MATLAB: Problem in creating symbolic function with normcdf

hessiannormcdfsymbolic

Hi everyone,
I have a problem when creating a symbolic function with normcdf. I read some related postings and guess that might be the case that 'less than equal to' is not defined in 'syms'. Ultimately, I need to use this symbolic function to get the Hessian matrix. Can anyone please give me some idea on how to solve this problem? Thanks very much!
Here is my code:
syms mu sigma lembda eta
f2 = -(-N_M*log(eta+lembda*(1-normcdf(log(M_minw),mu,sigma)))+N_M*log(lembda)+Nu_M*log(1-normcdf(log(M_minw),mu,sigma))+Nu_M*log(eta)-Ne_M*log((sqrt(2*pi)*sigma))-sum(log(M(n,2)))-sum((log(M(n,2))-ones(n,1)*mu).^2/(2*sigma^2))-lembda*(1-normcdf(log(M_minw),mu,sigma))*sum(M(n(end)+1:end,1)));
This is the error msg:
??? Error using ==> sym.sym>notimplemented at 2514
Function 'le' is not implemented for MuPAD symbolic objects.
Error in ==> sym.sym>sym.le at 825
            notimplemented('le');
Error in ==> normcdf at 57
sigma(sigma <= 0) = NaN;
Thanks!
Sonia

Best Answer

It seems that normcdf is not defined for sym objects. You can try to express normcdf for syms in a more elementary way, like this:
normcdfsym = @(x, mu, sigma)(1/2 - erf((2^(1/2)*(mu - x))/(2*(sigma^2)^(1/2)))/2)
With this your formular would look like this:
 f2 = -(-N_M*log(eta+lembda*(1-normcdfsym(log(M_minw),mu,sigma)))+N_M*log(lembda)+Nu_M*log(1-normcdfsym(log(M_minw),mu,sigma))+Nu_M*log(eta)-Ne_M*log((sqrt(2*pi)*sigma))-sum(log(M(n,2)))-sum((log(M(n,2))-ones(n,1)*mu).^2/(2*sigma^2))-lembda*(1-normcdfsym(log(M_minw),mu,sigma))*sum(M(n(end)+1:end,1)));
However there are still some undefined variables, like N_M or M.
Related Question