65290-trying-to-integrate-an-problem-with-no-analytic-solution-can-t-figure-out-why-my-function-file-isn

[Matt J]

Incidentally, your current code doesn't guarantee that T will be included in the range to be integrated, e.g.,

>> T=51; 50:.3:T

ans =

     50.0000   50.3000   50.6000   50.9000

Better to do something like this.

 function rang = range(T)
    rang = [50:0.01:T, T];
 end

Answer 1

[Matt J]

lsqcurvefit(@tsdcfit,x0,T,J,[],[],options)

does not make much sense if T and presumably also J are scalar constants. It means you are curve fitting based on 1 data point.

Also, you are not passing T to tsdcfit and should be getting error messages. I question whether we are seeing your actual code.

Also, the sensitivity of fun(x,T) would depend on x. If x(2) is set to zero, for example, it would make sense that fun(x,T) is independent of T.

Finally, the integral of exp(-x(2)/T) has a closed form solution as a function of T and doesn't need to be numerically approximated using TRAPZ. Note that after making the change of variables y=-x(2)/T, the integral becomes

 integral(y^2 * exp(y),dy)

which can be computed symbolically by integration by parts. It would be better to use the closed form formula.

[Russell]

T and J aren't constants, they are both arrays.

And no you can't solve the integral analytically. int(exp(-c/x))dx is unsolvable. Can't be solved by parts.

[Matt J]

And no you can't solve the integral analytically. int(exp(-c/x))dx is unsolvable.

yeah, forget that part (but only that part!!).

Answer 2

[Matt J]

If I put in an array of T values, say T=201:1:210, and then ask for xint(T),I get one value back, but I'm looking for 10 values...

You have to for-loop over T(i). range(T) will always return a vector to be integrated, regardless of whether or not T is a scalar, and the integral over that range will of course be a scalar as well.