Hi, I have a vector of dim Nx1,fnl0 which depends on a vector X0 of dim 3Nx1. I would like to obtain the parcial derivatives of this vectorfnl0 respective X0 by finite differences, in order to calculate the Jacobian, dfnl0_dX . I´m trying to construct the Jacobian column by column, by concatenating the results of each step k:
X0(vector dim 3Nx1) fnl0(vector dim Nx1) delta_X0=sqrt(eps)*norm(X0) dfnl0_dX=Zeros[N,3N] % Jacobian
for k=1:3*N
X0pert=X0; X0pert(k,1)=X0pert(k,1)+delta_X0; fnl0_pert=f_nonlinear(dx0pert,param); derivative= (fnl0_pert - fnl0) / delta_X0; dfnl0_dX=horzcat(dfnl0_dX,derivative);
end
The Problem is that the elements of vector X0 are very different between them, some elements 1e-20 and others of order 1e-6, and so it seems that I am not obtaining correct results, as I have been trying to do the same Operation with different delta_X0 and the results vary a lot.
Could anyone help me in obatining an adecuate step delta_X0 to solve this problem?
Thank your very much!
