Fitting to an intergral

Question

Jason Ngo 2020-3-27

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/513456-fitting-to-an-intergral

回答： Torsten 2020-3-27

I am trying to fit a set of data to an integral with the following code but I get an error message. The parameters I am trying to obtain is x(1),x(2), and u, from xdata and ydata. Thanks.

fun= @(x, xdata) (1-((6*x(1))/(pi*sqrt(x(2)))))*integral(@(u) ((exp(-(xdata))*((u*cos(u)-sin(u))^2))/((u^2)*(((u^2)*(sin(u))^2)+(x(2))*(((x(1))/(x(2)))*(u*cos(u)-sin(u))+sin(u))^2))),0,Inf)
x0=(1,1)
lsqcurvefit(fun, x0, xdata, ydata) 
Error using  * 
Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix.
To perform elementwise multiplication, use '.*'.
Error in @(u)((exp(-(xdata))*((u*cos(u)-sin(u))^2))/((u^2)*(((u^2)*(sin(u))^2)+(x(2))*(((x(1))/(x(2)))*(u*cos(u)-sin(u))+sin(u))^2)))
Error in integralCalc/iterateScalarValued (line 314)
                fx = FUN(t);
Error in integralCalc/vadapt (line 132)
            [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);
Error in integralCalc (line 83)
        [q,errbnd] = vadapt(@AToInfInvTransform,interval);
Error in integral (line 88)
Q = integralCalc(fun,a,b,opstruct);
Error in
@(x,xdata)(1-((6*x(1))/(pi*sqrt(x(2)))))*integral(@(u)((exp(-(xdata))*((u*cos(u)-sin(u))^2))/((u^2)*(((u^2)*(sin(u))^2)+(x(2))*(((x(1))/(x(2)))*(u*cos(u)-sin(u))+sin(u))^2))),0,Inf)
Error in lsqcurvefit (line 213)
            initVals.F = feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:});
Caused by:
    Failure in initial objective function evaluation. LSQCURVEFIT cannot continue.