Problem with "lsqnonlin" function in matlab

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fsalehi 2011-8-24

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https://ww2.mathworks.cn/matlabcentral/answers/14426-problem-with-lsqnonlin-function-in-matlab

Dear all,

I have a problem with 'lsqnonlin' function in matlab. I used it to optimizing this function:

    objfun = @(z) y - ( z(5).*exp(-z(1).*(t-z(7)).^2).*cos(2*pi.*z(2).*(t-z(7))+z(3)) + z(6).*exp(-z(1).*(t-z(8)).^2).*cos(2*pi.*z(2).*(t-z(8))+z(4)) );

% y is my signal and I optimize a guassian pulse function for Model Base Estimation

    options = optimset(options, 'MaxFunEvals', 10000, 'TolX', 1e-3, 'TolFun', 1e-2, 'MaxIter', 800, 'LargeScale', 'on', 'LevenbergMarquardt', 'on', 'DiffMaxChange', 1e-7, 'DiffMinChange', 1e-10, 'Display', 'off', 'Diagnostics', 'off');
    [Z,q,w,e,r]=lsqnonlin(objfun,...
    [alpha         Fc       amptf(1:4) phase phase],...
    [alpha-(2e6)^2 Fc-(2e6) toll(1:4)  []    [] ],...        
    [alpha+(2e6)^2 Fc+(2e6) tolu(1:4)  []    [] ],options);

the problem is the result of optimization, I have 8 variable to optimizing, but in result Z, only 7 of them changes and one of them (z(1)) doesnt change. I should note that 'alpha', 'Fc', 'tolu' and 'toll' are known.

why this happend?!