I am trying to solve a large system of non-linear equations (about a few hundred equations and variable but with less variable than equations). Given that the system is really sparse and large I am using the
optimize.least_square solver of SciPy with the Trust Regions method.
But for some examples, it takes quite long to find a solution and sometimes it lands on what I suppose are local minimums or saddle points.
I assume these problems may come from the fact that the problem is poorly conditioned. So I tried to add weights on the equations in order to give the approximatively the same scale to all the residuals, it improved the speed and convergence but not completely.
So I wanted to know: is there a tool in python either do detect if the function is badly conditioned or to precondition it before calling the solver?
Here is the parameters I use for the solver :
solution = optimize.least_squares(system, xinput, method='trf, loss='soft_l1', f_scale=10, x_scale='jac')