How can I fit a nonlinear function to my experimental data to find the unknowns?

The Following equation is the theoretical equation of the cumulative density function:

Answer 1

[Matt J]

Yes, lsqcurvefit is applicable.

[Farnood83]

My code is as follows:

fun = @(p1,emp_cdf_MaxLF1_Trace_n_x_new) 1-exp{-[p1(:,1)./(Vel.*K_eff1_array(:,1))]...
    .*[exp(-Beta.*(p1(:,2)-DeltaX1_2(:,1).*...
    (Average_Trace1(:,2))))].*(Average_Trace1(:,2))}*...
    {1+((Beta)^2).*[p1(:,1)./(Vel.*K_eff1_array(:,1))].*[exp(-Beta.*(p1(:,2)-DeltaX1_2(:,1).*...
    (Average_Trace1(:,2))))].*[p1(:,3)+((Average_Trace1(:,2)).^2).*...
    (StDeviation_Trace1(:,4).^2)].*(Average_Trace1(:,2))};


for i = 1:numCol1    %%%%%%%%For Initial Values
     p01(i,1) = 1;
     p01(i,2) = 1;
     p01(i,3) = 1;
end

p1 = lsqcurvefit(fun,p01,emp_cdf_MaxLF1_Trace_n_x_new,emp_cdf_MaxLF1_Trace_n_new)
f_o1 = p1(:,1);          %The first unknown in the equation  f_0
U_o1 = p1(:,2);          %The second unknown in the equation U_0
Var_U_o = p1(:,3);       %The third unknown in the equation  σ_(U_0)^2

yfit1 = fun(p1,emp_cdf_MaxLF1_Trace_n_x_new);

This is the error that I got:

Undefined variable exp.

Error in

Test2>@(p1,emp_cdf_MaxLF1_Trace_n_x_new)1-exp{-[p1(:,1)./(Vel.*K_eff1_array(:,1))].*[exp(-Beta.*(p1(:,2)-DeltaX1_2(:,1).*(Average_Trace1(:,2))))].*(Average_Trace1(:,2))}*{1+((Beta)^2).*[p1(:,1)./(Vel.*K_eff1_array(:,1))].*[exp(-Beta.*(p1(:,2)-DeltaX1_2(:,1).*(Average_Trace1(:,2))))].*[p1(:,3)+((Average_Trace1(:,2)).^2).*(StDeviation_Trace1(:,4).^2)].*(Average_Trace1(:,2))}

(line 217)

fun = @(p1,emp_cdf_MaxLF1_Trace_n_x_new) 1-exp{-[p1(:,1)./(Vel.*K_eff1_array(:,1))]...

Error in lsqcurvefit (line 225)

initVals.F = feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:});

Error in Test2 (line 238)

p1 = lsqcurvefit(fun,p01,emp_cdf_MaxLF1_Trace_n_x_new,emp_cdf_MaxLF1_Trace_n_new)

Caused by:

Failure in initial objective function evaluation. LSQCURVEFIT cannot continue.

Would you mind help me to find the unknowns using the LSQCURVEFIT?

Thank you so much in advance,

Farnood

[Matt J]

Make sure your model function fun() works before you give it to lsqcurvefit. You have an exp{ } in your objective function which should be exp() an the other braces probably don't belong there either.

[Farnood83]

Thank you! It is working now