lsqcurvefit of a summation function where the parameter to evaluate is the last index of the summation (so an integer)

Hi, I'm doing the fit of a function substantially similar to this one: f(x)= sum ( exp(1i * x * jz * c) ) , where: - sum represent the summation over the index jz - x is the variable, - jz = 1,2,...,nz where nz is a parameter to find using the fit, - c is another parameter. The complete function is the product of several series of this type.

In the curve fitting tool I can't enter a summation neither using symsum nor using an iteration. Moreover I can't use nz as a parameter.

Any idea?

Many thanks, Gianluca

Answer 1

[Oleg Komarov]

lsqcurvefit is already MIN oof the SUM of euclidean distances of x from y. So, you don't have to use inlcude a sum in your handle and 1:x(2) but:

fh = @(x,xdata) exp(1i.*x(1).*xdata.*x(2)) .* conj(exp(1i.*x(1).*xdata.*x(2)));

[gianluca messina]

My function is the sum of x(2) (integer) elements, this is the point.

Gianluca

[Oleg Komarov]

DO you have a reference to the problem you're rtying to solve?

[gianluca messina]

Sorry, reference in what sense?

I'm fitting an experimental diffraction pattern obtained by xray diffraction from a crystal using the square of an exponential summation (the square because we measure the intensity), and the nz (x(2)) parameter is the number of atomic planes composing the sample

[Oleg Komarov]

I am not sure that you are supplying your problem in the required form, i.e. in lsqcurvefit you can supply a zero ydata and you'll end up with the min wrt nz of SUM{f(.)^2} where the fcn handle is cast in the form I supplied in the body.

Answer 2

[Walter Roberson]

f = @(x) sum(exp(1i.*c.*x.*(1:nz)))

[gianluca messina]

Thanks for your help, but I find this error when I run that function:

Undefined function or method 'isnan' for input arguments of type 'function_handle'.

Gianluca

Answer 3

[Arnaud Miege]

I'm not sure this is something that can be done with the Curve Fitting Toolbox. I think a better approach would be to use the Optimization Toolbox with one of the Least Squares (Curve Fitting) functions, such as lsqcurvefit.

HTH,

Arnaud

[Oleg Komarov]

Your x is nz.

@(nz,xdata) ...

Answer 4

[gianluca messina]

Hi Arnaud, I followed your advice, the problem is that when I calculate the sum both using an iteration and f = @(x,xdata) sum(exp(1i.*x(1).*xdata.*(1:(x(2))))), matlab doesn't recognize that is a function of xdata. So I can't fit it because it sees f and ydata as data of different dimension. Thanks for your help. (And thanks Oleg).

[Oleg Komarov]

Please post the code snippet you're using (preferably editing this question) and the whole error message. Additional info about the size of your inputs would be beneficial.

Answer 5

[gianluca messina]

Here is the code:

clear all; close all;

load 'C:\Users\gianluca\Desktop\002Cr-V_Lscan\Cr_MgO_69.txt';

xdata = (Cr_MgO_69(:,1)*2/292.094)'; ydata = (Cr_MgO_69(:,2))';

fh = @(x,xdata) sum(exp(1i.*x(1).*xdata.*(1:x(2)))) .* conj(sum(exp(1i.*x(1).*xdata.*(1:x(2)))));

x0 = [3e-10; 100]; x = lsqcurvefit(fh,x0,xdata,ydata);

and this is the error:

??? Error using ==> lsqncommon at 101 LSQCURVEFIT cannot continue because user supplied objective function failed with the following error: Error using ==> times Matrix dimensions must agree.

Error in ==> lsqcurvefit at 186 [x,Resnorm,FVAL,EXITFLAG,OUTPUT,LAMBDA,JACOB] = ...

Should I try to use an iteration maybe to define the funtion, instead of fh = @(x,xdata)...*(1:x(2))..? I tried but I don't know how to insert x(2) as parameter if it is at the beginning of the for cycle and so before the statement of the funtion:

for jz = 1 : x(2) ... f(jz) = @(x,xdata) ...jz...

end

Yesterday I was using some different code, and I got another error:

??? Error using ==> lsqncommon at 134 Function value and YDATA sizes are incommensurate. (but I think the code I used contained some mistakes)

Many thanks Gianluca

[gianluca messina]

xdata and ydata are two vectors composed by 81 components

Gianluca